Offset 1, 9 lines modified | Offset 1, 9 lines modified | ||
1 | ·1eaf3c6f26458a427c5b1d19458ff3db·11856272·debug·optional·coq-dbgsym_8.16.1+dfsg-1_armhf.deb | 1 | ·1eaf3c6f26458a427c5b1d19458ff3db·11856272·debug·optional·coq-dbgsym_8.16.1+dfsg-1_armhf.deb |
2 | · | 2 | ·3f46fe009fa77ac63bab8ea14755cefa·89868272·math·optional·coq_8.16.1+dfsg-1_armhf.deb |
3 | ·579f604be64da650161528cc3d81342a·653524·debug·optional·coqide-dbgsym_8.16.1+dfsg-1_armhf.deb | 3 | ·579f604be64da650161528cc3d81342a·653524·debug·optional·coqide-dbgsym_8.16.1+dfsg-1_armhf.deb |
4 | ·e682adb250352eafe15c2ef6802d5919·1835288·math·optional·coqide_8.16.1+dfsg-1_armhf.deb | 4 | ·e682adb250352eafe15c2ef6802d5919·1835288·math·optional·coqide_8.16.1+dfsg-1_armhf.deb |
5 | ·a0ea08501e72bf42861ebb1ec7878e08·1811244·debug·optional·libcoq-core-ocaml-dbgsym_8.16.1+dfsg-1_armhf.deb | 5 | ·a0ea08501e72bf42861ebb1ec7878e08·1811244·debug·optional·libcoq-core-ocaml-dbgsym_8.16.1+dfsg-1_armhf.deb |
6 | ·bd17457b6bfc69b7d93e11f87128342c·43111820·ocaml·optional·libcoq-core-ocaml-dev_8.16.1+dfsg-1_armhf.deb | ||
7 | ·66b51481933950d1ce221917ffd9558f·22262480·ocaml·optional·libcoq-core-ocaml_8.16.1+dfsg-1_armhf.deb | ||
8 | · | 6 | ·fd0a003b2b144e9889ec0a84607193fe·43110040·ocaml·optional·libcoq-core-ocaml-dev_8.16.1+dfsg-1_armhf.deb |
7 | ·212d771670264bcd87872a3ebce23509·22259440·ocaml·optional·libcoq-core-ocaml_8.16.1+dfsg-1_armhf.deb | ||
8 | ·d3261b397ea916b7be30f0b2ceb24e98·21526188·math·optional·libcoq-stdlib_8.16.1+dfsg-1_armhf.deb |
Offset 1, 3 lines modified | Offset 1, 3 lines modified | ||
1 | -rw-r--r--···0········0········0········4·2022-11-29·08:28:08.000000·debian-binary | 1 | -rw-r--r--···0········0········0········4·2022-11-29·08:28:08.000000·debian-binary |
2 | -rw-r--r--···0········0········0·····2328·2022-11-29·08:28:08.000000·control.tar.xz | 2 | -rw-r--r--···0········0········0·····2328·2022-11-29·08:28:08.000000·control.tar.xz |
3 | -rw-r--r--···0········0········0·89865 | 3 | -rw-r--r--···0········0········0·89865752·2022-11-29·08:28:08.000000·data.tar.xz |
Offset 1, 12 lines modified | Offset 1, 12 lines modified | ||
1 | Package:·coq | 1 | Package:·coq |
2 | Version:·8.16.1+dfsg-1 | 2 | Version:·8.16.1+dfsg-1 |
3 | Architecture:·armhf | 3 | Architecture:·armhf |
4 | Maintainer:·Debian·OCaml·Maintainers·<debian-ocaml-maint@lists.debian.org> | 4 | Maintainer:·Debian·OCaml·Maintainers·<debian-ocaml-maint@lists.debian.org> |
5 | Installed-Size:·28618 | 5 | Installed-Size:·286183 |
6 | Depends:·libcoq-stdlib·(=·8.16.1+dfsg-1),·libcoq-core-ocaml-4ew58,·libfindlib-ocaml-3yei3,·libzarith-ocaml-aip06,·ocaml-base-4.13.1,·python3:any,·libc6·(>=·2.35),·libgmp10·(>=·2:6.2.1+dfsg1),·ocaml-nox,·ocaml-findlib | 6 | Depends:·libcoq-stdlib·(=·8.16.1+dfsg-1),·libcoq-core-ocaml-4ew58,·libfindlib-ocaml-3yei3,·libzarith-ocaml-aip06,·ocaml-base-4.13.1,·python3:any,·libc6·(>=·2.35),·libgmp10·(>=·2:6.2.1+dfsg1),·ocaml-nox,·ocaml-findlib |
7 | Suggests:·coqide·|·proofgeneral,·ledit·|·readline-editor,·libcoq-core-ocaml-dev,·why·(>=·2.19),·coq-doc | 7 | Suggests:·coqide·|·proofgeneral,·ledit·|·readline-editor,·libcoq-core-ocaml-dev,·why·(>=·2.19),·coq-doc |
8 | Breaks:·coq-libs·(<<·8.2.pl1) | 8 | Breaks:·coq-libs·(<<·8.2.pl1) |
9 | Replaces:·coq-libs·(<<·8.2.pl1) | 9 | Replaces:·coq-libs·(<<·8.2.pl1) |
10 | Provides:·coq-8.16.1+4.13.1 | 10 | Provides:·coq-8.16.1+4.13.1 |
11 | Section:·math | 11 | Section:·math |
12 | Priority:·optional | 12 | Priority:·optional |
Offset 3, 27 lines modified | Offset 3, 27 lines modified | ||
3 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2022-11-29·08:28:08.000000·./usr/bin/ | 3 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2022-11-29·08:28:08.000000·./usr/bin/ |
4 | -rwxr-xr-x···0·root·········(0)·root·········(0)······891·2022-11-29·08:28:08.000000·./usr/bin/coq-makefile-make-both-single-timing-files | 4 | -rwxr-xr-x···0·root·········(0)·root·········(0)······891·2022-11-29·08:28:08.000000·./usr/bin/coq-makefile-make-both-single-timing-files |
5 | -rwxr-xr-x···0·root·········(0)·root·········(0)······931·2022-11-29·08:28:08.000000·./usr/bin/coq-makefile-make-both-time-files | 5 | -rwxr-xr-x···0·root·········(0)·root·········(0)······931·2022-11-29·08:28:08.000000·./usr/bin/coq-makefile-make-both-time-files |
6 | -rwxr-xr-x···0·root·········(0)·root·········(0)······697·2022-11-29·08:28:08.000000·./usr/bin/coq-makefile-make-one-time-file | 6 | -rwxr-xr-x···0·root·········(0)·root·········(0)······697·2022-11-29·08:28:08.000000·./usr/bin/coq-makefile-make-one-time-file |
7 | -rwxr-xr-x···0·root·········(0)·root·········(0)···714660·2022-11-29·08:28:08.000000·./usr/bin/coq-tex | 7 | -rwxr-xr-x···0·root·········(0)·root·········(0)···714660·2022-11-29·08:28:08.000000·./usr/bin/coq-tex |
8 | -rwxr-xr-x···0·root·········(0)·root·········(0)··1433548·2022-11-29·08:28:08.000000·./usr/bin/coq_makefile | 8 | -rwxr-xr-x···0·root·········(0)·root·········(0)··1433548·2022-11-29·08:28:08.000000·./usr/bin/coq_makefile |
9 | -rwxr-xr-x···0·root·········(0)·root·········(0)·14663372·2022-11-29·08:28:08.000000·./usr/bin/coqc | 9 | -rwxr-xr-x···0·root·········(0)·root·········(0)·14663372·2022-11-29·08:28:08.000000·./usr/bin/coqc |
10 | -rwxr-xr-x···0·root·········(0)·root·········(0)·400650 | 10 | -rwxr-xr-x···0·root·········(0)·root·········(0)·40065026·2022-11-29·08:28:08.000000·./usr/bin/coqc.byte |
11 | -rwxr-xr-x···0·root·········(0)·root·········(0)··5285088·2022-11-29·08:28:08.000000·./usr/bin/coqchk | 11 | -rwxr-xr-x···0·root·········(0)·root·········(0)··5285088·2022-11-29·08:28:08.000000·./usr/bin/coqchk |
12 | -rwxr-xr-x···0·root·········(0)·root·········(0)··2093316·2022-11-29·08:28:08.000000·./usr/bin/coqdep | 12 | -rwxr-xr-x···0·root·········(0)·root·········(0)··2093316·2022-11-29·08:28:08.000000·./usr/bin/coqdep |
13 | -rwxr-xr-x···0·root·········(0)·root·········(0)··1823120·2022-11-29·08:28:08.000000·./usr/bin/coqdoc | 13 | -rwxr-xr-x···0·root·········(0)·root·········(0)··1823120·2022-11-29·08:28:08.000000·./usr/bin/coqdoc |
14 | -rwxr-xr-x···0·root·········(0)·root·········(0)·40628463·2022-11-29·08:28:08.000000·./usr/bin/coqidetop.byte | 14 | -rwxr-xr-x···0·root·········(0)·root·········(0)·40628463·2022-11-29·08:28:08.000000·./usr/bin/coqidetop.byte |
15 | -rwxr-xr-x···0·root·········(0)·root·········(0)·14847864·2022-11-29·08:28:08.000000·./usr/bin/coqidetop.opt | 15 | -rwxr-xr-x···0·root·········(0)·root·········(0)·14847864·2022-11-29·08:28:08.000000·./usr/bin/coqidetop.opt |
16 | -rwxr-xr-x···0·root·········(0)·root·········(0)··5428976·2022-11-29·08:28:08.000000·./usr/bin/coqnative | 16 | -rwxr-xr-x···0·root·········(0)·root·········(0)··5428976·2022-11-29·08:28:08.000000·./usr/bin/coqnative |
17 | -rwxr-xr-x···0·root·········(0)·root·········(0)···928428·2022-11-29·08:28:08.000000·./usr/bin/coqpp | 17 | -rwxr-xr-x···0·root·········(0)·root·········(0)···928428·2022-11-29·08:28:08.000000·./usr/bin/coqpp |
18 | -rwxr-xr-x···0·root·········(0)·root·········(0)·14663692·2022-11-29·08:28:08.000000·./usr/bin/coqproofworker.opt | 18 | -rwxr-xr-x···0·root·········(0)·root·········(0)·14663692·2022-11-29·08:28:08.000000·./usr/bin/coqproofworker.opt |
19 | -rwxr-xr-x···0·root·········(0)·root·········(0)·14663692·2022-11-29·08:28:08.000000·./usr/bin/coqqueryworker.opt | 19 | -rwxr-xr-x···0·root·········(0)·root·········(0)·14663692·2022-11-29·08:28:08.000000·./usr/bin/coqqueryworker.opt |
20 | -rwxr-xr-x···0·root·········(0)·root·········(0)·14663696·2022-11-29·08:28:08.000000·./usr/bin/coqtacticworker.opt | 20 | -rwxr-xr-x···0·root·········(0)·root·········(0)·14663696·2022-11-29·08:28:08.000000·./usr/bin/coqtacticworker.opt |
21 | -rwxr-xr-x···0·root·········(0)·root·········(0)·14663468·2022-11-29·08:28:08.000000·./usr/bin/coqtop | 21 | -rwxr-xr-x···0·root·········(0)·root·········(0)·14663468·2022-11-29·08:28:08.000000·./usr/bin/coqtop |
22 | -rwxr-xr-x···0·root·········(0)·root·········(0)·575884 | 22 | -rwxr-xr-x···0·root·········(0)·root·········(0)·57588438·2022-11-29·08:28:08.000000·./usr/bin/coqtop.byte |
23 | -rwxr-xr-x···0·root·········(0)·root·········(0)·14663468·2022-11-29·08:28:08.000000·./usr/bin/coqtop.opt | 23 | -rwxr-xr-x···0·root·········(0)·root·········(0)·14663468·2022-11-29·08:28:08.000000·./usr/bin/coqtop.opt |
24 | -rwxr-xr-x···0·root·········(0)·root·········(0)···562828·2022-11-29·08:28:08.000000·./usr/bin/coqwc | 24 | -rwxr-xr-x···0·root·········(0)·root·········(0)···562828·2022-11-29·08:28:08.000000·./usr/bin/coqwc |
25 | -rwxr-xr-x···0·root·········(0)·root·········(0)·14580776·2022-11-29·08:28:08.000000·./usr/bin/coqworkmgr | 25 | -rwxr-xr-x···0·root·········(0)·root·········(0)·14580776·2022-11-29·08:28:08.000000·./usr/bin/coqworkmgr |
26 | -rwxr-xr-x···0·root·········(0)·root·········(0)·17068032·2022-11-29·08:28:08.000000·./usr/bin/csdpcert | 26 | -rwxr-xr-x···0·root·········(0)·root·········(0)·17068032·2022-11-29·08:28:08.000000·./usr/bin/csdpcert |
27 | -rwxr-xr-x···0·root·········(0)·root·········(0)···866872·2022-11-29·08:28:08.000000·./usr/bin/ocamllibdep | 27 | -rwxr-xr-x···0·root·········(0)·root·········(0)···866872·2022-11-29·08:28:08.000000·./usr/bin/ocamllibdep |
28 | -rwxr-xr-x···0·root·········(0)·root·········(0)···968392·2022-11-29·08:28:08.000000·./usr/bin/votour | 28 | -rwxr-xr-x···0·root·········(0)·root·········(0)···968392·2022-11-29·08:28:08.000000·./usr/bin/votour |
29 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2022-11-29·08:28:08.000000·./usr/lib/ | 29 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2022-11-29·08:28:08.000000·./usr/lib/ |
Offset 2249410, 254655 lines modified | Offset 2249410, 254656 lines modified | ||
02252c10:·4140·4084·95a6·be00·0000·5200·0000·0600··A@@.......R..... | 02252c10:·4140·4084·95a6·be00·0000·5200·0000·0600··A@@.......R..... | ||
02252c20:·0000·2100·0000·17a0·302e·2f5f·6275·696c··..!.....0./_buil | 02252c20:·0000·2100·0000·17a0·302e·2f5f·6275·696c··..!.....0./_buil | ||
02252c30:·642f·6465·6661·756c·74a0·352e·2f5f·6275··d/default.5./_bu | 02252c30:·642f·6465·6661·756c·74a0·352e·2f5f·6275··d/default.5./_bu | ||
02252c40:·696c·642f·6465·6661·756c·742f·636c·6962··ild/default/clib | 02252c40:·696c·642f·6465·6661·756c·742f·636c·6962··ild/default/clib | ||
02252c50:·a009·252e·2f5f·6275·696c·642f·6465·6661··..%./_build/defa | 02252c50:·a009·252e·2f5f·6275·696c·642f·6465·6661··..%./_build/defa | ||
02252c60:·756c·742f·636c·6962·2f2e·636c·6962·2e6f··ult/clib/.clib.o | 02252c60:·756c·742f·636c·6962·2f2e·636c·6962·2e6f··ult/clib/.clib.o | ||
02252c70:·626a·732f·6279·7465·4000·0874·fc84·95a6··bjs/byte@..t.... | 02252c70:·626a·732f·6279·7465·4000·0874·fc84·95a6··bjs/byte@..t.... | ||
02252c80:·be00·005a· | 02252c80:·be00·005a·6500·000f·3900·0041·0600·0040··...Ze...9..A...@ | ||
02252c90:·3 | 02252c90:·3da0·0800·002c·0001·0fe8·2443·4f62·6ab0··=....,....$CObj. | ||
02252ca0:·c026·5f6e·6f6e·655f·4040·00ff·0402·4141··.&_none_@@....AA | 02252ca0:·c026·5f6e·6f6e·655f·4040·00ff·0402·4141··.&_none_@@....AA | ||
02252cb0:·223f·3f41·40d0·4040·4040·40b0·4040·4040··"??A@.@@@@@.@@@@ | 02252cb0:·223f·3f41·40d0·4040·4040·40b0·4040·4040··"??A@.@@@@@.@@@@ | ||
02252cc0:·40a0·0800·002c·0001·0fa4·0409·0408·4122··@....,........A" | 02252cc0:·40a0·0800·002c·0001·0fa4·0409·0408·4122··@....,........A" | ||
02252cd0:·3f3f·41b0·b0b0·b0b0·b0b0·b0b0·b0b0·b0b0··??A............. | 02252cd0:·3f3f·41b0·b0b0·b0b0·b0b0·b0b0·b0b0·b0b0··??A............. | Diff chunk too large, falling back to line-by-line diff (3803 lines added, 3803 lines removed) | |
02252ce0:·b0b0·b0b0·b0b0·b0b0·b0b0·c3b0·b0b0·b0b0··................ | 02252ce0:·b0b0·b0b0·b0b0·b0b0·b0b0·c3b0·b0b0·b0b0··................ | ||
02252cf0:·b0b0·aba | 02252cf0:·b0b0·abab·a7b1·b2b2·b2b2·b2b2·b2b2·b2b2··................ | ||
02252d00:·b2b | 02252d00:·b2b2·b1b1·b1b1·b1b1·b1b1·b1b1·b1b1·b1b1··................ | ||
02252d10:·b140 | 02252d10:·b1b1·40a3·2a66·6c6f·6174·6172·7261·7951··..@.*floatarrayQ | ||
02252d20:·0 | 02252d20:·0800·0038·0040·4040·4140·4040·4040·044b··...8.@@@A@@@@@.K | ||
02252d30:·4040·9204 | 02252d30:·4040·4092·0403·a335·6578·7465·6e73·696f··@@@....5extensio | ||
02252d40:·5f63 | 02252d40:·6e5f·636f·6e73·7472·7563·746f·7250·0800··n_constructorP.. | ||
02252d50:· | 02252d50:·0038·0040·4040·4140·4040·4040·044f·4040··.8.@@@A@@@@@.O@@ | ||
02252d60:·9204 | 02252d60:·4092·0403·a323·696e·7441·0800·0038·0040··@....#intA...8.@ | ||
02252d70:·404 | 02252d70:·4040·4140·4040·4040·0453·4041·4092·0403··@@A@@@@@.S@A@... | ||
02252d80:·2463 | 02252d80:·a324·6368·6172·4208·0000·3800·4040·4041··.$charB...8.@@@A | ||
02252d90:·4040·4040·04 | 02252d90:·4040·4040·4004·5740·4140·9204·03a3·2673··@@@@@.W@A@....&s | ||
02252da0:·7269 | 02252da0:·7472·696e·674f·0800·0038·0040·4040·4140··tringO...8.@@@A@ | ||
02252db0:·4040·40 | 02252db0:·4040·4040·045b·4040·4092·0403·a325·666c··@@@@.[@@@....%fl | ||
02252dc0:·6174 | 02252dc0:·6f61·7444·0800·0038·0040·4040·4140·4040··oatD...8.@@@A@@@ | ||
02252dd0:·40 | 02252dd0:·4040·045f·4040·4092·0403·a324·626f·6f6c··@@._@@@....$bool | ||
02252de0:·0800 | 02252de0:·4508·0000·3800·4040·a1a0·e0a3·2566·616c··E...8.@@....%fal | ||
02252df0:·655e | 02252df0:·7365·5e90·4040·0469·4092·0403·a0e0·a324··se^.@@.i@......$ | ||
02252e00:·7275 | 02252e00:·7472·7565·5f90·4040·046f·4092·0403·4040··true_.@@.o@...@@ | ||
02252e10:·4 | 02252e10:·4140·4040·4040·0470·4041·4092·0410·a324··A@@@@@.p@A@....$ | ||
02252e20:·6e69 | 02252e20:·756e·6974·4608·0000·3800·4040·a1a0·e0a3··unitF...8.@@.... | ||
02252e30:·2829 | 02252e30:·2228·2960·9040·4004·7a40·9204·0340·4041··"()`.@@.z@...@@A | ||
02252e40:·4040·4040·04 | 02252e40:·4040·4040·4004·7b40·4140·9204·0aa3·2365··@@@@@.{@A@....#e | ||
02252e50:·6e47 | 02252e50:·786e·4708·0000·3800·4040·4141·4040·4040··xnG...8.@@AA@@@@ | ||
02252e60:·047 | 02252e60:·4004·7f40·4040·9204·03a3·2561·7272·6179··@..@@@....%array | ||
02252e70:·0800 | 02252e70:·4808·0000·3800·a0c0·9040·0205·f5e1·0040··H...8....@.....@ | ||
02252e80:·4 | 02252e80:·4f40·4140·4140·a000·7f40·a040·4040·4004··O@A@A@...@.@@@@. | ||
02252e90:·4040 | 02252e90:·8840·4040·9204·08a3·246c·6973·7449·0800··.@@@....$listI.. | ||
02252ea0:·38 | 02252ea0:·0038·00a0·c004·0902·05f5·e100·4050·4041··.8..........@P@A | ||
02252eb0:·a0e0 | 02252eb0:·a1a0·e0a3·225b·5d61·9040·4004·9440·9204··...."[]a.@@..@.. | ||
02252ec0:·a0e0 | 02252ec0:·03a0·e0a3·223a·3a62·90a0·040e·a0c0·b390··...."::b........ | ||
02252ed0:·16a0 | 02252ed0:·0416·a004·1340·9040·0205·f5e1·0040·5140··.....@.@.....@Q@ | ||
02252ee0:·04 | 02252ee0:·4004·a140·9204·0a40·4041·40a0·5940·a040··@..@...@@A@.Y@.@ | ||
02252ef0:·4040·04a | 02252ef0:·4040·4004·a440·4040·9204·1ba3·266f·7074··@@@..@@@....&opt | ||
02252f00:·6f6e | 02252f00:·696f·6e4a·0800·0038·00a0·c004·2502·05f5··ionJ...8....%... | ||
02252f10:·0040 | 02252f10:·e100·4053·4041·a1a0·e0a3·244e·6f6e·6563··..@S@A....$Nonec | ||
02252f20:· | 02252f20:·9040·4004·b040·9204·03a0·e0a3·2453·6f6d··.@@..@......$Som | ||
02252f30:·6490 | 02252f30:·6564·90a0·040e·4040·04b7·4092·0404·4040··ed....@@..@...@@ | ||
02252f40:·40a0 | 02252f40:·4140·a059·40a0·4040·4040·04ba·4040·4092··A@.Y@.@@@@..@@@. | ||
02252f50:·15a3 | 02252f50:·0415·a326·6c61·7a79·5f74·4e08·0000·3800··...&lazy_tN...8. | ||
02252f60:·c004 | 02252f60:·a0c0·043b·0205·f5e1·0040·5540·4140·4140··...;.....@U@A@A@ | ||
02252f70:·5940· | 02252f70:·a059·40a0·4040·4040·04c2·4040·4092·0407··.Y@.@@@@..@@@... | ||
02252f80:·296e | 02252f80:·a329·6e61·7469·7665·696e·744b·0800·0038··.)nativeintK...8 | ||
02252f90:· | 02252f90:·0040·4040·4140·4040·4040·04c6·4040·4092··.@@@A@@@@@..@@@. | ||
02252fa0:·03a3 | 02252fa0:·0403·a325·696e·7433·324c·0800·0038·0040··...%int32L...8.@ | ||
02252fb0:·404 | 02252fb0:·4040·4140·4040·4040·04ca·4040·4092·0403··@@A@@@@@..@@@... | ||
02252fc0:·2569 | 02252fc0:·a325·696e·7436·344d·0800·0038·0040·4040··.%int64M...8.@@@ | ||
02252fd0:·4 | 02252fd0:·4140·4040·4040·04ce·4040·4092·0403·a33a··A@@@@@..@@@....: | ||
02252fe0:·6e64 | 02252fe0:·556e·6465·6669·6e65·645f·7265·6375·7273··Undefined_recurs | ||
02252ff0:·7665 | 02252ff0:·6976·655f·6d6f·6475·6c65·5d08·0000·2000··ive_module]...·. | ||
02253000:·0457 | 02253000:·9004·5740·90a0·c092·a0c0·b390·0483·4090··..W@..........@. | ||
02253010:·0205 | 02253010:·4002·05f5·e100·404a·a0c0·b390·0490·4090··@.....@J......@. | ||
02253020:·0205 | 02253020:·4002·05f5·e100·4040·a004·0540·0205·f5e1··@.....@@...@.... | ||
02253030:·4056 | 02253030:·0040·5640·4041·04e2·a0b0·a03d·6f63·616d··.@V@@A.....=ocam | ||
02253040:·2e | 02253040:·6c2e·7761·726e·5f6f·6e5f·6c69·7465·7261··l.warn_on_litera | ||
02253050:·5f70 | 02253050:·6c5f·7061·7474·6572·6e04·e604·6104·e640··l_pattern...a..@ | ||
02253060:·0417 | 02253060:·9204·17a3·2e41·7373·6572·745f·6661·696c··.....Assert_fail | ||
02253070:·7265 | 02253070:·7572·655c·0800·0020·0004·1840·90a0·c092··ure\...·...@.... | ||
02253080:·0417 | 02253080:·a004·17a0·0413·a004·1440·0205·f5e1·0040··.........@.....@ | ||
02253090:·4040 | 02253090:·5840·4041·04f1·a0b0·a004·0f04·f404·6f04··X@@A..........o. | ||
022530a0:·4092 | 022530a0:·f440·9204·0da3·3044·6976·6973·696f·6e5f··.@....0Division_ | ||
022530b0:·795f | 022530b0:·6279·5f7a·6572·6f59·0800·0020·0004·2640··by_zeroY...·..&@ | ||
022530c0:· | 022530c0:·9040·4041·04f9·a0b0·a004·1704·fc04·7704··.@@A..........w. | ||
022530d0:·4092 | 022530d0:·fc40·9204·07a3·2b45·6e64·5f6f·665f·6669··.@....+End_of_fi | ||
022530e0:·6 | 022530e0:·6c65·5808·0000·2000·042e·4090·4040·4105··leX...·...@.@@A. | ||
022530f0:·00a0 | 022530f0:·0101·a0b0·a004·1f05·0104·047f·0501·0440··...............@ | ||
02253100:·0407 | 02253100:·9204·07a3·2953·7973·5f65·7272·6f72·5708··....)Sys_errorW. | ||
02253110:·00 | 02253110:·0000·2000·0436·4090·a004·3240·4041·0501··..·..6@...2@@A.. | ||
02253120:·a0b0 | 02253120:·0aa0·b0a0·0428·0501·0d04·8805·010d·4092··.....(........@. | ||
02253130:·08a3 | 02253130:·0408·a32e·5379·735f·626c·6f63·6b65·645f··....Sys_blocked_ | ||
02253140:·6f5b | 02253140:·696f·5b08·0000·2000·043f·4090·4040·4105··io[...·..?@.@@A. | ||
02253150:·11a0 | 02253150:·0112·a0b0·a004·3005·0115·0490·0501·1540··......0........@ | ||
02253160:·0407 | 02253160:·9204·07a3·294e·6f74·5f66·6f75·6e64·5608··....)Not_foundV. | ||
02253170:·00 | 02253170:·0000·2000·0447·4090·4040·4105·011a·a0b0··..·..G@.@@A..... | ||
02253180:·0438 | 02253180:·a004·3805·011d·0498·0501·1d40·9204·07a3··..8........@.... | ||
02253190:·4661 | 02253190:·2746·6169·6c75·7265·5508·0000·2000·044f··'FailureU...·..O | ||
022531a0:·90a0 | 022531a0:·4090·a004·4b40·4041·0501·23a0·b0a0·0441··@...K@@A..#....A | ||
022531b0:·01 | 022531b0:·0501·2604·a105·0126·4092·0408·a330·496e··..&....&@....0In | ||
022531c0:·616c | 022531c0:·7661·6c69·645f·6172·6775·6d65·6e74·5408··valid_argumentT. | ||
022531d0:·00 | 022531d0:·0000·2000·0458·4090·a004·5440·4041·0501··..·..X@...T@@A.. | ||
022531e0:·a0b0 | 022531e0:·2ca0·b0a0·044a·0501·2f04·aa05·012f·4092··,....J../..../@. | ||
022531f0:·08a3 | 022531f0:·0408·a32e·5374·6163·6b5f·6f76·6572·666c··....Stack_overfl | ||
02253200:·775a | 02253200:·6f77·5a08·0000·2000·0461·4090·4040·4105··owZ...·..a@.@@A. | ||
02253210:·3 | 02253210:·0134·a0b0·a004·5205·0137·04b2·0501·3740··.4....R..7....7@ | ||
02253220:·0407 | 02253220:·9204·07a3·2d4f·7574·5f6f·665f·6d65·6d6f··....-Out_of_memo | ||
02253230:·7953 | 02253230:·7279·5308·0000·2000·0469·4090·4040·4105··ryS...·..i@.@@A. | ||
02253240:·3 | 02253240:·013c·a0b0·a004·5a05·013f·04ba·0501·3f40··.<....Z..?....?@ | ||
02253250:·0407 | 02253250:·9204·07a3·2d4d·6174·6368·5f66·6169·6c75··....-Match_failu | ||
02253260:·6552 | 02253260:·7265·5208·0000·2000·0471·4090·a0c0·92a0··reR...·..q@..... | ||
02253270:·70a0 | 02253270:·0470·a004·6ca0·046d·4002·05f5·e100·4063··.p..l..m@.....@c | ||
02253280:·404 | 02253280:·4040·4105·014a·a0b0·a004·6805·014d·04c8··@@A..J....h..M.. | ||
02253290:·01 | 02253290:·0501·4d40·9204·0da3·2562·7974·6573·4308··..M@....%bytesC. | ||
022532a0:·00 | 022532a0:·0000·3800·4040·4041·4040·4040·4005·0151··..8.@@@A@@@@@..Q | ||
022532b0:·4040·9204 | 022532b0:·4040·4092·0403·9092·2653·7464·6c69·6292··@@@.....&Stdlib. | ||
022532c0:·4f70·7469·6f6e·a021·63 | 022532c0:·2349·6e74·9226·4f70·7469·6f6e·a021·6300··#Int.&Option.!c. | ||
022532d0:·a190·9226·5374·646c·696 | 022532d0:·51d0·c096·c0b3·a190·9226·5374·646c·6962··Q........&Stdlib | ||
022532e0:· | 022532e0:·2372·6566·a0c0·96c0·b304·8b40·9040·0205··#ref.......@.@.. | ||
022532f0:· | 022532f0:·f5e1·0040·0103·1b41·4001·0319·4090·4002··...@...A@...@.@. | ||
02253300:·0 | 02253300:·05f5·e100·4001·0318·4140·0103·1540·b0c0··....@...A@...@.. | ||
02253310:·634f·626a·2e6d·6c4f·0102· | 02253310:·2c63·6c69·622f·634f·626a·2e6d·6c4f·0102··,clib/cObj.mlO.. | ||
02253320:· | 02253320:·f101·02f5·c004·024f·0102·f101·02f6·4040··.......O......@@ | ||
02253330:· | 02253330:·a105·0172·40a0·2173·0052·d0c0·96c0·b304··...r@.!s.R...... | ||
02253340:· | 02253340:·18a0·c096·c0b3·049e·4090·4002·05f5·e100··........@.@..... | ||
02253350:· | 02253350:·4001·0323·4140·0103·2140·9040·0205·f5e1··@..#A@..!@.@.... | ||
02253360:· | 02253360:·0040·0103·2041·4001·031d·40b0·c004·1350··.@..·A@...@....P | ||
02253370:· | 02253370:·0102·ff01·0303·c004·1450·0102·ff01·0304··.........P...... | ||
02253380:·4 | 02253380:·4040·a105·0184·41a0·2162·0053·d0c0·96c0··@@....A.!b.S.... | ||
02253390:· | 02253390:·b304·2aa0·c096·c0b3·04b0·4090·4002·05f5··..*.......@.@... | ||
022533a0:· | 022533a0:·e100·4001·032b·4140·0103·2940·9040·0205··..@..+A@..)@.@.. | ||
022533b0:· | 022533b0:·f5e1·0040·0103·2841·4001·0325·40b0·c004··...@..(A@..%@... | ||
022533c0:· | 022533c0:·2551·0103·0d01·0311·c004·2651·0103·0d01··%Q........&Q.... | ||
022533d0:·0 | 022533d0:·0312·4040·a105·0196·42a0·216d·0054·d0c0··..@@....B.!m.T.. | ||
022533e0:· | 022533e0:·96c0·b304·3ca0·c096·c0b3·04c2·4090·4002··....<.......@.@. | ||
Max diff block lines reached; 34611066/35137091 bytes (98.50%) of diff not shown. |
Offset 2415500, 1183778 lines modified | Offset 2415500, 1183779 lines modified | ||
024db8b0:·4340·4042·4041·4040·8495·a6be·0000·0052··C@@B@A@@.......R | 024db8b0:·4340·4042·4041·4040·8495·a6be·0000·0052··C@@B@A@@.......R | ||
024db8c0:·0000·0006·0000·0021·0000·0017·a030·2e2f··.......!.....0./ | 024db8c0:·0000·0006·0000·0021·0000·0017·a030·2e2f··.......!.....0./ | ||
024db8d0:·5f62·7569·6c64·2f64·6566·6175·6c74·a035··_build/default.5 | 024db8d0:·5f62·7569·6c64·2f64·6566·6175·6c74·a035··_build/default.5 | ||
024db8e0:·2e2f·5f62·7569·6c64·2f64·6566·6175·6c74··./_build/default | 024db8e0:·2e2f·5f62·7569·6c64·2f64·6566·6175·6c74··./_build/default | ||
024db8f0:·2f63·6c69·62a0·0925·2e2f·5f62·7569·6c64··/clib..%./_build | 024db8f0:·2f63·6c69·62a0·0925·2e2f·5f62·7569·6c64··/clib..%./_build | ||
024db900:·2f64·6566·6175·6c74·2f63·6c69·622f·2e63··/default/clib/.c | 024db900:·2f64·6566·6175·6c74·2f63·6c69·622f·2e63··/default/clib/.c | ||
024db910:·6c69·622e·6f62·6a73·2f62·7974·6540·002b··lib.objs/byte@.+ | 024db910:·6c69·622e·6f62·6a73·2f62·7974·6540·002b··lib.objs/byte@.+ | ||
024db920:·10b8·8495·a6be·0000·5a | 024db920:·10b8·8495·a6be·0000·5a65·0000·0f39·0000··........Ze...9.. | ||
024db930:·4 | 024db930:·4106·0000·403d·a008·0000·2c00·010f·e824··A...@=....,....$ | ||
024db940:·434f·626a·b0c0·265f·6e6f·6e65·5f40·4000··CObj..&_none_@@. | 024db940:·434f·626a·b0c0·265f·6e6f·6e65·5f40·4000··CObj..&_none_@@. | ||
024db950:·ff04·0241·4122·3f3f·4140·d040·4040·4040··...AA"??A@.@@@@@ | 024db950:·ff04·0241·4122·3f3f·4140·d040·4040·4040··...AA"??A@.@@@@@ | ||
024db960:·b040·4040·4040·a008·0000·2c00·010f·a404··.@@@@@....,..... | 024db960:·b040·4040·4040·a008·0000·2c00·010f·a404··.@@@@@....,..... | ||
024db970:·0904·0841·223f·3f41·b0b0·b0b0·b0b0·b0b0··...A"??A........ | 024db970:·0904·0841·223f·3f41·b0b0·b0b0·b0b0·b0b0··...A"??A........ | Diff chunk too large, falling back to line-by-line diff (3804 lines added, 3804 lines removed) | |
024db980:·b0b0·b0b0·b0b0·b0b0·b0b0·b0b0·b0b0·b0c3··................ | 024db980:·b0b0·b0b0·b0b0·b0b0·b0b0·b0b0·b0b0·b0c3··................ | ||
024db990:·b0b0·b0b0·b0b0·b0ab·a | 024db990:·b0b0·b0b0·b0b0·b0ab·aba7·b1b2·b2b2·b2b2··................ | ||
024db9a0:·b2b2·b2b2·b2b2·b | 024db9a0:·b2b2·b2b2·b2b2·b2b1·b1b1·b1b1·b1b1·b1b1··................ | ||
024db9b0:·b1b1·b1b1·b1b1·40a3 | 024db9b0:·b1b1·b1b1·b1b1·b140·a32a·666c·6f61·7461··.......@.*floata | ||
024db9c0:·7261 | 024db9c0:·7272·6179·5108·0000·3800·4040·4041·4040··rrayQ...8.@@@A@@ | ||
024db9d0:·4040·0 | 024db9d0:·4040·4004·4b40·4040·9204·03a3·3565·7874··@@@.K@@@....5ext | ||
024db9e0:·6e73 | 024db9e0:·656e·7369·6f6e·5f63·6f6e·7374·7275·6374··ension_construct | ||
024db9f0:·7250 | 024db9f0:·6f72·5008·0000·3800·4040·4041·4040·4040··orP...8.@@@A@@@@ | ||
024dba00:·0 | 024dba00:·4004·4f40·4040·9204·03a3·2369·6e74·4108··@.O@@@....#intA. | ||
024dba10:·00 | 024dba10:·0000·3800·4040·4041·4040·4040·4004·5340··..8.@@@A@@@@@.S@ | ||
024dba20:·4092 | 024dba20:·4140·9204·03a3·2463·6861·7242·0800·0038··A@....$charB...8 | ||
024dba30:· | 024dba30:·0040·4040·4140·4040·4040·0457·4041·4092··.@@@A@@@@@.W@A@. | ||
024dba40:·03a3 | 024dba40:·0403·a326·7374·7269·6e67·4f08·0000·3800··...&stringO...8. | ||
024dba50:·4040·4 | 024dba50:·4040·4041·4040·4040·4004·5b40·4040·9204··@@@A@@@@@.[@@@.. | ||
024dba60:·a325 | 024dba60:·03a3·2566·6c6f·6174·4408·0000·3800·4040··..%floatD...8.@@ | ||
024dba70:·4 | 024dba70:·4041·4040·4040·4004·5f40·4040·9204·03a3··@A@@@@@._@@@.... | ||
024dba80:·626f | 024dba80:·2462·6f6f·6c45·0800·0038·0040·40a1·a0e0··$boolE...8.@@... | ||
024dba90:·25 | 024dba90:·a325·6661·6c73·655e·9040·4004·6940·9204··.%false^.@@.i@.. | ||
024dbaa0:·a0e0 | 024dbaa0:·03a0·e0a3·2474·7275·655f·9040·4004·6f40··....$true_.@@.o@ | ||
024dbab0:· | 024dbab0:·9204·0340·4041·4040·4040·4004·7040·4140··...@@A@@@@@.p@A@ | ||
024dbac0:·0410 | 024dbac0:·9204·10a3·2475·6e69·7446·0800·0038·0040··....$unitF...8.@ | ||
024dbad0:·a1a0 | 024dbad0:·40a1·a0e0·a322·2829·6090·4040·047a·4092··@...."()`.@@.z@. | ||
024dbae0:·0 | 024dbae0:·0403·4040·4140·4040·4040·047b·4041·4092··..@@A@@@@@.{@A@. | ||
024dbaf0:·0aa3 | 024dbaf0:·040a·a323·6578·6e47·0800·0038·0040·4041··...#exnG...8.@@A | ||
024dbb00:·4 | 024dbb00:·4140·4040·4040·047f·4040·4092·0403·a325··A@@@@@..@@@....% | ||
024dbb10:·7272 | 024dbb10:·6172·7261·7948·0800·0038·00a0·c090·4002··arrayH...8....@. | ||
024dbb20:·f5e1 | 024dbb20:·05f5·e100·404f·4041·4041·40a0·007f·40a0··....@O@A@A@...@. | ||
024dbb30:·4040·4004 | 024dbb30:·4040·4040·0488·4040·4092·0408·a324·6c69··@@@@..@@@....$li | ||
024dbb40:·7449 | 024dbb40:·7374·4908·0000·3800·a0c0·0409·0205·f5e1··stI...8......... | ||
024dbb50:·4050 | 024dbb50:·0040·5040·41a1·a0e0·a322·5b5d·6190·4040··.@P@A...."[]a.@@ | ||
024dbb60:·9 | 024dbb60:·0494·4092·0403·a0e0·a322·3a3a·6290·a004··..@......"::b... | ||
024dbb70:·a0c0 | 024dbb70:·0ea0·c0b3·9004·16a0·0413·4090·4002·05f5··..........@.@... | ||
024dbb80:·0040 | 024dbb80:·e100·4051·4040·04a1·4092·040a·4040·4140··..@Q@@..@...@@A@ | ||
024dbb90:·5940· | 024dbb90:·a059·40a0·4040·4040·04a4·4040·4092·041b··.Y@.@@@@..@@@... | ||
024dbba0:·266f | 024dbba0:·a326·6f70·7469·6f6e·4a08·0000·3800·a0c0··.&optionJ...8... | ||
024dbbb0:·2502 | 024dbbb0:·0425·0205·f5e1·0040·5340·41a1·a0e0·a324··.%.....@S@A....$ | ||
024dbbc0:·6f6e | 024dbbc0:·4e6f·6e65·6390·4040·04b0·4092·0403·a0e0··Nonec.@@..@..... | ||
024dbbd0:·2453 | 024dbbd0:·a324·536f·6d65·6490·a004·0e40·4004·b740··.$Somed....@@..@ | ||
024dbbe0:· | 024dbbe0:·9204·0440·4041·40a0·5940·a040·4040·4004··...@@A@.Y@.@@@@. | ||
024dbbf0:·4040 | 024dbbf0:·ba40·4040·9204·15a3·266c·617a·795f·744e··.@@@....&lazy_tN | ||
024dbc00:·0000 | 024dbc00:·0800·0038·00a0·c004·3b02·05f5·e100·4055··...8....;.....@U | ||
024dbc10:·4 | 024dbc10:·4041·4041·40a0·5940·a040·4040·4004·c240··@A@A@.Y@.@@@@..@ | ||
024dbc20:·4092 | 024dbc20:·4040·9204·07a3·296e·6174·6976·6569·6e74··@@....)nativeint | ||
024dbc30:· | 024dbc30:·4b08·0000·3800·4040·4041·4040·4040·4004··K...8.@@@A@@@@@. | ||
024dbc40:·4040 | 024dbc40:·c640·4040·9204·03a3·2569·6e74·3332·4c08··.@@@....%int32L. | ||
024dbc50:·00 | 024dbc50:·0000·3800·4040·4041·4040·4040·4004·ca40··..8.@@@A@@@@@..@ | ||
024dbc60:·4092 | 024dbc60:·4040·9204·03a3·2569·6e74·3634·4d08·0000··@@....%int64M... | ||
024dbc70:· | 024dbc70:·3800·4040·4041·4040·4040·4004·ce40·4040··8.@@@A@@@@@..@@@ | ||
024dbc80:·0403 | 024dbc80:·9204·03a3·3a55·6e64·6566·696e·6564·5f72··....:Undefined_r | ||
024dbc90:·6375 | 024dbc90:·6563·7572·7369·7665·5f6d·6f64·756c·655d··ecursive_module] | ||
024dbca0:·0000 | 024dbca0:·0800·0020·0090·0457·4090·a0c0·92a0·c0b3··...·...W@....... | ||
024dbcb0:·0483 | 024dbcb0:·9004·8340·9040·0205·f5e1·0040·4aa0·c0b3··...@.@.....@J... | ||
024dbcc0:·0490 | 024dbcc0:·9004·9040·9040·0205·f5e1·0040·40a0·0405··...@.@.....@@... | ||
024dbcd0:·0205 | 024dbcd0:·4002·05f5·e100·4056·4040·4104·e2a0·b0a0··@.....@V@@A..... | ||
024dbce0:·6f63 | 024dbce0:·3d6f·6361·6d6c·2e77·6172·6e5f·6f6e·5f6c··=ocaml.warn_on_l | ||
024dbcf0:·7465 | 024dbcf0:·6974·6572·616c·5f70·6174·7465·726e·04e6··iteral_pattern.. | ||
024dbd00:·6104 | 024dbd00:·0461·04e6·4092·0417·a32e·4173·7365·7274··.a..@.....Assert | ||
024dbd10:·6661 | 024dbd10:·5f66·6169·6c75·7265·5c08·0000·2000·0418··_failure\...·... | ||
024dbd20:·90a0 | 024dbd20:·4090·a0c0·92a0·0417·a004·13a0·0414·4002··@.............@. | ||
024dbd30:·f5e1 | 024dbd30:·05f5·e100·4058·4040·4104·f1a0·b0a0·040f··....@X@@A....... | ||
024dbd40:·f | 024dbd40:·04f4·046f·04f4·4092·040d·a330·4469·7669··...o..@....0Divi | ||
024dbd50:·696f | 024dbd50:·7369·6f6e·5f62·795f·7a65·726f·5908·0000··sion_by_zeroY... | ||
024dbd60:·000 | 024dbd60:·2000·0426·4090·4040·4104·f9a0·b0a0·0417···..&@.@@A....... | ||
024dbd70:·f | 024dbd70:·04fc·0477·04fc·4092·0407·a32b·456e·645f··...w..@....+End_ | ||
024dbd80:·665f | 024dbd80:·6f66·5f66·696c·6558·0800·0020·0004·2e40··of_fileX...·...@ | ||
024dbd90:· | 024dbd90:·9040·4041·0501·01a0·b0a0·041f·0501·0404··.@@A............ | ||
024dbda0:·0501 | 024dbda0:·7f05·0104·4092·0407·a329·5379·735f·6572··....@....)Sys_er | ||
024dbdb0:·6f72 | 024dbdb0:·726f·7257·0800·0020·0004·3640·90a0·0432··rorW...·..6@...2 | ||
024dbdc0:·404 | 024dbdc0:·4040·4105·010a·a0b0·a004·2805·010d·0488··@@A.......(..... | ||
024dbdd0:·0 | 024dbdd0:·0501·0d40·9204·08a3·2e53·7973·5f62·6c6f··...@.....Sys_blo | ||
024dbde0:·6b65 | 024dbde0:·636b·6564·5f69·6f5b·0800·0020·0004·3f40··cked_io[...·..?@ | ||
024dbdf0:· | 024dbdf0:·9040·4041·0501·12a0·b0a0·0430·0501·1504··.@@A.......0.... | ||
024dbe00:·0501 | 024dbe00:·9005·0115·4092·0407·a329·4e6f·745f·666f··....@....)Not_fo | ||
024dbe10:·6e64 | 024dbe10:·756e·6456·0800·0020·0004·4740·9040·4041··undV...·..G@.@@A | ||
024dbe20:·01 | 024dbe20:·0501·1aa0·b0a0·0438·0501·1d04·9805·011d··.......8........ | ||
024dbe30:·9204 | 024dbe30:·4092·0407·a327·4661·696c·7572·6555·0800··@....'FailureU.. | ||
024dbe40:·20 | 024dbe40:·0020·0004·4f40·90a0·044b·4040·4105·0123··.·..O@...K@@A..# | ||
024dbe50:·b0a0 | 024dbe50:·a0b0·a004·4105·0126·04a1·0501·2640·9204··....A..&....&@.. | ||
024dbe60:·a330 | 024dbe60:·08a3·3049·6e76·616c·6964·5f61·7267·756d··..0Invalid_argum | ||
024dbe70:·6e74 | 024dbe70:·656e·7454·0800·0020·0004·5840·90a0·0454··entT...·..X@...T | ||
024dbe80:·404 | 024dbe80:·4040·4105·012c·a0b0·a004·4a05·012f·04aa··@@A..,....J../.. | ||
024dbe90:·01 | 024dbe90:·0501·2f40·9204·08a3·2e53·7461·636b·5f6f··../@.....Stack_o | ||
024dbea0:·6572 | 024dbea0:·7665·7266·6c6f·775a·0800·0020·0004·6140··verflowZ...·..a@ | ||
024dbeb0:· | 024dbeb0:·9040·4041·0501·34a0·b0a0·0452·0501·3704··.@@A..4....R..7. | ||
024dbec0:·0501 | 024dbec0:·b205·0137·4092·0407·a32d·4f75·745f·6f66··...7@....-Out_of | ||
024dbed0:·6d65 | 024dbed0:·5f6d·656d·6f72·7953·0800·0020·0004·6940··_memoryS...·..i@ | ||
024dbee0:· | 024dbee0:·9040·4041·0501·3ca0·b0a0·045a·0501·3f04··.@@A..<....Z..?. | ||
024dbef0:·0501 | 024dbef0:·ba05·013f·4092·0407·a32d·4d61·7463·685f··...?@....-Match_ | ||
024dbf00:·6169 | 024dbf00:·6661·696c·7572·6552·0800·0020·0004·7140··failureR...·..q@ | ||
024dbf10:·a0c0 | 024dbf10:·90a0·c092·a004·70a0·046c·a004·6d40·0205··......p..l..m@.. | ||
024dbf20:·e1 | 024dbf20:·f5e1·0040·6340·4041·0501·4aa0·b0a0·0468··...@c@@A..J....h | ||
024dbf30:·01 | 024dbf30:·0501·4d04·c805·014d·4092·040d·a325·6279··..M....M@....%by | ||
024dbf40:·6573 | 024dbf40:·7465·7343·0800·0038·0040·4040·4140·4040··tesC...8.@@@A@@@ | ||
024dbf50:·4005· | 024dbf50:·4040·0501·5140·4040·9204·0390·9226·5374··@@..Q@@@.....&St | ||
024dbf60:·6c69 | 024dbf60:·646c·6962·9223·496e·7492·264f·7074·696f··dlib.#Int.&Optio | ||
024dbf70:·d0c0·96c0·b3a1·9092·2653 | 024dbf70:·6ea0·2163·0051·d0c0·96c0·b3a1·9092·2653··n.!c.Q........&S | ||
024dbf80:·7 | 024dbf80:·7464·6c69·6223·7265·66a0·c096·c0b3·048b··tdlib#ref....... | ||
024dbf90:· | 024dbf90:·4090·4002·05f5·e100·4001·031b·4140·0103··@.@.....@...A@.. | ||
024dbfa0:· | 024dbfa0:·1940·9040·0205·f5e1·0040·0103·1841·4001··.@.@.....@...A@. | ||
024dbfb0:·636c·6962·2f63·4f62·6a2e | 024dbfb0:·0315·40b0·c02c·636c·6962·2f63·4f62·6a2e··..@..,clib/cObj. | ||
024dbfc0:· | 024dbfc0:·6d6c·4f01·02f1·0102·f5c0·0402·4f01·02f1··mlO.........O... | ||
024dbfd0:·0 | 024dbfd0:·0102·f640·40a1·0501·7240·a021·7300·52d0··...@@...r@.!s.R. | ||
024dbfe0:· | 024dbfe0:·c096·c0b3·0418·a0c0·96c0·b304·9e40·9040··.............@.@ | ||
024dbff0:·0 | 024dbff0:·0205·f5e1·0040·0103·2341·4001·0321·4090··.....@..#A@..!@. | ||
024dc000:·400 | 024dc000:·4002·05f5·e100·4001·0320·4140·0103·1d40··@.....@..·A@...@ | ||
024dc010:· | 024dc010:·b0c0·0413·5001·02ff·0103·03c0·0414·5001··....P.........P. | ||
024dc020:· | 024dc020:·02ff·0103·0440·40a1·0501·8441·a021·6200··.....@@....A.!b. | ||
024dc030:· | 024dc030:·53d0·c096·c0b3·042a·a0c0·96c0·b304·b040··S......*.......@ | ||
024dc040:· | 024dc040:·9040·0205·f5e1·0040·0103·2b41·4001·0329··.@.....@..+A@..) | ||
024dc050:· | 024dc050:·4090·4002·05f5·e100·4001·0328·4140·0103··@.@.....@..(A@.. | ||
024dc060:·5 | 024dc060:·2540·b0c0·0425·5101·030d·0103·11c0·0426··%@...%Q........& | ||
024dc070:· | 024dc070:·5101·030d·0103·1240·40a1·0501·9642·a021··Q......@@....B.! | ||
024dc080:· | 024dc080:·6d00·54d0·c096·c0b3·043c·a0c0·96c0·b304··m.T......<...... | ||
Max diff block lines reached; 162813695/163339860 bytes (99.68%) of diff not shown. |
Offset 1, 3 lines modified | Offset 1, 3 lines modified | ||
1 | -rw-r--r--···0········0········0········4·2022-11-29·08:28:08.000000·debian-binary | 1 | -rw-r--r--···0········0········0········4·2022-11-29·08:28:08.000000·debian-binary |
2 | -rw-r--r--···0········0········0····611 | 2 | -rw-r--r--···0········0········0····61180·2022-11-29·08:28:08.000000·control.tar.xz |
3 | -rw-r--r--···0········0········0·430 | 3 | -rw-r--r--···0········0········0·43048668·2022-11-29·08:28:08.000000·data.tar.xz |
Offset 46, 21 lines modified | Offset 46, 21 lines modified | ||
46 | -rw-r--r--···0·root·········(0)·root·········(0)····58810·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cList.cmi | 46 | -rw-r--r--···0·root·········(0)·root·········(0)····58810·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cList.cmi |
47 | -rw-r--r--···0·root·········(0)·root·········(0)···485301·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cList.cmt | 47 | -rw-r--r--···0·root·········(0)·root·········(0)···485301·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cList.cmt |
48 | -rw-r--r--···0·root·········(0)·root·········(0)···203741·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cList.cmti | 48 | -rw-r--r--···0·root·········(0)·root·········(0)···203741·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cList.cmti |
49 | -rw-r--r--···0·root·········(0)·root·········(0)······658·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cList.cmx | 49 | -rw-r--r--···0·root·········(0)·root·········(0)······658·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cList.cmx |
50 | -rw-r--r--···0·root·········(0)·root·········(0)····30739·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cList.ml | 50 | -rw-r--r--···0·root·········(0)·root·········(0)····30739·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cList.ml |
51 | -rw-r--r--···0·root·········(0)·root·········(0)····17954·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cList.mli | 51 | -rw-r--r--···0·root·········(0)·root·········(0)····17954·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cList.mli |
52 | -rw-r--r--···0·root·········(0)·root·········(0)····17516·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cMap.cmi | 52 | -rw-r--r--···0·root·········(0)·root·········(0)····17516·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cMap.cmi |
53 | -rw-r--r--···0·root·········(0)·root·········(0)···1539 | 53 | -rw-r--r--···0·root·········(0)·root·········(0)···153974·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cMap.cmt |
54 | -rw-r--r--···0·root·········(0)·root·········(0)····53414·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cMap.cmti | 54 | -rw-r--r--···0·root·········(0)·root·········(0)····53414·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cMap.cmti |
55 | -rw-r--r--···0·root·········(0)·root·········(0)······452·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cMap.cmx | 55 | -rw-r--r--···0·root·········(0)·root·········(0)······452·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cMap.cmx |
56 | -rw-r--r--···0·root·········(0)·root·········(0)·····7431·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cMap.ml | 56 | -rw-r--r--···0·root·········(0)·root·········(0)·····7431·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cMap.ml |
57 | -rw-r--r--···0·root·········(0)·root·········(0)·····3103·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cMap.mli | 57 | -rw-r--r--···0·root·········(0)·root·········(0)·····3103·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cMap.mli |
58 | -rw-r--r--···0·root·········(0)·root·········(0)·····1079·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cObj.cmi | 58 | -rw-r--r--···0·root·········(0)·root·········(0)·····1079·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cObj.cmi |
59 | -rw-r--r--···0·root·········(0)·root·········(0)····76 | 59 | -rw-r--r--···0·root·········(0)·root·········(0)····76602·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cObj.cmt |
60 | -rw-r--r--···0·root·········(0)·root·········(0)····10151·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cObj.cmti | 60 | -rw-r--r--···0·root·········(0)·root·········(0)····10151·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cObj.cmti |
61 | -rw-r--r--···0·root·········(0)·root·········(0)······553·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cObj.cmx | 61 | -rw-r--r--···0·root·········(0)·root·········(0)······553·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cObj.cmx |
62 | -rw-r--r--···0·root·········(0)·root·········(0)·····6267·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cObj.ml | 62 | -rw-r--r--···0·root·········(0)·root·········(0)·····6267·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cObj.ml |
63 | -rw-r--r--···0·root·········(0)·root·········(0)·····2333·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cObj.mli | 63 | -rw-r--r--···0·root·········(0)·root·········(0)·····2333·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cObj.mli |
64 | -rw-r--r--···0·root·········(0)·root·········(0)·····7306·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cSet.cmi | 64 | -rw-r--r--···0·root·········(0)·root·········(0)·····7306·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cSet.cmi |
65 | -rw-r--r--···0·root·········(0)·root·········(0)····38339·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cSet.cmt | 65 | -rw-r--r--···0·root·········(0)·root·········(0)····38339·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cSet.cmt |
66 | -rw-r--r--···0·root·········(0)·root·········(0)····20724·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cSet.cmti | 66 | -rw-r--r--···0·root·········(0)·root·········(0)····20724·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cSet.cmti |
Offset 1, 9623 lines modified | Offset 1, 9624 lines modified | ||
00000000:·4361·6d6c·3139·3939·5430·3330·8495·a6be··Caml1999T030.... | 00000000:·4361·6d6c·3139·3939·5430·3330·8495·a6be··Caml1999T030.... | ||
00000010:·0002·595 | 00000010:·0002·5956·0000·6b52·0001·b40a·0001·b128··..YV..kR.......( | ||
00000020:·0800·0034·0024·434d·6170·91b0·a0b0·98d0··...4.$CMap...... | 00000020:·0800·0034·0024·434d·6170·91b0·a0b0·98d0··...4.$CMap...... | ||
00000030:·b12b·4f72·6465·7265·6454·7970·6500·5342··.+OrderedType.SB | 00000030:·b12b·4f72·6465·7265·6454·7970·6500·5342··.+OrderedType.SB | ||
00000040:·a004·02b0·c02c·636c·6962·2f63·4d61·702e··.....,clib/cMap. | 00000040:·a004·02b0·c02c·636c·6962·2f63·4d61·702e··.....,clib/cMap. | ||
00000050:·6d6c·4b01·02a4·0102·b0c0·0402·4b01·02a4··mlK.........K... | 00000050:·6d6c·4b01·02a4·0102·b0c0·0402·4b01·02a4··mlK.........K... | ||
00000060:·0102·bb40·90d0·91b0·a0b0·a141·a008·0000··...@.......A.... | 00000060:·0102·bb40·90d0·91b0·a0b0·a141·a008·0000··...@.......A.... | ||
00000070:·2800·b121·7400·5141·a004·02b0·c004·104d··(..!t.QA.......M | 00000070:·2800·b121·7400·5141·a004·02b0·c004·104d··(..!t.QA.......M | ||
00000080:·0102·c201·02c9·c004·114d·0102·c201·02ca··.........M...... | 00000080:·0102·c201·02c9·c004·114d·0102·c201·02ca··.........M...... | ||
00000090:·4040·0800·0038·0040·4040·4140·4040·4040··@@...8.@@@A@@@@@ | 00000090:·4040·0800·0038·0040·4040·4140·4040·4040··@@...8.@@@A@@@@@ | ||
000000a0:·b0c0·0414·4d01·02c2·0102·c404·0440·4040··....M........@@@ | 000000a0:·b0c0·0414·4d01·02c2·0102·c404·0440·4040··....M........@@@ | ||
000000b0:·40a1·0421·4040·4041·4004·0340·4008·0000··@..!@@@A@..@@... | 000000b0:·40a1·0421·4040·4041·4004·0340·4008·0000··@..!@@@A@..@@... | Diff chunk too large, falling back to line-by-line diff (8584 lines added, 8584 lines removed) | |
000000c0:·3000·a040·4004·0104·0104·0104·0104·0104··0..@@........... | 000000c0:·3000·a040·4004·0104·0104·0104·0104·0104··0..@@........... | ||
000000d0:·0104·0140·aba | 000000d0:·0104·0140·abab·a7b1·b2b2·b2b2·b2b2·b2b2··...@............ | ||
000000e0:·b2b2·b2b | 000000e0:·b2b2·b2b2·b1b1·b1b1·b1b1·b1b1·b1b1·b1b1··................ | ||
000000f0:·b1b1·b140 | 000000f0:·b1b1·b1b1·40a3·2a66·6c6f·6174·6172·7261··....@.*floatarra | ||
00000100:·5108 | 00000100:·7951·0800·0038·0040·4040·4140·4040·4040··yQ...8.@@@A@@@@@ | ||
00000110:·c026 | 00000110:·b0c0·265f·6e6f·6e65·5f40·4000·ff04·0241··..&_none_@@....A | ||
00000120:·4040·9204 | 00000120:·4040·4092·0406·a335·6578·7465·6e73·696f··@@@....5extensio | ||
00000130:·5f63 | 00000130:·6e5f·636f·6e73·7472·7563·746f·7250·0800··n_constructorP.. | ||
00000140:· | 00000140:·0038·0040·4040·4140·4040·4040·0407·4040··.8.@@@A@@@@@..@@ | ||
00000150:·9204 | 00000150:·4092·0403·a323·696e·7441·0800·0038·0040··@....#intA...8.@ | ||
00000160:·404 | 00000160:·4040·4140·4040·4040·040b·4041·4092·0403··@@A@@@@@..@A@... | ||
00000170:·2463 | 00000170:·a324·6368·6172·4208·0000·3800·4040·4041··.$charB...8.@@@A | ||
00000180:·4040·4040·040f | 00000180:·4040·4040·4004·0f40·4140·9204·03a3·2673··@@@@@..@A@....&s | ||
00000190:·7269 | 00000190:·7472·696e·674f·0800·0038·0040·4040·4140··tringO...8.@@@A@ | ||
000001a0:·4040·400 | 000001a0:·4040·4040·0413·4040·4092·0403·a325·666c··@@@@..@@@....%fl | ||
000001b0:·6174 | 000001b0:·6f61·7444·0800·0038·0040·4040·4140·4040··oatD...8.@@@A@@@ | ||
000001c0:·400 | 000001c0:·4040·0417·4040·4092·0403·a324·626f·6f6c··@@..@@@....$bool | ||
000001d0:·0800 | 000001d0:·4508·0000·3800·4040·a1a0·e0a3·2566·616c··E...8.@@....%fal | ||
000001e0:·655e | 000001e0:·7365·5e90·4040·0421·4092·0403·a0e0·a324··se^.@@.!@......$ | ||
000001f0:·7275 | 000001f0:·7472·7565·5f90·4040·0427·4092·0403·4040··true_.@@.'@...@@ | ||
00000200:·4 | 00000200:·4140·4040·4040·0428·4041·4092·0410·a324··A@@@@@.(@A@....$ | ||
00000210:·6e69 | 00000210:·756e·6974·4608·0000·3800·4040·a1a0·e0a3··unitF...8.@@.... | ||
00000220:·2829 | 00000220:·2228·2960·9040·4004·3240·9204·0340·4041··"()`.@@.2@...@@A | ||
00000230:·4040·4040·04 | 00000230:·4040·4040·4004·3340·4140·9204·0aa3·2365··@@@@@.3@A@....#e | ||
00000240:·6e47 | 00000240:·786e·4708·0000·3800·4040·4141·4040·4040··xnG...8.@@AA@@@@ | ||
00000250:·0437·4040· | 00000250:·4004·3740·4040·9204·03a3·2561·7272·6179··@.7@@@....%array | ||
00000260:·0800 | 00000260:·4808·0000·3800·a0c0·9040·0205·f5e1·0040··H...8....@.....@ | ||
00000270:·4 | 00000270:·4f40·4140·4140·a000·7f40·a040·4040·4004··O@A@A@...@.@@@@. | ||
00000280:·4040·4092 | 00000280:·4040·4040·9204·08a3·246c·6973·7449·0800··@@@@....$listI.. | ||
00000290:·38 | 00000290:·0038·00a0·c004·0902·05f5·e100·4050·4041··.8..........@P@A | ||
000002a0:·a0e0 | 000002a0:·a1a0·e0a3·225b·5d61·9040·4004·4c40·9204··...."[]a.@@.L@.. | ||
000002b0:·a0e0 | 000002b0:·03a0·e0a3·223a·3a62·90a0·040e·a0c0·b390··...."::b........ | ||
000002c0:·16a0 | 000002c0:·0416·a004·1340·9040·0205·f5e1·0040·5140··.....@.@.....@Q@ | ||
000002d0:·0459 | 000002d0:·4004·5940·9204·0a40·4041·40a0·5940·a040··@.Y@...@@A@.Y@.@ | ||
000002e0:·4040·045c·4040· | 000002e0:·4040·4004·5c40·4040·9204·1ba3·266f·7074··@@@.\@@@....&opt | ||
000002f0:·6f6e | 000002f0:·696f·6e4a·0800·0038·00a0·c004·2502·05f5··ionJ...8....%... | ||
00000300:·0040 | 00000300:·e100·4053·4041·a1a0·e0a3·244e·6f6e·6563··..@S@A....$Nonec | ||
00000310:· | 00000310:·9040·4004·6840·9204·03a0·e0a3·2453·6f6d··.@@.h@......$Som | ||
00000320:·6490 | 00000320:·6564·90a0·040e·4040·046f·4092·0404·4040··ed....@@.o@...@@ | ||
00000330:·40a0 | 00000330:·4140·a059·40a0·4040·4040·0472·4040·4092··A@.Y@.@@@@.r@@@. | ||
00000340:·15a3 | 00000340:·0415·a326·6c61·7a79·5f74·4e08·0000·3800··...&lazy_tN...8. | ||
00000350:·c004 | 00000350:·a0c0·043b·0205·f5e1·0040·5540·4140·4140··...;.....@U@A@A@ | ||
00000360:·5940· | 00000360:·a059·40a0·4040·4040·047a·4040·4092·0407··.Y@.@@@@.z@@@... | ||
00000370:·296e | 00000370:·a329·6e61·7469·7665·696e·744b·0800·0038··.)nativeintK...8 | ||
00000380:· | 00000380:·0040·4040·4140·4040·4040·047e·4040·4092··.@@@A@@@@@.~@@@. | ||
00000390:·03a3 | 00000390:·0403·a325·696e·7433·324c·0800·0038·0040··...%int32L...8.@ | ||
000003a0:·404 | 000003a0:·4040·4140·4040·4040·0482·4040·4092·0403··@@A@@@@@..@@@... | ||
000003b0:·2569 | 000003b0:·a325·696e·7436·344d·0800·0038·0040·4040··.%int64M...8.@@@ | ||
000003c0:·4 | 000003c0:·4140·4040·4040·0486·4040·4092·0403·a33a··A@@@@@..@@@....: | ||
000003d0:·6e64 | 000003d0:·556e·6465·6669·6e65·645f·7265·6375·7273··Undefined_recurs | ||
000003e0:·7665 | 000003e0:·6976·655f·6d6f·6475·6c65·5d08·0000·2000··ive_module]...·. | ||
000003f0:·0457 | 000003f0:·9004·5740·90a0·c092·a0c0·b390·0483·4090··..W@..........@. | ||
00000400:·0205 | 00000400:·4002·05f5·e100·404a·a0c0·b390·0490·4090··@.....@J......@. | ||
00000410:·0205 | 00000410:·4002·05f5·e100·4040·a004·0540·0205·f5e1··@.....@@...@.... | ||
00000420:·4056 | 00000420:·0040·5640·4041·049a·a0b0·a03d·6f63·616d··.@V@@A.....=ocam | ||
00000430:·2e | 00000430:·6c2e·7761·726e·5f6f·6e5f·6c69·7465·7261··l.warn_on_litera | ||
00000440:·5f70 | 00000440:·6c5f·7061·7474·6572·6e04·9e04·6104·9e40··l_pattern...a..@ | ||
00000450:·0417 | 00000450:·9204·17a3·2e41·7373·6572·745f·6661·696c··.....Assert_fail | ||
00000460:·7265 | 00000460:·7572·655c·0800·0020·0004·1840·90a0·c092··ure\...·...@.... | ||
00000470:·0417 | 00000470:·a004·17a0·0413·a004·1440·0205·f5e1·0040··.........@.....@ | ||
00000480:·4040 | 00000480:·5840·4041·04a9·a0b0·a004·0f04·ac04·6f04··X@@A..........o. | ||
00000490:·4092 | 00000490:·ac40·9204·0da3·3044·6976·6973·696f·6e5f··.@....0Division_ | ||
000004a0:·795f | 000004a0:·6279·5f7a·6572·6f59·0800·0020·0004·2640··by_zeroY...·..&@ | ||
000004b0:· | 000004b0:·9040·4041·04b1·a0b0·a004·1704·b404·7704··.@@A..........w. | ||
000004c0:·4092 | 000004c0:·b440·9204·07a3·2b45·6e64·5f6f·665f·6669··.@....+End_of_fi | ||
000004d0:·6 | 000004d0:·6c65·5808·0000·2000·042e·4090·4040·4104··leX...·...@.@@A. | ||
000004e0:·a0b0 | 000004e0:·b9a0·b0a0·041f·04bc·047f·04bc·4092·0407··............@... | ||
000004f0:·2953 | 000004f0:·a329·5379·735f·6572·726f·7257·0800·0020··.)Sys_errorW...· | ||
00000500:·0436 | 00000500:·0004·3640·90a0·0432·4040·4104·c2a0·b0a0··..6@...2@@A..... | ||
00000510:·2804 | 00000510:·0428·04c5·0488·04c5·4092·0408·a32e·5379··.(......@.....Sy | ||
00000520:·5f62 | 00000520:·735f·626c·6f63·6b65·645f·696f·5b08·0000··s_blocked_io[... | ||
00000530:·000 | 00000530:·2000·043f·4090·4040·4104·caa0·b0a0·0430···..?@.@@A......0 | ||
00000540:·cd04 | 00000540:·04cd·0490·04cd·4092·0407·a329·4e6f·745f··......@....)Not_ | ||
00000550:·6f75 | 00000550:·666f·756e·6456·0800·0020·0004·4740·9040··foundV...·..G@.@ | ||
00000560:·4104 | 00000560:·4041·04d2·a0b0·a004·3804·d504·9804·d540··@A......8......@ | ||
00000570:·0407 | 00000570:·9204·07a3·2746·6169·6c75·7265·5508·0000··....'FailureU... | ||
00000580:·000 | 00000580:·2000·044f·4090·a004·4b40·4041·04db·a0b0···..O@...K@@A.... | ||
00000590:·0441 | 00000590:·a004·4104·de04·a104·de40·9204·08a3·3049··..A......@....0I | ||
000005a0:·7661 | 000005a0:·6e76·616c·6964·5f61·7267·756d·656e·7454··nvalid_argumentT | ||
000005b0:·0000 | 000005b0:·0800·0020·0004·5840·90a0·0454·4040·4104··...·..X@...T@@A. | ||
000005c0:·a0b0 | 000005c0:·e4a0·b0a0·044a·04e7·04aa·04e7·4092·0408··.....J......@... | ||
000005d0:·2e53 | 000005d0:·a32e·5374·6163·6b5f·6f76·6572·666c·6f77··..Stack_overflow | ||
000005e0:· | 000005e0:·5a08·0000·2000·0461·4090·4040·4104·eca0··Z...·..a@.@@A... | ||
000005f0:·a004 | 000005f0:·b0a0·0452·04ef·04b2·04ef·4092·0407·a32d··...R......@....- | ||
00000600:·7574 | 00000600:·4f75·745f·6f66·5f6d·656d·6f72·7953·0800··Out_of_memoryS.. | ||
00000610:·20 | 00000610:·0020·0004·6940·9040·4041·04f4·a0b0·a004··.·..i@.@@A...... | ||
00000620:·04f7 | 00000620:·5a04·f704·ba04·f740·9204·07a3·2d4d·6174··Z......@....-Mat | ||
00000630:·685f | 00000630:·6368·5f66·6169·6c75·7265·5208·0000·2000··ch_failureR...·. | ||
00000640:·7140 | 00000640:·0471·4090·a0c0·92a0·0470·a004·6ca0·046d··.q@......p..l..m | ||
00000650:·0205 | 00000650:·4002·05f5·e100·4063·4040·4105·0102·a0b0··@.....@c@@A..... | ||
00000660:·0468 | 00000660:·a004·6805·0105·04c8·0501·0540·9204·0da3··..h........@.... | ||
00000670:·6279 | 00000670:·2562·7974·6573·4308·0000·3800·4040·4041··%bytesC...8.@@@A | ||
00000680:·4040·4040·0501 | 00000680:·4040·4040·4005·0109·4040·4092·0403·9092··@@@@@...@@@..... | ||
00000690:·5374 | 00000690:·2653·7464·6c69·6292·2349·6e74·9226·4f70··&Stdlib.#Int.&Op | ||
000006a0:·b005·013 | 000006a0:·7469·6f6e·4041·b005·0139·0501·3c40·a0b0··tion@A...9..<@.. | ||
000006b0:·6d70·6172·6500·52a0·0402 | 000006b0:·90f0·a027·636f·6d70·6172·6500·52a0·0402··...'compare.R... | ||
000006c0:· | 000006c0:·b0c0·0501·554e·0102·cb01·02d1·c005·0156··....UN.........V | ||
000006d0:· | 000006d0:·4e01·02cb·0102·d840·d0b1·40d0·b390·0501··N......@..@..... | ||
000006e0:· | 000006e0:·50a0·9021·74b0·c005·0160·4e01·02cb·0102··P..!t....`N..... | ||
000006f0:· | 000006f0:·dbc0·0501·614e·0102·cb01·02dc·4040·c0b3··....aN......@@.. | ||
00000700:·0 | 00000700:·0409·4090·4002·05f5·e100·4001·0315·0800··..@.@.....@..... | ||
00000710:·0 | 00000710:·0030·0005·014f·0501·4f05·014f·0501·4f05··.0...O..O..O..O. | ||
00000720:·014 | 00000720:·014f·0501·4f05·014f·0501·4f40·b105·014f··.O..O..O..O@...O | ||
00000730:· | 00000730:·0501·5b05·0155·4041·b004·0804·0740·40d0··..[..U@A.....@@. | ||
00000740:· | 00000740:·b140·d0b3·9005·0161·a090·2174·b0c0·0501··.@.....a..!t.... | ||
00000750:· | 00000750:·714e·0102·cb01·02e0·c005·0172·4e01·02cb··qN.........rN... | ||
00000760:· | 00000760:·0102·e140·40c0·b304·0940·9040·0205·f5e1··...@@....@.@.... | ||
00000770:· | 00000770:·0040·0103·1604·11b0·0406·0405·4040·d0b3··.@..........@@.. | ||
00000780:· | 00000780:·9005·0137·a090·2369·6e74·b0c0·0501·7e4e··...7..#int....~N | ||
00000790:· | 00000790:·0102·cb01·02e5·c005·017f·4e01·02cb·0102··..........N..... | ||
000007a0:· | 000007a0:·e840·40c0·b304·0940·9040·0205·f5e1·0040··.@@....@.@.....@ | ||
000007b0:·0 | 000007b0:·0103·1704·1eb0·0406·0405·4040·c0c1·4004··..........@@..@. | ||
000007c0:· | 000007c0:·1304·0640·0205·f5e1·0040·0103·1804·21b0··...@.....@....!. | ||
000007d0:· | 000007d0:·0416·0408·4040·c0c1·4004·2704·0540·0205··....@@..@.'..@.. | ||
Max diff block lines reached; 140888/1326537 bytes (10.62%) of diff not shown. |
Offset 1, 4788 lines modified | Offset 1, 4788 lines modified | ||
00000000:·4361·6d6c·3139·3939·5430·3330·8495·a6be··Caml1999T030.... | 00000000:·4361·6d6c·3139·3939·5430·3330·8495·a6be··Caml1999T030.... | ||
00000010:·0001·2b1 | 00000010:·0001·2b1a·0000·3704·0000·df72·0000·dbc4··..+...7....r.... | ||
00000020:·0800·0034·0024·434f·626a·91b0·a0b0·9db0··...4.$CObj...... | 00000020:·0800·0034·0024·434f·626a·91b0·a0b0·9db0··...4.$CObj...... | ||
00000030:·a02a·6f63·616d·6c2e·7465·7874·b0c0·265f··.*ocaml.text..&_ | 00000030:·a02a·6f63·616d·6c2e·7465·7874·b0c0·265f··.*ocaml.text..&_ | ||
00000040:·6e6f·6e65·5f40·4000·ff04·0241·90a0·a0a0··none_@@....A.... | 00000040:·6e6f·6e65·5f40·4000·ff04·0241·90a0·a0a0··none_@@....A.... | ||
00000050:·c091·b233·207b·3620·4c6f·6769·6361·6c20··...3·{6·Logical· | 00000050:·c091·b233·207b·3620·4c6f·6769·6361·6c20··...3·{6·Logical· | ||
00000060:·7369·7a65·737d·20b0·c02c·636c·6962·2f63··sizes}·..,clib/c | 00000060:·7369·7a65·737d·20b0·c02c·636c·6962·2f63··sizes}·..,clib/c | ||
00000070:·4f62·6a2e·6d6c·4d01·02d7·0102·d7c0·0402··Obj.mlM......... | 00000070:·4f62·6a2e·6d6c·4d01·02d7·0102·d7c0·0402··Obj.mlM......... | ||
00000080:·4d01·02d7·0102·ef40·4004·0440·4040·0404··M......@@..@@@.. | 00000080:·4d01·02d7·0102·ef40·4004·0440·4040·0404··M......@@..@@@.. | Diff chunk too large, falling back to line-by-line diff (4555 lines added, 4555 lines removed) | |
00000090:·4004·0404·0408·0000·3000·a040·4004·0104··@.......0..@@... | 00000090:·4004·0404·0408·0000·3000·a040·4004·0104··@.......0..@@... | ||
000000a0:·0104·0104·0104·0104·0104·0140·aba | 000000a0:·0104·0104·0104·0104·0104·0140·abab·a7b1··...........@.... | ||
000000b0:·b2b2·b2b2·b2b2·b2b2·b2b2·b2b | 000000b0:·b2b2·b2b2·b2b2·b2b2·b2b2·b2b2·b1b1·b1b1··................ | ||
000000c0:·b1b1·b1b1·b1b1·b1b1·b1b1·b140 | 000000c0:·b1b1·b1b1·b1b1·b1b1·b1b1·b1b1·40a3·2a66··............@.*f | ||
000000d0:·6f61 | 000000d0:·6c6f·6174·6172·7261·7951·0800·0038·0040··loatarrayQ...8.@ | ||
000000e0:·404 | 000000e0:·4040·4140·4040·4040·0434·4040·4092·0403··@@A@@@@@.4@@@... | ||
000000f0:·3565 | 000000f0:·a335·6578·7465·6e73·696f·6e5f·636f·6e73··.5extension_cons | ||
00000100:·7275 | 00000100:·7472·7563·746f·7250·0800·0038·0040·4040··tructorP...8.@@@ | ||
00000110:·4 | 00000110:·4140·4040·4040·0438·4040·4092·0403·a323··A@@@@@.8@@@....# | ||
00000120:·6e74 | 00000120:·696e·7441·0800·0038·0040·4040·4140·4040··intA...8.@@@A@@@ | ||
00000130:·4004 | 00000130:·4040·043c·4041·4092·0403·a324·6368·6172··@@.<@A@....$char | ||
00000140:· | 00000140:·4208·0000·3800·4040·4041·4040·4040·4004··B...8.@@@A@@@@@. | ||
00000150:·404 | 00000150:·4040·4140·9204·03a3·2673·7472·696e·674f··@@A@....&stringO | ||
00000160:·0 | 00000160:·0800·0038·0040·4040·4140·4040·4040·0444··...8.@@@A@@@@@.D | ||
00000170:·4040·9204 | 00000170:·4040·4092·0403·a325·666c·6f61·7444·0800··@@@....%floatD.. | ||
00000180:· | 00000180:·0038·0040·4040·4140·4040·4040·0448·4040··.8.@@@A@@@@@.H@@ | ||
00000190:·9204 | 00000190:·4092·0403·a324·626f·6f6c·4508·0000·3800··@....$boolE...8. | ||
000001a0:·40a1 | 000001a0:·4040·a1a0·e0a3·2566·616c·7365·5e90·4040··@@....%false^.@@ | ||
000001b0:·5 | 000001b0:·0452·4092·0403·a0e0·a324·7472·7565·5f90··.R@......$true_. | ||
000001c0:·4004 | 000001c0:·4040·0458·4092·0403·4040·4140·4040·4040··@@.X@...@@A@@@@@ | ||
000001d0:·5 | 000001d0:·0459·4041·4092·0410·a324·756e·6974·4608··.Y@A@....$unitF. | ||
000001e0:·0038 | 000001e0:·0000·3800·4040·a1a0·e0a3·2228·2960·9040··..8.@@...."()`.@ | ||
000001f0:·04 | 000001f0:·4004·6340·9204·0340·4041·4040·4040·4004··@.c@...@@A@@@@@. | ||
00000200:·4041 | 00000200:·6440·4140·9204·0aa3·2365·786e·4708·0000··d@A@....#exnG... | ||
00000210:· | 00000210:·3800·4040·4141·4040·4040·4004·6840·4040··8.@@AA@@@@@.h@@@ | ||
00000220:·0403 | 00000220:·9204·03a3·2561·7272·6179·4808·0000·3800··....%arrayH...8. | ||
00000230:·c090 | 00000230:·a0c0·9040·0205·f5e1·0040·4f40·4140·4140··...@.....@O@A@A@ | ||
00000240:·007f· | 00000240:·a000·7f40·a040·4040·4004·7140·4040·9204··...@.@@@@.q@@@.. | ||
00000250:·a324 | 00000250:·08a3·246c·6973·7449·0800·0038·00a0·c004··..$listI...8.... | ||
00000260:·0205 | 00000260:·0902·05f5·e100·4050·4041·a1a0·e0a3·225b··......@P@A...."[ | ||
00000270:·6190 | 00000270:·5d61·9040·4004·7d40·9204·03a0·e0a3·223a··]a.@@.}@......": | ||
00000280:·6290 | 00000280:·3a62·90a0·040e·a0c0·b390·0416·a004·1340··:b.............@ | ||
00000290:·4002 | 00000290:·9040·0205·f5e1·0040·5140·4004·8a40·9204··.@.....@Q@@..@.. | ||
000002a0:· | 000002a0:·0a40·4041·40a0·5940·a040·4040·4004·8d40··.@@A@.Y@.@@@@..@ | ||
000002b0:·4092 | 000002b0:·4040·9204·1ba3·266f·7074·696f·6e4a·0800··@@....&optionJ.. | ||
000002c0:·38 | 000002c0:·0038·00a0·c004·2502·05f5·e100·4053·4041··.8....%.....@S@A | ||
000002d0:·a0e0 | 000002d0:·a1a0·e0a3·244e·6f6e·6563·9040·4004·9940··....$Nonec.@@..@ | ||
000002e0:·0403 | 000002e0:·9204·03a0·e0a3·2453·6f6d·6564·90a0·040e··......$Somed.... | ||
000002f0:·4004 | 000002f0:·4040·04a0·4092·0404·4040·4140·a059·40a0··@@..@...@@A@.Y@. | ||
00000300:·4040·40 | 00000300:·4040·4040·04a3·4040·4092·0415·a326·6c61··@@@@..@@@....&la | ||
00000310:·795f | 00000310:·7a79·5f74·4e08·0000·3800·a0c0·043b·0205··zy_tN...8....;.. | ||
00000320:·e1 | 00000320:·f5e1·0040·5540·4140·4140·a059·40a0·4040··...@U@A@A@.Y@.@@ | ||
00000330:·40 | 00000330:·4040·04ab·4040·4092·0407·a329·6e61·7469··@@..@@@....)nati | ||
00000340:·6569 | 00000340:·7665·696e·744b·0800·0038·0040·4040·4140··veintK...8.@@@A@ | ||
00000350:·4040·40 | 00000350:·4040·4040·04af·4040·4092·0403·a325·696e··@@@@..@@@....%in | ||
00000360:·3332 | 00000360:·7433·324c·0800·0038·0040·4040·4140·4040··t32L...8.@@@A@@@ | ||
00000370:·40 | 00000370:·4040·04b3·4040·4092·0403·a325·696e·7436··@@..@@@....%int6 | ||
00000380:·4d08 | 00000380:·344d·0800·0038·0040·4040·4140·4040·4040··4M...8.@@@A@@@@@ | ||
00000390:· | 00000390:·04b7·4040·4092·0403·a33a·556e·6465·6669··..@@@....:Undefi | ||
000003a0:·6564 | 000003a0:·6e65·645f·7265·6375·7273·6976·655f·6d6f··ned_recursive_mo | ||
000003b0:·756c | 000003b0:·6475·6c65·5d08·0000·2000·9004·5740·90a0··dule]...·...W@.. | ||
000003c0:·92a0 | 000003c0:·c092·a0c0·b390·0483·4090·4002·05f5·e100··........@.@..... | ||
000003d0:·4aa0 | 000003d0:·404a·a0c0·b390·0490·4090·4002·05f5·e100··@J......@.@..... | ||
000003e0:·40 | 000003e0:·4040·a004·0540·0205·f5e1·0040·5640·4041··@@...@.....@V@@A | ||
000003f0:·c | 000003f0:·04cb·a0b0·a03d·6f63·616d·6c2e·7761·726e··.....=ocaml.warn | ||
00000400:·6f6e | 00000400:·5f6f·6e5f·6c69·7465·7261·6c5f·7061·7474··_on_literal_patt | ||
00000410:·726e | 00000410:·6572·6e04·cf04·6104·cf40·9204·17a3·2e41··ern...a..@.....A | ||
00000420:·7365 | 00000420:·7373·6572·745f·6661·696c·7572·655c·0800··ssert_failure\.. | ||
00000430:·20 | 00000430:·0020·0004·1840·90a0·c092·a004·17a0·0413··.·...@.......... | ||
00000440:·0414 | 00000440:·a004·1440·0205·f5e1·0040·5840·4041·04da··...@.....@X@@A.. | ||
00000450:·b0a0 | 00000450:·a0b0·a004·0f04·dd04·6f04·dd40·9204·0da3··........o..@.... | ||
00000460:·4469 | 00000460:·3044·6976·6973·696f·6e5f·6279·5f7a·6572··0Division_by_zer | ||
00000470:·5908 | 00000470:·6f59·0800·0020·0004·2640·9040·4041·04e2··oY...·..&@.@@A.. | ||
00000480:·b0a0 | 00000480:·a0b0·a004·1704·e504·7704·e540·9204·07a3··........w..@.... | ||
00000490:·456e | 00000490:·2b45·6e64·5f6f·665f·6669·6c65·5808·0000··+End_of_fileX... | ||
000004a0:·000 | 000004a0:·2000·042e·4090·4040·4104·eaa0·b0a0·041f···...@.@@A....... | ||
000004b0:·e | 000004b0:·04ed·047f·04ed·4092·0407·a329·5379·735f··......@....)Sys_ | ||
000004c0:·7272 | 000004c0:·6572·726f·7257·0800·0020·0004·3640·90a0··errorW...·..6@.. | ||
000004d0:·3240 | 000004d0:·0432·4040·4104·f3a0·b0a0·0428·04f6·0488··.2@@A......(.... | ||
000004e0:·f | 000004e0:·04f6·4092·0408·a32e·5379·735f·626c·6f63··..@.....Sys_bloc | ||
000004f0:·6564 | 000004f0:·6b65·645f·696f·5b08·0000·2000·043f·4090··ked_io[...·..?@. | ||
00000500:·404 | 00000500:·4040·4104·fba0·b0a0·0430·04fe·0490·04fe··@@A......0...... | ||
00000510:·9204 | 00000510:·4092·0407·a329·4e6f·745f·666f·756e·6456··@....)Not_foundV | ||
00000520:·0 | 00000520:·0800·0020·0004·4740·9040·4041·0501·03a0··...·..G@.@@A.... | ||
00000530:·a004 | 00000530:·b0a0·0438·0501·0604·9805·0106·4092·0407··...8........@... | ||
00000540:·2746 | 00000540:·a327·4661·696c·7572·6555·0800·0020·0004··.'FailureU...·.. | ||
00000550:·4090 | 00000550:·4f40·90a0·044b·4040·4105·010c·a0b0·a004··O@...K@@A....... | ||
00000560:·0501 | 00000560:·4105·010f·04a1·0501·0f40·9204·08a3·3049··A........@....0I | ||
00000570:·7661 | 00000570:·6e76·616c·6964·5f61·7267·756d·656e·7454··nvalid_argumentT | ||
00000580:·0000 | 00000580:·0800·0020·0004·5840·90a0·0454·4040·4105··...·..X@...T@@A. | ||
00000590:·1 | 00000590:·0115·a0b0·a004·4a05·0118·04aa·0501·1840··......J........@ | ||
000005a0:·0408 | 000005a0:·9204·08a3·2e53·7461·636b·5f6f·7665·7266··.....Stack_overf | ||
000005b0:·6f | 000005b0:·6c6f·775a·0800·0020·0004·6140·9040·4041··lowZ...·..a@.@@A | ||
000005c0:·01 | 000005c0:·0501·1da0·b0a0·0452·0501·2004·b205·0120··.......R..·....· | ||
000005d0:·9204 | 000005d0:·4092·0407·a32d·4f75·745f·6f66·5f6d·656d··@....-Out_of_mem | ||
000005e0:·7279 | 000005e0:·6f72·7953·0800·0020·0004·6940·9040·4041··oryS...·..i@.@@A | ||
000005f0:·01 | 000005f0:·0501·25a0·b0a0·045a·0501·2804·ba05·0128··..%....Z..(....( | ||
00000600:·9204 | 00000600:·4092·0407·a32d·4d61·7463·685f·6661·696c··@....-Match_fail | ||
00000610:·7265 | 00000610:·7572·6552·0800·0020·0004·7140·90a0·c092··ureR...·..q@.... | ||
00000620:·0470 | 00000620:·a004·70a0·046c·a004·6d40·0205·f5e1·0040··..p..l..m@.....@ | ||
00000630:·4040 | 00000630:·6340·4041·0501·33a0·b0a0·0468·0501·3604··c@@A..3....h..6. | ||
00000640:·0501 | 00000640:·c805·0136·4092·040d·a325·6279·7465·7343··...6@....%bytesC | ||
00000650:·0000 | 00000650:·0800·0038·0040·4040·4140·4040·4040·0501··...8.@@@A@@@@@.. | ||
00000660:·4040 | 00000660:·3a40·4040·9204·0390·9226·5374·646c·6962··:@@@.....&Stdlib | ||
00000670:·264f·7074·696f·6e40·40a | 00000670:·9223·496e·7492·264f·7074·696f·6e40·40a0··.#Int.&Option@@. | ||
00000680:· | 00000680:·b0a1·40a0·c0e0·a0a0·2163·0051·a004·02b0··..@.....!c.Q.... | ||
00000690:· | 00000690:·c005·0141·4f01·02f1·0102·f5c0·0501·424f··...AO.........BO | ||
000006a0:· | 000006a0:·0102·f101·02f6·40b0·0403·0402·4040·c096··......@.....@@.. | ||
000006b0:·5374·646c·6962·2372·6566 | 000006b0:·c0b3·a190·9226·5374·646c·6962·2372·6566··.....&Stdlib#ref | ||
000006c0:· | 000006c0:·a0c0·96c0·b304·9640·9040·0205·f5e1·0040··.......@.@.....@ | ||
000006d0:·0 | 000006d0:·0103·1b41·4001·0319·4090·4002·05f5·e100··...A@...@.@..... | ||
000006e0:· | 000006e0:·4001·0318·4140·0103·1505·0151·40e0·a4e0··@...A@.....Q@... | ||
000006f0:·6566·a090·0403·b0c0·0501 | 000006f0:·b0a1·042a·2372·6566·a090·0403·b0c0·0501··...*#ref........ | ||
00000700:· | 00000700:·5d4f·0102·f101·02f9·c005·015e·4f01·02f1··]O.........^O... | ||
00000710:· | 00000710:·0102·fc40·d0c0·c140·c090·9021·6102·05f5··...@...@...!a... | ||
00000720:· | 00000720:·e100·4001·02b8·c0b3·0420·a004·0740·9040··..@......·...@.@ | ||
00000730:·0 | 00000730:·0205·f5e1·0040·0102·b740·0205·f5e1·0040··.....@...@.....@ | ||
00000740:·256d·616b·656d·7574·6162 | 00000740:·0102·b690·e02c·256d·616b·656d·7574·6162··.....,%makemutab | ||
00000750:·4040·40b0·c02a·7374·646c· | 00000750:·6c65·4141·20a0·4040·40b0·c02a·7374·646c··leAA·.@@@..*stdl | ||
00000760:· | 00000760:·6962·2e6d·6c69·0104·bc02·0000·b467·0200··ib.mli.......g.. | ||
00000770:·0 | 00000770:·00b4·67c0·0402·0104·bc02·0000·b467·0200··..g..........g.. | ||
00000780:·0 | 00000780:·00b4·9340·40a1·0429·0100·d2b0·0418·0417··...@@..)........ | ||
00000790:· | 00000790:·4040·c0c1·4004·2904·3140·4140·0103·1705··@@..@.).1@A@.... | ||
000007a0:· | 000007a0:·0174·40a0·a040·90e0·9190·40b0·c005·017e··.t@..@....@....~ | ||
000007b0:· | 000007b0:·4f01·02f1·0102·fdc0·0501·7f4f·0102·f101··O..........O.... | ||
000007c0:·0 | 000007c0:·02fe·4040·0430·0501·7d40·40b0·0424·0402··..@@.0..}@@..$.. | ||
000007d0:· | 000007d0:·4040·043b·0501·7e40·40b0·c005·0182·4f01··@@.;..~@@.....O. | ||
Max diff block lines reached; 30066/659506 bytes (4.56%) of diff not shown. |
Offset 348, 1394 lines modified | Offset 348, 1395 lines modified | ||
000015b0:·a038·4361·6d6c·696e·7465·726e·616c·466f··.8CamlinternalFo | 000015b0:·a038·4361·6d6c·696e·7465·726e·616c·466f··.8CamlinternalFo | ||
000015c0:·726d·6174·4261·7369·6373·9030·c4b5·83a7··rmatBasics.0.... | 000015c0:·726d·6174·4261·7369·6373·9030·c4b5·83a7··rmatBasics.0.... | ||
000015d0:·27ec·28f5·bc9b·a36a·dc64·cfc7·a0a0·2443··'.(....j.d....$C | 000015d0:·27ec·28f5·bc9b·a36a·dc64·cfc7·a0a0·2443··'.(....j.d....$C | ||
000015e0:·5369·6790·303f·15ce·d987·9a20·03e4·319b··Sig.0?.....·..1. | 000015e0:·5369·6790·303f·15ce·d987·9a20·03e4·319b··Sig.0?.....·..1. | ||
000015f0:·37b8·b6e4·6340·8495·a6be·0000·0008·0000··7...c@.......... | 000015f0:·37b8·b6e4·6340·8495·a6be·0000·0008·0000··7...c@.......... | ||
00001600:·0004·0000·000b·0000·000b·a040·a041·a090··...........@.A.. | 00001600:·0004·0000·000b·0000·000b·a040·a041·a090··...........@.A.. | ||
00001610:·4040·4361·6d6c·3139·3939·5430·3330·8495··@@Caml1999T030.. | 00001610:·4040·4361·6d6c·3139·3939·5430·3330·8495··@@Caml1999T030.. | ||
00001620:·a6be·0000·569 | 00001620:·a6be·0000·569f·0000·0df8·0000·3bbc·0000··....V.......;... | ||
00001630:·39 | 00001630:·39c4·0800·0034·0023·4479·6e92·b0a0·b09e··9....4.#Dyn..... | ||
00001640:·b0a0·2a6f·6361·6d6c·2e74·6578·74b0·c026··..*ocaml.text..& | 00001640:·b0a0·2a6f·6361·6d6c·2e74·6578·74b0·c026··..*ocaml.text..& | ||
00001650:·5f6e·6f6e·655f·4040·00ff·0402·4190·a0a0··_none_@@....A... | 00001650:·5f6e·6f6e·655f·4040·00ff·0402·4190·a0a0··_none_@@....A... | ||
00001660:·a0c0·91b2·3a20·4479·6e61·6d69·6361·6c6c··....:·Dynamicall | 00001660:·a0c0·91b2·3a20·4479·6e61·6d69·6361·6c6c··....:·Dynamicall | ||
00001670:·7920·7479·7065·6420·7661·6c75·6573·20b0··y·typed·values·. | 00001670:·7920·7479·7065·6420·7661·6c75·6573·20b0··y·typed·values·. | ||
00001680:·c02c·636c·6962·2f64·796e·2e6d·6c69·4b01··.,clib/dyn.mliK. | 00001680:·c02c·636c·6962·2f64·796e·2e6d·6c69·4b01··.,clib/dyn.mliK. | ||
00001690:·02a4·0102·a4c0·0402·4b01·02a4·0102·c340··........K......@ | 00001690:·02a4·0102·a4c0·0402·4b01·02a4·0102·c340··........K......@ | ||
000016a0:·4004·0440·4040·0404·4004·0408·0000·3000··@..@@@..@.....0. | 000016a0:·4004·0440·4040·0404·4004·0408·0000·3000··@..@@@..@.....0. | Diff chunk too large, falling back to line-by-line diff (1212 lines added, 1212 lines removed) | |
000016b0:·a040·4004·0104·0104·0104·0104·0104·0104··.@@............. | 000016b0:·a040·4004·0104·0104·0104·0104·0104·0104··.@@............. | ||
000016c0:·0140·aba | 000016c0:·0140·abab·a7b1·b2b2·b2b2·b2b2·b2b2·b2b2··.@.............. | ||
000016d0:·b2b | 000016d0:·b2b2·b1b1·b1b1·b1b1·b1b1·b1b1·b1b1·b1b1··................ | ||
000016e0:·b140 | 000016e0:·b1b1·40a3·2a66·6c6f·6174·6172·7261·7951··..@.*floatarrayQ | ||
000016f0:·0 | 000016f0:·0800·0038·0040·4040·4140·4040·4040·0434··...8.@@@A@@@@@.4 | ||
00001700:·4040·9204 | 00001700:·4040·4092·0403·a335·6578·7465·6e73·696f··@@@....5extensio | ||
00001710:·5f63 | 00001710:·6e5f·636f·6e73·7472·7563·746f·7250·0800··n_constructorP.. | ||
00001720:· | 00001720:·0038·0040·4040·4140·4040·4040·0438·4040··.8.@@@A@@@@@.8@@ | ||
00001730:·9204 | 00001730:·4092·0403·a323·696e·7441·0800·0038·0040··@....#intA...8.@ | ||
00001740:·404 | 00001740:·4040·4140·4040·4040·043c·4041·4092·0403··@@A@@@@@.<@A@... | ||
00001750:·2463 | 00001750:·a324·6368·6172·4208·0000·3800·4040·4041··.$charB...8.@@@A | ||
00001760:·4040·4040·04 | 00001760:·4040·4040·4004·4040·4140·9204·03a3·2673··@@@@@.@@A@....&s | ||
00001770:·7269 | 00001770:·7472·696e·674f·0800·0038·0040·4040·4140··tringO...8.@@@A@ | ||
00001780:·4040·40 | 00001780:·4040·4040·0444·4040·4092·0403·a325·666c··@@@@.D@@@....%fl | ||
00001790:·6174 | 00001790:·6f61·7444·0800·0038·0040·4040·4140·4040··oatD...8.@@@A@@@ | ||
000017a0:·40 | 000017a0:·4040·0448·4040·4092·0403·a324·626f·6f6c··@@.H@@@....$bool | ||
000017b0:·0800 | 000017b0:·4508·0000·3800·4040·a1a0·e0a3·2566·616c··E...8.@@....%fal | ||
000017c0:·655e | 000017c0:·7365·5e90·4040·0452·4092·0403·a0e0·a324··se^.@@.R@......$ | ||
000017d0:·7275 | 000017d0:·7472·7565·5f90·4040·0458·4092·0403·4040··true_.@@.X@...@@ | ||
000017e0:·4 | 000017e0:·4140·4040·4040·0459·4041·4092·0410·a324··A@@@@@.Y@A@....$ | ||
000017f0:·6e69 | 000017f0:·756e·6974·4608·0000·3800·4040·a1a0·e0a3··unitF...8.@@.... | ||
00001800:·2829 | 00001800:·2228·2960·9040·4004·6340·9204·0340·4041··"()`.@@.c@...@@A | ||
00001810:·4040·4040·04 | 00001810:·4040·4040·4004·6440·4140·9204·0aa3·2365··@@@@@.d@A@....#e | ||
00001820:·6e47 | 00001820:·786e·4708·0000·3800·4040·4141·4040·4040··xnG...8.@@AA@@@@ | ||
00001830:·046 | 00001830:·4004·6840·4040·9204·03a3·2561·7272·6179··@.h@@@....%array | ||
00001840:·0800 | 00001840:·4808·0000·3800·a0c0·9040·0205·f5e1·0040··H...8....@.....@ | ||
00001850:·4 | 00001850:·4f40·4140·4140·a000·7f40·a040·4040·4004··O@A@A@...@.@@@@. | ||
00001860:·4040 | 00001860:·7140·4040·9204·08a3·246c·6973·7449·0800··q@@@....$listI.. | ||
00001870:·38 | 00001870:·0038·00a0·c004·0902·05f5·e100·4050·4041··.8..........@P@A | ||
00001880:·a0e0 | 00001880:·a1a0·e0a3·225b·5d61·9040·4004·7d40·9204··...."[]a.@@.}@.. | ||
00001890:·a0e0 | 00001890:·03a0·e0a3·223a·3a62·90a0·040e·a0c0·b390··...."::b........ | ||
000018a0:·16a0 | 000018a0:·0416·a004·1340·9040·0205·f5e1·0040·5140··.....@.@.....@Q@ | ||
000018b0:·04 | 000018b0:·4004·8a40·9204·0a40·4041·40a0·5940·a040··@..@...@@A@.Y@.@ | ||
000018c0:·4040·048 | 000018c0:·4040·4004·8d40·4040·9204·1ba3·266f·7074··@@@..@@@....&opt | ||
000018d0:·6f6e | 000018d0:·696f·6e4a·0800·0038·00a0·c004·2502·05f5··ionJ...8....%... | ||
000018e0:·0040 | 000018e0:·e100·4053·4041·a1a0·e0a3·244e·6f6e·6563··..@S@A....$Nonec | ||
000018f0:· | 000018f0:·9040·4004·9940·9204·03a0·e0a3·2453·6f6d··.@@..@......$Som | ||
00001900:·6490 | 00001900:·6564·90a0·040e·4040·04a0·4092·0404·4040··ed....@@..@...@@ | ||
00001910:·40a0 | 00001910:·4140·a059·40a0·4040·4040·04a3·4040·4092··A@.Y@.@@@@..@@@. | ||
00001920:·15a3 | 00001920:·0415·a326·6c61·7a79·5f74·4e08·0000·3800··...&lazy_tN...8. | ||
00001930:·c004 | 00001930:·a0c0·043b·0205·f5e1·0040·5540·4140·4140··...;.....@U@A@A@ | ||
00001940:·5940· | 00001940:·a059·40a0·4040·4040·04ab·4040·4092·0407··.Y@.@@@@..@@@... | ||
00001950:·296e | 00001950:·a329·6e61·7469·7665·696e·744b·0800·0038··.)nativeintK...8 | ||
00001960:· | 00001960:·0040·4040·4140·4040·4040·04af·4040·4092··.@@@A@@@@@..@@@. | ||
00001970:·03a3 | 00001970:·0403·a325·696e·7433·324c·0800·0038·0040··...%int32L...8.@ | ||
00001980:·404 | 00001980:·4040·4140·4040·4040·04b3·4040·4092·0403··@@A@@@@@..@@@... | ||
00001990:·2569 | 00001990:·a325·696e·7436·344d·0800·0038·0040·4040··.%int64M...8.@@@ | ||
000019a0:·4 | 000019a0:·4140·4040·4040·04b7·4040·4092·0403·a33a··A@@@@@..@@@....: | ||
000019b0:·6e64 | 000019b0:·556e·6465·6669·6e65·645f·7265·6375·7273··Undefined_recurs | ||
000019c0:·7665 | 000019c0:·6976·655f·6d6f·6475·6c65·5d08·0000·2000··ive_module]...·. | ||
000019d0:·0457 | 000019d0:·9004·5740·90a0·c092·a0c0·b390·0483·4090··..W@..........@. | ||
000019e0:·0205 | 000019e0:·4002·05f5·e100·404a·a0c0·b390·0490·4090··@.....@J......@. | ||
000019f0:·0205 | 000019f0:·4002·05f5·e100·4040·a004·0540·0205·f5e1··@.....@@...@.... | ||
00001a00:·4056 | 00001a00:·0040·5640·4041·04cb·a0b0·a03d·6f63·616d··.@V@@A.....=ocam | ||
00001a10:·2e | 00001a10:·6c2e·7761·726e·5f6f·6e5f·6c69·7465·7261··l.warn_on_litera | ||
00001a20:·5f70 | 00001a20:·6c5f·7061·7474·6572·6e04·cf04·6104·cf40··l_pattern...a..@ | ||
00001a30:·0417 | 00001a30:·9204·17a3·2e41·7373·6572·745f·6661·696c··.....Assert_fail | ||
00001a40:·7265 | 00001a40:·7572·655c·0800·0020·0004·1840·90a0·c092··ure\...·...@.... | ||
00001a50:·0417 | 00001a50:·a004·17a0·0413·a004·1440·0205·f5e1·0040··.........@.....@ | ||
00001a60:·4040 | 00001a60:·5840·4041·04da·a0b0·a004·0f04·dd04·6f04··X@@A..........o. | ||
00001a70:·4092 | 00001a70:·dd40·9204·0da3·3044·6976·6973·696f·6e5f··.@....0Division_ | ||
00001a80:·795f | 00001a80:·6279·5f7a·6572·6f59·0800·0020·0004·2640··by_zeroY...·..&@ | ||
00001a90:· | 00001a90:·9040·4041·04e2·a0b0·a004·1704·e504·7704··.@@A..........w. | ||
00001aa0:·4092 | 00001aa0:·e540·9204·07a3·2b45·6e64·5f6f·665f·6669··.@....+End_of_fi | ||
00001ab0:·6 | 00001ab0:·6c65·5808·0000·2000·042e·4090·4040·4104··leX...·...@.@@A. | ||
00001ac0:·a0b0 | 00001ac0:·eaa0·b0a0·041f·04ed·047f·04ed·4092·0407··............@... | ||
00001ad0:·2953 | 00001ad0:·a329·5379·735f·6572·726f·7257·0800·0020··.)Sys_errorW...· | ||
00001ae0:·0436 | 00001ae0:·0004·3640·90a0·0432·4040·4104·f3a0·b0a0··..6@...2@@A..... | ||
00001af0:·2804 | 00001af0:·0428·04f6·0488·04f6·4092·0408·a32e·5379··.(......@.....Sy | ||
00001b00:·5f62 | 00001b00:·735f·626c·6f63·6b65·645f·696f·5b08·0000··s_blocked_io[... | ||
00001b10:·000 | 00001b10:·2000·043f·4090·4040·4104·fba0·b0a0·0430···..?@.@@A......0 | ||
00001b20:·f | 00001b20:·04fe·0490·04fe·4092·0407·a329·4e6f·745f··......@....)Not_ | ||
00001b30:·6f75 | 00001b30:·666f·756e·6456·0800·0020·0004·4740·9040··foundV...·..G@.@ | ||
00001b40:·4105 | 00001b40:·4041·0501·03a0·b0a0·0438·0501·0604·9805··@A.......8...... | ||
00001b50:·0 | 00001b50:·0106·4092·0407·a327·4661·696c·7572·6555··..@....'FailureU | ||
00001b60:·0000 | 00001b60:·0800·0020·0004·4f40·90a0·044b·4040·4105··...·..O@...K@@A. | ||
00001b70:·0 | 00001b70:·010c·a0b0·a004·4105·010f·04a1·0501·0f40··......A........@ | ||
00001b80:·0408 | 00001b80:·9204·08a3·3049·6e76·616c·6964·5f61·7267··....0Invalid_arg | ||
00001b90:·6d65 | 00001b90:·756d·656e·7454·0800·0020·0004·5840·90a0··umentT...·..X@.. | ||
00001ba0:·5440 | 00001ba0:·0454·4040·4105·0115·a0b0·a004·4a05·0118··.T@@A.......J... | ||
00001bb0:·aa05 | 00001bb0:·04aa·0501·1840·9204·08a3·2e53·7461·636b··.....@.....Stack | ||
00001bc0:·6f76 | 00001bc0:·5f6f·7665·7266·6c6f·775a·0800·0020·0004··_overflowZ...·.. | ||
00001bd0:·4090 | 00001bd0:·6140·9040·4041·0501·1da0·b0a0·0452·0501··a@.@@A.......R.. | ||
00001be0:·04b2 | 00001be0:·2004·b205·0120·4092·0407·a32d·4f75·745f···....·@....-Out_ | ||
00001bf0:·665f | 00001bf0:·6f66·5f6d·656d·6f72·7953·0800·0020·0004··of_memoryS...·.. | ||
00001c00:·4090 | 00001c00:·6940·9040·4041·0501·25a0·b0a0·045a·0501··i@.@@A..%....Z.. | ||
00001c10:·04ba | 00001c10:·2804·ba05·0128·4092·0407·a32d·4d61·7463··(....(@....-Matc | ||
00001c20:·5f | 00001c20:·685f·6661·696c·7572·6552·0800·0020·0004··h_failureR...·.. | ||
00001c30:·4090 | 00001c30:·7140·90a0·c092·a004·70a0·046c·a004·6d40··q@......p..l..m@ | ||
00001c40:·05f5 | 00001c40:·0205·f5e1·0040·6340·4041·0501·33a0·b0a0··.....@c@@A..3... | ||
00001c50:·6805 | 00001c50:·0468·0501·3604·c805·0136·4092·040d·a325··.h..6....6@....% | ||
00001c60:·7974 | 00001c60:·6279·7465·7343·0800·0038·0040·4040·4140··bytesC...8.@@@A@ | ||
00001c70:·4040·400 | 00001c70:·4040·4040·0501·3a40·4040·9204·0390·9226··@@@@..:@@@.....& | ||
00001c80:·7464 | 00001c80:·5374·646c·6962·9223·496e·7492·264f·7074··Stdlib.#Int.&Opt | ||
00001c90:·013 | 00001c90:·696f·6e40·4105·0137·a0b0·98d0·b126·5661··ion@A..7.....&Va | ||
00001ca0:· | 00001ca0:·6c75·6553·0052·42a0·0402·b0c0·0501·3e4d··lueS.RB.......>M | ||
00001cb0:· | 00001cb0:·0102·c501·02d1·c005·013f·4d01·02c5·0102··.........?M..... | ||
00001cc0:· | 00001cc0:·d740·90d0·91b0·a0b0·a141·a008·0000·2800··.@.......A....(. | ||
00001cd0:· | 00001cd0:·b121·7400·5141·a004·02b0·c005·014d·4f01··.!t.QA.......MO. | ||
00001ce0:·0 | 00001ce0:·02de·0102·e8c0·0501·4e4f·0102·de01·02e9··........NO...... | ||
00001cf0:· | 00001cf0:·40a0·a0d0·9021·61c0·9090·0404·0205·f5e1··@....!a......... | ||
00001d00:·00 | 00001d00:·0040·0103·1608·0000·3000·0501·5405·0154··.@......0...T..T | ||
00001d10:·0501·5 | 00001d10:·0501·5405·0154·0501·5405·0154·0501·5405··..T..T..T..T..T. | ||
00001d20:· | 00001d20:·0154·40b1·0501·5404·1008·0000·3800·a0c0··.T@...T.....8... | ||
00001d30:· | 00001d30:·9040·0205·f5e1·0040·0103·1540·4140·4140··.@.....@...@A@A@ | ||
00001d40:· | 00001d40:·a047·40a0·4240·4040·b0c0·0501·604f·0102··.G@.B@@@....`O.. | ||
00001d50:· | 00001d50:·de01·02e0·0413·4040·4040·a105·0177·4040··......@@@@...w@@ | ||
00001d60:·4 | 00001d60:·41b0·c005·0163·4f01·02de·0102·e5c0·0501··A....cO......... | ||
00001d70:·02e7·4040·a042·4140·08 | 00001d70:·644f·0102·de01·02e7·4040·a042·4140·0800··dO......@@.BA@.. | ||
00001d80:· | 00001d80:·0038·00a0·0414·4041·4041·40a0·4740·a042··.8....@A@A@.G@.B | ||
Max diff block lines reached; 22129/190791 bytes (11.60%) of diff not shown. |
Offset 52, 350 lines modified | Offset 52, 350 lines modified | ||
00000330:·7464·6c69·6290·302d·0826·66be·7fc2·ba91··tdlib.0-.&f..... | 00000330:·7464·6c69·6290·302d·0826·66be·7fc2·ba91··tdlib.0-.&f..... | ||
00000340:·6e72·3339·7491·dfa0·a038·4361·6d6c·696e··nr39t....8Camlin | 00000340:·6e72·3339·7491·dfa0·a038·4361·6d6c·696e··nr39t....8Camlin | ||
00000350:·7465·726e·616c·466f·726d·6174·4261·7369··ternalFormatBasi | 00000350:·7465·726e·616c·466f·726d·6174·4261·7369··ternalFormatBasi | ||
00000360:·6373·9030·c4b5·83a7·27ec·28f5·bc9b·a36a··cs.0....'.(....j | 00000360:·6373·9030·c4b5·83a7·27ec·28f5·bc9b·a36a··cs.0....'.(....j | ||
00000370:·dc64·cfc7·4084·95a6·be00·0000·0800·0000··.d..@........... | 00000370:·dc64·cfc7·4084·95a6·be00·0000·0800·0000··.d..@........... | ||
00000380:·0400·0000·0b00·0000·0ba0·40a0·41a0·9040··..........@.A..@ | 00000380:·0400·0000·0b00·0000·0ba0·40a0·41a0·9040··..........@.A..@ | ||
00000390:·4043·616d·6c31·3939·3954·3033·3084·95a6··@Caml1999T030... | 00000390:·4043·616d·6c31·3939·3954·3033·3084·95a6··@Caml1999T030... | ||
000003a0:·be00·0015·5 | 000003a0:·be00·0015·5f00·0003·7b00·000e·ec00·000e··...._...{....... | ||
000003b0:· | 000003b0:·3108·0000·3400·2b4f·7264·6572·6564·5479··1...4.+OrderedTy | ||
000003c0:·7065·92b0·a0b0·98d0·b121·5300·5342·a004··pe.......!S.SB.. | 000003c0:·7065·92b0·a0b0·98d0·b121·5300·5342·a004··pe.......!S.SB.. | ||
000003d0:·02b0·c034·636c·6962·2f6f·7264·6572·6564··...4clib/ordered | 000003d0:·02b0·c034·636c·6962·2f6f·7264·6572·6564··...4clib/ordered | ||
000003e0:·5479·7065·2e6d·6c69·4b01·02a4·0102·b0c0··Type.mliK....... | 000003e0:·5479·7065·2e6d·6c69·4b01·02a4·0102·b0c0··Type.mliK....... | ||
000003f0:·0402·4b01·02a4·0102·b140·90d0·91b0·a0b0··..K......@...... | 000003f0:·0402·4b01·02a4·0102·b140·90d0·91b0·a0b0··..K......@...... | ||
00000400:·a141·a008·0000·2800·b121·7400·5141·a004··.A....(..!t.QA.. | 00000400:·a141·a008·0000·2800·b121·7400·5141·a004··.A....(..!t.QA.. | ||
00000410:·02b0·c004·104d·0102·b801·02bf·c004·114d··.....M.........M | 00000410:·02b0·c004·104d·0102·b801·02bf·c004·114d··.....M.........M | ||
00000420:·0102·b801·02c0·4040·0800·0038·0040·4040··......@@...8.@@@ | 00000420:·0102·b801·02c0·4040·0800·0038·0040·4040··......@@...8.@@@ | ||
00000430:·4140·4040·4040·b0c0·0414·4d01·02b8·0102··A@@@@@....M..... | 00000430:·4140·4040·4040·b0c0·0414·4d01·02b8·0102··A@@@@@....M..... | ||
00000440:·ba04·0440·4040·40a1·0421·4040·4041·4004··...@@@@..!@@@A@. | 00000440:·ba04·0440·4040·40a1·0421·4040·4041·4004··...@@@@..!@@@A@. | ||
00000450:·0340·4008·0000·3000·a040·4004·0104·0104··.@@...0..@@..... | 00000450:·0340·4008·0000·3000·a040·4004·0104·0104··.@@...0..@@..... | ||
00000460:·0104·0104·0104·0104·0140·aba | 00000460:·0104·0104·0104·0104·0140·abab·a7b1·b2b2··.........@...... | ||
00000470:·b2b2·b2b2·b2b2·b2b2·b2b | 00000470:·b2b2·b2b2·b2b2·b2b2·b2b2·b1b1·b1b1·b1b1··................ | ||
00000480:·b1b1·b1b1·b1b1·b1b1·b140 | 00000480:·b1b1·b1b1·b1b1·b1b1·b1b1·40a3·2a66·6c6f··..........@.*flo | ||
00000490:·7461·7272·6179·5108·0000·3800·4040·4041··tarrayQ...8.@@@A | |||
000004 | 00000490:·6174·6172·7261·7951·0800·0038·0040·4040··atarrayQ...8.@@@ | ||
000004a0:·4140·4040·4040·b0c0·265f·6e6f·6e65·5f40··A@@@@@..&_none_@ | |||
000004b0:·00 | 000004b0:·4000·ff04·0241·4040·4092·0406·a335·6578··@....A@@@....5ex | ||
000004c0:·656e | 000004c0:·7465·6e73·696f·6e5f·636f·6e73·7472·7563··tension_construc | ||
000004d0:·6f72 | 000004d0:·746f·7250·0800·0038·0040·4040·4140·4040··torP...8.@@@A@@@ | ||
000004e0:·40 | 000004e0:·4040·0407·4040·4092·0403·a323·696e·7441··@@..@@@....#intA | ||
000004f0:·0 | 000004f0:·0800·0038·0040·4040·4140·4040·4040·040b··...8.@@@A@@@@@.. | ||
00000500:·4140 | 00000500:·4041·4092·0403·a324·6368·6172·4208·0000··@A@....$charB... | ||
00000510:·3800·4040·4041·4040·4040·4004·0f40·4140··8.@@@A@@@@@..@A@ | |||
00000520:·9204·03a3·2673·7472·696e·674f·0800·0038··....&stringO...8 | |||
000005 | 00000530:·0040·4040·4140·4040·4040·0413·4040·4092··.@@@A@@@@@..@@@. | ||
00000520:·0403·a326·7374·7269·6e67·4f08·0000·3800··...&stringO...8. | |||
00000530:·4040·4041·4040·4040·4004·1340·4040·9204··@@@A@@@@@..@@@.. | |||
00000540:·03a3 | 00000540:·0403·a325·666c·6f61·7444·0800·0038·0040··...%floatD...8.@ | ||
00000550:·404 | 00000550:·4040·4140·4040·4040·0417·4040·4092·0403··@@A@@@@@..@@@... | ||
00000560:·2462 | 00000560:·a324·626f·6f6c·4508·0000·3800·4040·a1a0··.$boolE...8.@@.. | ||
00000570:·a325 | 00000570:·e0a3·2566·616c·7365·5e90·4040·0421·4092··..%false^.@@.!@. | ||
00000580:·03a0 | 00000580:·0403·a0e0·a324·7472·7565·5f90·4040·0427··.....$true_.@@.' | ||
00000590:·4092·0403·4040·4140·4040·4040·0428·4041··@...@@A@@@@@.(@A | |||
000005a0:·4092·0410·a324·756e·6974·4608·0000·3800··@....$unitF...8. | |||
000005b0:·4040·a1a0·e0a3·2228·2960·9040·4004·3240··@@...."()`.@@.2@ | |||
000005 | 000005c0:·9204·0340·4041·4040·4040·4004·3340·4140··...@@A@@@@@.3@A@ | ||
000005a0:·9204·10a3·2475·6e69·7446·0800·0038·0040··....$unitF...8.@ | |||
000005b0:·40a1·a0e0·a322·2829·6090·4040·0432·4092··@...."()`.@@.2@. | |||
000005c0:·0403·4040·4140·4040·4040·0433·4041·4092··..@@A@@@@@.3@A@. | |||
000005d0:·040a | 000005d0:·9204·0aa3·2365·786e·4708·0000·3800·4040··....#exnG...8.@@ | ||
000005e0:·414 | 000005e0:·4141·4040·4040·4004·3740·4040·9204·03a3··AA@@@@@.7@@@.... | ||
000005f0:·6172·7261·7948·0800·0038·00a0·c090·4002··arrayH...8....@. | |||
00000600:·05f5·e100·404f·4041·4041·40a0·007f·40a0··....@O@A@A@...@. | |||
00000610:·4040·4040·0440·4040·4092·0408·a324·6c69··@@@@.@@@@....$li | |||
00000620:·7374·4908·0000·3800·a0c0·0409·0205·f5e1··stI...8......... | |||
00000630:·0040·5040·41a1·a0e0·a322·5b5d·6190·4040··.@P@A...."[]a.@@ | |||
00000640:·044c·4092·0403·a0e0·a322·3a3a·6290·a004··.L@......"::b... | |||
00000650:·0ea0·c0b3·9004·16a0·0413·4090·4002·05f5··..........@.@... | |||
00000 | 000005f0:·2561·7272·6179·4808·0000·3800·a0c0·9040··%arrayH...8....@ | ||
00000600:·0205·f5e1·0040·4f40·4140·4140·a000·7f40··.....@O@A@A@...@ | |||
00000610:·a040·4040·4004·4040·4040·9204·08a3·246c··.@@@@.@@@@....$l | |||
00000620:·6973·7449·0800·0038·00a0·c004·0902·05f5··istI...8........ | |||
00000630:·e100·4050·4041·a1a0·e0a3·225b·5d61·9040··..@P@A...."[]a.@ | |||
00000640:·4004·4c40·9204·03a0·e0a3·223a·3a62·90a0··@.L@......"::b.. | |||
00000650:·040e·a0c0·b390·0416·a004·1340·9040·0205··...........@.@.. | |||
00000660:·f5e1·0040·5140·4004·5940·9204·0a40·4041··...@Q@@.Y@...@@A | |||
00000670:· | 00000670:·40a0·5940·a040·4040·4004·5c40·4040·9204··@.Y@.@@@@.\@@@.. | ||
00000680:·a326·6f70·7469·6f6e·4a08·0000·3800·a0c0··.&optionJ...8... | |||
000006 | 00000680:·1ba3·266f·7074·696f·6e4a·0800·0038·00a0··..&optionJ...8.. | ||
00000690:·c004·2502·05f5·e100·4053·4041·a1a0·e0a3··..%.....@S@A.... | |||
000006a0:·4e6f | 000006a0:·244e·6f6e·6563·9040·4004·6840·9204·03a0··$Nonec.@@.h@.... | ||
000006b0:·a324 | 000006b0:·e0a3·2453·6f6d·6564·90a0·040e·4040·046f··..$Somed....@@.o | ||
000006c0:·9204 | 000006c0:·4092·0404·4040·4140·a059·40a0·4040·4040··@...@@A@.Y@.@@@@ | ||
000006d0:·7240 | 000006d0:·0472·4040·4092·0415·a326·6c61·7a79·5f74··.r@@@....&lazy_t | ||
000006e0:·0800 | 000006e0:·4e08·0000·3800·a0c0·043b·0205·f5e1·0040··N...8....;.....@ | ||
000006f0:·4041 | 000006f0:·5540·4140·4140·a059·40a0·4040·4040·047a··U@A@A@.Y@.@@@@.z | ||
00000700:·4040·9204 | 00000700:·4040·4092·0407·a329·6e61·7469·7665·696e··@@@....)nativein | ||
00000710:·4b08 | 00000710:·744b·0800·0038·0040·4040·4140·4040·4040··tK...8.@@@A@@@@@ | ||
00000720:·7e40 | 00000720:·047e·4040·4092·0403·a325·696e·7433·324c··.~@@@....%int32L | ||
00000730:·0000 | 00000730:·0800·0038·0040·4040·4140·4040·4040·0482··...8.@@@A@@@@@.. | ||
00000740:·4040·9204 | 00000740:·4040·4092·0403·a325·696e·7436·344d·0800··@@@....%int64M.. | ||
00000750:·0038·0040·4040·4140·4040·4040·0486·4040··.8.@@@A@@@@@..@@ | |||
00000760:·4092·0403·a33a·556e·6465·6669·6e65·645f··@....:Undefined_ | |||
00000770:·7265·6375·7273·6976·655f·6d6f·6475·6c65··recursive_module | |||
00000780:·5d08·0000·2000·9004·5740·90a0·c092·a0c0··]...·...W@...... | |||
00000790:·b390·0483·4090·4002·05f5·e100·404a·a0c0··....@.@.....@J.. | |||
000007a0:·b390·0490·4090·4002·05f5·e100·4040·a004··....@.@.....@@.. | |||
000007b0:·0540·0205·f5e1·0040·5640·4041·049a·a0b0··.@.....@V@@A.... | |||
000007c0:·a03d·6f63·616d·6c2e·7761·726e·5f6f·6e5f··.=ocaml.warn_on_ | |||
000007d0:·6c69·7465·7261·6c5f·7061·7474·6572·6e04··literal_pattern. | |||
000007e0:·9e04·6104·9e40·9204·17a3·2e41·7373·6572··..a..@.....Asser | |||
000007f0:·745f·6661·696c·7572·655c·0800·0020·0004··t_failure\...·.. | |||
00000800:·1840·90a0·c092·a004·17a0·0413·a004·1440··.@.............@ | |||
00000810:·0205·f5e1·0040·5840·4041·04a9·a0b0·a004··.....@X@@A...... | |||
00000820:·0f04·ac04·6f04·ac40·9204·0da3·3044·6976··....o..@....0Div | |||
00000830:·6973·696f·6e5f·6279·5f7a·6572·6f59·0800··ision_by_zeroY.. | |||
00000840:·0020·0004·2640·9040·4041·04b1·a0b0·a004··.·..&@.@@A...... | |||
00000850:·1704·b404·7704·b440·9204·07a3·2b45·6e64··....w..@....+End | |||
00000860:·5f6f·665f·6669·6c65·5808·0000·2000·042e··_of_fileX...·... | |||
00000870:·4090·4040·4104·b9a0·b0a0·041f·04bc·047f··@.@@A........... | |||
00000880:·04bc·4092·0407·a329·5379·735f·6572·726f··..@....)Sys_erro | |||
00000890:·7257·0800·0020·0004·3640·90a0·0432·4040··rW...·..6@...2@@ | |||
000008a0:·4104·c2a0·b0a0·0428·04c5·0488·04c5·4092··A......(......@. | |||
000008b0:·0408·a32e·5379·735f·626c·6f63·6b65·645f··....Sys_blocked_ | |||
000008c0:·696f·5b08·0000·2000·043f·4090·4040·4104··io[...·..?@.@@A. | |||
000008d0:·caa0·b0a0·0430·04cd·0490·04cd·4092·0407··.....0......@... | |||
000008e0:·a329·4e6f·745f·666f·756e·6456·0800·0020··.)Not_foundV...· | |||
000008f0:·0004·4740·9040·4041·04d2·a0b0·a004·3804··..G@.@@A......8. | |||
00000900:·d504·9804·d540·9204·07a3·2746·6169·6c75··.....@....'Failu | |||
00000910:·7265·5508·0000·2000·044f·4090·a004·4b40··reU...·..O@...K@ | |||
00000920:·4041·04db·a0b0·a004·4104·de04·a104·de40··@A......A......@ | |||
00000930:·9204·08a3·3049·6e76·616c·6964·5f61·7267··....0Invalid_arg | |||
00000940:·756d·656e·7454·0800·0020·0004·5840·90a0··umentT...·..X@.. | |||
00000950:·0454·4040·4104·e4a0·b0a0·044a·04e7·04aa··.T@@A......J.... | |||
00000960:·04e7·4092·0408·a32e·5374·6163·6b5f·6f76··..@.....Stack_ov | |||
00000970:·6572·666c·6f77·5a08·0000·2000·0461·4090··erflowZ...·..a@. | |||
00000980:·4040·4104·eca0·b0a0·0452·04ef·04b2·04ef··@@A......R...... | |||
00000990:·4092·0407·a32d·4f75·745f·6f66·5f6d·656d··@....-Out_of_mem | |||
000009a0:·6f72·7953·0800·0020·0004·6940·9040·4041··oryS...·..i@.@@A | |||
000009b0:·04f4·a0b0·a004·5a04·f704·ba04·f740·9204··......Z......@.. | |||
000009c0:·07a3·2d4d·6174·6368·5f66·6169·6c75·7265··..-Match_failure | |||
000009d0:·5208·0000·2000·0471·4090·a0c0·92a0·0470··R...·..q@......p | |||
000009e0:·a004·6ca0·046d·4002·05f5·e100·4063·4040··..l..m@.....@c@@ | |||
000009f0:·4105·0102·a0b0·a004·6805·0105·04c8·0501··A.......h....... | |||
00000a00:·0540·9204·0da3·2562·7974·6573·4308·0000··.@....%bytesC... | |||
00000 | 00000a10:·3800·4040·4041·4040·4040·4005·0109·4040··8.@@@A@@@@@...@@ | ||
00000760:·9204·03a3·3a55·6e64·6566·696e·6564·5f72··....:Undefined_r | |||
00000770:·6563·7572·7369·7665·5f6d·6f64·756c·655d··ecursive_module] | |||
Max diff block lines reached; 11100/46588 bytes (23.83%) of diff not shown. |
Offset 91, 15 lines modified | Offset 91, 15 lines modified | ||
000005a0:·6962·9030·2d08·2666·be7f·c2ba·916e·7233··ib.0-.&f.....nr3 | 000005a0:·6962·9030·2d08·2666·be7f·c2ba·916e·7233··ib.0-.&f.....nr3 | ||
000005b0:·3974·91df·a0a0·3843·616d·6c69·6e74·6572··9t....8Camlinter | 000005b0:·3974·91df·a0a0·3843·616d·6c69·6e74·6572··9t....8Camlinter | ||
000005c0:·6e61·6c46·6f72·6d61·7442·6173·6963·7390··nalFormatBasics. | 000005c0:·6e61·6c46·6f72·6d61·7442·6173·6963·7390··nalFormatBasics. | ||
000005d0:·30c4·b583·a727·ec28·f5bc·9ba3·6adc·64cf··0....'.(....j.d. | 000005d0:·30c4·b583·a727·ec28·f5bc·9ba3·6adc·64cf··0....'.(....j.d. | ||
000005e0:·c740·8495·a6be·0000·0008·0000·0004·0000··.@.............. | 000005e0:·c740·8495·a6be·0000·0008·0000·0004·0000··.@.............. | ||
000005f0:·000b·0000·000b·a040·a041·a090·4040·4361··.......@.A..@@Ca | 000005f0:·000b·0000·000b·a040·a041·a090·4040·4361··.......@.A..@@Ca | ||
00000600:·6d6c·3139·3939·5430·3330·8495·a6be·0000··ml1999T030...... | 00000600:·6d6c·3139·3939·5430·3330·8495·a6be·0000··ml1999T030...... | ||
00000610:·20 | 00000610:·20f7·0000·056c·0000·1708·0000·160e·0800···....l.......... | ||
00000620:·0034·0025·5261·6e67·6592·b0a0·b09e·b0a0··.4.%Range....... | 00000620:·0034·0025·5261·6e67·6592·b0a0·b09e·b0a0··.4.%Range....... | ||
00000630:·2a6f·6361·6d6c·2e74·6578·74b0·c026·5f6e··*ocaml.text..&_n | 00000630:·2a6f·6361·6d6c·2e74·6578·74b0·c026·5f6e··*ocaml.text..&_n | ||
00000640:·6f6e·655f·4040·00ff·0402·4190·a0a0·a0c0··one_@@....A..... | 00000640:·6f6e·655f·4040·00ff·0402·4190·a0a0·a0c0··one_@@....A..... | ||
00000650:·91b2·09b1·2053·6b65·7765·6420·6c69·7374··....·Skewed·list | 00000650:·91b2·09b1·2053·6b65·7765·6420·6c69·7374··....·Skewed·list | ||
00000660:·730a·0a20·2020·2054·6869·7320·6973·2061··s..····This·is·a | 00000660:·730a·0a20·2020·2054·6869·7320·6973·2061··s..····This·is·a | ||
00000670:·2070·7572·656c·7920·6675·6e63·7469·6f6e···purely·function | 00000670:·2070·7572·656c·7920·6675·6e63·7469·6f6e···purely·function | ||
00000680:·616c·2064·6174·6173·7472·7563·7475·7265··al·datastructure | 00000680:·616c·2064·6174·6173·7472·7563·7475·7265··al·datastructure |
Offset 1, 3 lines modified | Offset 1, 3 lines modified | ||
1 | -rw-r--r--···0········0········0········4·2022-11-29·08:28:08.000000·debian-binary | 1 | -rw-r--r--···0········0········0········4·2022-11-29·08:28:08.000000·debian-binary |
2 | -rw-r--r--···0········0········0·····28 | 2 | -rw-r--r--···0········0········0·····2840·2022-11-29·08:28:08.000000·control.tar.xz |
3 | -rw-r--r--···0········0········0·2225 | 3 | -rw-r--r--···0········0········0·22256408·2022-11-29·08:28:08.000000·data.tar.xz |
Offset 4, 15 lines modified | Offset 4, 15 lines modified | ||
4 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2022-11-29·08:28:08.000000·./usr/lib/ocaml/ | 4 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2022-11-29·08:28:08.000000·./usr/lib/ocaml/ |
5 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/ | 5 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/ |
6 | -rw-r--r--···0·root·········(0)·root·········(0)····11238·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/META | 6 | -rw-r--r--···0·root·········(0)·root·········(0)····11238·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/META |
7 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/boot/ | 7 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/boot/ |
8 | -rw-r--r--···0·root·········(0)·root·········(0)····41714·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/boot/boot.cma | 8 | -rw-r--r--···0·root·········(0)·root·········(0)····41714·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/boot/boot.cma |
9 | -rw-r--r--···0·root·········(0)·root·········(0)····28288·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/boot/boot.cmxs | 9 | -rw-r--r--···0·root·········(0)·root·········(0)····28288·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/boot/boot.cmxs |
10 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/ | 10 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/ |
11 | -rw-r--r--···0·root·········(0)·root·········(0)··14633 | 11 | -rw-r--r--···0·root·········(0)·root·········(0)··1463389·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/clib.cma |
12 | -rw-r--r--···0·root·········(0)·root·········(0)···749232·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/clib.cmxs | 12 | -rw-r--r--···0·root·········(0)·root·········(0)···749232·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/clib.cmxs |
13 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/config/ | 13 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/config/ |
14 | -rw-r--r--···0·root·········(0)·root·········(0)·····7830·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/config/config.cma | 14 | -rw-r--r--···0·root·········(0)·root·········(0)·····7830·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/config/config.cma |
15 | -rw-r--r--···0·root·········(0)·root·········(0)·····7364·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/config/config.cmxs | 15 | -rw-r--r--···0·root·········(0)·root·········(0)·····7364·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/config/config.cmxs |
16 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/engine/ | 16 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/engine/ |
17 | -rw-r--r--···0·root·········(0)·root·········(0)··2022255·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/engine/engine.cma | 17 | -rw-r--r--···0·root·········(0)·root·········(0)··2022255·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/engine/engine.cma |
18 | -rw-r--r--···0·root·········(0)·root·········(0)···781180·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/engine/engine.cmxs | 18 | -rw-r--r--···0·root·········(0)·root·········(0)···781180·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/engine/engine.cmxs |
Offset 1, 8 lines modified | Offset 1, 8 lines modified | ||
00000000:·4361·6d6c·3139·3939·4130·3330·0012·44 | 00000000:·4361·6d6c·3139·3939·4130·3330·0012·441a··Caml1999A030..D. | ||
00000010:·5400·0000·9e01·0000·2900·0000·2a00·0000··T.......)...*... | 00000010:·5400·0000·9e01·0000·2900·0000·2a00·0000··T.......)...*... | ||
00000020:·0100·0000·0100·0000·0b00·0000·1b00·0000··................ | 00000020:·0100·0000·0100·0000·0b00·0000·1b00·0000··................ | ||
00000030:·2200·0000·0a00·0000·4700·0000·0800·0000··".......G....... | 00000030:·2200·0000·0a00·0000·4700·0000·0800·0000··".......G....... | ||
00000040:·0b00·0000·4700·0000·0700·0000·0c00·0000··....G........... | 00000040:·0b00·0000·4700·0000·0700·0000·0c00·0000··....G........... | ||
00000050:·4700·0000·0600·0000·0d00·0000·4700·0000··G...........G... | 00000050:·4700·0000·0600·0000·0d00·0000·4700·0000··G...........G... | ||
00000060:·0400·0000·0e00·0000·4600·0000·0f00·0000··........F....... | 00000060:·0400·0000·0e00·0000·4600·0000·0f00·0000··........F....... | ||
00000070:·4300·0000·3e00·0000·0600·0000·0000·0000··C...>........... | 00000070:·4300·0000·3e00·0000·0600·0000·0000·0000··C...>........... |
Offset 1, 3 lines modified | Offset 1, 3 lines modified | ||
1 | -rw-r--r--···0········0········0········4·2022-11-29·08:28:08.000000·debian-binary | 1 | -rw-r--r--···0········0········0········4·2022-11-29·08:28:08.000000·debian-binary |
2 | -rw-r--r--···0········0········0····481 | 2 | -rw-r--r--···0········0········0····48120·2022-11-29·08:28:08.000000·control.tar.xz |
3 | -rw-r--r--···0········0········0·214778 | 3 | -rw-r--r--···0········0········0·21477876·2022-11-29·08:28:08.000000·data.tar.xz |
Offset 1246, 26 lines modified | Offset 1246, 26 lines modified | ||
1246 | -rw-r--r--···0·root·········(0)·root·········(0)···102177·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Arith_prebase.html | 1246 | -rw-r--r--···0·root·········(0)·root·········(0)···102177·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Arith_prebase.html |
1247 | -rw-r--r--···0·root·········(0)·root·········(0)····55916·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Between.html | 1247 | -rw-r--r--···0·root·········(0)·root·········(0)····55916·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Between.html |
1248 | -rw-r--r--···0·root·········(0)·root·········(0)····13646·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Bool_nat.html | 1248 | -rw-r--r--···0·root·········(0)·root·········(0)····13646·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Bool_nat.html |
1249 | -rw-r--r--···0·root·········(0)·root·········(0)····21939·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Cantor.html | 1249 | -rw-r--r--···0·root·········(0)·root·········(0)····21939·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Cantor.html |
1250 | -rw-r--r--···0·root·········(0)·root·········(0)····14226·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Compare.html | 1250 | -rw-r--r--···0·root·········(0)·root·········(0)····14226·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Compare.html |
1251 | -rw-r--r--···0·root·········(0)·root·········(0)····64268·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Compare_dec.html | 1251 | -rw-r--r--···0·root·········(0)·root·········(0)····64268·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Compare_dec.html |
1252 | -rw-r--r--···0·root·········(0)·root·········(0)····42751·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Div2.html | 1252 | -rw-r--r--···0·root·········(0)·root·········(0)····42751·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Div2.html |
1253 | -rw-r--r--···0·root·········(0)·root·········(0)····2150 | 1253 | -rw-r--r--···0·root·········(0)·root·········(0)····21503·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.EqNat.html |
1254 | -rw-r--r--···0·root·········(0)·root·········(0)····13970·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Euclid.html | 1254 | -rw-r--r--···0·root·········(0)·root·········(0)····13970·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Euclid.html |
1255 | -rw-r--r--···0·root·········(0)·root·········(0)····7637 | 1255 | -rw-r--r--···0·root·········(0)·root·········(0)····76375·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Even.html |
1256 | -rw-r--r--···0·root·········(0)·root·········(0)·····7674·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Factorial.html | 1256 | -rw-r--r--···0·root·········(0)·root·········(0)·····7674·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Factorial.html |
1257 | -rw-r--r--···0·root·········(0)·root·········(0)····2552 | 1257 | -rw-r--r--···0·root·········(0)·root·········(0)····25529·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Gt.html |
1258 | -rw-r--r--···0·root·········(0)·root·········(0)····1806 | 1258 | -rw-r--r--···0·root·········(0)·root·········(0)····18062·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Le.html |
1259 | -rw-r--r--···0·root·········(0)·root·········(0)····2410 | 1259 | -rw-r--r--···0·root·········(0)·root·········(0)····24104·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Lt.html |
1260 | -rw-r--r--···0·root·········(0)·root·········(0)····15941·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Max.html | 1260 | -rw-r--r--···0·root·········(0)·root·········(0)····15941·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Max.html |
1261 | -rw-r--r--···0·root·········(0)·root·········(0)····1516 | 1261 | -rw-r--r--···0·root·········(0)·root·········(0)····15169·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Min.html |
1262 | -rw-r--r--···0·root·········(0)·root·········(0)····17 | 1262 | -rw-r--r--···0·root·········(0)·root·········(0)····17399·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Minus.html |
1263 | -rw-r--r--···0·root·········(0)·root·········(0)····308 | 1263 | -rw-r--r--···0·root·········(0)·root·········(0)····30832·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Mult.html |
1264 | -rw-r--r--···0·root·········(0)·root·········(0)···2771 | 1264 | -rw-r--r--···0·root·········(0)·root·········(0)···277179·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.PeanoNat.html |
1265 | -rw-r--r--···0·root·········(0)·root·········(0)·····9262·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Peano_dec.html | 1265 | -rw-r--r--···0·root·········(0)·root·········(0)·····9262·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Peano_dec.html |
1266 | -rw-r--r--···0·root·········(0)·root·········(0)····41541·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Plus.html | 1266 | -rw-r--r--···0·root·········(0)·root·········(0)····41541·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Plus.html |
1267 | -rw-r--r--···0·root·········(0)·root·········(0)····79298·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Wf_nat.html | 1267 | -rw-r--r--···0·root·········(0)·root·········(0)····79298·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Wf_nat.html |
1268 | -rw-r--r--···0·root·········(0)·root·········(0)····40548·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Array.PArray.html | 1268 | -rw-r--r--···0·root·········(0)·root·········(0)····40548·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Array.PArray.html |
1269 | -rw-r--r--···0·root·········(0)·root·········(0)···223957·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Bool.Bool.html | 1269 | -rw-r--r--···0·root·········(0)·root·········(0)···223957·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Bool.Bool.html |
1270 | -rw-r--r--···0·root·········(0)·root·········(0)····16136·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Bool.BoolEq.html | 1270 | -rw-r--r--···0·root·········(0)·root·········(0)····16136·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Bool.BoolEq.html |
1271 | -rw-r--r--···0·root·········(0)·root·········(0)····28376·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Bool.BoolOrder.html | 1271 | -rw-r--r--···0·root·········(0)·root·········(0)····28376·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Bool.BoolOrder.html |
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="lab9 | 49 | <a·id="lab997"></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="lab9 | 57 | <a·id="lab998"></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="lab9 | 59 | <a·id="lab999"></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="lab | 57 | <a·id="lab1027"></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/> |
Offset 69, 15 lines modified | Offset 69, 15 lines modified | ||
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="lab | 74 | <a·id="lab1023"></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/> |
Offset 48, 30 lines modified | Offset 48, 30 lines modified | ||
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="lab | 53 | <a·id="lab1015"></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="lab | 63 | <a·id="lab1016"></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 48, 27 lines modified | Offset 48, 27 lines modified | ||
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="lab | 53 | <a·id="lab984"></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="lab | 61 | <a·id="lab985"></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/> |
Offset 48, 39 lines modified | Offset 48, 39 lines modified | ||
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="lab | 53 | <a·id="lab1029"></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="lab | 61 | <a·id="lab1030"></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="lab | 70 | <a·id="lab1031"></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/> |
Offset 45, 15 lines modified | Offset 45, 15 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="lab9 | 49 | <a·id="lab975"></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 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab1000"></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="lab | 53 | <a·id="lab990"></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="lab | 63 | <a·id="lab991"></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="lab | 72 | <a·id="lab992"></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/> |
Offset 45, 76 lines modified | Offset 45, 76 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 | 49 | <a·id="lab1039"></a><h1·class="section">Properties·of·multiplication.</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | <a·id="lab | 51 | <a·id="lab1040"></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="lab | 61 | <a·id="lab1041"></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="lab | 63 | <a·id="lab1042"></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="lab | 73 | <a·id="lab1043"></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="lab | 83 | <a·id="lab1044"></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="lab | 92 | <a·id="lab1045"></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 144, 15 lines modified | Offset 144, 15 lines modified | ||
144 | <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/> | 144 | <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 | <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/> | 145 | <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 | <br/> | 146 | <br/> |
147 | </div> | 147 | </div> |
148 | <div·class="doc"> | 148 | <div·class="doc"> |
149 | <a·id="lab | 149 | <a·id="lab1001"></a><h2·class="section">Remaining·constants·not·defined·in·Coq.Init.Nat</h2> |
150 | <div·class="paragraph">·</div> | 150 | <div·class="paragraph">·</div> |
151 | ·NB:·Aliasing·<span·class="inlinecode"><span·class="id"·title="var">le</span></span>·is·mandatory,·since·only·a·Definition·can·implement | 151 | ·NB:·Aliasing·<span·class="inlinecode"><span·class="id"·title="var">le</span></span>·is·mandatory,·since·only·a·Definition·can·implement |
152 | ····an·interface·Parameter...· | 152 | ····an·interface·Parameter...· |
153 | </div> | 153 | </div> |
154 | <div·class="code"> | 154 | <div·class="code"> |
Offset 48, 30 lines modified | Offset 48, 30 lines modified | ||
48 | <br/> | 48 | <br/> |
49 | </div> | 49 | </div> |
50 | <div·class="doc"> | 50 | <div·class="doc"> |
51 | Properties·of·addition.· | 51 | Properties·of·addition.· |
52 | <div·class="paragraph">·</div> | 52 | <div·class="paragraph">·</div> |
53 | <a·id="lab9 | 53 | <a·id="lab976"></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="lab97 | 63 | <a·id="lab977"></a><h1·class="section">Neutrality·of·0,·commutativity,·associativity</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.Plus·file·is·obsolete.·Use·Nat.add_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.Plus·file·is·obsolete.·Use·Nat.add_0_l·instead.")]<br/> |
68 | <span·class="id"·title="keyword">Notation</span>·<a·id="plus_0_l"·class="idref"·href="#plus_0_l"><span·class="id"·title="abbreviation">plus_0_l</span></a>·:=·<a·class="idref"·href="Coq.Arith.PeanoNat.html#Nat.add_0_l"><span·class="id"·title="lemma">Nat.add_0_l</span></a>·(<span·class="id"·title="var">only</span>·<span·class="id"·title="var">parsing</span>).<br/> | 68 | <span·class="id"·title="keyword">Notation</span>·<a·id="plus_0_l"·class="idref"·href="#plus_0_l"><span·class="id"·title="abbreviation">plus_0_l</span></a>·:=·<a·class="idref"·href="Coq.Arith.PeanoNat.html#Nat.add_0_l"><span·class="id"·title="lemma">Nat.add_0_l</span></a>·(<span·class="id"·title="var">only</span>·<span·class="id"·title="var">parsing</span>).<br/> |
Offset 80, 27 lines modified | Offset 80, 27 lines modified | ||
80 | |·<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/> | 80 | |·<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/> |
81 | <span·class="id"·title="keyword">end</span>.<br/> | 81 | <span·class="id"·title="keyword">end</span>.<br/> |
82 | <br/> | 82 | <br/> |
83 | </div> | 83 | </div> |
84 | <div·class="doc"> | 84 | <div·class="doc"> |
85 | <a·id="lab | 85 | <a·id="lab316"></a><h1·class="section">Decidability</h1> |
86 | </div> | 86 | </div> |
87 | <div·class="code"> | 87 | <div·class="code"> |
88 | <br/> | 88 | <br/> |
89 | <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/> | 89 | <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/> |
90 | <br/> | 90 | <br/> |
91 | </div> | 91 | </div> |
92 | <div·class="doc"> | 92 | <div·class="doc"> |
93 | <a·id="lab | 93 | <a·id="lab317"></a><h1·class="section">Discrimination</h1> |
94 | </div> | 94 | </div> |
95 | <div·class="code"> | 95 | <div·class="code"> |
96 | <br/> | 96 | <br/> |
97 | <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/> | 97 | <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/> |
98 | #[<span·class="id"·title="var">global</span>]<br/> | 98 | #[<span·class="id"·title="var">global</span>]<br/> |
Offset 61, 15 lines modified | Offset 61, 15 lines modified | ||
61 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Structures.Orders.html#"><span·class="id"·title="library">Orders</span></a>.<br/> | 61 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Structures.Orders.html#"><span·class="id"·title="library">Orders</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/> | 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 | <br/> | 63 | <br/> |
64 | </div> | 64 | </div> |
65 | <div·class="doc"> | 65 | <div·class="doc"> |
66 | <a·id="lab | 66 | <a·id="lab331"></a><h1·class="section">Order·<span·class="inlinecode"><span·class="id"·title="var">le</span></span></h1> |
67 | </div> | 67 | </div> |
68 | <div·class="code"> | 68 | <div·class="code"> |
69 | <br/> | 69 | <br/> |
70 | <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/> | 70 | <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 | · | 71 | · |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab770"></a><h1·class="section">Typeclass-based·setoids.·Definitions·on·<span·class="inlinecode"><span·class="id"·title="var">Equivalence</span></span>.</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ···Author:·Matthieu·Sozeau | 51 | ···Author:·Matthieu·Sozeau |
52 | ···Institution:·LRI,·CNRS·UMR·8623·-·University·Paris·Sud | 52 | ···Institution:·LRI,·CNRS·UMR·8623·-·University·Paris·Sud |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab760"></a><h1·class="section">Typeclass-based·morphism·definition·and·standard,·minimal·instances</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ···Author:·Matthieu·Sozeau | 51 | ···Author:·Matthieu·Sozeau |
52 | ···Institution:·LRI,·CNRS·UMR·8623·-·University·Paris·Sud | 52 | ···Institution:·LRI,·CNRS·UMR·8623·-·University·Paris·Sud |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab766"></a><h1·class="section">Typeclass-based·relations,·tactics·and·standard·instances</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ···This·is·the·basic·theory·needed·to·formalize·morphisms·and·setoids. | 51 | ···This·is·the·basic·theory·needed·to·formalize·morphisms·and·setoids. |
52 | <div·class="paragraph">·</div> | 52 | <div·class="paragraph">·</div> |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab765"></a><h1·class="section">A·typeclass·to·ease·the·handling·of·decidable·properties.</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ·A·proposition·is·decidable·whenever·it·is·reflected·by·a·boolean.· | 51 | ·A·proposition·is·decidable·whenever·it·is·reflected·by·a·boolean.· |
52 | </div> | 52 | </div> |
53 | <div·class="code"> | 53 | <div·class="code"> |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab769"></a><h1·class="section">Decidable·equivalences.</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ···Author:·Matthieu·Sozeau | 51 | ···Author:·Matthieu·Sozeau |
52 | ···Institution:·LRI,·CNRS·UMR·8623·-·University·Paris·Sud | 52 | ···Institution:·LRI,·CNRS·UMR·8623·-·University·Paris·Sud |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab764"></a><h1·class="section">Typeclass-based·setoids.·Definitions·on·<span·class="inlinecode"><span·class="id"·title="var">Equivalence</span></span>.</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ···Author:·Matthieu·Sozeau | 51 | ···Author:·Matthieu·Sozeau |
52 | ···Institution:·LRI,·CNRS·UMR·8623·-·University·Paris·Sud | 52 | ···Institution:·LRI,·CNRS·UMR·8623·-·University·Paris·Sud |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab759"></a><h1·class="section">Initialization·code·for·typeclasses,·setting·up·the·default·tactic</h1> |
50 | ···for·instance·search. | 50 | ···for·instance·search. |
51 | <div·class="paragraph">·</div> | 51 | <div·class="paragraph">·</div> |
52 | ···Author:·Matthieu·Sozeau | 52 | ···Author:·Matthieu·Sozeau |
53 | ···Institution:·LRI,·CNRS·UMR·8623·-·University·Paris·Sud | 53 | ···Institution:·LRI,·CNRS·UMR·8623·-·University·Paris·Sud |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab776"></a><h1·class="section">Typeclass-based·morphism·definition·and·standard,·minimal·instances</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ···Author:·Matthieu·Sozeau | 51 | ···Author:·Matthieu·Sozeau |
52 | ···Institution:·LRI,·CNRS·UMR·8623·-·University·Paris·Sud | 52 | ···Institution:·LRI,·CNRS·UMR·8623·-·University·Paris·Sud |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab772"></a><h1·class="section"><span·class="inlinecode"><span·class="id"·title="var">Proper</span></span>·instances·for·propositional·connectives.</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ···Author:·Matthieu·Sozeau | 51 | ···Author:·Matthieu·Sozeau |
52 | ···Institution:·LRI,·CNRS·UMR·8623·-·University·Paris·Sud | 52 | ···Institution:·LRI,·CNRS·UMR·8623·-·University·Paris·Sud |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab763"></a><h1·class="section">Morphism·instances·for·relations.</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ···Author:·Matthieu·Sozeau | 51 | ···Author:·Matthieu·Sozeau |
52 | ···Institution:·LRI,·CNRS·UMR·8623·-·University·Paris·Sud | 52 | ···Institution:·LRI,·CNRS·UMR·8623·-·University·Paris·Sud |
Offset 103, 15 lines modified | Offset 103, 15 lines modified | ||
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:·6c61·623 | 000006d0:·6c61·6237·3733·223e·3c2f·613e·3c68·3120··lab773"></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>. |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab762"></a><h1·class="section">Relations·over·pairs</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.Lists.SetoidList.html#"><span·class="id"·title="library">SetoidList</span></a>.<br/> | 53 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Lists.SetoidList.html#"><span·class="id"·title="library">SetoidList</span></a>.<br/> |
54 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Relations.Relations.html#"><span·class="id"·title="library">Relations</span></a>·<a·class="idref"·href="Coq.Classes.Morphisms.html#"><span·class="id"·title="library">Morphisms</span></a>.<br/> | 54 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Relations.Relations.html#"><span·class="id"·title="library">Relations</span></a>·<a·class="idref"·href="Coq.Classes.Morphisms.html#"><span·class="id"·title="library">Morphisms</span></a>.<br/> |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab778"></a><h1·class="section">Typeclass-based·setoids,·tactics·and·standard·instances.</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ···Author:·Matthieu·Sozeau | 51 | ···Author:·Matthieu·Sozeau |
52 | ···Institution:·LRI,·CNRS·UMR·8623·-·University·Paris·Sud | 52 | ···Institution:·LRI,·CNRS·UMR·8623·-·University·Paris·Sud |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab771"></a><h1·class="section">Decidable·setoid·equality·theory.</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ···Author:·Matthieu·Sozeau | 51 | ···Author:·Matthieu·Sozeau |
52 | ···Institution:·LRI,·CNRS·UMR·8623·-·University·Paris·Sud | 52 | ···Institution:·LRI,·CNRS·UMR·8623·-·University·Paris·Sud |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab758"></a><h1·class="section">Tactics·for·typeclass-based·setoids.</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ···Author:·Matthieu·Sozeau | 51 | ···Author:·Matthieu·Sozeau |
52 | ···Institution:·LRI,·CNRS·UMR·8623·-·University·Paris·Sud | 52 | ···Institution:·LRI,·CNRS·UMR·8623·-·University·Paris·Sud |
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="lab | 51 | <a·id="lab615"></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 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab519"></a><h1·class="section">Finite·maps·library</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ·This·functor·derives·additional·facts·from·<span·class="inlinecode"><span·class="id"·title="var">FMapInterface.S</span></span>.·These | 51 | ·This·functor·derives·additional·facts·from·<span·class="inlinecode"><span·class="id"·title="var">FMapInterface.S</span></span>.·These |
52 | ··facts·are·mainly·the·specifications·of·<span·class="inlinecode"><span·class="id"·title="var">FMapInterface.S</span></span>·written·using | 52 | ··facts·are·mainly·the·specifications·of·<span·class="inlinecode"><span·class="id"·title="var">FMapInterface.S</span></span>·written·using |
53 | ··different·styles:·equivalence·and·boolean·equalities. | 53 | ··different·styles:·equivalence·and·boolean·equalities. |
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="lab | 51 | <a·id="lab577"></a><h1·class="section">FMapFullAVL</h1> |
52 | <div·class="paragraph">·</div> | 52 | <div·class="paragraph">·</div> |
53 | ···This·file·contains·some·complements·to·<span·class="inlinecode"><span·class="id"·title="var">FMapAVL</span></span>. | 53 | ···This·file·contains·some·complements·to·<span·class="inlinecode"><span·class="id"·title="var">FMapAVL</span></span>. |
54 | <div·class="paragraph">·</div> | 54 | <div·class="paragraph">·</div> |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab551"></a><h1·class="section">Finite·map·library</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ·This·file·proposes·interfaces·for·finite·maps· | 51 | ·This·file·proposes·interfaces·for·finite·maps· |
52 | </div> | 52 | </div> |
53 | <div·class="code"> | 53 | <div·class="code"> |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab539"></a><h1·class="section">Finite·map·library</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ·This·file·proposes·an·implementation·of·the·non-dependent·interface | 51 | ·This·file·proposes·an·implementation·of·the·non-dependent·interface |
52 | ·<span·class="inlinecode"><span·class="id"·title="var">FMapInterface.S</span></span>·using·lists·of·pairs·ordered·(increasing)·with·respect·to | 52 | ·<span·class="inlinecode"><span·class="id"·title="var">FMapInterface.S</span></span>·using·lists·of·pairs·ordered·(increasing)·with·respect·to |
53 | ·left·projection.· | 53 | ·left·projection.· |
54 | </div> | 54 | </div> |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab576"></a><h1·class="section">FMapPositive·:·an·implementation·of·FMapInterface·for·<span·class="inlinecode"><span·class="id"·title="var">positive</span></span>·keys.</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.Bool.Bool.html#"><span·class="id"·title="library">Bool</span></a>·<a·class="idref"·href="Coq.Structures.OrderedType.html#"><span·class="id"·title="library">OrderedType</span></a>·<a·class="idref"·href="Coq.ZArith.ZArith.html#"><span·class="id"·title="library">ZArith</span></a>·<a·class="idref"·href="Coq.Structures.OrderedType.html#"><span·class="id"·title="library">OrderedType</span></a>·<a·class="idref"·href="Coq.Structures.OrderedTypeEx.html#"><span·class="id"·title="library">OrderedTypeEx</span></a>·<a·class="idref"·href="Coq.FSets.FMapInterface.html#"><span·class="id"·title="library">FMapInterface</span></a>.<br/> | 53 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Bool.Bool.html#"><span·class="id"·title="library">Bool</span></a>·<a·class="idref"·href="Coq.Structures.OrderedType.html#"><span·class="id"·title="library">OrderedType</span></a>·<a·class="idref"·href="Coq.ZArith.ZArith.html#"><span·class="id"·title="library">ZArith</span></a>·<a·class="idref"·href="Coq.Structures.OrderedType.html#"><span·class="id"·title="library">OrderedType</span></a>·<a·class="idref"·href="Coq.Structures.OrderedTypeEx.html#"><span·class="id"·title="library">OrderedTypeEx</span></a>·<a·class="idref"·href="Coq.FSets.FMapInterface.html#"><span·class="id"·title="library">FMapInterface</span></a>.<br/> |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab664"></a><h1·class="section">Finite·map·library</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ·This·file·proposes·an·implementation·of·the·non-dependent·interface | 51 | ·This·file·proposes·an·implementation·of·the·non-dependent·interface |
52 | ·<span·class="inlinecode"><span·class="id"·title="var">FMapInterface.WS</span></span>·using·lists·of·pairs,·unordered·but·without·redundancy.· | 52 | ·<span·class="inlinecode"><span·class="id"·title="var">FMapInterface.WS</span></span>·using·lists·of·pairs,·unordered·but·without·redundancy.· |
53 | </div> | 53 | </div> |
54 | <div·class="code"> | 54 | <div·class="code"> |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab538"></a><h1·class="section">FSetAVL·:·Implementation·of·FSetInterface·via·AVL·trees</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ·This·module·implements·finite·sets·using·AVL·trees. | 51 | ·This·module·implements·finite·sets·using·AVL·trees. |
52 | ····It·follows·the·implementation·from·Ocaml's·standard·library, | 52 | ····It·follows·the·implementation·from·Ocaml's·standard·library, |
53 | <div·class="paragraph">·</div> | 53 | <div·class="paragraph">·</div> |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab678"></a><h1·class="section">Finite·sets·library</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ·This·module·implements·bridges·(as·functors)·from·dependent | 51 | ·This·module·implements·bridges·(as·functors)·from·dependent |
52 | ····to/from·non-dependent·set·signature.· | 52 | ····to/from·non-dependent·set·signature.· |
53 | </div> | 53 | </div> |
54 | <div·class="code"> | 54 | <div·class="code"> |
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="lab | 49 | <a·id="lab557"></a><h1·class="section">Compatibility·functors·between·FSetInterface·and·MSetInterface.</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.FSets.FSetInterface.html#"><span·class="id"·title="library">FSetInterface</span></a>·<a·class="idref"·href="Coq.FSets.FSetFacts.html#"><span·class="id"·title="library">FSetFacts</span></a>·<a·class="idref"·href="Coq.MSets.MSetInterface.html#"><span·class="id"·title="library">MSetInterface</span></a>·<a·class="idref"·href="Coq.MSets.MSetFacts.html#"><span·class="id"·title="library">MSetFacts</span></a>.<br/> | 53 | <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.FSetFacts.html#"><span·class="id"·title="library">FSetFacts</span></a>·<a·class="idref"·href="Coq.MSets.MSetInterface.html#"><span·class="id"·title="library">MSetInterface</span></a>·<a·class="idref"·href="Coq.MSets.MSetFacts.html#"><span·class="id"·title="library">MSetFacts</span></a>.<br/> |
54 | <span·class="id"·title="keyword">Set·Implicit·Arguments</span>.<br/> | 54 | <span·class="id"·title="keyword">Set·Implicit·Arguments</span>.<br/> |
55 | <br/> | 55 | <br/> |
56 | </div> | 56 | </div> |
57 | <div·class="doc"> | 57 | <div·class="doc"> |
58 | <a·id="lab | 58 | <a·id="lab558"></a><h1·class="section">From·new·Weak·Sets·to·old·ones</h1> |
59 | </div> | 59 | </div> |
60 | <div·class="code"> | 60 | <div·class="code"> |
61 | <br/> | 61 | <br/> |
62 | <span·class="id"·title="keyword">Module</span>·<a·id="Backport_WSets"·class="idref"·href="#Backport_WSets"><span·class="id"·title="module">Backport_WSets</span></a><br/> | 62 | <span·class="id"·title="keyword">Module</span>·<a·id="Backport_WSets"·class="idref"·href="#Backport_WSets"><span·class="id"·title="module">Backport_WSets</span></a><br/> |
63 | (<span·class="id"·title="var">E</span>:<a·class="idref"·href="Coq.Structures.DecidableType.html#DecidableType"><span·class="id"·title="module">DecidableType.DecidableType</span></a>)<br/> | 63 | (<span·class="id"·title="var">E</span>:<a·class="idref"·href="Coq.Structures.DecidableType.html#DecidableType"><span·class="id"·title="module">DecidableType.DecidableType</span></a>)<br/> |
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="lab | 76 | <a·id="lab591"></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, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab537"></a><h1·class="section">Finite·sets·library</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ·This·module·proves·many·properties·of·finite·sets·that | 51 | ·This·module·proves·many·properties·of·finite·sets·that |
52 | ····are·consequences·of·the·axiomatization·in·<span·class="inlinecode"><span·class="id"·title="var">FsetInterface</span></span> | 52 | ····are·consequences·of·the·axiomatization·in·<span·class="inlinecode"><span·class="id"·title="var">FsetInterface</span></span> |
53 | ····Contrary·to·the·functor·in·<span·class="inlinecode"><span·class="id"·title="var">FsetProperties</span></span>·it·uses | 53 | ····Contrary·to·the·functor·in·<span·class="inlinecode"><span·class="id"·title="var">FsetProperties</span></span>·it·uses |
54 | ····sets·operations·instead·of·predicates·over·sets,·i.e. | 54 | ····sets·operations·instead·of·predicates·over·sets,·i.e. |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab660"></a><h1·class="section">Finite·sets·library</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ·This·functor·derives·additional·facts·from·<span·class="inlinecode"><span·class="id"·title="var">FSetInterface.S</span></span>.·These | 51 | ·This·functor·derives·additional·facts·from·<span·class="inlinecode"><span·class="id"·title="var">FSetInterface.S</span></span>.·These |
52 | ··facts·are·mainly·the·specifications·of·<span·class="inlinecode"><span·class="id"·title="var">FSetInterface.S</span></span>·written·using | 52 | ··facts·are·mainly·the·specifications·of·<span·class="inlinecode"><span·class="id"·title="var">FSetInterface.S</span></span>·written·using |
53 | ··different·styles:·equivalence·and·boolean·equalities. | 53 | ··different·styles:·equivalence·and·boolean·equalities. |
54 | ··Moreover,·we·prove·that·<span·class="inlinecode"><span·class="id"·title="var">E.Eq</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">Equal</span></span>·are·setoid·equalities. | 54 | ··Moreover,·we·prove·that·<span·class="inlinecode"><span·class="id"·title="var">E.Eq</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">Equal</span></span>·are·setoid·equalities. |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab607"></a><h1·class="section">Finite·set·library</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ·Set·interfaces,·inspired·by·the·one·of·Ocaml.·When·compared·with | 51 | ·Set·interfaces,·inspired·by·the·one·of·Ocaml.·When·compared·with |
52 | ····Ocaml,·the·main·differences·are: | 52 | ····Ocaml,·the·main·differences·are: |
53 | <ul·class="doclist"> | 53 | <ul·class="doclist"> |
54 | <li>·the·lack·of·<span·class="inlinecode"><span·class="id"·title="var">iter</span></span>·function,·useless·since·Coq·is·purely·functional | 54 | <li>·the·lack·of·<span·class="inlinecode"><span·class="id"·title="var">iter</span></span>·function,·useless·since·Coq·is·purely·functional |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab675"></a><h1·class="section">Finite·sets·library</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ·This·file·proposes·an·implementation·of·the·non-dependent | 51 | ·This·file·proposes·an·implementation·of·the·non-dependent |
52 | ····interface·<span·class="inlinecode"><span·class="id"·title="var">FSetInterface.S</span></span>·using·strictly·ordered·list.· | 52 | ····interface·<span·class="inlinecode"><span·class="id"·title="var">FSetInterface.S</span></span>·using·strictly·ordered·list.· |
53 | </div> | 53 | </div> |
54 | <div·class="code"> | 54 | <div·class="code"> |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab562"></a><h1·class="section">Finite·sets·library</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ·This·functor·derives·additional·properties·from·<span·class="inlinecode"><span·class="id"·title="var">FSetInterface.S</span></span>. | 51 | ·This·functor·derives·additional·properties·from·<span·class="inlinecode"><span·class="id"·title="var">FSetInterface.S</span></span>. |
52 | ····Contrary·to·the·functor·in·<span·class="inlinecode"><span·class="id"·title="var">FSetEqProperties</span></span>·it·uses | 52 | ····Contrary·to·the·functor·in·<span·class="inlinecode"><span·class="id"·title="var">FSetEqProperties</span></span>·it·uses |
53 | ····predicates·over·sets·instead·of·sets·operations,·i.e. | 53 | ····predicates·over·sets·instead·of·sets·operations,·i.e. |
54 | ····<span·class="inlinecode"><span·class="id"·title="var">In</span></span>·<span·class="inlinecode"><span·class="id"·title="var">x</span></span>·<span·class="inlinecode"><span·class="id"·title="var">s</span></span>·instead·of·<span·class="inlinecode"><span·class="id"·title="var">mem</span></span>·<span·class="inlinecode"><span·class="id"·title="var">x</span></span>·<span·class="inlinecode"><span·class="id"·title="var">s</span>=<span·class="id"·title="var">true</span></span>, | 54 | ····<span·class="inlinecode"><span·class="id"·title="var">In</span></span>·<span·class="inlinecode"><span·class="id"·title="var">x</span></span>·<span·class="inlinecode"><span·class="id"·title="var">s</span></span>·instead·of·<span·class="inlinecode"><span·class="id"·title="var">mem</span></span>·<span·class="inlinecode"><span·class="id"·title="var">x</span></span>·<span·class="inlinecode"><span·class="id"·title="var">s</span>=<span·class="id"·title="var">true</span></span>, |
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="lab | 49 | <a·id="lab676"></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="lab | 58 | <a·id="lab677"></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/> |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab590"></a><h1·class="section">Finite·sets·library</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ·This·file·proposes·an·implementation·of·the·non-dependent | 51 | ·This·file·proposes·an·implementation·of·the·non-dependent |
52 | ····interface·<span·class="inlinecode"><span·class="id"·title="var">FSetInterface.WS</span></span>·using·lists·without·redundancy.· | 52 | ····interface·<span·class="inlinecode"><span·class="id"·title="var">FSetInterface.WS</span></span>·using·lists·without·redundancy.· |
53 | </div> | 53 | </div> |
54 | <div·class="code"> | 54 | <div·class="code"> |
Offset 48, 15 lines modified | Offset 48, 15 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.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 | 53 | <a·id="lab154"></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 | 54 | <a·id="lab153"></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, 15 lines modified | Offset 48, 15 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.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>.<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>.<br/> |
50 | <br/> | 50 | <br/> |
51 | </div> | 51 | </div> |
52 | <div·class="doc"> | 52 | <div·class="doc"> |
53 | <a·id="lab | 53 | <a·id="lab166"></a><h1·class="section">Derived·operations·and·mapping·between·primitive·<span·class="inlinecode"><span·class="id"·title="var">float</span></span>s·and·<span·class="inlinecode"><span·class="id"·title="var">spec_float</span></span>s</h1> |
54 | </div> | 54 | </div> |
55 | <div·class="code"> | 55 | <div·class="code"> |
56 | <br/> | 56 | <br/> |
57 | <span·class="id"·title="keyword">Definition</span>·<a·id="prec"·class="idref"·href="#prec"><span·class="id"·title="definition">prec</span></a>·:=·53%<span·class="id"·title="var">Z</span>.<br/> | 57 | <span·class="id"·title="keyword">Definition</span>·<a·id="prec"·class="idref"·href="#prec"><span·class="id"·title="definition">prec</span></a>·:=·53%<span·class="id"·title="var">Z</span>.<br/> |
58 | <span·class="id"·title="keyword">Definition</span>·<a·id="emax"·class="idref"·href="#emax"><span·class="id"·title="definition">emax</span></a>·:=·1024%<span·class="id"·title="var">Z</span>.<br/> | 58 | <span·class="id"·title="keyword">Definition</span>·<a·id="emax"·class="idref"·href="#emax"><span·class="id"·title="definition">emax</span></a>·:=·1024%<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 | 53 | <a·id="lab155"></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 | 58 | <a·id="lab156"></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 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.ZArith.ZArith.html#"><span·class="id"·title="library">ZArith</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.ZArith.ZArith.html#"><span·class="id"·title="library">ZArith</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 | 53 | <a·id="lab167"></a><h1·class="section">Specification·of·floating-point·arithmetic</h1> |
54 | <div·class="paragraph">·</div> | 54 | <div·class="paragraph">·</div> |
55 | This·specification·is·mostly·borrowed·from·the·<span·class="inlinecode"><span·class="id"·title="var">IEEE754.Binary</span></span>·module | 55 | This·specification·is·mostly·borrowed·from·the·<span·class="inlinecode"><span·class="id"·title="var">IEEE754.Binary</span></span>·module |
56 | of·the·Flocq·library·(see·<a·href="http://flocq.gforge.inria.fr/">http://flocq.gforge.inria.fr/</a>)· | 56 | of·the·Flocq·library·(see·<a·href="http://flocq.gforge.inria.fr/">http://flocq.gforge.inria.fr/</a>)· |
57 | <div·class="paragraph">·</div> | 57 | <div·class="paragraph">·</div> |
58 | <a·id="lab | 58 | <a·id="lab168"></a><h2·class="section">Inductive·specification·of·floating-point·numbers</h2> |
59 | <div·class="paragraph">·</div> | 59 | <div·class="paragraph">·</div> |
60 | Similar·to·<span·class="inlinecode"><span·class="id"·title="var">Flocq.IEEE754.Binary.full_float</span></span>,·but·with·no·NaN·payload.· | 60 | Similar·to·<span·class="inlinecode"><span·class="id"·title="var">Flocq.IEEE754.Binary.full_float</span></span>,·but·with·no·NaN·payload.· |
61 | </div> | 61 | </div> |
62 | <div·class="code"> | 62 | <div·class="code"> |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab1255"></a><h1·class="section">Bytes</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.Init.Ltac.html#"><span·class="id"·title="library">Coq.Init.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">Coq.Init.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.Datatypes.html#"><span·class="id"·title="library">Coq.Init.Datatypes</span></a>.<br/> | 54 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Init.Datatypes.html#"><span·class="id"·title="library">Coq.Init.Datatypes</span></a>.<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="lab | 58 | <a·id="lab1261"></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 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab1260"></a><h1·class="section">Decimal·numbers</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ·These·numbers·coded·in·base·10·will·be·used·for·parsing·and·printing | 51 | ·These·numbers·coded·in·base·10·will·be·used·for·parsing·and·printing |
52 | ····other·Coq·numeral·datatypes·in·an·human-readable·way. | 52 | ····other·Coq·numeral·datatypes·in·an·human-readable·way. |
53 | ····See·the·<span·class="inlinecode"><span·class="id"·title="var">Number</span></span>·<span·class="inlinecode"><span·class="id"·title="keyword">Notation</span></span>·command. | 53 | ····See·the·<span·class="inlinecode"><span·class="id"·title="var">Number</span></span>·<span·class="inlinecode"><span·class="id"·title="keyword">Notation</span></span>·command. |
54 | ····We·represent·numbers·in·base·10·as·lists·of·decimal·digits, | 54 | ····We·represent·numbers·in·base·10·as·lists·of·decimal·digits, |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab1235"></a><h1·class="section">Hexadecimal·numbers</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ·These·numbers·coded·in·base·16·will·be·used·for·parsing·and·printing | 51 | ·These·numbers·coded·in·base·16·will·be·used·for·parsing·and·printing |
52 | ····other·Coq·numeral·datatypes·in·an·human-readable·way. | 52 | ····other·Coq·numeral·datatypes·in·an·human-readable·way. |
53 | ····See·the·<span·class="inlinecode"><span·class="id"·title="var">Number</span></span>·<span·class="inlinecode"><span·class="id"·title="keyword">Notation</span></span>·command. | 53 | ····See·the·<span·class="inlinecode"><span·class="id"·title="var">Number</span></span>·<span·class="inlinecode"><span·class="id"·title="keyword">Notation</span></span>·command. |
54 | ····We·represent·numbers·in·base·16·as·lists·of·hexadecimal·digits, | 54 | ····We·represent·numbers·in·base·16·as·lists·of·hexadecimal·digits, |
Offset 158, 32971 lines modified | Offset 158, 32971 lines modified | ||
000009d0:·733d·2269·6422·2074·6974·6c65·3d22·7661··s="id"·title="va | 000009d0:·733d·2269·6422·2074·6974·6c65·3d22·7661··s="id"·title="va | ||
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 | Diff chunk too large, falling back to line-by-line diff (32964 lines added, 32964 lines removed) | |
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·6120·6964·3d22·6c61·623 | 00000a40:·6f63·223e·0a3c·6120·6964·3d22·6c61·6231··oc">.<a·id="lab1 | ||
00000a50:·3 | 00000a50:·3235·3622·3e3c·2f61·3e3c·6831·2063·6c61··256"></a><h1·cla | ||
00000a60:·733d | 00000a60:·7373·3d22·7365·6374·696f·6e22·3e50·726f··ss="section">Pro | ||
00000a70:·6f73 | 00000a70:·706f·7369·7469·6f6e·616c·2063·6f6e·6e65··positional·conne | ||
00000a80:·7469 | 00000a80:·6374·6976·6573·3c2f·6831·3e0a·0a3c·6469··ctives</h1>..<di | ||
00000a90:·2063 | 00000a90:·7620·636c·6173·733d·2270·6172·6167·7261··v·class="paragra | ||
00000aa0:·68 | 00000aa0:·7068·223e·203c·2f64·6976·3e0a·0a20·3c73··ph">·</div>..·<s | ||
00000ab0:·616e | 00000ab0:·7061·6e20·636c·6173·733d·2269·6e6c·696e··pan·class="inlin | ||
00000ac0:·636f | 00000ac0:·6563·6f64·6522·3e3c·7370·616e·2063·6c61··ecode"><span·cla | ||
00000ad0:·733d | 00000ad0:·7373·3d22·6964·2220·7469·746c·653d·2276··ss="id"·title="v | ||
00000ae0:·72 | 00000ae0:·6172·223e·5472·7565·3c2f·7370·616e·3e3c··ar">True</span>< | ||
00000af0:·7370 | 00000af0:·2f73·7061·6e3e·2069·7320·7468·6520·616c··/span>·is·the·al | ||
00000b00:·6179 | 00000b00:·7761·7973·2074·7275·6520·7072·6f70·6f73··ways·true·propos | ||
00000b10:·7469 | 00000b10:·6974·696f·6e20·0a3c·2f64·6976·3e0a·3c64··ition·.</div>.<d | ||
00000b20:·7620 | 00000b20:·6976·2063·6c61·7373·3d22·636f·6465·223e··iv·class="code"> | ||
00000b30:·0a3c | 00000b30:·0a0a·3c62·722f·3e0a·3c73·7061·6e20·636c··..<br/>.<span·cl | ||
00000b40:·7373 | 00000b40:·6173·733d·2269·6422·2074·6974·6c65·3d22··ass="id"·title=" | ||
00000b50:·6579 | 00000b50:·6b65·7977·6f72·6422·3e49·6e64·7563·7469··keyword">Inducti | ||
00000b60:·653c | 00000b60:·7665·3c2f·7370·616e·3e20·3c61·2069·643d··ve</span>·<a·id= | ||
00000b70:·5472 | 00000b70:·2254·7275·6522·2063·6c61·7373·3d22·6964··"True"·class="id | ||
00000b80:·6566 | 00000b80:·7265·6622·2068·7265·663d·2223·5472·7565··ref"·href="#True | ||
00000b90:·3e3c | 00000b90:·223e·3c73·7061·6e20·636c·6173·733d·2269··"><span·class="i | ||
00000ba0:·2220 | 00000ba0:·6422·2074·6974·6c65·3d22·696e·6475·6374··d"·title="induct | ||
00000bb0:·7665 | 00000bb0:·6976·6522·3e54·7275·653c·2f73·7061·6e3e··ive">True</span> | ||
00000bc0:·2f61 | 00000bc0:·3c2f·613e·203a·203c·7370·616e·2063·6c61··</a>·:·<span·cla | ||
00000bd0:·733d | 00000bd0:·7373·3d22·6964·2220·7469·746c·653d·226b··ss="id"·title="k | ||
00000be0:·79 | 00000be0:·6579·776f·7264·223e·5072·6f70·3c2f·7370··eyword">Prop</sp | ||
00000bf0:·6e3e | 00000bf0:·616e·3e20·3a3d·3c62·722f·3e0a·266e·6273··an>·:=<br/>.&nbs | ||
00000c00:·3b26 | 00000c00:·703b·266e·6273·703b·3c61·2069·643d·2249··p; <a·id="I | ||
00000c10:·2063 | 00000c10:·2220·636c·6173·733d·2269·6472·6566·2220··"·class="idref"· | ||
00000c20:·7265 | 00000c20:·6872·6566·3d22·2349·223e·3c73·7061·6e20··href="#I"><span· | ||
00000c30:·6c61 | 00000c30:·636c·6173·733d·2269·6422·2074·6974·6c65··class="id"·title | ||
00000c40:·2263 | 00000c40:·3d22·636f·6e73·7472·7563·746f·7222·3e49··="constructor">I | ||
00000c50:·2f73 | 00000c50:·3c2f·7370·616e·3e3c·2f61·3e20·3a20·3c61··</span></a>·:·<a | ||
00000c60:·636c | 00000c60:·2063·6c61·7373·3d22·6964·7265·6622·2068···class="idref"·h | ||
00000c70:·65 | 00000c70:·7265·663d·2243·6f71·2e49·6e69·742e·4c6f··ref="Coq.Init.Lo | ||
00000c80:·6963 | 00000c80:·6769·632e·6874·6d6c·2354·7275·653a·3122··gic.html#True:1" | ||
00000c90:·3c73 | 00000c90:·3e3c·7370·616e·2063·6c61·7373·3d22·6964··><span·class="id | ||
00000ca0:·2074 | 00000ca0:·2220·7469·746c·653d·2269·6e64·7563·7469··"·title="inducti | ||
00000cb0:·65 | 00000cb0:·7665·223e·5472·7565·3c2f·7370·616e·3e3c··ve">True</span>< | ||
00000cc0:·613e | 00000cc0:·2f61·3e2e·3c62·722f·3e0a·0a3c·6272·2f3e··/a>.<br/>..<br/> | ||
00000cd0:·3c73 | 00000cd0:·0a3c·7370·616e·2063·6c61·7373·3d22·6964··.<span·class="id | ||
00000ce0:·2074 | 00000ce0:·2220·7469·746c·653d·226b·6579·776f·7264··"·title="keyword | ||
00000cf0:·3e52 | 00000cf0:·223e·5265·6769·7374·6572·3c2f·7370·616e··">Register</span | ||
00000d00:·203c | 00000d00:·3e20·3c73·7061·6e20·636c·6173·733d·2269··>·<span·class="i | ||
00000d10:·2220 | 00000d10:·6422·2074·6974·6c65·3d22·7661·7222·3e54··d"·title="var">T | ||
00000d20:·7565 | 00000d20:·7275·653c·2f73·7061·6e3e·203c·7370·616e··rue</span>·<span | ||
00000d30:·636c | 00000d30:·2063·6c61·7373·3d22·6964·2220·7469·746c···class="id"·titl | ||
00000d40:·3d | 00000d40:·653d·226b·6579·776f·7264·223e·6173·3c2f··e="keyword">as</ | ||
00000d50:·7061 | 00000d50:·7370·616e·3e20·3c73·7061·6e20·636c·6173··span>·<span·clas | ||
00000d60:·3d | 00000d60:·733d·2269·6422·2074·6974·6c65·3d22·7661··s="id"·title="va | ||
00000d70:·223e | 00000d70:·7222·3e63·6f72·652e·5472·7565·2e74·7970··r">core.True.typ | ||
00000d80:·3c2f | 00000d80:·653c·2f73·7061·6e3e·2e3c·6272·2f3e·0a3c··e</span>.<br/>.< | ||
00000d90:·7061 | 00000d90:·7370·616e·2063·6c61·7373·3d22·6964·2220··span·class="id"· | ||
00000da0:·6974 | 00000da0:·7469·746c·653d·226b·6579·776f·7264·223e··title="keyword"> | ||
00000db0:·6567 | 00000db0:·5265·6769·7374·6572·3c2f·7370·616e·3e20··Register</span>· | ||
00000dc0:·7370 | 00000dc0:·3c73·7061·6e20·636c·6173·733d·2269·6422··<span·class="id" | ||
00000dd0:·7469 | 00000dd0:·2074·6974·6c65·3d22·7661·7222·3e49·3c2f···title="var">I</ | ||
00000de0:·7061 | 00000de0:·7370·616e·3e20·3c73·7061·6e20·636c·6173··span>·<span·clas | ||
00000df0:·3d | 00000df0:·733d·2269·6422·2074·6974·6c65·3d22·6b65··s="id"·title="ke | ||
00000e00:·776f | 00000e00:·7977·6f72·6422·3e61·733c·2f73·7061·6e3e··yword">as</span> | ||
00000e10:·3c73 | 00000e10:·203c·7370·616e·2063·6c61·7373·3d22·6964···<span·class="id | ||
00000e20:·2074 | 00000e20:·2220·7469·746c·653d·2276·6172·223e·636f··"·title="var">co | ||
00000e30:·652e | 00000e30:·7265·2e54·7275·652e·493c·2f73·7061·6e3e··re.True.I</span> | ||
00000e40:·3c62 | 00000e40:·2e3c·6272·2f3e·0a0a·3c62·722f·3e0a·3c2f··.<br/>..<br/>.</ | ||
00000e50:·6976 | 00000e50:·6469·763e·0a0a·3c64·6976·2063·6c61·7373··div>..<div·class | ||
00000e60:·2264 | 00000e60:·3d22·646f·6322·3e0a·3c73·7061·6e20·636c··="doc">.<span·cl | ||
00000e70:·7373 | 00000e70:·6173·733d·2269·6e6c·696e·6563·6f64·6522··ass="inlinecode" | ||
00000e80:·3c73 | 00000e80:·3e3c·7370·616e·2063·6c61·7373·3d22·6964··><span·class="id | ||
00000e90:·2074 | 00000e90:·2220·7469·746c·653d·2276·6172·223e·4661··"·title="var">Fa | ||
00000ea0:·7365 | 00000ea0:·6c73·653c·2f73·7061·6e3e·3c2f·7370·616e··lse</span></span | ||
00000eb0:·2069 | 00000eb0:·3e20·6973·2074·6865·2061·6c77·6179·7320··>·is·the·always· | ||
00000ec0:·616c | 00000ec0:·6661·6c73·6520·7072·6f70·6f73·6974·696f··false·propositio | ||
00000ed0:·200a | 00000ed0:·6e20·0a3c·2f64·6976·3e0a·3c64·6976·2063··n·.</div>.<div·c | ||
00000ee0:·6173 | 00000ee0:·6c61·7373·3d22·636f·6465·223e·0a3c·7370··lass="code">.<sp | ||
00000ef0:·6e20 | 00000ef0:·616e·2063·6c61·7373·3d22·6964·2220·7469··an·class="id"·ti | ||
00000f00:·6c65 | 00000f00:·746c·653d·226b·6579·776f·7264·223e·496e··tle="keyword">In | ||
00000f10:·7563 | 00000f10:·6475·6374·6976·653c·2f73·7061·6e3e·203c··ductive</span>·< | ||
00000f20:·2069 | 00000f20:·6120·6964·3d22·4661·6c73·6522·2063·6c61··a·id="False"·cla | ||
00000f30:·733d | 00000f30:·7373·3d22·6964·7265·6622·2068·7265·663d··ss="idref"·href= | ||
00000f40:·2346 | 00000f40:·2223·4661·6c73·6522·3e3c·7370·616e·2063··"#False"><span·c | ||
00000f50:·6173 | 00000f50:·6c61·7373·3d22·6964·2220·7469·746c·653d··lass="id"·title= | ||
00000f60:·696e | 00000f60:·2269·6e64·7563·7469·7665·223e·4661·6c73··"inductive">Fals | ||
00000f70:·3c2f | 00000f70:·653c·2f73·7061·6e3e·3c2f·613e·203a·203c··e</span></a>·:·< | ||
00000f80:·7061 | 00000f80:·7370·616e·2063·6c61·7373·3d22·6964·2220··span·class="id"· | ||
00000f90:·6974 | 00000f90:·7469·746c·653d·226b·6579·776f·7264·223e··title="keyword"> | ||
00000fa0:·726f | 00000fa0:·5072·6f70·3c2f·7370·616e·3e20·3a3d·2e3c··Prop</span>·:=.< | ||
00000fb0:·722f | 00000fb0:·6272·2f3e·0a0a·3c62·722f·3e0a·3c73·7061··br/>..<br/>.<spa | ||
00000fc0:·2063 | 00000fc0:·6e20·636c·6173·733d·2269·6422·2074·6974··n·class="id"·tit | ||
00000fd0:·653d | 00000fd0:·6c65·3d22·6b65·7977·6f72·6422·3e52·6567··le="keyword">Reg | ||
00000fe0:·7374 | 00000fe0:·6973·7465·723c·2f73·7061·6e3e·203c·7370··ister</span>·<sp | ||
00000ff0:·6e20 | 00000ff0:·616e·2063·6c61·7373·3d22·6964·2220·7469··an·class="id"·ti | ||
00001000:·6c65 | 00001000:·746c·653d·2276·6172·223e·4661·6c73·653c··tle="var">False< | ||
00001010:·7370 | 00001010:·2f73·7061·6e3e·203c·7370·616e·2063·6c61··/span>·<span·cla | ||
00001020:·733d | 00001020:·7373·3d22·6964·2220·7469·746c·653d·226b··ss="id"·title="k | ||
00001030:·79 | 00001030:·6579·776f·7264·223e·6173·3c2f·7370·616e··eyword">as</span | ||
00001040:·203c | 00001040:·3e20·3c73·7061·6e20·636c·6173·733d·2269··>·<span·class="i | ||
00001050:·2220 | 00001050:·6422·2074·6974·6c65·3d22·7661·7222·3e63··d"·title="var">c | ||
00001060:·7265 | 00001060:·6f72·652e·4661·6c73·652e·7479·7065·3c2f··ore.False.type</ | ||
00001070:·7061 | 00001070:·7370·616e·3e2e·3c62·722f·3e0a·0a3c·6272··span>.<br/>..<br | ||
00001080:·3e0a | 00001080:·2f3e·0a3c·2f64·6976·3e0a·0a3c·6469·7620··/>.</div>..<div· | ||
00001090:·6c61 | 00001090:·636c·6173·733d·2264·6f63·223e·0a3c·7370··class="doc">.<sp | ||
000010a0:·6e20 | 000010a0:·616e·2063·6c61·7373·3d22·696e·6c69·6e65··an·class="inline | ||
000010b0:·6f64 | 000010b0:·636f·6465·223e·3c73·7061·6e20·636c·6173··code"><span·clas | ||
000010c0:·3d | 000010c0:·733d·2269·6422·2074·6974·6c65·3d22·7661··s="id"·title="va | ||
000010d0:·223e | 000010d0:·7222·3e6e·6f74·3c2f·7370·616e·3e3c·2f73··r">not</span></s | ||
000010e0:·616e | 000010e0:·7061·6e3e·203c·7370·616e·2063·6c61·7373··pan>·<span·class | ||
000010f0:·2269 | 000010f0:·3d22·696e·6c69·6e65·636f·6465·223e·3c73··="inlinecode"><s | ||
00001100:·616e | 00001100:·7061·6e20·636c·6173·733d·2269·6422·2074··pan·class="id"·t | ||
00001110:·746c | 00001110:·6974·6c65·3d22·7661·7222·3e41·3c2f·7370··itle="var">A</sp | ||
00001120:·6e3e | 00001120:·616e·3e3c·2f73·7061·6e3e·2c20·7772·6974··an></span>,·writ | ||
00001130:·656e | 00001130:·7465·6e20·3c73·7061·6e20·636c·6173·733d··ten·<span·class= | ||
00001140:·696e | 00001140:·2269·6e6c·696e·6563·6f64·6522·3e7e·3c73··"inlinecode">~<s | ||
00001150:·616e | 00001150:·7061·6e20·636c·6173·733d·2269·6422·2074··pan·class="id"·t | ||
00001160:·746c | 00001160:·6974·6c65·3d22·7661·7222·3e41·3c2f·7370··itle="var">A</sp | ||
00001170:·6e3e | 00001170:·616e·3e3c·2f73·7061·6e3e·2c20·6973·2074··an></span>,·is·t | ||
00001180:·6520 | 00001180:·6865·206e·6567·6174·696f·6e20·6f66·203c··he·negation·of·< | ||
00001190:·7061 | 00001190:·7370·616e·2063·6c61·7373·3d22·696e·6c69··span·class="inli | ||
000011a0:·6563 | 000011a0:·6e65·636f·6465·223e·3c73·7061·6e20·636c··necode"><span·cl | ||
Max diff block lines reached; -1/4549533 bytes (-0.00%) of diff not shown. |
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="lab | 55 | <a·id="lab1241"></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 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab1238"></a><h1·class="section">Decimal·or·Hexadecimal·numbers</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.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>.<br/> | 53 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</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>.<br/> |
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="lab | 56 | <a·id="lab1236"></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">elimtype</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">elimtype</span></span>·<span·class="inlinecode"><span·class="id"·title="var">False</span></span> |
60 | ····and·other·<span·class="inlinecode"><span·class="id"·title="tactic">cut</span></span>·<span·class="inlinecode"><span·class="id"·title="var">False</span></span>.· | 60 | ····and·other·<span·class="inlinecode"><span·class="id"·title="tactic">cut</span></span>·<span·class="inlinecode"><span·class="id"·title="var">False</span></span>.· |
61 | </div> | 61 | </div> |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab1240"></a><h1·class="section">The·tauto·and·intuition·tactics</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.Init.Notations.html#"><span·class="id"·title="library">Notations</span></a>.<br/> | 53 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Init.Notations.html#"><span·class="id"·title="library">Notations</span></a>.<br/> |
54 | <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.Ltac.html#"><span·class="id"·title="library">Ltac</span></a>.<br/> |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab1239"></a><h1·class="section">This·module·proves·the·validity·of</h1> |
50 | <ul·class="doclist"> | 50 | <ul·class="doclist"> |
51 | <li>·well-founded·recursion·(also·known·as·course·of·values) | 51 | <li>·well-founded·recursion·(also·known·as·course·of·values) |
52 | </li> | 52 | </li> |
53 | <li>·well-founded·induction | 53 | <li>·well-founded·induction |
Offset 51, 15 lines modified | Offset 51, 15 lines modified | ||
51 | <br/> | 51 | <br/> |
52 | <span·class="id"·title="keyword">Set·Implicit·Arguments</span>.<br/> | 52 | <span·class="id"·title="keyword">Set·Implicit·Arguments</span>.<br/> |
53 | <br/> | 53 | <br/> |
54 | </div> | 54 | </div> |
55 | <div·class="doc"> | 55 | <div·class="doc"> |
56 | <a·id="lab | 56 | <a·id="lab942"></a><h1·class="section">Basics:·definition·of·polymorphic·lists·and·some·operations</h1> |
57 | <div·class="paragraph">·</div> | 57 | <div·class="paragraph">·</div> |
58 | ·The·definition·of·<span·class="inlinecode"><span·class="id"·title="var">list</span></span>·is·now·in·<span·class="inlinecode"><span·class="id"·title="var">Init</span>/<span·class="id"·title="var">Datatypes</span></span>, | 58 | ·The·definition·of·<span·class="inlinecode"><span·class="id"·title="var">list</span></span>·is·now·in·<span·class="inlinecode"><span·class="id"·title="var">Init</span>/<span·class="id"·title="var">Datatypes</span></span>, |
59 | ····as·well·as·the·definitions·of·<span·class="inlinecode"><span·class="id"·title="var">length</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">app</span></span>· | 59 | ····as·well·as·the·definitions·of·<span·class="inlinecode"><span·class="id"·title="var">length</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">app</span></span>· |
60 | </div> | 60 | </div> |
61 | <div·class="code"> | 61 | <div·class="code"> |
Offset 49, 15 lines modified | Offset 49, 15 lines modified | ||
49 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Export</span>·<a·class="idref"·href="Coq.Lists.List.html#"><span·class="id"·title="library">List</span></a>.<br/> | 49 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Export</span>·<a·class="idref"·href="Coq.Lists.List.html#"><span·class="id"·title="library">List</span></a>.<br/> |
50 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Export</span>·<a·class="idref"·href="Coq.Sorting.Sorted.html#"><span·class="id"·title="library">Sorted</span></a>.<br/> | 50 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Export</span>·<a·class="idref"·href="Coq.Sorting.Sorted.html#"><span·class="id"·title="library">Sorted</span></a>.<br/> |
51 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Export</span>·<a·class="idref"·href="Coq.Setoids.Setoid.html#"><span·class="id"·title="library">Setoid</span></a>·<a·class="idref"·href="Coq.Program.Basics.html#"><span·class="id"·title="library">Basics</span></a>·<a·class="idref"·href="Coq.Classes.Morphisms.html#"><span·class="id"·title="library">Morphisms</span></a>.<br/> | 51 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Export</span>·<a·class="idref"·href="Coq.Setoids.Setoid.html#"><span·class="id"·title="library">Setoid</span></a>·<a·class="idref"·href="Coq.Program.Basics.html#"><span·class="id"·title="library">Basics</span></a>·<a·class="idref"·href="Coq.Classes.Morphisms.html#"><span·class="id"·title="library">Morphisms</span></a>.<br/> |
52 | <span·class="id"·title="keyword">Set·Implicit·Arguments</span>.<br/> | 52 | <span·class="id"·title="keyword">Set·Implicit·Arguments</span>.<br/> |
53 | </div> | 53 | </div> |
54 | <div·class="doc"> | 54 | <div·class="doc"> |
55 | <a·id="lab | 55 | <a·id="lab974"></a><h1·class="section">Logical·relations·over·lists·with·respect·to·a·setoid·equality</h1> |
56 | ······or·ordering.· | 56 | ······or·ordering.· |
57 | <div·class="paragraph">·</div> | 57 | <div·class="paragraph">·</div> |
58 | ·This·can·be·seen·as·a·complement·of·predicate·<span·class="inlinecode"><span·class="id"·title="var">lelistA</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">sort</span></span> | 58 | ·This·can·be·seen·as·a·complement·of·predicate·<span·class="inlinecode"><span·class="id"·title="var">lelistA</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">sort</span></span> |
59 | ····found·in·<span·class="inlinecode"><span·class="id"·title="var">Sorting</span></span>.· | 59 | ····found·in·<span·class="inlinecode"><span·class="id"·title="var">Sorting</span></span>.· |
60 | </div> | 60 | </div> |
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.Logic.Eqdep_dec.html#"><span·class="id"·title="library">Eqdep_dec</span></a>.<br/> | 49 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Logic.Eqdep_dec.html#"><span·class="id"·title="library">Eqdep_dec</span></a>.<br/> |
50 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Lists.Streams.html#"><span·class="id"·title="library">Streams</span></a>.<br/> | 50 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Lists.Streams.html#"><span·class="id"·title="library">Streams</span></a>.<br/> |
51 | <br/> | 51 | <br/> |
52 | </div> | 52 | </div> |
53 | <div·class="doc"> | 53 | <div·class="doc"> |
54 | <a·id="lab | 54 | <a·id="lab973"></a><h1·class="section">Memoization</h1> |
55 | <div·class="paragraph">·</div> | 55 | <div·class="paragraph">·</div> |
56 | ·Successive·outputs·of·a·given·function·<span·class="inlinecode"><span·class="id"·title="var">f</span></span>·are·stored·in | 56 | ·Successive·outputs·of·a·given·function·<span·class="inlinecode"><span·class="id"·title="var">f</span></span>·are·stored·in |
57 | ····a·stream·in·order·to·avoid·duplicated·computations.· | 57 | ····a·stream·in·order·to·avoid·duplicated·computations.· |
58 | </div> | 58 | </div> |
59 | <div·class="code"> | 59 | <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="lab | 51 | ·······intuitionistic·logic.·<a·id="lab892"></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="lab | 134 | <a·id="lab921"></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/> |
Offset 110, 15 lines modified | Offset 110, 15 lines modified | ||
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="lab8 | 113 | <a·id="lab824"></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> |
Offset 104, 15 lines modified | Offset 104, 15 lines modified | ||
104 | <div·class="code"> | 104 | <div·class="code"> |
105 | <span·class="id"·title="keyword">Require</span>·<a·class="idref"·href="Coq.Logic.ClassicalFacts.html#"><span·class="id"·title="library">ClassicalFacts</span></a>·<a·class="idref"·href="Coq.Logic.ChoiceFacts.html#"><span·class="id"·title="library">ChoiceFacts</span></a>.<br/> | 105 | <span·class="id"·title="keyword">Require</span>·<a·class="idref"·href="Coq.Logic.ClassicalFacts.html#"><span·class="id"·title="library">ClassicalFacts</span></a>·<a·class="idref"·href="Coq.Logic.ChoiceFacts.html#"><span·class="id"·title="library">ChoiceFacts</span></a>.<br/> |
106 | <br/> | 106 | <br/> |
107 | </div> | 107 | </div> |
108 | <div·class="doc"> | 108 | <div·class="doc"> |
109 | <a·id="lab | 109 | <a·id="lab838"></a><h1·class="section">Pred.·Ext.·+·Rel.·Axiom·of·Choice·->·Excluded-Middle</h1> |
110 | </div> | 110 | </div> |
111 | <div·class="code"> | 111 | <div·class="code"> |
112 | <br/> | 112 | <br/> |
113 | <span·class="id"·title="keyword">Section</span>·<a·id="PredExt_RelChoice_imp_EM"·class="idref"·href="#PredExt_RelChoice_imp_EM"><span·class="id"·title="section">PredExt_RelChoice_imp_EM</span></a>.<br/> | 113 | <span·class="id"·title="keyword">Section</span>·<a·id="PredExt_RelChoice_imp_EM"·class="idref"·href="#PredExt_RelChoice_imp_EM"><span·class="id"·title="section">PredExt_RelChoice_imp_EM</span></a>.<br/> |
Offset 112, 15 lines modified | Offset 112, 15 lines modified | ||
112 | ···equalities·assuming·axiom·eq_rect_eq | 112 | ···equalities·assuming·axiom·eq_rect_eq |
113 | <div·class="paragraph">·</div> | 113 | <div·class="paragraph">·</div> |
114 | <div·class="paragraph">·</div> | 114 | <div·class="paragraph">·</div> |
115 | <a·id="lab | 115 | <a·id="lab881"></a><h1·class="section">Definition·of·dependent·equality·and·equivalence·with·equality·of·dependent·pairs</h1> |
116 | </div> | 116 | </div> |
117 | <div·class="code"> | 117 | <div·class="code"> |
118 | <br/> | 118 | <br/> |
119 | <span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Init.Logic.html#EqNotations"><span·class="id"·title="module">EqNotations</span></a>.<br/> | 119 | <span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Init.Logic.html#EqNotations"><span·class="id"·title="module">EqNotations</span></a>.<br/> |
Offset 84, 15 lines modified | Offset 84, 15 lines modified | ||
84 | ·····from·a·proof·of·decidability·of·equality·for·a·set·in·Set | 84 | ·····from·a·proof·of·decidability·of·equality·for·a·set·in·Set |
85 | <div·class="paragraph">·</div> | 85 | <div·class="paragraph">·</div> |
86 | <div·class="paragraph">·</div> | 86 | <div·class="paragraph">·</div> |
87 | <a·id="lab8 | 87 | <a·id="lab884"></a><h1·class="section">Streicher's·K·and·injectivity·of·dependent·pair·hold·on·decidable·types</h1> |
88 | </div> | 88 | </div> |
89 | <div·class="code"> | 89 | <div·class="code"> |
90 | <br/> | 90 | <br/> |
91 | <span·class="id"·title="keyword">Set·Implicit·Arguments</span>.<br/> | 91 | <span·class="id"·title="keyword">Set·Implicit·Arguments</span>.<br/> |
Offset 101, 15 lines modified | Offset 101, 15 lines modified | ||
101 | <br/> | 101 | <br/> |
102 | <span·class="id"·title="keyword">Set·Implicit·Arguments</span>.<br/> | 102 | <span·class="id"·title="keyword">Set·Implicit·Arguments</span>.<br/> |
103 | <br/> | 103 | <br/> |
104 | </div> | 104 | </div> |
105 | <div·class="doc"> | 105 | <div·class="doc"> |
106 | <a·id="lab9 | 106 | <a·id="lab922"></a><h1·class="section">Definitions</h1> |
107 | <div·class="paragraph">·</div> | 107 | <div·class="paragraph">·</div> |
108 | ·Being·an·inverse· | 108 | ·Being·an·inverse· |
109 | </div> | 109 | </div> |
110 | <div·class="code"> | 110 | <div·class="code"> |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab926"></a><h1·class="section">Functions·on·finite·domains</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ·Main·result·:·for·functions·<span·class="inlinecode"><span·class="id"·title="var">f</span>:<span·class="id"·title="var">A</span>-><span·class="id"·title="var">A</span></span>·with·finite·<span·class="inlinecode"><span·class="id"·title="var">A</span></span>, | 51 | ·Main·result·:·for·functions·<span·class="inlinecode"><span·class="id"·title="var">f</span>:<span·class="id"·title="var">A</span>-><span·class="id"·title="var">A</span></span>·with·finite·<span·class="inlinecode"><span·class="id"·title="var">A</span></span>, |
52 | ····f·injective·<->·f·bijective·<->·f·surjective.· | 52 | ····f·injective·<->·f·bijective·<->·f·surjective.· |
53 | </div> | 53 | </div> |
54 | <div·class="code"> | 54 | <div·class="code"> |
Offset 172, 15 lines modified | Offset 172, 15 lines modified | ||
172 | <br/> | 172 | <br/> |
173 | <br/> | 173 | <br/> |
174 | </div> | 174 | </div> |
175 | <div·class="doc"> | 175 | <div·class="doc"> |
176 | <a·id="lab8 | 176 | <a·id="lab841"></a><h1·class="section">A·modular·proof·of·Hurkens's·paradox.</h1> |
177 | <div·class="paragraph">·</div> | 177 | <div·class="paragraph">·</div> |
178 | ·It·relies·on·an·axiomatisation·of·a·shallow·embedding·of·system·U- | 178 | ·It·relies·on·an·axiomatisation·of·a·shallow·embedding·of·system·U- |
179 | ····(i.e.··types·of·U-·are·interpreted·by·types·of·Coq).·The | 179 | ····(i.e.··types·of·U-·are·interpreted·by·types·of·Coq).·The |
180 | ····universes·are·encoded·in·a·style,·due·to·Martin-Löf,·where·they | 180 | ····universes·are·encoded·in·a·style,·due·to·Martin-Löf,·where·they |
181 | ····are·given·by·a·set·of·names·and·a·family·<span·class="inlinecode"><span·class="id"·title="var">El</span>:<span·class="id"·title="var">Name</span>-><span·class="id"·title="keyword">Type</span></span>·which | 181 | ····are·given·by·a·set·of·names·and·a·family·<span·class="inlinecode"><span·class="id"·title="var">El</span>:<span·class="id"·title="var">Name</span>-><span·class="id"·title="keyword">Type</span></span>·which |
Offset 113, 15 lines modified | Offset 113, 15 lines modified | ||
113 | <br/> | 113 | <br/> |
114 | <span·class="id"·title="keyword">Set·Implicit·Arguments</span>.<br/> | 114 | <span·class="id"·title="keyword">Set·Implicit·Arguments</span>.<br/> |
115 | <br/> | 115 | <br/> |
116 | </div> | 116 | </div> |
117 | <div·class="doc"> | 117 | <div·class="doc"> |
118 | <a·id="lab8 | 118 | <a·id="lab887"></a><h1·class="section">Definitions</h1> |
119 | <div·class="paragraph">·</div> | 119 | <div·class="paragraph">·</div> |
120 | ·Propositional·extensionality· | 120 | ·Propositional·extensionality· |
121 | </div> | 121 | </div> |
122 | <div·class="code"> | 122 | <div·class="code"> |
Offset 45, 15 lines modified | Offset 45, 15 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="lab8 | 49 | <a·id="lab880"></a><h1·class="section">Basic·facts·about·Prop·as·a·type</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ·An·intuitionistic·theorem·from·topos·theory·<span·class="inlinecode">[<span·class="id"·title="var">LambekScott</span>]</span> | 51 | ·An·intuitionistic·theorem·from·topos·theory·<span·class="inlinecode">[<span·class="id"·title="var">LambekScott</span>]</span> |
52 | <div·class="paragraph">·</div> | 52 | <div·class="paragraph">·</div> |
Offset 45, 15 lines modified | Offset 45, 15 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="lab8 | 49 | <a·id="lab879"></a><h1·class="section">The·Set·universe·seen·as·a·synonym·for·Type</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ·After·loading·this·file,·Set·becomes·just·another·name·for·Type. | 51 | ·After·loading·this·file,·Set·becomes·just·another·name·for·Type. |
52 | ····This·allows·easily·performing·a·Set-to-Type·migration,·or·at·least | 52 | ····This·allows·easily·performing·a·Set-to-Type·migration,·or·at·least |
53 | ····test·whether·a·development·relies·or·not·on·specific·features·of | 53 | ····test·whether·a·development·relies·or·not·on·specific·features·of |
54 | ····Set:·simply·insert·some·Require·Export·of·this·file·at·starting | 54 | ····Set:·simply·insert·some·Require·Export·of·this·file·at·starting |
Offset 45, 15 lines modified | Offset 45, 15 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="lab1 | 49 | <a·id="lab1171"></a><h1·class="section">MSetAVL·:·Implementation·of·MSetInterface·via·AVL·trees</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ·This·module·implements·finite·sets·using·AVL·trees. | 51 | ·This·module·implements·finite·sets·using·AVL·trees. |
52 | ····It·follows·the·implementation·from·Ocaml's·standard·library, | 52 | ····It·follows·the·implementation·from·Ocaml's·standard·library, |
53 | <div·class="paragraph">·</div> | 53 | <div·class="paragraph">·</div> |
Offset 71, 15 lines modified | Offset 71, 15 lines modified | ||
71 | <span·class="id"·title="keyword">Module</span>·<a·id="WDecideOn"·class="idref"·href="#WDecideOn"><span·class="id"·title="module">WDecideOn</span></a>·(<span·class="id"·title="var">E</span>·:·<a·class="idref"·href="Coq.Structures.Equalities.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.MSets.MSetInterface.html#WSetsOn"><span·class="id"·title="module">WSetsOn</span></a>·<a·class="idref"·href="Coq.MSets.MSetDecide.html#E"><span·class="id"·title="module">E</span></a>).<br/> | 71 | <span·class="id"·title="keyword">Module</span>·<a·id="WDecideOn"·class="idref"·href="#WDecideOn"><span·class="id"·title="module">WDecideOn</span></a>·(<span·class="id"·title="var">E</span>·:·<a·class="idref"·href="Coq.Structures.Equalities.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.MSets.MSetInterface.html#WSetsOn"><span·class="id"·title="module">WSetsOn</span></a>·<a·class="idref"·href="Coq.MSets.MSetDecide.html#E"><span·class="id"·title="module">E</span></a>).<br/> |
72 | <span·class="id"·title="keyword">Module</span>·<a·id="WDecideOn.F"·class="idref"·href="#WDecideOn.F"><span·class="id"·title="module">F</span></a>·:=·<a·class="idref"·href="Coq.MSets.MSetFacts.html#WFactsOn"><span·class="id"·title="module">MSetFacts.WFactsOn</span></a>·<a·class="idref"·href="Coq.MSets.MSetDecide.html#E"><span·class="id"·title="module">E</span></a>·<a·class="idref"·href="Coq.MSets.MSetDecide.html#M"><span·class="id"·title="module">M</span></a>.<br/> | 72 | <span·class="id"·title="keyword">Module</span>·<a·id="WDecideOn.F"·class="idref"·href="#WDecideOn.F"><span·class="id"·title="module">F</span></a>·:=·<a·class="idref"·href="Coq.MSets.MSetFacts.html#WFactsOn"><span·class="id"·title="module">MSetFacts.WFactsOn</span></a>·<a·class="idref"·href="Coq.MSets.MSetDecide.html#E"><span·class="id"·title="module">E</span></a>·<a·class="idref"·href="Coq.MSets.MSetDecide.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="lab1 | 76 | <a·id="lab1127"></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, 15 lines modified | Offset 45, 15 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="lab1 | 49 | <a·id="lab1143"></a><h1·class="section">Finite·sets·library</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ·This·module·proves·many·properties·of·finite·sets·that | 51 | ·This·module·proves·many·properties·of·finite·sets·that |
52 | ····are·consequences·of·the·axiomatization·in·<span·class="inlinecode"><span·class="id"·title="var">FsetInterface</span></span> | 52 | ····are·consequences·of·the·axiomatization·in·<span·class="inlinecode"><span·class="id"·title="var">FsetInterface</span></span> |
53 | ····Contrary·to·the·functor·in·<span·class="inlinecode"><span·class="id"·title="var">FsetProperties</span></span>·it·uses | 53 | ····Contrary·to·the·functor·in·<span·class="inlinecode"><span·class="id"·title="var">FsetProperties</span></span>·it·uses |
54 | ····sets·operations·instead·of·predicates·over·sets,·i.e. | 54 | ····sets·operations·instead·of·predicates·over·sets,·i.e. |
Offset 45, 15 lines modified | Offset 45, 15 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="lab1 | 49 | <a·id="lab1205"></a><h1·class="section">Finite·sets·library</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ·This·functor·derives·additional·facts·from·<span·class="inlinecode"><span·class="id"·title="var">MSetInterface.S</span></span>.·These | 51 | ·This·functor·derives·additional·facts·from·<span·class="inlinecode"><span·class="id"·title="var">MSetInterface.S</span></span>.·These |
52 | ··facts·are·mainly·the·specifications·of·<span·class="inlinecode"><span·class="id"·title="var">MSetInterface.S</span></span>·written·using | 52 | ··facts·are·mainly·the·specifications·of·<span·class="inlinecode"><span·class="id"·title="var">MSetInterface.S</span></span>·written·using |
53 | ··different·styles:·equivalence·and·boolean·equalities. | 53 | ··different·styles:·equivalence·and·boolean·equalities. |
54 | ··Moreover,·we·prove·that·<span·class="inlinecode"><span·class="id"·title="var">E.Eq</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">Equal</span></span>·are·setoid·equalities. | 54 | ··Moreover,·we·prove·that·<span·class="inlinecode"><span·class="id"·title="var">E.Eq</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">Equal</span></span>·are·setoid·equalities. |
Offset 45, 15 lines modified | Offset 45, 15 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="lab1 | 49 | <a·id="lab1144"></a><h1·class="section">MSetGenTree·:·sets·via·generic·trees</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ····This·module·factorizes·common·parts·in·implementations | 51 | ····This·module·factorizes·common·parts·in·implementations |
52 | ····of·finite·sets·as·AVL·trees·and·as·Red-Black·trees.·The·nodes | 52 | ····of·finite·sets·as·AVL·trees·and·as·Red-Black·trees.·The·nodes |
53 | ····of·the·trees·defined·here·include·an·generic·information | 53 | ····of·the·trees·defined·here·include·an·generic·information |
Offset 45, 15 lines modified | Offset 45, 15 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="lab1 | 49 | <a·id="lab1078"></a><h1·class="section">Finite·set·library</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ·Set·interfaces,·inspired·by·the·one·of·Ocaml.·When·compared·with | 51 | ·Set·interfaces,·inspired·by·the·one·of·Ocaml.·When·compared·with |
52 | ····Ocaml,·the·main·differences·are: | 52 | ····Ocaml,·the·main·differences·are: |
53 | <ul·class="doclist"> | 53 | <ul·class="doclist"> |
54 | <li>·the·lack·of·<span·class="inlinecode"><span·class="id"·title="var">iter</span></span>·function,·useless·since·Coq·is·purely·functional | 54 | <li>·the·lack·of·<span·class="inlinecode"><span·class="id"·title="var">iter</span></span>·function,·useless·since·Coq·is·purely·functional |
Offset 45, 15 lines modified | Offset 45, 15 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="lab1 | 49 | <a·id="lab1073"></a><h1·class="section">Finite·sets·library</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ·This·file·proposes·an·implementation·of·the·non-dependent | 51 | ·This·file·proposes·an·implementation·of·the·non-dependent |
52 | ····interface·<span·class="inlinecode"><span·class="id"·title="var">MSetInterface.S</span></span>·using·strictly·ordered·list.· | 52 | ····interface·<span·class="inlinecode"><span·class="id"·title="var">MSetInterface.S</span></span>·using·strictly·ordered·list.· |
53 | </div> | 53 | </div> |
54 | <div·class="code"> | 54 | <div·class="code"> |
Offset 45, 15 lines modified | Offset 45, 15 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="lab1 | 49 | <a·id="lab1054"></a><h1·class="section">Finite·sets·library</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ·This·functor·derives·additional·properties·from·<span·class="inlinecode"><span·class="id"·title="var">MSetInterface.S</span></span>. | 51 | ·This·functor·derives·additional·properties·from·<span·class="inlinecode"><span·class="id"·title="var">MSetInterface.S</span></span>. |
52 | ····Contrary·to·the·functor·in·<span·class="inlinecode"><span·class="id"·title="var">MSetEqProperties</span></span>·it·uses | 52 | ····Contrary·to·the·functor·in·<span·class="inlinecode"><span·class="id"·title="var">MSetEqProperties</span></span>·it·uses |
53 | ····predicates·over·sets·instead·of·sets·operations,·i.e. | 53 | ····predicates·over·sets·instead·of·sets·operations,·i.e. |
54 | ····<span·class="inlinecode"><span·class="id"·title="var">In</span></span>·<span·class="inlinecode"><span·class="id"·title="var">x</span></span>·<span·class="inlinecode"><span·class="id"·title="var">s</span></span>·instead·of·<span·class="inlinecode"><span·class="id"·title="var">mem</span></span>·<span·class="inlinecode"><span·class="id"·title="var">x</span></span>·<span·class="inlinecode"><span·class="id"·title="var">s</span>=<span·class="id"·title="var">true</span></span>, | 54 | ····<span·class="inlinecode"><span·class="id"·title="var">In</span></span>·<span·class="inlinecode"><span·class="id"·title="var">x</span></span>·<span·class="inlinecode"><span·class="id"·title="var">s</span></span>·instead·of·<span·class="inlinecode"><span·class="id"·title="var">mem</span></span>·<span·class="inlinecode"><span·class="id"·title="var">x</span></span>·<span·class="inlinecode"><span·class="id"·title="var">s</span>=<span·class="id"·title="var">true</span></span>, |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab1085"></a><h1·class="section">MSetRBT·:·Implementation·of·MSetInterface·via·Red-Black·trees</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ·Initial·author:·Andrew·W.·Appel,·2011. | 51 | ·Initial·author:·Andrew·W.·Appel,·2011. |
52 | ····Extra·modifications·by:·Pierre·Letouzey | 52 | ····Extra·modifications·by:·Pierre·Letouzey |
53 | <div·class="paragraph">·</div> | 53 | <div·class="paragraph">·</div> |
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="lab | 49 | <a·id="lab1052"></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.MSets.MSetInterface.html#"><span·class="id"·title="library">MSetInterface</span></a>·<a·class="idref"·href="Coq.MSets.MSetProperties.html#"><span·class="id"·title="library">MSetProperties</span></a>·<a·class="idref"·href="Coq.Structures.OrdersEx.html#"><span·class="id"·title="library">OrdersEx</span></a>.<br/> | 54 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.MSets.MSetInterface.html#"><span·class="id"·title="library">MSetInterface</span></a>·<a·class="idref"·href="Coq.MSets.MSetProperties.html#"><span·class="id"·title="library">MSetProperties</span></a>·<a·class="idref"·href="Coq.Structures.OrdersEx.html#"><span·class="id"·title="library">OrdersEx</span></a>.<br/> |
55 | <br/> | 55 | <br/> |
56 | </div> | 56 | </div> |
57 | <div·class="doc"> | 57 | <div·class="doc"> |
58 | <a·id="lab | 58 | <a·id="lab1053"></a><h1·class="section">Going·from·<span·class="inlinecode"><span·class="id"·title="var">MSets</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.Equalities.html#UsualDecidableType"><span·class="id"·title="module">UsualDecidableType</span></a>)(<span·class="id"·title="var">M</span>:·<a·class="idref"·href="Coq.MSets.MSetInterface.html#WSetsOn"><span·class="id"·title="module">WSetsOn</span></a>·<a·class="idref"·href="Coq.MSets.MSetToFiniteSet.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.Equalities.html#UsualDecidableType"><span·class="id"·title="module">UsualDecidableType</span></a>)(<span·class="id"·title="var">M</span>:·<a·class="idref"·href="Coq.MSets.MSetInterface.html#WSetsOn"><span·class="id"·title="module">WSetsOn</span></a>·<a·class="idref"·href="Coq.MSets.MSetToFiniteSet.html#U"><span·class="id"·title="module">U</span></a>).<br/> |
Offset 45, 15 lines modified | Offset 45, 15 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="lab1 | 49 | <a·id="lab1068"></a><h1·class="section">Finite·sets·library</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ·This·file·proposes·an·implementation·of·the·non-dependent | 51 | ·This·file·proposes·an·implementation·of·the·non-dependent |
52 | ····interface·<span·class="inlinecode"><span·class="id"·title="var">MSetWeakInterface.S</span></span>·using·lists·without·redundancy.· | 52 | ····interface·<span·class="inlinecode"><span·class="id"·title="var">MSetWeakInterface.S</span></span>·using·lists·without·redundancy.· |
53 | </div> | 53 | </div> |
54 | <div·class="code"> | 54 | <div·class="code"> |
Offset 51, 15 lines modified | Offset 51, 15 lines modified | ||
51 | <a·class="idref"·href="Coq.Structures.Equalities.html#"><span·class="id"·title="library">Equalities</span></a>·<a·class="idref"·href="Coq.Structures.OrdersFacts.html#"><span·class="id"·title="library">OrdersFacts</span></a>·<a·class="idref"·href="Coq.Structures.GenericMinMax.html#"><span·class="id"·title="library">GenericMinMax</span></a>·<a·class="idref"·href="Coq.Bool.Bool.html#"><span·class="id"·title="library">Bool</span></a>·<a·class="idref"·href="Coq.Numbers.Natural.Abstract.NAxioms.html#"><span·class="id"·title="library">NAxioms</span></a>·<a·class="idref"·href="Coq.Numbers.Natural.Abstract.NMaxMin.html#"><span·class="id"·title="library">NMaxMin</span></a>·<a·class="idref"·href="Coq.Numbers.Natural.Abstract.NProperties.html#"><span·class="id"·title="library">NProperties</span></a>.<br/> | 51 | <a·class="idref"·href="Coq.Structures.Equalities.html#"><span·class="id"·title="library">Equalities</span></a>·<a·class="idref"·href="Coq.Structures.OrdersFacts.html#"><span·class="id"·title="library">OrdersFacts</span></a>·<a·class="idref"·href="Coq.Structures.GenericMinMax.html#"><span·class="id"·title="library">GenericMinMax</span></a>·<a·class="idref"·href="Coq.Bool.Bool.html#"><span·class="id"·title="library">Bool</span></a>·<a·class="idref"·href="Coq.Numbers.Natural.Abstract.NAxioms.html#"><span·class="id"·title="library">NAxioms</span></a>·<a·class="idref"·href="Coq.Numbers.Natural.Abstract.NMaxMin.html#"><span·class="id"·title="library">NMaxMin</span></a>·<a·class="idref"·href="Coq.Numbers.Natural.Abstract.NProperties.html#"><span·class="id"·title="library">NProperties</span></a>.<br/> |
52 | <span·class="id"·title="keyword">Require</span>·<a·class="idref"·href="Coq.NArith.BinNatDef.html#"><span·class="id"·title="library">BinNatDef</span></a>.<br/> | 52 | <span·class="id"·title="keyword">Require</span>·<a·class="idref"·href="Coq.NArith.BinNatDef.html#"><span·class="id"·title="library">BinNatDef</span></a>.<br/> |
53 | <br/> | 53 | <br/> |
54 | </div> | 54 | </div> |
55 | <div·class="doc"> | 55 | <div·class="doc"> |
56 | <a·id="lab | 56 | <a·id="lab151"></a><h1·class="section">Binary·natural·numbers,·operations·and·properties</h1> |
57 | <div·class="paragraph">·</div> | 57 | <div·class="paragraph">·</div> |
58 | ·The·type·<span·class="inlinecode"><span·class="id"·title="var">N</span></span>·and·its·constructors·<span·class="inlinecode"><span·class="id"·title="var">N0</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">Npos</span></span>·are·now | 58 | ·The·type·<span·class="inlinecode"><span·class="id"·title="var">N</span></span>·and·its·constructors·<span·class="inlinecode"><span·class="id"·title="var">N0</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">Npos</span></span>·are·now |
59 | ····defined·in·<span·class="inlinecode"><span·class="id"·title="var">BinNums.v</span></span>· | 59 | ····defined·in·<span·class="inlinecode"><span·class="id"·title="var">BinNums.v</span></span>· |
60 | <div·class="paragraph">·</div> | 60 | <div·class="paragraph">·</div> |
Offset 54, 56 lines modified | Offset 54, 56 lines modified | ||
54 | <br/> | 54 | <br/> |
55 | <br/> | 55 | <br/> |
56 | </div> | 56 | </div> |
57 | <div·class="doc"> | 57 | <div·class="doc"> |
58 | <a·id="lab | 58 | <a·id="lab142"></a><h1·class="section">Binary·natural·numbers,·definitions·of·operations</h1> |
59 | </div> | 59 | </div> |
60 | <div·class="code"> | 60 | <div·class="code"> |
61 | <br/> | 61 | <br/> |
62 | <span·class="id"·title="keyword">Module</span>·<a·id="N"·class="idref"·href="#N"><span·class="id"·title="module">N</span></a>.<br/> | 62 | <span·class="id"·title="keyword">Module</span>·<a·id="N"·class="idref"·href="#N"><span·class="id"·title="module">N</span></a>.<br/> |
63 | <br/> | 63 | <br/> |
64 | <span·class="id"·title="keyword">Definition</span>·<a·id="N.t"·class="idref"·href="#N.t"><span·class="id"·title="definition">t</span></a>·:=·<a·class="idref"·href="Coq.Numbers.BinNums.html#N"><span·class="id"·title="inductive">N</span></a>.<br/> | 64 | <span·class="id"·title="keyword">Definition</span>·<a·id="N.t"·class="idref"·href="#N.t"><span·class="id"·title="definition">t</span></a>·:=·<a·class="idref"·href="Coq.Numbers.BinNums.html#N"><span·class="id"·title="inductive">N</span></a>.<br/> |
65 | <br/> | 65 | <br/> |
66 | </div> | 66 | </div> |
67 | <div·class="doc"> | 67 | <div·class="doc"> |
68 | <a·id="lab | 68 | <a·id="lab143"></a><h2·class="section">Nicer·name·<span·class="inlinecode"><span·class="id"·title="var">N.pos</span></span>·for·constructor·<span·class="inlinecode"><span·class="id"·title="var">Npos</span></span></h2> |
69 | </div> | 69 | </div> |
70 | <div·class="code"> | 70 | <div·class="code"> |
71 | <br/> | 71 | <br/> |
72 | <span·class="id"·title="keyword">Notation</span>·<a·id="N.pos"·class="idref"·href="#N.pos"><span·class="id"·title="abbreviation">pos</span></a>·:=·<a·class="idref"·href="Coq.Numbers.BinNums.html#Npos"><span·class="id"·title="constructor">Npos</span></a>.<br/> | 72 | <span·class="id"·title="keyword">Notation</span>·<a·id="N.pos"·class="idref"·href="#N.pos"><span·class="id"·title="abbreviation">pos</span></a>·:=·<a·class="idref"·href="Coq.Numbers.BinNums.html#Npos"><span·class="id"·title="constructor">Npos</span></a>.<br/> |
73 | <br/> | 73 | <br/> |
74 | </div> | 74 | </div> |
75 | <div·class="doc"> | 75 | <div·class="doc"> |
76 | <a·id="lab | 76 | <a·id="lab144"></a><h2·class="section">Constants</h2> |
77 | </div> | 77 | </div> |
78 | <div·class="code"> | 78 | <div·class="code"> |
79 | <br/> | 79 | <br/> |
80 | <span·class="id"·title="keyword">Definition</span>·<a·id="N.zero"·class="idref"·href="#N.zero"><span·class="id"·title="definition">zero</span></a>·:=·0.<br/> | 80 | <span·class="id"·title="keyword">Definition</span>·<a·id="N.zero"·class="idref"·href="#N.zero"><span·class="id"·title="definition">zero</span></a>·:=·0.<br/> |
81 | <span·class="id"·title="keyword">Definition</span>·<a·id="N.one"·class="idref"·href="#N.one"><span·class="id"·title="definition">one</span></a>·:=·1.<br/> | 81 | <span·class="id"·title="keyword">Definition</span>·<a·id="N.one"·class="idref"·href="#N.one"><span·class="id"·title="definition">one</span></a>·:=·1.<br/> |
82 | <span·class="id"·title="keyword">Definition</span>·<a·id="N.two"·class="idref"·href="#N.two"><span·class="id"·title="definition">two</span></a>·:=·2.<br/> | 82 | <span·class="id"·title="keyword">Definition</span>·<a·id="N.two"·class="idref"·href="#N.two"><span·class="id"·title="definition">two</span></a>·:=·2.<br/> |
83 | <br/> | 83 | <br/> |
84 | </div> | 84 | </div> |
85 | <div·class="doc"> | 85 | <div·class="doc"> |
86 | <a·id="lab | 86 | <a·id="lab145"></a><h2·class="section">Operation·<span·class="inlinecode"><span·class="id"·title="var">x</span></span>·<span·class="inlinecode">-></span>·<span·class="inlinecode">2*<span·class="id"·title="var">x</span>+1</span></h2> |
87 | </div> | 87 | </div> |
88 | <div·class="code"> | 88 | <div·class="code"> |
89 | <br/> | 89 | <br/> |
90 | <span·class="id"·title="keyword">Definition</span>·<a·id="N.succ_double"·class="idref"·href="#N.succ_double"><span·class="id"·title="definition">succ_double</span></a>·<a·id="x:1"·class="idref"·href="#x:1"><span·class="id"·title="binder">x</span></a>·:=<br/> | 90 | <span·class="id"·title="keyword">Definition</span>·<a·id="N.succ_double"·class="idref"·href="#N.succ_double"><span·class="id"·title="definition">succ_double</span></a>·<a·id="x:1"·class="idref"·href="#x:1"><span·class="id"·title="binder">x</span></a>·:=<br/> |
91 | <span·class="id"·title="keyword">match</span>·<a·class="idref"·href="Coq.NArith.BinNatDef.html#x:1"><span·class="id"·title="variable">x</span></a>·<span·class="id"·title="keyword">with</span><br/> | 91 | <span·class="id"·title="keyword">match</span>·<a·class="idref"·href="Coq.NArith.BinNatDef.html#x:1"><span·class="id"·title="variable">x</span></a>·<span·class="id"·title="keyword">with</span><br/> |
Offset 48, 15 lines modified | Offset 48, 15 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.PArith.BinPos.html#"><span·class="id"·title="library">BinPos</span></a>·<a·class="idref"·href="Coq.NArith.BinNat.html#"><span·class="id"·title="library">BinNat</span></a>·<a·class="idref"·href="Coq.Arith.PeanoNat.html#"><span·class="id"·title="library">PeanoNat</span></a>·<a·class="idref"·href="Coq.PArith.Pnat.html#"><span·class="id"·title="library">Pnat</span></a>.<br/> | 49 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.PArith.BinPos.html#"><span·class="id"·title="library">BinPos</span></a>·<a·class="idref"·href="Coq.NArith.BinNat.html#"><span·class="id"·title="library">BinNat</span></a>·<a·class="idref"·href="Coq.Arith.PeanoNat.html#"><span·class="id"·title="library">PeanoNat</span></a>·<a·class="idref"·href="Coq.PArith.Pnat.html#"><span·class="id"·title="library">Pnat</span></a>.<br/> |
50 | <br/> | 50 | <br/> |
51 | </div> | 51 | </div> |
52 | <div·class="doc"> | 52 | <div·class="doc"> |
53 | <a·id="lab | 53 | <a·id="lab140"></a><h1·class="section">Conversions·from·<span·class="inlinecode"><span·class="id"·title="var">N</span></span>·to·<span·class="inlinecode"><span·class="id"·title="var">nat</span></span></h1> |
54 | </div> | 54 | </div> |
55 | <div·class="code"> | 55 | <div·class="code"> |
56 | <br/> | 56 | <br/> |
57 | <span·class="id"·title="keyword">Module</span>·<a·id="N2Nat"·class="idref"·href="#N2Nat"><span·class="id"·title="module">N2Nat</span></a>.<br/> | 57 | <span·class="id"·title="keyword">Module</span>·<a·id="N2Nat"·class="idref"·href="#N2Nat"><span·class="id"·title="module">N2Nat</span></a>.<br/> |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab718"></a><h1·class="section">Alternative·Binary·Number·Notations</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ·Faster·but·less·safe·parsers·and·printers·of·<span·class="inlinecode"><span·class="id"·title="var">positive</span></span>,·<span·class="inlinecode"><span·class="id"·title="var">N</span></span>,·<span·class="inlinecode"><span·class="id"·title="var">Z</span></span>.· | 51 | ·Faster·but·less·safe·parsers·and·printers·of·<span·class="inlinecode"><span·class="id"·title="var">positive</span></span>,·<span·class="inlinecode"><span·class="id"·title="var">N</span></span>,·<span·class="inlinecode"><span·class="id"·title="var">Z</span></span>.· |
52 | <div·class="paragraph">·</div> | 52 | <div·class="paragraph">·</div> |
53 | ·By·default,·literals·in·types·<span·class="inlinecode"><span·class="id"·title="var">positive</span></span>,·<span·class="inlinecode"><span·class="id"·title="var">N</span></span>,·<span·class="inlinecode"><span·class="id"·title="var">Z</span></span>·are·parsed·and | 53 | ·By·default,·literals·in·types·<span·class="inlinecode"><span·class="id"·title="var">positive</span></span>,·<span·class="inlinecode"><span·class="id"·title="var">N</span></span>,·<span·class="inlinecode"><span·class="id"·title="var">Z</span></span>·are·parsed·and |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab682"></a><h1·class="section">Binary·Numerical·Datatypes</h1> |
50 | </div> | 50 | </div> |
51 | <div·class="code"> | 51 | <div·class="code"> |
52 | <br/> | 52 | <br/> |
53 | <span·class="id"·title="keyword">Set·Implicit·Arguments</span>.<br/> | 53 | <span·class="id"·title="keyword">Set·Implicit·Arguments</span>.<br/> |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab746"></a><h1·class="section">Signature·and·specification·of·a·bounded·integer·structure</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ·This·file·specifies·how·to·represent·<span·class="inlinecode"><span·class="id"·title="var">Z</span>/<span·class="id"·title="var">nZ</span></span>·when·<span·class="inlinecode"><span·class="id"·title="var">n</span>=2^<span·class="id"·title="var">d</span></span>, | 51 | ·This·file·specifies·how·to·represent·<span·class="inlinecode"><span·class="id"·title="var">Z</span>/<span·class="id"·title="var">nZ</span></span>·when·<span·class="inlinecode"><span·class="id"·title="var">n</span>=2^<span·class="id"·title="var">d</span></span>, |
52 | ····<span·class="inlinecode"><span·class="id"·title="var">d</span></span>·being·the·number·of·digits·of·these·bounded·integers.· | 52 | ····<span·class="inlinecode"><span·class="id"·title="var">d</span></span>·being·the·number·of·digits·of·these·bounded·integers.· |
53 | </div> | 53 | </div> |
54 | <div·class="code"> | 54 | <div·class="code"> |
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.Numbers.Cyclic.Abstract.CyclicAxioms.html#"><span·class="id"·title="library">CyclicAxioms</span></a>.<br/> | 53 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Numbers.Cyclic.Abstract.CyclicAxioms.html#"><span·class="id"·title="library">CyclicAxioms</span></a>.<br/> |
54 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.micromega.Lia.html#"><span·class="id"·title="library">Lia</span></a>.<br/> | 54 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.micromega.Lia.html#"><span·class="id"·title="library">Lia</span></a>.<br/> |
55 | <br/> | 55 | <br/> |
56 | </div> | 56 | </div> |
57 | <div·class="doc"> | 57 | <div·class="doc"> |
58 | <a·id="lab | 58 | <a·id="lab745"></a><h1·class="section">From·<span·class="inlinecode"><span·class="id"·title="var">CyclicType</span></span>·to·<span·class="inlinecode"><span·class="id"·title="var">NZAxiomsSig</span></span></h1> |
59 | <div·class="paragraph">·</div> | 59 | <div·class="paragraph">·</div> |
60 | ·A·<span·class="inlinecode"><span·class="id"·title="var">Z</span>/<span·class="id"·title="var">nZ</span></span>·representation·given·by·a·module·type·<span·class="inlinecode"><span·class="id"·title="var">CyclicType</span></span> | 60 | ·A·<span·class="inlinecode"><span·class="id"·title="var">Z</span>/<span·class="id"·title="var">nZ</span></span>·representation·given·by·a·module·type·<span·class="inlinecode"><span·class="id"·title="var">CyclicType</span></span> |
61 | ····implements·<span·class="inlinecode"><span·class="id"·title="var">NZAxiomsSig</span></span>,·e.g.·the·common·properties·between | 61 | ····implements·<span·class="inlinecode"><span·class="id"·title="var">NZAxiomsSig</span></span>,·e.g.·the·common·properties·between |
62 | ····N·and·Z·with·no·ordering.·Notice·that·the·<span·class="inlinecode"><span·class="id"·title="var">n</span></span>·in·<span·class="inlinecode"><span·class="id"·title="var">Z</span>/<span·class="id"·title="var">nZ</span></span>·is | 62 | ····N·and·Z·with·no·ordering.·Notice·that·the·<span·class="inlinecode"><span·class="id"·title="var">n</span></span>·in·<span·class="inlinecode"><span·class="id"·title="var">Z</span>/<span·class="id"·title="var">nZ</span></span>·is |
63 | ····a·power·of·2. | 63 | ····a·power·of·2. |
Offset 48, 15 lines modified | Offset 48, 15 lines modified | ||
48 | <br/> | 48 | <br/> |
49 | </div> | 49 | </div> |
50 | <div·class="doc"> | 50 | <div·class="doc"> |
51 | This·library·has·been·deprecated·since·Coq·version·8.10.· | 51 | This·library·has·been·deprecated·since·Coq·version·8.10.· |
52 | <div·class="paragraph">·</div> | 52 | <div·class="paragraph">·</div> |
53 | <a·id="lab | 53 | <a·id="lab722"></a><h1·class="section">Int31·numbers·defines·indeed·a·cyclic·structure·:·Z/(2^31)Z</h1> |
54 | <div·class="paragraph">·</div> | 54 | <div·class="paragraph">·</div> |
55 | <div·class="paragraph">·</div> | 55 | <div·class="paragraph">·</div> |
56 | Author:·Arnaud·Spiwack·(+·Pierre·Letouzey) | 56 | Author:·Arnaud·Spiwack·(+·Pierre·Letouzey) |
Offset 61, 15 lines modified | Offset 61, 15 lines modified | ||
61 | <br/> | 61 | <br/> |
62 | <br/> | 62 | <br/> |
63 | </div> | 63 | </div> |
64 | <div·class="doc"> | 64 | <div·class="doc"> |
65 | <a·id="lab | 65 | <a·id="lab735"></a><h1·class="section">31-bit·integers</h1> |
66 | <div·class="paragraph">·</div> | 66 | <div·class="paragraph">·</div> |
67 | ·This·file·contains·basic·definitions·of·a·31-bit·integer | 67 | ·This·file·contains·basic·definitions·of·a·31-bit·integer |
68 | ··arithmetic.·In·fact·it·is·more·general·than·that.·The·only·reason | 68 | ··arithmetic.·In·fact·it·is·more·general·than·that.·The·only·reason |
69 | ··for·this·use·of·31·is·the·underlying·mechanism·for·hardware-efficient | 69 | ··for·this·use·of·31·is·the·underlying·mechanism·for·hardware-efficient |
70 | ··computations·by·A.·Spiwack.·Apart·from·this,·a·switch·to,·say, | 70 | ··computations·by·A.·Spiwack.·Apart·from·this,·a·switch·to,·say, |
Offset 48, 15 lines modified | Offset 48, 15 lines modified | ||
48 | <br/> | 48 | <br/> |
49 | </div> | 49 | </div> |
50 | <div·class="doc"> | 50 | <div·class="doc"> |
51 | This·library·has·been·deprecated·since·Coq·version·8.10.· | 51 | This·library·has·been·deprecated·since·Coq·version·8.10.· |
52 | <div·class="paragraph">·</div> | 52 | <div·class="paragraph">·</div> |
53 | <a·id="lab | 53 | <a·id="lab744"></a><h1·class="section">Int31·numbers·defines·Z/(2^31)Z,·and·can·hence·be·equipped</h1> |
54 | ······with·a·ring·structure·and·a·ring·tactic· | 54 | ······with·a·ring·structure·and·a·ring·tactic· |
55 | </div> | 55 | </div> |
56 | <div·class="code"> | 56 | <div·class="code"> |
57 | <br/> | 57 | <br/> |
58 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.micromega.Lia.html#"><span·class="id"·title="library">Lia</span></a>·<a·class="idref"·href="Coq.Numbers.Cyclic.Int31.Int31.html#"><span·class="id"·title="library">Int31</span></a>·<a·class="idref"·href="Coq.Numbers.Cyclic.Int31.Cyclic31.html#"><span·class="id"·title="library">Cyclic31</span></a>·<a·class="idref"·href="Coq.Numbers.Cyclic.Abstract.CyclicAxioms.html#"><span·class="id"·title="library">CyclicAxioms</span></a>.<br/> | 58 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.micromega.Lia.html#"><span·class="id"·title="library">Lia</span></a>·<a·class="idref"·href="Coq.Numbers.Cyclic.Int31.Int31.html#"><span·class="id"·title="library">Int31</span></a>·<a·class="idref"·href="Coq.Numbers.Cyclic.Int31.Cyclic31.html#"><span·class="id"·title="library">Cyclic31</span></a>·<a·class="idref"·href="Coq.Numbers.Cyclic.Abstract.CyclicAxioms.html#"><span·class="id"·title="library">CyclicAxioms</span></a>.<br/> |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab747"></a><h1·class="section">Uint63·numbers·defines·indeed·a·cyclic·structure·:·Z/(2^63)Z</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | <div·class="paragraph">·</div> | 51 | <div·class="paragraph">·</div> |
52 | Author:·Arnaud·Spiwack·(+·Pierre·Letouzey) | 52 | Author:·Arnaud·Spiwack·(+·Pierre·Letouzey) |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab748"></a><h1·class="section">Uint63·numbers·defines·Z/(2^63)Z,·and·can·hence·be·equipped</h1> |
50 | ······with·a·ring·structure·and·a·ring·tactic· | 50 | ······with·a·ring·structure·and·a·ring·tactic· |
51 | </div> | 51 | </div> |
52 | <div·class="code"> | 52 | <div·class="code"> |
53 | <br/> | 53 | <br/> |
54 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Numbers.Cyclic.Int63.Cyclic63.html#"><span·class="id"·title="library">Cyclic63</span></a>·<a·class="idref"·href="Coq.Numbers.Cyclic.Abstract.CyclicAxioms.html#"><span·class="id"·title="library">CyclicAxioms</span></a>.<br/> | 54 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Numbers.Cyclic.Int63.Cyclic63.html#"><span·class="id"·title="library">Cyclic63</span></a>·<a·class="idref"·href="Coq.Numbers.Cyclic.Abstract.CyclicAxioms.html#"><span·class="id"·title="library">CyclicAxioms</span></a>.<br/> |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab749"></a><h1·class="section">Type·<span·class="inlinecode"><span·class="id"·title="var">Z</span></span>·viewed·modulo·a·particular·constant·corresponds·to·<span·class="inlinecode"><span·class="id"·title="var">Z</span>/<span·class="id"·title="var">nZ</span></span></h1> |
50 | ······as·defined·abstractly·in·CyclicAxioms.· | 50 | ······as·defined·abstractly·in·CyclicAxioms.· |
51 | <div·class="paragraph">·</div> | 51 | <div·class="paragraph">·</div> |
52 | ·Even·if·the·construction·provided·here·is·not·reused·for·building | 52 | ·Even·if·the·construction·provided·here·is·not·reused·for·building |
53 | ··the·efficient·arbitrary·precision·numbers,·it·provides·a·simple | 53 | ··the·efficient·arbitrary·precision·numbers,·it·provides·a·simple |
54 | ··implementation·of·CyclicAxioms,·hence·ensuring·its·coherence.· | 54 | ··implementation·of·CyclicAxioms,·hence·ensuring·its·coherence.· |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab692"></a><h1·class="section">DecimalFacts·:·some·facts·about·Decimal·numbers</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.Init.Decimal.html#"><span·class="id"·title="library">Decimal</span></a>·<a·class="idref"·href="Coq.Arith.Arith.html#"><span·class="id"·title="library">Arith</span></a>·<a·class="idref"·href="Coq.ZArith.ZArith.html#"><span·class="id"·title="library">ZArith</span></a>.<br/> | 53 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Init.Decimal.html#"><span·class="id"·title="library">Decimal</span></a>·<a·class="idref"·href="Coq.Arith.Arith.html#"><span·class="id"·title="library">Arith</span></a>·<a·class="idref"·href="Coq.ZArith.ZArith.html#"><span·class="id"·title="library">ZArith</span></a>.<br/> |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab684"></a><h1·class="section">DecimalN</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ····Proofs·that·conversions·between·decimal·numbers·and·<span·class="inlinecode"><span·class="id"·title="var">N</span></span> | 51 | ····Proofs·that·conversions·between·decimal·numbers·and·<span·class="inlinecode"><span·class="id"·title="var">N</span></span> |
52 | ····are·bijections· | 52 | ····are·bijections· |
53 | </div> | 53 | </div> |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab688"></a><h1·class="section">DecimalNat</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ····Proofs·that·conversions·between·decimal·numbers·and·<span·class="inlinecode"><span·class="id"·title="var">nat</span></span> | 51 | ····Proofs·that·conversions·between·decimal·numbers·and·<span·class="inlinecode"><span·class="id"·title="var">nat</span></span> |
52 | ····are·bijections.· | 52 | ····are·bijections.· |
53 | </div> | 53 | </div> |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab694"></a><h1·class="section">DecimalPos</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ····Proofs·that·conversions·between·decimal·numbers·and·<span·class="inlinecode"><span·class="id"·title="var">positive</span></span> | 51 | ····Proofs·that·conversions·between·decimal·numbers·and·<span·class="inlinecode"><span·class="id"·title="var">positive</span></span> |
52 | ····are·bijections.· | 52 | ····are·bijections.· |
53 | </div> | 53 | </div> |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab683"></a><h1·class="section">DecimalQ</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ····Proofs·that·conversions·between·decimal·numbers·and·<span·class="inlinecode"><span·class="id"·title="var">Q</span></span> | 51 | ····Proofs·that·conversions·between·decimal·numbers·and·<span·class="inlinecode"><span·class="id"·title="var">Q</span></span> |
52 | ····are·bijections.· | 52 | ····are·bijections.· |
53 | </div> | 53 | </div> |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab720"></a><h1·class="section">DecimalR</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ····Proofs·that·conversions·between·decimal·numbers·and·<span·class="inlinecode"><span·class="id"·title="var">R</span></span> | 51 | ····Proofs·that·conversions·between·decimal·numbers·and·<span·class="inlinecode"><span·class="id"·title="var">R</span></span> |
52 | ····are·bijections.· | 52 | ····are·bijections.· |
53 | </div> | 53 | </div> |
Offset 48, 15 lines modified | Offset 48, 15 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.Init.Decimal.html#"><span·class="id"·title="library">Decimal</span></a>·<a·class="idref"·href="Coq.Strings.Ascii.html#"><span·class="id"·title="library">Ascii</span></a>·<a·class="idref"·href="Coq.Strings.String.html#"><span·class="id"·title="library">String</span></a>.<br/> | 49 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Init.Decimal.html#"><span·class="id"·title="library">Decimal</span></a>·<a·class="idref"·href="Coq.Strings.Ascii.html#"><span·class="id"·title="library">Ascii</span></a>·<a·class="idref"·href="Coq.Strings.String.html#"><span·class="id"·title="library">String</span></a>.<br/> |
50 | <br/> | 50 | <br/> |
51 | </div> | 51 | </div> |
52 | <div·class="doc"> | 52 | <div·class="doc"> |
53 | <a·id="lab | 53 | <a·id="lab719"></a><h1·class="section">Conversion·between·decimal·numbers·and·Coq·strings</h1> |
54 | <div·class="paragraph">·</div> | 54 | <div·class="paragraph">·</div> |
55 | ·Pretty·straightforward,·which·is·precisely·the·point·of·the | 55 | ·Pretty·straightforward,·which·is·precisely·the·point·of·the |
56 | ····<span·class="inlinecode"><span·class="id"·title="var">Decimal.int</span></span>·datatype.·The·only·catch·is·<span·class="inlinecode"><span·class="id"·title="var">Decimal.Nil</span></span>·:·we·could | 56 | ····<span·class="inlinecode"><span·class="id"·title="var">Decimal.int</span></span>·datatype.·The·only·catch·is·<span·class="inlinecode"><span·class="id"·title="var">Decimal.Nil</span></span>·:·we·could |
57 | ····choose·to·convert·it·as·<span·class="inlinecode">""</span>·or·as·<span·class="inlinecode">"0"</span>.·In·the·first·case,·it·is | 57 | ····choose·to·convert·it·as·<span·class="inlinecode">""</span>·or·as·<span·class="inlinecode">"0"</span>.·In·the·first·case,·it·is |
58 | ····awkward·to·consider·""·(or·"-")·as·a·number,·while·in·the·second·case | 58 | ····awkward·to·consider·""·(or·"-")·as·a·number,·while·in·the·second·case |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab695"></a><h1·class="section">DecimalZ</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ····Proofs·that·conversions·between·decimal·numbers·and·<span·class="inlinecode"><span·class="id"·title="var">Z</span></span> | 51 | ····Proofs·that·conversions·between·decimal·numbers·and·<span·class="inlinecode"><span·class="id"·title="var">Z</span></span> |
52 | ····are·bijections.· | 52 | ····are·bijections.· |
53 | </div> | 53 | </div> |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab721"></a><h1·class="section">HexadecimalFacts·:·some·facts·about·Hexadecimal·numbers</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.Init.Hexadecimal.html#"><span·class="id"·title="library">Hexadecimal</span></a>·<a·class="idref"·href="Coq.Arith.Arith.html#"><span·class="id"·title="library">Arith</span></a>·<a·class="idref"·href="Coq.ZArith.ZArith.html#"><span·class="id"·title="library">ZArith</span></a>.<br/> | 53 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Init.Hexadecimal.html#"><span·class="id"·title="library">Hexadecimal</span></a>·<a·class="idref"·href="Coq.Arith.Arith.html#"><span·class="id"·title="library">Arith</span></a>·<a·class="idref"·href="Coq.ZArith.ZArith.html#"><span·class="id"·title="library">ZArith</span></a>.<br/> |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab690"></a><h1·class="section">HexadecimalN</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ····Proofs·that·conversions·between·hexadecimal·numbers·and·<span·class="inlinecode"><span·class="id"·title="var">N</span></span> | 51 | ····Proofs·that·conversions·between·hexadecimal·numbers·and·<span·class="inlinecode"><span·class="id"·title="var">N</span></span> |
52 | ····are·bijections· | 52 | ····are·bijections· |
53 | </div> | 53 | </div> |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab685"></a><h1·class="section">HexadecimalNat</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ····Proofs·that·conversions·between·hexadecimal·numbers·and·<span·class="inlinecode"><span·class="id"·title="var">nat</span></span> | 51 | ····Proofs·that·conversions·between·hexadecimal·numbers·and·<span·class="inlinecode"><span·class="id"·title="var">nat</span></span> |
52 | ····are·bijections.· | 52 | ····are·bijections.· |
53 | </div> | 53 | </div> |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab687"></a><h1·class="section">HexadecimalPos</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ····Proofs·that·conversions·between·hexadecimal·numbers·and·<span·class="inlinecode"><span·class="id"·title="var">positive</span></span> | 51 | ····Proofs·that·conversions·between·hexadecimal·numbers·and·<span·class="inlinecode"><span·class="id"·title="var">positive</span></span> |
52 | ····are·bijections.· | 52 | ····are·bijections.· |
53 | </div> | 53 | </div> |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab689"></a><h1·class="section">HexadecimalQ</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ····Proofs·that·conversions·between·hexadecimal·numbers·and·<span·class="inlinecode"><span·class="id"·title="var">Q</span></span> | 51 | ····Proofs·that·conversions·between·hexadecimal·numbers·and·<span·class="inlinecode"><span·class="id"·title="var">Q</span></span> |
52 | ····are·bijections.· | 52 | ····are·bijections.· |
53 | </div> | 53 | </div> |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab681"></a><h1·class="section">HexadecimalR</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ····Proofs·that·conversions·between·hexadecimal·numbers·and·<span·class="inlinecode"><span·class="id"·title="var">R</span></span> | 51 | ····Proofs·that·conversions·between·hexadecimal·numbers·and·<span·class="inlinecode"><span·class="id"·title="var">R</span></span> |
52 | ····are·bijections.· | 52 | ····are·bijections.· |
53 | </div> | 53 | </div> |
Offset 48, 15 lines modified | Offset 48, 15 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.Init.Hexadecimal.html#"><span·class="id"·title="library">Hexadecimal</span></a>·<a·class="idref"·href="Coq.Strings.Ascii.html#"><span·class="id"·title="library">Ascii</span></a>·<a·class="idref"·href="Coq.Strings.String.html#"><span·class="id"·title="library">String</span></a>.<br/> | 49 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Init.Hexadecimal.html#"><span·class="id"·title="library">Hexadecimal</span></a>·<a·class="idref"·href="Coq.Strings.Ascii.html#"><span·class="id"·title="library">Ascii</span></a>·<a·class="idref"·href="Coq.Strings.String.html#"><span·class="id"·title="library">String</span></a>.<br/> |
50 | <br/> | 50 | <br/> |
51 | </div> | 51 | </div> |
52 | <div·class="doc"> | 52 | <div·class="doc"> |
53 | <a·id="lab | 53 | <a·id="lab691"></a><h1·class="section">Conversion·between·hexadecimal·numbers·and·Coq·strings</h1> |
54 | <div·class="paragraph">·</div> | 54 | <div·class="paragraph">·</div> |
55 | ·Pretty·straightforward,·which·is·precisely·the·point·of·the | 55 | ·Pretty·straightforward,·which·is·precisely·the·point·of·the |
56 | ····<span·class="inlinecode"><span·class="id"·title="var">Hexadecimal.int</span></span>·datatype.·The·only·catch·is·<span·class="inlinecode"><span·class="id"·title="var">Hexadecimal.Nil</span></span>·:·we·could | 56 | ····<span·class="inlinecode"><span·class="id"·title="var">Hexadecimal.int</span></span>·datatype.·The·only·catch·is·<span·class="inlinecode"><span·class="id"·title="var">Hexadecimal.Nil</span></span>·:·we·could |
57 | ····choose·to·convert·it·as·<span·class="inlinecode">""</span>·or·as·<span·class="inlinecode">"0"</span>.·In·the·first·case,·it·is | 57 | ····choose·to·convert·it·as·<span·class="inlinecode">""</span>·or·as·<span·class="inlinecode">"0"</span>.·In·the·first·case,·it·is |
58 | ····awkward·to·consider·""·(or·"-")·as·a·number,·while·in·the·second·case | 58 | ····awkward·to·consider·""·(or·"-")·as·a·number,·while·in·the·second·case |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab693"></a><h1·class="section">HexadecimalZ</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ····Proofs·that·conversions·between·hexadecimal·numbers·and·<span·class="inlinecode"><span·class="id"·title="var">Z</span></span> | 51 | ····Proofs·that·conversions·between·hexadecimal·numbers·and·<span·class="inlinecode"><span·class="id"·title="var">Z</span></span> |
52 | ····are·bijections.· | 52 | ····are·bijections.· |
53 | </div> | 53 | </div> |
Offset 467, 15 lines modified | Offset 467, 15 lines modified | ||
467 | <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.Logic.html#::type_scope:x_'<->'_x"><span·class="id"·title="notation">(</span></a><a·class="idref"·href="Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span·class="id"·title="notation">exists</span></a>·<a·id="n:114"·class="idref"·href="#n:114"><span·class="id"·title="binder">n</span></a><a·class="idref"·href="Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span·class="id"·title="notation">,</span></a>·<span·class="id"·title="keyword">forall</span>·<a·id="m:115"·class="idref"·href="#m:115"><span·class="id"·title="binder">m</span></a>,·0<a·class="idref"·href="Coq.Structures.Orders.html#6733f1c73babd16d47d3db78628c74d6"><span·class="id"·title="notation"><=</span></a><a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZBits.html#m:115"><span·class="id"·title="variable">m</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.Numbers.Integer.Abstract.ZBits.html#f:113"><span·class="id"·title="variable">f</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZBits.html#m:115"><span·class="id"·title="variable">m</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZBits.html#n:114"><span·class="id"·title="variable">n</span></a><a·class="idref"·href="Coq.Numbers.NatInt.NZBits.html#08f35bb78d3f8b8e58903b9564c9213c"><span·class="id"·title="notation">.[</span></a><a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZBits.html#m:115"><span·class="id"·title="variable">m</span></a><a·class="idref"·href="Coq.Numbers.NatInt.NZBits.html#08f35bb78d3f8b8e58903b9564c9213c"><span·class="id"·title="notation">]</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.Logic.html#::type_scope:x_'<->'_x"><span·class="id"·title="notation"><-></span></a><br/> | 467 | <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.Logic.html#::type_scope:x_'<->'_x"><span·class="id"·title="notation">(</span></a><a·class="idref"·href="Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span·class="id"·title="notation">exists</span></a>·<a·id="n:114"·class="idref"·href="#n:114"><span·class="id"·title="binder">n</span></a><a·class="idref"·href="Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span·class="id"·title="notation">,</span></a>·<span·class="id"·title="keyword">forall</span>·<a·id="m:115"·class="idref"·href="#m:115"><span·class="id"·title="binder">m</span></a>,·0<a·class="idref"·href="Coq.Structures.Orders.html#6733f1c73babd16d47d3db78628c74d6"><span·class="id"·title="notation"><=</span></a><a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZBits.html#m:115"><span·class="id"·title="variable">m</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.Numbers.Integer.Abstract.ZBits.html#f:113"><span·class="id"·title="variable">f</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZBits.html#m:115"><span·class="id"·title="variable">m</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZBits.html#n:114"><span·class="id"·title="variable">n</span></a><a·class="idref"·href="Coq.Numbers.NatInt.NZBits.html#08f35bb78d3f8b8e58903b9564c9213c"><span·class="id"·title="notation">.[</span></a><a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZBits.html#m:115"><span·class="id"·title="variable">m</span></a><a·class="idref"·href="Coq.Numbers.NatInt.NZBits.html#08f35bb78d3f8b8e58903b9564c9213c"><span·class="id"·title="notation">]</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.Logic.html#::type_scope:x_'<->'_x"><span·class="id"·title="notation"><-></span></a><br/> |
468 | <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.Logic.html#a883bdd010993579f99d60b3775bcf54"><span·class="id"·title="notation">exists</span></a>·<a·id="k:116"·class="idref"·href="#k:116"><span·class="id"·title="binder">k</span></a><a·class="idref"·href="Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span·class="id"·title="notation">,</span></a>·<span·class="id"·title="keyword">forall</span>·<a·id="m:117"·class="idref"·href="#m:117"><span·class="id"·title="binder">m</span></a>,·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZBits.html#k:116"><span·class="id"·title="variable">k</span></a><a·class="idref"·href="Coq.Structures.Orders.html#6733f1c73babd16d47d3db78628c74d6"><span·class="id"·title="notation"><=</span></a><a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZBits.html#m:117"><span·class="id"·title="variable">m</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.Numbers.Integer.Abstract.ZBits.html#f:113"><span·class="id"·title="variable">f</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZBits.html#m:117"><span·class="id"·title="variable">m</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZBits.html#f:113"><span·class="id"·title="variable">f</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZBits.html#k:116"><span·class="id"·title="variable">k</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.Logic.html#::type_scope:x_'->'_x"><span·class="id"·title="notation">)</span></a>.<br/> | 468 | <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.Logic.html#a883bdd010993579f99d60b3775bcf54"><span·class="id"·title="notation">exists</span></a>·<a·id="k:116"·class="idref"·href="#k:116"><span·class="id"·title="binder">k</span></a><a·class="idref"·href="Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span·class="id"·title="notation">,</span></a>·<span·class="id"·title="keyword">forall</span>·<a·id="m:117"·class="idref"·href="#m:117"><span·class="id"·title="binder">m</span></a>,·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZBits.html#k:116"><span·class="id"·title="variable">k</span></a><a·class="idref"·href="Coq.Structures.Orders.html#6733f1c73babd16d47d3db78628c74d6"><span·class="id"·title="notation"><=</span></a><a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZBits.html#m:117"><span·class="id"·title="variable">m</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.Numbers.Integer.Abstract.ZBits.html#f:113"><span·class="id"·title="variable">f</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZBits.html#m:117"><span·class="id"·title="variable">m</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZBits.html#f:113"><span·class="id"·title="variable">f</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZBits.html#k:116"><span·class="id"·title="variable">k</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.Logic.html#::type_scope:x_'->'_x"><span·class="id"·title="notation">)</span></a>.<br/> |
469 | <br/> | 469 | <br/> |
470 | </div> | 470 | </div> |
471 | <div·class="doc"> | 471 | <div·class="doc"> |
472 | <a·id="lab | 472 | <a·id="lab700"></a><h1·class="section">Properties·of·shifts</h1> |
473 | <div·class="paragraph">·</div> | 473 | <div·class="paragraph">·</div> |
474 | ·First,·a·unified·specification·for·<span·class="inlinecode"><span·class="id"·title="var">shiftl</span></span>·:·the·<span·class="inlinecode"><span·class="id"·title="var">shiftl_spec</span></span> | 474 | ·First,·a·unified·specification·for·<span·class="inlinecode"><span·class="id"·title="var">shiftl</span></span>·:·the·<span·class="inlinecode"><span·class="id"·title="var">shiftl_spec</span></span> |
475 | ···below·(combined·with·<span·class="inlinecode"><span·class="id"·title="var">testbit_neg_r</span></span>)·is·equivalent·to | 475 | ···below·(combined·with·<span·class="inlinecode"><span·class="id"·title="var">testbit_neg_r</span></span>)·is·equivalent·to |
476 | ···<span·class="inlinecode"><span·class="id"·title="var">shiftl_spec_low</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">shiftl_spec_high</span></span>.· | 476 | ···<span·class="inlinecode"><span·class="id"·title="var">shiftl_spec_low</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">shiftl_spec_high</span></span>.· |
477 | </div> | 477 | </div> |
Offset 48, 15 lines modified | Offset 48, 15 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.Integer.Abstract.ZAxioms.html#"><span·class="id"·title="library">ZAxioms</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZMulOrder.html#"><span·class="id"·title="library">ZMulOrder</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZSgnAbs.html#"><span·class="id"·title="library">ZSgnAbs</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZDiv.html#"><span·class="id"·title="library">NZDiv</span></a>.<br/> | 49 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZAxioms.html#"><span·class="id"·title="library">ZAxioms</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZMulOrder.html#"><span·class="id"·title="library">ZMulOrder</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZSgnAbs.html#"><span·class="id"·title="library">ZSgnAbs</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZDiv.html#"><span·class="id"·title="library">NZDiv</span></a>.<br/> |
50 | <br/> | 50 | <br/> |
51 | </div> | 51 | </div> |
52 | <div·class="doc"> | 52 | <div·class="doc"> |
53 | <a·id="lab | 53 | <a·id="lab696"></a><h1·class="section">Euclidean·Division·for·integers,·Euclid·convention</h1> |
54 | <div·class="paragraph">·</div> | 54 | <div·class="paragraph">·</div> |
55 | ····We·use·here·the·"usual"·formulation·of·the·Euclid·Theorem | 55 | ····We·use·here·the·"usual"·formulation·of·the·Euclid·Theorem |
56 | ····<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">b</span><>0</span>·<span·class="inlinecode">-></span>·<span·class="inlinecode"><span·class="id"·title="tactic">exists</span></span>·<span·class="inlinecode"><span·class="id"·title="var">r</span></span>·<span·class="inlinecode"><span·class="id"·title="var">q</span>,</span>·<span·class="inlinecode"><span·class="id"·title="var">a</span></span>·<span·class="inlinecode">=</span>·<span·class="inlinecode"><span·class="id"·title="var">b</span>*<span·class="id"·title="var">q</span>+<span·class="id"·title="var">r</span></span>·<span·class="inlinecode">/\</span>·<span·class="inlinecode">0</span>·<span·class="inlinecode"><=</span>·<span·class="inlinecode"><span·class="id"·title="var">r</span></span>·<span·class="inlinecode"><</span>·<span·class="inlinecode">|<span·class="id"·title="var">b</span>|</span>·<span·class="inlinecode"></span> | 56 | ····<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">b</span><>0</span>·<span·class="inlinecode">-></span>·<span·class="inlinecode"><span·class="id"·title="tactic">exists</span></span>·<span·class="inlinecode"><span·class="id"·title="var">r</span></span>·<span·class="inlinecode"><span·class="id"·title="var">q</span>,</span>·<span·class="inlinecode"><span·class="id"·title="var">a</span></span>·<span·class="inlinecode">=</span>·<span·class="inlinecode"><span·class="id"·title="var">b</span>*<span·class="id"·title="var">q</span>+<span·class="id"·title="var">r</span></span>·<span·class="inlinecode">/\</span>·<span·class="inlinecode">0</span>·<span·class="inlinecode"><=</span>·<span·class="inlinecode"><span·class="id"·title="var">r</span></span>·<span·class="inlinecode"><</span>·<span·class="inlinecode">|<span·class="id"·title="var">b</span>|</span>·<span·class="inlinecode"></span> |
Offset 48, 15 lines modified | Offset 48, 15 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.Integer.Abstract.ZAxioms.html#"><span·class="id"·title="library">ZAxioms</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZMulOrder.html#"><span·class="id"·title="library">ZMulOrder</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZSgnAbs.html#"><span·class="id"·title="library">ZSgnAbs</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZDiv.html#"><span·class="id"·title="library">NZDiv</span></a>.<br/> | 49 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZAxioms.html#"><span·class="id"·title="library">ZAxioms</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZMulOrder.html#"><span·class="id"·title="library">ZMulOrder</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZSgnAbs.html#"><span·class="id"·title="library">ZSgnAbs</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZDiv.html#"><span·class="id"·title="library">NZDiv</span></a>.<br/> |
50 | <br/> | 50 | <br/> |
51 | </div> | 51 | </div> |
52 | <div·class="doc"> | 52 | <div·class="doc"> |
53 | <a·id="lab | 53 | <a·id="lab702"></a><h1·class="section">Euclidean·Division·for·integers·(Floor·convention)</h1> |
54 | <div·class="paragraph">·</div> | 54 | <div·class="paragraph">·</div> |
55 | ····We·use·here·the·convention·known·as·Floor,·or·Round-Toward-Bottom, | 55 | ····We·use·here·the·convention·known·as·Floor,·or·Round-Toward-Bottom, |
56 | ····where·<span·class="inlinecode"><span·class="id"·title="var">a</span>/<span·class="id"·title="var">b</span></span>·is·the·closest·integer·below·the·exact·fraction. | 56 | ····where·<span·class="inlinecode"><span·class="id"·title="var">a</span>/<span·class="id"·title="var">b</span></span>·is·the·closest·integer·below·the·exact·fraction. |
57 | ····It·can·be·summarized·by: | 57 | ····It·can·be·summarized·by: |
Offset 48, 15 lines modified | Offset 48, 15 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.Integer.Abstract.ZAxioms.html#"><span·class="id"·title="library">ZAxioms</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZMulOrder.html#"><span·class="id"·title="library">ZMulOrder</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZSgnAbs.html#"><span·class="id"·title="library">ZSgnAbs</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZDiv.html#"><span·class="id"·title="library">NZDiv</span></a>.<br/> | 49 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZAxioms.html#"><span·class="id"·title="library">ZAxioms</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZMulOrder.html#"><span·class="id"·title="library">ZMulOrder</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZSgnAbs.html#"><span·class="id"·title="library">ZSgnAbs</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZDiv.html#"><span·class="id"·title="library">NZDiv</span></a>.<br/> |
50 | <br/> | 50 | <br/> |
51 | </div> | 51 | </div> |
52 | <div·class="doc"> | 52 | <div·class="doc"> |
53 | <a·id="lab | 53 | <a·id="lab707"></a><h1·class="section">Euclidean·Division·for·integers·(Trunc·convention)</h1> |
54 | <div·class="paragraph">·</div> | 54 | <div·class="paragraph">·</div> |
55 | ····We·use·here·the·convention·known·as·Trunc,·or·Round-Toward-Zero, | 55 | ····We·use·here·the·convention·known·as·Trunc,·or·Round-Toward-Zero, |
56 | ····where·<span·class="inlinecode"><span·class="id"·title="var">a</span>/<span·class="id"·title="var">b</span></span>·is·the·integer·with·the·largest·absolute·value·to | 56 | ····where·<span·class="inlinecode"><span·class="id"·title="var">a</span>/<span·class="id"·title="var">b</span></span>·is·the·integer·with·the·largest·absolute·value·to |
57 | ····be·between·zero·and·the·exact·fraction.·It·can·be·summarized·by: | 57 | ····be·between·zero·and·the·exact·fraction.·It·can·be·summarized·by: |
Offset 48, 15 lines modified | Offset 48, 15 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.Integer.Abstract.ZAxioms.html#"><span·class="id"·title="library">ZAxioms</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZMulOrder.html#"><span·class="id"·title="library">ZMulOrder</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZSgnAbs.html#"><span·class="id"·title="library">ZSgnAbs</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZGcd.html#"><span·class="id"·title="library">ZGcd</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZDivTrunc.html#"><span·class="id"·title="library">ZDivTrunc</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZDivFloor.html#"><span·class="id"·title="library">ZDivFloor</span></a>.<br/> | 49 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZAxioms.html#"><span·class="id"·title="library">ZAxioms</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZMulOrder.html#"><span·class="id"·title="library">ZMulOrder</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZSgnAbs.html#"><span·class="id"·title="library">ZSgnAbs</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZGcd.html#"><span·class="id"·title="library">ZGcd</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZDivTrunc.html#"><span·class="id"·title="library">ZDivTrunc</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZDivFloor.html#"><span·class="id"·title="library">ZDivFloor</span></a>.<br/> |
50 | <br/> | 50 | <br/> |
51 | </div> | 51 | </div> |
52 | <div·class="doc"> | 52 | <div·class="doc"> |
53 | <a·id="lab | 53 | <a·id="lab701"></a><h1·class="section">Least·Common·Multiple</h1> |
54 | <div·class="paragraph">·</div> | 54 | <div·class="paragraph">·</div> |
55 | ·Unlike·other·functions·around,·we·will·define·lcm·below·instead·of | 55 | ·Unlike·other·functions·around,·we·will·define·lcm·below·instead·of |
56 | ··axiomatizing·it.·Indeed,·there·is·no·"prior·art"·about·lcm·in·the | 56 | ··axiomatizing·it.·Indeed,·there·is·no·"prior·art"·about·lcm·in·the |
57 | ··standard·library·to·be·compliant·with,·and·the·generic·definition | 57 | ··standard·library·to·be·compliant·with,·and·the·generic·definition |
58 | ··of·lcm·via·gcd·is·quite·reasonable. | 58 | ··of·lcm·via·gcd·is·quite·reasonable. |
Offset 48, 15 lines modified | Offset 48, 15 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.Integer.Abstract.ZAxioms.html#"><span·class="id"·title="library">ZAxioms</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZMulOrder.html#"><span·class="id"·title="library">ZMulOrder</span></a>·<a·class="idref"·href="Coq.Structures.GenericMinMax.html#"><span·class="id"·title="library">GenericMinMax</span></a>.<br/> | 49 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZAxioms.html#"><span·class="id"·title="library">ZAxioms</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZMulOrder.html#"><span·class="id"·title="library">ZMulOrder</span></a>·<a·class="idref"·href="Coq.Structures.GenericMinMax.html#"><span·class="id"·title="library">GenericMinMax</span></a>.<br/> |
50 | <br/> | 50 | <br/> |
51 | </div> | 51 | </div> |
52 | <div·class="doc"> | 52 | <div·class="doc"> |
53 | <a·id="lab | 53 | <a·id="lab706"></a><h1·class="section">Properties·of·minimum·and·maximum·specific·to·integer·numbers</h1> |
54 | </div> | 54 | </div> |
55 | <div·class="code"> | 55 | <div·class="code"> |
56 | <br/> | 56 | <br/> |
57 | <span·class="id"·title="keyword">Module</span>·<span·class="id"·title="keyword">Type</span>·<a·id="ZMaxMinProp"·class="idref"·href="#ZMaxMinProp"><span·class="id"·title="module">ZMaxMinProp</span></a>·(<span·class="id"·title="keyword">Import</span>·<span·class="id"·title="var">Z</span>·:·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZAxioms.html#ZAxiomsMiniSig'"><span·class="id"·title="module">ZAxiomsMiniSig'</span></a>).<br/> | 57 | <span·class="id"·title="keyword">Module</span>·<span·class="id"·title="keyword">Type</span>·<a·id="ZMaxMinProp"·class="idref"·href="#ZMaxMinProp"><span·class="id"·title="module">ZMaxMinProp</span></a>·(<span·class="id"·title="keyword">Import</span>·<span·class="id"·title="var">Z</span>·:·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZAxioms.html#ZAxiomsMiniSig'"><span·class="id"·title="module">ZAxiomsMiniSig'</span></a>).<br/> |
58 | <span·class="id"·title="keyword">Include</span>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZMulOrder.html#ZMulOrderProp"><span·class="id"·title="module">ZMulOrderProp</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZMaxMin.html#Z"><span·class="id"·title="module">Z</span></a>.<br/> | 58 | <span·class="id"·title="keyword">Include</span>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZMulOrder.html#ZMulOrderProp"><span·class="id"·title="module">ZMulOrderProp</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZMaxMin.html#Z"><span·class="id"·title="module">Z</span></a>.<br/> |
Offset 65, 15 lines modified | Offset 65, 15 lines modified | ||
65 | <:·<a·class="idref"·href="Coq.Structures.Equalities.html#UsualDecidableTypeFull"><span·class="id"·title="module">UsualDecidableTypeFull</span></a><br/> | 65 | <:·<a·class="idref"·href="Coq.Structures.Equalities.html#UsualDecidableTypeFull"><span·class="id"·title="module">UsualDecidableTypeFull</span></a><br/> |
66 | :=·<a·class="idref"·href="Coq.ZArith.BinInt.html#Z"><span·class="id"·title="module">BinInt.Z</span></a>.<br/> | 66 | :=·<a·class="idref"·href="Coq.ZArith.BinInt.html#Z"><span·class="id"·title="module">BinInt.Z</span></a>.<br/> |
67 | <br/> | 67 | <br/> |
68 | </div> | 68 | </div> |
69 | <div·class="doc"> | 69 | <div·class="doc"> |
70 | <a·id="lab | 70 | <a·id="lab711"></a><h1·class="section">An·<span·class="inlinecode"><span·class="id"·title="var">order</span></span>·tactic·for·integers</h1> |
71 | </div> | 71 | </div> |
72 | <div·class="code"> | 72 | <div·class="code"> |
73 | <br/> | 73 | <br/> |
74 | <span·class="id"·title="keyword">Ltac</span>·<span·class="id"·title="var">z_order</span>·:=·<span·class="id"·title="var">Z.order</span>.<br/> | 74 | <span·class="id"·title="keyword">Ltac</span>·<span·class="id"·title="var">z_order</span>·:=·<span·class="id"·title="var">Z.order</span>.<br/> |
Offset 51, 15 lines modified | Offset 51, 15 lines modified | ||
51 | <br/> | 51 | <br/> |
52 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Lists.List.html#"><span·class="id"·title="library">List</span></a>.<br/> | 52 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Lists.List.html#"><span·class="id"·title="library">List</span></a>.<br/> |
53 | <br/> | 53 | <br/> |
54 | </div> | 54 | </div> |
55 | <div·class="doc"> | 55 | <div·class="doc"> |
56 | <a·id="lab | 56 | <a·id="lab686"></a><h1·class="section">Generic·dependently-typed·operators·about·<span·class="inlinecode"><span·class="id"·title="var">n</span></span>-ary·functions</h1> |
57 | <div·class="paragraph">·</div> | 57 | <div·class="paragraph">·</div> |
58 | ·The·type·of·<span·class="inlinecode"><span·class="id"·title="var">n</span></span>-ary·function:·<span·class="inlinecode"><span·class="id"·title="var">nfun</span></span>·<span·class="inlinecode"><span·class="id"·title="var">A</span></span>·<span·class="inlinecode"><span·class="id"·title="var">n</span></span>·<span·class="inlinecode"><span·class="id"·title="var">B</span></span>·is | 58 | ·The·type·of·<span·class="inlinecode"><span·class="id"·title="var">n</span></span>-ary·function:·<span·class="inlinecode"><span·class="id"·title="var">nfun</span></span>·<span·class="inlinecode"><span·class="id"·title="var">A</span></span>·<span·class="inlinecode"><span·class="id"·title="var">n</span></span>·<span·class="inlinecode"><span·class="id"·title="var">B</span></span>·is |
59 | ····<span·class="inlinecode"><span·class="id"·title="var">A</span></span>·<span·class="inlinecode">-></span>·<span·class="inlinecode">...</span>·<span·class="inlinecode">-></span>·<span·class="inlinecode"><span·class="id"·title="var">A</span></span>·<span·class="inlinecode">-></span>·<span·class="inlinecode"><span·class="id"·title="var">B</span></span>·with·<span·class="inlinecode"><span·class="id"·title="var">n</span></span>·occurrences·of·<span·class="inlinecode"><span·class="id"·title="var">A</span></span>·in·this·type.· | 59 | ····<span·class="inlinecode"><span·class="id"·title="var">A</span></span>·<span·class="inlinecode">-></span>·<span·class="inlinecode">...</span>·<span·class="inlinecode">-></span>·<span·class="inlinecode"><span·class="id"·title="var">A</span></span>·<span·class="inlinecode">-></span>·<span·class="inlinecode"><span·class="id"·title="var">B</span></span>·with·<span·class="inlinecode"><span·class="id"·title="var">n</span></span>·occurrences·of·<span·class="inlinecode"><span·class="id"·title="var">A</span></span>·in·this·type.· |
60 | </div> | 60 | </div> |
61 | <div·class="code"> | 61 | <div·class="code"> |
Offset 172, 15 lines modified | Offset 172, 15 lines modified | ||
172 | <br/> | 172 | <br/> |
173 | <span·class="id"·title="keyword">Theorem</span>·<a·id="NZDivProp.mod_small"·class="idref"·href="#NZDivProp.mod_small"><span·class="id"·title="lemma">mod_small</span></a>:·<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>,·0<a·class="idref"·href="Coq.Structures.Orders.html#62fc7208ddb2fa310e7ae9ec2d794c92"><span·class="id"·title="notation"><=</span></a><a·class="idref"·href="Coq.Numbers.NatInt.NZDiv.html#a:37"><span·class="id"·title="variable">a</span></a><a·class="idref"·href="Coq.Structures.Orders.html#62fc7208ddb2fa310e7ae9ec2d794c92"><span·class="id"·title="notation"><</span></a><a·class="idref"·href="Coq.Numbers.NatInt.NZDiv.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>·<a·class="idref"·href="Coq.Numbers.NatInt.NZDiv.html#a:37"><span·class="id"·title="variable">a</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZDiv.html#DivModNotation.:::x_'mod'_x"><span·class="id"·title="notation">mod</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZDiv.html#b:38"><span·class="id"·title="variable">b</span></a>·<a·class="idref"·href="Coq.Structures.Equalities.html#a3a0575149632d194e420f6edb9b2362"><span·class="id"·title="notation">==</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZDiv.html#a:37"><span·class="id"·title="variable">a</span></a>.<br/> | 173 | <span·class="id"·title="keyword">Theorem</span>·<a·id="NZDivProp.mod_small"·class="idref"·href="#NZDivProp.mod_small"><span·class="id"·title="lemma">mod_small</span></a>:·<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>,·0<a·class="idref"·href="Coq.Structures.Orders.html#62fc7208ddb2fa310e7ae9ec2d794c92"><span·class="id"·title="notation"><=</span></a><a·class="idref"·href="Coq.Numbers.NatInt.NZDiv.html#a:37"><span·class="id"·title="variable">a</span></a><a·class="idref"·href="Coq.Structures.Orders.html#62fc7208ddb2fa310e7ae9ec2d794c92"><span·class="id"·title="notation"><</span></a><a·class="idref"·href="Coq.Numbers.NatInt.NZDiv.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>·<a·class="idref"·href="Coq.Numbers.NatInt.NZDiv.html#a:37"><span·class="id"·title="variable">a</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZDiv.html#DivModNotation.:::x_'mod'_x"><span·class="id"·title="notation">mod</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZDiv.html#b:38"><span·class="id"·title="variable">b</span></a>·<a·class="idref"·href="Coq.Structures.Equalities.html#a3a0575149632d194e420f6edb9b2362"><span·class="id"·title="notation">==</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZDiv.html#a:37"><span·class="id"·title="variable">a</span></a>.<br/> |
174 | <br/> | 174 | <br/> |
175 | </div> | 175 | </div> |
176 | <div·class="doc"> | 176 | <div·class="doc"> |
177 | <a·id="lab | 177 | <a·id="lab753"></a><h1·class="section">Basic·values·of·divisions·and·modulo.</h1> |
178 | </div> | 178 | </div> |
179 | <div·class="code"> | 179 | <div·class="code"> |
180 | <br/> | 180 | <br/> |
181 | <span·class="id"·title="keyword">Lemma</span>·<a·id="NZDivProp.div_0_l"·class="idref"·href="#NZDivProp.div_0_l"><span·class="id"·title="lemma">div_0_l</span></a>:·<span·class="id"·title="keyword">forall</span>·<a·id="a:39"·class="idref"·href="#a:39"><span·class="id"·title="binder">a</span></a>,·0<a·class="idref"·href="Coq.Structures.Orders.html#LtNotation.:::x_'<'_x"><span·class="id"·title="notation"><</span></a><a·class="idref"·href="Coq.Numbers.NatInt.NZDiv.html#a:39"><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>·0<a·class="idref"·href="Coq.Numbers.NatInt.NZDiv.html#553b1e0c6dfeea0fb5d9a4a0a1c7f719"><span·class="id"·title="notation">/</span></a><a·class="idref"·href="Coq.Numbers.NatInt.NZDiv.html#a:39"><span·class="id"·title="variable">a</span></a>·<a·class="idref"·href="Coq.Structures.Equalities.html#a3a0575149632d194e420f6edb9b2362"><span·class="id"·title="notation">==</span></a>·0.<br/> | 181 | <span·class="id"·title="keyword">Lemma</span>·<a·id="NZDivProp.div_0_l"·class="idref"·href="#NZDivProp.div_0_l"><span·class="id"·title="lemma">div_0_l</span></a>:·<span·class="id"·title="keyword">forall</span>·<a·id="a:39"·class="idref"·href="#a:39"><span·class="id"·title="binder">a</span></a>,·0<a·class="idref"·href="Coq.Structures.Orders.html#LtNotation.:::x_'<'_x"><span·class="id"·title="notation"><</span></a><a·class="idref"·href="Coq.Numbers.NatInt.NZDiv.html#a:39"><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>·0<a·class="idref"·href="Coq.Numbers.NatInt.NZDiv.html#553b1e0c6dfeea0fb5d9a4a0a1c7f719"><span·class="id"·title="notation">/</span></a><a·class="idref"·href="Coq.Numbers.NatInt.NZDiv.html#a:39"><span·class="id"·title="variable">a</span></a>·<a·class="idref"·href="Coq.Structures.Equalities.html#a3a0575149632d194e420f6edb9b2362"><span·class="id"·title="notation">==</span></a>·0.<br/> |
Offset 71, 15 lines modified | Offset 71, 15 lines modified | ||
71 | <span·class="id"·title="keyword">Module</span>·<a·id="NZDomainProp"·class="idref"·href="#NZDomainProp"><span·class="id"·title="module">NZDomainProp</span></a>·(<span·class="id"·title="keyword">Import</span>·<span·class="id"·title="var">NZ</span>:<a·class="idref"·href="Coq.Numbers.NatInt.NZAxioms.html#NZDomainSig'"><span·class="id"·title="module">NZDomainSig'</span></a>).<br/> | 71 | <span·class="id"·title="keyword">Module</span>·<a·id="NZDomainProp"·class="idref"·href="#NZDomainProp"><span·class="id"·title="module">NZDomainProp</span></a>·(<span·class="id"·title="keyword">Import</span>·<span·class="id"·title="var">NZ</span>:<a·class="idref"·href="Coq.Numbers.NatInt.NZAxioms.html#NZDomainSig'"><span·class="id"·title="module">NZDomainSig'</span></a>).<br/> |
72 | <span·class="id"·title="keyword">Include</span>·<a·class="idref"·href="Coq.Numbers.NatInt.NZBase.html#NZBaseProp"><span·class="id"·title="module">NZBaseProp</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZDomain.html#NZ"><span·class="id"·title="module">NZ</span></a>.<br/> | 72 | <span·class="id"·title="keyword">Include</span>·<a·class="idref"·href="Coq.Numbers.NatInt.NZBase.html#NZBaseProp"><span·class="id"·title="module">NZBaseProp</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZDomain.html#NZ"><span·class="id"·title="module">NZ</span></a>.<br/> |
73 | <br/> | 73 | <br/> |
74 | </div> | 74 | </div> |
75 | <div·class="doc"> | 75 | <div·class="doc"> |
76 | <a·id="lab | 76 | <a·id="lab750"></a><h1·class="section">Relationship·between·points·thanks·to·<span·class="inlinecode"><span·class="id"·title="var">succ</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">pred</span></span>.</h1> |
77 | <div·class="paragraph">·</div> | 77 | <div·class="paragraph">·</div> |
78 | ·For·any·two·points,·one·is·an·iterated·successor·of·the·other.· | 78 | ·For·any·two·points,·one·is·an·iterated·successor·of·the·other.· |
79 | </div> | 79 | </div> |
80 | <div·class="code"> | 80 | <div·class="code"> |
Offset 414, 15 lines modified | Offset 414, 15 lines modified | ||
414 | (<span·class="id"·title="keyword">Import</span>·<span·class="id"·title="var">E</span>·:·<a·class="idref"·href="Coq.Numbers.NatInt.NZPow.html#NZPowProp"><span·class="id"·title="module">NZPowProp</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZLog.html#A"><span·class="id"·title="module">A</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZLog.html#B"><span·class="id"·title="module">B</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZLog.html#D"><span·class="id"·title="module">D</span></a>)<br/> | 414 | (<span·class="id"·title="keyword">Import</span>·<span·class="id"·title="var">E</span>·:·<a·class="idref"·href="Coq.Numbers.NatInt.NZPow.html#NZPowProp"><span·class="id"·title="module">NZPowProp</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZLog.html#A"><span·class="id"·title="module">A</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZLog.html#B"><span·class="id"·title="module">B</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZLog.html#D"><span·class="id"·title="module">D</span></a>)<br/> |
415 | (<span·class="id"·title="keyword">Import</span>·<span·class="id"·title="var">F</span>·:·<a·class="idref"·href="Coq.Numbers.NatInt.NZLog.html#NZLog2Prop"><span·class="id"·title="module">NZLog2Prop</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZLog.html#A"><span·class="id"·title="module">A</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZLog.html#B"><span·class="id"·title="module">B</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZLog.html#C"><span·class="id"·title="module">C</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZLog.html#D"><span·class="id"·title="module">D</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZLog.html#E"><span·class="id"·title="module">E</span></a>).<br/> | 415 | (<span·class="id"·title="keyword">Import</span>·<span·class="id"·title="var">F</span>·:·<a·class="idref"·href="Coq.Numbers.NatInt.NZLog.html#NZLog2Prop"><span·class="id"·title="module">NZLog2Prop</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZLog.html#A"><span·class="id"·title="module">A</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZLog.html#B"><span·class="id"·title="module">B</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZLog.html#C"><span·class="id"·title="module">C</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZLog.html#D"><span·class="id"·title="module">D</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZLog.html#E"><span·class="id"·title="module">E</span></a>).<br/> |
416 | <br/> | 416 | <br/> |
417 | </div> | 417 | </div> |
418 | <div·class="doc"> | 418 | <div·class="doc"> |
419 | <a·id="lab | 419 | <a·id="lab757"></a><h1·class="section"><span·class="inlinecode"><span·class="id"·title="var">log2_up</span></span>·:·a·binary·logarithm·that·rounds·up·instead·of·down</h1> |
420 | <div·class="paragraph">·</div> | 420 | <div·class="paragraph">·</div> |
421 | ·For·once,·we·define·instead·of·axiomatizing,·thanks·to·log2· | 421 | ·For·once,·we·define·instead·of·axiomatizing,·thanks·to·log2· |
422 | </div> | 422 | </div> |
423 | <div·class="code"> | 423 | <div·class="code"> |
Offset 343, 15 lines modified | Offset 343, 15 lines modified | ||
343 | (<span·class="id"·title="keyword">Import</span>·<span·class="id"·title="var">C</span>·:·<a·class="idref"·href="Coq.Numbers.NatInt.NZMulOrder.html#NZMulOrderProp"><span·class="id"·title="module">NZMulOrderProp</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZSqrt.html#A"><span·class="id"·title="module">A</span></a>)<br/> | 343 | (<span·class="id"·title="keyword">Import</span>·<span·class="id"·title="var">C</span>·:·<a·class="idref"·href="Coq.Numbers.NatInt.NZMulOrder.html#NZMulOrderProp"><span·class="id"·title="module">NZMulOrderProp</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZSqrt.html#A"><span·class="id"·title="module">A</span></a>)<br/> |
344 | (<span·class="id"·title="keyword">Import</span>·<span·class="id"·title="var">D</span>·:·<a·class="idref"·href="Coq.Numbers.NatInt.NZSqrt.html#NZSqrtProp"><span·class="id"·title="module">NZSqrtProp</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZSqrt.html#A"><span·class="id"·title="module">A</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZSqrt.html#B"><span·class="id"·title="module">B</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZSqrt.html#C"><span·class="id"·title="module">C</span></a>).<br/> | 344 | (<span·class="id"·title="keyword">Import</span>·<span·class="id"·title="var">D</span>·:·<a·class="idref"·href="Coq.Numbers.NatInt.NZSqrt.html#NZSqrtProp"><span·class="id"·title="module">NZSqrtProp</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZSqrt.html#A"><span·class="id"·title="module">A</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZSqrt.html#B"><span·class="id"·title="module">B</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZSqrt.html#C"><span·class="id"·title="module">C</span></a>).<br/> |
345 | <br/> | 345 | <br/> |
346 | </div> | 346 | </div> |
347 | <div·class="doc"> | 347 | <div·class="doc"> |
348 | <a·id="lab | 348 | <a·id="lab756"></a><h1·class="section"><span·class="inlinecode"><span·class="id"·title="var">sqrt_up</span></span>·:·a·square·root·that·rounds·up·instead·of·down</h1> |
349 | </div> | 349 | </div> |
350 | <div·class="code"> | 350 | <div·class="code"> |
351 | <br/> | 351 | <br/> |
352 | <br/> | 352 | <br/> |
Offset 154, 15 lines modified | Offset 154, 15 lines modified | ||
154 | <br/> | 154 | <br/> |
155 | <span·class="id"·title="keyword">Theorem</span>·<a·id="NDivProp.mod_small"·class="idref"·href="#NDivProp.mod_small"><span·class="id"·title="lemma">mod_small</span></a>:·<span·class="id"·title="keyword">forall</span>·<a·id="a:25"·class="idref"·href="#a:25"><span·class="id"·title="binder">a</span></a>·<a·id="b:26"·class="idref"·href="#b:26"><span·class="id"·title="binder">b</span></a>,·<a·class="idref"·href="Coq.Numbers.Natural.Abstract.NDiv.html#a:25"><span·class="id"·title="variable">a</span></a><a·class="idref"·href="Coq.Structures.Orders.html#LtNotation.:::x_'<'_x"><span·class="id"·title="notation"><</span></a><a·class="idref"·href="Coq.Numbers.Natural.Abstract.NDiv.html#b:26"><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>·<a·class="idref"·href="Coq.Numbers.Natural.Abstract.NDiv.html#a:25"><span·class="id"·title="variable">a</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZDiv.html#DivModNotation.:::x_'mod'_x"><span·class="id"·title="notation">mod</span></a>·<a·class="idref"·href="Coq.Numbers.Natural.Abstract.NDiv.html#b:26"><span·class="id"·title="variable">b</span></a>·<a·class="idref"·href="Coq.Structures.Equalities.html#a3a0575149632d194e420f6edb9b2362"><span·class="id"·title="notation">==</span></a>·<a·class="idref"·href="Coq.Numbers.Natural.Abstract.NDiv.html#a:25"><span·class="id"·title="variable">a</span></a>.<br/> | 155 | <span·class="id"·title="keyword">Theorem</span>·<a·id="NDivProp.mod_small"·class="idref"·href="#NDivProp.mod_small"><span·class="id"·title="lemma">mod_small</span></a>:·<span·class="id"·title="keyword">forall</span>·<a·id="a:25"·class="idref"·href="#a:25"><span·class="id"·title="binder">a</span></a>·<a·id="b:26"·class="idref"·href="#b:26"><span·class="id"·title="binder">b</span></a>,·<a·class="idref"·href="Coq.Numbers.Natural.Abstract.NDiv.html#a:25"><span·class="id"·title="variable">a</span></a><a·class="idref"·href="Coq.Structures.Orders.html#LtNotation.:::x_'<'_x"><span·class="id"·title="notation"><</span></a><a·class="idref"·href="Coq.Numbers.Natural.Abstract.NDiv.html#b:26"><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>·<a·class="idref"·href="Coq.Numbers.Natural.Abstract.NDiv.html#a:25"><span·class="id"·title="variable">a</span></a>·<a·class="idref"·href="Coq.Numbers.NatInt.NZDiv.html#DivModNotation.:::x_'mod'_x"><span·class="id"·title="notation">mod</span></a>·<a·class="idref"·href="Coq.Numbers.Natural.Abstract.NDiv.html#b:26"><span·class="id"·title="variable">b</span></a>·<a·class="idref"·href="Coq.Structures.Equalities.html#a3a0575149632d194e420f6edb9b2362"><span·class="id"·title="notation">==</span></a>·<a·class="idref"·href="Coq.Numbers.Natural.Abstract.NDiv.html#a:25"><span·class="id"·title="variable">a</span></a>.<br/> |
156 | · | 156 | · |
157 | <br/> | 157 | <br/> |
158 | </div> | 158 | </div> |
159 | <div·class="doc"> | 159 | <div·class="doc"> |
160 | <a·id="lab | 160 | <a·id="lab712"></a><h1·class="section">Basic·values·of·divisions·and·modulo.</h1> |
161 | </div> | 161 | </div> |
162 | <div·class="code"> | 162 | <div·class="code"> |
163 | <br/> | 163 | <br/> |
164 | <span·class="id"·title="keyword">Lemma</span>·<a·id="NDivProp.div_0_l"·class="idref"·href="#NDivProp.div_0_l"><span·class="id"·title="lemma">div_0_l</span></a>:·<span·class="id"·title="keyword">forall</span>·<a·id="a:27"·class="idref"·href="#a:27"><span·class="id"·title="binder">a</span></a>,·<a·class="idref"·href="Coq.Numbers.Natural.Abstract.NDiv.html#a:27"><span·class="id"·title="variable">a</span></a><a·class="idref"·href="Coq.Structures.Equalities.html#9cff58ff8ba6db8841aeeecf7f406093"><span·class="id"·title="notation">~=</span></a>0·<a·class="idref"·href="Coq.Init.Logic.html#::type_scope:x_'->'_x"><span·class="id"·title="notation">-></span></a>·0<a·class="idref"·href="Coq.Numbers.NatInt.NZDiv.html#553b1e0c6dfeea0fb5d9a4a0a1c7f719"><span·class="id"·title="notation">/</span></a><a·class="idref"·href="Coq.Numbers.Natural.Abstract.NDiv.html#a:27"><span·class="id"·title="variable">a</span></a>·<a·class="idref"·href="Coq.Structures.Equalities.html#a3a0575149632d194e420f6edb9b2362"><span·class="id"·title="notation">==</span></a>·0.<br/> | 164 | <span·class="id"·title="keyword">Lemma</span>·<a·id="NDivProp.div_0_l"·class="idref"·href="#NDivProp.div_0_l"><span·class="id"·title="lemma">div_0_l</span></a>:·<span·class="id"·title="keyword">forall</span>·<a·id="a:27"·class="idref"·href="#a:27"><span·class="id"·title="binder">a</span></a>,·<a·class="idref"·href="Coq.Numbers.Natural.Abstract.NDiv.html#a:27"><span·class="id"·title="variable">a</span></a><a·class="idref"·href="Coq.Structures.Equalities.html#9cff58ff8ba6db8841aeeecf7f406093"><span·class="id"·title="notation">~=</span></a>0·<a·class="idref"·href="Coq.Init.Logic.html#::type_scope:x_'->'_x"><span·class="id"·title="notation">-></span></a>·0<a·class="idref"·href="Coq.Numbers.NatInt.NZDiv.html#553b1e0c6dfeea0fb5d9a4a0a1c7f719"><span·class="id"·title="notation">/</span></a><a·class="idref"·href="Coq.Numbers.Natural.Abstract.NDiv.html#a:27"><span·class="id"·title="variable">a</span></a>·<a·class="idref"·href="Coq.Structures.Equalities.html#a3a0575149632d194e420f6edb9b2362"><span·class="id"·title="notation">==</span></a>·0.<br/> |
165 | · | 165 | · |
Offset 48, 15 lines modified | Offset 48, 15 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.Natural.Abstract.NAxioms.html#"><span·class="id"·title="library">NAxioms</span></a>·<a·class="idref"·href="Coq.Numbers.Natural.Abstract.NSub.html#"><span·class="id"·title="library">NSub</span></a>·<a·class="idref"·href="Coq.Numbers.Natural.Abstract.NDiv.html#"><span·class="id"·title="library">NDiv</span></a>·<a·class="idref"·href="Coq.Numbers.Natural.Abstract.NGcd.html#"><span·class="id"·title="library">NGcd</span></a>.<br/> | 49 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Numbers.Natural.Abstract.NAxioms.html#"><span·class="id"·title="library">NAxioms</span></a>·<a·class="idref"·href="Coq.Numbers.Natural.Abstract.NSub.html#"><span·class="id"·title="library">NSub</span></a>·<a·class="idref"·href="Coq.Numbers.Natural.Abstract.NDiv.html#"><span·class="id"·title="library">NDiv</span></a>·<a·class="idref"·href="Coq.Numbers.Natural.Abstract.NGcd.html#"><span·class="id"·title="library">NGcd</span></a>.<br/> |
50 | <br/> | 50 | <br/> |
51 | </div> | 51 | </div> |
52 | <div·class="doc"> | 52 | <div·class="doc"> |
53 | <a·id="lab | 53 | <a·id="lab715"></a><h1·class="section">Least·Common·Multiple</h1> |
54 | <div·class="paragraph">·</div> | 54 | <div·class="paragraph">·</div> |
55 | ·Unlike·other·functions·around,·we·will·define·lcm·below·instead·of | 55 | ·Unlike·other·functions·around,·we·will·define·lcm·below·instead·of |
56 | ··axiomatizing·it.·Indeed,·there·is·no·"prior·art"·about·lcm·in·the | 56 | ··axiomatizing·it.·Indeed,·there·is·no·"prior·art"·about·lcm·in·the |
57 | ··standard·library·to·be·compliant·with,·and·the·generic·definition | 57 | ··standard·library·to·be·compliant·with,·and·the·generic·definition |
58 | ··of·lcm·via·gcd·is·quite·reasonable. | 58 | ··of·lcm·via·gcd·is·quite·reasonable. |
Offset 48, 15 lines modified | Offset 48, 15 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.Natural.Abstract.NAxioms.html#"><span·class="id"·title="library">NAxioms</span></a>·<a·class="idref"·href="Coq.Numbers.Natural.Abstract.NSub.html#"><span·class="id"·title="library">NSub</span></a>·<a·class="idref"·href="Coq.Structures.GenericMinMax.html#"><span·class="id"·title="library">GenericMinMax</span></a>.<br/> | 49 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Numbers.Natural.Abstract.NAxioms.html#"><span·class="id"·title="library">NAxioms</span></a>·<a·class="idref"·href="Coq.Numbers.Natural.Abstract.NSub.html#"><span·class="id"·title="library">NSub</span></a>·<a·class="idref"·href="Coq.Structures.GenericMinMax.html#"><span·class="id"·title="library">GenericMinMax</span></a>.<br/> |
50 | <br/> | 50 | <br/> |
51 | </div> | 51 | </div> |
52 | <div·class="doc"> | 52 | <div·class="doc"> |
53 | <a·id="lab | 53 | <a·id="lab716"></a><h1·class="section">Properties·of·minimum·and·maximum·specific·to·natural·numbers</h1> |
54 | </div> | 54 | </div> |
55 | <div·class="code"> | 55 | <div·class="code"> |
56 | <br/> | 56 | <br/> |
57 | <span·class="id"·title="keyword">Module</span>·<span·class="id"·title="keyword">Type</span>·<a·id="NMaxMinProp"·class="idref"·href="#NMaxMinProp"><span·class="id"·title="module">NMaxMinProp</span></a>·(<span·class="id"·title="keyword">Import</span>·<span·class="id"·title="var">N</span>·:·<a·class="idref"·href="Coq.Numbers.Natural.Abstract.NAxioms.html#NAxiomsMiniSig'"><span·class="id"·title="module">NAxiomsMiniSig'</span></a>).<br/> | 57 | <span·class="id"·title="keyword">Module</span>·<span·class="id"·title="keyword">Type</span>·<a·id="NMaxMinProp"·class="idref"·href="#NMaxMinProp"><span·class="id"·title="module">NMaxMinProp</span></a>·(<span·class="id"·title="keyword">Import</span>·<span·class="id"·title="var">N</span>·:·<a·class="idref"·href="Coq.Numbers.Natural.Abstract.NAxioms.html#NAxiomsMiniSig'"><span·class="id"·title="module">NAxiomsMiniSig'</span></a>).<br/> |
58 | <span·class="id"·title="keyword">Include</span>·<a·class="idref"·href="Coq.Numbers.Natural.Abstract.NSub.html#NSubProp"><span·class="id"·title="module">NSubProp</span></a>·<a·class="idref"·href="Coq.Numbers.Natural.Abstract.NMaxMin.html#N"><span·class="id"·title="module">N</span></a>.<br/> | 58 | <span·class="id"·title="keyword">Include</span>·<a·class="idref"·href="Coq.Numbers.Natural.Abstract.NSub.html#NSubProp"><span·class="id"·title="module">NSubProp</span></a>·<a·class="idref"·href="Coq.Numbers.Natural.Abstract.NMaxMin.html#N"><span·class="id"·title="module">N</span></a>.<br/> |
Offset 53, 15 lines modified | Offset 53, 15 lines modified | ||
53 | <br/> | 53 | <br/> |
54 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">N_scope</span>.<br/> | 54 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">N_scope</span>.<br/> |
55 | <br/> | 55 | <br/> |
56 | </div> | 56 | </div> |
57 | <div·class="doc"> | 57 | <div·class="doc"> |
58 | <a·id="lab | 58 | <a·id="lab717"></a><h1·class="section"><span·class="inlinecode"><span·class="id"·title="var">BinNat.N</span></span>·already·implements·<span·class="inlinecode"><span·class="id"·title="var">NAxiomSig</span></span></h1> |
59 | </div> | 59 | </div> |
60 | <div·class="code"> | 60 | <div·class="code"> |
61 | <br/> | 61 | <br/> |
62 | <span·class="id"·title="keyword">Module</span>·<a·id="N"·class="idref"·href="#N"><span·class="id"·title="module">N</span></a>·<:·<a·class="idref"·href="Coq.Numbers.Natural.Abstract.NAxioms.html#NAxiomsSig"><span·class="id"·title="module">NAxiomsSig</span></a>·:=·<a·class="idref"·href="Coq.NArith.BinNat.html#N"><span·class="id"·title="module">N</span></a>.<br/> | 62 | <span·class="id"·title="keyword">Module</span>·<a·id="N"·class="idref"·href="#N"><span·class="id"·title="module">N</span></a>·<:·<a·class="idref"·href="Coq.Numbers.Natural.Abstract.NAxioms.html#NAxiomsSig"><span·class="id"·title="module">NAxiomsSig</span></a>·:=·<a·class="idref"·href="Coq.NArith.BinNat.html#N"><span·class="id"·title="module">N</span></a>.<br/> |
Offset 53, 15 lines modified | Offset 53, 15 lines modified | ||
53 | <br/> | 53 | <br/> |
54 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Export</span>·<a·class="idref"·href="Coq.PArith.BinPosDef.html#"><span·class="id"·title="library">BinPosDef</span></a>.<br/> | 54 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Export</span>·<a·class="idref"·href="Coq.PArith.BinPosDef.html#"><span·class="id"·title="library">BinPosDef</span></a>.<br/> |
55 | <br/> | 55 | <br/> |
56 | </div> | 56 | </div> |
57 | <div·class="doc"> | 57 | <div·class="doc"> |
58 | <a·id="lab | 58 | <a·id="lab82"></a><h1·class="section">Binary·positive·numbers,·operations·and·properties</h1> |
59 | <div·class="paragraph">·</div> | 59 | <div·class="paragraph">·</div> |
60 | ·Initial·development·by·Pierre·Crégut,·CNET,·Lannion,·France· | 60 | ·Initial·development·by·Pierre·Crégut,·CNET,·Lannion,·France· |
61 | <div·class="paragraph">·</div> | 61 | <div·class="paragraph">·</div> |
62 | ·The·type·<span·class="inlinecode"><span·class="id"·title="var">positive</span></span>·and·its·constructors·<span·class="inlinecode"><span·class="id"·title="var">xI</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">xO</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">xH</span></span> | 62 | ·The·type·<span·class="inlinecode"><span·class="id"·title="var">positive</span></span>·and·its·constructors·<span·class="inlinecode"><span·class="id"·title="var">xI</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">xO</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">xH</span></span> |
Offset 45, 15 lines modified | Offset 45, 15 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="lab5 | 49 | <a·id="lab55"></a><h1·class="section">Binary·positive·numbers,·operations</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ·Initial·development·by·Pierre·Crégut,·CNET,·Lannion,·France· | 51 | ·Initial·development·by·Pierre·Crégut,·CNET,·Lannion,·France· |
52 | <div·class="paragraph">·</div> | 52 | <div·class="paragraph">·</div> |
53 | ·The·type·<span·class="inlinecode"><span·class="id"·title="var">positive</span></span>·and·its·constructors·<span·class="inlinecode"><span·class="id"·title="var">xI</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">xO</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">xH</span></span> | 53 | ·The·type·<span·class="inlinecode"><span·class="id"·title="var">positive</span></span>·and·its·constructors·<span·class="inlinecode"><span·class="id"·title="var">xI</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">xO</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">xH</span></span> |
Offset 51, 15 lines modified | Offset 51, 15 lines modified | ||
51 | <br/> | 51 | <br/> |
52 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">positive_scope</span>.<br/> | 52 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">positive_scope</span>.<br/> |
53 | <br/> | 53 | <br/> |
54 | </div> | 54 | </div> |
55 | <div·class="doc"> | 55 | <div·class="doc"> |
56 | <a·id="lab | 56 | <a·id="lab137"></a><h1·class="section">DecidableType·structure·for·<span·class="inlinecode"><span·class="id"·title="var">positive</span></span>·numbers</h1> |
57 | </div> | 57 | </div> |
58 | <div·class="code"> | 58 | <div·class="code"> |
59 | <br/> | 59 | <br/> |
60 | <span·class="id"·title="keyword">Module</span>·<a·id="Positive_as_DT"·class="idref"·href="#Positive_as_DT"><span·class="id"·title="module">Positive_as_DT</span></a>·<:·<a·class="idref"·href="Coq.Structures.Equalities.html#UsualDecidableTypeFull"><span·class="id"·title="module">UsualDecidableTypeFull</span></a>·:=·<a·class="idref"·href="Coq.PArith.BinPos.html#Pos"><span·class="id"·title="module">Pos</span></a>.<br/> | 60 | <span·class="id"·title="keyword">Module</span>·<a·id="Positive_as_DT"·class="idref"·href="#Positive_as_DT"><span·class="id"·title="module">Positive_as_DT</span></a>·<:·<a·class="idref"·href="Coq.Structures.Equalities.html#UsualDecidableTypeFull"><span·class="id"·title="module">UsualDecidableTypeFull</span></a>·:=·<a·class="idref"·href="Coq.PArith.BinPos.html#Pos"><span·class="id"·title="module">Pos</span></a>.<br/> |
Offset 43, 15 lines modified | Offset 43, 15 lines modified | ||
43 | <h1·class="libtitle">Library·Coq.Program.Combinators</h1> | 43 | <h1·class="libtitle">Library·Coq.Program.Combinators</h1> |
44 | <div·class="code"> | 44 | <div·class="code"> |
45 | </div> | 45 | </div> |
46 | <div·class="doc"> | 46 | <div·class="doc"> |
47 | <a·id="lab | 47 | <a·id="lab823"></a><h1·class="section">Proofs·about·standard·combinators,·exports·functional·extensionality.</h1> |
48 | <div·class="paragraph">·</div> | 48 | <div·class="paragraph">·</div> |
49 | ···Author:·Matthieu·Sozeau | 49 | ···Author:·Matthieu·Sozeau |
50 | ···Institution:·LRI,·CNRS·UMR·8623·-·University·Paris·Sud | 50 | ···Institution:·LRI,·CNRS·UMR·8623·-·University·Paris·Sud |
Offset 51, 15 lines modified | Offset 51, 15 lines modified | ||
51 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Export</span>·<a·class="idref"·href="Coq.ZArith.BinInt.html#"><span·class="id"·title="library">ZArith.BinInt</span></a>.<br/> | 51 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Export</span>·<a·class="idref"·href="Coq.ZArith.BinInt.html#"><span·class="id"·title="library">ZArith.BinInt</span></a>.<br/> |
52 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Export</span>·<a·class="idref"·href="Coq.Classes.Morphisms.html#"><span·class="id"·title="library">Morphisms</span></a>·<a·class="idref"·href="Coq.Setoids.Setoid.html#"><span·class="id"·title="library">Setoid</span></a>·<a·class="idref"·href="Coq.Bool.Bool.html#"><span·class="id"·title="library">Bool</span></a>.<br/> | 52 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Export</span>·<a·class="idref"·href="Coq.Classes.Morphisms.html#"><span·class="id"·title="library">Morphisms</span></a>·<a·class="idref"·href="Coq.Setoids.Setoid.html#"><span·class="id"·title="library">Setoid</span></a>·<a·class="idref"·href="Coq.Bool.Bool.html#"><span·class="id"·title="library">Bool</span></a>.<br/> |
53 | <br/> | 53 | <br/> |
54 | </div> | 54 | </div> |
55 | <div·class="doc"> | 55 | <div·class="doc"> |
56 | <a·id="lab | 56 | <a·id="lab798"></a><h1·class="section">Definition·of·<span·class="inlinecode"><span·class="id"·title="var">Q</span></span>·and·basic·properties</h1> |
57 | <div·class="paragraph">·</div> | 57 | <div·class="paragraph">·</div> |
58 | ·Rationals·are·pairs·of·<span·class="inlinecode"><span·class="id"·title="var">Z</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">positive</span></span>·numbers.· | 58 | ·Rationals·are·pairs·of·<span·class="inlinecode"><span·class="id"·title="var">Z</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">positive</span></span>·numbers.· |
59 | </div> | 59 | </div> |
60 | <div·class="code"> | 60 | <div·class="code"> |
Offset 51, 15 lines modified | Offset 51, 15 lines modified | ||
51 | <br/> | 51 | <br/> |
52 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">Q_scope</span>.<br/> | 52 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">Q_scope</span>.<br/> |
53 | <br/> | 53 | <br/> |
54 | </div> | 54 | </div> |
55 | <div·class="doc"> | 55 | <div·class="doc"> |
56 | <a·id="lab | 56 | <a·id="lab816"></a><h1·class="section">DecidableType·structure·for·rational·numbers</h1> |
57 | </div> | 57 | </div> |
58 | <div·class="code"> | 58 | <div·class="code"> |
59 | <br/> | 59 | <br/> |
60 | <span·class="id"·title="keyword">Module</span>·<a·id="Q_as_DT"·class="idref"·href="#Q_as_DT"><span·class="id"·title="module">Q_as_DT</span></a>·<:·<a·class="idref"·href="Coq.Structures.Equalities.html#DecidableTypeFull"><span·class="id"·title="module">DecidableTypeFull</span></a>.<br/> | 60 | <span·class="id"·title="keyword">Module</span>·<a·id="Q_as_DT"·class="idref"·href="#Q_as_DT"><span·class="id"·title="module">Q_as_DT</span></a>·<:·<a·class="idref"·href="Coq.Structures.Equalities.html#DecidableTypeFull"><span·class="id"·title="module">DecidableTypeFull</span></a>.<br/> |
61 | <span·class="id"·title="keyword">Definition</span>·<a·id="Q_as_DT.t"·class="idref"·href="#Q_as_DT.t"><span·class="id"·title="definition">t</span></a>·:=·<a·class="idref"·href="Coq.QArith.QArith_base.html#Q"><span·class="id"·title="record">Q</span></a>.<br/> | 61 | <span·class="id"·title="keyword">Definition</span>·<a·id="Q_as_DT.t"·class="idref"·href="#Q_as_DT.t"><span·class="id"·title="definition">t</span></a>·:=·<a·class="idref"·href="Coq.QArith.QArith_base.html#Q"><span·class="id"·title="record">Q</span></a>.<br/> |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab821"></a><h1·class="section">An·absolute·value·for·normalized·rational·numbers.</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ·Contributed·by·Cédric·Auger· | 51 | ·Contributed·by·Cédric·Auger· |
52 | </div> | 52 | </div> |
53 | <div·class="code"> | 53 | <div·class="code"> |
Offset 50, 15 lines modified | Offset 50, 15 lines modified | ||
50 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Export</span>·<a·class="idref"·href="Coq.QArith.QArith_base.html#"><span·class="id"·title="library">QArith_base</span></a>.<br/> | 50 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Export</span>·<a·class="idref"·href="Coq.QArith.QArith_base.html#"><span·class="id"·title="library">QArith_base</span></a>.<br/> |
51 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.setoid_ring.NArithRing.html#"><span·class="id"·title="library">NArithRing</span></a>.<br/> | 51 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.setoid_ring.NArithRing.html#"><span·class="id"·title="library">NArithRing</span></a>.<br/> |
52 | <br/> | 52 | <br/> |
53 | </div> | 53 | </div> |
54 | <div·class="doc"> | 54 | <div·class="doc"> |
55 | <a·id="lab | 55 | <a·id="lab822"></a><h1·class="section">field·and·ring·tactics·for·rational·numbers</h1> |
56 | </div> | 56 | </div> |
57 | <div·class="code"> | 57 | <div·class="code"> |
58 | <br/> | 58 | <br/> |
59 | <span·class="id"·title="keyword">Definition</span>·<a·id="Qsrt"·class="idref"·href="#Qsrt"><span·class="id"·title="definition">Qsrt</span></a>·:·<a·class="idref"·href="Coq.setoid_ring.Ring_theory.html#ring_theory"><span·class="id"·title="record">ring_theory</span></a>·0·1·<a·class="idref"·href="Coq.QArith.QArith_base.html#Qplus"><span·class="id"·title="definition">Qplus</span></a>·<a·class="idref"·href="Coq.QArith.QArith_base.html#Qmult"><span·class="id"·title="definition">Qmult</span></a>·<a·class="idref"·href="Coq.QArith.QArith_base.html#Qminus"><span·class="id"·title="definition">Qminus</span></a>·<a·class="idref"·href="Coq.QArith.QArith_base.html#Qopp"><span·class="id"·title="definition">Qopp</span></a>·<a·class="idref"·href="Coq.QArith.QArith_base.html#Qeq"><span·class="id"·title="definition">Qeq</span></a>.<br/> | 59 | <span·class="id"·title="keyword">Definition</span>·<a·id="Qsrt"·class="idref"·href="#Qsrt"><span·class="id"·title="definition">Qsrt</span></a>·:·<a·class="idref"·href="Coq.setoid_ring.Ring_theory.html#ring_theory"><span·class="id"·title="record">ring_theory</span></a>·0·1·<a·class="idref"·href="Coq.QArith.QArith_base.html#Qplus"><span·class="id"·title="definition">Qplus</span></a>·<a·class="idref"·href="Coq.QArith.QArith_base.html#Qmult"><span·class="id"·title="definition">Qmult</span></a>·<a·class="idref"·href="Coq.QArith.QArith_base.html#Qminus"><span·class="id"·title="definition">Qminus</span></a>·<a·class="idref"·href="Coq.QArith.QArith_base.html#Qopp"><span·class="id"·title="definition">Qopp</span></a>·<a·class="idref"·href="Coq.QArith.QArith_base.html#Qeq"><span·class="id"·title="definition">Qeq</span></a>.<br/> |
Offset 48, 15 lines modified | Offset 48, 15 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.QArith.QArith_base.html#"><span·class="id"·title="library">QArith_base</span></a>·<a·class="idref"·href="Coq.Structures.Orders.html#"><span·class="id"·title="library">Orders</span></a>·<a·class="idref"·href="Coq.QArith.QOrderedType.html#"><span·class="id"·title="library">QOrderedType</span></a>·<a·class="idref"·href="Coq.Structures.GenericMinMax.html#"><span·class="id"·title="library">GenericMinMax</span></a>.<br/> | 49 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.QArith.QArith_base.html#"><span·class="id"·title="library">QArith_base</span></a>·<a·class="idref"·href="Coq.Structures.Orders.html#"><span·class="id"·title="library">Orders</span></a>·<a·class="idref"·href="Coq.QArith.QOrderedType.html#"><span·class="id"·title="library">QOrderedType</span></a>·<a·class="idref"·href="Coq.Structures.GenericMinMax.html#"><span·class="id"·title="library">GenericMinMax</span></a>.<br/> |
50 | <br/> | 50 | <br/> |
51 | </div> | 51 | </div> |
52 | <div·class="doc"> | 52 | <div·class="doc"> |
53 | <a·id="lab | 53 | <a·id="lab819"></a><h1·class="section">Maximum·and·Minimum·of·two·rational·numbers</h1> |
54 | </div> | 54 | </div> |
55 | <div·class="code"> | 55 | <div·class="code"> |
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">Q_scope</span>.<br/> | 57 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">Q_scope</span>.<br/> |
Offset 48, 64 lines modified | Offset 48, 64 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.ZArith.Zpow_facts.html#"><span·class="id"·title="library">Zpow_facts</span></a>·<a·class="idref"·href="Coq.QArith.Qfield.html#"><span·class="id"·title="library">Qfield</span></a>·<a·class="idref"·href="Coq.QArith.Qreduction.html#"><span·class="id"·title="library">Qreduction</span></a>.<br/> | 49 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.ZArith.Zpow_facts.html#"><span·class="id"·title="library">Zpow_facts</span></a>·<a·class="idref"·href="Coq.QArith.Qfield.html#"><span·class="id"·title="library">Qfield</span></a>·<a·class="idref"·href="Coq.QArith.Qreduction.html#"><span·class="id"·title="library">Qreduction</span></a>.<br/> |
50 | <br/> | 50 | <br/> |
51 | </div> | 51 | </div> |
52 | <div·class="doc"> | 52 | <div·class="doc"> |
53 | <a·id="lab | 53 | <a·id="lab779"></a><h1·class="section">Properties·of·Qpower_positive</h1> |
54 | <div·class="paragraph">·</div> | 54 | <div·class="paragraph">·</div> |
55 | <a·id="lab | 55 | <a·id="lab780"></a><h2·class="section">Values·of·Qpower_positive·for·specific·arguments</h2> |
56 | </div> | 56 | </div> |
57 | <div·class="code"> | 57 | <div·class="code"> |
58 | <br/> | 58 | <br/> |
59 | <span·class="id"·title="keyword">Lemma</span>·<a·id="Qpower_positive_1"·class="idref"·href="#Qpower_positive_1"><span·class="id"·title="lemma">Qpower_positive_1</span></a>·:·<span·class="id"·title="keyword">forall</span>·<a·id="n:1"·class="idref"·href="#n:1"><span·class="id"·title="binder">n</span></a>,·<a·class="idref"·href="Coq.QArith.QArith_base.html#Qpower_positive"><span·class="id"·title="definition">Qpower_positive</span></a>·1·<a·class="idref"·href="Coq.QArith.Qpower.html#n:1"><span·class="id"·title="variable">n</span></a>·<a·class="idref"·href="Coq.QArith.QArith_base.html#0eaf04f08ecf51ebfc2703f9e1d22838"><span·class="id"·title="notation">==</span></a>·1.<br/> | 59 | <span·class="id"·title="keyword">Lemma</span>·<a·id="Qpower_positive_1"·class="idref"·href="#Qpower_positive_1"><span·class="id"·title="lemma">Qpower_positive_1</span></a>·:·<span·class="id"·title="keyword">forall</span>·<a·id="n:1"·class="idref"·href="#n:1"><span·class="id"·title="binder">n</span></a>,·<a·class="idref"·href="Coq.QArith.QArith_base.html#Qpower_positive"><span·class="id"·title="definition">Qpower_positive</span></a>·1·<a·class="idref"·href="Coq.QArith.Qpower.html#n:1"><span·class="id"·title="variable">n</span></a>·<a·class="idref"·href="Coq.QArith.QArith_base.html#0eaf04f08ecf51ebfc2703f9e1d22838"><span·class="id"·title="notation">==</span></a>·1.<br/> |
60 | <br/> | 60 | <br/> |
61 | <span·class="id"·title="keyword">Lemma</span>·<a·id="Qpower_positive_0"·class="idref"·href="#Qpower_positive_0"><span·class="id"·title="lemma">Qpower_positive_0</span></a>·:·<span·class="id"·title="keyword">forall</span>·<a·id="n:2"·class="idref"·href="#n:2"><span·class="id"·title="binder">n</span></a>,·<a·class="idref"·href="Coq.QArith.QArith_base.html#Qpower_positive"><span·class="id"·title="definition">Qpower_positive</span></a>·0·<a·class="idref"·href="Coq.QArith.Qpower.html#n:2"><span·class="id"·title="variable">n</span></a>·<a·class="idref"·href="Coq.QArith.QArith_base.html#0eaf04f08ecf51ebfc2703f9e1d22838"><span·class="id"·title="notation">==</span></a>·0.<br/> | 61 | <span·class="id"·title="keyword">Lemma</span>·<a·id="Qpower_positive_0"·class="idref"·href="#Qpower_positive_0"><span·class="id"·title="lemma">Qpower_positive_0</span></a>·:·<span·class="id"·title="keyword">forall</span>·<a·id="n:2"·class="idref"·href="#n:2"><span·class="id"·title="binder">n</span></a>,·<a·class="idref"·href="Coq.QArith.QArith_base.html#Qpower_positive"><span·class="id"·title="definition">Qpower_positive</span></a>·0·<a·class="idref"·href="Coq.QArith.Qpower.html#n:2"><span·class="id"·title="variable">n</span></a>·<a·class="idref"·href="Coq.QArith.QArith_base.html#0eaf04f08ecf51ebfc2703f9e1d22838"><span·class="id"·title="notation">==</span></a>·0.<br/> |
62 | <br/> | 62 | <br/> |
63 | </div> | 63 | </div> |
64 | <div·class="doc"> | 64 | <div·class="doc"> |
65 | <a·id="lab | 65 | <a·id="lab781"></a><h2·class="section">Relation·of·Qpower_positive·to·zero</h2> |
66 | </div> | 66 | </div> |
67 | <div·class="code"> | 67 | <div·class="code"> |
68 | <br/> | 68 | <br/> |
69 | <span·class="id"·title="keyword">Lemma</span>·<a·id="Qpower_not_0_positive"·class="idref"·href="#Qpower_not_0_positive"><span·class="id"·title="lemma">Qpower_not_0_positive</span></a>·:·<span·class="id"·title="keyword">forall</span>·<a·id="a:3"·class="idref"·href="#a:3"><span·class="id"·title="binder">a</span></a>·<a·id="n:4"·class="idref"·href="#n:4"><span·class="id"·title="binder">n</span></a>,·<a·class="idref"·href="Coq.Init.Logic.html#63a68285c81db8f9bc456233bb9ed181"><span·class="id"·title="notation">~</span></a><a·class="idref"·href="Coq.QArith.Qpower.html#a:3"><span·class="id"·title="variable">a</span></a><a·class="idref"·href="Coq.QArith.QArith_base.html#0eaf04f08ecf51ebfc2703f9e1d22838"><span·class="id"·title="notation">==</span></a>0·<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.Logic.html#63a68285c81db8f9bc456233bb9ed181"><span·class="id"·title="notation">~</span></a><a·class="idref"·href="Coq.QArith.QArith_base.html#Qpower_positive"><span·class="id"·title="definition">Qpower_positive</span></a>·<a·class="idref"·href="Coq.QArith.Qpower.html#a:3"><span·class="id"·title="variable">a</span></a>·<a·class="idref"·href="Coq.QArith.Qpower.html#n:4"><span·class="id"·title="variable">n</span></a>·<a·class="idref"·href="Coq.QArith.QArith_base.html#0eaf04f08ecf51ebfc2703f9e1d22838"><span·class="id"·title="notation">==</span></a>·0.<br/> | 69 | <span·class="id"·title="keyword">Lemma</span>·<a·id="Qpower_not_0_positive"·class="idref"·href="#Qpower_not_0_positive"><span·class="id"·title="lemma">Qpower_not_0_positive</span></a>·:·<span·class="id"·title="keyword">forall</span>·<a·id="a:3"·class="idref"·href="#a:3"><span·class="id"·title="binder">a</span></a>·<a·id="n:4"·class="idref"·href="#n:4"><span·class="id"·title="binder">n</span></a>,·<a·class="idref"·href="Coq.Init.Logic.html#63a68285c81db8f9bc456233bb9ed181"><span·class="id"·title="notation">~</span></a><a·class="idref"·href="Coq.QArith.Qpower.html#a:3"><span·class="id"·title="variable">a</span></a><a·class="idref"·href="Coq.QArith.QArith_base.html#0eaf04f08ecf51ebfc2703f9e1d22838"><span·class="id"·title="notation">==</span></a>0·<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.Logic.html#63a68285c81db8f9bc456233bb9ed181"><span·class="id"·title="notation">~</span></a><a·class="idref"·href="Coq.QArith.QArith_base.html#Qpower_positive"><span·class="id"·title="definition">Qpower_positive</span></a>·<a·class="idref"·href="Coq.QArith.Qpower.html#a:3"><span·class="id"·title="variable">a</span></a>·<a·class="idref"·href="Coq.QArith.Qpower.html#n:4"><span·class="id"·title="variable">n</span></a>·<a·class="idref"·href="Coq.QArith.QArith_base.html#0eaf04f08ecf51ebfc2703f9e1d22838"><span·class="id"·title="notation">==</span></a>·0.<br/> |
70 | <br/> | 70 | <br/> |
71 | <span·class="id"·title="keyword">Lemma</span>·<a·id="Qpower_pos_positive"·class="idref"·href="#Qpower_pos_positive"><span·class="id"·title="lemma">Qpower_pos_positive</span></a>·:·<span·class="id"·title="keyword">forall</span>·<a·id="p:5"·class="idref"·href="#p:5"><span·class="id"·title="binder">p</span></a>·<a·id="n:6"·class="idref"·href="#n:6"><span·class="id"·title="binder">n</span></a>,·0·<a·class="idref"·href="Coq.QArith.QArith_base.html#bb2ae1e3b1d37b46a15737373eedf343"><span·class="id"·title="notation"><=</span></a>·<a·class="idref"·href="Coq.QArith.Qpower.html#p:5"><span·class="id"·title="variable">p</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#::type_scope:x_'->'_x"><span·class="id"·title="notation">-></span></a>·0·<a·class="idref"·href="Coq.QArith.QArith_base.html#bb2ae1e3b1d37b46a15737373eedf343"><span·class="id"·title="notation"><=</span></a>·<a·class="idref"·href="Coq.QArith.QArith_base.html#Qpower_positive"><span·class="id"·title="definition">Qpower_positive</span></a>·<a·class="idref"·href="Coq.QArith.Qpower.html#p:5"><span·class="id"·title="variable">p</span></a>·<a·class="idref"·href="Coq.QArith.Qpower.html#n:6"><span·class="id"·title="variable">n</span></a>.<br/> | 71 | <span·class="id"·title="keyword">Lemma</span>·<a·id="Qpower_pos_positive"·class="idref"·href="#Qpower_pos_positive"><span·class="id"·title="lemma">Qpower_pos_positive</span></a>·:·<span·class="id"·title="keyword">forall</span>·<a·id="p:5"·class="idref"·href="#p:5"><span·class="id"·title="binder">p</span></a>·<a·id="n:6"·class="idref"·href="#n:6"><span·class="id"·title="binder">n</span></a>,·0·<a·class="idref"·href="Coq.QArith.QArith_base.html#bb2ae1e3b1d37b46a15737373eedf343"><span·class="id"·title="notation"><=</span></a>·<a·class="idref"·href="Coq.QArith.Qpower.html#p:5"><span·class="id"·title="variable">p</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#::type_scope:x_'->'_x"><span·class="id"·title="notation">-></span></a>·0·<a·class="idref"·href="Coq.QArith.QArith_base.html#bb2ae1e3b1d37b46a15737373eedf343"><span·class="id"·title="notation"><=</span></a>·<a·class="idref"·href="Coq.QArith.QArith_base.html#Qpower_positive"><span·class="id"·title="definition">Qpower_positive</span></a>·<a·class="idref"·href="Coq.QArith.Qpower.html#p:5"><span·class="id"·title="variable">p</span></a>·<a·class="idref"·href="Coq.QArith.Qpower.html#n:6"><span·class="id"·title="variable">n</span></a>.<br/> |
72 | <br/> | 72 | <br/> |
73 | </div> | 73 | </div> |
74 | <div·class="doc"> | 74 | <div·class="doc"> |
75 | <a·id="lab | 75 | <a·id="lab782"></a><h2·class="section">Qpower_positive·and·multiplication,·exponent·subtraction</h2> |
76 | </div> | 76 | </div> |
77 | <div·class="code"> | 77 | <div·class="code"> |
78 | <br/> | 78 | <br/> |
79 | <span·class="id"·title="keyword">Lemma</span>·<a·id="Qmult_power_positive"·class="idref"·href="#Qmult_power_positive"><span·class="id"·title="lemma">Qmult_power_positive</span></a>··:·<span·class="id"·title="keyword">forall</span>·<a·id="a:7"·class="idref"·href="#a:7"><span·class="id"·title="binder">a</span></a>·<a·id="b:8"·class="idref"·href="#b:8"><span·class="id"·title="binder">b</span></a>·<a·id="n:9"·class="idref"·href="#n:9"><span·class="id"·title="binder">n</span></a>,·<a·class="idref"·href="Coq.QArith.QArith_base.html#Qpower_positive"><span·class="id"·title="definition">Qpower_positive</span></a>·(<a·class="idref"·href="Coq.QArith.Qpower.html#a:7"><span·class="id"·title="variable">a</span></a><a·class="idref"·href="Coq.QArith.QArith_base.html#a913d2882dcbf2c07ae6ccbc47eaad45"><span·class="id"·title="notation">*</span></a><a·class="idref"·href="Coq.QArith.Qpower.html#b:8"><span·class="id"·title="variable">b</span></a>)·<a·class="idref"·href="Coq.QArith.Qpower.html#n:9"><span·class="id"·title="variable">n</span></a>·<a·class="idref"·href="Coq.QArith.QArith_base.html#0eaf04f08ecf51ebfc2703f9e1d22838"><span·class="id"·title="notation">==</span></a>·<a·class="idref"·href="Coq.QArith.QArith_base.html#a913d2882dcbf2c07ae6ccbc47eaad45"><span·class="id"·title="notation">(</span></a><a·class="idref"·href="Coq.QArith.QArith_base.html#Qpower_positive"><span·class="id"·title="definition">Qpower_positive</span></a>·<a·class="idref"·href="Coq.QArith.Qpower.html#a:7"><span·class="id"·title="variable">a</span></a>·<a·class="idref"·href="Coq.QArith.Qpower.html#n:9"><span·class="id"·title="variable">n</span></a><a·class="idref"·href="Coq.QArith.QArith_base.html#a913d2882dcbf2c07ae6ccbc47eaad45"><span·class="id"·title="notation">)*(</span></a><a·class="idref"·href="Coq.QArith.QArith_base.html#Qpower_positive"><span·class="id"·title="definition">Qpower_positive</span></a>·<a·class="idref"·href="Coq.QArith.Qpower.html#b:8"><span·class="id"·title="variable">b</span></a>·<a·class="idref"·href="Coq.QArith.Qpower.html#n:9"><span·class="id"·title="variable">n</span></a><a·class="idref"·href="Coq.QArith.QArith_base.html#a913d2882dcbf2c07ae6ccbc47eaad45"><span·class="id"·title="notation">)</span></a>.<br/> | 79 | <span·class="id"·title="keyword">Lemma</span>·<a·id="Qmult_power_positive"·class="idref"·href="#Qmult_power_positive"><span·class="id"·title="lemma">Qmult_power_positive</span></a>··:·<span·class="id"·title="keyword">forall</span>·<a·id="a:7"·class="idref"·href="#a:7"><span·class="id"·title="binder">a</span></a>·<a·id="b:8"·class="idref"·href="#b:8"><span·class="id"·title="binder">b</span></a>·<a·id="n:9"·class="idref"·href="#n:9"><span·class="id"·title="binder">n</span></a>,·<a·class="idref"·href="Coq.QArith.QArith_base.html#Qpower_positive"><span·class="id"·title="definition">Qpower_positive</span></a>·(<a·class="idref"·href="Coq.QArith.Qpower.html#a:7"><span·class="id"·title="variable">a</span></a><a·class="idref"·href="Coq.QArith.QArith_base.html#a913d2882dcbf2c07ae6ccbc47eaad45"><span·class="id"·title="notation">*</span></a><a·class="idref"·href="Coq.QArith.Qpower.html#b:8"><span·class="id"·title="variable">b</span></a>)·<a·class="idref"·href="Coq.QArith.Qpower.html#n:9"><span·class="id"·title="variable">n</span></a>·<a·class="idref"·href="Coq.QArith.QArith_base.html#0eaf04f08ecf51ebfc2703f9e1d22838"><span·class="id"·title="notation">==</span></a>·<a·class="idref"·href="Coq.QArith.QArith_base.html#a913d2882dcbf2c07ae6ccbc47eaad45"><span·class="id"·title="notation">(</span></a><a·class="idref"·href="Coq.QArith.QArith_base.html#Qpower_positive"><span·class="id"·title="definition">Qpower_positive</span></a>·<a·class="idref"·href="Coq.QArith.Qpower.html#a:7"><span·class="id"·title="variable">a</span></a>·<a·class="idref"·href="Coq.QArith.Qpower.html#n:9"><span·class="id"·title="variable">n</span></a><a·class="idref"·href="Coq.QArith.QArith_base.html#a913d2882dcbf2c07ae6ccbc47eaad45"><span·class="id"·title="notation">)*(</span></a><a·class="idref"·href="Coq.QArith.QArith_base.html#Qpower_positive"><span·class="id"·title="definition">Qpower_positive</span></a>·<a·class="idref"·href="Coq.QArith.Qpower.html#b:8"><span·class="id"·title="variable">b</span></a>·<a·class="idref"·href="Coq.QArith.Qpower.html#n:9"><span·class="id"·title="variable">n</span></a><a·class="idref"·href="Coq.QArith.QArith_base.html#a913d2882dcbf2c07ae6ccbc47eaad45"><span·class="id"·title="notation">)</span></a>.<br/> |
80 | <br/> | 80 | <br/> |
81 | <span·class="id"·title="keyword">Lemma</span>·<a·id="Qpower_plus_positive"·class="idref"·href="#Qpower_plus_positive"><span·class="id"·title="lemma">Qpower_plus_positive</span></a>·:·<span·class="id"·title="keyword">forall</span>·<a·id="a:10"·class="idref"·href="#a:10"><span·class="id"·title="binder">a</span></a>·<a·id="n:11"·class="idref"·href="#n:11"><span·class="id"·title="binder">n</span></a>·<a·id="m:12"·class="idref"·href="#m:12"><span·class="id"·title="binder">m</span></a>,·<a·class="idref"·href="Coq.QArith.QArith_base.html#Qpower_positive"><span·class="id"·title="definition">Qpower_positive</span></a>·<a·class="idref"·href="Coq.QArith.Qpower.html#a:10"><span·class="id"·title="variable">a</span></a>·(<a·class="idref"·href="Coq.QArith.Qpower.html#n:11"><span·class="id"·title="variable">n</span></a><a·class="idref"·href="Coq.PArith.BinPos.html#50efadf7a9f9d41adb2b162cbba3bda7"><span·class="id"·title="notation">+</span></a><a·class="idref"·href="Coq.QArith.Qpower.html#m:12"><span·class="id"·title="variable">m</span></a>)·<a·class="idref"·href="Coq.QArith.QArith_base.html#0eaf04f08ecf51ebfc2703f9e1d22838"><span·class="id"·title="notation">==</span></a>·<a·class="idref"·href="Coq.QArith.QArith_base.html#a913d2882dcbf2c07ae6ccbc47eaad45"><span·class="id"·title="notation">(</span></a><a·class="idref"·href="Coq.QArith.QArith_base.html#Qpower_positive"><span·class="id"·title="definition">Qpower_positive</span></a>·<a·class="idref"·href="Coq.QArith.Qpower.html#a:10"><span·class="id"·title="variable">a</span></a>·<a·class="idref"·href="Coq.QArith.Qpower.html#n:11"><span·class="id"·title="variable">n</span></a><a·class="idref"·href="Coq.QArith.QArith_base.html#a913d2882dcbf2c07ae6ccbc47eaad45"><span·class="id"·title="notation">)*(</span></a><a·class="idref"·href="Coq.QArith.QArith_base.html#Qpower_positive"><span·class="id"·title="definition">Qpower_positive</span></a>·<a·class="idref"·href="Coq.QArith.Qpower.html#a:10"><span·class="id"·title="variable">a</span></a>·<a·class="idref"·href="Coq.QArith.Qpower.html#m:12"><span·class="id"·title="variable">m</span></a><a·class="idref"·href="Coq.QArith.QArith_base.html#a913d2882dcbf2c07ae6ccbc47eaad45"><span·class="id"·title="notation">)</span></a>.<br/> | 81 | <span·class="id"·title="keyword">Lemma</span>·<a·id="Qpower_plus_positive"·class="idref"·href="#Qpower_plus_positive"><span·class="id"·title="lemma">Qpower_plus_positive</span></a>·:·<span·class="id"·title="keyword">forall</span>·<a·id="a:10"·class="idref"·href="#a:10"><span·class="id"·title="binder">a</span></a>·<a·id="n:11"·class="idref"·href="#n:11"><span·class="id"·title="binder">n</span></a>·<a·id="m:12"·class="idref"·href="#m:12"><span·class="id"·title="binder">m</span></a>,·<a·class="idref"·href="Coq.QArith.QArith_base.html#Qpower_positive"><span·class="id"·title="definition">Qpower_positive</span></a>·<a·class="idref"·href="Coq.QArith.Qpower.html#a:10"><span·class="id"·title="variable">a</span></a>·(<a·class="idref"·href="Coq.QArith.Qpower.html#n:11"><span·class="id"·title="variable">n</span></a><a·class="idref"·href="Coq.PArith.BinPos.html#50efadf7a9f9d41adb2b162cbba3bda7"><span·class="id"·title="notation">+</span></a><a·class="idref"·href="Coq.QArith.Qpower.html#m:12"><span·class="id"·title="variable">m</span></a>)·<a·class="idref"·href="Coq.QArith.QArith_base.html#0eaf04f08ecf51ebfc2703f9e1d22838"><span·class="id"·title="notation">==</span></a>·<a·class="idref"·href="Coq.QArith.QArith_base.html#a913d2882dcbf2c07ae6ccbc47eaad45"><span·class="id"·title="notation">(</span></a><a·class="idref"·href="Coq.QArith.QArith_base.html#Qpower_positive"><span·class="id"·title="definition">Qpower_positive</span></a>·<a·class="idref"·href="Coq.QArith.Qpower.html#a:10"><span·class="id"·title="variable">a</span></a>·<a·class="idref"·href="Coq.QArith.Qpower.html#n:11"><span·class="id"·title="variable">n</span></a><a·class="idref"·href="Coq.QArith.QArith_base.html#a913d2882dcbf2c07ae6ccbc47eaad45"><span·class="id"·title="notation">)*(</span></a><a·class="idref"·href="Coq.QArith.QArith_base.html#Qpower_positive"><span·class="id"·title="definition">Qpower_positive</span></a>·<a·class="idref"·href="Coq.QArith.Qpower.html#a:10"><span·class="id"·title="variable">a</span></a>·<a·class="idref"·href="Coq.QArith.Qpower.html#m:12"><span·class="id"·title="variable">m</span></a><a·class="idref"·href="Coq.QArith.QArith_base.html#a913d2882dcbf2c07ae6ccbc47eaad45"><span·class="id"·title="notation">)</span></a>.<br/> |
82 | <br/> | 82 | <br/> |
83 | </div> | 83 | </div> |
84 | <div·class="doc"> | 84 | <div·class="doc"> |
85 | <a·id="lab | 85 | <a·id="lab783"></a><h2·class="section">Qpower_positive·and·inversion,·division,·exponent·subtraction</h2> |
86 | </div> | 86 | </div> |
87 | <div·class="code"> | 87 | <div·class="code"> |
88 | <br/> | 88 | <br/> |
89 | <span·class="id"·title="keyword">Lemma</span>·<a·id="Qinv_power_positive"·class="idref"·href="#Qinv_power_positive"><span·class="id"·title="lemma">Qinv_power_positive</span></a>··:·<span·class="id"·title="keyword">forall</span>·<a·id="a:13"·class="idref"·href="#a:13"><span·class="id"·title="binder">a</span></a>·<a·id="n:14"·class="idref"·href="#n:14"><span·class="id"·title="binder">n</span></a>,·<a·class="idref"·href="Coq.QArith.QArith_base.html#Qpower_positive"><span·class="id"·title="definition">Qpower_positive</span></a>·(<a·class="idref"·href="Coq.QArith.QArith_base.html#8bbb7e6c4363db1e6ff873634c45a65e"><span·class="id"·title="notation">/</span></a><a·class="idref"·href="Coq.QArith.Qpower.html#a:13"><span·class="id"·title="variable">a</span></a>)·<a·class="idref"·href="Coq.QArith.Qpower.html#n:14"><span·class="id"·title="variable">n</span></a>·<a·class="idref"·href="Coq.QArith.QArith_base.html#0eaf04f08ecf51ebfc2703f9e1d22838"><span·class="id"·title="notation">==</span></a>·<a·class="idref"·href="Coq.QArith.QArith_base.html#8bbb7e6c4363db1e6ff873634c45a65e"><span·class="id"·title="notation">/(</span></a><a·class="idref"·href="Coq.QArith.QArith_base.html#Qpower_positive"><span·class="id"·title="definition">Qpower_positive</span></a>·<a·class="idref"·href="Coq.QArith.Qpower.html#a:13"><span·class="id"·title="variable">a</span></a>·<a·class="idref"·href="Coq.QArith.Qpower.html#n:14"><span·class="id"·title="variable">n</span></a><a·class="idref"·href="Coq.QArith.QArith_base.html#8bbb7e6c4363db1e6ff873634c45a65e"><span·class="id"·title="notation">)</span></a>.<br/> | 89 | <span·class="id"·title="keyword">Lemma</span>·<a·id="Qinv_power_positive"·class="idref"·href="#Qinv_power_positive"><span·class="id"·title="lemma">Qinv_power_positive</span></a>··:·<span·class="id"·title="keyword">forall</span>·<a·id="a:13"·class="idref"·href="#a:13"><span·class="id"·title="binder">a</span></a>·<a·id="n:14"·class="idref"·href="#n:14"><span·class="id"·title="binder">n</span></a>,·<a·class="idref"·href="Coq.QArith.QArith_base.html#Qpower_positive"><span·class="id"·title="definition">Qpower_positive</span></a>·(<a·class="idref"·href="Coq.QArith.QArith_base.html#8bbb7e6c4363db1e6ff873634c45a65e"><span·class="id"·title="notation">/</span></a><a·class="idref"·href="Coq.QArith.Qpower.html#a:13"><span·class="id"·title="variable">a</span></a>)·<a·class="idref"·href="Coq.QArith.Qpower.html#n:14"><span·class="id"·title="variable">n</span></a>·<a·class="idref"·href="Coq.QArith.QArith_base.html#0eaf04f08ecf51ebfc2703f9e1d22838"><span·class="id"·title="notation">==</span></a>·<a·class="idref"·href="Coq.QArith.QArith_base.html#8bbb7e6c4363db1e6ff873634c45a65e"><span·class="id"·title="notation">/(</span></a><a·class="idref"·href="Coq.QArith.QArith_base.html#Qpower_positive"><span·class="id"·title="definition">Qpower_positive</span></a>·<a·class="idref"·href="Coq.QArith.Qpower.html#a:13"><span·class="id"·title="variable">a</span></a>·<a·class="idref"·href="Coq.QArith.Qpower.html#n:14"><span·class="id"·title="variable">n</span></a><a·class="idref"·href="Coq.QArith.QArith_base.html#8bbb7e6c4363db1e6ff873634c45a65e"><span·class="id"·title="notation">)</span></a>.<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.Reals.PartSum.html#"><span·class="id"·title="library">PartSum</span></a>.<br/> | 53 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Reals.PartSum.html#"><span·class="id"·title="library">PartSum</span></a>.<br/> |
54 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">R_scope</span>.<br/> | 54 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">R_scope</span>.<br/> |
55 | <br/> | 55 | <br/> |
56 | </div> | 56 | </div> |
57 | <div·class="doc"> | 57 | <div·class="doc"> |
58 | <a·id="lab | 58 | <a·id="lab412"></a><h1·class="section">Formalization·of·alternated·series</h1> |
59 | </div> | 59 | </div> |
60 | <div·class="code"> | 60 | <div·class="code"> |
61 | <span·class="id"·title="keyword">Definition</span>·<a·id="tg_alt"·class="idref"·href="#tg_alt"><span·class="id"·title="definition">tg_alt</span></a>·(<a·id="Un:1"·class="idref"·href="#Un:1"><span·class="id"·title="binder">Un</span></a>:<a·class="idref"·href="Coq.Init.Datatypes.html#nat"><span·class="id"·title="inductive">nat</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.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>)·(<a·id="i:2"·class="idref"·href="#i:2"><span·class="id"·title="binder">i</span></a>:<a·class="idref"·href="Coq.Init.Datatypes.html#nat"><span·class="id"·title="inductive">nat</span></a>)·:·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>·:=·<a·class="idref"·href="Coq.Reals.Rfunctions.html#1fc859ef9f60fc2e3a52c48371d07707"><span·class="id"·title="notation">(</span></a>-1<a·class="idref"·href="Coq.Reals.Rfunctions.html#1fc859ef9f60fc2e3a52c48371d07707"><span·class="id"·title="notation">)</span></a>·<a·class="idref"·href="Coq.Reals.Rfunctions.html#1fc859ef9f60fc2e3a52c48371d07707"><span·class="id"·title="notation">^</span></a>·<a·class="idref"·href="Coq.Reals.AltSeries.html#i:2"><span·class="id"·title="variable">i</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#e1dae7ed53bffa765009199d058dd327"><span·class="id"·title="notation">*</span></a>·<a·class="idref"·href="Coq.Reals.AltSeries.html#Un:1"><span·class="id"·title="variable">Un</span></a>·<a·class="idref"·href="Coq.Reals.AltSeries.html#i:2"><span·class="id"·title="variable">i</span></a>.<br/> | 61 | <span·class="id"·title="keyword">Definition</span>·<a·id="tg_alt"·class="idref"·href="#tg_alt"><span·class="id"·title="definition">tg_alt</span></a>·(<a·id="Un:1"·class="idref"·href="#Un:1"><span·class="id"·title="binder">Un</span></a>:<a·class="idref"·href="Coq.Init.Datatypes.html#nat"><span·class="id"·title="inductive">nat</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.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>)·(<a·id="i:2"·class="idref"·href="#i:2"><span·class="id"·title="binder">i</span></a>:<a·class="idref"·href="Coq.Init.Datatypes.html#nat"><span·class="id"·title="inductive">nat</span></a>)·:·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>·:=·<a·class="idref"·href="Coq.Reals.Rfunctions.html#1fc859ef9f60fc2e3a52c48371d07707"><span·class="id"·title="notation">(</span></a>-1<a·class="idref"·href="Coq.Reals.Rfunctions.html#1fc859ef9f60fc2e3a52c48371d07707"><span·class="id"·title="notation">)</span></a>·<a·class="idref"·href="Coq.Reals.Rfunctions.html#1fc859ef9f60fc2e3a52c48371d07707"><span·class="id"·title="notation">^</span></a>·<a·class="idref"·href="Coq.Reals.AltSeries.html#i:2"><span·class="id"·title="variable">i</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#e1dae7ed53bffa765009199d058dd327"><span·class="id"·title="notation">*</span></a>·<a·class="idref"·href="Coq.Reals.AltSeries.html#Un:1"><span·class="id"·title="variable">Un</span></a>·<a·class="idref"·href="Coq.Reals.AltSeries.html#i:2"><span·class="id"·title="variable">i</span></a>.<br/> |
62 | <span·class="id"·title="keyword">Definition</span>·<a·id="positivity_seq"·class="idref"·href="#positivity_seq"><span·class="id"·title="definition">positivity_seq</span></a>·(<a·id="Un:3"·class="idref"·href="#Un:3"><span·class="id"·title="binder">Un</span></a>:<a·class="idref"·href="Coq.Init.Datatypes.html#nat"><span·class="id"·title="inductive">nat</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.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>)·:·<span·class="id"·title="keyword">Prop</span>·:=·<span·class="id"·title="keyword">forall</span>·<a·id="n:4"·class="idref"·href="#n:4"><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>,·0·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#77d341fe206b2891763e25999ffddca2"><span·class="id"·title="notation"><=</span></a>·<a·class="idref"·href="Coq.Reals.AltSeries.html#Un:3"><span·class="id"·title="variable">Un</span></a>·<a·class="idref"·href="Coq.Reals.AltSeries.html#n:4"><span·class="id"·title="variable">n</span></a>.<br/> | 62 | <span·class="id"·title="keyword">Definition</span>·<a·id="positivity_seq"·class="idref"·href="#positivity_seq"><span·class="id"·title="definition">positivity_seq</span></a>·(<a·id="Un:3"·class="idref"·href="#Un:3"><span·class="id"·title="binder">Un</span></a>:<a·class="idref"·href="Coq.Init.Datatypes.html#nat"><span·class="id"·title="inductive">nat</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.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>)·:·<span·class="id"·title="keyword">Prop</span>·:=·<span·class="id"·title="keyword">forall</span>·<a·id="n:4"·class="idref"·href="#n:4"><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>,·0·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#77d341fe206b2891763e25999ffddca2"><span·class="id"·title="notation"><=</span></a>·<a·class="idref"·href="Coq.Reals.AltSeries.html#Un:3"><span·class="id"·title="variable">Un</span></a>·<a·class="idref"·href="Coq.Reals.AltSeries.html#n:4"><span·class="id"·title="variable">n</span></a>.<br/> |
63 | <br/> | 63 | <br/> |
Offset 404, 15 lines modified | Offset 404, 15 lines modified | ||
404 | :·<a·class="idref"·href="Coq.Classes.CMorphisms.html#Proper"><span·class="id"·title="class">CMorphisms.Proper</span></a><br/> | 404 | :·<a·class="idref"·href="Coq.Classes.CMorphisms.html#Proper"><span·class="id"·title="class">CMorphisms.Proper</span></a><br/> |
405 | (<a·class="idref"·href="Coq.Classes.CMorphisms.html#respectful"><span·class="id"·title="definition">CMorphisms.respectful</span></a>·<a·class="idref"·href="Coq.QArith.QArith_base.html#Qeq"><span·class="id"·title="definition">Qeq</span></a>·<a·class="idref"·href="Coq.Reals.Cauchy.ConstructiveCauchyReals.html#CRealEq"><span·class="id"·title="definition">CRealEq</span></a>)·<a·class="idref"·href="Coq.Reals.Cauchy.ConstructiveCauchyReals.html#inject_Q"><span·class="id"·title="definition">inject_Q</span></a>.<br/> | 405 | (<a·class="idref"·href="Coq.Classes.CMorphisms.html#respectful"><span·class="id"·title="definition">CMorphisms.respectful</span></a>·<a·class="idref"·href="Coq.QArith.QArith_base.html#Qeq"><span·class="id"·title="definition">Qeq</span></a>·<a·class="idref"·href="Coq.Reals.Cauchy.ConstructiveCauchyReals.html#CRealEq"><span·class="id"·title="definition">CRealEq</span></a>)·<a·class="idref"·href="Coq.Reals.Cauchy.ConstructiveCauchyReals.html#inject_Q"><span·class="id"·title="definition">inject_Q</span></a>.<br/> |
406 | <br/> | 406 | <br/> |
407 | </div> | 407 | </div> |
408 | <div·class="doc"> | 408 | <div·class="doc"> |
409 | <a·id="lab | 409 | <a·id="lab463"></a><h1·class="section">Algebraic·operations</h1> |
410 | <div·class="paragraph">·</div> | 410 | <div·class="paragraph">·</div> |
411 | ·We·reduce·the·rational·numbers·to·accelerate·calculations.· | 411 | ·We·reduce·the·rational·numbers·to·accelerate·calculations.· |
412 | </div> | 412 | </div> |
413 | <div·class="code"> | 413 | <div·class="code"> |
414 | <span·class="id"·title="keyword">Definition</span>·<a·id="CReal_plus_seq"·class="idref"·href="#CReal_plus_seq"><span·class="id"·title="definition">CReal_plus_seq</span></a>·(<a·id="x:112"·class="idref"·href="#x:112"><span·class="id"·title="binder">x</span></a>·<a·id="y:113"·class="idref"·href="#y:113"><span·class="id"·title="binder">y</span></a>·:·<a·class="idref"·href="Coq.Reals.Cauchy.ConstructiveCauchyReals.html#CReal"><span·class="id"·title="record">CReal</span></a>)·:=<br/> | 414 | <span·class="id"·title="keyword">Definition</span>·<a·id="CReal_plus_seq"·class="idref"·href="#CReal_plus_seq"><span·class="id"·title="definition">CReal_plus_seq</span></a>·(<a·id="x:112"·class="idref"·href="#x:112"><span·class="id"·title="binder">x</span></a>·<a·id="y:113"·class="idref"·href="#y:113"><span·class="id"·title="binder">y</span></a>·:·<a·class="idref"·href="Coq.Reals.Cauchy.ConstructiveCauchyReals.html#CReal"><span·class="id"·title="record">CReal</span></a>)·:=<br/> |
Offset 5040, 15 lines modified | Offset 5040, 15 lines modified | ||
00013af0:·7952·6561·6c73·4d75·6c74·2e68·746d·6c23··yRealsMult.html# | 00013af0:·7952·6561·6c73·4d75·6c74·2e68·746d·6c23··yRealsMult.html# | ||
00013b00:·783a·3130·3522·3e3c·7370·616e·2063·6c61··x:105"><span·cla | 00013b00:·783a·3130·3522·3e3c·7370·616e·2063·6c61··x:105"><span·cla | ||
00013b10:·7373·3d22·6964·2220·7469·746c·653d·2276··ss="id"·title="v | 00013b10:·7373·3d22·6964·2220·7469·746c·653d·2276··ss="id"·title="v | ||
00013b20:·6172·6961·626c·6522·3e78·3c2f·7370·616e··ariable">x</span | 00013b20:·6172·6961·626c·6522·3e78·3c2f·7370·616e··ariable">x</span | ||
00013b30:·3e3c·2f61·3e2e·3c62·722f·3e0a·0a3c·6272··></a>.<br/>..<br | 00013b30:·3e3c·2f61·3e2e·3c62·722f·3e0a·0a3c·6272··></a>.<br/>..<br | ||
00013b40:·2f3e·0a3c·2f64·6976·3e0a·0a3c·6469·7620··/>.</div>..<div· | 00013b40:·2f3e·0a3c·2f64·6976·3e0a·0a3c·6469·7620··/>.</div>..<div· | ||
00013b50:·636c·6173·733d·2264·6f63·223e·0a3c·6120··class="doc">.<a· | 00013b50:·636c·6173·733d·2264·6f63·223e·0a3c·6120··class="doc">.<a· | ||
00013b60:·6964·3d22·6c61·623 | 00013b60:·6964·3d22·6c61·6234·3632·223e·3c2f·613e··id="lab462"></a> | ||
00013b70:·3c68·3120·636c·6173·733d·2273·6563·7469··<h1·class="secti | 00013b70:·3c68·3120·636c·6173·733d·2273·6563·7469··<h1·class="secti | ||
00013b80:·6f6e·223e·4669·656c·643c·2f68·313e·0a0a··on">Field</h1>.. | 00013b80:·6f6e·223e·4669·656c·643c·2f68·313e·0a0a··on">Field</h1>.. | ||
00013b90:·3c2f·6469·763e·0a3c·6469·7620·636c·6173··</div>.<div·clas | 00013b90:·3c2f·6469·763e·0a3c·6469·7620·636c·6173··</div>.<div·clas | ||
00013ba0:·733d·2263·6f64·6522·3e0a·0a3c·6272·2f3e··s="code">..<br/> | 00013ba0:·733d·2263·6f64·6522·3e0a·0a3c·6272·2f3e··s="code">..<br/> | ||
00013bb0:·0a3c·7370·616e·2063·6c61·7373·3d22·6964··.<span·class="id | 00013bb0:·0a3c·7370·616e·2063·6c61·7373·3d22·6964··.<span·class="id | ||
00013bc0:·2220·7469·746c·653d·226b·6579·776f·7264··"·title="keyword | 00013bc0:·2220·7469·746c·653d·226b·6579·776f·7264··"·title="keyword | ||
00013bd0:·223e·4c65·6d6d·613c·2f73·7061·6e3e·203c··">Lemma</span>·< | 00013bd0:·223e·4c65·6d6d·613c·2f73·7061·6e3e·203c··">Lemma</span>·< |
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.micromega.Lia.html#"><span·class="id"·title="library">Lia</span></a>.<br/> | 51 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.micromega.Lia.html#"><span·class="id"·title="library">Lia</span></a>.<br/> |
52 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.micromega.Lqa.html#"><span·class="id"·title="library">Lqa</span></a>.·<span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Reals.Cauchy.PosExtra.html#"><span·class="id"·title="library">PosExtra</span></a>.<br/> | 52 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.micromega.Lqa.html#"><span·class="id"·title="library">Lqa</span></a>.·<span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Reals.Cauchy.PosExtra.html#"><span·class="id"·title="library">PosExtra</span></a>.<br/> |
53 | <br/> | 53 | <br/> |
54 | </div> | 54 | </div> |
55 | <div·class="doc"> | 55 | <div·class="doc"> |
56 | <a·id="lab | 56 | <a·id="lab464"></a><h1·class="section">Power·of·2·open·and·closed·upper·and·lower·bounds·for·<span·class="inlinecode"><span·class="id"·title="var">q</span></span>·<span·class="inlinecode">:</span>·<span·class="inlinecode"><span·class="id"·title="var">Q</span></span></h1> |
57 | </div> | 57 | </div> |
58 | <div·class="code"> | 58 | <div·class="code"> |
59 | <br/> | 59 | <br/> |
60 | <span·class="id"·title="keyword">Fixpoint</span>·<a·id="Pos_log2floor_plus1"·class="idref"·href="#Pos_log2floor_plus1"><span·class="id"·title="definition">Pos_log2floor_plus1</span></a>·(<a·id="p:1"·class="idref"·href="#p:1"><span·class="id"·title="binder">p</span></a>·:·<a·class="idref"·href="Coq.Numbers.BinNums.html#positive"><span·class="id"·title="inductive">positive</span></a>)·:·<a·class="idref"·href="Coq.Numbers.BinNums.html#positive"><span·class="id"·title="inductive">positive</span></a>·:=<br/> | 60 | <span·class="id"·title="keyword">Fixpoint</span>·<a·id="Pos_log2floor_plus1"·class="idref"·href="#Pos_log2floor_plus1"><span·class="id"·title="definition">Pos_log2floor_plus1</span></a>·(<a·id="p:1"·class="idref"·href="#p:1"><span·class="id"·title="binder">p</span></a>·:·<a·class="idref"·href="Coq.Numbers.BinNums.html#positive"><span·class="id"·title="inductive">positive</span></a>)·:·<a·class="idref"·href="Coq.Numbers.BinNums.html#positive"><span·class="id"·title="inductive">positive</span></a>·:=<br/> |
61 | <span·class="id"·title="keyword">match</span>·<a·class="idref"·href="Coq.Reals.Cauchy.QExtra.html#p:1"><span·class="id"·title="variable">p</span></a>·<span·class="id"·title="keyword">with</span><br/> | 61 | <span·class="id"·title="keyword">match</span>·<a·class="idref"·href="Coq.Reals.Cauchy.QExtra.html#p:1"><span·class="id"·title="variable">p</span></a>·<span·class="id"·title="keyword">with</span><br/> |
Offset 59, 15 lines modified | Offset 59, 15 lines modified | ||
59 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Reals.Cauchy.QExtra.html#"><span·class="id"·title="library">QExtra</span></a>.<br/> | 59 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Reals.Cauchy.QExtra.html#"><span·class="id"·title="library">QExtra</span></a>.<br/> |
60 | <span·class="id"·title="keyword">Require</span>·<a·class="idref"·href="Coq.Classes.CMorphisms.html#"><span·class="id"·title="library">CMorphisms</span></a>.<br/> | 60 | <span·class="id"·title="keyword">Require</span>·<a·class="idref"·href="Coq.Classes.CMorphisms.html#"><span·class="id"·title="library">CMorphisms</span></a>.<br/> |
61 | <br/> | 61 | <br/> |
62 | </div> | 62 | </div> |
63 | <div·class="doc"> | 63 | <div·class="doc"> |
64 | <a·id="lab | 64 | <a·id="lab399"></a><h1·class="section">Q·Auxiliary·Lemmas</h1> |
65 | </div> | 65 | </div> |
66 | <div·class="code"> | 66 | <div·class="code"> |
67 | <br/> | 67 | <br/> |
68 | <br/> | 68 | <br/> |
Offset 102, 15 lines modified | Offset 102, 15 lines modified | ||
00000650:·6e74·223e·0a0a·3c68·3120·636c·6173·733d··nt">..<h1·class= | 00000650:·6e74·223e·0a0a·3c68·3120·636c·6173·733d··nt">..<h1·class= | ||
00000660:·226c·6962·7469·746c·6522·3e4c·6962·7261··"libtitle">Libra | 00000660:·226c·6962·7469·746c·6522·3e4c·6962·7261··"libtitle">Libra | ||
00000670:·7279·2043·6f71·2e52·6561·6c73·2e52·496e··ry·Coq.Reals.RIn | 00000670:·7279·2043·6f71·2e52·6561·6c73·2e52·496e··ry·Coq.Reals.RIn | ||
00000680:·6571·3c2f·6831·3e0a·0a3c·6469·7620·636c··eq</h1>..<div·cl | 00000680:·6571·3c2f·6831·3e0a·0a3c·6469·7620·636c··eq</h1>..<div·cl | ||
00000690:·6173·733d·2263·6f64·6522·3e0a·0a3c·6272··ass="code">..<br | 00000690:·6173·733d·2263·6f64·6522·3e0a·0a3c·6272··ass="code">..<br | ||
000006a0:·2f3e·0a3c·2f64·6976·3e0a·0a3c·6469·7620··/>.</div>..<div· | 000006a0:·2f3e·0a3c·2f64·6976·3e0a·0a3c·6469·7620··/>.</div>..<div· | ||
000006b0:·636c·6173·733d·2264·6f63·223e·0a3c·6120··class="doc">.<a· | 000006b0:·636c·6173·733d·2264·6f63·223e·0a3c·6120··class="doc">.<a· | ||
000006c0:·6964·3d22·6c61·623 | 000006c0:·6964·3d22·6c61·6234·3138·223e·3c2f·613e··id="lab418"></a> | ||
000006d0:·3c68·3120·636c·6173·733d·2273·6563·7469··<h1·class="secti | 000006d0:·3c68·3120·636c·6173·733d·2273·6563·7469··<h1·class="secti | ||
000006e0:·6f6e·223e·4261·7369·6320·6c65·6d6d·6173··on">Basic·lemmas | 000006e0:·6f6e·223e·4261·7369·6320·6c65·6d6d·6173··on">Basic·lemmas | ||
000006f0:·2066·6f72·2074·6865·2063·6c61·7373·6963···for·the·classic | 000006f0:·2066·6f72·2074·6865·2063·6c61·7373·6963···for·the·classic | ||
00000700:·616c·2072·6561·6c20·6e75·6d62·6572·733c··al·real·numbers< | 00000700:·616c·2072·6561·6c20·6e75·6d62·6572·733c··al·real·numbers< | ||
00000710:·2f68·313e·0a0a·3c2f·6469·763e·0a3c·6469··/h1>..</div>.<di | 00000710:·2f68·313e·0a0a·3c2f·6469·763e·0a3c·6469··/h1>..</div>.<di | ||
00000720:·7620·636c·6173·733d·2263·6f64·6522·3e0a··v·class="code">. | 00000720:·7620·636c·6173·733d·2263·6f64·6522·3e0a··v·class="code">. | ||
00000730:·0a3c·6272·2f3e·0a3c·7370·616e·2063·6c61··.<br/>.<span·cla | 00000730:·0a3c·6272·2f3e·0a3c·7370·616e·2063·6c61··.<br/>.<span·cla |
Offset 51, 15 lines modified | Offset 51, 15 lines modified | ||
51 | <br/> | 51 | <br/> |
52 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">R_scope</span>.<br/> | 52 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">R_scope</span>.<br/> |
53 | <br/> | 53 | <br/> |
54 | </div> | 54 | </div> |
55 | <div·class="doc"> | 55 | <div·class="doc"> |
56 | <a·id="lab | 56 | <a·id="lab505"></a><h1·class="section">DecidableType·structure·for·real·numbers</h1> |
57 | </div> | 57 | </div> |
58 | <div·class="code"> | 58 | <div·class="code"> |
59 | <br/> | 59 | <br/> |
60 | <span·class="id"·title="keyword">Lemma</span>·<a·id="Req_dec"·class="idref"·href="#Req_dec"><span·class="id"·title="lemma">Req_dec</span></a>·:·<span·class="id"·title="keyword">forall</span>·<a·id="r1:1"·class="idref"·href="#r1:1"><span·class="id"·title="binder">r1</span></a>·<a·id="r2:2"·class="idref"·href="#r2:2"><span·class="id"·title="binder">r2</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>,·<a·class="idref"·href="Coq.Init.Specif.html#87727981cdc1579fef00b9d9c1d3b9da"><span·class="id"·title="notation">{</span></a><a·class="idref"·href="Coq.Reals.ROrderedType.html#r1:1"><span·class="id"·title="variable">r1</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·<a·class="idref"·href="Coq.Reals.ROrderedType.html#r2:2"><span·class="id"·title="variable">r2</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.Reals.ROrderedType.html#r1:1"><span·class="id"·title="variable">r1</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.Reals.ROrderedType.html#r2:2"><span·class="id"·title="variable">r2</span></a><a·class="idref"·href="Coq.Init.Specif.html#87727981cdc1579fef00b9d9c1d3b9da"><span·class="id"·title="notation">}</span></a>.<br/> | 60 | <span·class="id"·title="keyword">Lemma</span>·<a·id="Req_dec"·class="idref"·href="#Req_dec"><span·class="id"·title="lemma">Req_dec</span></a>·:·<span·class="id"·title="keyword">forall</span>·<a·id="r1:1"·class="idref"·href="#r1:1"><span·class="id"·title="binder">r1</span></a>·<a·id="r2:2"·class="idref"·href="#r2:2"><span·class="id"·title="binder">r2</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>,·<a·class="idref"·href="Coq.Init.Specif.html#87727981cdc1579fef00b9d9c1d3b9da"><span·class="id"·title="notation">{</span></a><a·class="idref"·href="Coq.Reals.ROrderedType.html#r1:1"><span·class="id"·title="variable">r1</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·<a·class="idref"·href="Coq.Reals.ROrderedType.html#r2:2"><span·class="id"·title="variable">r2</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.Reals.ROrderedType.html#r1:1"><span·class="id"·title="variable">r1</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.Reals.ROrderedType.html#r2:2"><span·class="id"·title="variable">r2</span></a><a·class="idref"·href="Coq.Init.Specif.html#87727981cdc1579fef00b9d9c1d3b9da"><span·class="id"·title="notation">}</span></a>.<br/> |
Offset 58, 15 lines modified | Offset 58, 15 lines modified | ||
58 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.micromega.Ztac.html#"><span·class="id"·title="library">Ztac</span></a>.<br/> | 58 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.micromega.Ztac.html#"><span·class="id"·title="library">Ztac</span></a>.<br/> |
59 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">R_scope</span>.<br/> | 59 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">R_scope</span>.<br/> |
60 | <br/> | 60 | <br/> |
61 | </div> | 61 | </div> |
62 | <div·class="doc"> | 62 | <div·class="doc"> |
63 | <a·id="lab | 63 | <a·id="lab516"></a><h1·class="section">Fractional·part</h1> |
64 | <div·class="paragraph">·</div> | 64 | <div·class="paragraph">·</div> |
65 | </div> | 65 | </div> |
66 | <div·class="code"> | 66 | <div·class="code"> |
67 | <span·class="id"·title="keyword">Definition</span>·<a·id="Int_part"·class="idref"·href="#Int_part"><span·class="id"·title="definition">Int_part</span></a>·(<a·id="r:1"·class="idref"·href="#r:1"><span·class="id"·title="binder">r</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>)·:·<a·class="idref"·href="Coq.Numbers.BinNums.html#Z"><span·class="id"·title="inductive">Z</span></a>·:=·(<a·class="idref"·href="Coq.Reals.Rdefinitions.html#up"><span·class="id"·title="definition">up</span></a>·<a·class="idref"·href="Coq.Reals.R_Ifp.html#r:1"><span·class="id"·title="variable">r</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#::Z_scope:x_'-'_x"><span·class="id"·title="notation">-</span></a>·1)%<span·class="id"·title="var">Z</span>.<br/> | 67 | <span·class="id"·title="keyword">Definition</span>·<a·id="Int_part"·class="idref"·href="#Int_part"><span·class="id"·title="definition">Int_part</span></a>·(<a·id="r:1"·class="idref"·href="#r:1"><span·class="id"·title="binder">r</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>)·:·<a·class="idref"·href="Coq.Numbers.BinNums.html#Z"><span·class="id"·title="inductive">Z</span></a>·:=·(<a·class="idref"·href="Coq.Reals.Rdefinitions.html#up"><span·class="id"·title="definition">up</span></a>·<a·class="idref"·href="Coq.Reals.R_Ifp.html#r:1"><span·class="id"·title="variable">r</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#::Z_scope:x_'-'_x"><span·class="id"·title="notation">-</span></a>·1)%<span·class="id"·title="var">Z</span>.<br/> |
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.Reals.Rsqrt_def.html#"><span·class="id"·title="library">Rsqrt_def</span></a>.<br/> | 51 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Reals.Rsqrt_def.html#"><span·class="id"·title="library">Rsqrt_def</span></a>.<br/> |
52 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">R_scope</span>.<br/> | 52 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">R_scope</span>.<br/> |
53 | <br/> | 53 | <br/> |
54 | </div> | 54 | </div> |
55 | <div·class="doc"> | 55 | <div·class="doc"> |
56 | <a·id="lab | 56 | <a·id="lab410"></a><h1·class="section">Continuous·extension·of·Rsqrt·on·R</h1> |
57 | </div> | 57 | </div> |
58 | <div·class="code"> | 58 | <div·class="code"> |
59 | <span·class="id"·title="keyword">Definition</span>·<a·id="sqrt"·class="idref"·href="#sqrt"><span·class="id"·title="definition">sqrt</span></a>·(<a·id="x:1"·class="idref"·href="#x:1"><span·class="id"·title="binder">x</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>)·:·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>·:=<br/> | 59 | <span·class="id"·title="keyword">Definition</span>·<a·id="sqrt"·class="idref"·href="#sqrt"><span·class="id"·title="definition">sqrt</span></a>·(<a·id="x:1"·class="idref"·href="#x:1"><span·class="id"·title="binder">x</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>)·:·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>·:=<br/> |
60 | <span·class="id"·title="keyword">match</span>·<a·class="idref"·href="Coq.Reals.Rbasic_fun.html#Rcase_abs"><span·class="id"·title="lemma">Rcase_abs</span></a>·<a·class="idref"·href="Coq.Reals.R_sqrt.html#x:1"><span·class="id"·title="variable">x</span></a>·<span·class="id"·title="keyword">with</span><br/> | 60 | <span·class="id"·title="keyword">match</span>·<a·class="idref"·href="Coq.Reals.Rbasic_fun.html#Rcase_abs"><span·class="id"·title="lemma">Rcase_abs</span></a>·<a·class="idref"·href="Coq.Reals.R_sqrt.html#x:1"><span·class="id"·title="variable">x</span></a>·<span·class="id"·title="keyword">with</span><br/> |
61 | |·<a·class="idref"·href="Coq.Init.Specif.html#left"><span·class="id"·title="constructor">left</span></a>·<span·class="id"·title="var">_</span>·=>·0<br/> | 61 | |·<a·class="idref"·href="Coq.Init.Specif.html#left"><span·class="id"·title="constructor">left</span></a>·<span·class="id"·title="var">_</span>·=>·0<br/> |
62 | |·<a·class="idref"·href="Coq.Init.Specif.html#right"><span·class="id"·title="constructor">right</span></a>·<span·class="id"·title="var">a</span>·=>·<a·class="idref"·href="Coq.Reals.Rsqrt_def.html#Rsqrt"><span·class="id"·title="definition">Rsqrt</span></a>·(<a·class="idref"·href="Coq.Reals.RIneq.html#mknonnegreal"><span·class="id"·title="constructor">mknonnegreal</span></a>·<a·class="idref"·href="Coq.Reals.R_sqrt.html#x:1"><span·class="id"·title="variable">x</span></a>·(<a·class="idref"·href="Coq.Reals.RIneq.html#Rge_le"><span·class="id"·title="lemma">Rge_le</span></a>·<span·class="id"·title="var">_</span>·<span·class="id"·title="var">_</span>·<span·class="id"·title="var">a</span>))<br/> | 62 | |·<a·class="idref"·href="Coq.Init.Specif.html#right"><span·class="id"·title="constructor">right</span></a>·<span·class="id"·title="var">a</span>·=>·<a·class="idref"·href="Coq.Reals.Rsqrt_def.html#Rsqrt"><span·class="id"·title="definition">Rsqrt</span></a>·(<a·class="idref"·href="Coq.Reals.RIneq.html#mknonnegreal"><span·class="id"·title="constructor">mknonnegreal</span></a>·<a·class="idref"·href="Coq.Reals.R_sqrt.html#x:1"><span·class="id"·title="variable">x</span></a>·(<a·class="idref"·href="Coq.Reals.RIneq.html#Rge_le"><span·class="id"·title="lemma">Rge_le</span></a>·<span·class="id"·title="var">_</span>·<span·class="id"·title="var">_</span>·<span·class="id"·title="var">a</span>))<br/> |
Offset 53, 15 lines modified | Offset 53, 15 lines modified | ||
53 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">R_scope</span>.<br/> | 53 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">R_scope</span>.<br/> |
54 | <span·class="id"·title="keyword">Implicit</span>·<span·class="id"·title="keyword">Type</span>·<span·class="id"·title="var">f</span>·:·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</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.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>.<br/> | 54 | <span·class="id"·title="keyword">Implicit</span>·<span·class="id"·title="keyword">Type</span>·<span·class="id"·title="var">f</span>·:·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</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.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>.<br/> |
55 | <br/> | 55 | <br/> |
56 | </div> | 56 | </div> |
57 | <div·class="doc"> | 57 | <div·class="doc"> |
58 | <a·id="lab | 58 | <a·id="lab479"></a><h1·class="section">Basic·operations·on·functions</h1> |
59 | </div> | 59 | </div> |
60 | <div·class="code"> | 60 | <div·class="code"> |
61 | <span·class="id"·title="keyword">Definition</span>·<a·id="plus_fct"·class="idref"·href="#plus_fct"><span·class="id"·title="definition">plus_fct</span></a>·<a·id="f1:1"·class="idref"·href="#f1:1"><span·class="id"·title="binder">f1</span></a>·<a·id="f2:2"·class="idref"·href="#f2:2"><span·class="id"·title="binder">f2</span></a>·(<a·id="x:3"·class="idref"·href="#x:3"><span·class="id"·title="binder">x</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>)·:·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>·:=·<a·class="idref"·href="Coq.Reals.Ranalysis1.html#f1:1"><span·class="id"·title="variable">f1</span></a>·<a·class="idref"·href="Coq.Reals.Ranalysis1.html#x:3"><span·class="id"·title="variable">x</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#3e57074ab0a6a36b253e873a1bdac6ad"><span·class="id"·title="notation">+</span></a>·<a·class="idref"·href="Coq.Reals.Ranalysis1.html#f2:2"><span·class="id"·title="variable">f2</span></a>·<a·class="idref"·href="Coq.Reals.Ranalysis1.html#x:3"><span·class="id"·title="variable">x</span></a>.<br/> | 61 | <span·class="id"·title="keyword">Definition</span>·<a·id="plus_fct"·class="idref"·href="#plus_fct"><span·class="id"·title="definition">plus_fct</span></a>·<a·id="f1:1"·class="idref"·href="#f1:1"><span·class="id"·title="binder">f1</span></a>·<a·id="f2:2"·class="idref"·href="#f2:2"><span·class="id"·title="binder">f2</span></a>·(<a·id="x:3"·class="idref"·href="#x:3"><span·class="id"·title="binder">x</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>)·:·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>·:=·<a·class="idref"·href="Coq.Reals.Ranalysis1.html#f1:1"><span·class="id"·title="variable">f1</span></a>·<a·class="idref"·href="Coq.Reals.Ranalysis1.html#x:3"><span·class="id"·title="variable">x</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#3e57074ab0a6a36b253e873a1bdac6ad"><span·class="id"·title="notation">+</span></a>·<a·class="idref"·href="Coq.Reals.Ranalysis1.html#f2:2"><span·class="id"·title="variable">f2</span></a>·<a·class="idref"·href="Coq.Reals.Ranalysis1.html#x:3"><span·class="id"·title="variable">x</span></a>.<br/> |
62 | <span·class="id"·title="keyword">Definition</span>·<a·id="opp_fct"·class="idref"·href="#opp_fct"><span·class="id"·title="definition">opp_fct</span></a>·<a·id="f:4"·class="idref"·href="#f:4"><span·class="id"·title="binder">f</span></a>·(<a·id="x:5"·class="idref"·href="#x:5"><span·class="id"·title="binder">x</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>)·:·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>·:=·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#::R_scope:'-'_x"><span·class="id"·title="notation">-</span></a>·<a·class="idref"·href="Coq.Reals.Ranalysis1.html#f:4"><span·class="id"·title="variable">f</span></a>·<a·class="idref"·href="Coq.Reals.Ranalysis1.html#x:5"><span·class="id"·title="variable">x</span></a>.<br/> | 62 | <span·class="id"·title="keyword">Definition</span>·<a·id="opp_fct"·class="idref"·href="#opp_fct"><span·class="id"·title="definition">opp_fct</span></a>·<a·id="f:4"·class="idref"·href="#f:4"><span·class="id"·title="binder">f</span></a>·(<a·id="x:5"·class="idref"·href="#x:5"><span·class="id"·title="binder">x</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>)·:·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>·:=·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#::R_scope:'-'_x"><span·class="id"·title="notation">-</span></a>·<a·class="idref"·href="Coq.Reals.Ranalysis1.html#f:4"><span·class="id"·title="variable">f</span></a>·<a·class="idref"·href="Coq.Reals.Ranalysis1.html#x:5"><span·class="id"·title="variable">x</span></a>.<br/> |
63 | <span·class="id"·title="keyword">Definition</span>·<a·id="mult_fct"·class="idref"·href="#mult_fct"><span·class="id"·title="definition">mult_fct</span></a>·<a·id="f1:6"·class="idref"·href="#f1:6"><span·class="id"·title="binder">f1</span></a>·<a·id="f2:7"·class="idref"·href="#f2:7"><span·class="id"·title="binder">f2</span></a>·(<a·id="x:8"·class="idref"·href="#x:8"><span·class="id"·title="binder">x</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>)·:·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>·:=·<a·class="idref"·href="Coq.Reals.Ranalysis1.html#f1:6"><span·class="id"·title="variable">f1</span></a>·<a·class="idref"·href="Coq.Reals.Ranalysis1.html#x:8"><span·class="id"·title="variable">x</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#e1dae7ed53bffa765009199d058dd327"><span·class="id"·title="notation">*</span></a>·<a·class="idref"·href="Coq.Reals.Ranalysis1.html#f2:7"><span·class="id"·title="variable">f2</span></a>·<a·class="idref"·href="Coq.Reals.Ranalysis1.html#x:8"><span·class="id"·title="variable">x</span></a>.<br/> | 63 | <span·class="id"·title="keyword">Definition</span>·<a·id="mult_fct"·class="idref"·href="#mult_fct"><span·class="id"·title="definition">mult_fct</span></a>·<a·id="f1:6"·class="idref"·href="#f1:6"><span·class="id"·title="binder">f1</span></a>·<a·id="f2:7"·class="idref"·href="#f2:7"><span·class="id"·title="binder">f2</span></a>·(<a·id="x:8"·class="idref"·href="#x:8"><span·class="id"·title="binder">x</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>)·:·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>·:=·<a·class="idref"·href="Coq.Reals.Ranalysis1.html#f1:6"><span·class="id"·title="variable">f1</span></a>·<a·class="idref"·href="Coq.Reals.Ranalysis1.html#x:8"><span·class="id"·title="variable">x</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#e1dae7ed53bffa765009199d058dd327"><span·class="id"·title="notation">*</span></a>·<a·class="idref"·href="Coq.Reals.Ranalysis1.html#f2:7"><span·class="id"·title="variable">f2</span></a>·<a·class="idref"·href="Coq.Reals.Ranalysis1.html#x:8"><span·class="id"·title="variable">x</span></a>.<br/> |
64 | <span·class="id"·title="keyword">Definition</span>·<a·id="mult_real_fct"·class="idref"·href="#mult_real_fct"><span·class="id"·title="definition">mult_real_fct</span></a>·(<a·id="a:9"·class="idref"·href="#a:9"><span·class="id"·title="binder">a</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>)·<a·id="f:10"·class="idref"·href="#f:10"><span·class="id"·title="binder">f</span></a>·(<a·id="x:11"·class="idref"·href="#x:11"><span·class="id"·title="binder">x</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>)·:·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>·:=·<a·class="idref"·href="Coq.Reals.Ranalysis1.html#a:9"><span·class="id"·title="variable">a</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#e1dae7ed53bffa765009199d058dd327"><span·class="id"·title="notation">*</span></a>·<a·class="idref"·href="Coq.Reals.Ranalysis1.html#f:10"><span·class="id"·title="variable">f</span></a>·<a·class="idref"·href="Coq.Reals.Ranalysis1.html#x:11"><span·class="id"·title="variable">x</span></a>.<br/> | 64 | <span·class="id"·title="keyword">Definition</span>·<a·id="mult_real_fct"·class="idref"·href="#mult_real_fct"><span·class="id"·title="definition">mult_real_fct</span></a>·(<a·id="a:9"·class="idref"·href="#a:9"><span·class="id"·title="binder">a</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>)·<a·id="f:10"·class="idref"·href="#f:10"><span·class="id"·title="binder">f</span></a>·(<a·id="x:11"·class="idref"·href="#x:11"><span·class="id"·title="binder">x</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>)·:·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>·:=·<a·class="idref"·href="Coq.Reals.Ranalysis1.html#a:9"><span·class="id"·title="variable">a</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#e1dae7ed53bffa765009199d058dd327"><span·class="id"·title="notation">*</span></a>·<a·class="idref"·href="Coq.Reals.Ranalysis1.html#f:10"><span·class="id"·title="variable">f</span></a>·<a·class="idref"·href="Coq.Reals.Ranalysis1.html#x:11"><span·class="id"·title="variable">x</span></a>.<br/> |
Offset 56, 15 lines modified | Offset 56, 15 lines modified | ||
56 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.micromega.Lra.html#"><span·class="id"·title="library">Lra</span></a>.<br/> | 56 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.micromega.Lra.html#"><span·class="id"·title="library">Lra</span></a>.<br/> |
57 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">R_scope</span>.<br/> | 57 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">R_scope</span>.<br/> |
58 | <br/> | 58 | <br/> |
59 | </div> | 59 | </div> |
60 | <div·class="doc"> | 60 | <div·class="doc"> |
61 | <a·id="lab | 61 | <a·id="lab354"></a><h1·class="section">Preliminaries·lemmas</h1> |
62 | </div> | 62 | </div> |
63 | <div·class="code"> | 63 | <div·class="code"> |
64 | <br/> | 64 | <br/> |
65 | <span·class="id"·title="keyword">Lemma</span>·<a·id="f_incr_implies_g_incr_interv"·class="idref"·href="#f_incr_implies_g_incr_interv"><span·class="id"·title="lemma">f_incr_implies_g_incr_interv</span></a>·:·<span·class="id"·title="keyword">forall</span>·<a·id="f:1"·class="idref"·href="#f:1"><span·class="id"·title="binder">f</span></a>·<a·id="g:2"·class="idref"·href="#g:2"><span·class="id"·title="binder">g</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</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.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>,·<span·class="id"·title="keyword">forall</span>·<a·id="lb:3"·class="idref"·href="#lb:3"><span·class="id"·title="binder">lb</span></a>·<a·id="ub:4"·class="idref"·href="#ub:4"><span·class="id"·title="binder">ub</span></a>,<br/> | 65 | <span·class="id"·title="keyword">Lemma</span>·<a·id="f_incr_implies_g_incr_interv"·class="idref"·href="#f_incr_implies_g_incr_interv"><span·class="id"·title="lemma">f_incr_implies_g_incr_interv</span></a>·:·<span·class="id"·title="keyword">forall</span>·<a·id="f:1"·class="idref"·href="#f:1"><span·class="id"·title="binder">f</span></a>·<a·id="g:2"·class="idref"·href="#g:2"><span·class="id"·title="binder">g</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</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.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>,·<span·class="id"·title="keyword">forall</span>·<a·id="lb:3"·class="idref"·href="#lb:3"><span·class="id"·title="binder">lb</span></a>·<a·id="ub:4"·class="idref"·href="#ub:4"><span·class="id"·title="binder">ub</span></a>,<br/> |
66 | <a·class="idref"·href="Coq.Reals.Ranalysis5.html#lb:3"><span·class="id"·title="variable">lb</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#::R_scope:x_'<'_x"><span·class="id"·title="notation"><</span></a>·<a·class="idref"·href="Coq.Reals.Ranalysis5.html#ub:4"><span·class="id"·title="variable">ub</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#::type_scope:x_'->'_x"><span·class="id"·title="notation">-></span></a><br/> | 66 | <a·class="idref"·href="Coq.Reals.Ranalysis5.html#lb:3"><span·class="id"·title="variable">lb</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#::R_scope:x_'<'_x"><span·class="id"·title="notation"><</span></a>·<a·class="idref"·href="Coq.Reals.Ranalysis5.html#ub:4"><span·class="id"·title="variable">ub</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#::type_scope:x_'->'_x"><span·class="id"·title="notation">-></span></a><br/> |
Offset 290, 21 lines modified | Offset 290, 21 lines modified | ||
00001210:·2220·7469·746c·653d·226b·6579·776f·7264··"·title="keyword | 00001210:·2220·7469·746c·653d·226b·6579·776f·7264··"·title="keyword | ||
00001220:·223e·5363·6f70·653c·2f73·7061·6e3e·203c··">Scope</span>·< | 00001220:·223e·5363·6f70·653c·2f73·7061·6e3e·203c··">Scope</span>·< | ||
00001230:·7370·616e·2063·6c61·7373·3d22·6964·2220··span·class="id"· | 00001230:·7370·616e·2063·6c61·7373·3d22·6964·2220··span·class="id"· | ||
00001240:·7469·746c·653d·2276·6172·223e·525f·7363··title="var">R_sc | 00001240:·7469·746c·653d·2276·6172·223e·525f·7363··title="var">R_sc | ||
00001250:·6f70·653c·2f73·7061·6e3e·2e3c·6272·2f3e··ope</span>.<br/> | 00001250:·6f70·653c·2f73·7061·6e3e·2e3c·6272·2f3e··ope</span>.<br/> | ||
00001260:·0a0a·3c62·722f·3e0a·3c2f·6469·763e·0a0a··..<br/>.</div>.. | 00001260:·0a0a·3c62·722f·3e0a·3c2f·6469·763e·0a0a··..<br/>.</div>.. | ||
00001270:·3c64·6976·2063·6c61·7373·3d22·646f·6322··<div·class="doc" | 00001270:·3c64·6976·2063·6c61·7373·3d22·646f·6322··<div·class="doc" | ||
00001280:·3e0a·3c61·2069·643d·226c·6162·3 | 00001280:·3e0a·3c61·2069·643d·226c·6162·3337·3422··>.<a·id="lab374" | ||
00001290:·3e3c·2f61·3e3c·6831·2063·6c61·7373·3d22··></a><h1·class=" | 00001290:·3e3c·2f61·3e3c·6831·2063·6c61·7373·3d22··></a><h1·class=" | ||
000012a0:·7365·6374·696f·6e22·3e50·7265·6c69·6d69··section">Prelimi | 000012a0:·7365·6374·696f·6e22·3e50·7265·6c69·6d69··section">Prelimi | ||
000012b0:·6e61·7269·6573·3c2f·6831·3e0a·0a3c·6469··naries</h1>..<di | 000012b0:·6e61·7269·6573·3c2f·6831·3e0a·0a3c·6469··naries</h1>..<di | ||
000012c0:·7620·636c·6173·733d·2270·6172·6167·7261··v·class="paragra | 000012c0:·7620·636c·6173·733d·2270·6172·6167·7261··v·class="paragra | ||
000012d0:·7068·223e·203c·2f64·6976·3e0a·0a3c·6120··ph">·</div>..<a· | 000012d0:·7068·223e·203c·2f64·6976·3e0a·0a3c·6120··ph">·</div>..<a· | ||
000012e0:·6964·3d22·6c61·623 | 000012e0:·6964·3d22·6c61·6233·3735·223e·3c2f·613e··id="lab375"></a> | ||
000012f0:·3c68·3220·636c·6173·733d·2273·6563·7469··<h2·class="secti | 000012f0:·3c68·3220·636c·6173·733d·2273·6563·7469··<h2·class="secti | ||
00001300:·6f6e·223e·5661·7269·6f75·7320·6765·6e65··on">Various·gene | 00001300:·6f6e·223e·5661·7269·6f75·7320·6765·6e65··on">Various·gene | ||
00001310:·7269·6320·6c65·6d6d·6173·2077·6869·6368··ric·lemmas·which | 00001310:·7269·6320·6c65·6d6d·6173·2077·6869·6368··ric·lemmas·which | ||
00001320:·2070·726f·6261·626c·7920·7368·6f75·6c64···probably·should | 00001320:·2070·726f·6261·626c·7920·7368·6f75·6c64···probably·should | ||
00001330:·2067·6f20·736f·6d65·7768·6572·6520·656c···go·somewhere·el | 00001330:·2067·6f20·736f·6d65·7768·6572·6520·656c···go·somewhere·el | ||
00001340:·7365·3c2f·6832·3e0a·0a3c·2f64·6976·3e0a··se</h2>..</div>. | 00001340:·7365·3c2f·6832·3e0a·0a3c·2f64·6976·3e0a··se</h2>..</div>. | ||
00001350:·3c64·6976·2063·6c61·7373·3d22·636f·6465··<div·class="code | 00001350:·3c64·6976·2063·6c61·7373·3d22·636f·6465··<div·class="code |
Offset 65, 19 lines modified | Offset 65, 19 lines modified | ||
65 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Export</span>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#"><span·class="id"·title="library">Rdefinitions</span></a>.<br/> | 65 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Export</span>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#"><span·class="id"·title="library">Rdefinitions</span></a>.<br/> |
66 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">R_scope</span>.<br/> | 66 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">R_scope</span>.<br/> |
67 | <br/> | 67 | <br/> |
68 | </div> | 68 | </div> |
69 | <div·class="doc"> | 69 | <div·class="doc"> |
70 | <a·id="lab | 70 | <a·id="lab496"></a><h1·class="section">Field·operations</h1> |
71 | <div·class="paragraph">·</div> | 71 | <div·class="paragraph">·</div> |
72 | <a·id="lab | 72 | <a·id="lab497"></a><h2·class="section">Addition</h2> |
73 | </div> | 73 | </div> |
74 | <div·class="code"> | 74 | <div·class="code"> |
75 | <br/> | 75 | <br/> |
76 | <span·class="id"·title="keyword">Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">CReal_scope</span>.<br/> | 76 | <span·class="id"·title="keyword">Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">CReal_scope</span>.<br/> |
Offset 61, 15 lines modified | Offset 61, 15 lines modified | ||
61 | <br/> | 61 | <br/> |
62 | <span·class="id"·title="keyword">Implicit</span>·<span·class="id"·title="keyword">Type</span>·<span·class="id"·title="var">r</span>·:·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>.<br/> | 62 | <span·class="id"·title="keyword">Implicit</span>·<span·class="id"·title="keyword">Type</span>·<span·class="id"·title="var">r</span>·:·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>.<br/> |
63 | <br/> | 63 | <br/> |
64 | </div> | 64 | </div> |
65 | <div·class="doc"> | 65 | <div·class="doc"> |
66 | <a·id="lab | 66 | <a·id="lab472"></a><h1·class="section">Rmin</h1> |
67 | <div·class="paragraph">·</div> | 67 | <div·class="paragraph">·</div> |
68 | </div> | 68 | </div> |
69 | <div·class="code"> | 69 | <div·class="code"> |
70 | <span·class="id"·title="keyword">Definition</span>·<a·id="Rmin"·class="idref"·href="#Rmin"><span·class="id"·title="definition">Rmin</span></a>·(<a·id="x:1"·class="idref"·href="#x:1"><span·class="id"·title="binder">x</span></a>·<a·id="y:2"·class="idref"·href="#y:2"><span·class="id"·title="binder">y</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>)·:·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>·:=<br/> | 70 | <span·class="id"·title="keyword">Definition</span>·<a·id="Rmin"·class="idref"·href="#Rmin"><span·class="id"·title="definition">Rmin</span></a>·(<a·id="x:1"·class="idref"·href="#x:1"><span·class="id"·title="binder">x</span></a>·<a·id="y:2"·class="idref"·href="#y:2"><span·class="id"·title="binder">y</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>)·:·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>·:=<br/> |
Offset 174, 15 lines modified | Offset 174, 15 lines modified | ||
174 | <span·class="id"·title="keyword">Notation</span>·<a·id="::R_scope:x_'<'_x_'<'_x"·class="idref"·href="#::R_scope:x_'<'_x_'<'_x"><span·class="id"·title="notation">"</span></a>x·<·y·<·z"···:=·(<span·class="id"·title="var">x</span>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#::R_scope:x_'<'_x"><span·class="id"·title="notation"><</span></a>··<span·class="id"·title="var">y</span>·<a·class="idref"·href="Coq.Init.Logic.html#ba2b0e492d2b4675a0acf3ea92aabadd"><span·class="id"·title="notation">/\</span></a>·<span·class="id"·title="var">y</span>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#::R_scope:x_'<'_x"><span·class="id"·title="notation"><</span></a>··<span·class="id"·title="var">z</span>)·:·<span·class="id"·title="var">R_scope</span>.<br/> | 174 | <span·class="id"·title="keyword">Notation</span>·<a·id="::R_scope:x_'<'_x_'<'_x"·class="idref"·href="#::R_scope:x_'<'_x_'<'_x"><span·class="id"·title="notation">"</span></a>x·<·y·<·z"···:=·(<span·class="id"·title="var">x</span>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#::R_scope:x_'<'_x"><span·class="id"·title="notation"><</span></a>··<span·class="id"·title="var">y</span>·<a·class="idref"·href="Coq.Init.Logic.html#ba2b0e492d2b4675a0acf3ea92aabadd"><span·class="id"·title="notation">/\</span></a>·<span·class="id"·title="var">y</span>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#::R_scope:x_'<'_x"><span·class="id"·title="notation"><</span></a>··<span·class="id"·title="var">z</span>)·:·<span·class="id"·title="var">R_scope</span>.<br/> |
175 | <span·class="id"·title="keyword">Notation</span>·<a·id="655439258f20e6256090528bc533ae29"·class="idref"·href="#655439258f20e6256090528bc533ae29"><span·class="id"·title="notation">"</span></a>x·<·y·<=·z"··:=·(<span·class="id"·title="var">x</span>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#::R_scope:x_'<'_x"><span·class="id"·title="notation"><</span></a>··<span·class="id"·title="var">y</span>·<a·class="idref"·href="Coq.Init.Logic.html#ba2b0e492d2b4675a0acf3ea92aabadd"><span·class="id"·title="notation">/\</span></a>·<span·class="id"·title="var">y</span>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#77d341fe206b2891763e25999ffddca2"><span·class="id"·title="notation"><=</span></a>·<span·class="id"·title="var">z</span>)·:·<span·class="id"·title="var">R_scope</span>.<br/> | 175 | <span·class="id"·title="keyword">Notation</span>·<a·id="655439258f20e6256090528bc533ae29"·class="idref"·href="#655439258f20e6256090528bc533ae29"><span·class="id"·title="notation">"</span></a>x·<·y·<=·z"··:=·(<span·class="id"·title="var">x</span>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#::R_scope:x_'<'_x"><span·class="id"·title="notation"><</span></a>··<span·class="id"·title="var">y</span>·<a·class="idref"·href="Coq.Init.Logic.html#ba2b0e492d2b4675a0acf3ea92aabadd"><span·class="id"·title="notation">/\</span></a>·<span·class="id"·title="var">y</span>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#77d341fe206b2891763e25999ffddca2"><span·class="id"·title="notation"><=</span></a>·<span·class="id"·title="var">z</span>)·:·<span·class="id"·title="var">R_scope</span>.<br/> |
176 | <br/> | 176 | <br/> |
177 | </div> | 177 | </div> |
178 | <div·class="doc"> | 178 | <div·class="doc"> |
179 | <a·id="lab | 179 | <a·id="lab494"></a><h1·class="section">Injection·from·<span·class="inlinecode"><span·class="id"·title="var">Z</span></span>·to·<span·class="inlinecode"><span·class="id"·title="var">R</span></span></h1> |
180 | </div> | 180 | </div> |
181 | <div·class="code"> | 181 | <div·class="code"> |
182 | <br/> | 182 | <br/> |
183 | <span·class="id"·title="keyword">Fixpoint</span>·<a·id="IPR_2"·class="idref"·href="#IPR_2"><span·class="id"·title="definition">IPR_2</span></a>·(<a·id="p:50"·class="idref"·href="#p:50"><span·class="id"·title="binder">p</span></a>:<a·class="idref"·href="Coq.Numbers.BinNums.html#positive"><span·class="id"·title="inductive">positive</span></a>)·:·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#R"><span·class="id"·title="abbreviation">R</span></a>·:=<br/> | 183 | <span·class="id"·title="keyword">Fixpoint</span>·<a·id="IPR_2"·class="idref"·href="#IPR_2"><span·class="id"·title="definition">IPR_2</span></a>·(<a·id="p:50"·class="idref"·href="#p:50"><span·class="id"·title="binder">p</span></a>:<a·class="idref"·href="Coq.Numbers.BinNums.html#positive"><span·class="id"·title="inductive">positive</span></a>)·:·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#R"><span·class="id"·title="abbreviation">R</span></a>·:=<br/> |
184 | <span·class="id"·title="keyword">match</span>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#p:50"><span·class="id"·title="variable">p</span></a>·<span·class="id"·title="keyword">with</span><br/> | 184 | <span·class="id"·title="keyword">match</span>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#p:50"><span·class="id"·title="variable">p</span></a>·<span·class="id"·title="keyword">with</span><br/> |
Offset 70, 15 lines modified | Offset 70, 15 lines modified | ||
70 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">nat_scope</span>.<br/> | 70 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">nat_scope</span>.<br/> |
71 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">R_scope</span>.<br/> | 71 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">R_scope</span>.<br/> |
72 | <br/> | 72 | <br/> |
73 | </div> | 73 | </div> |
74 | <div·class="doc"> | 74 | <div·class="doc"> |
75 | <a·id="lab | 75 | <a·id="lab455"></a><h1·class="section">Lemmas·about·factorial</h1> |
76 | </div> | 76 | </div> |
77 | <div·class="code"> | 77 | <div·class="code"> |
78 | <span·class="id"·title="keyword">Lemma</span>·<a·id="INR_fact_neq_0"·class="idref"·href="#INR_fact_neq_0"><span·class="id"·title="lemma">INR_fact_neq_0</span></a>·:·<span·class="id"·title="keyword">forall</span>·<a·id="n:1"·class="idref"·href="#n:1"><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.Reals.Raxioms.html#INR"><span·class="id"·title="definition">INR</span></a>·(<a·class="idref"·href="Coq.Arith.Factorial.html#fact"><span·class="id"·title="definition">fact</span></a>·<a·class="idref"·href="Coq.Reals.Rfunctions.html#n:1"><span·class="id"·title="variable">n</span></a>)·<a·class="idref"·href="Coq.Init.Logic.html#::type_scope:x_'<>'_x"><span·class="id"·title="notation"><></span></a>·0.<br/> | 78 | <span·class="id"·title="keyword">Lemma</span>·<a·id="INR_fact_neq_0"·class="idref"·href="#INR_fact_neq_0"><span·class="id"·title="lemma">INR_fact_neq_0</span></a>·:·<span·class="id"·title="keyword">forall</span>·<a·id="n:1"·class="idref"·href="#n:1"><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.Reals.Raxioms.html#INR"><span·class="id"·title="definition">INR</span></a>·(<a·class="idref"·href="Coq.Arith.Factorial.html#fact"><span·class="id"·title="definition">fact</span></a>·<a·class="idref"·href="Coq.Reals.Rfunctions.html#n:1"><span·class="id"·title="variable">n</span></a>)·<a·class="idref"·href="Coq.Init.Logic.html#::type_scope:x_'<>'_x"><span·class="id"·title="notation"><></span></a>·0.<br/> |
79 | <br/> | 79 | <br/> |
80 | <span·class="id"·title="keyword">Lemma</span>·<a·id="fact_simpl"·class="idref"·href="#fact_simpl"><span·class="id"·title="lemma">fact_simpl</span></a>·:·<span·class="id"·title="keyword">forall</span>·<a·id="n:2"·class="idref"·href="#n:2"><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.Factorial.html#fact"><span·class="id"·title="definition">fact</span></a>·(<a·class="idref"·href="Coq.Init.Datatypes.html#S"><span·class="id"·title="constructor">S</span></a>·<a·class="idref"·href="Coq.Reals.Rfunctions.html#n:2"><span·class="id"·title="variable">n</span></a>)·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·(<a·class="idref"·href="Coq.Init.Datatypes.html#S"><span·class="id"·title="constructor">S</span></a>·<a·class="idref"·href="Coq.Reals.Rfunctions.html#n:2"><span·class="id"·title="variable">n</span></a>·<a·class="idref"·href="Coq.Init.Peano.html#ea2ff3d561159081cea6fb2e8113cc54"><span·class="id"·title="notation">*</span></a>·<a·class="idref"·href="Coq.Arith.Factorial.html#fact"><span·class="id"·title="definition">fact</span></a>·<a·class="idref"·href="Coq.Reals.Rfunctions.html#n:2"><span·class="id"·title="variable">n</span></a>)%<span·class="id"·title="var">nat</span>.<br/> | 80 | <span·class="id"·title="keyword">Lemma</span>·<a·id="fact_simpl"·class="idref"·href="#fact_simpl"><span·class="id"·title="lemma">fact_simpl</span></a>·:·<span·class="id"·title="keyword">forall</span>·<a·id="n:2"·class="idref"·href="#n:2"><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.Factorial.html#fact"><span·class="id"·title="definition">fact</span></a>·(<a·class="idref"·href="Coq.Init.Datatypes.html#S"><span·class="id"·title="constructor">S</span></a>·<a·class="idref"·href="Coq.Reals.Rfunctions.html#n:2"><span·class="id"·title="variable">n</span></a>)·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·(<a·class="idref"·href="Coq.Init.Datatypes.html#S"><span·class="id"·title="constructor">S</span></a>·<a·class="idref"·href="Coq.Reals.Rfunctions.html#n:2"><span·class="id"·title="variable">n</span></a>·<a·class="idref"·href="Coq.Init.Peano.html#ea2ff3d561159081cea6fb2e8113cc54"><span·class="id"·title="notation">*</span></a>·<a·class="idref"·href="Coq.Arith.Factorial.html#fact"><span·class="id"·title="definition">fact</span></a>·<a·class="idref"·href="Coq.Reals.Rfunctions.html#n:2"><span·class="id"·title="variable">n</span></a>)%<span·class="id"·title="var">nat</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.Reals.R_sqrt.html#"><span·class="id"·title="library">R_sqrt</span></a>.<br/> | 53 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Reals.R_sqrt.html#"><span·class="id"·title="library">R_sqrt</span></a>.<br/> |
54 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">R_scope</span>.<br/> | 54 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">R_scope</span>.<br/> |
55 | <br/> | 55 | <br/> |
56 | </div> | 56 | </div> |
57 | <div·class="doc"> | 57 | <div·class="doc"> |
58 | <a·id="lab | 58 | <a·id="lab475"></a><h1·class="section">Distance</h1> |
59 | </div> | 59 | </div> |
60 | <div·class="code"> | 60 | <div·class="code"> |
61 | <br/> | 61 | <br/> |
62 | <span·class="id"·title="keyword">Definition</span>·<a·id="dist_euc"·class="idref"·href="#dist_euc"><span·class="id"·title="definition">dist_euc</span></a>·(<a·id="x0:1"·class="idref"·href="#x0:1"><span·class="id"·title="binder">x0</span></a>·<a·id="y0:2"·class="idref"·href="#y0:2"><span·class="id"·title="binder">y0</span></a>·<a·id="x1:3"·class="idref"·href="#x1:3"><span·class="id"·title="binder">x1</span></a>·<a·id="y1:4"·class="idref"·href="#y1:4"><span·class="id"·title="binder">y1</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>)·:·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>·:=<br/> | 62 | <span·class="id"·title="keyword">Definition</span>·<a·id="dist_euc"·class="idref"·href="#dist_euc"><span·class="id"·title="definition">dist_euc</span></a>·(<a·id="x0:1"·class="idref"·href="#x0:1"><span·class="id"·title="binder">x0</span></a>·<a·id="y0:2"·class="idref"·href="#y0:2"><span·class="id"·title="binder">y0</span></a>·<a·id="x1:3"·class="idref"·href="#x1:3"><span·class="id"·title="binder">x1</span></a>·<a·id="y1:4"·class="idref"·href="#y1:4"><span·class="id"·title="binder">y1</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>)·:·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>·:=<br/> |
63 | <a·class="idref"·href="Coq.Reals.R_sqrt.html#sqrt"><span·class="id"·title="definition">sqrt</span></a>·(<a·class="idref"·href="Coq.Reals.RIneq.html#Rsqr"><span·class="id"·title="definition">Rsqr</span></a>·(<a·class="idref"·href="Coq.Reals.Rgeom.html#x0:1"><span·class="id"·title="variable">x0</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#::R_scope:x_'-'_x"><span·class="id"·title="notation">-</span></a>·<a·class="idref"·href="Coq.Reals.Rgeom.html#x1:3"><span·class="id"·title="variable">x1</span></a>)·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#3e57074ab0a6a36b253e873a1bdac6ad"><span·class="id"·title="notation">+</span></a>·<a·class="idref"·href="Coq.Reals.RIneq.html#Rsqr"><span·class="id"·title="definition">Rsqr</span></a>·(<a·class="idref"·href="Coq.Reals.Rgeom.html#y0:2"><span·class="id"·title="variable">y0</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#::R_scope:x_'-'_x"><span·class="id"·title="notation">-</span></a>·<a·class="idref"·href="Coq.Reals.Rgeom.html#y1:4"><span·class="id"·title="variable">y1</span></a>)).<br/> | 63 | <a·class="idref"·href="Coq.Reals.R_sqrt.html#sqrt"><span·class="id"·title="definition">sqrt</span></a>·(<a·class="idref"·href="Coq.Reals.RIneq.html#Rsqr"><span·class="id"·title="definition">Rsqr</span></a>·(<a·class="idref"·href="Coq.Reals.Rgeom.html#x0:1"><span·class="id"·title="variable">x0</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#::R_scope:x_'-'_x"><span·class="id"·title="notation">-</span></a>·<a·class="idref"·href="Coq.Reals.Rgeom.html#x1:3"><span·class="id"·title="variable">x1</span></a>)·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#3e57074ab0a6a36b253e873a1bdac6ad"><span·class="id"·title="notation">+</span></a>·<a·class="idref"·href="Coq.Reals.RIneq.html#Rsqr"><span·class="id"·title="definition">Rsqr</span></a>·(<a·class="idref"·href="Coq.Reals.Rgeom.html#y0:2"><span·class="id"·title="variable">y0</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#::R_scope:x_'-'_x"><span·class="id"·title="notation">-</span></a>·<a·class="idref"·href="Coq.Reals.Rgeom.html#y1:4"><span·class="id"·title="variable">y1</span></a>)).<br/> |
Offset 57, 15 lines modified | Offset 57, 15 lines modified | ||
57 | <br/> | 57 | <br/> |
58 | <span·class="id"·title="keyword">Set·Implicit·Arguments</span>.<br/> | 58 | <span·class="id"·title="keyword">Set·Implicit·Arguments</span>.<br/> |
59 | <br/> | 59 | <br/> |
60 | </div> | 60 | </div> |
61 | <div·class="doc"> | 61 | <div·class="doc"> |
62 | <a·id="lab | 62 | <a·id="lab508"></a><h1·class="section">Each·bounded·subset·of·N·has·a·maximal·element</h1> |
63 | </div> | 63 | </div> |
64 | <div·class="code"> | 64 | <div·class="code"> |
65 | <br/> | 65 | <br/> |
66 | <span·class="id"·title="keyword">Definition</span>·<a·id="Nbound"·class="idref"·href="#Nbound"><span·class="id"·title="definition">Nbound</span></a>·(<a·id="I:1"·class="idref"·href="#I:1"><span·class="id"·title="binder">I</span></a>:<a·class="idref"·href="Coq.Init.Datatypes.html#nat"><span·class="id"·title="inductive">nat</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>)·:·<span·class="id"·title="keyword">Prop</span>·:=<br/> | 66 | <span·class="id"·title="keyword">Definition</span>·<a·id="Nbound"·class="idref"·href="#Nbound"><span·class="id"·title="definition">Nbound</span></a>·(<a·id="I:1"·class="idref"·href="#I:1"><span·class="id"·title="binder">I</span></a>:<a·class="idref"·href="Coq.Init.Datatypes.html#nat"><span·class="id"·title="inductive">nat</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>)·:·<span·class="id"·title="keyword">Prop</span>·:=<br/> |
67 | <a·class="idref"·href="Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span·class="id"·title="notation">exists</span></a>·<a·id="n:2"·class="idref"·href="#n:2"><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.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span·class="id"·title="notation">,</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span·class="id"·title="notation">(</span></a><span·class="id"·title="keyword">forall</span>·<a·id="i:3"·class="idref"·href="#i:3"><span·class="id"·title="binder">i</span></a>:<a·class="idref"·href="Coq.Init.Datatypes.html#nat"><span·class="id"·title="inductive">nat</span></a>,·<a·class="idref"·href="Coq.Reals.RiemannInt_SF.html#I:1"><span·class="id"·title="variable">I</span></a>·<a·class="idref"·href="Coq.Reals.RiemannInt_SF.html#i:3"><span·class="id"·title="variable">i</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.Reals.RiemannInt_SF.html#i:3"><span·class="id"·title="variable">i</span></a>·<a·class="idref"·href="Coq.Init.Peano.html#cb53cf0ee22c036a03b4a9281c68b5a3"><span·class="id"·title="notation"><=</span></a>·<a·class="idref"·href="Coq.Reals.RiemannInt_SF.html#n:2"><span·class="id"·title="variable">n</span></a>)%<span·class="id"·title="var">nat</span><a·class="idref"·href="Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span·class="id"·title="notation">)</span></a>.<br/> | 67 | <a·class="idref"·href="Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span·class="id"·title="notation">exists</span></a>·<a·id="n:2"·class="idref"·href="#n:2"><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.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span·class="id"·title="notation">,</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span·class="id"·title="notation">(</span></a><span·class="id"·title="keyword">forall</span>·<a·id="i:3"·class="idref"·href="#i:3"><span·class="id"·title="binder">i</span></a>:<a·class="idref"·href="Coq.Init.Datatypes.html#nat"><span·class="id"·title="inductive">nat</span></a>,·<a·class="idref"·href="Coq.Reals.RiemannInt_SF.html#I:1"><span·class="id"·title="variable">I</span></a>·<a·class="idref"·href="Coq.Reals.RiemannInt_SF.html#i:3"><span·class="id"·title="variable">i</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.Reals.RiemannInt_SF.html#i:3"><span·class="id"·title="variable">i</span></a>·<a·class="idref"·href="Coq.Init.Peano.html#cb53cf0ee22c036a03b4a9281c68b5a3"><span·class="id"·title="notation"><=</span></a>·<a·class="idref"·href="Coq.Reals.RiemannInt_SF.html#n:2"><span·class="id"·title="variable">n</span></a>)%<span·class="id"·title="var">nat</span><a·class="idref"·href="Coq.Init.Logic.html#a883bdd010993579f99d60b3775bcf54"><span·class="id"·title="notation">)</span></a>.<br/> |
Offset 59, 15 lines modified | Offset 59, 15 lines modified | ||
59 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.micromega.Lra.html#"><span·class="id"·title="library">Lra</span></a>.<br/> | 59 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.micromega.Lra.html#"><span·class="id"·title="library">Lra</span></a>.<br/> |
60 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">R_scope</span>.<br/> | 60 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">R_scope</span>.<br/> |
61 | <br/> | 61 | <br/> |
62 | </div> | 62 | </div> |
63 | <div·class="doc"> | 63 | <div·class="doc"> |
64 | <a·id="lab | 64 | <a·id="lab369"></a><h1·class="section">Calculus</h1> |
65 | </div> | 65 | </div> |
66 | <div·class="code"> | 66 | <div·class="code"> |
67 | <span·class="id"·title="keyword">Lemma</span>·<a·id="eps2_Rgt_R0"·class="idref"·href="#eps2_Rgt_R0"><span·class="id"·title="lemma">eps2_Rgt_R0</span></a>·:·<span·class="id"·title="keyword">forall</span>·<a·id="eps:1"·class="idref"·href="#eps:1"><span·class="id"·title="binder">eps</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>,·<a·class="idref"·href="Coq.Reals.Rlimit.html#eps:1"><span·class="id"·title="variable">eps</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#::R_scope:x_'>'_x"><span·class="id"·title="notation">></span></a>·0·<a·class="idref"·href="Coq.Init.Logic.html#::type_scope:x_'->'_x"><span·class="id"·title="notation">-></span></a>·<a·class="idref"·href="Coq.Reals.Rlimit.html#eps:1"><span·class="id"·title="variable">eps</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#e1dae7ed53bffa765009199d058dd327"><span·class="id"·title="notation">*</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#2299a6ef56270a66cc1b95489d0f6e3a"><span·class="id"·title="notation">/</span></a>·2·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#::R_scope:x_'>'_x"><span·class="id"·title="notation">></span></a>·0.<br/> | 67 | <span·class="id"·title="keyword">Lemma</span>·<a·id="eps2_Rgt_R0"·class="idref"·href="#eps2_Rgt_R0"><span·class="id"·title="lemma">eps2_Rgt_R0</span></a>·:·<span·class="id"·title="keyword">forall</span>·<a·id="eps:1"·class="idref"·href="#eps:1"><span·class="id"·title="binder">eps</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>,·<a·class="idref"·href="Coq.Reals.Rlimit.html#eps:1"><span·class="id"·title="variable">eps</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#::R_scope:x_'>'_x"><span·class="id"·title="notation">></span></a>·0·<a·class="idref"·href="Coq.Init.Logic.html#::type_scope:x_'->'_x"><span·class="id"·title="notation">-></span></a>·<a·class="idref"·href="Coq.Reals.Rlimit.html#eps:1"><span·class="id"·title="variable">eps</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#e1dae7ed53bffa765009199d058dd327"><span·class="id"·title="notation">*</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#2299a6ef56270a66cc1b95489d0f6e3a"><span·class="id"·title="notation">/</span></a>·2·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#::R_scope:x_'>'_x"><span·class="id"·title="notation">></span></a>·0.<br/> |
68 | <br/> | 68 | <br/> |
69 | <span·class="id"·title="keyword">Lemma</span>·<a·id="eps2"·class="idref"·href="#eps2"><span·class="id"·title="lemma">eps2</span></a>·:·<span·class="id"·title="keyword">forall</span>·<a·id="eps:2"·class="idref"·href="#eps:2"><span·class="id"·title="binder">eps</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>,·<a·class="idref"·href="Coq.Reals.Rlimit.html#eps:2"><span·class="id"·title="variable">eps</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#e1dae7ed53bffa765009199d058dd327"><span·class="id"·title="notation">*</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#2299a6ef56270a66cc1b95489d0f6e3a"><span·class="id"·title="notation">/</span></a>·2·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#3e57074ab0a6a36b253e873a1bdac6ad"><span·class="id"·title="notation">+</span></a>·<a·class="idref"·href="Coq.Reals.Rlimit.html#eps:2"><span·class="id"·title="variable">eps</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#e1dae7ed53bffa765009199d058dd327"><span·class="id"·title="notation">*</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#2299a6ef56270a66cc1b95489d0f6e3a"><span·class="id"·title="notation">/</span></a>·2·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·<a·class="idref"·href="Coq.Reals.Rlimit.html#eps:2"><span·class="id"·title="variable">eps</span></a>.<br/> | 69 | <span·class="id"·title="keyword">Lemma</span>·<a·id="eps2"·class="idref"·href="#eps2"><span·class="id"·title="lemma">eps2</span></a>·:·<span·class="id"·title="keyword">forall</span>·<a·id="eps:2"·class="idref"·href="#eps:2"><span·class="id"·title="binder">eps</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>,·<a·class="idref"·href="Coq.Reals.Rlimit.html#eps:2"><span·class="id"·title="variable">eps</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#e1dae7ed53bffa765009199d058dd327"><span·class="id"·title="notation">*</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#2299a6ef56270a66cc1b95489d0f6e3a"><span·class="id"·title="notation">/</span></a>·2·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#3e57074ab0a6a36b253e873a1bdac6ad"><span·class="id"·title="notation">+</span></a>·<a·class="idref"·href="Coq.Reals.Rlimit.html#eps:2"><span·class="id"·title="variable">eps</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#e1dae7ed53bffa765009199d058dd327"><span·class="id"·title="notation">*</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#2299a6ef56270a66cc1b95489d0f6e3a"><span·class="id"·title="notation">/</span></a>·2·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·<a·class="idref"·href="Coq.Reals.Rlimit.html#eps:2"><span·class="id"·title="variable">eps</span></a>.<br/> |
Offset 71, 15 lines modified | Offset 71, 15 lines modified | ||
71 | <br/> | 71 | <br/> |
72 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Reals.RIneq.html#"><span·class="id"·title="library">RIneq</span></a>.<br/> | 72 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Reals.RIneq.html#"><span·class="id"·title="library">RIneq</span></a>.<br/> |
73 | <br/> | 73 | <br/> |
74 | </div> | 74 | </div> |
75 | <div·class="doc"> | 75 | <div·class="doc"> |
76 | <a·id="lab | 76 | <a·id="lab415"></a><h1·class="section">Decidability·of·arithmetical·statements</h1> |
77 | <div·class="paragraph">·</div> | 77 | <div·class="paragraph">·</div> |
78 | ·One·can·iterate·this·lemma·and·use·classical·logic·to·decide·any | 78 | ·One·can·iterate·this·lemma·and·use·classical·logic·to·decide·any |
79 | statement·in·the·arithmetical·hierarchy.· | 79 | statement·in·the·arithmetical·hierarchy.· |
80 | </div> | 80 | </div> |
81 | <div·class="code"> | 81 | <div·class="code"> |
Offset 48, 15 lines modified | Offset 48, 15 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.Structures.Orders.html#"><span·class="id"·title="library">Orders</span></a>·<a·class="idref"·href="Coq.Reals.Rbase.html#"><span·class="id"·title="library">Rbase</span></a>·<a·class="idref"·href="Coq.Reals.Rbasic_fun.html#"><span·class="id"·title="library">Rbasic_fun</span></a>·<a·class="idref"·href="Coq.Reals.ROrderedType.html#"><span·class="id"·title="library">ROrderedType</span></a>·<a·class="idref"·href="Coq.Structures.GenericMinMax.html#"><span·class="id"·title="library">GenericMinMax</span></a>.<br/> | 49 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Structures.Orders.html#"><span·class="id"·title="library">Orders</span></a>·<a·class="idref"·href="Coq.Reals.Rbase.html#"><span·class="id"·title="library">Rbase</span></a>·<a·class="idref"·href="Coq.Reals.Rbasic_fun.html#"><span·class="id"·title="library">Rbasic_fun</span></a>·<a·class="idref"·href="Coq.Reals.ROrderedType.html#"><span·class="id"·title="library">ROrderedType</span></a>·<a·class="idref"·href="Coq.Structures.GenericMinMax.html#"><span·class="id"·title="library">GenericMinMax</span></a>.<br/> |
50 | <br/> | 50 | <br/> |
51 | </div> | 51 | </div> |
52 | <div·class="doc"> | 52 | <div·class="doc"> |
53 | <a·id="lab | 53 | <a·id="lab345"></a><h1·class="section">Maximum·and·Minimum·of·two·real·numbers</h1> |
54 | </div> | 54 | </div> |
55 | <div·class="code"> | 55 | <div·class="code"> |
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">R_scope</span>.<br/> | 57 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">R_scope</span>.<br/> |
Offset 72, 15 lines modified | Offset 72, 15 lines modified | ||
72 | <br/> | 72 | <br/> |
73 | <span·class="id"·title="keyword">Lemma</span>·<a·id="exp_le_3"·class="idref"·href="#exp_le_3"><span·class="id"·title="lemma">exp_le_3</span></a>·:·<a·class="idref"·href="Coq.Reals.Rtrigo_def.html#exp"><span·class="id"·title="definition">exp</span></a>·1·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#77d341fe206b2891763e25999ffddca2"><span·class="id"·title="notation"><=</span></a>·3.<br/> | 73 | <span·class="id"·title="keyword">Lemma</span>·<a·id="exp_le_3"·class="idref"·href="#exp_le_3"><span·class="id"·title="lemma">exp_le_3</span></a>·:·<a·class="idref"·href="Coq.Reals.Rtrigo_def.html#exp"><span·class="id"·title="definition">exp</span></a>·1·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#77d341fe206b2891763e25999ffddca2"><span·class="id"·title="notation"><=</span></a>·3.<br/> |
74 | <br/> | 74 | <br/> |
75 | </div> | 75 | </div> |
76 | <div·class="doc"> | 76 | <div·class="doc"> |
77 | <a·id="lab | 77 | <a·id="lab347"></a><h1·class="section">Properties·of··Exp</h1> |
78 | </div> | 78 | </div> |
79 | <div·class="code"> | 79 | <div·class="code"> |
80 | <br/> | 80 | <br/> |
81 | <span·class="id"·title="keyword">Lemma</span>·<a·id="exp_neq_0"·class="idref"·href="#exp_neq_0"><span·class="id"·title="lemma">exp_neq_0</span></a>·:·<span·class="id"·title="keyword">forall</span>·<a·id="x:14"·class="idref"·href="#x:14"><span·class="id"·title="binder">x</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>,·<a·class="idref"·href="Coq.Reals.Rtrigo_def.html#exp"><span·class="id"·title="definition">exp</span></a>·<a·class="idref"·href="Coq.Reals.Rpower.html#x:14"><span·class="id"·title="variable">x</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#::type_scope:x_'<>'_x"><span·class="id"·title="notation"><></span></a>·0.<br/> | 81 | <span·class="id"·title="keyword">Lemma</span>·<a·id="exp_neq_0"·class="idref"·href="#exp_neq_0"><span·class="id"·title="lemma">exp_neq_0</span></a>·:·<span·class="id"·title="keyword">forall</span>·<a·id="x:14"·class="idref"·href="#x:14"><span·class="id"·title="binder">x</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>,·<a·class="idref"·href="Coq.Reals.Rtrigo_def.html#exp"><span·class="id"·title="definition">exp</span></a>·<a·class="idref"·href="Coq.Reals.Rpower.html#x:14"><span·class="id"·title="variable">x</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#::type_scope:x_'<>'_x"><span·class="id"·title="notation"><></span></a>·0.<br/> |
Offset 54, 15 lines modified | Offset 54, 15 lines modified | ||
54 | <br/> | 54 | <br/> |
55 | <span·class="id"·title="keyword">Implicit</span>·<span·class="id"·title="keyword">Type</span>·<span·class="id"·title="var">r</span>·:·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>.<br/> | 55 | <span·class="id"·title="keyword">Implicit</span>·<span·class="id"·title="keyword">Type</span>·<span·class="id"·title="var">r</span>·:·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>.<br/> |
56 | <br/> | 56 | <br/> |
57 | </div> | 57 | </div> |
58 | <div·class="doc"> | 58 | <div·class="doc"> |
59 | <a·id="lab | 59 | <a·id="lab352"></a><h1·class="section">Definition·of·sequence·and·properties</h1> |
60 | </div> | 60 | </div> |
61 | <div·class="code"> | 61 | <div·class="code"> |
62 | <br/> | 62 | <br/> |
63 | <span·class="id"·title="keyword">Section</span>·<a·id="sequence"·class="idref"·href="#sequence"><span·class="id"·title="section">sequence</span></a>.<br/> | 63 | <span·class="id"·title="keyword">Section</span>·<a·id="sequence"·class="idref"·href="#sequence"><span·class="id"·title="section">sequence</span></a>.<br/> |
Offset 55, 15 lines modified | Offset 55, 15 lines modified | ||
55 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Logic.Classical_Pred_Type.html#"><span·class="id"·title="library">Classical_Pred_Type</span></a>.<br/> | 55 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Logic.Classical_Pred_Type.html#"><span·class="id"·title="library">Classical_Pred_Type</span></a>.<br/> |
56 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">R_scope</span>.<br/> | 56 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">R_scope</span>.<br/> |
57 | <br/> | 57 | <br/> |
58 | </div> | 58 | </div> |
59 | <div·class="doc"> | 59 | <div·class="doc"> |
60 | <a·id="lab | 60 | <a·id="lab513"></a><h1·class="section">General·definitions·and·propositions</h1> |
61 | </div> | 61 | </div> |
62 | <div·class="code"> | 62 | <div·class="code"> |
63 | <br/> | 63 | <br/> |
64 | <span·class="id"·title="keyword">Definition</span>·<a·id="included"·class="idref"·href="#included"><span·class="id"·title="definition">included</span></a>·(<a·id="D1:1"·class="idref"·href="#D1:1"><span·class="id"·title="binder">D1</span></a>·<a·id="D2:2"·class="idref"·href="#D2:2"><span·class="id"·title="binder">D2</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</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>)·:·<span·class="id"·title="keyword">Prop</span>·:=·<span·class="id"·title="keyword">forall</span>·<a·id="x:3"·class="idref"·href="#x:3"><span·class="id"·title="binder">x</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>,·<a·class="idref"·href="Coq.Reals.Rtopology.html#D1:1"><span·class="id"·title="variable">D1</span></a>·<a·class="idref"·href="Coq.Reals.Rtopology.html#x:3"><span·class="id"·title="variable">x</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.Reals.Rtopology.html#D2:2"><span·class="id"·title="variable">D2</span></a>·<a·class="idref"·href="Coq.Reals.Rtopology.html#x:3"><span·class="id"·title="variable">x</span></a>.<br/> | 64 | <span·class="id"·title="keyword">Definition</span>·<a·id="included"·class="idref"·href="#included"><span·class="id"·title="definition">included</span></a>·(<a·id="D1:1"·class="idref"·href="#D1:1"><span·class="id"·title="binder">D1</span></a>·<a·id="D2:2"·class="idref"·href="#D2:2"><span·class="id"·title="binder">D2</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</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>)·:·<span·class="id"·title="keyword">Prop</span>·:=·<span·class="id"·title="keyword">forall</span>·<a·id="x:3"·class="idref"·href="#x:3"><span·class="id"·title="binder">x</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>,·<a·class="idref"·href="Coq.Reals.Rtopology.html#D1:1"><span·class="id"·title="variable">D1</span></a>·<a·class="idref"·href="Coq.Reals.Rtopology.html#x:3"><span·class="id"·title="variable">x</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.Reals.Rtopology.html#D2:2"><span·class="id"·title="variable">D2</span></a>·<a·class="idref"·href="Coq.Reals.Rtopology.html#x:3"><span·class="id"·title="variable">x</span></a>.<br/> |
65 | <span·class="id"·title="keyword">Definition</span>·<a·id="disc"·class="idref"·href="#disc"><span·class="id"·title="definition">disc</span></a>·(<a·id="x:4"·class="idref"·href="#x:4"><span·class="id"·title="binder">x</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>)·(<a·id="delta:5"·class="idref"·href="#delta:5"><span·class="id"·title="binder">delta</span></a>:<a·class="idref"·href="Coq.Reals.RIneq.html#posreal"><span·class="id"·title="record">posreal</span></a>)·(<a·id="y:6"·class="idref"·href="#y:6"><span·class="id"·title="binder">y</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>)·:·<span·class="id"·title="keyword">Prop</span>·:=·<a·class="idref"·href="Coq.Reals.Rbasic_fun.html#Rabs"><span·class="id"·title="definition">Rabs</span></a>·(<a·class="idref"·href="Coq.Reals.Rtopology.html#y:6"><span·class="id"·title="variable">y</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#::R_scope:x_'-'_x"><span·class="id"·title="notation">-</span></a>·<a·class="idref"·href="Coq.Reals.Rtopology.html#x:4"><span·class="id"·title="variable">x</span></a>)·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#::R_scope:x_'<'_x"><span·class="id"·title="notation"><</span></a>·<a·class="idref"·href="Coq.Reals.Rtopology.html#delta:5"><span·class="id"·title="variable">delta</span></a>.<br/> | 65 | <span·class="id"·title="keyword">Definition</span>·<a·id="disc"·class="idref"·href="#disc"><span·class="id"·title="definition">disc</span></a>·(<a·id="x:4"·class="idref"·href="#x:4"><span·class="id"·title="binder">x</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>)·(<a·id="delta:5"·class="idref"·href="#delta:5"><span·class="id"·title="binder">delta</span></a>:<a·class="idref"·href="Coq.Reals.RIneq.html#posreal"><span·class="id"·title="record">posreal</span></a>)·(<a·id="y:6"·class="idref"·href="#y:6"><span·class="id"·title="binder">y</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>)·:·<span·class="id"·title="keyword">Prop</span>·:=·<a·class="idref"·href="Coq.Reals.Rbasic_fun.html#Rabs"><span·class="id"·title="definition">Rabs</span></a>·(<a·class="idref"·href="Coq.Reals.Rtopology.html#y:6"><span·class="id"·title="variable">y</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#::R_scope:x_'-'_x"><span·class="id"·title="notation">-</span></a>·<a·class="idref"·href="Coq.Reals.Rtopology.html#x:4"><span·class="id"·title="variable">x</span></a>)·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#::R_scope:x_'<'_x"><span·class="id"·title="notation"><</span></a>·<a·class="idref"·href="Coq.Reals.Rtopology.html#delta:5"><span·class="id"·title="variable">delta</span></a>.<br/> |
Offset 160, 15 lines modified | Offset 160, 15 lines modified | ||
160 | 1·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#::R_scope:x_'-'_x"><span·class="id"·title="notation">-</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo1.html#tan"><span·class="id"·title="definition">tan</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo1.html#x:52"><span·class="id"·title="variable">x</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#e1dae7ed53bffa765009199d058dd327"><span·class="id"·title="notation">*</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo1.html#tan"><span·class="id"·title="definition">tan</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo1.html#y:53"><span·class="id"·title="variable">y</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#::type_scope:x_'<>'_x"><span·class="id"·title="notation"><></span></a>·0·<a·class="idref"·href="Coq.Init.Logic.html#::type_scope:x_'->'_x"><span·class="id"·title="notation">-></span></a><br/> | 160 | 1·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#::R_scope:x_'-'_x"><span·class="id"·title="notation">-</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo1.html#tan"><span·class="id"·title="definition">tan</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo1.html#x:52"><span·class="id"·title="variable">x</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#e1dae7ed53bffa765009199d058dd327"><span·class="id"·title="notation">*</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo1.html#tan"><span·class="id"·title="definition">tan</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo1.html#y:53"><span·class="id"·title="variable">y</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#::type_scope:x_'<>'_x"><span·class="id"·title="notation"><></span></a>·0·<a·class="idref"·href="Coq.Init.Logic.html#::type_scope:x_'->'_x"><span·class="id"·title="notation">-></span></a><br/> |
161 | <a·class="idref"·href="Coq.Reals.Rtrigo1.html#tan"><span·class="id"·title="definition">tan</span></a>·(<a·class="idref"·href="Coq.Reals.Rtrigo1.html#x:52"><span·class="id"·title="variable">x</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#3e57074ab0a6a36b253e873a1bdac6ad"><span·class="id"·title="notation">+</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo1.html#y:53"><span·class="id"·title="variable">y</span></a>)·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#3942bfc45fbeaeee49010b741755982b"><span·class="id"·title="notation">(</span></a><a·class="idref"·href="Coq.Reals.Rtrigo1.html#tan"><span·class="id"·title="definition">tan</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo1.html#x:52"><span·class="id"·title="variable">x</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#3e57074ab0a6a36b253e873a1bdac6ad"><span·class="id"·title="notation">+</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo1.html#tan"><span·class="id"·title="definition">tan</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo1.html#y:53"><span·class="id"·title="variable">y</span></a><a·class="idref"·href="Coq.Reals.Rdefinitions.html#3942bfc45fbeaeee49010b741755982b"><span·class="id"·title="notation">)</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#3942bfc45fbeaeee49010b741755982b"><span·class="id"·title="notation">/</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#3942bfc45fbeaeee49010b741755982b"><span·class="id"·title="notation">(</span></a>1·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#::R_scope:x_'-'_x"><span·class="id"·title="notation">-</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo1.html#tan"><span·class="id"·title="definition">tan</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo1.html#x:52"><span·class="id"·title="variable">x</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#e1dae7ed53bffa765009199d058dd327"><span·class="id"·title="notation">*</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo1.html#tan"><span·class="id"·title="definition">tan</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo1.html#y:53"><span·class="id"·title="variable">y</span></a><a·class="idref"·href="Coq.Reals.Rdefinitions.html#3942bfc45fbeaeee49010b741755982b"><span·class="id"·title="notation">)</span></a>.<br/> | 161 | <a·class="idref"·href="Coq.Reals.Rtrigo1.html#tan"><span·class="id"·title="definition">tan</span></a>·(<a·class="idref"·href="Coq.Reals.Rtrigo1.html#x:52"><span·class="id"·title="variable">x</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#3e57074ab0a6a36b253e873a1bdac6ad"><span·class="id"·title="notation">+</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo1.html#y:53"><span·class="id"·title="variable">y</span></a>)·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#3942bfc45fbeaeee49010b741755982b"><span·class="id"·title="notation">(</span></a><a·class="idref"·href="Coq.Reals.Rtrigo1.html#tan"><span·class="id"·title="definition">tan</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo1.html#x:52"><span·class="id"·title="variable">x</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#3e57074ab0a6a36b253e873a1bdac6ad"><span·class="id"·title="notation">+</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo1.html#tan"><span·class="id"·title="definition">tan</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo1.html#y:53"><span·class="id"·title="variable">y</span></a><a·class="idref"·href="Coq.Reals.Rdefinitions.html#3942bfc45fbeaeee49010b741755982b"><span·class="id"·title="notation">)</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#3942bfc45fbeaeee49010b741755982b"><span·class="id"·title="notation">/</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#3942bfc45fbeaeee49010b741755982b"><span·class="id"·title="notation">(</span></a>1·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#::R_scope:x_'-'_x"><span·class="id"·title="notation">-</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo1.html#tan"><span·class="id"·title="definition">tan</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo1.html#x:52"><span·class="id"·title="variable">x</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#e1dae7ed53bffa765009199d058dd327"><span·class="id"·title="notation">*</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo1.html#tan"><span·class="id"·title="definition">tan</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo1.html#y:53"><span·class="id"·title="variable">y</span></a><a·class="idref"·href="Coq.Reals.Rdefinitions.html#3942bfc45fbeaeee49010b741755982b"><span·class="id"·title="notation">)</span></a>.<br/> |
162 | <br/> | 162 | <br/> |
163 | </div> | 163 | </div> |
164 | <div·class="doc"> | 164 | <div·class="doc"> |
165 | <a·id="lab | 165 | <a·id="lab469"></a><h1·class="section">Some·properties·of·cos,·sin·and·tan</h1> |
166 | </div> | 166 | </div> |
167 | <div·class="code"> | 167 | <div·class="code"> |
168 | <br/> | 168 | <br/> |
169 | <span·class="id"·title="keyword">Lemma</span>·<a·id="sin_2a"·class="idref"·href="#sin_2a"><span·class="id"·title="lemma">sin_2a</span></a>·:·<span·class="id"·title="keyword">forall</span>·<a·id="x:54"·class="idref"·href="#x:54"><span·class="id"·title="binder">x</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>,·<a·class="idref"·href="Coq.Reals.Rtrigo_def.html#sin"><span·class="id"·title="definition">sin</span></a>·(2·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#e1dae7ed53bffa765009199d058dd327"><span·class="id"·title="notation">*</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo1.html#x:54"><span·class="id"·title="variable">x</span></a>)·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·2·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#e1dae7ed53bffa765009199d058dd327"><span·class="id"·title="notation">*</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo_def.html#sin"><span·class="id"·title="definition">sin</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo1.html#x:54"><span·class="id"·title="variable">x</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#e1dae7ed53bffa765009199d058dd327"><span·class="id"·title="notation">*</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo_def.html#cos"><span·class="id"·title="definition">cos</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo1.html#x:54"><span·class="id"·title="variable">x</span></a>.<br/> | 169 | <span·class="id"·title="keyword">Lemma</span>·<a·id="sin_2a"·class="idref"·href="#sin_2a"><span·class="id"·title="lemma">sin_2a</span></a>·:·<span·class="id"·title="keyword">forall</span>·<a·id="x:54"·class="idref"·href="#x:54"><span·class="id"·title="binder">x</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>,·<a·class="idref"·href="Coq.Reals.Rtrigo_def.html#sin"><span·class="id"·title="definition">sin</span></a>·(2·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#e1dae7ed53bffa765009199d058dd327"><span·class="id"·title="notation">*</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo1.html#x:54"><span·class="id"·title="variable">x</span></a>)·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·2·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#e1dae7ed53bffa765009199d058dd327"><span·class="id"·title="notation">*</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo_def.html#sin"><span·class="id"·title="definition">sin</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo1.html#x:54"><span·class="id"·title="variable">x</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#e1dae7ed53bffa765009199d058dd327"><span·class="id"·title="notation">*</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo_def.html#cos"><span·class="id"·title="definition">cos</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo1.html#x:54"><span·class="id"·title="variable">x</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.Reals.Rbase.html#"><span·class="id"·title="library">Rbase</span></a>·<a·class="idref"·href="Coq.Reals.Rfunctions.html#"><span·class="id"·title="library">Rfunctions</span></a>·<a·class="idref"·href="Coq.Reals.SeqSeries.html#"><span·class="id"·title="library">SeqSeries</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo_fun.html#"><span·class="id"·title="library">Rtrigo_fun</span></a>.<br/> | 49 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Reals.Rbase.html#"><span·class="id"·title="library">Rbase</span></a>·<a·class="idref"·href="Coq.Reals.Rfunctions.html#"><span·class="id"·title="library">Rfunctions</span></a>·<a·class="idref"·href="Coq.Reals.SeqSeries.html#"><span·class="id"·title="library">SeqSeries</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo_fun.html#"><span·class="id"·title="library">Rtrigo_fun</span></a>.<br/> |
50 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">R_scope</span>.<br/> | 50 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">R_scope</span>.<br/> |
51 | <br/> | 51 | <br/> |
52 | </div> | 52 | </div> |
53 | <div·class="doc"> | 53 | <div·class="doc"> |
54 | <a·id="lab | 54 | <a·id="lab366"></a><h1·class="section">Definition·of·exponential</h1> |
55 | </div> | 55 | </div> |
56 | <div·class="code"> | 56 | <div·class="code"> |
57 | <span·class="id"·title="keyword">Definition</span>·<a·id="exp_in"·class="idref"·href="#exp_in"><span·class="id"·title="definition">exp_in</span></a>·(<a·id="x:1"·class="idref"·href="#x:1"><span·class="id"·title="binder">x</span></a>·<a·id="l:2"·class="idref"·href="#l:2"><span·class="id"·title="binder">l</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>)·:·<span·class="id"·title="keyword">Prop</span>·:=<br/> | 57 | <span·class="id"·title="keyword">Definition</span>·<a·id="exp_in"·class="idref"·href="#exp_in"><span·class="id"·title="definition">exp_in</span></a>·(<a·id="x:1"·class="idref"·href="#x:1"><span·class="id"·title="binder">x</span></a>·<a·id="l:2"·class="idref"·href="#l:2"><span·class="id"·title="binder">l</span></a>:<a·class="idref"·href="Coq.Reals.Rdefinitions.html#RbaseSymbolsImpl.R"><span·class="id"·title="axiom">R</span></a>)·:·<span·class="id"·title="keyword">Prop</span>·:=<br/> |
58 | <a·class="idref"·href="Coq.Reals.Rfunctions.html#infinite_sum"><span·class="id"·title="definition">infinite_sum</span></a>·(<span·class="id"·title="keyword">fun</span>·<a·id="i:3"·class="idref"·href="#i:3"><span·class="id"·title="binder">i</span></a>:<a·class="idref"·href="Coq.Init.Datatypes.html#nat"><span·class="id"·title="inductive">nat</span></a>·=>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#2299a6ef56270a66cc1b95489d0f6e3a"><span·class="id"·title="notation">/</span></a>·<a·class="idref"·href="Coq.Reals.Raxioms.html#INR"><span·class="id"·title="definition">INR</span></a>·(<a·class="idref"·href="Coq.Arith.Factorial.html#fact"><span·class="id"·title="definition">fact</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo_def.html#i:3"><span·class="id"·title="variable">i</span></a>)·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#e1dae7ed53bffa765009199d058dd327"><span·class="id"·title="notation">*</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo_def.html#x:1"><span·class="id"·title="variable">x</span></a>·<a·class="idref"·href="Coq.Reals.Rfunctions.html#1fc859ef9f60fc2e3a52c48371d07707"><span·class="id"·title="notation">^</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo_def.html#i:3"><span·class="id"·title="variable">i</span></a>)·<a·class="idref"·href="Coq.Reals.Rtrigo_def.html#l:2"><span·class="id"·title="variable">l</span></a>.<br/> | 58 | <a·class="idref"·href="Coq.Reals.Rfunctions.html#infinite_sum"><span·class="id"·title="definition">infinite_sum</span></a>·(<span·class="id"·title="keyword">fun</span>·<a·id="i:3"·class="idref"·href="#i:3"><span·class="id"·title="binder">i</span></a>:<a·class="idref"·href="Coq.Init.Datatypes.html#nat"><span·class="id"·title="inductive">nat</span></a>·=>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#2299a6ef56270a66cc1b95489d0f6e3a"><span·class="id"·title="notation">/</span></a>·<a·class="idref"·href="Coq.Reals.Raxioms.html#INR"><span·class="id"·title="definition">INR</span></a>·(<a·class="idref"·href="Coq.Arith.Factorial.html#fact"><span·class="id"·title="definition">fact</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo_def.html#i:3"><span·class="id"·title="variable">i</span></a>)·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#e1dae7ed53bffa765009199d058dd327"><span·class="id"·title="notation">*</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo_def.html#x:1"><span·class="id"·title="variable">x</span></a>·<a·class="idref"·href="Coq.Reals.Rfunctions.html#1fc859ef9f60fc2e3a52c48371d07707"><span·class="id"·title="notation">^</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo_def.html#i:3"><span·class="id"·title="variable">i</span></a>)·<a·class="idref"·href="Coq.Reals.Rtrigo_def.html#l:2"><span·class="id"·title="variable">l</span></a>.<br/> |
59 | <br/> | 59 | <br/> |
Offset 57, 15 lines modified | Offset 57, 15 lines modified | ||
57 | <br/> | 57 | <br/> |
58 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">R_scope</span>.<br/> | 58 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">R_scope</span>.<br/> |
59 | <br/> | 59 | <br/> |
60 | </div> | 60 | </div> |
61 | <div·class="doc"> | 61 | <div·class="doc"> |
62 | <a·id="lab | 62 | <a·id="lab360"></a><h1·class="section">Bounds·of·expressions·with·trigonometric·functions</h1> |
63 | </div> | 63 | </div> |
64 | <div·class="code"> | 64 | <div·class="code"> |
65 | <br/> | 65 | <br/> |
66 | <span·class="id"·title="keyword">Lemma</span>·<a·id="sin2_bound"·class="idref"·href="#sin2_bound"><span·class="id"·title="lemma">sin2_bound</span></a>·:·<span·class="id"·title="keyword">forall</span>·<a·id="x:1"·class="idref"·href="#x:1"><span·class="id"·title="binder">x</span></a>,<br/> | 66 | <span·class="id"·title="keyword">Lemma</span>·<a·id="sin2_bound"·class="idref"·href="#sin2_bound"><span·class="id"·title="lemma">sin2_bound</span></a>·:·<span·class="id"·title="keyword">forall</span>·<a·id="x:1"·class="idref"·href="#x:1"><span·class="id"·title="binder">x</span></a>,<br/> |
67 | 0·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#fbdebc8c1a732d40499de973c18a9a13"><span·class="id"·title="notation"><=</span></a>·<a·class="idref"·href="Coq.Reals.RIneq.html#2774338496db27b8a3a3c51e5609a509"><span·class="id"·title="notation">(</span></a><a·class="idref"·href="Coq.Reals.Rtrigo_def.html#sin"><span·class="id"·title="definition">sin</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo_facts.html#x:1"><span·class="id"·title="variable">x</span></a><a·class="idref"·href="Coq.Reals.RIneq.html#2774338496db27b8a3a3c51e5609a509"><span·class="id"·title="notation">)²</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#fbdebc8c1a732d40499de973c18a9a13"><span·class="id"·title="notation"><=</span></a>·1.<br/> | 67 | 0·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#fbdebc8c1a732d40499de973c18a9a13"><span·class="id"·title="notation"><=</span></a>·<a·class="idref"·href="Coq.Reals.RIneq.html#2774338496db27b8a3a3c51e5609a509"><span·class="id"·title="notation">(</span></a><a·class="idref"·href="Coq.Reals.Rtrigo_def.html#sin"><span·class="id"·title="definition">sin</span></a>·<a·class="idref"·href="Coq.Reals.Rtrigo_facts.html#x:1"><span·class="id"·title="variable">x</span></a><a·class="idref"·href="Coq.Reals.RIneq.html#2774338496db27b8a3a3c51e5609a509"><span·class="id"·title="notation">)²</span></a>·<a·class="idref"·href="Coq.Reals.Rdefinitions.html#fbdebc8c1a732d40499de973c18a9a13"><span·class="id"·title="notation"><=</span></a>·1.<br/> |
Offset 45, 16 lines modified | Offset 45, 16 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="lab1 | 49 | <a·id="lab1212"></a><h1·class="section">Some·properties·of·the·operators·on·relations</h1> |
50 | <a·id="lab1 | 50 | <a·id="lab1213"></a><h1·class="section">Initial·version·by·Bruno·Barras</h1> |
51 | </div> | 51 | </div> |
52 | <div·class="code"> | 52 | <div·class="code"> |
53 | <br/> | 53 | <br/> |
54 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Relations.Relation_Definitions.html#"><span·class="id"·title="library">Relation_Definitions</span></a>.<br/> | 54 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Relations.Relation_Definitions.html#"><span·class="id"·title="library">Relation_Definitions</span></a>.<br/> |
55 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Relations.Relation_Operators.html#"><span·class="id"·title="library">Relation_Operators</span></a>.<br/> | 55 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Relations.Relation_Operators.html#"><span·class="id"·title="library">Relation_Operators</span></a>.<br/> |
Offset 45, 34 lines modified | Offset 45, 34 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 | 49 | <a·id="lab1216"></a><h1·class="section">Some·operators·on·relations</h1> |
50 | <a·id="lab | 50 | <a·id="lab1217"></a><h1·class="section">Initial·authors:·Bruno·Barras,·Cristina·Cornes</h1> |
51 | <a·id="lab | 51 | <a·id="lab1218"></a><h1·class="section">···································································</h1> |
52 | <a·id="lab | 52 | <a·id="lab1219"></a><h1·class="section">Some·of·the·initial·definitions·were·taken·from·:</h1> |
53 | <a·id="lab | 53 | <a·id="lab1220"></a><h1·class="section">Constructing·Recursion·Operators·in·Type·Theory</h1> |
54 | <a·id="lab | 54 | <a·id="lab1221"></a><h1·class="section">L.·Paulson··JSC·(1986)·2,·325-355</h1> |
55 | <a·id="lab | 55 | <a·id="lab1222"></a><h1·class="section">···································································</h1> |
56 | <a·id="lab | 56 | <a·id="lab1223"></a><h1·class="section">Further·extensions·by·Pierre·Castéran</h1> |
57 | </div> | 57 | </div> |
58 | <div·class="code"> | 58 | <div·class="code"> |
59 | <br/> | 59 | <br/> |
60 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Relations.Relation_Definitions.html#"><span·class="id"·title="library">Relation_Definitions</span></a>.<br/> | 60 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Relations.Relation_Definitions.html#"><span·class="id"·title="library">Relation_Definitions</span></a>.<br/> |
61 | <br/> | 61 | <br/> |
62 | </div> | 62 | </div> |
63 | <div·class="doc"> | 63 | <div·class="doc"> |
64 | <a·id="lab | 64 | <a·id="lab1224"></a><h2·class="section">Transitive·closure</h2> |
65 | </div> | 65 | </div> |
66 | <div·class="code"> | 66 | <div·class="code"> |
67 | <br/> | 67 | <br/> |
68 | <span·class="id"·title="keyword">Section</span>·<a·id="Transitive_Closure"·class="idref"·href="#Transitive_Closure"><span·class="id"·title="section">Transitive_Closure</span></a>.<br/> | 68 | <span·class="id"·title="keyword">Section</span>·<a·id="Transitive_Closure"·class="idref"·href="#Transitive_Closure"><span·class="id"·title="section">Transitive_Closure</span></a>.<br/> |
69 | <span·class="id"·title="keyword">Variable</span>·<a·id="Transitive_Closure.A"·class="idref"·href="#Transitive_Closure.A"><span·class="id"·title="variable">A</span></a>·:·<span·class="id"·title="keyword">Type</span>.<br/> | 69 | <span·class="id"·title="keyword">Variable</span>·<a·id="Transitive_Closure.A"·class="idref"·href="#Transitive_Closure.A"><span·class="id"·title="variable">A</span></a>·:·<span·class="id"·title="keyword">Type</span>.<br/> |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab937"></a><h1·class="section">Circular·Shifts·(aka·Cyclic·Permutations)</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ·The·main·inductive·<span·class="inlinecode"><span·class="id"·title="var">CPermutation</span></span>·relates·lists·up·to·circular·shifts·of·their·elements. | 51 | ·The·main·inductive·<span·class="inlinecode"><span·class="id"·title="var">CPermutation</span></span>·relates·lists·up·to·circular·shifts·of·their·elements. |
52 | <div·class="paragraph">·</div> | 52 | <div·class="paragraph">·</div> |
Offset 66, 19 lines modified | Offset 66, 19 lines modified | ||
66 | <br/> | 66 | <br/> |
67 | <span·class="id"·title="keyword">Section</span>·<a·id="defs"·class="idref"·href="#defs"><span·class="id"·title="section">defs</span></a>.<br/> | 67 | <span·class="id"·title="keyword">Section</span>·<a·id="defs"·class="idref"·href="#defs"><span·class="id"·title="section">defs</span></a>.<br/> |
68 | <br/> | 68 | <br/> |
69 | </div> | 69 | </div> |
70 | <div·class="doc"> | 70 | <div·class="doc"> |
71 | <a·id="lab | 71 | <a·id="lab927"></a><h1·class="section">Trees·and·heap·trees</h1> |
72 | <div·class="paragraph">·</div> | 72 | <div·class="paragraph">·</div> |
73 | <a·id="lab | 73 | <a·id="lab928"></a><h2·class="section">Definition·of·trees·over·an·ordered·set</h2> |
74 | </div> | 74 | </div> |
75 | <div·class="code"> | 75 | <div·class="code"> |
76 | <br/> | 76 | <br/> |
77 | <span·class="id"·title="keyword">Variable</span>·<a·id="defs.A"·class="idref"·href="#defs.A"><span·class="id"·title="variable">A</span></a>·:·<span·class="id"·title="keyword">Type</span>.<br/> | 77 | <span·class="id"·title="keyword">Variable</span>·<a·id="defs.A"·class="idref"·href="#defs.A"><span·class="id"·title="variable">A</span></a>·:·<span·class="id"·title="keyword">Type</span>.<br/> |
78 | <span·class="id"·title="keyword">Variable</span>·<a·id="defs.leA"·class="idref"·href="#defs.leA"><span·class="id"·title="variable">leA</span></a>·:·<a·class="idref"·href="Coq.Relations.Relation_Definitions.html#relation"><span·class="id"·title="definition">relation</span></a>·<a·class="idref"·href="Coq.Sorting.Heap.html#defs.A"><span·class="id"·title="variable">A</span></a>.<br/> | 78 | <span·class="id"·title="keyword">Variable</span>·<a·id="defs.leA"·class="idref"·href="#defs.leA"><span·class="id"·title="variable">leA</span></a>·:·<a·class="idref"·href="Coq.Relations.Relation_Definitions.html#relation"><span·class="id"·title="definition">relation</span></a>·<a·class="idref"·href="Coq.Sorting.Heap.html#defs.A"><span·class="id"·title="variable">A</span></a>.<br/> |
Offset 83, 15 lines modified | Offset 83, 15 lines modified | ||
83 | <br/> | 83 | <br/> |
84 | <span·class="id"·title="keyword">Section</span>·<a·id="Permut"·class="idref"·href="#Permut"><span·class="id"·title="section">Permut</span></a>.<br/> | 84 | <span·class="id"·title="keyword">Section</span>·<a·id="Permut"·class="idref"·href="#Permut"><span·class="id"·title="section">Permut</span></a>.<br/> |
85 | <br/> | 85 | <br/> |
86 | </div> | 86 | </div> |
87 | <div·class="doc"> | 87 | <div·class="doc"> |
88 | <a·id="lab | 88 | <a·id="lab939"></a><h1·class="section">From·lists·to·multisets</h1> |
89 | </div> | 89 | </div> |
90 | <div·class="code"> | 90 | <div·class="code"> |
91 | <br/> | 91 | <br/> |
92 | <span·class="id"·title="keyword">Variable</span>·<a·id="Permut.A"·class="idref"·href="#Permut.A"><span·class="id"·title="variable">A</span></a>·:·<span·class="id"·title="keyword">Type</span>.<br/> | 92 | <span·class="id"·title="keyword">Variable</span>·<a·id="Permut.A"·class="idref"·href="#Permut.A"><span·class="id"·title="variable">A</span></a>·:·<span·class="id"·title="keyword">Type</span>.<br/> |
93 | <span·class="id"·title="keyword">Variable</span>·<a·id="Permut.eqA"·class="idref"·href="#Permut.eqA"><span·class="id"·title="variable">eqA</span></a>·:·<a·class="idref"·href="Coq.Relations.Relation_Definitions.html#relation"><span·class="id"·title="definition">relation</span></a>·<a·class="idref"·href="Coq.Sorting.PermutSetoid.html#Permut.A"><span·class="id"·title="variable">A</span></a>.<br/> | 93 | <span·class="id"·title="keyword">Variable</span>·<a·id="Permut.eqA"·class="idref"·href="#Permut.eqA"><span·class="id"·title="variable">eqA</span></a>·:·<a·class="idref"·href="Coq.Relations.Relation_Definitions.html#relation"><span·class="id"·title="definition">relation</span></a>·<a·class="idref"·href="Coq.Sorting.PermutSetoid.html#Permut.A"><span·class="id"·title="variable">A</span></a>.<br/> |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab938"></a><h1·class="section">List·permutations·as·a·composition·of·adjacent·transpositions</h1> |
50 | </div> | 50 | </div> |
51 | <div·class="code"> | 51 | <div·class="code"> |
52 | <br/> | 52 | <br/> |
53 | <br/> | 53 | <br/> |
Offset 58, 15 lines modified | Offset 58, 15 lines modified | ||
58 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Bool.Bool.html#"><span·class="id"·title="library">Bool</span></a>·<a·class="idref"·href="Coq.PArith.BinPos.html#"><span·class="id"·title="library">BinPos</span></a>·<a·class="idref"·href="Coq.NArith.BinNat.html#"><span·class="id"·title="library">BinNat</span></a>·<a·class="idref"·href="Coq.Arith.PeanoNat.html#"><span·class="id"·title="library">PeanoNat</span></a>·<a·class="idref"·href="Coq.NArith.Nnat.html#"><span·class="id"·title="library">Nnat</span></a>·<a·class="idref"·href="Coq.Strings.Byte.html#"><span·class="id"·title="library">Coq.Strings.Byte</span></a>.<br/> | 58 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Bool.Bool.html#"><span·class="id"·title="library">Bool</span></a>·<a·class="idref"·href="Coq.PArith.BinPos.html#"><span·class="id"·title="library">BinPos</span></a>·<a·class="idref"·href="Coq.NArith.BinNat.html#"><span·class="id"·title="library">BinNat</span></a>·<a·class="idref"·href="Coq.Arith.PeanoNat.html#"><span·class="id"·title="library">PeanoNat</span></a>·<a·class="idref"·href="Coq.NArith.Nnat.html#"><span·class="id"·title="library">Nnat</span></a>·<a·class="idref"·href="Coq.Strings.Byte.html#"><span·class="id"·title="library">Coq.Strings.Byte</span></a>.<br/> |
59 | <span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Init.Notations.html#IfNotations"><span·class="id"·title="module">IfNotations</span></a>.<br/> | 59 | <span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Init.Notations.html#IfNotations"><span·class="id"·title="module">IfNotations</span></a>.<br/> |
60 | <br/> | 60 | <br/> |
61 | </div> | 61 | </div> |
62 | <div·class="doc"> | 62 | <div·class="doc"> |
63 | <a·id="lab | 63 | <a·id="lab342"></a><h1·class="section">Definition·of·ascii·characters</h1> |
64 | <div·class="paragraph">·</div> | 64 | <div·class="paragraph">·</div> |
65 | ·Definition·of·ascii·character·as·a·8·bits·constructor· | 65 | ·Definition·of·ascii·character·as·a·8·bits·constructor· |
66 | </div> | 66 | </div> |
67 | <div·class="code"> | 67 | <div·class="code"> |
Offset 61, 15 lines modified | Offset 61, 15 lines modified | ||
61 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Strings.Byte.html#"><span·class="id"·title="library">Coq.Strings.Byte</span></a>.<br/> | 61 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Strings.Byte.html#"><span·class="id"·title="library">Coq.Strings.Byte</span></a>.<br/> |
62 | <span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Init.Notations.html#IfNotations"><span·class="id"·title="module">IfNotations</span></a>.<br/> | 62 | <span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Init.Notations.html#IfNotations"><span·class="id"·title="module">IfNotations</span></a>.<br/> |
63 | <br/> | 63 | <br/> |
64 | </div> | 64 | </div> |
65 | <div·class="doc"> | 65 | <div·class="doc"> |
66 | <a·id="lab | 66 | <a·id="lab334"></a><h3·class="section">Definition·of·strings</h3> |
67 | <div·class="paragraph">·</div> | 67 | <div·class="paragraph">·</div> |
68 | ·Implementation·of·string·as·list·of·ascii·characters· | 68 | ·Implementation·of·string·as·list·of·ascii·characters· |
69 | </div> | 69 | </div> |
70 | <div·class="code"> | 70 | <div·class="code"> |
Offset 56, 39 lines modified | Offset 56, 39 lines modified | ||
56 | </div> | 56 | </div> |
57 | <div·class="doc"> | 57 | <div·class="doc"> |
58 | NB:·This·file·is·here·only·for·compatibility·with·earlier·version·of | 58 | NB:·This·file·is·here·only·for·compatibility·with·earlier·version·of |
59 | ····<span·class="inlinecode"><span·class="id"·title="var">FSets</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">FMap</span></span>.·Please·use·<span·class="inlinecode"><span·class="id"·title="var">Structures</span>/<span·class="id"·title="var">Equalities.v</span></span>·directly·now.· | 59 | ····<span·class="inlinecode"><span·class="id"·title="var">FSets</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">FMap</span></span>.·Please·use·<span·class="inlinecode"><span·class="id"·title="var">Structures</span>/<span·class="id"·title="var">Equalities.v</span></span>·directly·now.· |
60 | <div·class="paragraph">·</div> | 60 | <div·class="paragraph">·</div> |
61 | <a·id="lab | 61 | <a·id="lab2"></a><h1·class="section">Types·with·Equalities,·and·nothing·more·(for·subtyping·purpose)</h1> |
62 | </div> | 62 | </div> |
63 | <div·class="code"> | 63 | <div·class="code"> |
64 | <br/> | 64 | <br/> |
65 | <span·class="id"·title="keyword">Module</span>·<span·class="id"·title="keyword">Type</span>·<a·id="EqualityType"·class="idref"·href="#EqualityType"><span·class="id"·title="module">EqualityType</span></a>·:=·<a·class="idref"·href="Coq.Structures.Equalities.html#EqualityTypeOrig"><span·class="id"·title="module">Equalities.EqualityTypeOrig</span></a>.<br/> | 65 | <span·class="id"·title="keyword">Module</span>·<span·class="id"·title="keyword">Type</span>·<a·id="EqualityType"·class="idref"·href="#EqualityType"><span·class="id"·title="module">EqualityType</span></a>·:=·<a·class="idref"·href="Coq.Structures.Equalities.html#EqualityTypeOrig"><span·class="id"·title="module">Equalities.EqualityTypeOrig</span></a>.<br/> |
66 | <br/> | 66 | <br/> |
67 | </div> | 67 | </div> |
68 | <div·class="doc"> | 68 | <div·class="doc"> |
69 | <a·id="lab | 69 | <a·id="lab3"></a><h1·class="section">Types·with·decidable·Equalities·(but·no·ordering)</h1> |
70 | </div> | 70 | </div> |
71 | <div·class="code"> | 71 | <div·class="code"> |
72 | <br/> | 72 | <br/> |
73 | <span·class="id"·title="keyword">Module</span>·<span·class="id"·title="keyword">Type</span>·<a·id="DecidableType"·class="idref"·href="#DecidableType"><span·class="id"·title="module">DecidableType</span></a>·:=·<a·class="idref"·href="Coq.Structures.Equalities.html#DecidableTypeOrig"><span·class="id"·title="module">Equalities.DecidableTypeOrig</span></a>.<br/> | 73 | <span·class="id"·title="keyword">Module</span>·<span·class="id"·title="keyword">Type</span>·<a·id="DecidableType"·class="idref"·href="#DecidableType"><span·class="id"·title="module">DecidableType</span></a>·:=·<a·class="idref"·href="Coq.Structures.Equalities.html#DecidableTypeOrig"><span·class="id"·title="module">Equalities.DecidableTypeOrig</span></a>.<br/> |
74 | <br/> | 74 | <br/> |
75 | </div> | 75 | </div> |
76 | <div·class="doc"> | 76 | <div·class="doc"> |
77 | <a·id="lab | 77 | <a·id="lab4"></a><h1·class="section">Additional·notions·about·keys·and·datas·used·in·FMap</h1> |
78 | </div> | 78 | </div> |
79 | <div·class="code"> | 79 | <div·class="code"> |
80 | <br/> | 80 | <br/> |
81 | <span·class="id"·title="keyword">Module</span>·<a·id="KeyDecidableType"·class="idref"·href="#KeyDecidableType"><span·class="id"·title="module">KeyDecidableType</span></a>(<span·class="id"·title="var">D</span>:<a·class="idref"·href="Coq.Structures.DecidableType.html#DecidableType"><span·class="id"·title="module">DecidableType</span></a>).<br/> | 81 | <span·class="id"·title="keyword">Module</span>·<a·id="KeyDecidableType"·class="idref"·href="#KeyDecidableType"><span·class="id"·title="module">KeyDecidableType</span></a>(<span·class="id"·title="var">D</span>:<a·class="idref"·href="Coq.Structures.DecidableType.html#DecidableType"><span·class="id"·title="module">DecidableType</span></a>).<br/> |
82 | <span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Structures.DecidableType.html#D"><span·class="id"·title="module">D</span></a>.<br/> | 82 | <span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Structures.DecidableType.html#D"><span·class="id"·title="module">D</span></a>.<br/> |
Offset 53, 15 lines modified | Offset 53, 15 lines modified | ||
53 | </div> | 53 | </div> |
54 | <div·class="doc"> | 54 | <div·class="doc"> |
55 | NB:·This·file·is·here·only·for·compatibility·with·earlier·version·of | 55 | NB:·This·file·is·here·only·for·compatibility·with·earlier·version·of |
56 | ····<span·class="inlinecode"><span·class="id"·title="var">FSets</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">FMap</span></span>.·Please·use·<span·class="inlinecode"><span·class="id"·title="var">Structures</span>/<span·class="id"·title="var">Equalities.v</span></span>·directly·now.· | 56 | ····<span·class="inlinecode"><span·class="id"·title="var">FSets</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">FMap</span></span>.·Please·use·<span·class="inlinecode"><span·class="id"·title="var">Structures</span>/<span·class="id"·title="var">Equalities.v</span></span>·directly·now.· |
57 | <div·class="paragraph">·</div> | 57 | <div·class="paragraph">·</div> |
58 | <a·id="lab1 | 58 | <a·id="lab1"></a><h1·class="section">Examples·of·Decidable·Type·structures.</h1> |
59 | <div·class="paragraph">·</div> | 59 | <div·class="paragraph">·</div> |
60 | ·A·particular·case·of·<span·class="inlinecode"><span·class="id"·title="var">DecidableType</span></span>·where | 60 | ·A·particular·case·of·<span·class="inlinecode"><span·class="id"·title="var">DecidableType</span></span>·where |
61 | ····the·equality·is·the·usual·one·of·Coq.· | 61 | ····the·equality·is·the·usual·one·of·Coq.· |
62 | </div> | 62 | </div> |
63 | <div·class="code"> | 63 | <div·class="code"> |
Offset 65, 29 lines modified | Offset 65, 29 lines modified | ||
65 | <span·class="id"·title="keyword">Module</span>·<span·class="id"·title="keyword">Type</span>·<a·id="Nop"·class="idref"·href="#Nop"><span·class="id"·title="module">Nop</span></a>.<br/> | 65 | <span·class="id"·title="keyword">Module</span>·<span·class="id"·title="keyword">Type</span>·<a·id="Nop"·class="idref"·href="#Nop"><span·class="id"·title="module">Nop</span></a>.<br/> |
66 | <span·class="id"·title="keyword">End</span>·<a·class="idref"·href="Coq.Structures.Equalities.html#Nop"><span·class="id"·title="module">Nop</span></a>.<br/> | 66 | <span·class="id"·title="keyword">End</span>·<a·class="idref"·href="Coq.Structures.Equalities.html#Nop"><span·class="id"·title="module">Nop</span></a>.<br/> |
67 | <br/> | 67 | <br/> |
68 | </div> | 68 | </div> |
69 | <div·class="doc"> | 69 | <div·class="doc"> |
70 | <a·id="lab | 70 | <a·id="lab40"></a><h1·class="section">Structure·with·just·a·base·type·<span·class="inlinecode"><span·class="id"·title="var">t</span></span></h1> |
71 | </div> | 71 | </div> |
72 | <div·class="code"> | 72 | <div·class="code"> |
73 | <br/> | 73 | <br/> |
74 | <span·class="id"·title="keyword">Module</span>·<span·class="id"·title="keyword">Type</span>·<a·id="Typ"·class="idref"·href="#Typ"><span·class="id"·title="module">Typ</span></a>.<br/> | 74 | <span·class="id"·title="keyword">Module</span>·<span·class="id"·title="keyword">Type</span>·<a·id="Typ"·class="idref"·href="#Typ"><span·class="id"·title="module">Typ</span></a>.<br/> |
75 | <span·class="id"·title="keyword">Parameter</span>·<span·class="id"·title="keyword">Inline</span>(10)·<a·id="Typ.t"·class="idref"·href="#Typ.t"><span·class="id"·title="axiom">t</span></a>·:·<span·class="id"·title="keyword">Type</span>.<br/> | 75 | <span·class="id"·title="keyword">Parameter</span>·<span·class="id"·title="keyword">Inline</span>(10)·<a·id="Typ.t"·class="idref"·href="#Typ.t"><span·class="id"·title="axiom">t</span></a>·:·<span·class="id"·title="keyword">Type</span>.<br/> |
76 | <span·class="id"·title="keyword">End</span>·<a·class="idref"·href="Coq.Structures.Equalities.html#Typ"><span·class="id"·title="module">Typ</span></a>.<br/> | 76 | <span·class="id"·title="keyword">End</span>·<a·class="idref"·href="Coq.Structures.Equalities.html#Typ"><span·class="id"·title="module">Typ</span></a>.<br/> |
77 | <br/> | 77 | <br/> |
78 | </div> | 78 | </div> |
79 | <div·class="doc"> | 79 | <div·class="doc"> |
80 | <a·id="lab | 80 | <a·id="lab41"></a><h1·class="section">Structure·with·an·equality·relation·<span·class="inlinecode"><span·class="id"·title="var">eq</span></span></h1> |
81 | </div> | 81 | </div> |
82 | <div·class="code"> | 82 | <div·class="code"> |
83 | <br/> | 83 | <br/> |
84 | <span·class="id"·title="keyword">Module</span>·<span·class="id"·title="keyword">Type</span>·<a·id="HasEq"·class="idref"·href="#HasEq"><span·class="id"·title="module">HasEq</span></a>·(<span·class="id"·title="keyword">Import</span>·<span·class="id"·title="var">T</span>:<a·class="idref"·href="Coq.Structures.Equalities.html#Typ"><span·class="id"·title="module">Typ</span></a>).<br/> | 84 | <span·class="id"·title="keyword">Module</span>·<span·class="id"·title="keyword">Type</span>·<a·id="HasEq"·class="idref"·href="#HasEq"><span·class="id"·title="module">HasEq</span></a>·(<span·class="id"·title="keyword">Import</span>·<span·class="id"·title="var">T</span>:<a·class="idref"·href="Coq.Structures.Equalities.html#Typ"><span·class="id"·title="module">Typ</span></a>).<br/> |
85 | <span·class="id"·title="keyword">Parameter</span>·<span·class="id"·title="keyword">Inline</span>(30)·<a·id="HasEq.eq"·class="idref"·href="#HasEq.eq"><span·class="id"·title="axiom">eq</span></a>·:·<a·class="idref"·href="Coq.Structures.Equalities.html#T.t"><span·class="id"·title="axiom">t</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.Structures.Equalities.html#T.t"><span·class="id"·title="axiom">t</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/> | 85 | <span·class="id"·title="keyword">Parameter</span>·<span·class="id"·title="keyword">Inline</span>(30)·<a·id="HasEq.eq"·class="idref"·href="#HasEq.eq"><span·class="id"·title="axiom">eq</span></a>·:·<a·class="idref"·href="Coq.Structures.Equalities.html#T.t"><span·class="id"·title="axiom">t</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.Structures.Equalities.html#T.t"><span·class="id"·title="axiom">t</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/> |
Offset 51, 15 lines modified | Offset 51, 15 lines modified | ||
51 | <br/> | 51 | <br/> |
52 | <span·class="id"·title="keyword">Set·Implicit·Arguments</span>.<br/> | 52 | <span·class="id"·title="keyword">Set·Implicit·Arguments</span>.<br/> |
53 | <br/> | 53 | <br/> |
54 | </div> | 54 | </div> |
55 | <div·class="doc"> | 55 | <div·class="doc"> |
56 | <a·id="lab | 56 | <a·id="lab38"></a><h1·class="section">Keys·and·datas·used·in·the·future·MMaps</h1> |
57 | </div> | 57 | </div> |
58 | <div·class="code"> | 58 | <div·class="code"> |
59 | <br/> | 59 | <br/> |
60 | <span·class="id"·title="keyword">Module</span>·<a·id="KeyDecidableType"·class="idref"·href="#KeyDecidableType"><span·class="id"·title="module">KeyDecidableType</span></a>(<span·class="id"·title="var">D</span>:<a·class="idref"·href="Coq.Structures.Equalities.html#DecidableType"><span·class="id"·title="module">DecidableType</span></a>).<br/> | 60 | <span·class="id"·title="keyword">Module</span>·<a·id="KeyDecidableType"·class="idref"·href="#KeyDecidableType"><span·class="id"·title="module">KeyDecidableType</span></a>(<span·class="id"·title="var">D</span>:<a·class="idref"·href="Coq.Structures.Equalities.html#DecidableType"><span·class="id"·title="module">DecidableType</span></a>).<br/> |
Offset 48, 19 lines modified | Offset 48, 19 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.Structures.Orders.html#"><span·class="id"·title="library">Orders</span></a>·<a·class="idref"·href="Coq.Structures.OrdersTac.html#"><span·class="id"·title="library">OrdersTac</span></a>·<a·class="idref"·href="Coq.Structures.OrdersFacts.html#"><span·class="id"·title="library">OrdersFacts</span></a>·<a·class="idref"·href="Coq.Setoids.Setoid.html#"><span·class="id"·title="library">Setoid</span></a>·<a·class="idref"·href="Coq.Classes.Morphisms.html#"><span·class="id"·title="library">Morphisms</span></a>·<a·class="idref"·href="Coq.Program.Basics.html#"><span·class="id"·title="library">Basics</span></a>.<br/> | 49 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Structures.Orders.html#"><span·class="id"·title="library">Orders</span></a>·<a·class="idref"·href="Coq.Structures.OrdersTac.html#"><span·class="id"·title="library">OrdersTac</span></a>·<a·class="idref"·href="Coq.Structures.OrdersFacts.html#"><span·class="id"·title="library">OrdersFacts</span></a>·<a·class="idref"·href="Coq.Setoids.Setoid.html#"><span·class="id"·title="library">Setoid</span></a>·<a·class="idref"·href="Coq.Classes.Morphisms.html#"><span·class="id"·title="library">Morphisms</span></a>·<a·class="idref"·href="Coq.Program.Basics.html#"><span·class="id"·title="library">Basics</span></a>.<br/> |
50 | <br/> | 50 | <br/> |
51 | </div> | 51 | </div> |
52 | <div·class="doc"> | 52 | <div·class="doc"> |
53 | <a·id="lab1 | 53 | <a·id="lab10"></a><h1·class="section">A·Generic·construction·of·min·and·max</h1> |
54 | <div·class="paragraph">·</div> | 54 | <div·class="paragraph">·</div> |
55 | <a·id="lab1 | 55 | <a·id="lab11"></a><h2·class="section">First,·an·interface·for·types·with·<span·class="inlinecode"><span·class="id"·title="var">max</span></span>·and/or·<span·class="inlinecode"><span·class="id"·title="var">min</span></span></h2> |
56 | </div> | 56 | </div> |
57 | <div·class="code"> | 57 | <div·class="code"> |
58 | <br/> | 58 | <br/> |
59 | <span·class="id"·title="keyword">Module</span>·<span·class="id"·title="keyword">Type</span>·<a·id="HasMax"·class="idref"·href="#HasMax"><span·class="id"·title="module">HasMax</span></a>·(<span·class="id"·title="keyword">Import</span>·<span·class="id"·title="var">E</span>:<a·class="idref"·href="Coq.Structures.Orders.html#EqLe'"><span·class="id"·title="module">EqLe'</span></a>).<br/> | 59 | <span·class="id"·title="keyword">Module</span>·<span·class="id"·title="keyword">Type</span>·<a·id="HasMax"·class="idref"·href="#HasMax"><span·class="id"·title="module">HasMax</span></a>·(<span·class="id"·title="keyword">Import</span>·<span·class="id"·title="var">E</span>:<a·class="idref"·href="Coq.Structures.Orders.html#EqLe'"><span·class="id"·title="module">EqLe'</span></a>).<br/> |
60 | <span·class="id"·title="keyword">Parameter</span>·<span·class="id"·title="keyword">Inline</span>·<a·id="HasMax.max"·class="idref"·href="#HasMax.max"><span·class="id"·title="axiom">max</span></a>·:·<a·class="idref"·href="Coq.Structures.GenericMinMax.html#E.t"><span·class="id"·title="axiom">t</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.Structures.GenericMinMax.html#E.t"><span·class="id"·title="axiom">t</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.Structures.GenericMinMax.html#E.t"><span·class="id"·title="axiom">t</span></a>.<br/> | 60 | <span·class="id"·title="keyword">Parameter</span>·<span·class="id"·title="keyword">Inline</span>·<a·id="HasMax.max"·class="idref"·href="#HasMax.max"><span·class="id"·title="axiom">max</span></a>·:·<a·class="idref"·href="Coq.Structures.GenericMinMax.html#E.t"><span·class="id"·title="axiom">t</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.Structures.GenericMinMax.html#E.t"><span·class="id"·title="axiom">t</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.Structures.GenericMinMax.html#E.t"><span·class="id"·title="axiom">t</span></a>.<br/> |
Offset 53, 15 lines modified | Offset 53, 15 lines modified | ||
53 | </div> | 53 | </div> |
54 | <div·class="doc"> | 54 | <div·class="doc"> |
55 | NB:·This·file·is·here·only·for·compatibility·with·earlier·version·of | 55 | NB:·This·file·is·here·only·for·compatibility·with·earlier·version·of |
56 | ·····<span·class="inlinecode"><span·class="id"·title="var">FSets</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">FMap</span></span>.·Please·use·<span·class="inlinecode"><span·class="id"·title="var">Structures</span>/<span·class="id"·title="var">Orders.v</span></span>·directly·now.· | 56 | ·····<span·class="inlinecode"><span·class="id"·title="var">FSets</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">FMap</span></span>.·Please·use·<span·class="inlinecode"><span·class="id"·title="var">Structures</span>/<span·class="id"·title="var">Orders.v</span></span>·directly·now.· |
57 | <div·class="paragraph">·</div> | 57 | <div·class="paragraph">·</div> |
58 | <a·id="lab | 58 | <a·id="lab22"></a><h1·class="section">Ordered·types</h1> |
59 | </div> | 59 | </div> |
60 | <div·class="code"> | 60 | <div·class="code"> |
61 | <br/> | 61 | <br/> |
62 | <span·class="id"·title="keyword">Inductive</span>·<a·id="Compare"·class="idref"·href="#Compare"><span·class="id"·title="inductive">Compare</span></a>·(<a·id="X:1"·class="idref"·href="#X:1"><span·class="id"·title="binder">X</span></a>·:·<span·class="id"·title="keyword">Type</span>)·(<a·id="lt:2"·class="idref"·href="#lt:2"><span·class="id"·title="binder">lt</span></a>·<a·id="eq:3"·class="idref"·href="#eq:3"><span·class="id"·title="binder">eq</span></a>·:·<a·class="idref"·href="Coq.Structures.OrderedType.html#X:1"><span·class="id"·title="variable">X</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.Structures.OrderedType.html#X:1"><span·class="id"·title="variable">X</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>)·(<a·id="x:4"·class="idref"·href="#x:4"><span·class="id"·title="binder">x</span></a>·<a·id="y:5"·class="idref"·href="#y:5"><span·class="id"·title="binder">y</span></a>·:·<a·class="idref"·href="Coq.Structures.OrderedType.html#X:1"><span·class="id"·title="variable">X</span></a>)·:·<span·class="id"·title="keyword">Type</span>·:=<br/> | 62 | <span·class="id"·title="keyword">Inductive</span>·<a·id="Compare"·class="idref"·href="#Compare"><span·class="id"·title="inductive">Compare</span></a>·(<a·id="X:1"·class="idref"·href="#X:1"><span·class="id"·title="binder">X</span></a>·:·<span·class="id"·title="keyword">Type</span>)·(<a·id="lt:2"·class="idref"·href="#lt:2"><span·class="id"·title="binder">lt</span></a>·<a·id="eq:3"·class="idref"·href="#eq:3"><span·class="id"·title="binder">eq</span></a>·:·<a·class="idref"·href="Coq.Structures.OrderedType.html#X:1"><span·class="id"·title="variable">X</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.Structures.OrderedType.html#X:1"><span·class="id"·title="variable">X</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>)·(<a·id="x:4"·class="idref"·href="#x:4"><span·class="id"·title="binder">x</span></a>·<a·id="y:5"·class="idref"·href="#y:5"><span·class="id"·title="binder">y</span></a>·:·<a·class="idref"·href="Coq.Structures.OrderedType.html#X:1"><span·class="id"·title="variable">X</span></a>)·:·<span·class="id"·title="keyword">Type</span>·:=<br/> |
63 | |·<a·id="LT"·class="idref"·href="#LT"><span·class="id"·title="constructor">LT</span></a>·:·<a·class="idref"·href="Coq.Structures.OrderedType.html#lt:2"><span·class="id"·title="variable">lt</span></a>·<a·class="idref"·href="Coq.Structures.OrderedType.html#x:4"><span·class="id"·title="variable">x</span></a>·<a·class="idref"·href="Coq.Structures.OrderedType.html#y:5"><span·class="id"·title="variable">y</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.Structures.OrderedType.html#Compare:6"><span·class="id"·title="inductive">Compare</span></a>·<a·class="idref"·href="Coq.Structures.OrderedType.html#lt:2"><span·class="id"·title="variable">lt</span></a>·<a·class="idref"·href="Coq.Structures.OrderedType.html#eq:3"><span·class="id"·title="variable">eq</span></a>·<a·class="idref"·href="Coq.Structures.OrderedType.html#x:4"><span·class="id"·title="variable">x</span></a>·<a·class="idref"·href="Coq.Structures.OrderedType.html#y:5"><span·class="id"·title="variable">y</span></a><br/> | 63 | |·<a·id="LT"·class="idref"·href="#LT"><span·class="id"·title="constructor">LT</span></a>·:·<a·class="idref"·href="Coq.Structures.OrderedType.html#lt:2"><span·class="id"·title="variable">lt</span></a>·<a·class="idref"·href="Coq.Structures.OrderedType.html#x:4"><span·class="id"·title="variable">x</span></a>·<a·class="idref"·href="Coq.Structures.OrderedType.html#y:5"><span·class="id"·title="variable">y</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.Structures.OrderedType.html#Compare:6"><span·class="id"·title="inductive">Compare</span></a>·<a·class="idref"·href="Coq.Structures.OrderedType.html#lt:2"><span·class="id"·title="variable">lt</span></a>·<a·class="idref"·href="Coq.Structures.OrderedType.html#eq:3"><span·class="id"·title="variable">eq</span></a>·<a·class="idref"·href="Coq.Structures.OrderedType.html#x:4"><span·class="id"·title="variable">x</span></a>·<a·class="idref"·href="Coq.Structures.OrderedType.html#y:5"><span·class="id"·title="variable">y</span></a><br/> |
Offset 46, 15 lines modified | Offset 46, 15 lines modified | ||
46 | <div·class="code"> | 46 | <div·class="code"> |
47 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Structures.OrderedType.html#"><span·class="id"·title="library">OrderedType</span></a>.<br/> | 47 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Structures.OrderedType.html#"><span·class="id"·title="library">OrderedType</span></a>.<br/> |
48 | <br/> | 48 | <br/> |
49 | </div> | 49 | </div> |
50 | <div·class="doc"> | 50 | <div·class="doc"> |
51 | <a·id="lab | 51 | <a·id="lab37"></a><h1·class="section">An·alternative·(but·equivalent)·presentation·for·an·Ordered·Type</h1> |
52 | ···inferface.· | 52 | ···inferface.· |
53 | <div·class="paragraph">·</div> | 53 | <div·class="paragraph">·</div> |
54 | ·NB:·<span·class="inlinecode"><span·class="id"·title="var">comparison</span></span>,·defined·in·<span·class="inlinecode"><span·class="id"·title="var">Datatypes.v</span></span>·is·<span·class="inlinecode"><span·class="id"·title="var">Eq</span>|<span·class="id"·title="var">Lt</span>|<span·class="id"·title="var">Gt</span></span> | 54 | ·NB:·<span·class="inlinecode"><span·class="id"·title="var">comparison</span></span>,·defined·in·<span·class="inlinecode"><span·class="id"·title="var">Datatypes.v</span></span>·is·<span·class="inlinecode"><span·class="id"·title="var">Eq</span>|<span·class="id"·title="var">Lt</span>|<span·class="id"·title="var">Gt</span></span> |
55 | whereas·<span·class="inlinecode"><span·class="id"·title="var">compare</span></span>,·defined·in·<span·class="inlinecode"><span·class="id"·title="var">OrderedType.v</span></span>·is·<span·class="inlinecode"><span·class="id"·title="var">EQ</span></span>·<span·class="inlinecode"><span·class="id"·title="var">_</span></span>·<span·class="inlinecode">|</span>·<span·class="inlinecode"><span·class="id"·title="var">LT</span></span>·<span·class="inlinecode"><span·class="id"·title="var">_</span></span>·<span·class="inlinecode">|</span>·<span·class="inlinecode"><span·class="id"·title="var">GT</span></span>·<span·class="inlinecode"><span·class="id"·title="var">_</span></span>·<span·class="inlinecode"></span> | 55 | whereas·<span·class="inlinecode"><span·class="id"·title="var">compare</span></span>,·defined·in·<span·class="inlinecode"><span·class="id"·title="var">OrderedType.v</span></span>·is·<span·class="inlinecode"><span·class="id"·title="var">EQ</span></span>·<span·class="inlinecode"><span·class="id"·title="var">_</span></span>·<span·class="inlinecode">|</span>·<span·class="inlinecode"><span·class="id"·title="var">LT</span></span>·<span·class="inlinecode"><span·class="id"·title="var">_</span></span>·<span·class="inlinecode">|</span>·<span·class="inlinecode"><span·class="id"·title="var">GT</span></span>·<span·class="inlinecode"><span·class="id"·title="var">_</span></span>·<span·class="inlinecode"></span> |
Offset 52, 15 lines modified | Offset 52, 15 lines modified | ||
52 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Strings.Ascii.html#"><span·class="id"·title="library">Ascii</span></a>·<a·class="idref"·href="Coq.Strings.String.html#"><span·class="id"·title="library">String</span></a>.<br/> | 52 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Strings.Ascii.html#"><span·class="id"·title="library">Ascii</span></a>·<a·class="idref"·href="Coq.Strings.String.html#"><span·class="id"·title="library">String</span></a>.<br/> |
53 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.NArith.NArith.html#"><span·class="id"·title="library">NArith</span></a>·<a·class="idref"·href="Coq.NArith.Ndec.html#"><span·class="id"·title="library">Ndec</span></a>.<br/> | 53 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.NArith.NArith.html#"><span·class="id"·title="library">NArith</span></a>·<a·class="idref"·href="Coq.NArith.Ndec.html#"><span·class="id"·title="library">Ndec</span></a>.<br/> |
54 | <br/> | 54 | <br/> |
55 | </div> | 55 | </div> |
56 | <div·class="doc"> | 56 | <div·class="doc"> |
57 | <a·id="lab | 57 | <a·id="lab5"></a><h1·class="section">Examples·of·Ordered·Type·structures.</h1> |
58 | <div·class="paragraph">·</div> | 58 | <div·class="paragraph">·</div> |
59 | ·First,·a·particular·case·of·<span·class="inlinecode"><span·class="id"·title="var">OrderedType</span></span>·where | 59 | ·First,·a·particular·case·of·<span·class="inlinecode"><span·class="id"·title="var">OrderedType</span></span>·where |
60 | ····the·equality·is·the·usual·one·of·Coq.· | 60 | ····the·equality·is·the·usual·one·of·Coq.· |
61 | </div> | 61 | </div> |
62 | <div·class="code"> | 62 | <div·class="code"> |
Offset 49, 15 lines modified | Offset 49, 15 lines modified | ||
49 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Export</span>·<a·class="idref"·href="Coq.Relations.Relations.html#"><span·class="id"·title="library">Relations</span></a>·<a·class="idref"·href="Coq.Classes.Morphisms.html#"><span·class="id"·title="library">Morphisms</span></a>·<a·class="idref"·href="Coq.Setoids.Setoid.html#"><span·class="id"·title="library">Setoid</span></a>·<a·class="idref"·href="Coq.Structures.Equalities.html#"><span·class="id"·title="library">Equalities</span></a>.<br/> | 49 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Export</span>·<a·class="idref"·href="Coq.Relations.Relations.html#"><span·class="id"·title="library">Relations</span></a>·<a·class="idref"·href="Coq.Classes.Morphisms.html#"><span·class="id"·title="library">Morphisms</span></a>·<a·class="idref"·href="Coq.Setoids.Setoid.html#"><span·class="id"·title="library">Setoid</span></a>·<a·class="idref"·href="Coq.Structures.Equalities.html#"><span·class="id"·title="library">Equalities</span></a>.<br/> |
50 | <span·class="id"·title="keyword">Set·Implicit·Arguments</span>.<br/> | 50 | <span·class="id"·title="keyword">Set·Implicit·Arguments</span>.<br/> |
51 | <br/> | 51 | <br/> |
52 | </div> | 52 | </div> |
53 | <div·class="doc"> | 53 | <div·class="doc"> |
54 | <a·id="lab | 54 | <a·id="lab30"></a><h1·class="section">Ordered·types</h1> |
55 | <div·class="paragraph">·</div> | 55 | <div·class="paragraph">·</div> |
56 | ·First,·signatures·with·only·the·order·relations· | 56 | ·First,·signatures·with·only·the·order·relations· |
57 | </div> | 57 | </div> |
58 | <div·class="code"> | 58 | <div·class="code"> |
Offset 51, 32 lines modified | Offset 51, 32 lines modified | ||
51 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Structures.OrderedType.html#"><span·class="id"·title="library">OrderedType</span></a>·<a·class="idref"·href="Coq.Structures.Orders.html#"><span·class="id"·title="library">Orders</span></a>.<br/> | 51 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Structures.OrderedType.html#"><span·class="id"·title="library">OrderedType</span></a>·<a·class="idref"·href="Coq.Structures.Orders.html#"><span·class="id"·title="library">Orders</span></a>.<br/> |
52 | <span·class="id"·title="keyword">Set·Implicit·Arguments</span>.<br/> | 52 | <span·class="id"·title="keyword">Set·Implicit·Arguments</span>.<br/> |
53 | <br/> | 53 | <br/> |
54 | </div> | 54 | </div> |
55 | <div·class="doc"> | 55 | <div·class="doc"> |
56 | <a·id="lab | 56 | <a·id="lab49"></a><h1·class="section">Some·alternative·(but·equivalent)·presentations·for·an·Ordered·Type</h1> |
57 | ···inferface.· | 57 | ···inferface.· |
58 | <div·class="paragraph">·</div> | 58 | <div·class="paragraph">·</div> |
59 | <a·id="lab | 59 | <a·id="lab50"></a><h2·class="section">The·original·interface</h2> |
60 | </div> | 60 | </div> |
61 | <div·class="code"> | 61 | <div·class="code"> |
62 | <br/> | 62 | <br/> |
63 | <span·class="id"·title="keyword">Module</span>·<span·class="id"·title="keyword">Type</span>·<a·id="OrderedTypeOrig"·class="idref"·href="#OrderedTypeOrig"><span·class="id"·title="module">OrderedTypeOrig</span></a>·:=·<a·class="idref"·href="Coq.Structures.OrderedType.html#OrderedType"><span·class="id"·title="module">OrderedType.OrderedType</span></a>.<br/> | 63 | <span·class="id"·title="keyword">Module</span>·<span·class="id"·title="keyword">Type</span>·<a·id="OrderedTypeOrig"·class="idref"·href="#OrderedTypeOrig"><span·class="id"·title="module">OrderedTypeOrig</span></a>·:=·<a·class="idref"·href="Coq.Structures.OrderedType.html#OrderedType"><span·class="id"·title="module">OrderedType.OrderedType</span></a>.<br/> |
64 | <br/> | 64 | <br/> |
65 | </div> | 65 | </div> |
66 | <div·class="doc"> | 66 | <div·class="doc"> |
67 | <a·id="lab | 67 | <a·id="lab51"></a><h2·class="section">An·interface·based·on·compare</h2> |
68 | </div> | 68 | </div> |
69 | <div·class="code"> | 69 | <div·class="code"> |
70 | <br/> | 70 | <br/> |
71 | <span·class="id"·title="keyword">Module</span>·<span·class="id"·title="keyword">Type</span>·<a·id="OrderedTypeAlt"·class="idref"·href="#OrderedTypeAlt"><span·class="id"·title="module">OrderedTypeAlt</span></a>.<br/> | 71 | <span·class="id"·title="keyword">Module</span>·<span·class="id"·title="keyword">Type</span>·<a·id="OrderedTypeAlt"·class="idref"·href="#OrderedTypeAlt"><span·class="id"·title="module">OrderedTypeAlt</span></a>.<br/> |
Offset 52, 15 lines modified | Offset 52, 15 lines modified | ||
52 | <a·class="idref"·href="Coq.Classes.RelationPairs.html#"><span·class="id"·title="library">RelationPairs</span></a>·<a·class="idref"·href="Coq.Structures.EqualitiesFacts.html#"><span·class="id"·title="library">EqualitiesFacts</span></a>.<br/> | 52 | <a·class="idref"·href="Coq.Classes.RelationPairs.html#"><span·class="id"·title="library">RelationPairs</span></a>·<a·class="idref"·href="Coq.Structures.EqualitiesFacts.html#"><span·class="id"·title="library">EqualitiesFacts</span></a>.<br/> |
53 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Strings.Ascii.html#"><span·class="id"·title="library">Ascii</span></a>·<a·class="idref"·href="Coq.Strings.String.html#"><span·class="id"·title="library">String</span></a>.<br/> | 53 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Strings.Ascii.html#"><span·class="id"·title="library">Ascii</span></a>·<a·class="idref"·href="Coq.Strings.String.html#"><span·class="id"·title="library">String</span></a>.<br/> |
54 | <br/> | 54 | <br/> |
55 | </div> | 55 | </div> |
56 | <div·class="doc"> | 56 | <div·class="doc"> |
57 | <a·id="lab1 | 57 | <a·id="lab19"></a><h1·class="section">Examples·of·Ordered·Type·structures.</h1> |
58 | <div·class="paragraph">·</div> | 58 | <div·class="paragraph">·</div> |
59 | ·Ordered·Type·for·<span·class="inlinecode"><span·class="id"·title="var">bool</span></span>,·<span·class="inlinecode"><span·class="id"·title="var">nat</span></span>,·<span·class="inlinecode"><span·class="id"·title="var">Positive</span></span>,·<span·class="inlinecode"><span·class="id"·title="var">N</span></span>,·<span·class="inlinecode"><span·class="id"·title="var">Z</span></span>,·<span·class="inlinecode"><span·class="id"·title="var">ascii</span></span>,·<span·class="inlinecode"><span·class="id"·title="var">string</span></span>·with·the·usual·or·lexicographic·order.· | 59 | ·Ordered·Type·for·<span·class="inlinecode"><span·class="id"·title="var">bool</span></span>,·<span·class="inlinecode"><span·class="id"·title="var">nat</span></span>,·<span·class="inlinecode"><span·class="id"·title="var">Positive</span></span>,·<span·class="inlinecode"><span·class="id"·title="var">N</span></span>,·<span·class="inlinecode"><span·class="id"·title="var">Z</span></span>,·<span·class="inlinecode"><span·class="id"·title="var">ascii</span></span>,·<span·class="inlinecode"><span·class="id"·title="var">string</span></span>·with·the·usual·or·lexicographic·order.· |
60 | </div> | 60 | </div> |
61 | <div·class="code"> | 61 | <div·class="code"> |
Offset 52, 15 lines modified | Offset 52, 15 lines modified | ||
52 | <br/> | 52 | <br/> |
53 | <span·class="id"·title="keyword">Set·Implicit·Arguments</span>.<br/> | 53 | <span·class="id"·title="keyword">Set·Implicit·Arguments</span>.<br/> |
54 | <br/> | 54 | <br/> |
55 | </div> | 55 | </div> |
56 | <div·class="doc"> | 56 | <div·class="doc"> |
57 | <a·id="lab | 57 | <a·id="lab24"></a><h1·class="section">Properties·of·<span·class="inlinecode"><span·class="id"·title="var">compare</span></span></h1> |
58 | </div> | 58 | </div> |
59 | <div·class="code"> | 59 | <div·class="code"> |
60 | <br/> | 60 | <br/> |
61 | <span·class="id"·title="keyword">Module</span>·<span·class="id"·title="keyword">Type</span>·<a·id="CompareFacts"·class="idref"·href="#CompareFacts"><span·class="id"·title="module">CompareFacts</span></a>·(<span·class="id"·title="keyword">Import</span>·<span·class="id"·title="var">O</span>:<a·class="idref"·href="Coq.Structures.Orders.html#DecStrOrder'"><span·class="id"·title="module">DecStrOrder'</span></a>).<br/> | 61 | <span·class="id"·title="keyword">Module</span>·<span·class="id"·title="keyword">Type</span>·<a·id="CompareFacts"·class="idref"·href="#CompareFacts"><span·class="id"·title="module">CompareFacts</span></a>·(<span·class="id"·title="keyword">Import</span>·<span·class="id"·title="var">O</span>:<a·class="idref"·href="Coq.Structures.Orders.html#DecStrOrder'"><span·class="id"·title="module">DecStrOrder'</span></a>).<br/> |
Offset 51, 15 lines modified | Offset 51, 15 lines modified | ||
51 | <br/> | 51 | <br/> |
52 | <span·class="id"·title="keyword">Set·Implicit·Arguments</span>.<br/> | 52 | <span·class="id"·title="keyword">Set·Implicit·Arguments</span>.<br/> |
53 | <br/> | 53 | <br/> |
54 | </div> | 54 | </div> |
55 | <div·class="doc"> | 55 | <div·class="doc"> |
56 | <a·id="lab | 56 | <a·id="lab20"></a><h1·class="section">Specialization·of·results·about·lists·modulo.</h1> |
57 | </div> | 57 | </div> |
58 | <div·class="code"> | 58 | <div·class="code"> |
59 | <br/> | 59 | <br/> |
60 | <span·class="id"·title="keyword">Module</span>·<a·id="OrderedTypeLists"·class="idref"·href="#OrderedTypeLists"><span·class="id"·title="module">OrderedTypeLists</span></a>·(<span·class="id"·title="var">O</span>:<a·class="idref"·href="Coq.Structures.Orders.html#OrderedType"><span·class="id"·title="module">OrderedType</span></a>).<br/> | 60 | <span·class="id"·title="keyword">Module</span>·<a·id="OrderedTypeLists"·class="idref"·href="#OrderedTypeLists"><span·class="id"·title="module">OrderedTypeLists</span></a>·(<span·class="id"·title="var">O</span>:<a·class="idref"·href="Coq.Structures.Orders.html#OrderedType"><span·class="id"·title="module">OrderedType</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.Setoids.Setoid.html#"><span·class="id"·title="library">Setoid</span></a>·<a·class="idref"·href="Coq.Classes.Morphisms.html#"><span·class="id"·title="library">Morphisms</span></a>·<a·class="idref"·href="Coq.Program.Basics.html#"><span·class="id"·title="library">Basics</span></a>·<a·class="idref"·href="Coq.Structures.Equalities.html#"><span·class="id"·title="library">Equalities</span></a>·<a·class="idref"·href="Coq.Structures.Orders.html#"><span·class="id"·title="library">Orders</span></a>.<br/> | 49 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Setoids.Setoid.html#"><span·class="id"·title="library">Setoid</span></a>·<a·class="idref"·href="Coq.Classes.Morphisms.html#"><span·class="id"·title="library">Morphisms</span></a>·<a·class="idref"·href="Coq.Program.Basics.html#"><span·class="id"·title="library">Basics</span></a>·<a·class="idref"·href="Coq.Structures.Equalities.html#"><span·class="id"·title="library">Equalities</span></a>·<a·class="idref"·href="Coq.Structures.Orders.html#"><span·class="id"·title="library">Orders</span></a>.<br/> |
50 | <span·class="id"·title="keyword">Set·Implicit·Arguments</span>.<br/> | 50 | <span·class="id"·title="keyword">Set·Implicit·Arguments</span>.<br/> |
51 | <br/> | 51 | <br/> |
52 | </div> | 52 | </div> |
53 | <div·class="doc"> | 53 | <div·class="doc"> |
54 | <a·id="lab | 54 | <a·id="lab6"></a><h1·class="section">The·order·tactic</h1> |
55 | <div·class="paragraph">·</div> | 55 | <div·class="paragraph">·</div> |
56 | ·This·tactic·is·designed·to·solve·systems·of·(in)equations | 56 | ·This·tactic·is·designed·to·solve·systems·of·(in)equations |
57 | ····involving·<span·class="inlinecode"><span·class="id"·title="var">eq</span></span>,·<span·class="inlinecode"><span·class="id"·title="var">lt</span></span>,·<span·class="inlinecode"><span·class="id"·title="var">le</span></span>·and·<span·class="inlinecode">~<span·class="id"·title="var">eq</span></span>·on·some·type.·This·tactic·is | 57 | ····involving·<span·class="inlinecode"><span·class="id"·title="var">eq</span></span>,·<span·class="inlinecode"><span·class="id"·title="var">lt</span></span>,·<span·class="inlinecode"><span·class="id"·title="var">le</span></span>·and·<span·class="inlinecode">~<span·class="id"·title="var">eq</span></span>·on·some·type.·This·tactic·is |
58 | ····domain-agnostic;·it·will·only·use·equivalence+order·axioms,·and | 58 | ····domain-agnostic;·it·will·only·use·equivalence+order·axioms,·and |
59 | ····not·analyze·elements·of·the·domain.·Hypothesis·or·goal·of·the·form | 59 | ····not·analyze·elements·of·the·domain.·Hypothesis·or·goal·of·the·form |
Offset 5777, 4050 lines modified | Offset 5777, 4050 lines modified | ||
00016900:·663d·2223·4954·4552·4154·4f52·5322·3e3c··f="#ITERATORS">< | 00016900:·663d·2223·4954·4552·4154·4f52·5322·3e3c··f="#ITERATORS">< | ||
00016910:·7370·616e·2063·6c61·7373·3d22·6964·2220··span·class="id"· | 00016910:·7370·616e·2063·6c61·7373·3d22·6964·2220··span·class="id"· | ||
00016920:·7469·746c·653d·2273·6563·7469·6f6e·223e··title="section"> | 00016920:·7469·746c·653d·2273·6563·7469·6f6e·223e··title="section"> | ||
00016930:·4954·4552·4154·4f52·533c·2f73·7061·6e3e··ITERATORS</span> | 00016930:·4954·4552·4154·4f52·533c·2f73·7061·6e3e··ITERATORS</span> | ||
00016940:·3c2f·613e·2e3c·6272·2f3e·0a3c·2f64·6976··</a>.<br/>.</div | 00016940:·3c2f·613e·2e3c·6272·2f3e·0a3c·2f64·6976··</a>.<br/>.</div | ||
00016950:·3e0a·0a3c·6469·7620·636c·6173·733d·2264··>..<div·class="d | 00016950:·3e0a·0a3c·6469·7620·636c·6173·733d·2264··>..<div·class="d | Diff chunk too large, falling back to line-by-line diff (4043 lines added, 4043 lines removed) | |
00016960:·6f63·223e·0a3c·6120·6964·3d22·6c61·6231··oc">.<a·id="lab1 | 00016960:·6f63·223e·0a3c·6120·6964·3d22·6c61·6231··oc">.<a·id="lab1 | ||
00016970:·3 | 00016970:·3831·223e·3c2f·613e·3c68·3120·636c·6173··81"></a><h1·clas | ||
00016980:·73 | 00016980:·733d·2273·6563·7469·6f6e·223e·4865·7265··s="section">Here | ||
00016990:· | 00016990:·2061·7265·2073·7065·6369·616c·206e·6f6e···are·special·non | ||
000169a0:· | 000169a0:·2064·6570·656e·6465·6e74·2075·7365·6675···dependent·usefu | ||
000169b0:· | 000169b0:·6c20·696e·7374·616e·7469·6174·696f·6e20··l·instantiation· | ||
000169c0:· | 000169c0:·6f66·2069·6e64·7563·7469·6f6e·2073·6368··of·induction·sch | ||
000169d0:·6 | 000169d0:·656d·6573·3c2f·6831·3e0a·0a3c·6469·7620··emes</h1>..<div· | ||
000169e0:· | 000169e0:·636c·6173·733d·2270·6172·6167·7261·7068··class="paragraph | ||
000169f0:· | 000169f0:·223e·203c·2f64·6976·3e0a·0a20·556e·6966··">·</div>..·Unif | ||
00016a00:·6 | 00016a00:·6f72·6d20·6170·706c·6963·6174·696f·6e20··orm·application· | ||
00016a10:· | 00016a10:·6f6e·2074·6865·2061·7267·756d·656e·7473··on·the·arguments | ||
00016a20:· | 00016a20:·206f·6620·7468·6520·7665·6374·6f72·200a···of·the·vector·. | ||
00016a30:· | 00016a30:·3c2f·6469·763e·0a3c·6469·7620·636c·6173··</div>.<div·clas | ||
00016a40:·73 | 00016a40:·733d·2263·6f64·6522·3e0a·3c73·7061·6e20··s="code">.<span· | ||
00016a50:· | 00016a50:·636c·6173·733d·2269·6422·2074·6974·6c65··class="id"·title | ||
00016a60:· | 00016a60:·3d22·6b65·7977·6f72·6422·3e44·6566·696e··="keyword">Defin | ||
00016a70:·6 | 00016a70:·6974·696f·6e3c·2f73·7061·6e3e·203c·6120··ition</span>·<a· | ||
00016a80:· | 00016a80:·6964·3d22·6d61·7022·2063·6c61·7373·3d22··id="map"·class=" | ||
00016a90:· | 00016a90:·6964·7265·6622·2068·7265·663d·2223·6d61··idref"·href="#ma | ||
00016aa0:· | 00016aa0:·7022·3e3c·7370·616e·2063·6c61·7373·3d22··p"><span·class=" | ||
00016ab0:· | 00016ab0:·6964·2220·7469·746c·653d·2264·6566·696e··id"·title="defin | ||
00016ac0:·6 | 00016ac0:·6974·696f·6e22·3e6d·6170·3c2f·7370·616e··ition">map</span | ||
00016ad0:· | 00016ad0:·3e3c·2f61·3e20·7b3c·6120·6964·3d22·413a··></a>·{<a·id="A: | ||
00016ae0:·3 | 00016ae0:·3139·3622·2063·6c61·7373·3d22·6964·7265··196"·class="idre | ||
00016af0:·6 | 00016af0:·6622·2068·7265·663d·2223·413a·3139·3622··f"·href="#A:196" | ||
00016b00:· | 00016b00:·3e3c·7370·616e·2063·6c61·7373·3d22·6964··><span·class="id | ||
00016b10:· | 00016b10:·2220·7469·746c·653d·2262·696e·6465·7222··"·title="binder" | ||
00016b20:· | 00016b20:·3e41·3c2f·7370·616e·3e3c·2f61·3e7d·207b··>A</span></a>}·{ | ||
00016b30:· | 00016b30:·3c61·2069·643d·2242·3a31·3937·2220·636c··<a·id="B:197"·cl | ||
00016b40:·6 | 00016b40:·6173·733d·2269·6472·6566·2220·6872·6566··ass="idref"·href | ||
00016b50:· | 00016b50:·3d22·2342·3a31·3937·223e·3c73·7061·6e20··="#B:197"><span· | ||
00016b60:· | 00016b60:·636c·6173·733d·2269·6422·2074·6974·6c65··class="id"·title | ||
00016b70:· | 00016b70:·3d22·6269·6e64·6572·223e·423c·2f73·7061··="binder">B</spa | ||
00016b80:·6 | 00016b80:·6e3e·3c2f·613e·7d20·283c·6120·6964·3d22··n></a>}·(<a·id=" | ||
00016b90:· | 00016b90:·663a·3139·3822·2063·6c61·7373·3d22·6964··f:198"·class="id | ||
00016ba0:· | 00016ba0:·7265·6622·2068·7265·663d·2223·663a·3139··ref"·href="#f:19 | ||
00016bb0:·3 | 00016bb0:·3822·3e3c·7370·616e·2063·6c61·7373·3d22··8"><span·class=" | ||
00016bc0:· | 00016bc0:·6964·2220·7469·746c·653d·2262·696e·6465··id"·title="binde | ||
00016bd0:· | 00016bd0:·7222·3e66·3c2f·7370·616e·3e3c·2f61·3e20··r">f</span></a>· | ||
00016be0:· | 00016be0:·3a20·3c61·2063·6c61·7373·3d22·6964·7265··:·<a·class="idre | ||
00016bf0:·6 | 00016bf0:·6622·2068·7265·663d·2243·6f71·2e56·6563··f"·href="Coq.Vec | ||
00016c00:· | 00016c00:·746f·7273·2e56·6563·746f·7244·6566·2e68··tors.VectorDef.h | ||
00016c10:· | 00016c10:·746d·6c23·413a·3139·3622·3e3c·7370·616e··tml#A:196"><span | ||
00016c20:· | 00016c20:·2063·6c61·7373·3d22·6964·2220·7469·746c···class="id"·titl | ||
00016c30:·6 | 00016c30:·653d·2276·6172·6961·626c·6522·3e41·3c2f··e="variable">A</ | ||
00016c40:· | 00016c40:·7370·616e·3e3c·2f61·3e20·3c61·2063·6c61··span></a>·<a·cla | ||
00016c50:· | 00016c50:·7373·3d22·6964·7265·6622·2068·7265·663d··ss="idref"·href= | ||
00016c60:· | 00016c60:·2243·6f71·2e49·6e69·742e·4c6f·6769·632e··"Coq.Init.Logic. | ||
00016c70:· | 00016c70:·6874·6d6c·233a·3a74·7970·655f·7363·6f70··html#::type_scop | ||
00016c80:· | 00016c80:·653a·785f·272d·2667·743b·275f·7822·3e3c··e:x_'->'_x">< | ||
00016c90:· | 00016c90:·7370·616e·2063·6c61·7373·3d22·6964·2220··span·class="id"· | ||
00016ca0:· | 00016ca0:·7469·746c·653d·226e·6f74·6174·696f·6e22··title="notation" | ||
00016cb0:· | 00016cb0:·3e2d·2667·743b·3c2f·7370·616e·3e3c·2f61··>-></span></a | ||
00016cc0:· | 00016cc0:·3e20·3c61·2063·6c61·7373·3d22·6964·7265··>·<a·class="idre | ||
00016cd0:·6 | 00016cd0:·6622·2068·7265·663d·2243·6f71·2e56·6563··f"·href="Coq.Vec | ||
00016ce0:· | 00016ce0:·746f·7273·2e56·6563·746f·7244·6566·2e68··tors.VectorDef.h | ||
00016cf0:· | 00016cf0:·746d·6c23·423a·3139·3722·3e3c·7370·616e··tml#B:197"><span | ||
00016d00:· | 00016d00:·2063·6c61·7373·3d22·6964·2220·7469·746c···class="id"·titl | ||
00016d10:·6 | 00016d10:·653d·2276·6172·6961·626c·6522·3e42·3c2f··e="variable">B</ | ||
00016d20:· | 00016d20:·7370·616e·3e3c·2f61·3e29·203a·203c·7370··span></a>)·:·<sp | ||
00016d30:· | 00016d30:·616e·2063·6c61·7373·3d22·6964·2220·7469··an·class="id"·ti | ||
00016d40:· | 00016d40:·746c·653d·226b·6579·776f·7264·223e·666f··tle="keyword">fo | ||
00016d50:· | 00016d50:·7261·6c6c·3c2f·7370·616e·3e20·7b3c·6120··rall</span>·{<a· | ||
00016d60:· | 00016d60:·6964·3d22·6e3a·3139·3922·2063·6c61·7373··id="n:199"·class | ||
00016d70:· | 00016d70:·3d22·6964·7265·6622·2068·7265·663d·2223··="idref"·href="# | ||
00016d80:· | 00016d80:·6e3a·3139·3922·3e3c·7370·616e·2063·6c61··n:199"><span·cla | ||
00016d90:· | 00016d90:·7373·3d22·6964·2220·7469·746c·653d·2262··ss="id"·title="b | ||
00016da0:·6 | 00016da0:·696e·6465·7222·3e6e·3c2f·7370·616e·3e3c··inder">n</span>< | ||
00016db0:· | 00016db0:·2f61·3e7d·2028·3c61·2069·643d·2276·3a32··/a>}·(<a·id="v:2 | ||
00016dc0:·3 | 00016dc0:·3030·2220·636c·6173·733d·2269·6472·6566··00"·class="idref | ||
00016dd0:· | 00016dd0:·2220·6872·6566·3d22·2376·3a32·3030·223e··"·href="#v:200"> | ||
00016de0:·3 | 00016de0:·3c73·7061·6e20·636c·6173·733d·2269·6422··<span·class="id" | ||
00016df0:·2 | 00016df0:·2074·6974·6c65·3d22·6269·6e64·6572·223e···title="binder"> | ||
00016e00:· | 00016e00:·763c·2f73·7061·6e3e·3c2f·613e·3a3c·6120··v</span></a>:<a· | ||
00016e10:· | 00016e10:·636c·6173·733d·2269·6472·6566·2220·6872··class="idref"·hr | ||
00016e20:· | 00016e20:·6566·3d22·436f·712e·5665·6374·6f72·732e··ef="Coq.Vectors. | ||
00016e30:· | 00016e30:·5665·6374·6f72·4465·662e·6874·6d6c·2374··VectorDef.html#t | ||
00016e40:· | 00016e40:·223e·3c73·7061·6e20·636c·6173·733d·2269··"><span·class="i | ||
00016e50:·6 | 00016e50:·6422·2074·6974·6c65·3d22·696e·6475·6374··d"·title="induct | ||
00016e60:· | 00016e60:·6976·6522·3e74·3c2f·7370·616e·3e3c·2f61··ive">t</span></a | ||
00016e70:· | 00016e70:·3e20·3c61·2063·6c61·7373·3d22·6964·7265··>·<a·class="idre | ||
00016e80:·6 | 00016e80:·6622·2068·7265·663d·2243·6f71·2e56·6563··f"·href="Coq.Vec | ||
00016e90:· | 00016e90:·746f·7273·2e56·6563·746f·7244·6566·2e68··tors.VectorDef.h | ||
00016ea0:· | 00016ea0:·746d·6c23·413a·3139·3622·3e3c·7370·616e··tml#A:196"><span | ||
00016eb0:· | 00016eb0:·2063·6c61·7373·3d22·6964·2220·7469·746c···class="id"·titl | ||
00016ec0:·6 | 00016ec0:·653d·2276·6172·6961·626c·6522·3e41·3c2f··e="variable">A</ | ||
00016ed0:· | 00016ed0:·7370·616e·3e3c·2f61·3e20·3c61·2063·6c61··span></a>·<a·cla | ||
00016ee0:· | 00016ee0:·7373·3d22·6964·7265·6622·2068·7265·663d··ss="idref"·href= | ||
00016ef0:· | 00016ef0:·2243·6f71·2e56·6563·746f·7273·2e56·6563··"Coq.Vectors.Vec | ||
00016f00:· | 00016f00:·746f·7244·6566·2e68·746d·6c23·6e3a·3139··torDef.html#n:19 | ||
00016f10:·39 | 00016f10:·3922·3e3c·7370·616e·2063·6c61·7373·3d22··9"><span·class=" | ||
00016f20:· | 00016f20:·6964·2220·7469·746c·653d·2276·6172·6961··id"·title="varia | ||
00016f30:·6 | 00016f30:·626c·6522·3e6e·3c2f·7370·616e·3e3c·2f61··ble">n</span></a | ||
00016f40:· | 00016f40:·3e29·2c20·3c61·2063·6c61·7373·3d22·6964··>),·<a·class="id | ||
00016f50:· | 00016f50:·7265·6622·2068·7265·663d·2243·6f71·2e56··ref"·href="Coq.V | ||
00016f60:· | 00016f60:·6563·746f·7273·2e56·6563·746f·7244·6566··ectors.VectorDef | ||
00016f70:· | 00016f70:·2e68·746d·6c23·7422·3e3c·7370·616e·2063··.html#t"><span·c | ||
00016f80:·6 | 00016f80:·6c61·7373·3d22·6964·2220·7469·746c·653d··lass="id"·title= | ||
00016f90:· | 00016f90:·2269·6e64·7563·7469·7665·223e·743c·2f73··"inductive">t</s | ||
00016fa0:·7 | 00016fa0:·7061·6e3e·3c2f·613e·203c·6120·636c·6173··pan></a>·<a·clas | ||
00016fb0:·73 | 00016fb0:·733d·2269·6472·6566·2220·6872·6566·3d22··s="idref"·href=" | ||
00016fc0:· | 00016fc0:·436f·712e·5665·6374·6f72·732e·5665·6374··Coq.Vectors.Vect | ||
00016fd0:· | 00016fd0:·6f72·4465·662e·6874·6d6c·2342·3a31·3937··orDef.html#B:197 | ||
00016fe0:· | 00016fe0:·223e·3c73·7061·6e20·636c·6173·733d·2269··"><span·class="i | ||
00016ff0:·6 | 00016ff0:·6422·2074·6974·6c65·3d22·7661·7269·6162··d"·title="variab | ||
00017000:·6 | 00017000:·6c65·223e·423c·2f73·7061·6e3e·3c2f·613e··le">B</span></a> | ||
00017010:· | 00017010:·203c·6120·636c·6173·733d·2269·6472·6566···<a·class="idref | ||
00017020:· | 00017020:·2220·6872·6566·3d22·436f·712e·5665·6374··"·href="Coq.Vect | ||
00017030:· | 00017030:·6f72·732e·5665·6374·6f72·4465·662e·6874··ors.VectorDef.ht | ||
00017040:· | 00017040:·6d6c·236e·3a31·3939·223e·3c73·7061·6e20··ml#n:199"><span· | ||
00017050:· | 00017050:·636c·6173·733d·2269·6422·2074·6974·6c65··class="id"·title | ||
00017060:· | 00017060:·3d22·7661·7269·6162·6c65·223e·6e3c·2f73··="variable">n</s | ||
00017070:·7 | 00017070:·7061·6e3e·3c2f·613e·203a·3d3c·6272·2f3e··pan></a>·:=<br/> | ||
00017080:· | 00017080:·0a26·6e62·7370·3b26·6e62·7370·3b3c·7370··. <sp | ||
00017090:· | 00017090:·616e·2063·6c61·7373·3d22·6964·2220·7469··an·class="id"·ti | ||
000170a0:· | 000170a0:·746c·653d·226b·6579·776f·7264·223e·6669··tle="keyword">fi | ||
000170b0:· | 000170b0:·783c·2f73·7061·6e3e·203c·7370·616e·2063··x</span>·<span·c | ||
000170c0:·6 | 000170c0:·6c61·7373·3d22·6964·2220·7469·746c·653d··lass="id"·title= | ||
000170d0:· | 000170d0:·2276·6172·223e·6d61·705f·6669·783c·2f73··"var">map_fix</s | ||
Max diff block lines reached; -1/558431 bytes (-0.00%) of diff not shown. |
Offset 78, 15 lines modified | Offset 78, 15 lines modified | ||
78 | </div> | 78 | </div> |
79 | <div·class="doc"> | 79 | <div·class="doc"> |
80 | Lemmas·are·done·for·functions·that·use·<span·class="inlinecode"><span·class="id"·title="var">Fin.t</span></span>·but·thanks·to·<span·class="inlinecode"><span·class="id"·title="var">Peano_dec.le_unique</span></span>,·all | 80 | Lemmas·are·done·for·functions·that·use·<span·class="inlinecode"><span·class="id"·title="var">Fin.t</span></span>·but·thanks·to·<span·class="inlinecode"><span·class="id"·title="var">Peano_dec.le_unique</span></span>,·all |
81 | is·true·for·the·one·that·use·<span·class="inlinecode"><span·class="id"·title="var">lt</span></span>· | 81 | is·true·for·the·one·that·use·<span·class="inlinecode"><span·class="id"·title="var">lt</span></span>· |
82 | <div·class="paragraph">·</div> | 82 | <div·class="paragraph">·</div> |
83 | <a·id="lab1 | 83 | <a·id="lab171"></a><h2·class="section">Properties·of·<span·class="inlinecode"><span·class="id"·title="var">nth</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">nth_order</span></span></h2> |
84 | </div> | 84 | </div> |
85 | <div·class="code"> | 85 | <div·class="code"> |
86 | <br/> | 86 | <br/> |
87 | <span·class="id"·title="keyword">Lemma</span>·<a·id="eq_nth_iff"·class="idref"·href="#eq_nth_iff"><span·class="id"·title="lemma">eq_nth_iff</span></a>·<a·id="A:20"·class="idref"·href="#A:20"><span·class="id"·title="binder">A</span></a>·<a·id="n:21"·class="idref"·href="#n:21"><span·class="id"·title="binder">n</span></a>·(<a·id="v1:22"·class="idref"·href="#v1:22"><span·class="id"·title="binder">v1</span></a>·<a·id="v2:23"·class="idref"·href="#v2:23"><span·class="id"·title="binder">v2</span></a>:·<a·class="idref"·href="Coq.Vectors.VectorDef.html#t"><span·class="id"·title="inductive">t</span></a>·<a·class="idref"·href="Coq.Vectors.VectorSpec.html#A:20"><span·class="id"·title="variable">A</span></a>·<a·class="idref"·href="Coq.Vectors.VectorSpec.html#n:21"><span·class="id"·title="variable">n</span></a>):<br/> | 87 | <span·class="id"·title="keyword">Lemma</span>·<a·id="eq_nth_iff"·class="idref"·href="#eq_nth_iff"><span·class="id"·title="lemma">eq_nth_iff</span></a>·<a·id="A:20"·class="idref"·href="#A:20"><span·class="id"·title="binder">A</span></a>·<a·id="n:21"·class="idref"·href="#n:21"><span·class="id"·title="binder">n</span></a>·(<a·id="v1:22"·class="idref"·href="#v1:22"><span·class="id"·title="binder">v1</span></a>·<a·id="v2:23"·class="idref"·href="#v2:23"><span·class="id"·title="binder">v2</span></a>:·<a·class="idref"·href="Coq.Vectors.VectorDef.html#t"><span·class="id"·title="inductive">t</span></a>·<a·class="idref"·href="Coq.Vectors.VectorSpec.html#A:20"><span·class="id"·title="variable">A</span></a>·<a·class="idref"·href="Coq.Vectors.VectorSpec.html#n:21"><span·class="id"·title="variable">n</span></a>):<br/> |
88 | <a·class="idref"·href="Coq.Init.Logic.html#::type_scope:x_'<->'_x"><span·class="id"·title="notation">(</span></a><span·class="id"·title="keyword">forall</span>·<a·id="p1:24"·class="idref"·href="#p1:24"><span·class="id"·title="binder">p1</span></a>·<a·id="p2:25"·class="idref"·href="#p2:25"><span·class="id"·title="binder">p2</span></a>,·<a·class="idref"·href="Coq.Vectors.VectorSpec.html#p1:24"><span·class="id"·title="variable">p1</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·<a·class="idref"·href="Coq.Vectors.VectorSpec.html#p2:25"><span·class="id"·title="variable">p2</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.Vectors.VectorSpec.html#v1:22"><span·class="id"·title="variable">v1</span></a>·<a·class="idref"·href="Coq.Vectors.VectorDef.html#3e2ab5a54c52b47134e5ddb66aa31ebd"><span·class="id"·title="notation">[@</span></a>·<a·class="idref"·href="Coq.Vectors.VectorSpec.html#p1:24"><span·class="id"·title="variable">p1</span></a>·<a·class="idref"·href="Coq.Vectors.VectorDef.html#3e2ab5a54c52b47134e5ddb66aa31ebd"><span·class="id"·title="notation">]</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·<a·class="idref"·href="Coq.Vectors.VectorSpec.html#v2:23"><span·class="id"·title="variable">v2</span></a>·<a·class="idref"·href="Coq.Vectors.VectorDef.html#3e2ab5a54c52b47134e5ddb66aa31ebd"><span·class="id"·title="notation">[@</span></a>·<a·class="idref"·href="Coq.Vectors.VectorSpec.html#p2:25"><span·class="id"·title="variable">p2</span></a>·<a·class="idref"·href="Coq.Vectors.VectorDef.html#3e2ab5a54c52b47134e5ddb66aa31ebd"><span·class="id"·title="notation">]</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.Logic.html#::type_scope:x_'<->'_x"><span·class="id"·title="notation"><-></span></a>·<a·class="idref"·href="Coq.Vectors.VectorSpec.html#v1:22"><span·class="id"·title="variable">v1</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·<a·class="idref"·href="Coq.Vectors.VectorSpec.html#v2:23"><span·class="id"·title="variable">v2</span></a>.<br/> | 88 | <a·class="idref"·href="Coq.Init.Logic.html#::type_scope:x_'<->'_x"><span·class="id"·title="notation">(</span></a><span·class="id"·title="keyword">forall</span>·<a·id="p1:24"·class="idref"·href="#p1:24"><span·class="id"·title="binder">p1</span></a>·<a·id="p2:25"·class="idref"·href="#p2:25"><span·class="id"·title="binder">p2</span></a>,·<a·class="idref"·href="Coq.Vectors.VectorSpec.html#p1:24"><span·class="id"·title="variable">p1</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·<a·class="idref"·href="Coq.Vectors.VectorSpec.html#p2:25"><span·class="id"·title="variable">p2</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.Vectors.VectorSpec.html#v1:22"><span·class="id"·title="variable">v1</span></a>·<a·class="idref"·href="Coq.Vectors.VectorDef.html#3e2ab5a54c52b47134e5ddb66aa31ebd"><span·class="id"·title="notation">[@</span></a>·<a·class="idref"·href="Coq.Vectors.VectorSpec.html#p1:24"><span·class="id"·title="variable">p1</span></a>·<a·class="idref"·href="Coq.Vectors.VectorDef.html#3e2ab5a54c52b47134e5ddb66aa31ebd"><span·class="id"·title="notation">]</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·<a·class="idref"·href="Coq.Vectors.VectorSpec.html#v2:23"><span·class="id"·title="variable">v2</span></a>·<a·class="idref"·href="Coq.Vectors.VectorDef.html#3e2ab5a54c52b47134e5ddb66aa31ebd"><span·class="id"·title="notation">[@</span></a>·<a·class="idref"·href="Coq.Vectors.VectorSpec.html#p2:25"><span·class="id"·title="variable">p2</span></a>·<a·class="idref"·href="Coq.Vectors.VectorDef.html#3e2ab5a54c52b47134e5ddb66aa31ebd"><span·class="id"·title="notation">]</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.Logic.html#::type_scope:x_'<->'_x"><span·class="id"·title="notation"><-></span></a>·<a·class="idref"·href="Coq.Vectors.VectorSpec.html#v1:22"><span·class="id"·title="variable">v1</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·<a·class="idref"·href="Coq.Vectors.VectorSpec.html#v2:23"><span·class="id"·title="variable">v2</span></a>.<br/> |
Offset 51, 15 lines modified | Offset 51, 15 lines modified | ||
51 | <a·class="idref"·href="Coq.Structures.OrdersFacts.html#"><span·class="id"·title="library">OrdersFacts</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZAxioms.html#"><span·class="id"·title="library">ZAxioms</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZProperties.html#"><span·class="id"·title="library">ZProperties</span></a>.<br/> | 51 | <a·class="idref"·href="Coq.Structures.OrdersFacts.html#"><span·class="id"·title="library">OrdersFacts</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZAxioms.html#"><span·class="id"·title="library">ZAxioms</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZProperties.html#"><span·class="id"·title="library">ZProperties</span></a>.<br/> |
52 | <span·class="id"·title="keyword">Require</span>·<a·class="idref"·href="Coq.ZArith.BinIntDef.html#"><span·class="id"·title="library">BinIntDef</span></a>.<br/> | 52 | <span·class="id"·title="keyword">Require</span>·<a·class="idref"·href="Coq.ZArith.BinIntDef.html#"><span·class="id"·title="library">BinIntDef</span></a>.<br/> |
53 | <br/> | 53 | <br/> |
54 | </div> | 54 | </div> |
55 | <div·class="doc"> | 55 | <div·class="doc"> |
56 | <a·id="lab | 56 | <a·id="lab222"></a><h1·class="section">Binary·Integers</h1> |
57 | <div·class="paragraph">·</div> | 57 | <div·class="paragraph">·</div> |
58 | ·Initial·author:·Pierre·Crégut,·CNET,·Lannion,·France· | 58 | ·Initial·author:·Pierre·Crégut,·CNET,·Lannion,·France· |
59 | <div·class="paragraph">·</div> | 59 | <div·class="paragraph">·</div> |
60 | ·The·type·<span·class="inlinecode"><span·class="id"·title="var">Z</span></span>·and·its·constructors·<span·class="inlinecode"><span·class="id"·title="var">Z0</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">Zpos</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">Zneg</span></span> | 60 | ·The·type·<span·class="inlinecode"><span·class="id"·title="var">Z</span></span>·and·its·constructors·<span·class="inlinecode"><span·class="id"·title="var">Z0</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">Zpos</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">Zneg</span></span> |
Offset 54, 15 lines modified | Offset 54, 15 lines modified | ||
54 | <br/> | 54 | <br/> |
55 | <br/> | 55 | <br/> |
56 | </div> | 56 | </div> |
57 | <div·class="doc"> | 57 | <div·class="doc"> |
58 | <a·id="lab | 58 | <a·id="lab184"></a><h1·class="section">Binary·Integers,·Definitions·of·Operations</h1> |
59 | <div·class="paragraph">·</div> | 59 | <div·class="paragraph">·</div> |
60 | ·Initial·author:·Pierre·Crégut,·CNET,·Lannion,·France· | 60 | ·Initial·author:·Pierre·Crégut,·CNET,·Lannion,·France· |
61 | </div> | 61 | </div> |
62 | <div·class="code"> | 62 | <div·class="code"> |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab304"></a><h1·class="section">An·light·axiomatization·of·integers·(used·in·MSetAVL).</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ·We·define·a·signature·for·an·integer·datatype·based·on·<span·class="inlinecode"><span·class="id"·title="var">Z</span></span>. | 51 | ·We·define·a·signature·for·an·integer·datatype·based·on·<span·class="inlinecode"><span·class="id"·title="var">Z</span></span>. |
52 | ····The·goal·is·to·allow·a·switch·after·extraction·to·ocaml's | 52 | ····The·goal·is·to·allow·a·switch·after·extraction·to·ocaml's |
53 | ····<span·class="inlinecode"><span·class="id"·title="var">big_int</span></span>·or·even·<span·class="inlinecode"><span·class="id"·title="var">int</span></span>·when·finiteness·isn't·a·problem | 53 | ····<span·class="inlinecode"><span·class="id"·title="var">big_int</span></span>·or·even·<span·class="inlinecode"><span·class="id"·title="var">int</span></span>·when·finiteness·isn't·a·problem |
54 | ····(typically·:·when·measuring·the·height·of·an·AVL·tree). | 54 | ····(typically·:·when·measuring·the·height·of·an·AVL·tree). |
Offset 70, 15 lines modified | Offset 70, 15 lines modified | ||
70 | <br/> | 70 | <br/> |
71 | <span·class="id"·title="keyword">Variables</span>·<a·id="decidability.x"·class="idref"·href="#decidability.x"><span·class="id"·title="variable">x</span></a>·<a·id="decidability.y"·class="idref"·href="#decidability.y"><span·class="id"·title="variable">y</span></a>·:·<a·class="idref"·href="Coq.Numbers.BinNums.html#Z"><span·class="id"·title="inductive">Z</span></a>.<br/> | 71 | <span·class="id"·title="keyword">Variables</span>·<a·id="decidability.x"·class="idref"·href="#decidability.x"><span·class="id"·title="variable">x</span></a>·<a·id="decidability.y"·class="idref"·href="#decidability.y"><span·class="id"·title="variable">y</span></a>·:·<a·class="idref"·href="Coq.Numbers.BinNums.html#Z"><span·class="id"·title="inductive">Z</span></a>.<br/> |
72 | <br/> | 72 | <br/> |
73 | </div> | 73 | </div> |
74 | <div·class="doc"> | 74 | <div·class="doc"> |
75 | <a·id="lab | 75 | <a·id="lab308"></a><h1·class="section">Decidability·of·order·on·binary·integers</h1> |
76 | </div> | 76 | </div> |
77 | <div·class="code"> | 77 | <div·class="code"> |
78 | <br/> | 78 | <br/> |
79 | <span·class="id"·title="keyword">Definition</span>·<a·id="Z_lt_dec"·class="idref"·href="#Z_lt_dec"><span·class="id"·title="definition">Z_lt_dec</span></a>·:·<a·class="idref"·href="Coq.Init.Specif.html#87727981cdc1579fef00b9d9c1d3b9da"><span·class="id"·title="notation">{</span></a><a·class="idref"·href="Coq.ZArith.ZArith_dec.html#decidability.x"><span·class="id"·title="variable">x</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#::Z_scope:x_'<'_x"><span·class="id"·title="notation"><</span></a>·<a·class="idref"·href="Coq.ZArith.ZArith_dec.html#decidability.y"><span·class="id"·title="variable">y</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.Init.Logic.html#63a68285c81db8f9bc456233bb9ed181"><span·class="id"·title="notation">~</span></a>·<a·class="idref"·href="Coq.ZArith.ZArith_dec.html#decidability.x"><span·class="id"·title="variable">x</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#::Z_scope:x_'<'_x"><span·class="id"·title="notation"><</span></a>·<a·class="idref"·href="Coq.ZArith.ZArith_dec.html#decidability.y"><span·class="id"·title="variable">y</span></a><a·class="idref"·href="Coq.Init.Specif.html#87727981cdc1579fef00b9d9c1d3b9da"><span·class="id"·title="notation">}</span></a>.<br/> | 79 | <span·class="id"·title="keyword">Definition</span>·<a·id="Z_lt_dec"·class="idref"·href="#Z_lt_dec"><span·class="id"·title="definition">Z_lt_dec</span></a>·:·<a·class="idref"·href="Coq.Init.Specif.html#87727981cdc1579fef00b9d9c1d3b9da"><span·class="id"·title="notation">{</span></a><a·class="idref"·href="Coq.ZArith.ZArith_dec.html#decidability.x"><span·class="id"·title="variable">x</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#::Z_scope:x_'<'_x"><span·class="id"·title="notation"><</span></a>·<a·class="idref"·href="Coq.ZArith.ZArith_dec.html#decidability.y"><span·class="id"·title="variable">y</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.Init.Logic.html#63a68285c81db8f9bc456233bb9ed181"><span·class="id"·title="notation">~</span></a>·<a·class="idref"·href="Coq.ZArith.ZArith_dec.html#decidability.x"><span·class="id"·title="variable">x</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#::Z_scope:x_'<'_x"><span·class="id"·title="notation"><</span></a>·<a·class="idref"·href="Coq.ZArith.ZArith_dec.html#decidability.y"><span·class="id"·title="variable">y</span></a><a·class="idref"·href="Coq.Init.Specif.html#87727981cdc1579fef00b9d9c1d3b9da"><span·class="id"·title="notation">}</span></a>.<br/> |
Offset 70, 15 lines modified | Offset 70, 15 lines modified | ||
70 | <br/> | 70 | <br/> |
71 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">Z_scope</span>.<br/> | 71 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">Z_scope</span>.<br/> |
72 | <br/> | 72 | <br/> |
73 | </div> | 73 | </div> |
74 | <div·class="doc"> | 74 | <div·class="doc"> |
75 | <a·id="lab | 75 | <a·id="lab212"></a><h1·class="section">Properties·of·absolute·value</h1> |
76 | </div> | 76 | </div> |
77 | <div·class="code"> | 77 | <div·class="code"> |
78 | <br/> | 78 | <br/> |
79 | <span·class="id"·title="keyword">Notation</span>·<a·id="Zabs_non_eq"·class="idref"·href="#Zabs_non_eq"><span·class="id"·title="abbreviation">Zabs_non_eq</span></a>·:=·<a·class="idref"·href="Coq.ZArith.BinInt.html#Z.abs_neq"><span·class="id"·title="lemma">Z.abs_neq</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="Zabs_non_eq"·class="idref"·href="#Zabs_non_eq"><span·class="id"·title="abbreviation">Zabs_non_eq</span></a>·:=·<a·class="idref"·href="Coq.ZArith.BinInt.html#Z.abs_neq"><span·class="id"·title="lemma">Z.abs_neq</span></a>·(<span·class="id"·title="var">only</span>·<span·class="id"·title="var">parsing</span>).<br/> |
80 | <span·class="id"·title="keyword">Notation</span>·<a·id="Zabs_Zopp"·class="idref"·href="#Zabs_Zopp"><span·class="id"·title="abbreviation">Zabs_Zopp</span></a>·:=·<a·class="idref"·href="Coq.ZArith.BinInt.html#Z.abs_opp"><span·class="id"·title="lemma">Z.abs_opp</span></a>·(<span·class="id"·title="var">only</span>·<span·class="id"·title="var">parsing</span>).<br/> | 80 | <span·class="id"·title="keyword">Notation</span>·<a·id="Zabs_Zopp"·class="idref"·href="#Zabs_Zopp"><span·class="id"·title="abbreviation">Zabs_Zopp</span></a>·:=·<a·class="idref"·href="Coq.ZArith.BinInt.html#Z.abs_opp"><span·class="id"·title="lemma">Z.abs_opp</span></a>·(<span·class="id"·title="var">only</span>·<span·class="id"·title="var">parsing</span>).<br/> |
Offset 56, 15 lines modified | Offset 56, 15 lines modified | ||
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">Z_scope</span>.<br/> | 57 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">Z_scope</span>.<br/> |
58 | <br/> | 58 | <br/> |
59 | </div> | 59 | </div> |
60 | <div·class="doc"> | 60 | <div·class="doc"> |
61 | <a·id="lab | 61 | <a·id="lab216"></a><h1·class="section">Boolean·operations·from·decidability·of·order</h1> |
62 | ·The·decidability·of·equality·and·order·relations·over | 62 | ·The·decidability·of·equality·and·order·relations·over |
63 | ····type·<span·class="inlinecode"><span·class="id"·title="var">Z</span></span>·gives·some·boolean·functions·with·the·adequate·specification.· | 63 | ····type·<span·class="inlinecode"><span·class="id"·title="var">Z</span></span>·gives·some·boolean·functions·with·the·adequate·specification.· |
64 | </div> | 64 | </div> |
65 | <div·class="code"> | 65 | <div·class="code"> |
66 | <br/> | 66 | <br/> |
67 | <span·class="id"·title="keyword">Definition</span>·<a·id="Z_lt_ge_bool"·class="idref"·href="#Z_lt_ge_bool"><span·class="id"·title="definition">Z_lt_ge_bool</span></a>·(<a·id="x:1"·class="idref"·href="#x:1"><span·class="id"·title="binder">x</span></a>·<a·id="y:2"·class="idref"·href="#y:2"><span·class="id"·title="binder">y</span></a>:<a·class="idref"·href="Coq.Numbers.BinNums.html#Z"><span·class="id"·title="inductive">Z</span></a>)·:=·<a·class="idref"·href="Coq.Bool.Sumbool.html#bool_of_sumbool"><span·class="id"·title="definition">bool_of_sumbool</span></a>·(<a·class="idref"·href="Coq.ZArith.ZArith_dec.html#Z_lt_ge_dec"><span·class="id"·title="definition">Z_lt_ge_dec</span></a>·<a·class="idref"·href="Coq.ZArith.Zbool.html#x:1"><span·class="id"·title="variable">x</span></a>·<a·class="idref"·href="Coq.ZArith.Zbool.html#y:2"><span·class="id"·title="variable">y</span></a>).<br/> | 67 | <span·class="id"·title="keyword">Definition</span>·<a·id="Z_lt_ge_bool"·class="idref"·href="#Z_lt_ge_bool"><span·class="id"·title="definition">Z_lt_ge_bool</span></a>·(<a·id="x:1"·class="idref"·href="#x:1"><span·class="id"·title="binder">x</span></a>·<a·id="y:2"·class="idref"·href="#y:2"><span·class="id"·title="binder">y</span></a>:<a·class="idref"·href="Coq.Numbers.BinNums.html#Z"><span·class="id"·title="inductive">Z</span></a>)·:=·<a·class="idref"·href="Coq.Bool.Sumbool.html#bool_of_sumbool"><span·class="id"·title="definition">bool_of_sumbool</span></a>·(<a·class="idref"·href="Coq.ZArith.ZArith_dec.html#Z_lt_ge_dec"><span·class="id"·title="definition">Z_lt_ge_dec</span></a>·<a·class="idref"·href="Coq.ZArith.Zbool.html#x:1"><span·class="id"·title="variable">x</span></a>·<a·class="idref"·href="Coq.ZArith.Zbool.html#y:2"><span·class="id"·title="variable">y</span></a>).<br/> |
Offset 64, 30 lines modified | Offset 64, 30 lines modified | ||
64 | <br/> | 64 | <br/> |
65 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">Z_scope</span>.<br/> | 65 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">Z_scope</span>.<br/> |
66 | <br/> | 66 | <br/> |
67 | </div> | 67 | </div> |
68 | <div·class="doc"> | 68 | <div·class="doc"> |
69 | <a·id="lab | 69 | <a·id="lab286"></a><h1·class="section">Comparison·on·integers</h1> |
70 | </div> | 70 | </div> |
71 | <div·class="code"> | 71 | <div·class="code"> |
72 | <br/> | 72 | <br/> |
73 | <span·class="id"·title="keyword">Lemma</span>·<a·id="Zcompare_Gt_Lt_antisym"·class="idref"·href="#Zcompare_Gt_Lt_antisym"><span·class="id"·title="lemma">Zcompare_Gt_Lt_antisym</span></a>·:·<span·class="id"·title="keyword">forall</span>·<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>:<a·class="idref"·href="Coq.Numbers.BinNums.html#Z"><span·class="id"·title="inductive">Z</span></a>,·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">(</span></a><a·class="idref"·href="Coq.ZArith.Zcompare.html#n:1"><span·class="id"·title="variable">n</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#1718f1bc306f7edd524650b393f464a3"><span·class="id"·title="notation">?=</span></a>·<a·class="idref"·href="Coq.ZArith.Zcompare.html#m:2"><span·class="id"·title="variable">m</span></a><a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">)</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·<a·class="idref"·href="Coq.Init.Datatypes.html#Gt"><span·class="id"·title="constructor">Gt</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.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">(</span></a><a·class="idref"·href="Coq.ZArith.Zcompare.html#m:2"><span·class="id"·title="variable">m</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#1718f1bc306f7edd524650b393f464a3"><span·class="id"·title="notation">?=</span></a>·<a·class="idref"·href="Coq.ZArith.Zcompare.html#n:1"><span·class="id"·title="variable">n</span></a><a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">)</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·<a·class="idref"·href="Coq.Init.Datatypes.html#Lt"><span·class="id"·title="constructor">Lt</span></a>.<br/> | 73 | <span·class="id"·title="keyword">Lemma</span>·<a·id="Zcompare_Gt_Lt_antisym"·class="idref"·href="#Zcompare_Gt_Lt_antisym"><span·class="id"·title="lemma">Zcompare_Gt_Lt_antisym</span></a>·:·<span·class="id"·title="keyword">forall</span>·<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>:<a·class="idref"·href="Coq.Numbers.BinNums.html#Z"><span·class="id"·title="inductive">Z</span></a>,·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">(</span></a><a·class="idref"·href="Coq.ZArith.Zcompare.html#n:1"><span·class="id"·title="variable">n</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#1718f1bc306f7edd524650b393f464a3"><span·class="id"·title="notation">?=</span></a>·<a·class="idref"·href="Coq.ZArith.Zcompare.html#m:2"><span·class="id"·title="variable">m</span></a><a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">)</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·<a·class="idref"·href="Coq.Init.Datatypes.html#Gt"><span·class="id"·title="constructor">Gt</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.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">(</span></a><a·class="idref"·href="Coq.ZArith.Zcompare.html#m:2"><span·class="id"·title="variable">m</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#1718f1bc306f7edd524650b393f464a3"><span·class="id"·title="notation">?=</span></a>·<a·class="idref"·href="Coq.ZArith.Zcompare.html#n:1"><span·class="id"·title="variable">n</span></a><a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">)</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·<a·class="idref"·href="Coq.Init.Datatypes.html#Lt"><span·class="id"·title="constructor">Lt</span></a>.<br/> |
74 | <br/> | 74 | <br/> |
75 | <span·class="id"·title="keyword">Lemma</span>·<a·id="Zcompare_antisym"·class="idref"·href="#Zcompare_antisym"><span·class="id"·title="lemma">Zcompare_antisym</span></a>·<a·id="n:3"·class="idref"·href="#n:3"><span·class="id"·title="binder">n</span></a>·<a·id="m:4"·class="idref"·href="#m:4"><span·class="id"·title="binder">m</span></a>·:·<a·class="idref"·href="Coq.Init.Datatypes.html#CompOpp"><span·class="id"·title="definition">CompOpp</span></a>·(<a·class="idref"·href="Coq.ZArith.Zcompare.html#n:3"><span·class="id"·title="variable">n</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#1718f1bc306f7edd524650b393f464a3"><span·class="id"·title="notation">?=</span></a>·<a·class="idref"·href="Coq.ZArith.Zcompare.html#m:4"><span·class="id"·title="variable">m</span></a>)·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">(</span></a><a·class="idref"·href="Coq.ZArith.Zcompare.html#m:4"><span·class="id"·title="variable">m</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#1718f1bc306f7edd524650b393f464a3"><span·class="id"·title="notation">?=</span></a>·<a·class="idref"·href="Coq.ZArith.Zcompare.html#n:3"><span·class="id"·title="variable">n</span></a><a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">)</span></a>.<br/> | 75 | <span·class="id"·title="keyword">Lemma</span>·<a·id="Zcompare_antisym"·class="idref"·href="#Zcompare_antisym"><span·class="id"·title="lemma">Zcompare_antisym</span></a>·<a·id="n:3"·class="idref"·href="#n:3"><span·class="id"·title="binder">n</span></a>·<a·id="m:4"·class="idref"·href="#m:4"><span·class="id"·title="binder">m</span></a>·:·<a·class="idref"·href="Coq.Init.Datatypes.html#CompOpp"><span·class="id"·title="definition">CompOpp</span></a>·(<a·class="idref"·href="Coq.ZArith.Zcompare.html#n:3"><span·class="id"·title="variable">n</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#1718f1bc306f7edd524650b393f464a3"><span·class="id"·title="notation">?=</span></a>·<a·class="idref"·href="Coq.ZArith.Zcompare.html#m:4"><span·class="id"·title="variable">m</span></a>)·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">(</span></a><a·class="idref"·href="Coq.ZArith.Zcompare.html#m:4"><span·class="id"·title="variable">m</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#1718f1bc306f7edd524650b393f464a3"><span·class="id"·title="notation">?=</span></a>·<a·class="idref"·href="Coq.ZArith.Zcompare.html#n:3"><span·class="id"·title="variable">n</span></a><a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">)</span></a>.<br/> |
76 | <br/> | 76 | <br/> |
77 | </div> | 77 | </div> |
78 | <div·class="doc"> | 78 | <div·class="doc"> |
79 | <a·id="lab | 79 | <a·id="lab287"></a><h1·class="section">Transitivity·of·comparison</h1> |
80 | </div> | 80 | </div> |
81 | <div·class="code"> | 81 | <div·class="code"> |
82 | <br/> | 82 | <br/> |
83 | <span·class="id"·title="keyword">Lemma</span>·<a·id="Zcompare_Lt_trans"·class="idref"·href="#Zcompare_Lt_trans"><span·class="id"·title="lemma">Zcompare_Lt_trans</span></a>·:<br/> | 83 | <span·class="id"·title="keyword">Lemma</span>·<a·id="Zcompare_Lt_trans"·class="idref"·href="#Zcompare_Lt_trans"><span·class="id"·title="lemma">Zcompare_Lt_trans</span></a>·:<br/> |
84 | <span·class="id"·title="keyword">forall</span>·<a·id="n:5"·class="idref"·href="#n:5"><span·class="id"·title="binder">n</span></a>·<a·id="m:6"·class="idref"·href="#m:6"><span·class="id"·title="binder">m</span></a>·<a·id="p:7"·class="idref"·href="#p:7"><span·class="id"·title="binder">p</span></a>:<a·class="idref"·href="Coq.Numbers.BinNums.html#Z"><span·class="id"·title="inductive">Z</span></a>,·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">(</span></a><a·class="idref"·href="Coq.ZArith.Zcompare.html#n:5"><span·class="id"·title="variable">n</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#1718f1bc306f7edd524650b393f464a3"><span·class="id"·title="notation">?=</span></a>·<a·class="idref"·href="Coq.ZArith.Zcompare.html#m:6"><span·class="id"·title="variable">m</span></a><a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">)</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·<a·class="idref"·href="Coq.Init.Datatypes.html#Lt"><span·class="id"·title="constructor">Lt</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.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">(</span></a><a·class="idref"·href="Coq.ZArith.Zcompare.html#m:6"><span·class="id"·title="variable">m</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#1718f1bc306f7edd524650b393f464a3"><span·class="id"·title="notation">?=</span></a>·<a·class="idref"·href="Coq.ZArith.Zcompare.html#p:7"><span·class="id"·title="variable">p</span></a><a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">)</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·<a·class="idref"·href="Coq.Init.Datatypes.html#Lt"><span·class="id"·title="constructor">Lt</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.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">(</span></a><a·class="idref"·href="Coq.ZArith.Zcompare.html#n:5"><span·class="id"·title="variable">n</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#1718f1bc306f7edd524650b393f464a3"><span·class="id"·title="notation">?=</span></a>·<a·class="idref"·href="Coq.ZArith.Zcompare.html#p:7"><span·class="id"·title="variable">p</span></a><a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">)</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·<a·class="idref"·href="Coq.Init.Datatypes.html#Lt"><span·class="id"·title="constructor">Lt</span></a>.<br/> | 84 | <span·class="id"·title="keyword">forall</span>·<a·id="n:5"·class="idref"·href="#n:5"><span·class="id"·title="binder">n</span></a>·<a·id="m:6"·class="idref"·href="#m:6"><span·class="id"·title="binder">m</span></a>·<a·id="p:7"·class="idref"·href="#p:7"><span·class="id"·title="binder">p</span></a>:<a·class="idref"·href="Coq.Numbers.BinNums.html#Z"><span·class="id"·title="inductive">Z</span></a>,·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">(</span></a><a·class="idref"·href="Coq.ZArith.Zcompare.html#n:5"><span·class="id"·title="variable">n</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#1718f1bc306f7edd524650b393f464a3"><span·class="id"·title="notation">?=</span></a>·<a·class="idref"·href="Coq.ZArith.Zcompare.html#m:6"><span·class="id"·title="variable">m</span></a><a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">)</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·<a·class="idref"·href="Coq.Init.Datatypes.html#Lt"><span·class="id"·title="constructor">Lt</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.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">(</span></a><a·class="idref"·href="Coq.ZArith.Zcompare.html#m:6"><span·class="id"·title="variable">m</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#1718f1bc306f7edd524650b393f464a3"><span·class="id"·title="notation">?=</span></a>·<a·class="idref"·href="Coq.ZArith.Zcompare.html#p:7"><span·class="id"·title="variable">p</span></a><a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">)</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·<a·class="idref"·href="Coq.Init.Datatypes.html#Lt"><span·class="id"·title="constructor">Lt</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.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">(</span></a><a·class="idref"·href="Coq.ZArith.Zcompare.html#n:5"><span·class="id"·title="variable">n</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#1718f1bc306f7edd524650b393f464a3"><span·class="id"·title="notation">?=</span></a>·<a·class="idref"·href="Coq.ZArith.Zcompare.html#p:7"><span·class="id"·title="variable">p</span></a><a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">)</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·<a·class="idref"·href="Coq.Init.Datatypes.html#Lt"><span·class="id"·title="constructor">Lt</span></a>.<br/> |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab273"></a><h1·class="section">Euclidean·Division</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | ·Initial·Contribution·by·Claude·Marché·and·Xavier·Urbain· | 51 | ·Initial·Contribution·by·Claude·Marché·and·Xavier·Urbain· |
52 | </div> | 52 | </div> |
53 | <div·class="code"> | 53 | <div·class="code"> |
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.Classes.Morphisms.html#"><span·class="id"·title="library">Morphisms</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#"><span·class="id"·title="library">BinInt</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZDivEucl.html#"><span·class="id"·title="library">ZDivEucl</span></a>.<br/> | 49 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Classes.Morphisms.html#"><span·class="id"·title="library">Morphisms</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#"><span·class="id"·title="library">BinInt</span></a>·<a·class="idref"·href="Coq.Numbers.Integer.Abstract.ZDivEucl.html#"><span·class="id"·title="library">ZDivEucl</span></a>.<br/> |
50 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">Z_scope</span>.<br/> | 50 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">Z_scope</span>.<br/> |
51 | <br/> | 51 | <br/> |
52 | </div> | 52 | </div> |
53 | <div·class="doc"> | 53 | <div·class="doc"> |
54 | <a·id="lab | 54 | <a·id="lab262"></a><h1·class="section">Definitions·of·division·for·binary·integers,·Euclid·convention.</h1> |
55 | <div·class="paragraph">·</div> | 55 | <div·class="paragraph">·</div> |
56 | ·In·this·convention,·the·remainder·is·always·positive. | 56 | ·In·this·convention,·the·remainder·is·always·positive. |
57 | ····For·other·conventions,·see·<span·class="inlinecode"><span·class="id"·title="var">Z.div</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">Z.quot</span></span>·in·file·<span·class="inlinecode"><span·class="id"·title="var">BinIntDef</span></span>. | 57 | ····For·other·conventions,·see·<span·class="inlinecode"><span·class="id"·title="var">Z.div</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">Z.quot</span></span>·in·file·<span·class="inlinecode"><span·class="id"·title="var">BinIntDef</span></span>. |
58 | ····To·avoid·collision·with·the·other·divisions,·we·place·this·one | 58 | ····To·avoid·collision·with·the·other·divisions,·we·place·this·one |
59 | ····under·a·module. | 59 | ····under·a·module. |
Offset 169, 15 lines modified | Offset 169, 15 lines modified | ||
169 | <span·class="id"·title="keyword">Notation</span>·<a·id="Zodd_bool_succ"·class="idref"·href="#Zodd_bool_succ"><span·class="id"·title="abbreviation">Zodd_bool_succ</span></a>·:=·<a·class="idref"·href="Coq.ZArith.BinInt.html#Z.odd_succ"><span·class="id"·title="lemma">Z.odd_succ</span></a>·(<span·class="id"·title="var">only</span>·<span·class="id"·title="var">parsing</span>).<br/> | 169 | <span·class="id"·title="keyword">Notation</span>·<a·id="Zodd_bool_succ"·class="idref"·href="#Zodd_bool_succ"><span·class="id"·title="abbreviation">Zodd_bool_succ</span></a>·:=·<a·class="idref"·href="Coq.ZArith.BinInt.html#Z.odd_succ"><span·class="id"·title="lemma">Z.odd_succ</span></a>·(<span·class="id"·title="var">only</span>·<span·class="id"·title="var">parsing</span>).<br/> |
170 | <span·class="id"·title="keyword">Notation</span>·<a·id="Zodd_bool_pred"·class="idref"·href="#Zodd_bool_pred"><span·class="id"·title="abbreviation">Zodd_bool_pred</span></a>·:=·<a·class="idref"·href="Coq.ZArith.BinInt.html#Z.odd_pred"><span·class="id"·title="lemma">Z.odd_pred</span></a>·(<span·class="id"·title="var">only</span>·<span·class="id"·title="var">parsing</span>).<br/> | 170 | <span·class="id"·title="keyword">Notation</span>·<a·id="Zodd_bool_pred"·class="idref"·href="#Zodd_bool_pred"><span·class="id"·title="abbreviation">Zodd_bool_pred</span></a>·:=·<a·class="idref"·href="Coq.ZArith.BinInt.html#Z.odd_pred"><span·class="id"·title="lemma">Z.odd_pred</span></a>·(<span·class="id"·title="var">only</span>·<span·class="id"·title="var">parsing</span>).<br/> |
171 | <br/> | 171 | <br/> |
172 | </div> | 172 | </div> |
173 | <div·class="doc"> | 173 | <div·class="doc"> |
174 | <a·id="lab | 174 | <a·id="lab183"></a><h1·class="section">Definition·of·<span·class="inlinecode"><span·class="id"·title="var">Z.quot2</span></span>,·<span·class="inlinecode"><span·class="id"·title="var">Z.div2</span></span>·and·properties·wrt·<span·class="inlinecode"><span·class="id"·title="var">Zeven</span></span></h1> |
175 | ··and·<span·class="inlinecode"><span·class="id"·title="var">Zodd</span></span>· | 175 | ··and·<span·class="inlinecode"><span·class="id"·title="var">Zodd</span></span>· |
176 | <div·class="paragraph">·</div> | 176 | <div·class="paragraph">·</div> |
177 | ·Properties·of·<span·class="inlinecode"><span·class="id"·title="var">Z.div2</span></span>· | 177 | ·Properties·of·<span·class="inlinecode"><span·class="id"·title="var">Z.div2</span></span>· |
178 | </div> | 178 | </div> |
179 | <div·class="code"> | 179 | <div·class="code"> |
Offset 45, 15 lines modified | Offset 45, 15 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 | 49 | <a·id="lab283"></a><h1·class="section">Zgcd_alt·:·an·alternate·version·of·Z.gcd,·based·on·Euclid's·algorithm</h1> |
50 | <div·class="paragraph">·</div> | 50 | <div·class="paragraph">·</div> |
51 | <div·class="paragraph">·</div> | 51 | <div·class="paragraph">·</div> |
52 | Author:·Pierre·Letouzey | 52 | Author:·Pierre·Letouzey |
Offset 98, 29 lines modified | Offset 98, 29 lines modified | ||
98 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.ZArith.Zmisc.html#"><span·class="id"·title="library">Zmisc</span></a>.<br/> | 98 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.ZArith.Zmisc.html#"><span·class="id"·title="library">Zmisc</span></a>.<br/> |
99 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.ZArith.Wf_Z.html#"><span·class="id"·title="library">Wf_Z</span></a>.<br/> | 99 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.ZArith.Wf_Z.html#"><span·class="id"·title="library">Wf_Z</span></a>.<br/> |
100 | <br/> | 100 | <br/> |
101 | </div> | 101 | </div> |
102 | <div·class="doc"> | 102 | <div·class="doc"> |
103 | <a·id="lab | 103 | <a·id="lab219"></a><h1·class="section">Simplification·lemmas</h1> |
104 | <div·class="paragraph">·</div> | 104 | <div·class="paragraph">·</div> |
105 | ·No·subgoal·or·smaller·subgoals····································· | 105 | ·No·subgoal·or·smaller·subgoals····································· |
106 | </div> | 106 | </div> |
107 | <div·class="code"> | 107 | <div·class="code"> |
108 | <br/> | 108 | <br/> |
109 | #[<span·class="id"·title="var">global</span>]<br/> | 109 | #[<span·class="id"·title="var">global</span>]<br/> |
110 | <span·class="id"·title="keyword">Hint</span>·<span·class="id"·title="keyword">Resolve</span><br/> | 110 | <span·class="id"·title="keyword">Hint</span>·<span·class="id"·title="keyword">Resolve</span><br/> |
111 | </div> | 111 | </div> |
112 | <div·class="doc"> | 112 | <div·class="doc"> |
113 | <a·id="lab | 113 | <a·id="lab220"></a><h2·class="section">Reversible·simplification·lemmas·(no·loss·of·information)</h2> |
114 | ·Should·clearly·be·declared·as·hints······························· | 114 | ·Should·clearly·be·declared·as·hints······························· |
115 | <div·class="paragraph">·</div> | 115 | <div·class="paragraph">·</div> |
116 | ·Lemmas·ending·by·eq· | 116 | ·Lemmas·ending·by·eq· |
117 | </div> | 117 | </div> |
118 | <div·class="code"> | 118 | <div·class="code"> |
119 | <span·class="id"·title="var">Zsucc_eq_compat</span>·<br/> | 119 | <span·class="id"·title="var">Zsucc_eq_compat</span>·<br/> |
Offset 91, 15 lines modified | Offset 91, 15 lines modified | ||
91 | <li>·module·Zabs2Nat·:·from·Z·to·nat·(via·the·absolute·value) | 91 | <li>·module·Zabs2Nat·:·from·Z·to·nat·(via·the·absolute·value) |
92 | </li> | 92 | </li> |
93 | </ul> | 93 | </ul> |
94 | <div·class="paragraph">·</div> | 94 | <div·class="paragraph">·</div> |
95 | <a·id="lab | 95 | <a·id="lab313"></a><h1·class="section">Chains·of·conversions</h1> |
96 | <div·class="paragraph">·</div> | 96 | <div·class="paragraph">·</div> |
97 | ·When·combining·successive·conversions,·we·have·the·following | 97 | ·When·combining·successive·conversions,·we·have·the·following |
98 | ····commutative·diagram: | 98 | ····commutative·diagram: |
99 | <pre> | 99 | <pre> |
100 | ······--->·Nat·---- | 100 | ······--->·Nat·---- |
Offset 238, 15 lines modified | Offset 238, 15 lines modified | ||
238 | <span·class="id"·title="keyword">Lemma</span>·<a·id="Zdivide_mod_minus"·class="idref"·href="#Zdivide_mod_minus"><span·class="id"·title="lemma">Zdivide_mod_minus</span></a>·<a·id="a:44"·class="idref"·href="#a:44"><span·class="id"·title="binder">a</span></a>·<a·id="b:45"·class="idref"·href="#b:45"><span·class="id"·title="binder">b</span></a>·<a·id="c:46"·class="idref"·href="#c:46"><span·class="id"·title="binder">c</span></a>:<br/> | 238 | <span·class="id"·title="keyword">Lemma</span>·<a·id="Zdivide_mod_minus"·class="idref"·href="#Zdivide_mod_minus"><span·class="id"·title="lemma">Zdivide_mod_minus</span></a>·<a·id="a:44"·class="idref"·href="#a:44"><span·class="id"·title="binder">a</span></a>·<a·id="b:45"·class="idref"·href="#b:45"><span·class="id"·title="binder">b</span></a>·<a·id="c:46"·class="idref"·href="#c:46"><span·class="id"·title="binder">c</span></a>:<br/> |
239 | 0·<a·class="idref"·href="Coq.ZArith.BinInt.html#bdb3edde5f841a282ce8fc1b00e3d211"><span·class="id"·title="notation"><=</span></a>·<a·class="idref"·href="Coq.ZArith.Znumtheory.html#c:46"><span·class="id"·title="variable">c</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#bdb3edde5f841a282ce8fc1b00e3d211"><span·class="id"·title="notation"><</span></a>·<a·class="idref"·href="Coq.ZArith.Znumtheory.html#b:45"><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>·<a·class="idref"·href="Coq.ZArith.BinInt.html#5cd21895b4d5f127eb2c0acb80e8d6fc"><span·class="id"·title="notation">(</span></a><a·class="idref"·href="Coq.ZArith.Znumtheory.html#b:45"><span·class="id"·title="variable">b</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#5cd21895b4d5f127eb2c0acb80e8d6fc"><span·class="id"·title="notation">|</span></a>·<a·class="idref"·href="Coq.ZArith.Znumtheory.html#a:44"><span·class="id"·title="variable">a</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#::Z_scope:x_'-'_x"><span·class="id"·title="notation">-</span></a>·<a·class="idref"·href="Coq.ZArith.Znumtheory.html#c:46"><span·class="id"·title="variable">c</span></a><a·class="idref"·href="Coq.ZArith.BinInt.html#5cd21895b4d5f127eb2c0acb80e8d6fc"><span·class="id"·title="notation">)</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.ZArith.Znumtheory.html#a:44"><span·class="id"·title="variable">a</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#::Z_scope:x_'mod'_x"><span·class="id"·title="notation">mod</span></a>·<a·class="idref"·href="Coq.ZArith.Znumtheory.html#b:45"><span·class="id"·title="variable">b</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·<a·class="idref"·href="Coq.ZArith.Znumtheory.html#c:46"><span·class="id"·title="variable">c</span></a>.<br/> | 239 | 0·<a·class="idref"·href="Coq.ZArith.BinInt.html#bdb3edde5f841a282ce8fc1b00e3d211"><span·class="id"·title="notation"><=</span></a>·<a·class="idref"·href="Coq.ZArith.Znumtheory.html#c:46"><span·class="id"·title="variable">c</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#bdb3edde5f841a282ce8fc1b00e3d211"><span·class="id"·title="notation"><</span></a>·<a·class="idref"·href="Coq.ZArith.Znumtheory.html#b:45"><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>·<a·class="idref"·href="Coq.ZArith.BinInt.html#5cd21895b4d5f127eb2c0acb80e8d6fc"><span·class="id"·title="notation">(</span></a><a·class="idref"·href="Coq.ZArith.Znumtheory.html#b:45"><span·class="id"·title="variable">b</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#5cd21895b4d5f127eb2c0acb80e8d6fc"><span·class="id"·title="notation">|</span></a>·<a·class="idref"·href="Coq.ZArith.Znumtheory.html#a:44"><span·class="id"·title="variable">a</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#::Z_scope:x_'-'_x"><span·class="id"·title="notation">-</span></a>·<a·class="idref"·href="Coq.ZArith.Znumtheory.html#c:46"><span·class="id"·title="variable">c</span></a><a·class="idref"·href="Coq.ZArith.BinInt.html#5cd21895b4d5f127eb2c0acb80e8d6fc"><span·class="id"·title="notation">)</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.ZArith.Znumtheory.html#a:44"><span·class="id"·title="variable">a</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#::Z_scope:x_'mod'_x"><span·class="id"·title="notation">mod</span></a>·<a·class="idref"·href="Coq.ZArith.Znumtheory.html#b:45"><span·class="id"·title="variable">b</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·<a·class="idref"·href="Coq.ZArith.Znumtheory.html#c:46"><span·class="id"·title="variable">c</span></a>.<br/> |
240 | <br/> | 240 | <br/> |
241 | </div> | 241 | </div> |
242 | <div·class="doc"> | 242 | <div·class="doc"> |
243 | <a·id="lab | 243 | <a·id="lab263"></a><h1·class="section">Greatest·common·divisor·(gcd).</h1> |
244 | <div·class="paragraph">·</div> | 244 | <div·class="paragraph">·</div> |
245 | ·There·is·no·unicity·of·the·gcd;·hence·we·define·the·predicate | 245 | ·There·is·no·unicity·of·the·gcd;·hence·we·define·the·predicate |
246 | ····<span·class="inlinecode"><span·class="id"·title="var">Zis_gcd</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">g</span></span>·expressing·that·<span·class="inlinecode"><span·class="id"·title="var">g</span></span>·is·a·gcd·of·<span·class="inlinecode"><span·class="id"·title="var">a</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">b</span></span>. | 246 | ····<span·class="inlinecode"><span·class="id"·title="var">Zis_gcd</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">g</span></span>·expressing·that·<span·class="inlinecode"><span·class="id"·title="var">g</span></span>·is·a·gcd·of·<span·class="inlinecode"><span·class="id"·title="var">a</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">b</span></span>. |
247 | ····(We·show·later·that·the·<span·class="inlinecode"><span·class="id"·title="var">gcd</span></span>·is·actually·unique·if·we·discard·its·sign.)· | 247 | ····(We·show·later·that·the·<span·class="inlinecode"><span·class="id"·title="var">gcd</span></span>·is·actually·unique·if·we·discard·its·sign.)· |
248 | </div> | 248 | </div> |
Offset 67, 30 lines modified | Offset 67, 30 lines modified | ||
67 | <br/> | 67 | <br/> |
68 | </div> | 68 | </div> |
69 | <div·class="doc"> | 69 | <div·class="doc"> |
70 | Properties·of·the·order·relations·on·binary·integers· | 70 | Properties·of·the·order·relations·on·binary·integers· |
71 | <div·class="paragraph">·</div> | 71 | <div·class="paragraph">·</div> |
72 | <a·id="lab | 72 | <a·id="lab294"></a><h1·class="section">Trichotomy</h1> |
73 | </div> | 73 | </div> |
74 | <div·class="code"> | 74 | <div·class="code"> |
75 | <br/> | 75 | <br/> |
76 | <span·class="id"·title="keyword">Theorem</span>·<a·id="Ztrichotomy_inf"·class="idref"·href="#Ztrichotomy_inf"><span·class="id"·title="lemma">Ztrichotomy_inf</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>·:·<a·class="idref"·href="Coq.Init.Specif.html#87727981cdc1579fef00b9d9c1d3b9da"><span·class="id"·title="notation">{</span></a><a·class="idref"·href="Coq.ZArith.Zorder.html#n:1"><span·class="id"·title="variable">n</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#::Z_scope:x_'<'_x"><span·class="id"·title="notation"><</span></a>·<a·class="idref"·href="Coq.ZArith.Zorder.html#m:2"><span·class="id"·title="variable">m</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.ZArith.Zorder.html#n:1"><span·class="id"·title="variable">n</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·<a·class="idref"·href="Coq.ZArith.Zorder.html#m:2"><span·class="id"·title="variable">m</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#53e8e3b7ca0342c8b99a777b3c5faf3a"><span·class="id"·title="notation">+</span></a>·<a·class="idref"·href="Coq.Init.Specif.html#53e8e3b7ca0342c8b99a777b3c5faf3a"><span·class="id"·title="notation">{</span></a><a·class="idref"·href="Coq.ZArith.Zorder.html#n:1"><span·class="id"·title="variable">n</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#::Z_scope:x_'>'_x"><span·class="id"·title="notation">></span></a>·<a·class="idref"·href="Coq.ZArith.Zorder.html#m:2"><span·class="id"·title="variable">m</span></a><a·class="idref"·href="Coq.Init.Specif.html#53e8e3b7ca0342c8b99a777b3c5faf3a"><span·class="id"·title="notation">}</span></a>.<br/> | 76 | <span·class="id"·title="keyword">Theorem</span>·<a·id="Ztrichotomy_inf"·class="idref"·href="#Ztrichotomy_inf"><span·class="id"·title="lemma">Ztrichotomy_inf</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>·:·<a·class="idref"·href="Coq.Init.Specif.html#87727981cdc1579fef00b9d9c1d3b9da"><span·class="id"·title="notation">{</span></a><a·class="idref"·href="Coq.ZArith.Zorder.html#n:1"><span·class="id"·title="variable">n</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#::Z_scope:x_'<'_x"><span·class="id"·title="notation"><</span></a>·<a·class="idref"·href="Coq.ZArith.Zorder.html#m:2"><span·class="id"·title="variable">m</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.ZArith.Zorder.html#n:1"><span·class="id"·title="variable">n</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·<a·class="idref"·href="Coq.ZArith.Zorder.html#m:2"><span·class="id"·title="variable">m</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#53e8e3b7ca0342c8b99a777b3c5faf3a"><span·class="id"·title="notation">+</span></a>·<a·class="idref"·href="Coq.Init.Specif.html#53e8e3b7ca0342c8b99a777b3c5faf3a"><span·class="id"·title="notation">{</span></a><a·class="idref"·href="Coq.ZArith.Zorder.html#n:1"><span·class="id"·title="variable">n</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#::Z_scope:x_'>'_x"><span·class="id"·title="notation">></span></a>·<a·class="idref"·href="Coq.ZArith.Zorder.html#m:2"><span·class="id"·title="variable">m</span></a><a·class="idref"·href="Coq.Init.Specif.html#53e8e3b7ca0342c8b99a777b3c5faf3a"><span·class="id"·title="notation">}</span></a>.<br/> |
77 | <br/> | 77 | <br/> |
78 | <span·class="id"·title="keyword">Theorem</span>·<a·id="Ztrichotomy"·class="idref"·href="#Ztrichotomy"><span·class="id"·title="lemma">Ztrichotomy</span></a>·<a·id="n:3"·class="idref"·href="#n:3"><span·class="id"·title="binder">n</span></a>·<a·id="m:4"·class="idref"·href="#m:4"><span·class="id"·title="binder">m</span></a>·:·<a·class="idref"·href="Coq.ZArith.Zorder.html#n:3"><span·class="id"·title="variable">n</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#::Z_scope:x_'<'_x"><span·class="id"·title="notation"><</span></a>·<a·class="idref"·href="Coq.ZArith.Zorder.html#m:4"><span·class="id"·title="variable">m</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#f031fe1957c4a4a8e217aa46af2b4e25"><span·class="id"·title="notation">\/</span></a>·<a·class="idref"·href="Coq.ZArith.Zorder.html#n:3"><span·class="id"·title="variable">n</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·<a·class="idref"·href="Coq.ZArith.Zorder.html#m:4"><span·class="id"·title="variable">m</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#f031fe1957c4a4a8e217aa46af2b4e25"><span·class="id"·title="notation">\/</span></a>·<a·class="idref"·href="Coq.ZArith.Zorder.html#n:3"><span·class="id"·title="variable">n</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#::Z_scope:x_'>'_x"><span·class="id"·title="notation">></span></a>·<a·class="idref"·href="Coq.ZArith.Zorder.html#m:4"><span·class="id"·title="variable">m</span></a>.<br/> | 78 | <span·class="id"·title="keyword">Theorem</span>·<a·id="Ztrichotomy"·class="idref"·href="#Ztrichotomy"><span·class="id"·title="lemma">Ztrichotomy</span></a>·<a·id="n:3"·class="idref"·href="#n:3"><span·class="id"·title="binder">n</span></a>·<a·id="m:4"·class="idref"·href="#m:4"><span·class="id"·title="binder">m</span></a>·:·<a·class="idref"·href="Coq.ZArith.Zorder.html#n:3"><span·class="id"·title="variable">n</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#::Z_scope:x_'<'_x"><span·class="id"·title="notation"><</span></a>·<a·class="idref"·href="Coq.ZArith.Zorder.html#m:4"><span·class="id"·title="variable">m</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#f031fe1957c4a4a8e217aa46af2b4e25"><span·class="id"·title="notation">\/</span></a>·<a·class="idref"·href="Coq.ZArith.Zorder.html#n:3"><span·class="id"·title="variable">n</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·<a·class="idref"·href="Coq.ZArith.Zorder.html#m:4"><span·class="id"·title="variable">m</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#f031fe1957c4a4a8e217aa46af2b4e25"><span·class="id"·title="notation">\/</span></a>·<a·class="idref"·href="Coq.ZArith.Zorder.html#n:3"><span·class="id"·title="variable">n</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#::Z_scope:x_'>'_x"><span·class="id"·title="notation">></span></a>·<a·class="idref"·href="Coq.ZArith.Zorder.html#m:4"><span·class="id"·title="variable">m</span></a>.<br/> |
79 | <br/> | 79 | <br/> |
80 | </div> | 80 | </div> |
81 | <div·class="doc"> | 81 | <div·class="doc"> |
82 | <a·id="lab | 82 | <a·id="lab295"></a><h1·class="section">Decidability·of·equality·and·order·on·Z</h1> |
83 | </div> | 83 | </div> |
84 | <div·class="code"> | 84 | <div·class="code"> |
85 | <br/> | 85 | <br/> |
86 | <span·class="id"·title="keyword">Notation</span>·<a·id="dec_eq"·class="idref"·href="#dec_eq"><span·class="id"·title="abbreviation">dec_eq</span></a>·:=·<a·class="idref"·href="Coq.ZArith.BinInt.html#Z.eq_decidable"><span·class="id"·title="lemma">Z.eq_decidable</span></a>·(<span·class="id"·title="var">only</span>·<span·class="id"·title="var">parsing</span>).<br/> | 86 | <span·class="id"·title="keyword">Notation</span>·<a·id="dec_eq"·class="idref"·href="#dec_eq"><span·class="id"·title="abbreviation">dec_eq</span></a>·:=·<a·class="idref"·href="Coq.ZArith.BinInt.html#Z.eq_decidable"><span·class="id"·title="lemma">Z.eq_decidable</span></a>·(<span·class="id"·title="var">only</span>·<span·class="id"·title="var">parsing</span>).<br/> |
87 | <span·class="id"·title="keyword">Notation</span>·<a·id="dec_Zle"·class="idref"·href="#dec_Zle"><span·class="id"·title="abbreviation">dec_Zle</span></a>·:=·<a·class="idref"·href="Coq.ZArith.BinInt.html#Z.le_decidable"><span·class="id"·title="lemma">Z.le_decidable</span></a>·(<span·class="id"·title="var">only</span>·<span·class="id"·title="var">parsing</span>).<br/> | 87 | <span·class="id"·title="keyword">Notation</span>·<a·id="dec_Zle"·class="idref"·href="#dec_Zle"><span·class="id"·title="abbreviation">dec_Zle</span></a>·:=·<a·class="idref"·href="Coq.ZArith.BinInt.html#Z.le_decidable"><span·class="id"·title="lemma">Z.le_decidable</span></a>·(<span·class="id"·title="var">only</span>·<span·class="id"·title="var">parsing</span>).<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.BinInt.html#"><span·class="id"·title="library">BinInt</span></a>·<a·class="idref"·href="Coq.setoid_ring.Ring_theory.html#"><span·class="id"·title="library">Ring_theory</span></a>.<br/> | 49 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.ZArith.BinInt.html#"><span·class="id"·title="library">BinInt</span></a>·<a·class="idref"·href="Coq.setoid_ring.Ring_theory.html#"><span·class="id"·title="library">Ring_theory</span></a>.<br/> |
50 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">Z_scope</span>.<br/> | 50 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">Z_scope</span>.<br/> |
51 | <br/> | 51 | <br/> |
52 | </div> | 52 | </div> |
53 | <div·class="doc"> | 53 | <div·class="doc"> |
54 | <a·id="lab | 54 | <a·id="lab218"></a><h1·class="section">Power·functions·over·<span·class="inlinecode"><span·class="id"·title="var">Z</span></span></h1> |
55 | <div·class="paragraph">·</div> | 55 | <div·class="paragraph">·</div> |
56 | ·Nota·:·this·file·is·mostly·deprecated.·The·definition·of·<span·class="inlinecode"><span·class="id"·title="var">Z.pow</span></span> | 56 | ·Nota·:·this·file·is·mostly·deprecated.·The·definition·of·<span·class="inlinecode"><span·class="id"·title="var">Z.pow</span></span> |
57 | ····and·its·usual·properties·are·now·provided·by·module·<span·class="inlinecode"><span·class="id"·title="var">BinInt.Z</span></span>.· | 57 | ····and·its·usual·properties·are·now·provided·by·module·<span·class="inlinecode"><span·class="id"·title="var">BinInt.Z</span></span>.· |
58 | </div> | 58 | </div> |
59 | <div·class="code"> | 59 | <div·class="code"> |
Offset 128, 15 lines modified | Offset 128, 15 lines modified | ||
128 | <span·class="id"·title="keyword">Lemma</span>·<a·id="Zpower2_Psize"·class="idref"·href="#Zpower2_Psize"><span·class="id"·title="lemma">Zpower2_Psize</span></a>·<a·id="n:25"·class="idref"·href="#n:25"><span·class="id"·title="binder">n</span></a>·<a·id="p:26"·class="idref"·href="#p:26"><span·class="id"·title="binder">p</span></a>·:<br/> | 128 | <span·class="id"·title="keyword">Lemma</span>·<a·id="Zpower2_Psize"·class="idref"·href="#Zpower2_Psize"><span·class="id"·title="lemma">Zpower2_Psize</span></a>·<a·id="n:25"·class="idref"·href="#n:25"><span·class="id"·title="binder">n</span></a>·<a·id="p:26"·class="idref"·href="#p:26"><span·class="id"·title="binder">p</span></a>·:<br/> |
129 | <a·class="idref"·href="Coq.Numbers.BinNums.html#Zpos"><span·class="id"·title="constructor">Zpos</span></a>·<a·class="idref"·href="Coq.ZArith.Zpow_facts.html#p:26"><span·class="id"·title="variable">p</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#::Z_scope:x_'<'_x"><span·class="id"·title="notation"><</span></a>·2<a·class="idref"·href="Coq.ZArith.BinInt.html#14ef112b66e341f773bd1e9d05816f43"><span·class="id"·title="notation">^(</span></a><a·class="idref"·href="Coq.ZArith.BinInt.html#Z.of_nat"><span·class="id"·title="definition">Z.of_nat</span></a>·<a·class="idref"·href="Coq.ZArith.Zpow_facts.html#n:25"><span·class="id"·title="variable">n</span></a><a·class="idref"·href="Coq.ZArith.BinInt.html#14ef112b66e341f773bd1e9d05816f43"><span·class="id"·title="notation">)</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.PArith.BinPos.html#Pos.size_nat"><span·class="id"·title="definition">Pos.size_nat</span></a>·<a·class="idref"·href="Coq.ZArith.Zpow_facts.html#p:26"><span·class="id"·title="variable">p</span></a>·<a·class="idref"·href="Coq.Init.Peano.html#cb53cf0ee22c036a03b4a9281c68b5a3"><span·class="id"·title="notation"><=</span></a>·<a·class="idref"·href="Coq.ZArith.Zpow_facts.html#n:25"><span·class="id"·title="variable">n</span></a>)%<span·class="id"·title="var">nat</span>.<br/> | 129 | <a·class="idref"·href="Coq.Numbers.BinNums.html#Zpos"><span·class="id"·title="constructor">Zpos</span></a>·<a·class="idref"·href="Coq.ZArith.Zpow_facts.html#p:26"><span·class="id"·title="variable">p</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#::Z_scope:x_'<'_x"><span·class="id"·title="notation"><</span></a>·2<a·class="idref"·href="Coq.ZArith.BinInt.html#14ef112b66e341f773bd1e9d05816f43"><span·class="id"·title="notation">^(</span></a><a·class="idref"·href="Coq.ZArith.BinInt.html#Z.of_nat"><span·class="id"·title="definition">Z.of_nat</span></a>·<a·class="idref"·href="Coq.ZArith.Zpow_facts.html#n:25"><span·class="id"·title="variable">n</span></a><a·class="idref"·href="Coq.ZArith.BinInt.html#14ef112b66e341f773bd1e9d05816f43"><span·class="id"·title="notation">)</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.PArith.BinPos.html#Pos.size_nat"><span·class="id"·title="definition">Pos.size_nat</span></a>·<a·class="idref"·href="Coq.ZArith.Zpow_facts.html#p:26"><span·class="id"·title="variable">p</span></a>·<a·class="idref"·href="Coq.Init.Peano.html#cb53cf0ee22c036a03b4a9281c68b5a3"><span·class="id"·title="notation"><=</span></a>·<a·class="idref"·href="Coq.ZArith.Zpow_facts.html#n:25"><span·class="id"·title="variable">n</span></a>)%<span·class="id"·title="var">nat</span>.<br/> |
130 | <br/> | 130 | <br/> |
131 | </div> | 131 | </div> |
132 | <div·class="doc"> | 132 | <div·class="doc"> |
133 | <a·id="lab | 133 | <a·id="lab284"></a><h1·class="section">Z.pow·and·modulo</h1> |
134 | </div> | 134 | </div> |
135 | <div·class="code"> | 135 | <div·class="code"> |
136 | <br/> | 136 | <br/> |
137 | <span·class="id"·title="keyword">Theorem</span>·<a·id="Zpower_mod"·class="idref"·href="#Zpower_mod"><span·class="id"·title="lemma">Zpower_mod</span></a>·<a·id="p:27"·class="idref"·href="#p:27"><span·class="id"·title="binder">p</span></a>·<a·id="q:28"·class="idref"·href="#q:28"><span·class="id"·title="binder">q</span></a>·<a·id="n:29"·class="idref"·href="#n:29"><span·class="id"·title="binder">n</span></a>·:<br/> | 137 | <span·class="id"·title="keyword">Theorem</span>·<a·id="Zpower_mod"·class="idref"·href="#Zpower_mod"><span·class="id"·title="lemma">Zpower_mod</span></a>·<a·id="p:27"·class="idref"·href="#p:27"><span·class="id"·title="binder">p</span></a>·<a·id="q:28"·class="idref"·href="#q:28"><span·class="id"·title="binder">q</span></a>·<a·id="n:29"·class="idref"·href="#n:29"><span·class="id"·title="binder">n</span></a>·:<br/> |
138 | 0·<a·class="idref"·href="Coq.ZArith.BinInt.html#::Z_scope:x_'<'_x"><span·class="id"·title="notation"><</span></a>·<a·class="idref"·href="Coq.ZArith.Zpow_facts.html#n:29"><span·class="id"·title="variable">n</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.ZArith.BinInt.html#::Z_scope:x_'mod'_x"><span·class="id"·title="notation">(</span></a><a·class="idref"·href="Coq.ZArith.Zpow_facts.html#p:27"><span·class="id"·title="variable">p</span></a><a·class="idref"·href="Coq.ZArith.BinInt.html#14ef112b66e341f773bd1e9d05816f43"><span·class="id"·title="notation">^</span></a><a·class="idref"·href="Coq.ZArith.Zpow_facts.html#q:28"><span·class="id"·title="variable">q</span></a><a·class="idref"·href="Coq.ZArith.BinInt.html#::Z_scope:x_'mod'_x"><span·class="id"·title="notation">)</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#::Z_scope:x_'mod'_x"><span·class="id"·title="notation">mod</span></a>·<a·class="idref"·href="Coq.ZArith.Zpow_facts.html#n:29"><span·class="id"·title="variable">n</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#::Z_scope:x_'mod'_x"><span·class="id"·title="notation">(</span></a><a·class="idref"·href="Coq.ZArith.BinInt.html#14ef112b66e341f773bd1e9d05816f43"><span·class="id"·title="notation">(</span></a><a·class="idref"·href="Coq.ZArith.Zpow_facts.html#p:27"><span·class="id"·title="variable">p</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#::Z_scope:x_'mod'_x"><span·class="id"·title="notation">mod</span></a>·<a·class="idref"·href="Coq.ZArith.Zpow_facts.html#n:29"><span·class="id"·title="variable">n</span></a><a·class="idref"·href="Coq.ZArith.BinInt.html#14ef112b66e341f773bd1e9d05816f43"><span·class="id"·title="notation">)^</span></a><a·class="idref"·href="Coq.ZArith.Zpow_facts.html#q:28"><span·class="id"·title="variable">q</span></a><a·class="idref"·href="Coq.ZArith.BinInt.html#::Z_scope:x_'mod'_x"><span·class="id"·title="notation">)</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#::Z_scope:x_'mod'_x"><span·class="id"·title="notation">mod</span></a>·<a·class="idref"·href="Coq.ZArith.Zpow_facts.html#n:29"><span·class="id"·title="variable">n</span></a>.<br/> | 138 | 0·<a·class="idref"·href="Coq.ZArith.BinInt.html#::Z_scope:x_'<'_x"><span·class="id"·title="notation"><</span></a>·<a·class="idref"·href="Coq.ZArith.Zpow_facts.html#n:29"><span·class="id"·title="variable">n</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.ZArith.BinInt.html#::Z_scope:x_'mod'_x"><span·class="id"·title="notation">(</span></a><a·class="idref"·href="Coq.ZArith.Zpow_facts.html#p:27"><span·class="id"·title="variable">p</span></a><a·class="idref"·href="Coq.ZArith.BinInt.html#14ef112b66e341f773bd1e9d05816f43"><span·class="id"·title="notation">^</span></a><a·class="idref"·href="Coq.ZArith.Zpow_facts.html#q:28"><span·class="id"·title="variable">q</span></a><a·class="idref"·href="Coq.ZArith.BinInt.html#::Z_scope:x_'mod'_x"><span·class="id"·title="notation">)</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#::Z_scope:x_'mod'_x"><span·class="id"·title="notation">mod</span></a>·<a·class="idref"·href="Coq.ZArith.Zpow_facts.html#n:29"><span·class="id"·title="variable">n</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#::Z_scope:x_'mod'_x"><span·class="id"·title="notation">(</span></a><a·class="idref"·href="Coq.ZArith.BinInt.html#14ef112b66e341f773bd1e9d05816f43"><span·class="id"·title="notation">(</span></a><a·class="idref"·href="Coq.ZArith.Zpow_facts.html#p:27"><span·class="id"·title="variable">p</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#::Z_scope:x_'mod'_x"><span·class="id"·title="notation">mod</span></a>·<a·class="idref"·href="Coq.ZArith.Zpow_facts.html#n:29"><span·class="id"·title="variable">n</span></a><a·class="idref"·href="Coq.ZArith.BinInt.html#14ef112b66e341f773bd1e9d05816f43"><span·class="id"·title="notation">)^</span></a><a·class="idref"·href="Coq.ZArith.Zpow_facts.html#q:28"><span·class="id"·title="variable">q</span></a><a·class="idref"·href="Coq.ZArith.BinInt.html#::Z_scope:x_'mod'_x"><span·class="id"·title="notation">)</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#::Z_scope:x_'mod'_x"><span·class="id"·title="notation">mod</span></a>·<a·class="idref"·href="Coq.ZArith.Zpow_facts.html#n:29"><span·class="id"·title="variable">n</span></a>.<br/> |
Offset 50, 15 lines modified | Offset 50, 15 lines modified | ||
50 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Export</span>·<a·class="idref"·href="Coq.ZArith.Zpow_def.html#"><span·class="id"·title="library">Zpow_def</span></a>.<br/> | 50 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Export</span>·<a·class="idref"·href="Coq.ZArith.Zpow_def.html#"><span·class="id"·title="library">Zpow_def</span></a>.<br/> |
51 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">Z_scope</span>.<br/> | 51 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">Z_scope</span>.<br/> |
52 | <br/> | 52 | <br/> |
53 | </div> | 53 | </div> |
54 | <div·class="doc"> | 54 | <div·class="doc"> |
55 | <a·id="lab | 55 | <a·id="lab310"></a><h1·class="section">Power·functions·over·<span·class="inlinecode"><span·class="id"·title="var">Z</span></span></h1> |
56 | <div·class="paragraph">·</div> | 56 | <div·class="paragraph">·</div> |
57 | ·Nota·:·this·file·is·mostly·deprecated.·The·definition·of·<span·class="inlinecode"><span·class="id"·title="var">Z.pow</span></span> | 57 | ·Nota·:·this·file·is·mostly·deprecated.·The·definition·of·<span·class="inlinecode"><span·class="id"·title="var">Z.pow</span></span> |
58 | ····and·its·usual·properties·are·now·provided·by·module·<span·class="inlinecode"><span·class="id"·title="var">BinInt.Z</span></span>. | 58 | ····and·its·usual·properties·are·now·provided·by·module·<span·class="inlinecode"><span·class="id"·title="var">BinInt.Z</span></span>. |
59 | ····Powers·of·2·are·also·available·there·(see·<span·class="inlinecode"><span·class="id"·title="var">Z.shiftl</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">Z.shiftr</span></span>). | 59 | ····Powers·of·2·are·also·available·there·(see·<span·class="inlinecode"><span·class="id"·title="var">Z.shiftl</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">Z.shiftr</span></span>). |
60 | ····Only·remain·here: | 60 | ····Only·remain·here: |
Offset 149, 15 lines modified | Offset 149, 15 lines modified | ||
149 | <br/> | 149 | <br/> |
150 | <span·class="id"·title="keyword">Lemma</span>·<a·id="Z_rem_mult"·class="idref"·href="#Z_rem_mult"><span·class="id"·title="lemma">Z_rem_mult</span></a>·<a·id="a:6"·class="idref"·href="#a:6"><span·class="id"·title="binder">a</span></a>·<a·id="b:7"·class="idref"·href="#b:7"><span·class="id"·title="binder">b</span></a>·:·<a·class="idref"·href="Coq.ZArith.BinInt.html#Z.rem"><span·class="id"·title="definition">Z.rem</span></a>·(<a·class="idref"·href="Coq.ZArith.Zquot.html#a:6"><span·class="id"·title="variable">a</span></a><a·class="idref"·href="Coq.ZArith.BinInt.html#d3ea1afb7d81263dc23c4eb0da2a3c4e"><span·class="id"·title="notation">*</span></a><a·class="idref"·href="Coq.ZArith.Zquot.html#b:7"><span·class="id"·title="variable">b</span></a>)·<a·class="idref"·href="Coq.ZArith.Zquot.html#b:7"><span·class="id"·title="variable">b</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·0.<br/> | 150 | <span·class="id"·title="keyword">Lemma</span>·<a·id="Z_rem_mult"·class="idref"·href="#Z_rem_mult"><span·class="id"·title="lemma">Z_rem_mult</span></a>·<a·id="a:6"·class="idref"·href="#a:6"><span·class="id"·title="binder">a</span></a>·<a·id="b:7"·class="idref"·href="#b:7"><span·class="id"·title="binder">b</span></a>·:·<a·class="idref"·href="Coq.ZArith.BinInt.html#Z.rem"><span·class="id"·title="definition">Z.rem</span></a>·(<a·class="idref"·href="Coq.ZArith.Zquot.html#a:6"><span·class="id"·title="variable">a</span></a><a·class="idref"·href="Coq.ZArith.BinInt.html#d3ea1afb7d81263dc23c4eb0da2a3c4e"><span·class="id"·title="notation">*</span></a><a·class="idref"·href="Coq.ZArith.Zquot.html#b:7"><span·class="id"·title="variable">b</span></a>)·<a·class="idref"·href="Coq.ZArith.Zquot.html#b:7"><span·class="id"·title="variable">b</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·0.<br/> |
151 | · | 151 | · |
152 | <br/> | 152 | <br/> |
153 | </div> | 153 | </div> |
154 | <div·class="doc"> | 154 | <div·class="doc"> |
155 | <a·id="lab | 155 | <a·id="lab268"></a><h1·class="section">Division·and·Opposite</h1> |
156 | </div> | 156 | </div> |
157 | <div·class="code"> | 157 | <div·class="code"> |
158 | <br/> | 158 | <br/> |
159 | <br/> | 159 | <br/> |
Offset 64, 15 lines modified | Offset 64, 15 lines modified | ||
64 | <br/> | 64 | <br/> |
65 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">Z_scope</span>.<br/> | 65 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">Z_scope</span>.<br/> |
66 | <br/> | 66 | <br/> |
67 | </div> | 67 | </div> |
68 | <div·class="doc"> | 68 | <div·class="doc"> |
69 | <a·id="lab | 69 | <a·id="lab215"></a><h1·class="section">Moving·terms·from·one·side·to·the·other·of·an·inequality</h1> |
70 | </div> | 70 | </div> |
71 | <div·class="code"> | 71 | <div·class="code"> |
72 | <br/> | 72 | <br/> |
73 | <span·class="id"·title="keyword">Theorem</span>·<a·id="Zne_left"·class="idref"·href="#Zne_left"><span·class="id"·title="lemma">Zne_left</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>·:·<a·class="idref"·href="Coq.ZArith.BinInt.html#Zne"><span·class="id"·title="definition">Zne</span></a>·<a·class="idref"·href="Coq.ZArith.auxiliary.html#n:1"><span·class="id"·title="variable">n</span></a>·<a·class="idref"·href="Coq.ZArith.auxiliary.html#m:2"><span·class="id"·title="variable">m</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.ZArith.BinInt.html#Zne"><span·class="id"·title="definition">Zne</span></a>·(<a·class="idref"·href="Coq.ZArith.auxiliary.html#n:1"><span·class="id"·title="variable">n</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#46584eddd5fdb16176a10a2843177d3a"><span·class="id"·title="notation">+</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#::Z_scope:'-'_x"><span·class="id"·title="notation">-</span></a>·<a·class="idref"·href="Coq.ZArith.auxiliary.html#m:2"><span·class="id"·title="variable">m</span></a>)·0.<br/> | 73 | <span·class="id"·title="keyword">Theorem</span>·<a·id="Zne_left"·class="idref"·href="#Zne_left"><span·class="id"·title="lemma">Zne_left</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>·:·<a·class="idref"·href="Coq.ZArith.BinInt.html#Zne"><span·class="id"·title="definition">Zne</span></a>·<a·class="idref"·href="Coq.ZArith.auxiliary.html#n:1"><span·class="id"·title="variable">n</span></a>·<a·class="idref"·href="Coq.ZArith.auxiliary.html#m:2"><span·class="id"·title="variable">m</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.ZArith.BinInt.html#Zne"><span·class="id"·title="definition">Zne</span></a>·(<a·class="idref"·href="Coq.ZArith.auxiliary.html#n:1"><span·class="id"·title="variable">n</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#46584eddd5fdb16176a10a2843177d3a"><span·class="id"·title="notation">+</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#::Z_scope:'-'_x"><span·class="id"·title="notation">-</span></a>·<a·class="idref"·href="Coq.ZArith.auxiliary.html#m:2"><span·class="id"·title="variable">m</span></a>)·0.<br/> |
Offset 140, 15 lines modified | Offset 140, 15 lines modified | ||
140 | <br/> | 140 | <br/> |
141 | <span·class="id"·title="keyword">Section</span>·<a·id="Definitions"·class="idref"·href="#Definitions"><span·class="id"·title="section">Definitions</span></a>.<br/> | 141 | <span·class="id"·title="keyword">Section</span>·<a·id="Definitions"·class="idref"·href="#Definitions"><span·class="id"·title="section">Definitions</span></a>.<br/> |
142 | <br/> | 142 | <br/> |
143 | </div> | 143 | </div> |
144 | <div·class="doc"> | 144 | <div·class="doc"> |
145 | <a·id="lab | 145 | <a·id="lab1210"></a><h1·class="section">Global,·inductive·definitions.</h1> |
146 | <div·class="paragraph">·</div> | 146 | <div·class="paragraph">·</div> |
147 | ·A·Horner·polynomial·is·either·a·constant,·or·a·product·P·×·(i·+·Q),·where·i· | 147 | ·A·Horner·polynomial·is·either·a·constant,·or·a·product·P·×·(i·+·Q),·where·i· |
148 | ··is·a·variable.· | 148 | ··is·a·variable.· |
149 | </div> | 149 | </div> |
150 | <div·class="code"> | 150 | <div·class="code"> |
Offset 58, 19 lines modified | Offset 58, 19 lines modified | ||
58 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Arith.Arith.html#"><span·class="id"·title="library">Arith</span></a>.<br/> | 58 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Arith.Arith.html#"><span·class="id"·title="library">Arith</span></a>.<br/> |
59 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.extraction.ExtrHaskellNatNum.html#"><span·class="id"·title="library">ExtrHaskellNatNum</span></a>.<br/> | 59 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.extraction.ExtrHaskellNatNum.html#"><span·class="id"·title="library">ExtrHaskellNatNum</span></a>.<br/> |
60 | <br/> | 60 | <br/> |
61 | </div> | 61 | </div> |
62 | <div·class="doc"> | 62 | <div·class="doc"> |
63 | <a·id="lab | 63 | <a·id="lab1281"></a><h1·class="section">Disclaimer:·trying·to·obtain·efficient·certified·programs</h1> |
64 | <a·id="lab | 64 | <a·id="lab1282"></a><h1·class="section">by·extracting·<span·class="inlinecode"><span·class="id"·title="var">nat</span></span>·into·<span·class="inlinecode"><span·class="id"·title="var">Int</span></span>·is·definitively·*not*·a·good·idea.</h1> |
65 | <a·id="lab | 65 | <a·id="lab1283"></a><h1·class="section">See·comments·in·<span·class="inlinecode"><span·class="id"·title="var">ExtrOcamlNatInt.v</span></span>.</h1> |
66 | · | 66 | · |
67 | </div> | 67 | </div> |
68 | <div·class="code"> | 68 | <div·class="code"> |
69 | <br/> | 69 | <br/> |
70 | <span·class="id"·title="keyword">Extract</span>·<span·class="id"·title="keyword">Inductive</span>·<a·class="idref"·href="Coq.Init.Datatypes.html#nat"><span·class="id"·title="inductive">nat</span></a>·=>·"Prelude.Int"·[·"0"·"Prelude.succ"·]<br/> | 70 | <span·class="id"·title="keyword">Extract</span>·<span·class="id"·title="keyword">Inductive</span>·<a·class="idref"·href="Coq.Init.Datatypes.html#nat"><span·class="id"·title="inductive">nat</span></a>·=>·"Prelude.Int"·[·"0"·"Prelude.succ"·]<br/> |
Offset 58, 19 lines modified | Offset 58, 19 lines modified | ||
58 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Arith.Arith.html#"><span·class="id"·title="library">Arith</span></a>.<br/> | 58 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Arith.Arith.html#"><span·class="id"·title="library">Arith</span></a>.<br/> |
59 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.extraction.ExtrHaskellNatNum.html#"><span·class="id"·title="library">ExtrHaskellNatNum</span></a>.<br/> | 59 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.extraction.ExtrHaskellNatNum.html#"><span·class="id"·title="library">ExtrHaskellNatNum</span></a>.<br/> |
60 | <br/> | 60 | <br/> |
61 | </div> | 61 | </div> |
62 | <div·class="doc"> | 62 | <div·class="doc"> |
63 | <a·id="lab | 63 | <a·id="lab1267"></a><h1·class="section">Disclaimer:·trying·to·obtain·efficient·certified·programs</h1> |
64 | <a·id="lab | 64 | <a·id="lab1268"></a><h1·class="section">by·extracting·<span·class="inlinecode"><span·class="id"·title="var">nat</span></span>·into·<span·class="inlinecode"><span·class="id"·title="var">Integer</span></span>·isn't·necessarily·a·good·idea.</h1> |
65 | <a·id="lab | 65 | <a·id="lab1269"></a><h1·class="section">See·comments·in·<span·class="inlinecode"><span·class="id"·title="var">ExtrOcamlNatInt.v</span></span>.</h1> |
66 | </div> | 66 | </div> |
67 | <div·class="code"> | 67 | <div·class="code"> |
68 | <br/> | 68 | <br/> |
69 | <span·class="id"·title="keyword">Extract</span>·<span·class="id"·title="keyword">Inductive</span>·<a·class="idref"·href="Coq.Init.Datatypes.html#nat"><span·class="id"·title="inductive">nat</span></a>·=>·"Prelude.Integer"·[·"0"·"Prelude.succ"·]<br/> | 69 | <span·class="id"·title="keyword">Extract</span>·<span·class="id"·title="keyword">Inductive</span>·<a·class="idref"·href="Coq.Init.Datatypes.html#nat"><span·class="id"·title="inductive">nat</span></a>·=>·"Prelude.Integer"·[·"0"·"Prelude.succ"·]<br/> |
Offset 43, 23 lines modified | Offset 43, 23 lines modified | ||
43 | <h1·class="libtitle">Library·Coq.extraction.ExtrHaskellNatNum</h1> | 43 | <h1·class="libtitle">Library·Coq.extraction.ExtrHaskellNatNum</h1> |
44 | <div·class="code"> | 44 | <div·class="code"> |
45 | </div> | 45 | </div> |
46 | <div·class="doc"> | 46 | <div·class="doc"> |
47 | <a·id="lab | 47 | <a·id="lab1284"></a><h1·class="section">Efficient·(but·uncertified)·extraction·of·usual·<span·class="inlinecode"><span·class="id"·title="var">nat</span></span>·functions</h1> |
48 | <a·id="lab | 48 | <a·id="lab1285"></a><h1·class="section">into·equivalent·versions·in·Haskell's·Prelude·that·are·defined</h1> |
49 | <a·id="lab | 49 | <a·id="lab1286"></a><h1·class="section">for·any·<span·class="inlinecode"><span·class="id"·title="var">Num</span></span>·typeclass·instances.··Useful·in·combination·with</h1> |
50 | <a·id="lab | 50 | <a·id="lab1287"></a><h1·class="section"><span·class="inlinecode"><span·class="id"·title="keyword">Extract</span></span>·<span·class="inlinecode"><span·class="id"·title="keyword">Inductive</span></span>·<span·class="inlinecode"><span·class="id"·title="var">nat</span></span>·that·maps·<span·class="inlinecode"><span·class="id"·title="var">nat</span></span>·onto·a·Haskell·type·that</h1> |
51 | <a·id="lab | 51 | <a·id="lab1288"></a><h1·class="section">implements·<span·class="inlinecode"><span·class="id"·title="var">Num</span></span>.</h1> |
52 | · | 52 | · |
53 | </div> | 53 | </div> |
54 | <div·class="code"> | 54 | <div·class="code"> |
55 | <br/> | 55 | <br/> |
56 | <span·class="id"·title="keyword">Require</span>·<a·class="idref"·href="Coq.extraction.Extraction.html#"><span·class="id"·title="library">Coq.extraction.Extraction</span></a>.<br/> | 56 | <span·class="id"·title="keyword">Require</span>·<a·class="idref"·href="Coq.extraction.Extraction.html#"><span·class="id"·title="library">Coq.extraction.Extraction</span></a>.<br/> |
Offset 43, 15 lines modified | Offset 43, 15 lines modified | ||
43 | <h1·class="libtitle">Library·Coq.extraction.ExtrHaskellString</h1> | 43 | <h1·class="libtitle">Library·Coq.extraction.ExtrHaskellString</h1> |
44 | <div·class="code"> | 44 | <div·class="code"> |
45 | </div> | 45 | </div> |
46 | <div·class="doc"> | 46 | <div·class="doc"> |
47 | <a·id="lab | 47 | <a·id="lab1270"></a><h1·class="section">Special·handling·of·ascii·and·strings·for·extraction·to·Haskell.</h1> |
48 | · | 48 | · |
49 | </div> | 49 | </div> |
50 | <div·class="code"> | 50 | <div·class="code"> |
51 | <br/> | 51 | <br/> |
52 | <span·class="id"·title="keyword">Require</span>·<a·class="idref"·href="Coq.extraction.Extraction.html#"><span·class="id"·title="library">Coq.extraction.Extraction</span></a>.<br/> | 52 | <span·class="id"·title="keyword">Require</span>·<a·class="idref"·href="Coq.extraction.Extraction.html#"><span·class="id"·title="library">Coq.extraction.Extraction</span></a>.<br/> |
Offset 58, 19 lines modified | Offset 58, 19 lines modified | ||
58 | <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>.<br/> | 58 | <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>.<br/> |
59 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.extraction.ExtrHaskellZNum.html#"><span·class="id"·title="library">ExtrHaskellZNum</span></a>.<br/> | 59 | <span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.extraction.ExtrHaskellZNum.html#"><span·class="id"·title="library">ExtrHaskellZNum</span></a>.<br/> |
60 | <br/> | 60 | <br/> |
61 | </div> | 61 | </div> |
62 | <div·class="doc"> | 62 | <div·class="doc"> |
63 | <a·id="lab | 63 | <a·id="lab1289"></a><h1·class="section">Disclaimer:·trying·to·obtain·efficient·certified·programs</h1> |
64 | <a·id="lab | 64 | <a·id="lab1290"></a><h1·class="section">by·extracting·<span·class="inlinecode"><span·class="id"·title="var">Z</span></span>·into·<span·class="inlinecode"><span·class="id"·title="var">Int</span></span>·is·definitively·*not*·a·good·idea.</h1> |
65 | <a·id="lab | 65 | <a·id="lab1291"></a><h1·class="section">See·comments·in·<span·class="inlinecode"><span·class="id"·title="var">ExtrOcamlNatInt.v</span></span>.</h1> |
66 | · | 66 | · |
67 | </div> | 67 | </div> |
68 | <div·class="code"> | 68 | <div·class="code"> |
69 | <br/> | 69 | <br/> |
70 | <span·class="id"·title="keyword">Extract</span>·<span·class="id"·title="keyword">Inductive</span>·<a·class="idref"·href="Coq.Numbers.BinNums.html#positive"><span·class="id"·title="inductive">positive</span></a>·=>·"Prelude.Int"·[<br/> | 70 | <span·class="id"·title="keyword">Extract</span>·<span·class="id"·title="keyword">Inductive</span>·<a·class="idref"·href="Coq.Numbers.BinNums.html#positive"><span·class="id"·title="inductive">positive</span></a>·=>·"Prelude.Int"·[<br/> |
Offset 43, 23 lines modified | Offset 43, 23 lines modified | ||
43 | <h1·class="libtitle">Library·Coq.extraction.ExtrHaskellZNum</h1> | 43 | <h1·class="libtitle">Library·Coq.extraction.ExtrHaskellZNum</h1> |
44 | <div·class="code"> | 44 | <div·class="code"> |
45 | </div> | 45 | </div> |
46 | <div·class="doc"> | 46 | <div·class="doc"> |
47 | <a·id="lab | 47 | <a·id="lab1276"></a><h1·class="section">Efficient·(but·uncertified)·extraction·of·usual·<span·class="inlinecode"><span·class="id"·title="var">Z</span></span>·functions</h1> |
48 | <a·id="lab | 48 | <a·id="lab1277"></a><h1·class="section">into·equivalent·versions·in·Haskell's·Prelude·that·are·defined</h1> |
49 | <a·id="lab | 49 | <a·id="lab1278"></a><h1·class="section">for·any·<span·class="inlinecode"><span·class="id"·title="var">Num</span></span>·typeclass·instances.··Useful·in·combination·with</h1> |
50 | <a·id="lab | 50 | <a·id="lab1279"></a><h1·class="section"><span·class="inlinecode"><span·class="id"·title="keyword">Extract</span></span>·<span·class="inlinecode"><span·class="id"·title="keyword">Inductive</span></span>·<span·class="inlinecode"><span·class="id"·title="var">Z</span></span>·that·maps·<span·class="inlinecode"><span·class="id"·title="var">Z</span></span>·onto·a·Haskell·type·that</h1> |
51 | <a·id="lab | 51 | <a·id="lab1280"></a><h1·class="section">implements·<span·class="inlinecode"><span·class="id"·title="var">Num</span></span>.</h1> |
52 | · | 52 | · |
53 | </div> | 53 | </div> |
54 | <div·class="code"> | 54 | <div·class="code"> |
55 | <br/> | 55 | <br/> |
56 | <span·class="id"·title="keyword">Require</span>·<a·class="idref"·href="Coq.extraction.Extraction.html#"><span·class="id"·title="library">Coq.extraction.Extraction</span></a>.<br/> | 56 | <span·class="id"·title="keyword">Require</span>·<a·class="idref"·href="Coq.extraction.Extraction.html#"><span·class="id"·title="library">Coq.extraction.Extraction</span></a>.<br/> |
Offset 51, 15 lines modified | Offset 51, 15 lines modified | ||
51 | <br/> | 51 | <br/> |
52 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">Z_scope</span>.<br/> | 52 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">Z_scope</span>.<br/> |
53 | <br/> | 53 | <br/> |
54 | </div> | 54 | </div> |
55 | <div·class="doc"> | 55 | <div·class="doc"> |
56 | <a·id="lab | 56 | <a·id="lab518"></a><h1·class="section"><span·class="inlinecode"><span·class="id"·title="var">Z.div_mod_to_equations</span></span>,·<span·class="inlinecode"><span·class="id"·title="var">Z.quot_rem_to_equations</span></span>,·<span·class="inlinecode"><span·class="id"·title="var">Z.to_euclidean_division_equations</span></span>:</h1> |
57 | ·····the·tactics·for·preprocessing·<span·class="inlinecode"><span·class="id"·title="var">Z.div</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">Z.modulo</span></span>,·<span·class="inlinecode"><span·class="id"·title="var">Z.quot</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">Z.rem</span></span>· | 57 | ·····the·tactics·for·preprocessing·<span·class="inlinecode"><span·class="id"·title="var">Z.div</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">Z.modulo</span></span>,·<span·class="inlinecode"><span·class="id"·title="var">Z.quot</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">Z.rem</span></span>· |
58 | <div·class="paragraph">·</div> | 58 | <div·class="paragraph">·</div> |
59 | ·These·tactics·use·the·complete·specification·of·<span·class="inlinecode"><span·class="id"·title="var">Z.div</span></span>·and | 59 | ·These·tactics·use·the·complete·specification·of·<span·class="inlinecode"><span·class="id"·title="var">Z.div</span></span>·and |
60 | ····<span·class="inlinecode"><span·class="id"·title="var">Z.modulo</span></span>·(<span·class="inlinecode"><span·class="id"·title="var">Z.quot</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">Z.rem</span></span>,·respectively)·to·remove·these | 60 | ····<span·class="inlinecode"><span·class="id"·title="var">Z.modulo</span></span>·(<span·class="inlinecode"><span·class="id"·title="var">Z.quot</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">Z.rem</span></span>,·respectively)·to·remove·these |
61 | ····functions·from·the·goal·without·losing·information.··The | 61 | ····functions·from·the·goal·without·losing·information.··The |
Offset 6430, 19 lines modified | Offset 6430, 19 lines modified | ||
000191d0:·2f3e·0a3c·6120·6872·6566·3d22·436f·712e··/>.<a·href="Coq. | 000191d0:·2f3e·0a3c·6120·6872·6566·3d22·436f·712e··/>.<a·href="Coq. | ||
000191e0:·496e·6974·2e42·7974·652e·6874·6d6c·2362··Init.Byte.html#b | 000191e0:·496e·6974·2e42·7974·652e·6874·6d6c·2362··Init.Byte.html#b | ||
000191f0:·7974·6522·3e62·7974·653c·2f61·3e20·5b69··yte">byte</a>·[i | 000191f0:·7974·6522·3e62·7974·653c·2f61·3e20·5b69··yte">byte</a>·[i | ||
00019200:·6e64·7563·7469·7665·2c20·696e·203c·6120··nductive,·in·<a· | 00019200:·6e64·7563·7469·7665·2c20·696e·203c·6120··nductive,·in·<a· | ||
00019210:·6872·6566·3d22·436f·712e·496e·6974·2e42··href="Coq.Init.B | 00019210:·6872·6566·3d22·436f·712e·496e·6974·2e42··href="Coq.Init.B | ||
00019220:·7974·652e·6874·6d6c·223e·436f·712e·496e··yte.html">Coq.In | 00019220:·7974·652e·6874·6d6c·223e·436f·712e·496e··yte.html">Coq.In | ||
00019230:·6974·2e42·7974·653c·2f61·3e5d·3c62·722f··it.Byte</a>]<br/ | 00019230:·6974·2e42·7974·653c·2f61·3e5d·3c62·722f··it.Byte</a>]<br/ | ||
00019240:·3e0a·3c61·2068·7265·663d·2243·6f71·2e | 00019240:·3e0a·3c61·2068·7265·663d·2243·6f71·2e49··>.<a·href="Coq.I | ||
00019250:·7472·696e·6773·2e42·7974·652e·6874·6d6c··trings.Byte.html | |||
00019260:·223e·4279·7465·3c2f·613e·205b·6c69·6272··">Byte</a>·[libr | |||
00019270:·6172·795d·3c62·722f·3e0a·3c61·2068·7265··ary]<br/>.<a·hre | |||
000192 | 00019250:·6e69·742e·4279·7465·2e68·746d·6c22·3e42··nit.Byte.html">B | ||
00019260:·7974·653c·2f61·3e20·5b6c·6962·7261·7279··yte</a>·[library | |||
00019270:·5d3c·6272·2f3e·0a3c·6120·6872·6566·3d22··]<br/>.<a·href=" | |||
00019280:·436f·712e·5374·7269·6e67·732e·4279·7465··Coq.Strings.Byte | |||
00019290:·2e68·746d·6c22·3e42·7974·653c·2f61·3e20··.html">Byte</a>· | 00019290:·2e68·746d·6c22·3e42·7974·653c·2f61·3e20··.html">Byte</a>· | ||
000192a0:·5b6c·6962·7261·7279·5d3c·6272·2f3e·0a3c··[library]<br/>.< | 000192a0:·5b6c·6962·7261·7279·5d3c·6272·2f3e·0a3c··[library]<br/>.< | ||
000192b0:·6120·6872·6566·3d22·436f·712e·5374·7269··a·href="Coq.Stri | 000192b0:·6120·6872·6566·3d22·436f·712e·5374·7269··a·href="Coq.Stri | ||
000192c0:·6e67·732e·4279·7465·5665·6374·6f72·2e68··ngs.ByteVector.h | 000192c0:·6e67·732e·4279·7465·5665·6374·6f72·2e68··ngs.ByteVector.h | ||
000192d0:·746d·6c23·4279·7465·4e69·6c22·3e42·7974··tml#ByteNil">Byt | 000192d0:·746d·6c23·4279·7465·4e69·6c22·3e42·7974··tml#ByteNil">Byt | ||
000192e0:·654e·696c·3c2f·613e·205b·6465·6669·6e69··eNil</a>·[defini | 000192e0:·654e·696c·3c2f·613e·205b·6465·6669·6e69··eNil</a>·[defini | ||
000192f0:·7469·6f6e·2c20·696e·203c·6120·6872·6566··tion,·in·<a·href | 000192f0:·7469·6f6e·2c20·696e·203c·6120·6872·6566··tion,·in·<a·href |
Offset 558, 16 lines modified | Offset 558, 16 lines modified | ||
558 | <hr/><a·id="global_T"></a><h2>T·</h2> | 558 | <hr/><a·id="global_T"></a><h2>T·</h2> |
559 | <a·href="Coq.Numbers.Cyclic.ZModulo.ZModulo.html#t">t</a>·[definition,·in·<a·href="Coq.Numbers.Cyclic.ZModulo.ZModulo.html">Coq.Numbers.Cyclic.ZModulo.ZModulo</a>]<br/> | 559 | <a·href="Coq.Numbers.Cyclic.ZModulo.ZModulo.html#t">t</a>·[definition,·in·<a·href="Coq.Numbers.Cyclic.ZModulo.ZModulo.html">Coq.Numbers.Cyclic.ZModulo.ZModulo</a>]<br/> |
560 | <a·href="Coq.Init.Nat.html#t">t</a>·[definition,·in·<a·href="Coq.Init.Nat.html">Coq.Init.Nat</a>]<br/> | 560 | <a·href="Coq.Init.Nat.html#t">t</a>·[definition,·in·<a·href="Coq.Init.Nat.html">Coq.Init.Nat</a>]<br/> |
561 | <a·href="Coq.Vectors.Fin.html#t">t</a>·[inductive,·in·<a·href="Coq.Vectors.Fin.html">Coq.Vectors.Fin</a>]<br/> | 561 | <a·href="Coq.Vectors.Fin.html#t">t</a>·[inductive,·in·<a·href="Coq.Vectors.Fin.html">Coq.Vectors.Fin</a>]<br/> |
562 | <a·href="Coq.micromega.VarMap.html#t">t</a>·[abbreviation,·in·<a·href="Coq.micromega.VarMap.html">Coq.micromega.VarMap</a>]<br/> | 562 | <a·href="Coq.micromega.VarMap.html#t">t</a>·[abbreviation,·in·<a·href="Coq.micromega.VarMap.html">Coq.micromega.VarMap</a>]<br/> |
563 | <a·href="Coq.micromega.VarMap.html#t">t</a>·[inductive,·in·<a·href="Coq.micromega.VarMap.html">Coq.micromega.VarMap</a>]<br/> | 563 | <a·href="Coq.micromega.VarMap.html#t">t</a>·[inductive,·in·<a·href="Coq.micromega.VarMap.html">Coq.micromega.VarMap</a>]<br/> |
564 | <a·href="Coq.Vectors.VectorDef.html#t">t</a>·[inductive,·in·<a·href="Coq.Vectors.VectorDef.html">Coq.Vectors.VectorDef</a>]<br/> | 564 | <a·href="Coq.Vectors.VectorDef.html#t">t</a>·[inductive,·in·<a·href="Coq.Vectors.VectorDef.html">Coq.Vectors.VectorDef</a>]<br/> |
565 | <a·href="Coq.Program.Tactics.html">Tactics</a>·[library]<br/> | ||
566 | <a·href="Coq.Init.Tactics.html">Tactics</a>·[library]<br/> | 565 | <a·href="Coq.Init.Tactics.html">Tactics</a>·[library]<br/> |
566 | <a·href="Coq.Program.Tactics.html">Tactics</a>·[library]<br/> | ||
567 | <a·href="Coq.ssr.ssreflect.html#tactic_view">tactic_view</a>·[constructor,·in·<a·href="Coq.ssr.ssreflect.html">Coq.ssr.ssreflect</a>]<br/> | 567 | <a·href="Coq.ssr.ssreflect.html#tactic_view">tactic_view</a>·[constructor,·in·<a·href="Coq.ssr.ssreflect.html">Coq.ssr.ssreflect</a>]<br/> |
568 | <a·href="Coq.rtauto.Bintree.html#Tadd">Tadd</a>·[definition,·in·<a·href="Coq.rtauto.Bintree.html">Coq.rtauto.Bintree</a>]<br/> | 568 | <a·href="Coq.rtauto.Bintree.html#Tadd">Tadd</a>·[definition,·in·<a·href="Coq.rtauto.Bintree.html">Coq.rtauto.Bintree</a>]<br/> |
569 | <a·href="Coq.ssr.ssrfun.html#tag">tag</a>·[definition,·in·<a·href="Coq.ssr.ssrfun.html">Coq.ssr.ssrfun</a>]<br/> | 569 | <a·href="Coq.ssr.ssrfun.html#tag">tag</a>·[definition,·in·<a·href="Coq.ssr.ssrfun.html">Coq.ssr.ssrfun</a>]<br/> |
570 | <a·href="Coq.ssr.ssrfun.html#Tag">Tag</a>·[section,·in·<a·href="Coq.ssr.ssrfun.html">Coq.ssr.ssrfun</a>]<br/> | 570 | <a·href="Coq.ssr.ssrfun.html#Tag">Tag</a>·[section,·in·<a·href="Coq.ssr.ssrfun.html">Coq.ssr.ssrfun</a>]<br/> |
571 | <a·href="Coq.ssr.ssrfun.html#Tagged">Tagged</a>·[definition,·in·<a·href="Coq.ssr.ssrfun.html">Coq.ssr.ssrfun</a>]<br/> | 571 | <a·href="Coq.ssr.ssrfun.html#Tagged">Tagged</a>·[definition,·in·<a·href="Coq.ssr.ssrfun.html">Coq.ssr.ssrfun</a>]<br/> |
572 | <a·href="Coq.ssr.ssrfun.html#tagged">tagged</a>·[definition,·in·<a·href="Coq.ssr.ssrfun.html">Coq.ssr.ssrfun</a>]<br/> | 572 | <a·href="Coq.ssr.ssrfun.html#tagged">tagged</a>·[definition,·in·<a·href="Coq.ssr.ssrfun.html">Coq.ssr.ssrfun</a>]<br/> |
573 | <a·href="Coq.ssr.ssrfun.html#Tagged2">Tagged2</a>·[definition,·in·<a·href="Coq.ssr.ssrfun.html">Coq.ssr.ssrfun</a>]<br/> | 573 | <a·href="Coq.ssr.ssrfun.html#Tagged2">Tagged2</a>·[definition,·in·<a·href="Coq.ssr.ssrfun.html">Coq.ssr.ssrfun</a>]<br/> |
Offset 984, 16 lines modified | Offset 984, 16 lines modified | ||
984 | <a·href="Coq.FSets.FSetEqProperties.html#WEqProperties_fun.BasicProperties.s''">WEqProperties_fun.BasicProperties.s''</a>·[variable,·in·<a·href="Coq.FSets.FSetEqProperties.html">Coq.FSets.FSetEqProperties</a>]<br/> | 984 | <a·href="Coq.FSets.FSetEqProperties.html#WEqProperties_fun.BasicProperties.s''">WEqProperties_fun.BasicProperties.s''</a>·[variable,·in·<a·href="Coq.FSets.FSetEqProperties.html">Coq.FSets.FSetEqProperties</a>]<br/> |
985 | <a·href="Coq.FSets.FSetEqProperties.html#WEqProperties_fun.BasicProperties.s'">WEqProperties_fun.BasicProperties.s'</a>·[variable,·in·<a·href="Coq.FSets.FSetEqProperties.html">Coq.FSets.FSetEqProperties</a>]<br/> | 985 | <a·href="Coq.FSets.FSetEqProperties.html#WEqProperties_fun.BasicProperties.s'">WEqProperties_fun.BasicProperties.s'</a>·[variable,·in·<a·href="Coq.FSets.FSetEqProperties.html">Coq.FSets.FSetEqProperties</a>]<br/> |
986 | <a·href="Coq.FSets.FSetEqProperties.html#WEqProperties_fun.BasicProperties.s">WEqProperties_fun.BasicProperties.s</a>·[variable,·in·<a·href="Coq.FSets.FSetEqProperties.html">Coq.FSets.FSetEqProperties</a>]<br/> | 986 | <a·href="Coq.FSets.FSetEqProperties.html#WEqProperties_fun.BasicProperties.s">WEqProperties_fun.BasicProperties.s</a>·[variable,·in·<a·href="Coq.FSets.FSetEqProperties.html">Coq.FSets.FSetEqProperties</a>]<br/> |
987 | <a·href="Coq.FSets.FSetEqProperties.html#WEqProperties_fun.BasicProperties">WEqProperties_fun.BasicProperties</a>·[section,·in·<a·href="Coq.FSets.FSetEqProperties.html">Coq.FSets.FSetEqProperties</a>]<br/> | 987 | <a·href="Coq.FSets.FSetEqProperties.html#WEqProperties_fun.BasicProperties">WEqProperties_fun.BasicProperties</a>·[section,·in·<a·href="Coq.FSets.FSetEqProperties.html">Coq.FSets.FSetEqProperties</a>]<br/> |
988 | <a·href="Coq.FSets.FSetEqProperties.html#WEqProperties_fun.Add">WEqProperties_fun.Add</a>·[definition,·in·<a·href="Coq.FSets.FSetEqProperties.html">Coq.FSets.FSetEqProperties</a>]<br/> | 988 | <a·href="Coq.FSets.FSetEqProperties.html#WEqProperties_fun.Add">WEqProperties_fun.Add</a>·[definition,·in·<a·href="Coq.FSets.FSetEqProperties.html">Coq.FSets.FSetEqProperties</a>]<br/> |
989 | <a·href="Coq.FSets.FSetEqProperties.html#WEqProperties_fun.MP">WEqProperties_fun.MP</a>·[module,·in·<a·href="Coq.FSets.FSetEqProperties.html">Coq.FSets.FSetEqProperties</a>]<br/> | 989 | <a·href="Coq.FSets.FSetEqProperties.html#WEqProperties_fun.MP">WEqProperties_fun.MP</a>·[module,·in·<a·href="Coq.FSets.FSetEqProperties.html">Coq.FSets.FSetEqProperties</a>]<br/> |
990 | <a·href="Coq.FSets.FSetEqProperties.html#WEqProperties_fun">WEqProperties_fun</a>·[module,·in·<a·href="Coq.FSets.FSetEqProperties.html">Coq.FSets.FSetEqProperties</a>]<br/> | 990 | <a·href="Coq.FSets.FSetEqProperties.html#WEqProperties_fun">WEqProperties_fun</a>·[module,·in·<a·href="Coq.FSets.FSetEqProperties.html">Coq.FSets.FSetEqProperties</a>]<br/> |
991 | <a·href="Coq.Program.Wf.html">Wf</a>·[library]<br/> | ||
992 | <a·href="Coq.Init.Wf.html">Wf</a>·[library]<br/> | 991 | <a·href="Coq.Init.Wf.html">Wf</a>·[library]<br/> |
992 | <a·href="Coq.Program.Wf.html">Wf</a>·[library]<br/> | ||
993 | <a·href="Coq.FSets.FMapFacts.html#WFacts">WFacts</a>·[module,·in·<a·href="Coq.FSets.FMapFacts.html">Coq.FSets.FMapFacts</a>]<br/> | 993 | <a·href="Coq.FSets.FMapFacts.html#WFacts">WFacts</a>·[module,·in·<a·href="Coq.FSets.FMapFacts.html">Coq.FSets.FMapFacts</a>]<br/> |
994 | <a·href="Coq.MSets.MSetFacts.html#WFacts">WFacts</a>·[module,·in·<a·href="Coq.MSets.MSetFacts.html">Coq.MSets.MSetFacts</a>]<br/> | 994 | <a·href="Coq.MSets.MSetFacts.html#WFacts">WFacts</a>·[module,·in·<a·href="Coq.MSets.MSetFacts.html">Coq.MSets.MSetFacts</a>]<br/> |
995 | <a·href="Coq.FSets.FSetFacts.html#WFacts">WFacts</a>·[module,·in·<a·href="Coq.FSets.FSetFacts.html">Coq.FSets.FSetFacts</a>]<br/> | 995 | <a·href="Coq.FSets.FSetFacts.html#WFacts">WFacts</a>·[module,·in·<a·href="Coq.FSets.FSetFacts.html">Coq.FSets.FSetFacts</a>]<br/> |
996 | <a·href="Coq.MSets.MSetFacts.html#WFactsOn">WFactsOn</a>·[module,·in·<a·href="Coq.MSets.MSetFacts.html">Coq.MSets.MSetFacts</a>]<br/> | 996 | <a·href="Coq.MSets.MSetFacts.html#WFactsOn">WFactsOn</a>·[module,·in·<a·href="Coq.MSets.MSetFacts.html">Coq.MSets.MSetFacts</a>]<br/> |
997 | <a·href="Coq.MSets.MSetFacts.html#WFactsOn.add_s_m">WFactsOn.add_s_m</a>·[instance,·in·<a·href="Coq.MSets.MSetFacts.html">Coq.MSets.MSetFacts</a>]<br/> | 997 | <a·href="Coq.MSets.MSetFacts.html#WFactsOn.add_s_m">WFactsOn.add_s_m</a>·[instance,·in·<a·href="Coq.MSets.MSetFacts.html">Coq.MSets.MSetFacts</a>]<br/> |
998 | <a·href="Coq.MSets.MSetFacts.html#WFactsOn.add_m">WFactsOn.add_m</a>·[instance,·in·<a·href="Coq.MSets.MSetFacts.html">Coq.MSets.MSetFacts</a>]<br/> | 998 | <a·href="Coq.MSets.MSetFacts.html#WFactsOn.add_m">WFactsOn.add_m</a>·[instance,·in·<a·href="Coq.MSets.MSetFacts.html">Coq.MSets.MSetFacts</a>]<br/> |
999 | <a·href="Coq.MSets.MSetFacts.html#WFactsOn.add_neq_b">WFactsOn.add_neq_b</a>·[lemma,·in·<a·href="Coq.MSets.MSetFacts.html">Coq.MSets.MSetFacts</a>]<br/> | 999 | <a·href="Coq.MSets.MSetFacts.html#WFactsOn.add_neq_b">WFactsOn.add_neq_b</a>·[lemma,·in·<a·href="Coq.MSets.MSetFacts.html">Coq.MSets.MSetFacts</a>]<br/> |
Offset 573, 16 lines modified | Offset 573, 16 lines modified | ||
573 | <a·href="Ltac2.Bool.html">Bool</a>·<br/> | 573 | <a·href="Ltac2.Bool.html">Bool</a>·<br/> |
574 | <a·href="Coq.Bool.Bool.html">Bool</a>·<br/> | 574 | <a·href="Coq.Bool.Bool.html">Bool</a>·<br/> |
575 | <a·href="Coq.Bool.BoolEq.html">BoolEq</a>·<br/> | 575 | <a·href="Coq.Bool.BoolEq.html">BoolEq</a>·<br/> |
576 | <a·href="Coq.Bool.BoolOrder.html">BoolOrder</a>·<br/> | 576 | <a·href="Coq.Bool.BoolOrder.html">BoolOrder</a>·<br/> |
577 | <a·href="Coq.Arith.Bool_nat.html">Bool_nat</a>·<br/> | 577 | <a·href="Coq.Arith.Bool_nat.html">Bool_nat</a>·<br/> |
578 | <a·href="Coq.btauto.Btauto.html">Btauto</a>·<br/> | 578 | <a·href="Coq.btauto.Btauto.html">Btauto</a>·<br/> |
579 | <a·href="Coq.Bool.Bvector.html">Bvector</a>·<br/> | 579 | <a·href="Coq.Bool.Bvector.html">Bvector</a>·<br/> |
580 | <a·href="Coq.Strings.Byte.html">Byte</a>·<br/> | ||
581 | <a·href="Coq.Init.Byte.html">Byte</a>·<br/> | 580 | <a·href="Coq.Init.Byte.html">Byte</a>·<br/> |
581 | <a·href="Coq.Strings.Byte.html">Byte</a>·<br/> | ||
582 | <a·href="Coq.Strings.ByteVector.html">ByteVector</a>·<br/> | 582 | <a·href="Coq.Strings.ByteVector.html">ByteVector</a>·<br/> |
583 | <br/><br/>····<div·id="sidebarWrapper"> | 583 | <br/><br/>····<div·id="sidebarWrapper"> |
584 | ······<div·id="sidebar"> | 584 | ······<div·id="sidebar"> |
585 | ········<div·class="block"> | 585 | ········<div·class="block"> |
586 | ··········<h2·class="title">Navigation</h2> | 586 | ··········<h2·class="title">Navigation</h2> |
587 | ··········<div·class="content"> | 587 | ··········<div·class="content"> |
588 | ············<ul·class="menu"> | 588 | ············<ul·class="menu"> |
Offset 552, 18 lines modified | Offset 552, 18 lines modified | ||
552 | <td><a·href="index_record_Z.html">Z</a></td> | 552 | <td><a·href="index_record_Z.html">Z</a></td> |
553 | <td>_</td> | 553 | <td>_</td> |
554 | <td>other</td> | 554 | <td>other</td> |
555 | <td>(166·entries)</td> | 555 | <td>(166·entries)</td> |
556 | </tr> | 556 | </tr> |
557 | </table> | 557 | </table> |
558 | <hr/><a·id="library_T"></a><h2>T·(library)</h2> | 558 | <hr/><a·id="library_T"></a><h2>T·(library)</h2> |
559 | <a·href="Coq.Program.Tactics.html">Tactics</a>·<br/> | ||
560 | <a·href="Coq.Init.Tactics.html">Tactics</a>·<br/> | 559 | <a·href="Coq.Init.Tactics.html">Tactics</a>·<br/> |
561 | <a·href="Coq. | 560 | <a·href="Coq.Program.Tactics.html">Tactics</a>·<br/> |
562 | <a·href="Coq.Init.Tauto.html">Tauto</a>·<br/> | 561 | <a·href="Coq.Init.Tauto.html">Tauto</a>·<br/> |
562 | <a·href="Coq.micromega.Tauto.html">Tauto</a>·<br/> | ||
563 | <a·href="Coq.Wellfounded.Transitive_Closure.html">Transitive_Closure</a>·<br/> | 563 | <a·href="Coq.Wellfounded.Transitive_Closure.html">Transitive_Closure</a>·<br/> |
564 | <br/><br/>····<div·id="sidebarWrapper"> | 564 | <br/><br/>····<div·id="sidebarWrapper"> |
565 | ······<div·id="sidebar"> | 565 | ······<div·id="sidebar"> |
566 | ········<div·class="block"> | 566 | ········<div·class="block"> |
567 | ··········<h2·class="title">Navigation</h2> | 567 | ··········<h2·class="title">Navigation</h2> |
568 | ··········<div·class="content"> | 568 | ··········<div·class="content"> |
569 | ············<ul·class="menu"> | 569 | ············<ul·class="menu"> |
Offset 555, 16 lines modified | Offset 555, 16 lines modified | ||
555 | <td>(166·entries)</td> | 555 | <td>(166·entries)</td> |
556 | </tr> | 556 | </tr> |
557 | </table> | 557 | </table> |
558 | <hr/><a·id="library_W"></a><h2>W·(library)</h2> | 558 | <hr/><a·id="library_W"></a><h2>W·(library)</h2> |
559 | <a·href="Coq.Logic.WeakFan.html">WeakFan</a>·<br/> | 559 | <a·href="Coq.Logic.WeakFan.html">WeakFan</a>·<br/> |
560 | <a·href="Coq.Wellfounded.Wellfounded.html">Wellfounded</a>·<br/> | 560 | <a·href="Coq.Wellfounded.Wellfounded.html">Wellfounded</a>·<br/> |
561 | <a·href="Coq.Wellfounded.Well_Ordering.html">Well_Ordering</a>·<br/> | 561 | <a·href="Coq.Wellfounded.Well_Ordering.html">Well_Ordering</a>·<br/> |
562 | <a·href="Coq.Program.Wf.html">Wf</a>·<br/> | ||
563 | <a·href="Coq.Init.Wf.html">Wf</a>·<br/> | 562 | <a·href="Coq.Init.Wf.html">Wf</a>·<br/> |
563 | <a·href="Coq.Program.Wf.html">Wf</a>·<br/> | ||
564 | <a·href="Coq.Arith.Wf_nat.html">Wf_nat</a>·<br/> | 564 | <a·href="Coq.Arith.Wf_nat.html">Wf_nat</a>·<br/> |
565 | <a·href="Coq.ZArith.Wf_Z.html">Wf_Z</a>·<br/> | 565 | <a·href="Coq.ZArith.Wf_Z.html">Wf_Z</a>·<br/> |
566 | <a·href="Coq.Logic.WKL.html">WKL</a>·<br/> | 566 | <a·href="Coq.Logic.WKL.html">WKL</a>·<br/> |
567 | <br/><br/>····<div·id="sidebarWrapper"> | 567 | <br/><br/>····<div·id="sidebarWrapper"> |
568 | ······<div·id="sidebar"> | 568 | ······<div·id="sidebar"> |
569 | ········<div·class="block"> | 569 | ········<div·class="block"> |
570 | ··········<h2·class="title">Navigation</h2> | 570 | ··········<h2·class="title">Navigation</h2> |