| Offset 1, 9 lines modified | Offset 1, 9 lines modified | ||
| 1 | ·b2a9335c6c3a0d5848ae4fcf055c1917·15980008·debug·optional·coq-dbgsym_8.16.1+dfsg-1_amd64.deb | 1 | ·b2a9335c6c3a0d5848ae4fcf055c1917·15980008·debug·optional·coq-dbgsym_8.16.1+dfsg-1_amd64.deb |
| 2 | · | 2 | ·4d9dcd369f19112e6ae13723ae3fe08f·93216012·math·optional·coq_8.16.1+dfsg-1_amd64.deb |
| 3 | ·b8b5ab34c9df7c607a046180e44663c0·727396·debug·optional·coqide-dbgsym_8.16.1+dfsg-1_amd64.deb | 3 | ·b8b5ab34c9df7c607a046180e44663c0·727396·debug·optional·coqide-dbgsym_8.16.1+dfsg-1_amd64.deb |
| 4 | ·131fa12138a6f9573a852046ec2225a0·1988016·math·optional·coqide_8.16.1+dfsg-1_amd64.deb | 4 | ·131fa12138a6f9573a852046ec2225a0·1988016·math·optional·coqide_8.16.1+dfsg-1_amd64.deb |
| 5 | ·caef07fb7e4015404855126fb99e35a9·2149148·debug·optional·libcoq-core-ocaml-dbgsym_8.16.1+dfsg-1_amd64.deb | 5 | ·caef07fb7e4015404855126fb99e35a9·2149148·debug·optional·libcoq-core-ocaml-dbgsym_8.16.1+dfsg-1_amd64.deb |
| 6 | · | 6 | ·53f5bb9d13e051558ec270a36315f15b·42723920·ocaml·optional·libcoq-core-ocaml-dev_8.16.1+dfsg-1_amd64.deb |
| 7 | ·6af08844ea13b7aed4733f793cff40f8·22551684·ocaml·optional·libcoq-core-ocaml_8.16.1+dfsg-1_amd64.deb | ||
| 8 | · | 7 | ·ad8313a0110d28154c9c8b8f3f213683·22554664·ocaml·optional·libcoq-core-ocaml_8.16.1+dfsg-1_amd64.deb |
| 8 | ·0bebcbde213722073fb27c8926cc1092·21525168·math·optional·libcoq-stdlib_8.16.1+dfsg-1_amd64.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·····232 | 2 | -rw-r--r--···0········0········0·····2328·2022-11-29·08:28:08.000000·control.tar.xz |
| 3 | -rw-r--r--···0········0········0·9321 | 3 | -rw-r--r--···0········0········0·93213492·2022-11-29·08:28:08.000000·data.tar.xz |
| 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)··1033800·2022-11-29·08:28:08.000000·./usr/bin/coq-tex | 7 | -rwxr-xr-x···0·root·········(0)·root·········(0)··1033800·2022-11-29·08:28:08.000000·./usr/bin/coq-tex |
| 8 | -rwxr-xr-x···0·root·········(0)·root·········(0)··2056464·2022-11-29·08:28:08.000000·./usr/bin/coq_makefile | 8 | -rwxr-xr-x···0·root·········(0)·root·········(0)··2056464·2022-11-29·08:28:08.000000·./usr/bin/coq_makefile |
| 9 | -rwxr-xr-x···0·root·········(0)·root·········(0)·21084272·2022-11-29·08:28:08.000000·./usr/bin/coqc | 9 | -rwxr-xr-x···0·root·········(0)·root·········(0)·21084272·2022-11-29·08:28:08.000000·./usr/bin/coqc |
| 10 | -rwxr-xr-x···0·root·········(0)·root·········(0)·400552 | 10 | -rwxr-xr-x···0·root·········(0)·root·········(0)·40055226·2022-11-29·08:28:08.000000·./usr/bin/coqc.byte |
| 11 | -rwxr-xr-x···0·root·········(0)·root·········(0)··7838320·2022-11-29·08:28:08.000000·./usr/bin/coqchk | 11 | -rwxr-xr-x···0·root·········(0)·root·········(0)··7838320·2022-11-29·08:28:08.000000·./usr/bin/coqchk |
| 12 | -rwxr-xr-x···0·root·········(0)·root·········(0)··3375056·2022-11-29·08:28:08.000000·./usr/bin/coqdep | 12 | -rwxr-xr-x···0·root·········(0)·root·········(0)··3375056·2022-11-29·08:28:08.000000·./usr/bin/coqdep |
| 13 | -rwxr-xr-x···0·root·········(0)·root·········(0)··2974416·2022-11-29·08:28:08.000000·./usr/bin/coqdoc | 13 | -rwxr-xr-x···0·root·········(0)·root·········(0)··2974416·2022-11-29·08:28:08.000000·./usr/bin/coqdoc |
| 14 | -rwxr-xr-x···0·root·········(0)·root·········(0)·4061888 | 14 | -rwxr-xr-x···0·root·········(0)·root·········(0)·40618880·2022-11-29·08:28:08.000000·./usr/bin/coqidetop.byte |
| 15 | -rwxr-xr-x···0·root·········(0)·root·········(0)·20758032·2022-11-29·08:28:08.000000·./usr/bin/coqidetop.opt | 15 | -rwxr-xr-x···0·root·········(0)·root·········(0)·20758032·2022-11-29·08:28:08.000000·./usr/bin/coqidetop.opt |
| 16 | -rwxr-xr-x···0·root·········(0)·root·········(0)··8054928·2022-11-29·08:28:08.000000·./usr/bin/coqnative | 16 | -rwxr-xr-x···0·root·········(0)·root·········(0)··8054928·2022-11-29·08:28:08.000000·./usr/bin/coqnative |
| 17 | -rwxr-xr-x···0·root·········(0)·root·········(0)··1303432·2022-11-29·08:28:08.000000·./usr/bin/coqpp | 17 | -rwxr-xr-x···0·root·········(0)·root·········(0)··1303432·2022-11-29·08:28:08.000000·./usr/bin/coqpp |
| 18 | -rwxr-xr-x···0·root·········(0)·root·········(0)·21084688·2022-11-29·08:28:08.000000·./usr/bin/coqproofworker.opt | 18 | -rwxr-xr-x···0·root·········(0)·root·········(0)·21084688·2022-11-29·08:28:08.000000·./usr/bin/coqproofworker.opt |
| 19 | -rwxr-xr-x···0·root·········(0)·root·········(0)·21084688·2022-11-29·08:28:08.000000·./usr/bin/coqqueryworker.opt | 19 | -rwxr-xr-x···0·root·········(0)·root·········(0)·21084688·2022-11-29·08:28:08.000000·./usr/bin/coqqueryworker.opt |
| 20 | -rwxr-xr-x···0·root·········(0)·root·········(0)·21084688·2022-11-29·08:28:08.000000·./usr/bin/coqtacticworker.opt | 20 | -rwxr-xr-x···0·root·········(0)·root·········(0)·21084688·2022-11-29·08:28:08.000000·./usr/bin/coqtacticworker.opt |
| 21 | -rwxr-xr-x···0·root·········(0)·root·········(0)·21084400·2022-11-29·08:28:08.000000·./usr/bin/coqtop | 21 | -rwxr-xr-x···0·root·········(0)·root·········(0)·21084400·2022-11-29·08:28:08.000000·./usr/bin/coqtop |
| 22 | -rwxr-xr-x···0·root·········(0)·root·········(0)·57578 | 22 | -rwxr-xr-x···0·root·········(0)·root·········(0)·57578652·2022-11-29·08:28:08.000000·./usr/bin/coqtop.byte |
| 23 | -rwxr-xr-x···0·root·········(0)·root·········(0)·21084400·2022-11-29·08:28:08.000000·./usr/bin/coqtop.opt | 23 | -rwxr-xr-x···0·root·········(0)·root·········(0)·21084400·2022-11-29·08:28:08.000000·./usr/bin/coqtop.opt |
| 24 | -rwxr-xr-x···0·root·········(0)·root·········(0)···818440·2022-11-29·08:28:08.000000·./usr/bin/coqwc | 24 | -rwxr-xr-x···0·root·········(0)·root·········(0)···818440·2022-11-29·08:28:08.000000·./usr/bin/coqwc |
| 25 | -rwxr-xr-x···0·root·········(0)·root·········(0)·20972624·2022-11-29·08:28:08.000000·./usr/bin/coqworkmgr | 25 | -rwxr-xr-x···0·root·········(0)·root·········(0)·20972624·2022-11-29·08:28:08.000000·./usr/bin/coqworkmgr |
| 26 | -rwxr-xr-x···0·root·········(0)·root·········(0)·24421072·2022-11-29·08:28:08.000000·./usr/bin/csdpcert | 26 | -rwxr-xr-x···0·root·········(0)·root·········(0)·24421072·2022-11-29·08:28:08.000000·./usr/bin/csdpcert |
| 27 | -rwxr-xr-x···0·root·········(0)·root·········(0)··1245200·2022-11-29·08:28:08.000000·./usr/bin/ocamllibdep | 27 | -rwxr-xr-x···0·root·········(0)·root·········(0)··1245200·2022-11-29·08:28:08.000000·./usr/bin/ocamllibdep |
| 28 | -rwxr-xr-x···0·root·········(0)·root·········(0)··1396912·2022-11-29·08:28:08.000000·./usr/bin/votour | 28 | -rwxr-xr-x···0·root·········(0)·root·········(0)··1396912·2022-11-29·08:28:08.000000·./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 2271074, 232383 lines modified | Offset 2271074, 232379 lines modified | ||
| 022a7610:·4041·4042·4040·8495·a6be·0000·0052·0000··@A@B@@.......R.. | 022a7610:·4041·4042·4040·8495·a6be·0000·0052·0000··@A@B@@.......R.. | ||
| 022a7620:·0006·0000·0021·0000·0017·a030·2e2f·5f62··.....!.....0./_b | 022a7620:·0006·0000·0021·0000·0017·a030·2e2f·5f62··.....!.....0./_b | ||
| 022a7630:·7569·6c64·2f64·6566·6175·6c74·a035·2e2f··uild/default.5./ | 022a7630:·7569·6c64·2f64·6566·6175·6c74·a035·2e2f··uild/default.5./ | ||
| 022a7640:·5f62·7569·6c64·2f64·6566·6175·6c74·2f63··_build/default/c | 022a7640:·5f62·7569·6c64·2f64·6566·6175·6c74·2f63··_build/default/c | ||
| 022a7650:·6c69·62a0·0925·2e2f·5f62·7569·6c64·2f64··lib..%./_build/d | 022a7650:·6c69·62a0·0925·2e2f·5f62·7569·6c64·2f64··lib..%./_build/d | ||
| 022a7660:·6566·6175·6c74·2f63·6c69·622f·2e63·6c69··efault/clib/.cli | 022a7660:·6566·6175·6c74·2f63·6c69·622f·2e63·6c69··efault/clib/.cli | ||
| 022a7670:·622e·6f62·6a73·2f62·7974·6540·0007·d924··b.objs/byte@...$ | 022a7670:·622e·6f62·6a73·2f62·7974·6540·0007·d924··b.objs/byte@...$ | ||
| 022a7680:·8495·a6be·0000·2fc | 022a7680:·8495·a6be·0000·2fc4·0000·0842·0000·2367··....../....B..#g | ||
| 022a7690:·0000·22d | 022a7690:·0000·22d3·a008·0000·2c00·0106·ac27·4578··..".....,....'Ex | ||
| 022a76a0:·6e69·6e66·6fb0·c026·5f6e·6f6e·655f·4040··ninfo..&_none_@@ | 022a76a0:·6e69·6e66·6fb0·c026·5f6e·6f6e·655f·4040··ninfo..&_none_@@ | ||
| 022a76b0:·00ff·0402·4141·223f·3f41·40d0·4040·4040··....AA"??A@.@@@@ | 022a76b0:·00ff·0402·4141·223f·3f41·40d0·4040·4040··....AA"??A@.@@@@ | ||
| 022a76c0:·40b0·4040·4040·40a0·0800·002c·0001·0654··@.@@@@@....,...T | 022a76c0:·40b0·4040·4040·40a0·0800·002c·0001·0654··@.@@@@@....,...T | ||
| 022a76d0:·0409·0408·4122·3f3f·41b0·b0b0·b0b0·b0b0··....A"??A....... | 022a76d0:·0409·0408·4122·3f3f·41b0·b0b0·b0b0·b0b0··....A"??A....... | Diff chunk too large, falling back to line-by-line diff (4248 lines added, 4248 lines removed) | |
| 022a76e0:·b0b0·b0b1·b0b0·b0b0·b0b2·b0b0·b0b0·b1b1··................ | 022a76e0:·b0b0·b0b1·b0b0·b0b0·b0b2·b0b0·b0b0·b1b1··................ | ||
| 022a76f0:·b1c3·aba | 022a76f0:·b1c3·aba7·b1b2·b2b2·b2b2·b2b2·b2b2·b2b2··................ | ||
| 022a7700:·b2b | 022a7700:·b2b1·b1b1·b1b1·b1b1·b1b1·b1b1·b1b1·b1b1··................ | ||
| 022a7710:·b1 | 022a7710:·b140·a32a·666c·6f61·7461·7272·6179·5108··.@.*floatarrayQ. | ||
| 022a7720:·0 | 022a7720:·0000·3800·4040·4041·4040·4040·4004·4440··..8.@@@A@@@@@.D@ | ||
| 022a7730:·4040· | 022a7730:·4040·9204·03a3·3565·7874·656e·7369·6f6e··@@....5extension | ||
| 022a7740:· | 022a7740:·5f63·6f6e·7374·7275·6374·6f72·5008·0000··_constructorP... | ||
| 022a7750:· | 022a7750:·3800·4040·4041·4040·4040·4004·4840·4040··8.@@@A@@@@@.H@@@ | ||
| 022a7760:· | 022a7760:·9204·03a3·2369·6e74·4108·0000·3800·4040··....#intA...8.@@ | ||
| 022a7770:·404 | 022a7770:·4041·4040·4040·4004·4c40·4140·9204·03a3··@A@@@@@.L@A@.... | ||
| 022a7780:· | 022a7780:·2463·6861·7242·0800·0038·0040·4040·4140··$charB...8.@@@A@ | ||
| 022a7790:·4040·4040· | 022a7790:·4040·4040·0450·4041·4092·0403·a326·7374··@@@@.P@A@....&st | ||
| 022a77a0:·7 | 022a77a0:·7269·6e67·4f08·0000·3800·4040·4041·4040··ringO...8.@@@A@@ | ||
| 022a77b0:·4040·40 | 022a77b0:·4040·4004·5440·4040·9204·03a3·2566·6c6f··@@@.T@@@....%flo | ||
| 022a77c0:·6 | 022a77c0:·6174·4408·0000·3800·4040·4041·4040·4040··atD...8.@@@A@@@@ | ||
| 022a77d0:·40 | 022a77d0:·4004·5840·4040·9204·03a3·2462·6f6f·6c45··@.X@@@....$boolE | ||
| 022a77e0:· | 022a77e0:·0800·0038·0040·40a1·a0e0·a325·6661·6c73··...8.@@....%fals | ||
| 022a77f0:· | 022a77f0:·655e·9040·4004·6240·9204·03a0·e0a3·2474··e^.@@.b@......$t | ||
| 022a7800:·7 | 022a7800:·7275·655f·9040·4004·6840·9204·0340·4041··rue_.@@.h@...@@A | ||
| 022a7810:·4 | 022a7810:·4040·4040·4004·6940·4140·9204·10a3·2475··@@@@@.i@A@....$u | ||
| 022a7820:· | 022a7820:·6e69·7446·0800·0038·0040·40a1·a0e0·a322··nitF...8.@@...." | ||
| 022a7830:·2 | 022a7830:·2829·6090·4040·0473·4092·0403·4040·4140··()`.@@.s@...@@A@ | ||
| 022a7840:·4040·4040· | 022a7840:·4040·4040·0474·4041·4092·040a·a323·6578··@@@@.t@A@....#ex | ||
| 022a7850:· | 022a7850:·6e47·0800·0038·0040·4041·4140·4040·4040··nG...8.@@AA@@@@@ | ||
| 022a7860:· | 022a7860:·0478·4040·4092·0403·a325·6172·7261·7948··.x@@@....%arrayH | ||
| 022a7870:· | 022a7870:·0800·0038·00a0·c090·4002·05f5·e100·404f··...8....@.....@O | ||
| 022a7880:·4 | 022a7880:·4041·4041·40a0·007f·40a0·4040·4040·0481··@A@A@...@.@@@@.. | ||
| 022a7890:· | 022a7890:·4040·4092·0408·a324·6c69·7374·4908·0000··@@@....$listI... | ||
| 022a78a0:· | 022a78a0:·3800·a0c0·0409·0205·f5e1·0040·5040·41a1··8..........@P@A. | ||
| 022a78b0:·a | 022a78b0:·a0e0·a322·5b5d·6190·4040·048d·4092·0403··..."[]a.@@..@... | ||
| 022a78c0:· | 022a78c0:·a0e0·a322·3a3a·6290·a004·0ea0·c0b3·9004··..."::b......... | ||
| 022a78d0:· | 022a78d0:·16a0·0413·4090·4002·05f5·e100·4051·4040··....@.@.....@Q@@ | ||
| 022a78e0:· | 022a78e0:·049a·4092·040a·4040·4140·a059·40a0·4040··..@...@@A@.Y@.@@ | ||
| 022a78f0:·4040· | 022a78f0:·4040·049d·4040·4092·041b·a326·6f70·7469··@@..@@@....&opti | ||
| 022a7900:·6 | 022a7900:·6f6e·4a08·0000·3800·a0c0·0425·0205·f5e1··onJ...8....%.... | ||
| 022a7910:· | 022a7910:·0040·5340·41a1·a0e0·a324·4e6f·6e65·6390··.@S@A....$Nonec. | ||
| 022a7920:· | 022a7920:·4040·04a9·4092·0403·a0e0·a324·536f·6d65··@@..@......$Some | ||
| 022a7930:·6 | 022a7930:·6490·a004·0e40·4004·b040·9204·0440·4041··d....@@..@...@@A | ||
| 022a7940:·4 | 022a7940:·40a0·5940·a040·4040·4004·b340·4040·9204··@.Y@.@@@@..@@@.. | ||
| 022a7950:· | 022a7950:·15a3·266c·617a·795f·744e·0800·0038·00a0··..&lazy_tN...8.. | ||
| 022a7960:· | 022a7960:·c004·3b02·05f5·e100·4055·4041·4041·40a0··..;.....@U@A@A@. | ||
| 022a7970:· | 022a7970:·5940·a040·4040·4004·bb40·4040·9204·07a3··Y@.@@@@..@@@.... | ||
| 022a7980:· | 022a7980:·296e·6174·6976·6569·6e74·4b08·0000·3800··)nativeintK...8. | ||
| 022a7990:· | 022a7990:·4040·4041·4040·4040·4004·bf40·4040·9204··@@@A@@@@@..@@@.. | ||
| 022a79a0:·0 | 022a79a0:·03a3·2569·6e74·3332·4c08·0000·3800·4040··..%int32L...8.@@ | ||
| 022a79b0:·404 | 022a79b0:·4041·4040·4040·4004·c340·4040·9204·03a3··@A@@@@@..@@@.... | ||
| 022a79c0:· | 022a79c0:·2569·6e74·3634·4d08·0000·3800·4040·4041··%int64M...8.@@@A | ||
| 022a79d0:·4 | 022a79d0:·4040·4040·4004·c740·4040·9204·03a3·3a55··@@@@@..@@@....:U | ||
| 022a79e0:· | 022a79e0:·6e64·6566·696e·6564·5f72·6563·7572·7369··ndefined_recursi | ||
| 022a79f0:· | 022a79f0:·7665·5f6d·6f64·756c·655d·0800·0020·0090··ve_module]...·.. | ||
| 022a7a00:· | 022a7a00:·0457·4090·a0c0·92a0·c0b3·9004·8340·9040··.W@..........@.@ | ||
| 022a7a10:· | 022a7a10:·0205·f5e1·0040·4aa0·c0b3·9004·9040·9040··.....@J......@.@ | ||
| 022a7a20:· | 022a7a20:·0205·f5e1·0040·40a0·0405·4002·05f5·e100··.....@@...@..... | ||
| 022a7a30:· | 022a7a30:·4056·4040·4104·dba0·b0a0·3d6f·6361·6d6c··@V@@A.....=ocaml | ||
| 022a7a40:· | 022a7a40:·2e77·6172·6e5f·6f6e·5f6c·6974·6572·616c··.warn_on_literal | ||
| 022a7a50:· | 022a7a50:·5f70·6174·7465·726e·04df·0461·04df·4092··_pattern...a..@. | ||
| 022a7a60:· | 022a7a60:·0417·a32e·4173·7365·7274·5f66·6169·6c75··....Assert_failu | ||
| 022a7a70:·7 | 022a7a70:·7265·5c08·0000·2000·0418·4090·a0c0·92a0··re\...·...@..... | ||
| 022a7a80:· | 022a7a80:·0417·a004·13a0·0414·4002·05f5·e100·4058··........@.....@X | ||
| 022a7a90:· | 022a7a90:·4040·4104·eaa0·b0a0·040f·04ed·046f·04ed··@@A..........o.. | ||
| 022a7aa0:· | 022a7aa0:·4092·040d·a330·4469·7669·7369·6f6e·5f62··@....0Division_b | ||
| 022a7ab0:· | 022a7ab0:·795f·7a65·726f·5908·0000·2000·0426·4090··y_zeroY...·..&@. | ||
| 022a7ac0:· | 022a7ac0:·4040·4104·f2a0·b0a0·0417·04f5·0477·04f5··@@A..........w.. | ||
| 022a7ad0:· | 022a7ad0:·4092·0407·a32b·456e·645f·6f66·5f66·696c··@....+End_of_fil | ||
| 022a7ae0:·6 | 022a7ae0:·6558·0800·0020·0004·2e40·9040·4041·04fa··eX...·...@.@@A.. | ||
| 022a7af0:· | 022a7af0:·a0b0·a004·1f04·fd04·7f04·fd40·9204·07a3··...........@.... | ||
| 022a7b00:· | 022a7b00:·2953·7973·5f65·7272·6f72·5708·0000·2000··)Sys_errorW...·. | ||
| 022a7b10:·0 | 022a7b10:·0436·4090·a004·3240·4041·0501·03a0·b0a0··.6@...2@@A...... | ||
| 022a7b20:· | 022a7b20:·0428·0501·0604·8805·0106·4092·0408·a32e··.(........@..... | ||
| 022a7b30:· | 022a7b30:·5379·735f·626c·6f63·6b65·645f·696f·5b08··Sys_blocked_io[. | ||
| 022a7b40:·0 | 022a7b40:·0000·2000·043f·4090·4040·4105·010b·a0b0··..·..?@.@@A..... | ||
| 022a7b50:· | 022a7b50:·a004·3005·010e·0490·0501·0e40·9204·07a3··..0........@.... | ||
| 022a7b60:· | 022a7b60:·294e·6f74·5f66·6f75·6e64·5608·0000·2000··)Not_foundV...·. | ||
| 022a7b70:·0 | 022a7b70:·0447·4090·4040·4105·0113·a0b0·a004·3805··.G@.@@A.......8. | ||
| 022a7b80:·0 | 022a7b80:·0116·0498·0501·1640·9204·07a3·2746·6169··.......@....'Fai | ||
| 022a7b90:·6 | 022a7b90:·6c75·7265·5508·0000·2000·044f·4090·a004··lureU...·..O@... | ||
| 022a7ba0:· | 022a7ba0:·4b40·4041·0501·1ca0·b0a0·0441·0501·1f04··K@@A.......A.... | ||
| 022a7bb0:· | 022a7bb0:·a105·011f·4092·0408·a330·496e·7661·6c69··....@....0Invali | ||
| 022a7bc0:·6 | 022a7bc0:·645f·6172·6775·6d65·6e74·5408·0000·2000··d_argumentT...·. | ||
| 022a7bd0:·0 | 022a7bd0:·0458·4090·a004·5440·4041·0501·25a0·b0a0··.X@...T@@A..%... | ||
| 022a7be0:· | 022a7be0:·044a·0501·2804·aa05·0128·4092·0408·a32e··.J..(....(@..... | ||
| 022a7bf0:· | 022a7bf0:·5374·6163·6b5f·6f76·6572·666c·6f77·5a08··Stack_overflowZ. | ||
| 022a7c00:·0 | 022a7c00:·0000·2000·0461·4090·4040·4105·012d·a0b0··..·..a@.@@A..-.. | ||
| 022a7c10:· | 022a7c10:·a004·5205·0130·04b2·0501·3040·9204·07a3··..R..0....0@.... | ||
| 022a7c20:· | 022a7c20:·2d4f·7574·5f6f·665f·6d65·6d6f·7279·5308··-Out_of_memoryS. | ||
| 022a7c30:·0 | 022a7c30:·0000·2000·0469·4090·4040·4105·0135·a0b0··..·..i@.@@A..5.. | ||
| 022a7c40:· | 022a7c40:·a004·5a05·0138·04ba·0501·3840·9204·07a3··..Z..8....8@.... | ||
| 022a7c50:· | 022a7c50:·2d4d·6174·6368·5f66·6169·6c75·7265·5208··-Match_failureR. | ||
| 022a7c60:·0 | 022a7c60:·0000·2000·0471·4090·a0c0·92a0·0470·a004··..·..q@......p.. | ||
| 022a7c70:· | 022a7c70:·6ca0·046d·4002·05f5·e100·4063·4040·4105··l..m@.....@c@@A. | ||
| 022a7c80:·0 | 022a7c80:·0143·a0b0·a004·6805·0146·04c8·0501·4640··.C....h..F....F@ | ||
| 022a7c90:· | 022a7c90:·9204·0da3·2562·7974·6573·4308·0000·3800··....%bytesC...8. | ||
| 022a7ca0:· | 022a7ca0:·4040·4041·4040·4040·4005·014a·4040·4092··@@@A@@@@@..J@@@. | ||
| 022a7cb0:· | 022a7cb0:·0403·9092·2653·7464·6c69·6292·264f·7074··....&Stdlib.&Opt | ||
| 022a7cc0:· | 022a7cc0:·696f·6eb1·2553·746f·7265·0063·4140·c090··ion.%Store.cA@.. | ||
| 022a7cd0:· | 022a7cd0:·a190·9225·5374·6f72·6521·5340·b0c0·2f63··...%Store!S@../c | ||
| 022a7ce0:· | 022a7ce0:·6c69·622f·6578·6e69·6e66·6f2e·6d6c·4f01··lib/exninfo.mlO. | ||
| 022a7cf0:· | 022a7cf0:·0387·0103·87c0·0402·4f01·0387·0103·a340··........O......@ | ||
| 022a7d00:· | 022a7d00:·a105·015f·40b1·2174·0064·4208·0000·3800··..._@.!t.dB...8. | ||
| 022a7d10:· | 022a7d10:·a0c0·9090·2161·0205·f5e1·0040·0103·4e40··....!a.....@..N@ | ||
| 022a7d20:· | 022a7d20:·4140·4190·c0b3·a190·041b·2566·6965·6c64··A@A.......%field | ||
| 022a7d30:· | 022a7d30:·a0c0·9604·0d44·4001·0368·4090·4002·05f5··.....D@..h@.@... | ||
| 022a7d40:· | 022a7d40:·e100·4001·036a·a047·40a0·4240·4040·b0c0··..@..j.G@.B@@@.. | ||
| 022a7d50:· | 022a7d50:·0419·5101·03a5·0103·a5c0·041a·5101·03a5··..Q.........Q... | ||
| 022a7d60:·0 | 022a7d60:·0103·bf40·4040·40a1·0501·7741·b124·696e··...@@@@...wA.$in | ||
| 022a7d70:· | 022a7d70:·666f·0065·4308·0000·3800·4040·4041·90c0··fo.eC...8.@@@A.. | ||
| 022a7d80:· | 022a7d80:·b3a1·9004·2e21·7440·9040·0205·f5e1·0040··.....!t@.@.....@ | ||
| 022a7d90:·0 | 022a7d90:·0103·7b40·4040·40b0·c004·2753·0103·c101··..{@@@@...'S.... | ||
| 022a7da0:· | 022a7da0:·03c1·c004·2853·0103·c101·03d4·4040·4040··....(S......@@@@ | ||
| 022a7db0:· | 022a7db0:·a105·0185·42b1·2469·6578·6e00·6644·0800··....B.$iexn.fD.. | ||
| 022a7dc0:· | 022a7dc0:·0038·0040·4040·4190·c092·a0c0·b390·0501··.8.@@@A......... | ||
| 022a7dd0:· | 022a7dd0:·1940·9040·0205·f5e1·0040·0103·84a0·c0b3··.@.@.....@...... | ||
| 022a7de0:· | 022a7de0:·9004·1d40·9040·0205·f5e1·0040·0103·8540··...@.@.....@...@ | ||
| Max diff block lines reached; 31479036/32066471 bytes (98.17%) of diff not shown. | |||
| Offset 2324522, 214160 lines modified | Offset 2324522, 214159 lines modified | ||
| 02378290:·4640·4142·0440·043e·4340·4084·95a6·be00··F@AB.@.>C@@..... | 02378290:·4640·4142·0440·043e·4340·4084·95a6·be00··F@AB.@.>C@@..... | ||
| 023782a0:·0000·5200·0000·0600·0000·2100·0000·17a0··..R.......!..... | 023782a0:·0000·5200·0000·0600·0000·2100·0000·17a0··..R.......!..... | ||
| 023782b0:·302e·2f5f·6275·696c·642f·6465·6661·756c··0./_build/defaul | 023782b0:·302e·2f5f·6275·696c·642f·6465·6661·756c··0./_build/defaul | ||
| 023782c0:·74a0·352e·2f5f·6275·696c·642f·6465·6661··t.5./_build/defa | 023782c0:·74a0·352e·2f5f·6275·696c·642f·6465·6661··t.5./_build/defa | ||
| 023782d0:·756c·742f·636c·6962·a009·252e·2f5f·6275··ult/clib..%./_bu | 023782d0:·756c·742f·636c·6962·a009·252e·2f5f·6275··ult/clib..%./_bu | ||
| 023782e0:·696c·642f·6465·6661·756c·742f·636c·6962··ild/default/clib | 023782e0:·696c·642f·6465·6661·756c·742f·636c·6962··ild/default/clib | ||
| 023782f0:·2f2e·636c·6962·2e6f·626a·732f·6279·7465··/.clib.objs/byte | 023782f0:·2f2e·636c·6962·2e6f·626a·732f·6279·7465··/.clib.objs/byte | ||
| 02378300:·4000·073e·4484·95a6·be00·001f·2 | 02378300:·4000·073e·4484·95a6·be00·001f·2300·0006··@..>D.......#... | ||
| 02378310:·0 | 02378310:·0300·0018·8600·0018·25a0·0800·002c·0001··........%....,.. | ||
| 02378320:·0244·2553·746f·7265·b0c0·265f·6e6f·6e65··.D%Store..&_none | 02378320:·0244·2553·746f·7265·b0c0·265f·6e6f·6e65··.D%Store..&_none | ||
| 02378330:·5f40·4000·ff04·0241·4122·3f3f·4140·d040··_@@....AA"??A@.@ | 02378330:·5f40·4000·ff04·0241·4122·3f3f·4140·d040··_@@....AA"??A@.@ | Diff chunk too large, falling back to line-by-line diff (3608 lines added, 3608 lines removed) | |
| 02378340:·4040·4040·b040·4040·4040·a008·0000·2c00··@@@@.@@@@@....,. | 02378340:·4040·4040·b040·4040·4040·a008·0000·2c00··@@@@.@@@@@....,. | ||
| 02378350:·0102·3804·0904·0841·223f·3f41·c3b4·aba | 02378350:·0102·3804·0904·0841·223f·3f41·c3b4·aba7··..8....A"??A.... | ||
| 02378360:· | 02378360:·b1b2·b2b2·b2b2·b2b2·b2b2·b2b2·b2b1·b1b1··................ | ||
| 02378370:·b1b1·b1b1·b1b1·b1b1·b1b1·b1b1·b1 | 02378370:·b1b1·b1b1·b1b1·b1b1·b1b1·b1b1·b140·a32a··.............@.* | ||
| 02378380:· | 02378380:·666c·6f61·7461·7272·6179·5108·0000·3800··floatarrayQ...8. | ||
| 02378390:· | 02378390:·4040·4041·4040·4040·4004·2d40·4040·9204··@@@A@@@@@.-@@@.. | ||
| 023783a0:·0 | 023783a0:·03a3·3565·7874·656e·7369·6f6e·5f63·6f6e··..5extension_con | ||
| 023783b0:· | 023783b0:·7374·7275·6374·6f72·5008·0000·3800·4040··structorP...8.@@ | ||
| 023783c0:·404 | 023783c0:·4041·4040·4040·4004·3140·4040·9204·03a3··@A@@@@@.1@@@.... | ||
| 023783d0:· | 023783d0:·2369·6e74·4108·0000·3800·4040·4041·4040··#intA...8.@@@A@@ | ||
| 023783e0:·4040·40 | 023783e0:·4040·4004·3540·4140·9204·03a3·2463·6861··@@@.5@A@....$cha | ||
| 023783f0:· | 023783f0:·7242·0800·0038·0040·4040·4140·4040·4040··rB...8.@@@A@@@@@ | ||
| 02378400:· | 02378400:·0439·4041·4092·0403·a326·7374·7269·6e67··.9@A@....&string | ||
| 02378410:· | 02378410:·4f08·0000·3800·4040·4041·4040·4040·4004··O...8.@@@A@@@@@. | ||
| 02378420:· | 02378420:·3d40·4040·9204·03a3·2566·6c6f·6174·4408··=@@@....%floatD. | ||
| 02378430:·0 | 02378430:·0000·3800·4040·4041·4040·4040·4004·4140··..8.@@@A@@@@@.A@ | ||
| 02378440:·4040· | 02378440:·4040·9204·03a3·2462·6f6f·6c45·0800·0038··@@....$boolE...8 | ||
| 02378450:· | 02378450:·0040·40a1·a0e0·a325·6661·6c73·655e·9040··.@@....%false^.@ | ||
| 02378460:·40 | 02378460:·4004·4b40·9204·03a0·e0a3·2474·7275·655f··@.K@......$true_ | ||
| 02378470:· | 02378470:·9040·4004·5140·9204·0340·4041·4040·4040··.@@.Q@...@@A@@@@ | ||
| 02378480:·40 | 02378480:·4004·5240·4140·9204·10a3·2475·6e69·7446··@.R@A@....$unitF | ||
| 02378490:· | 02378490:·0800·0038·0040·40a1·a0e0·a322·2829·6090··...8.@@...."()`. | ||
| 023784a0:· | 023784a0:·4040·045c·4092·0403·4040·4140·4040·4040··@@.\@...@@A@@@@@ | ||
| 023784b0:· | 023784b0:·045d·4041·4092·040a·a323·6578·6e47·0800··.]@A@....#exnG.. | ||
| 023784c0:·00 | 023784c0:·0038·0040·4041·4140·4040·4040·0461·4040··.8.@@AA@@@@@.a@@ | ||
| 023784d0:·40 | 023784d0:·4092·0403·a325·6172·7261·7948·0800·0038··@....%arrayH...8 | ||
| 023784e0:· | 023784e0:·00a0·c090·4002·05f5·e100·404f·4041·4041··....@.....@O@A@A | ||
| 023784f0:·4 | 023784f0:·40a0·007f·40a0·4040·4040·046a·4040·4092··@...@.@@@@.j@@@. | ||
| 02378500:· | 02378500:·0408·a324·6c69·7374·4908·0000·3800·a0c0··...$listI...8... | ||
| 02378510:· | 02378510:·0409·0205·f5e1·0040·5040·41a1·a0e0·a322··.......@P@A...." | ||
| 02378520:· | 02378520:·5b5d·6190·4040·0476·4092·0403·a0e0·a322··[]a.@@.v@......" | ||
| 02378530:· | 02378530:·3a3a·6290·a004·0ea0·c0b3·9004·16a0·0413··::b............. | ||
| 02378540:· | 02378540:·4090·4002·05f5·e100·4051·4040·0483·4092··@.@.....@Q@@..@. | ||
| 02378550:· | 02378550:·040a·4040·4140·a059·40a0·4040·4040·0486··..@@A@.Y@.@@@@.. | ||
| 02378560:· | 02378560:·4040·4092·041b·a326·6f70·7469·6f6e·4a08··@@@....&optionJ. | ||
| 02378570:·0 | 02378570:·0000·3800·a0c0·0425·0205·f5e1·0040·5340··..8....%.....@S@ | ||
| 02378580:·4 | 02378580:·41a1·a0e0·a324·4e6f·6e65·6390·4040·0492··A....$Nonec.@@.. | ||
| 02378590:· | 02378590:·4092·0403·a0e0·a324·536f·6d65·6490·a004··@......$Somed... | ||
| 023785a0:·040 | 023785a0:·0e40·4004·9940·9204·0440·4041·40a0·5940··.@@..@...@@A@.Y@ | ||
| 023785b0:· | 023785b0:·a040·4040·4004·9c40·4040·9204·15a3·266c··.@@@@..@@@....&l | ||
| 023785c0:·6 | 023785c0:·617a·795f·744e·0800·0038·00a0·c004·3b02··azy_tN...8....;. | ||
| 023785d0:·0 | 023785d0:·05f5·e100·4055·4041·4041·40a0·5940·a040··....@U@A@A@.Y@.@ | ||
| 023785e0:·4040·40 | 023785e0:·4040·4004·a440·4040·9204·07a3·296e·6174··@@@..@@@....)nat | ||
| 023785f0:· | 023785f0:·6976·6569·6e74·4b08·0000·3800·4040·4041··iveintK...8.@@@A | ||
| 02378600:·4 | 02378600:·4040·4040·4004·a840·4040·9204·03a3·2569··@@@@@..@@@....%i | ||
| 02378610:·6 | 02378610:·6e74·3332·4c08·0000·3800·4040·4041·4040··nt32L...8.@@@A@@ | ||
| 02378620:·4040·40 | 02378620:·4040·4004·ac40·4040·9204·03a3·2569·6e74··@@@..@@@....%int | ||
| 02378630:· | 02378630:·3634·4d08·0000·3800·4040·4041·4040·4040··64M...8.@@@A@@@@ | ||
| 02378640:·404 | 02378640:·4004·b040·4040·9204·03a3·3a55·6e64·6566··@..@@@....:Undef | ||
| 02378650:·6 | 02378650:·696e·6564·5f72·6563·7572·7369·7665·5f6d··ined_recursive_m | ||
| 02378660:·6 | 02378660:·6f64·756c·655d·0800·0020·0090·0457·4090··odule]...·...W@. | ||
| 02378670:· | 02378670:·a0c0·92a0·c0b3·9004·8340·9040·0205·f5e1··.........@.@.... | ||
| 02378680:· | 02378680:·0040·4aa0·c0b3·9004·9040·9040·0205·f5e1··.@J......@.@.... | ||
| 02378690:· | 02378690:·0040·40a0·0405·4002·05f5·e100·4056·4040··.@@...@.....@V@@ | ||
| 023786a0:·404 | 023786a0:·4104·c4a0·b0a0·3d6f·6361·6d6c·2e77·6172··A.....=ocaml.war | ||
| 023786b0:· | 023786b0:·6e5f·6f6e·5f6c·6974·6572·616c·5f70·6174··n_on_literal_pat | ||
| 023786c0:·74 | 023786c0:·7465·726e·04c8·0461·04c8·4092·0417·a32e··tern...a..@..... | ||
| 023786d0:· | 023786d0:·4173·7365·7274·5f66·6169·6c75·7265·5c08··Assert_failure\. | ||
| 023786e0:·0 | 023786e0:·0000·2000·0418·4090·a0c0·92a0·0417·a004··..·...@......... | ||
| 023786f0:· | 023786f0:·13a0·0414·4002·05f5·e100·4058·4040·4104··....@.....@X@@A. | ||
| 02378700:· | 02378700:·d3a0·b0a0·040f·04d6·046f·04d6·4092·040d··.........o..@... | ||
| 02378710:· | 02378710:·a330·4469·7669·7369·6f6e·5f62·795f·7a65··.0Division_by_ze | ||
| 02378720:· | 02378720:·726f·5908·0000·2000·0426·4090·4040·4104··roY...·..&@.@@A. | ||
| 02378730:· | 02378730:·dba0·b0a0·0417·04de·0477·04de·4092·0407··.........w..@... | ||
| 02378740:· | 02378740:·a32b·456e·645f·6f66·5f66·696c·6558·0800··.+End_of_fileX.. | ||
| 02378750:·00 | 02378750:·0020·0004·2e40·9040·4041·04e3·a0b0·a004··.·...@.@@A...... | ||
| 02378760:· | 02378760:·1f04·e604·7f04·e640·9204·07a3·2953·7973··.......@....)Sys | ||
| 02378770:· | 02378770:·5f65·7272·6f72·5708·0000·2000·0436·4090··_errorW...·..6@. | ||
| 02378780:· | 02378780:·a004·3240·4041·04ec·a0b0·a004·2804·ef04··..2@@A......(... | ||
| 02378790:· | 02378790:·8804·ef40·9204·08a3·2e53·7973·5f62·6c6f··...@.....Sys_blo | ||
| 023787a0:·6 | 023787a0:·636b·6564·5f69·6f5b·0800·0020·0004·3f40··cked_io[...·..?@ | ||
| 023787b0:· | 023787b0:·9040·4041·04f4·a0b0·a004·3004·f704·9004··.@@A......0..... | ||
| 023787c0:· | 023787c0:·f740·9204·07a3·294e·6f74·5f66·6f75·6e64··.@....)Not_found | ||
| 023787d0:· | 023787d0:·5608·0000·2000·0447·4090·4040·4104·fca0··V...·..G@.@@A... | ||
| 023787e0:· | 023787e0:·b0a0·0438·04ff·0498·04ff·4092·0407·a327··...8......@....' | ||
| 023787f0:· | 023787f0:·4661·696c·7572·6555·0800·0020·0004·4f40··FailureU...·..O@ | ||
| 02378800:· | 02378800:·90a0·044b·4040·4105·0105·a0b0·a004·4105··...K@@A.......A. | ||
| 02378810:·0 | 02378810:·0108·04a1·0501·0840·9204·08a3·3049·6e76··.......@....0Inv | ||
| 02378820:· | 02378820:·616c·6964·5f61·7267·756d·656e·7454·0800··alid_argumentT.. | ||
| 02378830:· | 02378830:·0020·0004·5840·90a0·0454·4040·4105·010e··.·..X@...T@@A... | ||
| 02378840:·0 | 02378840:·a0b0·a004·4a05·0111·04aa·0501·1140·9204··....J........@.. | ||
| 02378850:· | 02378850:·08a3·2e53·7461·636b·5f6f·7665·7266·6c6f··...Stack_overflo | ||
| 02378860:· | 02378860:·775a·0800·0020·0004·6140·9040·4041·0501··wZ...·..a@.@@A.. | ||
| 02378870:· | 02378870:·16a0·b0a0·0452·0501·1904·b205·0119·4092··.....R........@. | ||
| 02378880:· | 02378880:·0407·a32d·4f75·745f·6f66·5f6d·656d·6f72··...-Out_of_memor | ||
| 02378890:· | 02378890:·7953·0800·0020·0004·6940·9040·4041·0501··yS...·..i@.@@A.. | ||
| 023788a0:· | 023788a0:·1ea0·b0a0·045a·0501·2104·ba05·0121·4092··.....Z..!....!@. | ||
| 023788b0:· | 023788b0:·0407·a32d·4d61·7463·685f·6661·696c·7572··...-Match_failur | ||
| 023788c0:·6 | 023788c0:·6552·0800·0020·0004·7140·90a0·c092·a004··eR...·..q@...... | ||
| 023788d0:· | 023788d0:·70a0·046c·a004·6d40·0205·f5e1·0040·6340··p..l..m@.....@c@ | ||
| 023788e0:·40 | 023788e0:·4041·0501·2ca0·b0a0·0468·0501·2f04·c805··@A..,....h../... | ||
| 023788f0:·0 | 023788f0:·012f·4092·040d·a325·6279·7465·7343·0800··./@....%bytesC.. | ||
| 02378900:· | 02378900:·0038·0040·4040·4140·4040·4040·0501·3340··.8.@@@A@@@@@..3@ | ||
| 02378910:· | 02378910:·4040·9204·0390·9226·5374·646c·6962·9226··@@.....&Stdlib.& | ||
| 02378920:· | 02378920:·4f70·7469·6f6e·b121·5300·5943·c090·91a0··Option.!S.YC.... | ||
| 02378930:· | 02378930:·c1b1·2174·0051·4108·0000·3800·4040·4041··..!t.QA...8.@@@A | ||
| 02378940:· | 02378940:·4040·4040·40b0·c02d·636c·6962·2f73·746f··@@@@@..-clib/sto | ||
| 02378950:· | 02378950:·7265·2e6d·6c55·0103·f001·03f2·c004·0255··re.mlU.........U | ||
| 02378960:·f001·03f | 02378960:·0103·f001·03f8·4040·4040·a105·0149·4041··......@@@@...I@A | ||
| 02378970:·40 | 02378970:·40a0·c1b1·2566·6965·6c64·0052·4208·0000··@...%field.RB... | ||
| 02378980:· | 02378980:·3800·a0c0·9090·2161·0205·f5e1·0040·0103··8.....!a.....@.. | ||
| 02378990:· | 02378990:·1640·4140·4140·a047·40a0·4240·4040·b0c0··.@A@A@.G@.B@@@.. | ||
| 023789a0:·4 | 023789a0:·0411·5601·03f9·0103·fbc0·0412·5601·03f9··..V.........V... | ||
| 023789b0:· | 023789b0:·0104·0840·4040·40a1·0501·5941·4140·a0b0··...@@@@...YAA@.. | ||
| 023789c0:· | 023789c0:·a025·6669·656c·6400·53d0·c0c1·40c0·b390··.%field.S...@... | ||
| 023789d0:· | 023789d0:·0501·0f40·9040·0205·f5e1·0040·0103·18c0··...@.@.....@.... | ||
| 023789e0:· | 023789e0:·b390·041c·a0c0·96c0·9090·2161·0205·f5e1··..........!a.... | ||
| 023789f0:· | 023789f0:·0040·0103·1e43·4001·0319·4090·4002·05f5··.@...C@...@.@... | ||
| 02378a00:· | 02378a00:·e100·4001·031b·4002·05f5·e100·4001·031c··..@...@.....@... | ||
| 02378a10:· | 02378a10:·40b0·c004·2b57·0104·0901·040b·c004·2c57··@...+W........,W | ||
| 02378a20:·0 | 02378a20:·0104·0901·0427·4040·a105·0173·4240·a0b0··.....'@@...sB@.. | ||
| 02378a30:·a | 02378a30:·a025·656d·7074·7900·54d0·c0b3·9004·3a40··.%empty.T.....:@ | ||
| 02378a40:· | 02378a40:·9040·0205·f5e1·0040·0103·1f40·b0c0·0438··.@.....@...@...8 | ||
| 02378a50:·010 | 02378a50:·5801·0428·0104·2ac0·0439·5801·0428·0104··X..(..*..9X..(.. | ||
| 02378a60:· | 02378a60:·3740·40a1·0501·8043·40a0·b0a0·2373·6574··7@@....C@...#set | ||
| Max diff block lines reached; 29050441/29549418 bytes (98.31%) of diff not shown. | |||
| Offset 2437165, 1161507 lines modified | Offset 2437165, 1161502 lines modified | ||
| 025302c0:·4d42·4040·4140·4240·4084·95a6·be00·0000··MB@@A@B@@....... | 025302c0:·4d42·4040·4140·4240·4084·95a6·be00·0000··MB@@A@B@@....... | ||
| 025302d0:·5200·0000·0600·0000·2100·0000·17a0·302e··R.......!.....0. | 025302d0:·5200·0000·0600·0000·2100·0000·17a0·302e··R.......!.....0. | ||
| 025302e0:·2f5f·6275·696c·642f·6465·6661·756c·74a0··/_build/default. | 025302e0:·2f5f·6275·696c·642f·6465·6661·756c·74a0··/_build/default. | ||
| 025302f0:·352e·2f5f·6275·696c·642f·6465·6661·756c··5./_build/defaul | 025302f0:·352e·2f5f·6275·696c·642f·6465·6661·756c··5./_build/defaul | ||
| 02530300:·742f·636c·6962·a009·252e·2f5f·6275·696c··t/clib..%./_buil | 02530300:·742f·636c·6962·a009·252e·2f5f·6275·696c··t/clib..%./_buil | ||
| 02530310:·642f·6465·6661·756c·742f·636c·6962·2f2e··d/default/clib/. | 02530310:·642f·6465·6661·756c·742f·636c·6962·2f2e··d/default/clib/. | ||
| 02530320:·636c·6962·2e6f·626a·732f·6279·7465·4000··clib.objs/byte@. | 02530320:·636c·6962·2e6f·626a·732f·6279·7465·4000··clib.objs/byte@. | ||
| 02530330:·2a74·e084·95a6·be00·002f·c | 02530330:·2a74·e084·95a6·be00·002f·c400·0008·4200··*t......./....B. | ||
| 02530340:·0023·6 | 02530340:·0023·6700·0022·d3a0·0800·002c·0001·06ac··.#g..".....,.... | ||
| 02530350:·2745·786e·696e·666f·b0c0·265f·6e6f·6e65··'Exninfo..&_none | 02530350:·2745·786e·696e·666f·b0c0·265f·6e6f·6e65··'Exninfo..&_none | ||
| 02530360:·5f40·4000·ff04·0241·4122·3f3f·4140·d040··_@@....AA"??A@.@ | 02530360:·5f40·4000·ff04·0241·4122·3f3f·4140·d040··_@@....AA"??A@.@ | ||
| 02530370:·4040·4040·b040·4040·4040·a008·0000·2c00··@@@@.@@@@@....,. | 02530370:·4040·4040·b040·4040·4040·a008·0000·2c00··@@@@.@@@@@....,. | ||
| 02530380:·0106·5404·0904·0841·223f·3f41·b0b0·b0b0··..T....A"??A.... | 02530380:·0106·5404·0904·0841·223f·3f41·b0b0·b0b0··..T....A"??A.... | Diff chunk too large, falling back to line-by-line diff (5926 lines added, 5926 lines removed) | |
| 02530390:·b0b0·b0b0·b0b0·b1b0·b0b0·b0b0·b2b0·b0b0··................ | 02530390:·b0b0·b0b0·b0b0·b1b0·b0b0·b0b0·b2b0·b0b0··................ | ||
| 025303a0:·b0b1·b1b1·c3ab·a | 025303a0:·b0b1·b1b1·c3ab·a7b1·b2b2·b2b2·b2b2·b2b2··................ | ||
| 025303b0:·b2b2·b2b2·b | 025303b0:·b2b2·b2b2·b1b1·b1b1·b1b1·b1b1·b1b1·b1b1··................ | ||
| 025303c0:·b1b1·b1b1· | 025303c0:·b1b1·b1b1·40a3·2a66·6c6f·6174·6172·7261··....@.*floatarra | ||
| 025303d0:· | 025303d0:·7951·0800·0038·0040·4040·4140·4040·4040··yQ...8.@@@A@@@@@ | ||
| 025303e0:· | 025303e0:·0444·4040·4092·0403·a335·6578·7465·6e73··.D@@@....5extens | ||
| 025303f0:· | 025303f0:·696f·6e5f·636f·6e73·7472·7563·746f·7250··ion_constructorP | ||
| 02530400:· | 02530400:·0800·0038·0040·4040·4140·4040·4040·0448··...8.@@@A@@@@@.H | ||
| 02530410:·4 | 02530410:·4040·4092·0403·a323·696e·7441·0800·0038··@@@....#intA...8 | ||
| 02530420:· | 02530420:·0040·4040·4140·4040·4040·044c·4041·4092··.@@@A@@@@@.L@A@. | ||
| 02530430:· | 02530430:·0403·a324·6368·6172·4208·0000·3800·4040··...$charB...8.@@ | ||
| 02530440:·404 | 02530440:·4041·4040·4040·4004·5040·4140·9204·03a3··@A@@@@@.P@A@.... | ||
| 02530450:· | 02530450:·2673·7472·696e·674f·0800·0038·0040·4040··&stringO...8.@@@ | ||
| 02530460:·4 | 02530460:·4140·4040·4040·0454·4040·4092·0403·a325··A@@@@@.T@@@....% | ||
| 02530470:· | 02530470:·666c·6f61·7444·0800·0038·0040·4040·4140··floatD...8.@@@A@ | ||
| 02530480:·4040·4040· | 02530480:·4040·4040·0458·4040·4092·0403·a324·626f··@@@@.X@@@....$bo | ||
| 02530490:·6f6 | 02530490:·6f6c·4508·0000·3800·4040·a1a0·e0a3·2566··olE...8.@@....%f | ||
| 025304a0:·6 | 025304a0:·616c·7365·5e90·4040·0462·4092·0403·a0e0··alse^.@@.b@..... | ||
| 025304b0:· | 025304b0:·a324·7472·7565·5f90·4040·0468·4092·0403··.$true_.@@.h@... | ||
| 025304c0:· | 025304c0:·4040·4140·4040·4040·0469·4041·4092·0410··@@A@@@@@.i@A@... | ||
| 025304d0:· | 025304d0:·a324·756e·6974·4608·0000·3800·4040·a1a0··.$unitF...8.@@.. | ||
| 025304e0:· | 025304e0:·e0a3·2228·2960·9040·4004·7340·9204·0340··.."()`.@@.s@...@ | ||
| 025304f0:·404 | 025304f0:·4041·4040·4040·4004·7440·4140·9204·0aa3··@A@@@@@.t@A@.... | ||
| 02530500:· | 02530500:·2365·786e·4708·0000·3800·4040·4141·4040··#exnG...8.@@AA@@ | ||
| 02530510:·4040·40 | 02530510:·4040·4004·7840·4040·9204·03a3·2561·7272··@@@.x@@@....%arr | ||
| 02530520:· | 02530520:·6179·4808·0000·3800·a0c0·9040·0205·f5e1··ayH...8....@.... | ||
| 02530530:· | 02530530:·0040·4f40·4140·4140·a000·7f40·a040·4040··.@O@A@A@...@.@@@ | ||
| 02530540:·40 | 02530540:·4004·8140·4040·9204·08a3·246c·6973·7449··@..@@@....$listI | ||
| 02530550:· | 02530550:·0800·0038·00a0·c004·0902·05f5·e100·4050··...8..........@P | ||
| 02530560:· | 02530560:·4041·a1a0·e0a3·225b·5d61·9040·4004·8d40··@A...."[]a.@@..@ | ||
| 02530570:· | 02530570:·9204·03a0·e0a3·223a·3a62·90a0·040e·a0c0··......"::b...... | ||
| 02530580:· | 02530580:·b390·0416·a004·1340·9040·0205·f5e1·0040··.......@.@.....@ | ||
| 02530590:· | 02530590:·5140·4004·9a40·9204·0a40·4041·40a0·5940··Q@@..@...@@A@.Y@ | ||
| 025305a0:· | 025305a0:·a040·4040·4004·9d40·4040·9204·1ba3·266f··.@@@@..@@@....&o | ||
| 025305b0:· | 025305b0:·7074·696f·6e4a·0800·0038·00a0·c004·2502··ptionJ...8....%. | ||
| 025305c0:·0 | 025305c0:·05f5·e100·4053·4041·a1a0·e0a3·244e·6f6e··....@S@A....$Non | ||
| 025305d0:·6 | 025305d0:·6563·9040·4004·a940·9204·03a0·e0a3·2453··ec.@@..@......$S | ||
| 025305e0:· | 025305e0:·6f6d·6564·90a0·040e·4040·04b0·4092·0404··omed....@@..@... | ||
| 025305f0:· | 025305f0:·4040·4140·a059·40a0·4040·4040·04b3·4040··@@A@.Y@.@@@@..@@ | ||
| 02530600:·40 | 02530600:·4092·0415·a326·6c61·7a79·5f74·4e08·0000··@....&lazy_tN... | ||
| 02530610:· | 02530610:·3800·a0c0·043b·0205·f5e1·0040·5540·4140··8....;.....@U@A@ | ||
| 02530620:·4 | 02530620:·4140·a059·40a0·4040·4040·04bb·4040·4092··A@.Y@.@@@@..@@@. | ||
| 02530630:· | 02530630:·0407·a329·6e61·7469·7665·696e·744b·0800··...)nativeintK.. | ||
| 02530640:·00 | 02530640:·0038·0040·4040·4140·4040·4040·04bf·4040··.8.@@@A@@@@@..@@ | ||
| 02530650:·40 | 02530650:·4092·0403·a325·696e·7433·324c·0800·0038··@....%int32L...8 | ||
| 02530660:· | 02530660:·0040·4040·4140·4040·4040·04c3·4040·4092··.@@@A@@@@@..@@@. | ||
| 02530670:· | 02530670:·0403·a325·696e·7436·344d·0800·0038·0040··...%int64M...8.@ | ||
| 02530680:·4040·4 | 02530680:·4040·4140·4040·4040·04c7·4040·4092·0403··@@A@@@@@..@@@... | ||
| 02530690:· | 02530690:·a33a·556e·6465·6669·6e65·645f·7265·6375··.:Undefined_recu | ||
| 025306a0:·7 | 025306a0:·7273·6976·655f·6d6f·6475·6c65·5d08·0000··rsive_module]... | ||
| 025306b0:· | 025306b0:·2000·9004·5740·90a0·c092·a0c0·b390·0483···...W@.......... | ||
| 025306c0:· | 025306c0:·4090·4002·05f5·e100·404a·a0c0·b390·0490··@.@.....@J...... | ||
| 025306d0:· | 025306d0:·4090·4002·05f5·e100·4040·a004·0540·0205··@.@.....@@...@.. | ||
| 025306e0:· | 025306e0:·f5e1·0040·5640·4041·04db·a0b0·a03d·6f63··...@V@@A.....=oc | ||
| 025306f0:·6 | 025306f0:·616d·6c2e·7761·726e·5f6f·6e5f·6c69·7465··aml.warn_on_lite | ||
| 02530700:· | 02530700:·7261·6c5f·7061·7474·6572·6e04·df04·6104··ral_pattern...a. | ||
| 02530710:· | 02530710:·df40·9204·17a3·2e41·7373·6572·745f·6661··.@.....Assert_fa | ||
| 02530720:·6 | 02530720:·696c·7572·655c·0800·0020·0004·1840·90a0··ilure\...·...@.. | ||
| 02530730:· | 02530730:·c092·a004·17a0·0413·a004·1440·0205·f5e1··...........@.... | ||
| 02530740:· | 02530740:·0040·5840·4041·04ea·a0b0·a004·0f04·ed04··.@X@@A.......... | ||
| 02530750:· | 02530750:·6f04·ed40·9204·0da3·3044·6976·6973·696f··o..@....0Divisio | ||
| 02530760:·6 | 02530760:·6e5f·6279·5f7a·6572·6f59·0800·0020·0004··n_by_zeroY...·.. | ||
| 02530770:· | 02530770:·2640·9040·4041·04f2·a0b0·a004·1704·f504··&@.@@A.......... | ||
| 02530780:· | 02530780:·7704·f540·9204·07a3·2b45·6e64·5f6f·665f··w..@....+End_of_ | ||
| 02530790:· | 02530790:·6669·6c65·5808·0000·2000·042e·4090·4040··fileX...·...@.@@ | ||
| 025307a0:·4 | 025307a0:·4104·faa0·b0a0·041f·04fd·047f·04fd·4092··A.............@. | ||
| 025307b0:· | 025307b0:·0407·a329·5379·735f·6572·726f·7257·0800··...)Sys_errorW.. | ||
| 025307c0:·00 | 025307c0:·0020·0004·3640·90a0·0432·4040·4105·0103··.·..6@...2@@A... | ||
| 025307d0:· | 025307d0:·a0b0·a004·2805·0106·0488·0501·0640·9204··....(........@.. | ||
| 025307e0:·0 | 025307e0:·08a3·2e53·7973·5f62·6c6f·636b·6564·5f69··...Sys_blocked_i | ||
| 025307f0:·6 | 025307f0:·6f5b·0800·0020·0004·3f40·9040·4041·0501··o[...·..?@.@@A.. | ||
| 02530800:·0 | 02530800:·0ba0·b0a0·0430·0501·0e04·9005·010e·4092··.....0........@. | ||
| 02530810:· | 02530810:·0407·a329·4e6f·745f·666f·756e·6456·0800··...)Not_foundV.. | ||
| 02530820:·00 | 02530820:·0020·0004·4740·9040·4041·0501·13a0·b0a0··.·..G@.@@A...... | ||
| 02530830:· | 02530830:·0438·0501·1604·9805·0116·4092·0407·a327··.8........@....' | ||
| 02530840:· | 02530840:·4661·696c·7572·6555·0800·0020·0004·4f40··FailureU...·..O@ | ||
| 02530850:· | 02530850:·90a0·044b·4040·4105·011c·a0b0·a004·4105··...K@@A.......A. | ||
| 02530860:·0 | 02530860:·011f·04a1·0501·1f40·9204·08a3·3049·6e76··.......@....0Inv | ||
| 02530870:· | 02530870:·616c·6964·5f61·7267·756d·656e·7454·0800··alid_argumentT.. | ||
| 02530880:·00 | 02530880:·0020·0004·5840·90a0·0454·4040·4105·0125··.·..X@...T@@A..% | ||
| 02530890:· | 02530890:·a0b0·a004·4a05·0128·04aa·0501·2840·9204··....J..(....(@.. | ||
| 025308a0:·0 | 025308a0:·08a3·2e53·7461·636b·5f6f·7665·7266·6c6f··...Stack_overflo | ||
| 025308b0:· | 025308b0:·775a·0800·0020·0004·6140·9040·4041·0501··wZ...·..a@.@@A.. | ||
| 025308c0:· | 025308c0:·2da0·b0a0·0452·0501·3004·b205·0130·4092··-....R..0....0@. | ||
| 025308d0:· | 025308d0:·0407·a32d·4f75·745f·6f66·5f6d·656d·6f72··...-Out_of_memor | ||
| 025308e0:·7 | 025308e0:·7953·0800·0020·0004·6940·9040·4041·0501··yS...·..i@.@@A.. | ||
| 025308f0:· | 025308f0:·35a0·b0a0·045a·0501·3804·ba05·0138·4092··5....Z..8....8@. | ||
| 02530900:· | 02530900:·0407·a32d·4d61·7463·685f·6661·696c·7572··...-Match_failur | ||
| 02530910:· | 02530910:·6552·0800·0020·0004·7140·90a0·c092·a004··eR...·..q@...... | ||
| 02530920:· | 02530920:·70a0·046c·a004·6d40·0205·f5e1·0040·6340··p..l..m@.....@c@ | ||
| 02530930:·404 | 02530930:·4041·0501·43a0·b0a0·0468·0501·4604·c805··@A..C....h..F... | ||
| 02530940:·0 | 02530940:·0146·4092·040d·a325·6279·7465·7343·0800··.F@....%bytesC.. | ||
| 02530950:·00 | 02530950:·0038·0040·4040·4140·4040·4040·0501·4a40··.8.@@@A@@@@@..J@ | ||
| 02530960:·4040· | 02530960:·4040·9204·0390·9226·5374·646c·6962·9226··@@.....&Stdlib.& | ||
| 02530970:· | 02530970:·4f70·7469·6f6e·b125·5374·6f72·6500·6341··Option.%Store.cA | ||
| 02530980:· | 02530980:·40c0·90a1·9092·2553·746f·7265·2153·40b0··@.....%Store!S@. | ||
| 02530990:· | 02530990:·c02f·636c·6962·2f65·786e·696e·666f·2e6d··./clib/exninfo.m | ||
| 025309a0:·6 | 025309a0:·6c4f·0103·8701·0387·c004·024f·0103·8701··lO.........O.... | ||
| 025309b0:·0 | 025309b0:·03a3·40a1·0501·5f40·b121·7400·6442·0800··..@..._@.!t.dB.. | ||
| 025309c0:· | 025309c0:·0038·00a0·c090·9021·6102·05f5·e100·4001··.8.....!a.....@. | ||
| 025309d0:·0 | 025309d0:·034e·4041·4041·90c0·b3a1·9004·1b25·6669··.N@A@A.......%fi | ||
| 025309e0:· | 025309e0:·656c·64a0·c096·040d·4440·0103·6840·9040··eld.....D@..h@.@ | ||
| 025309f0:·0 | 025309f0:·0205·f5e1·0040·0103·6aa0·4740·a042·4040··.....@..j.G@.B@@ | ||
| 02530a00:·4 | 02530a00:·40b0·c004·1951·0103·a501·03a5·c004·1a51··@....Q.........Q | ||
| 02530a10:·0 | 02530a10:·0103·a501·03bf·4040·4040·a105·0177·41b1··......@@@@...wA. | ||
| 02530a20:· | 02530a20:·2469·6e66·6f00·6543·0800·0038·0040·4040··$info.eC...8.@@@ | ||
| 02530a30:· | 02530a30:·4190·c0b3·a190·042e·2174·4090·4002·05f5··A.......!t@.@... | ||
| 02530a40:· | 02530a40:·e100·4001·037b·4040·4040·b0c0·0427·5301··..@..{@@@@...'S. | ||
| 02530a50:· | 02530a50:·03c1·0103·c1c0·0428·5301·03c1·0103·d440··.......(S......@ | ||
| 02530a60:· | 02530a60:·4040·40a1·0501·8542·b124·6965·786e·0066··@@@....B.$iexn.f | ||
| 02530a70:· | 02530a70:·4408·0000·3800·4040·4041·90c0·92a0·c0b3··D...8.@@@A...... | ||
| 02530a80:·90 | 02530a80:·9005·0119·4090·4002·05f5·e100·4001·0384··....@.@.....@... | ||
| 02530a90:· | 02530a90:·a0c0·b390·041d·4090·4002·05f5·e100·4001··......@.@.....@. | ||
| Max diff block lines reached; 159462156/160281157 bytes (99.49%) 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····61 | 2 | -rw-r--r--···0········0········0····61208·2022-11-29·08:28:08.000000·control.tar.xz |
| 3 | -rw-r--r--···0········0········0·426625 | 3 | -rw-r--r--···0········0········0·42662520·2022-11-29·08:28:08.000000·data.tar.xz |
| Offset 59, 15 lines modified | Offset 59, 15 lines modified | ||
| 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 | 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)····10160·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cObj.cmti | 60 | -rw-r--r--···0·root·········(0)·root·········(0)····10160·2022-11-29·08:28:08.000000·./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)····207 | 66 | -rw-r--r--···0·root·········(0)·root·········(0)····20718·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cSet.cmti |
| 67 | -rw-r--r--···0·root·········(0)·root·········(0)······412·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cSet.cmx | 67 | -rw-r--r--···0·root·········(0)·root·········(0)······412·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cSet.cmx |
| 68 | -rw-r--r--···0·root·········(0)·root·········(0)·····1924·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cSet.ml | 68 | -rw-r--r--···0·root·········(0)·root·········(0)·····1924·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cSet.ml |
| 69 | -rw-r--r--···0·root·········(0)·root·········(0)·····1181·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cSet.mli | 69 | -rw-r--r--···0·root·········(0)·root·········(0)·····1181·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cSet.mli |
| 70 | -rw-r--r--···0·root·········(0)·root·········(0)·····8503·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cSig.cmi | 70 | -rw-r--r--···0·root·········(0)·root·········(0)·····8503·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cSig.cmi |
| 71 | -rw-r--r--···0·root·········(0)·root·········(0)····39537·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cSig.cmti | 71 | -rw-r--r--···0·root·········(0)·root·········(0)····39537·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cSig.cmti |
| 72 | -rw-r--r--···0·root·········(0)·root·········(0)·····3238·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cSig.mli | 72 | -rw-r--r--···0·root·········(0)·root·········(0)·····3238·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cSig.mli |
| 73 | -rw-r--r--···0·root·········(0)·root·········(0)····57881·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cString.cmi | 73 | -rw-r--r--···0·root·········(0)·root·········(0)····57881·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/cString.cmi |
| Offset 451, 846 lines modified | Offset 451, 845 lines modified | ||
| 00001c20:·363f·a2a0·a028·4861·7368·636f·6e73·9030··6?...(Hashcons.0 | 00001c20:·363f·a2a0·a028·4861·7368·636f·6e73·9030··6?...(Hashcons.0 | ||
| 00001c30:·b0fc·2f01·7728·f7c9·7a23·66c2·95b8·4eef··../.w(..z#f...N. | 00001c30:·b0fc·2f01·7728·f7c9·7a23·66c2·95b8·4eef··../.w(..z#f...N. | ||
| 00001c40:·a0a0·3843·616d·6c69·6e74·6572·6e61·6c46··..8CamlinternalF | 00001c40:·a0a0·3843·616d·6c69·6e74·6572·6e61·6c46··..8CamlinternalF | ||
| 00001c50:·6f72·6d61·7442·6173·6963·7390·30c4·b583··ormatBasics.0... | 00001c50:·6f72·6d61·7442·6173·6963·7390·30c4·b583··ormatBasics.0... | ||
| 00001c60:·a727·ec28·f5bc·9ba3·6adc·64cf·c740·8495··.'.(....j.d..@.. | 00001c60:·a727·ec28·f5bc·9ba3·6adc·64cf·c740·8495··.'.(....j.d..@.. | ||
| 00001c70:·a6be·0000·0008·0000·0004·0000·000b·0000··................ | 00001c70:·a6be·0000·0008·0000·0004·0000·000b·0000··................ | ||
| 00001c80:·000b·a040·a041·a090·4040·4361·6d6c·3139··...@.A..@@Caml19 | 00001c80:·000b·a040·a041·a090·4040·4361·6d6c·3139··...@.A..@@Caml19 | ||
| 00001c90:·3939·5430·3330·8495·a6be·0000·344 | 00001c90:·3939·5430·3330·8495·a6be·0000·3444·0000··99T030......4D.. | ||
| 00001ca0:·090 | 00001ca0:·0908·0000·2526·0000·2404·0800·0034·0024··....%&..$....4.$ | ||
| 00001cb0:·4353·6574·92b0·a0b0·98d0·b12b·4f72·6465··CSet.......+Orde | 00001cb0:·4353·6574·92b0·a0b0·98d0·b12b·4f72·6465··CSet.......+Orde | ||
| 00001cc0:·7265·6454·7970·6500·5342·a004·02b0·c02d··redType.SB.....- | 00001cc0:·7265·6454·7970·6500·5342·a004·02b0·c02d··redType.SB.....- | ||
| 00001cd0:·636c·6962·2f63·5365·742e·6d6c·694b·0102··clib/cSet.mliK.. | 00001cd0:·636c·6962·2f63·5365·742e·6d6c·694b·0102··clib/cSet.mliK.. | ||
| 00001ce0:·a401·02b0·c004·024b·0102·a401·02bb·4090··.......K......@. | 00001ce0:·a401·02b0·c004·024b·0102·a401·02bb·4090··.......K......@. | ||
| 00001cf0:·d091·b0a0·b0a1·41a0·0800·0028·00b1·2174··......A....(..!t | 00001cf0:·d091·b0a0·b0a1·41a0·0800·0028·00b1·2174··......A....(..!t | ||
| 00001d00:·0051·41a0·0402·b0c0·0410·4d01·02c2·0102··.QA.......M..... | 00001d00:·0051·41a0·0402·b0c0·0410·4d01·02c2·0102··.QA.......M..... | ||
| 00001d10:·c9c0·0411·4d01·02c2·0102·ca40·4008·0000··....M......@@... | 00001d10:·c9c0·0411·4d01·02c2·0102·ca40·4008·0000··....M......@@... | ||
| 00001d20:·3800·4040·4041·4040·4040·40b0·c004·144d··8.@@@A@@@@@....M | 00001d20:·3800·4040·4041·4040·4040·40b0·c004·144d··8.@@@A@@@@@....M | ||
| 00001d30:·0102·c201·02c4·0404·4040·4040·a104·2140··........@@@@..!@ | 00001d30:·0102·c201·02c4·0404·4040·4040·a104·2140··........@@@@..!@ | ||
| 00001d40:·4040·4140·0403·4040·0800·0030·00a0·4040··@@A@..@@...0..@@ | 00001d40:·4040·4140·0403·4040·0800·0030·00a0·4040··@@A@..@@...0..@@ | Diff chunk too large, falling back to line-by-line diff (726 lines added, 726 lines removed) | |
| 00001d50:·0401·0401·0401·0401·0401·0401·0401·40ab··..............@. | 00001d50:·0401·0401·0401·0401·0401·0401·0401·40ab··..............@. | ||
| 00001d60:·a | 00001d60:·a7b1·b2b2·b2b2·b2b2·b2b2·b2b2·b2b2·b1b1··................ | ||
| 00001d70:·b1b1·b1b1·b1b1·b1b1·b1b1·b1b1·b1b1· | 00001d70:·b1b1·b1b1·b1b1·b1b1·b1b1·b1b1·b1b1·40a3··..............@. | ||
| 00001d80:· | 00001d80:·2a66·6c6f·6174·6172·7261·7951·0800·0038··*floatarrayQ...8 | ||
| 00001d90:· | 00001d90:·0040·4040·4140·4040·4040·b0c0·265f·6e6f··.@@@A@@@@@..&_no | ||
| 00001da0:·6 | 00001da0:·6e65·5f40·4000·ff04·0241·4040·4092·0406··ne_@@....A@@@... | ||
| 00001db0:· | 00001db0:·a335·6578·7465·6e73·696f·6e5f·636f·6e73··.5extension_cons | ||
| 00001dc0:·7 | 00001dc0:·7472·7563·746f·7250·0800·0038·0040·4040··tructorP...8.@@@ | ||
| 00001dd0:·4 | 00001dd0:·4140·4040·4040·0407·4040·4092·0403·a323··A@@@@@..@@@....# | ||
| 00001de0:· | 00001de0:·696e·7441·0800·0038·0040·4040·4140·4040··intA...8.@@@A@@@ | ||
| 00001df0:·4040· | 00001df0:·4040·040b·4041·4092·0403·a324·6368·6172··@@..@A@....$char | ||
| 00001e00:· | 00001e00:·4208·0000·3800·4040·4041·4040·4040·4004··B...8.@@@A@@@@@. | ||
| 00001e10:·040 | 00001e10:·0f40·4140·9204·03a3·2673·7472·696e·674f··.@A@....&stringO | ||
| 00001e20:· | 00001e20:·0800·0038·0040·4040·4140·4040·4040·0413··...8.@@@A@@@@@.. | ||
| 00001e30:· | 00001e30:·4040·4092·0403·a325·666c·6f61·7444·0800··@@@....%floatD.. | ||
| 00001e40:·00 | 00001e40:·0038·0040·4040·4140·4040·4040·0417·4040··.8.@@@A@@@@@..@@ | ||
| 00001e50:·40 | 00001e50:·4092·0403·a324·626f·6f6c·4508·0000·3800··@....$boolE...8. | ||
| 00001e60:· | 00001e60:·4040·a1a0·e0a3·2566·616c·7365·5e90·4040··@@....%false^.@@ | ||
| 00001e70:· | 00001e70:·0421·4092·0403·a0e0·a324·7472·7565·5f90··.!@......$true_. | ||
| 00001e80:· | 00001e80:·4040·0427·4092·0403·4040·4140·4040·4040··@@.'@...@@A@@@@@ | ||
| 00001e90:· | 00001e90:·0428·4041·4092·0410·a324·756e·6974·4608··.(@A@....$unitF. | ||
| 00001ea0:·0 | 00001ea0:·0000·3800·4040·a1a0·e0a3·2228·2960·9040··..8.@@...."()`.@ | ||
| 00001eb0:·40 | 00001eb0:·4004·3240·9204·0340·4041·4040·4040·4004··@.2@...@@A@@@@@. | ||
| 00001ec0:· | 00001ec0:·3340·4140·9204·0aa3·2365·786e·4708·0000··3@A@....#exnG... | ||
| 00001ed0:· | 00001ed0:·3800·4040·4141·4040·4040·4004·3740·4040··8.@@AA@@@@@.7@@@ | ||
| 00001ee0:· | 00001ee0:·9204·03a3·2561·7272·6179·4808·0000·3800··....%arrayH...8. | ||
| 00001ef0:· | 00001ef0:·a0c0·9040·0205·f5e1·0040·4f40·4140·4140··...@.....@O@A@A@ | ||
| 00001f00:· | 00001f00:·a000·7f40·a040·4040·4004·4040·4040·9204··...@.@@@@.@@@@.. | ||
| 00001f10:·0 | 00001f10:·08a3·246c·6973·7449·0800·0038·00a0·c004··..$listI...8.... | ||
| 00001f20:·0 | 00001f20:·0902·05f5·e100·4050·4041·a1a0·e0a3·225b··......@P@A...."[ | ||
| 00001f30:·5 | 00001f30:·5d61·9040·4004·4c40·9204·03a0·e0a3·223a··]a.@@.L@......": | ||
| 00001f40:·3a | 00001f40:·3a62·90a0·040e·a0c0·b390·0416·a004·1340··:b.............@ | ||
| 00001f50:· | 00001f50:·9040·0205·f5e1·0040·5140·4004·5940·9204··.@.....@Q@@.Y@.. | ||
| 00001f60:·040 | 00001f60:·0a40·4041·40a0·5940·a040·4040·4004·5c40··.@@A@.Y@.@@@@.\@ | ||
| 00001f70:·4040· | 00001f70:·4040·9204·1ba3·266f·7074·696f·6e4a·0800··@@....&optionJ.. | ||
| 00001f80:·00 | 00001f80:·0038·00a0·c004·2502·05f5·e100·4053·4041··.8....%.....@S@A | ||
| 00001f90:· | 00001f90:·a1a0·e0a3·244e·6f6e·6563·9040·4004·6840··....$Nonec.@@.h@ | ||
| 00001fa0:· | 00001fa0:·9204·03a0·e0a3·2453·6f6d·6564·90a0·040e··......$Somed.... | ||
| 00001fb0:· | 00001fb0:·4040·046f·4092·0404·4040·4140·a059·40a0··@@.o@...@@A@.Y@. | ||
| 00001fc0:· | 00001fc0:·4040·4040·0472·4040·4092·0415·a326·6c61··@@@@.r@@@....&la | ||
| 00001fd0:· | 00001fd0:·7a79·5f74·4e08·0000·3800·a0c0·043b·0205··zy_tN...8....;.. | ||
| 00001fe0:· | 00001fe0:·f5e1·0040·5540·4140·4140·a059·40a0·4040··...@U@A@A@.Y@.@@ | ||
| 00001ff0:·4040· | 00001ff0:·4040·047a·4040·4092·0407·a329·6e61·7469··@@.z@@@....)nati | ||
| 00002000:· | 00002000:·7665·696e·744b·0800·0038·0040·4040·4140··veintK...8.@@@A@ | ||
| 00002010:·4040·4040· | 00002010:·4040·4040·047e·4040·4092·0403·a325·696e··@@@@.~@@@....%in | ||
| 00002020:· | 00002020:·7433·324c·0800·0038·0040·4040·4140·4040··t32L...8.@@@A@@@ | ||
| 00002030:·4040· | 00002030:·4040·0482·4040·4092·0403·a325·696e·7436··@@..@@@....%int6 | ||
| 00002040:·3 | 00002040:·344d·0800·0038·0040·4040·4140·4040·4040··4M...8.@@@A@@@@@ | ||
| 00002050:· | 00002050:·0486·4040·4092·0403·a33a·556e·6465·6669··..@@@....:Undefi | ||
| 00002060:·6 | 00002060:·6e65·645f·7265·6375·7273·6976·655f·6d6f··ned_recursive_mo | ||
| 00002070:·6 | 00002070:·6475·6c65·5d08·0000·2000·9004·5740·90a0··dule]...·...W@.. | ||
| 00002080:· | 00002080:·c092·a0c0·b390·0483·4090·4002·05f5·e100··........@.@..... | ||
| 00002090:· | 00002090:·404a·a0c0·b390·0490·4090·4002·05f5·e100··@J......@.@..... | ||
| 000020a0:· | 000020a0:·4040·a004·0540·0205·f5e1·0040·5640·4041··@@...@.....@V@@A | ||
| 000020b0:· | 000020b0:·049a·a0b0·a03d·6f63·616d·6c2e·7761·726e··.....=ocaml.warn | ||
| 000020c0:· | 000020c0:·5f6f·6e5f·6c69·7465·7261·6c5f·7061·7474··_on_literal_patt | ||
| 000020d0:· | 000020d0:·6572·6e04·9e04·6104·9e40·9204·17a3·2e41··ern...a..@.....A | ||
| 000020e0:· | 000020e0:·7373·6572·745f·6661·696c·7572·655c·0800··ssert_failure\.. | ||
| 000020f0:·00 | 000020f0:·0020·0004·1840·90a0·c092·a004·17a0·0413··.·...@.......... | ||
| 00002100:· | 00002100:·a004·1440·0205·f5e1·0040·5840·4041·04a9··...@.....@X@@A.. | ||
| 00002110:·a | 00002110:·a0b0·a004·0f04·ac04·6f04·ac40·9204·0da3··........o..@.... | ||
| 00002120:· | 00002120:·3044·6976·6973·696f·6e5f·6279·5f7a·6572··0Division_by_zer | ||
| 00002130:· | 00002130:·6f59·0800·0020·0004·2640·9040·4041·04b1··oY...·..&@.@@A.. | ||
| 00002140:· | 00002140:·a0b0·a004·1704·b404·7704·b440·9204·07a3··........w..@.... | ||
| 00002150:· | 00002150:·2b45·6e64·5f6f·665f·6669·6c65·5808·0000··+End_of_fileX... | ||
| 00002160:· | 00002160:·2000·042e·4090·4040·4104·b9a0·b0a0·041f···...@.@@A....... | ||
| 00002170:· | 00002170:·04bc·047f·04bc·4092·0407·a329·5379·735f··......@....)Sys_ | ||
| 00002180:· | 00002180:·6572·726f·7257·0800·0020·0004·3640·90a0··errorW...·..6@.. | ||
| 00002190:· | 00002190:·0432·4040·4104·c2a0·b0a0·0428·04c5·0488··.2@@A......(.... | ||
| 000021a0:· | 000021a0:·04c5·4092·0408·a32e·5379·735f·626c·6f63··..@.....Sys_bloc | ||
| 000021b0:·6 | 000021b0:·6b65·645f·696f·5b08·0000·2000·043f·4090··ked_io[...·..?@. | ||
| 000021c0:· | 000021c0:·4040·4104·caa0·b0a0·0430·04cd·0490·04cd··@@A......0...... | ||
| 000021d0:· | 000021d0:·4092·0407·a329·4e6f·745f·666f·756e·6456··@....)Not_foundV | ||
| 000021e0:· | 000021e0:·0800·0020·0004·4740·9040·4041·04d2·a0b0··...·..G@.@@A.... | ||
| 000021f0:· | 000021f0:·a004·3804·d504·9804·d540·9204·07a3·2746··..8......@....'F | ||
| 00002200:· | 00002200:·6169·6c75·7265·5508·0000·2000·044f·4090··ailureU...·..O@. | ||
| 00002210:· | 00002210:·a004·4b40·4041·04db·a0b0·a004·4104·de04··..K@@A......A... | ||
| 00002220:· | 00002220:·a104·de40·9204·08a3·3049·6e76·616c·6964··...@....0Invalid | ||
| 00002230:· | 00002230:·5f61·7267·756d·656e·7454·0800·0020·0004··_argumentT...·.. | ||
| 00002240:· | 00002240:·5840·90a0·0454·4040·4104·e4a0·b0a0·044a··X@...T@@A......J | ||
| 00002250:· | 00002250:·04e7·04aa·04e7·4092·0408·a32e·5374·6163··......@.....Stac | ||
| 00002260:·6 | 00002260:·6b5f·6f76·6572·666c·6f77·5a08·0000·2000··k_overflowZ...·. | ||
| 00002270:·0 | 00002270:·0461·4090·4040·4104·eca0·b0a0·0452·04ef··.a@.@@A......R.. | ||
| 00002280:· | 00002280:·04b2·04ef·4092·0407·a32d·4f75·745f·6f66··....@....-Out_of | ||
| 00002290:· | 00002290:·5f6d·656d·6f72·7953·0800·0020·0004·6940··_memoryS...·..i@ | ||
| 000022a0:· | 000022a0:·9040·4041·04f4·a0b0·a004·5a04·f704·ba04··.@@A......Z..... | ||
| 000022b0:· | 000022b0:·f740·9204·07a3·2d4d·6174·6368·5f66·6169··.@....-Match_fai | ||
| 000022c0:·6 | 000022c0:·6c75·7265·5208·0000·2000·0471·4090·a0c0··lureR...·..q@... | ||
| 000022d0:· | 000022d0:·92a0·0470·a004·6ca0·046d·4002·05f5·e100··...p..l..m@..... | ||
| 000022e0:· | 000022e0:·4063·4040·4105·0102·a0b0·a004·6805·0105··@c@@A.......h... | ||
| 000022f0:·0 | 000022f0:·04c8·0501·0540·9204·0da3·2562·7974·6573··.....@....%bytes | ||
| 00002300:· | 00002300:·4308·0000·3800·4040·4041·4040·4040·4005··C...8.@@@A@@@@@. | ||
| 00002310:·0 | 00002310:·0109·4040·4092·0403·9092·2653·7464·6c69··..@@@.....&Stdli | ||
| 00002320:·6 | 00002320:·6292·264f·7074·696f·6e40·41b0·0501·3605··b.&Option@A...6. | ||
| 00002330:· | 00002330:·0139·40a0·b090·f0a0·2763·6f6d·7061·7265··.9@.....'compare | ||
| 00002340:· | 00002340:·0052·a004·02b0·c005·0152·4e01·02cb·0102··.R.......RN..... | ||
| 00002350:· | 00002350:·d1c0·0501·534e·0102·cb01·02d8·40d0·b140··....SN......@..@ | ||
| 00002360:· | 00002360:·d0b3·9005·014d·a090·2174·b0c0·0501·5d4e··.....M..!t....]N | ||
| 00002370:· | 00002370:·0102·cb01·02db·c005·015e·4e01·02cb·0102··.........^N..... | ||
| 00002380:· | 00002380:·dc40·40c0·b304·0940·9040·0205·f5e1·0040··.@@....@.@.....@ | ||
| 00002390:·0 | 00002390:·0103·1508·0000·3000·0501·4c05·014c·0501··......0...L..L.. | ||
| 000023a0:·4 | 000023a0:·4c05·014c·0501·4c05·014c·0501·4c05·014c··L..L..L..L..L..L | ||
| 000023b0:·0501·4 | 000023b0:·40b1·0501·4c05·0158·0501·5240·41b0·0408··@...L..X..R@A... | ||
| 000023c0:· | 000023c0:·0407·4040·d0b1·40d0·b390·0501·5ea0·9021··..@@..@.....^..! | ||
| 000023d0:· | 000023d0:·74b0·c005·016e·4e01·02cb·0102·e0c0·0501··t....nN......... | ||
| 000023e0:· | 000023e0:·6f4e·0102·cb01·02e1·4040·c0b3·0409·4090··oN......@@....@. | ||
| 000023f0:· | 000023f0:·4002·05f5·e100·4001·0316·0411·b004·0604··@.....@......... | ||
| Max diff block lines reached; 13027/114826 bytes (11.34%) of diff not shown. | |||
| Offset 1, 9 lines modified | Offset 1, 9 lines modified | ||
| 00000000:·4361·6d6c·3139·3939·5430·3330·8495·a6be··Caml1999T030.... | 00000000:·4361·6d6c·3139·3939·5430·3330·8495·a6be··Caml1999T030.... | ||
| 00000010:·0000·7b | 00000010:·0000·7b8e·0000·15e9·0000·5a82·0000·5822··..{.......Z...X" | ||
| 00000020:·0800·0034·0027·4578·6e69·6e66·6f91·b0a0··...4.'Exninfo... | 00000020:·0800·0034·0027·4578·6e69·6e66·6f91·b0a0··...4.'Exninfo... | ||
| 00000030:·b09d·b0a0·2a6f·6361·6d6c·2e74·6578·74b0··....*ocaml.text. | 00000030:·b09d·b0a0·2a6f·6361·6d6c·2e74·6578·74b0··....*ocaml.text. | ||
| 00000040:·c026·5f6e·6f6e·655f·4040·00ff·0402·4190··.&_none_@@....A. | 00000040:·c026·5f6e·6f6e·655f·4040·00ff·0402·4190··.&_none_@@....A. | ||
| 00000050:·a0a0·a0c0·91b2·09dc·2045·6e72·6963·6865··........·Enriche | 00000050:·a0a0·a0c0·91b2·09dc·2045·6e72·6963·6865··........·Enriche | ||
| 00000060:·6420·6578·6365·7074·696f·6e73·2068·6176··d·exceptions·hav | 00000060:·6420·6578·6365·7074·696f·6e73·2068·6176··d·exceptions·hav | ||
| 00000070:·6520·616e·2061·6464·6974·696f·6e61·6c20··e·an·additional· | 00000070:·6520·616e·2061·6464·6974·696f·6e61·6c20··e·an·additional· | ||
| 00000080:·6669·656c·6420·6174·2074·6865·2065·6e64··field·at·the·end | 00000080:·6669·656c·6420·6174·2074·6865·2065·6e64··field·at·the·end |
| Offset 689, 1034 lines modified | Offset 689, 1034 lines modified | ||
| 00002b00:·6373·9030·c4b5·83a7·27ec·28f5·bc9b·a36a··cs.0....'.(....j | 00002b00:·6373·9030·c4b5·83a7·27ec·28f5·bc9b·a36a··cs.0....'.(....j | ||
| 00002b10:·dc64·cfc7·a0a0·2443·5369·6790·303f·15ce··.d....$CSig.0?.. | 00002b10:·dc64·cfc7·a0a0·2443·5369·6790·303f·15ce··.d....$CSig.0?.. | ||
| 00002b20:·d987·9a20·03e4·319b·37b8·b6e4·63a0·a024··...·..1.7...c..$ | 00002b20:·d987·9a20·03e4·319b·37b8·b6e4·63a0·a024··...·..1.7...c..$ | ||
| 00002b30:·434d·6170·9030·c521·9eea·9ff8·a030·c33b··CMap.0.!.....0.; | 00002b30:·434d·6170·9030·c521·9eea·9ff8·a030·c33b··CMap.0.!.....0.; | ||
| 00002b40:·5031·f3eb·5df6·4084·95a6·be00·0000·0800··P1..].@......... | 00002b40:·5031·f3eb·5df6·4084·95a6·be00·0000·0800··P1..].@......... | ||
| 00002b50:·0000·0400·0000·0b00·0000·0ba0·40a0·41a0··............@.A. | 00002b50:·0000·0400·0000·0b00·0000·0ba0·40a0·41a0··............@.A. | ||
| 00002b60:·9040·4043·616d·6c31·3939·3954·3033·3084··.@@Caml1999T030. | 00002b60:·9040·4043·616d·6c31·3939·3954·3033·3084··.@@Caml1999T030. | ||
| 00002b70:·95a6·be00·0040·1 | 00002b70:·95a6·be00·0040·1500·000b·0d00·002c·de00··.....@.......,.. | ||
| 00002b80:·002b·4 | 00002b80:·002b·4108·0000·3400·2448·4d61·7092·b0a0··.+A...4.$HMap... | ||
| 00002b90:·b098·d0b1·2a48·6173·6865·6454·7970·6500··....*HashedType. | 00002b90:·b098·d0b1·2a48·6173·6865·6454·7970·6500··....*HashedType. | ||
| 00002ba0:·5442·a004·02b0·c02d·636c·6962·2f68·4d61··TB.....-clib/hMa | 00002ba0:·5442·a004·02b0·c02d·636c·6962·2f68·4d61··TB.....-clib/hMa | ||
| 00002bb0:·702e·6d6c·694b·0102·a401·02b0·c004·024b··p.mliK.........K | 00002bb0:·702e·6d6c·694b·0102·a401·02b0·c004·024b··p.mliK.........K | ||
| 00002bc0:·0102·a401·02ba·4090·d091·b0a0·b0a1·41a0··......@.......A. | 00002bc0:·0102·a401·02ba·4090·d091·b0a0·b0a1·41a0··......@.......A. | ||
| 00002bd0:·0800·0028·00b1·2174·0051·41a0·0402·b0c0··...(..!t.QA..... | 00002bd0:·0800·0028·00b1·2174·0051·41a0·0402·b0c0··...(..!t.QA..... | ||
| 00002be0:·0410·4d01·02c1·0102·c8c0·0411·4d01·02c1··..M.........M... | 00002be0:·0410·4d01·02c1·0102·c8c0·0411·4d01·02c1··..M.........M... | ||
| 00002bf0:·0102·c940·4008·0000·3800·4040·4041·4040··...@@...8.@@@A@@ | 00002bf0:·0102·c940·4008·0000·3800·4040·4041·4040··...@@...8.@@@A@@ | ||
| 00002c00:·4040·40b0·c004·144d·0102·c101·02c3·0404··@@@....M........ | 00002c00:·4040·40b0·c004·144d·0102·c101·02c3·0404··@@@....M........ | ||
| 00002c10:·4040·4040·a104·2140·4040·4140·0403·4040··@@@@..!@@@A@..@@ | 00002c10:·4040·4040·a104·2140·4040·4140·0403·4040··@@@@..!@@@A@..@@ | Diff chunk too large, falling back to line-by-line diff (886 lines added, 886 lines removed) | |
| 00002c20:·0800·0030·00a0·4040·0401·0401·0401·0401··...0..@@........ | 00002c20:·0800·0030·00a0·4040·0401·0401·0401·0401··...0..@@........ | ||
| 00002c30:·0401·0401·0401·40ab·a | 00002c30:·0401·0401·0401·40ab·a7b1·b2b2·b2b2·b2b2··......@......... | ||
| 00002c40:·b2b2·b2b2·b2b2·b | 00002c40:·b2b2·b2b2·b2b2·b1b1·b1b1·b1b1·b1b1·b1b1··................ | ||
| 00002c50:·b1b1·b1b1·b1b1· | 00002c50:·b1b1·b1b1·b1b1·40a3·2a66·6c6f·6174·6172··......@.*floatar | ||
| 00002c60:·72 | 00002c60:·7261·7951·0800·0038·0040·4040·4140·4040··rayQ...8.@@@A@@@ | ||
| 00002c70:·4040· | 00002c70:·4040·b0c0·265f·6e6f·6e65·5f40·4000·ff04··@@..&_none_@@... | ||
| 00002c80:·0 | 00002c80:·0241·4040·4092·0406·a335·6578·7465·6e73··.A@@@....5extens | ||
| 00002c90:· | 00002c90:·696f·6e5f·636f·6e73·7472·7563·746f·7250··ion_constructorP | ||
| 00002ca0:· | 00002ca0:·0800·0038·0040·4040·4140·4040·4040·0407··...8.@@@A@@@@@.. | ||
| 00002cb0:· | 00002cb0:·4040·4092·0403·a323·696e·7441·0800·0038··@@@....#intA...8 | ||
| 00002cc0:· | 00002cc0:·0040·4040·4140·4040·4040·040b·4041·4092··.@@@A@@@@@..@A@. | ||
| 00002cd0:· | 00002cd0:·0403·a324·6368·6172·4208·0000·3800·4040··...$charB...8.@@ | ||
| 00002ce0:·404 | 00002ce0:·4041·4040·4040·4004·0f40·4140·9204·03a3··@A@@@@@..@A@.... | ||
| 00002cf0:· | 00002cf0:·2673·7472·696e·674f·0800·0038·0040·4040··&stringO...8.@@@ | ||
| 00002d00:·4 | 00002d00:·4140·4040·4040·0413·4040·4092·0403·a325··A@@@@@..@@@....% | ||
| 00002d10:· | 00002d10:·666c·6f61·7444·0800·0038·0040·4040·4140··floatD...8.@@@A@ | ||
| 00002d20:·4040·4040· | 00002d20:·4040·4040·0417·4040·4092·0403·a324·626f··@@@@..@@@....$bo | ||
| 00002d30:·6f6 | 00002d30:·6f6c·4508·0000·3800·4040·a1a0·e0a3·2566··olE...8.@@....%f | ||
| 00002d40:·6 | 00002d40:·616c·7365·5e90·4040·0421·4092·0403·a0e0··alse^.@@.!@..... | ||
| 00002d50:· | 00002d50:·a324·7472·7565·5f90·4040·0427·4092·0403··.$true_.@@.'@... | ||
| 00002d60:· | 00002d60:·4040·4140·4040·4040·0428·4041·4092·0410··@@A@@@@@.(@A@... | ||
| 00002d70:· | 00002d70:·a324·756e·6974·4608·0000·3800·4040·a1a0··.$unitF...8.@@.. | ||
| 00002d80:· | 00002d80:·e0a3·2228·2960·9040·4004·3240·9204·0340··.."()`.@@.2@...@ | ||
| 00002d90:·404 | 00002d90:·4041·4040·4040·4004·3340·4140·9204·0aa3··@A@@@@@.3@A@.... | ||
| 00002da0:· | 00002da0:·2365·786e·4708·0000·3800·4040·4141·4040··#exnG...8.@@AA@@ | ||
| 00002db0:·4040·40 | 00002db0:·4040·4004·3740·4040·9204·03a3·2561·7272··@@@.7@@@....%arr | ||
| 00002dc0:· | 00002dc0:·6179·4808·0000·3800·a0c0·9040·0205·f5e1··ayH...8....@.... | ||
| 00002dd0:· | 00002dd0:·0040·4f40·4140·4140·a000·7f40·a040·4040··.@O@A@A@...@.@@@ | ||
| 00002de0:·40 | 00002de0:·4004·4040·4040·9204·08a3·246c·6973·7449··@.@@@@....$listI | ||
| 00002df0:· | 00002df0:·0800·0038·00a0·c004·0902·05f5·e100·4050··...8..........@P | ||
| 00002e00:· | 00002e00:·4041·a1a0·e0a3·225b·5d61·9040·4004·4c40··@A...."[]a.@@.L@ | ||
| 00002e10:· | 00002e10:·9204·03a0·e0a3·223a·3a62·90a0·040e·a0c0··......"::b...... | ||
| 00002e20:· | 00002e20:·b390·0416·a004·1340·9040·0205·f5e1·0040··.......@.@.....@ | ||
| 00002e30:· | 00002e30:·5140·4004·5940·9204·0a40·4041·40a0·5940··Q@@.Y@...@@A@.Y@ | ||
| 00002e40:· | 00002e40:·a040·4040·4004·5c40·4040·9204·1ba3·266f··.@@@@.\@@@....&o | ||
| 00002e50:· | 00002e50:·7074·696f·6e4a·0800·0038·00a0·c004·2502··ptionJ...8....%. | ||
| 00002e60:·0 | 00002e60:·05f5·e100·4053·4041·a1a0·e0a3·244e·6f6e··....@S@A....$Non | ||
| 00002e70:·6 | 00002e70:·6563·9040·4004·6840·9204·03a0·e0a3·2453··ec.@@.h@......$S | ||
| 00002e80:· | 00002e80:·6f6d·6564·90a0·040e·4040·046f·4092·0404··omed....@@.o@... | ||
| 00002e90:· | 00002e90:·4040·4140·a059·40a0·4040·4040·0472·4040··@@A@.Y@.@@@@.r@@ | ||
| 00002ea0:·40 | 00002ea0:·4092·0415·a326·6c61·7a79·5f74·4e08·0000··@....&lazy_tN... | ||
| 00002eb0:· | 00002eb0:·3800·a0c0·043b·0205·f5e1·0040·5540·4140··8....;.....@U@A@ | ||
| 00002ec0:·4 | 00002ec0:·4140·a059·40a0·4040·4040·047a·4040·4092··A@.Y@.@@@@.z@@@. | ||
| 00002ed0:· | 00002ed0:·0407·a329·6e61·7469·7665·696e·744b·0800··...)nativeintK.. | ||
| 00002ee0:·00 | 00002ee0:·0038·0040·4040·4140·4040·4040·047e·4040··.8.@@@A@@@@@.~@@ | ||
| 00002ef0:·40 | 00002ef0:·4092·0403·a325·696e·7433·324c·0800·0038··@....%int32L...8 | ||
| 00002f00:· | 00002f00:·0040·4040·4140·4040·4040·0482·4040·4092··.@@@A@@@@@..@@@. | ||
| 00002f10:· | 00002f10:·0403·a325·696e·7436·344d·0800·0038·0040··...%int64M...8.@ | ||
| 00002f20:·4040·4 | 00002f20:·4040·4140·4040·4040·0486·4040·4092·0403··@@A@@@@@..@@@... | ||
| 00002f30:· | 00002f30:·a33a·556e·6465·6669·6e65·645f·7265·6375··.:Undefined_recu | ||
| 00002f40:·7 | 00002f40:·7273·6976·655f·6d6f·6475·6c65·5d08·0000··rsive_module]... | ||
| 00002f50:· | 00002f50:·2000·9004·5740·90a0·c092·a0c0·b390·0483···...W@.......... | ||
| 00002f60:· | 00002f60:·4090·4002·05f5·e100·404a·a0c0·b390·0490··@.@.....@J...... | ||
| 00002f70:· | 00002f70:·4090·4002·05f5·e100·4040·a004·0540·0205··@.@.....@@...@.. | ||
| 00002f80:· | 00002f80:·f5e1·0040·5640·4041·049a·a0b0·a03d·6f63··...@V@@A.....=oc | ||
| 00002f90:·6 | 00002f90:·616d·6c2e·7761·726e·5f6f·6e5f·6c69·7465··aml.warn_on_lite | ||
| 00002fa0:· | 00002fa0:·7261·6c5f·7061·7474·6572·6e04·9e04·6104··ral_pattern...a. | ||
| 00002fb0:· | 00002fb0:·9e40·9204·17a3·2e41·7373·6572·745f·6661··.@.....Assert_fa | ||
| 00002fc0:·6 | 00002fc0:·696c·7572·655c·0800·0020·0004·1840·90a0··ilure\...·...@.. | ||
| 00002fd0:· | 00002fd0:·c092·a004·17a0·0413·a004·1440·0205·f5e1··...........@.... | ||
| 00002fe0:· | 00002fe0:·0040·5840·4041·04a9·a0b0·a004·0f04·ac04··.@X@@A.......... | ||
| 00002ff0:· | 00002ff0:·6f04·ac40·9204·0da3·3044·6976·6973·696f··o..@....0Divisio | ||
| 00003000:·6 | 00003000:·6e5f·6279·5f7a·6572·6f59·0800·0020·0004··n_by_zeroY...·.. | ||
| 00003010:· | 00003010:·2640·9040·4041·04b1·a0b0·a004·1704·b404··&@.@@A.......... | ||
| 00003020:· | 00003020:·7704·b440·9204·07a3·2b45·6e64·5f6f·665f··w..@....+End_of_ | ||
| 00003030:· | 00003030:·6669·6c65·5808·0000·2000·042e·4090·4040··fileX...·...@.@@ | ||
| 00003040:·404 | 00003040:·4104·b9a0·b0a0·041f·04bc·047f·04bc·4092··A.............@. | ||
| 00003050:· | 00003050:·0407·a329·5379·735f·6572·726f·7257·0800··...)Sys_errorW.. | ||
| 00003060:·00 | 00003060:·0020·0004·3640·90a0·0432·4040·4104·c2a0··.·..6@...2@@A... | ||
| 00003070:· | 00003070:·b0a0·0428·04c5·0488·04c5·4092·0408·a32e··...(......@..... | ||
| 00003080:· | 00003080:·5379·735f·626c·6f63·6b65·645f·696f·5b08··Sys_blocked_io[. | ||
| 00003090:·0 | 00003090:·0000·2000·043f·4090·4040·4104·caa0·b0a0··..·..?@.@@A..... | ||
| 000030a0:· | 000030a0:·0430·04cd·0490·04cd·4092·0407·a329·4e6f··.0......@....)No | ||
| 000030b0:· | 000030b0:·745f·666f·756e·6456·0800·0020·0004·4740··t_foundV...·..G@ | ||
| 000030c0:· | 000030c0:·9040·4041·04d2·a0b0·a004·3804·d504·9804··.@@A......8..... | ||
| 000030d0:· | 000030d0:·d540·9204·07a3·2746·6169·6c75·7265·5508··.@....'FailureU. | ||
| 000030e0:·0 | 000030e0:·0000·2000·044f·4090·a004·4b40·4041·04db··..·..O@...K@@A.. | ||
| 000030f0:· | 000030f0:·a0b0·a004·4104·de04·a104·de40·9204·08a3··....A......@.... | ||
| 00003100:· | 00003100:·3049·6e76·616c·6964·5f61·7267·756d·656e··0Invalid_argumen | ||
| 00003110:· | 00003110:·7454·0800·0020·0004·5840·90a0·0454·4040··tT...·..X@...T@@ | ||
| 00003120:·404 | 00003120:·4104·e4a0·b0a0·044a·04e7·04aa·04e7·4092··A......J......@. | ||
| 00003130:· | 00003130:·0408·a32e·5374·6163·6b5f·6f76·6572·666c··....Stack_overfl | ||
| 00003140:·6 | 00003140:·6f77·5a08·0000·2000·0461·4090·4040·4104··owZ...·..a@.@@A. | ||
| 00003150:· | 00003150:·eca0·b0a0·0452·04ef·04b2·04ef·4092·0407··.....R......@... | ||
| 00003160:· | 00003160:·a32d·4f75·745f·6f66·5f6d·656d·6f72·7953··.-Out_of_memoryS | ||
| 00003170:· | 00003170:·0800·0020·0004·6940·9040·4041·04f4·a0b0··...·..i@.@@A.... | ||
| 00003180:· | 00003180:·a004·5a04·f704·ba04·f740·9204·07a3·2d4d··..Z......@....-M | ||
| 00003190:· | 00003190:·6174·6368·5f66·6169·6c75·7265·5208·0000··atch_failureR... | ||
| 000031a0:· | 000031a0:·2000·0471·4090·a0c0·92a0·0470·a004·6ca0···..q@......p..l. | ||
| 000031b0:· | 000031b0:·046d·4002·05f5·e100·4063·4040·4105·0102··.m@.....@c@@A... | ||
| 000031c0:· | 000031c0:·a0b0·a004·6805·0105·04c8·0501·0540·9204··....h........@.. | ||
| 000031d0:·0 | 000031d0:·0da3·2562·7974·6573·4308·0000·3800·4040··..%bytesC...8.@@ | ||
| 000031e0:·404 | 000031e0:·4041·4040·4040·4005·0109·4040·4092·0403··@A@@@@@...@@@... | ||
| 000031f0:· | 000031f0:·9092·2653·7464·6c69·6292·264f·7074·696f··..&Stdlib.&Optio | ||
| 00003200:· | 00003200:·6e40·41b0·0501·3605·0139·40a0·b090·f0a0··n@A...6..9@..... | ||
| 00003210:· | 00003210:·2763·6f6d·7061·7265·0052·a004·02b0·c005··'compare.R...... | ||
| 00003220:· | 00003220:·0152·4e01·02ca·0102·d0c0·0501·534e·0102··.RN.........SN.. | ||
| 00003230:· | 00003230:·ca01·02d7·40d0·b140·d0b3·9005·014d·a090··....@..@.....M.. | ||
| 00003240:· | 00003240:·2174·b0c0·0501·5d4e·0102·ca01·02da·c005··!t....]N........ | ||
| 00003250:· | 00003250:·015e·4e01·02ca·0102·db40·40c0·b304·0940··.^N......@@....@ | ||
| 00003260:· | 00003260:·9040·0205·f5e1·0040·0103·1508·0000·3000··.@.....@......0. | ||
| 00003270:· | 00003270:·0501·4c05·014c·0501·4c05·014c·0501·4c05··..L..L..L..L..L. | ||
| 00003280:·014 | 00003280:·014c·0501·4c05·014c·40b1·0501·4c05·0158··.L..L..L@...L..X | ||
| 00003290:·0501· | 00003290:·0501·5240·41b0·0408·0407·4040·d0b1·40d0··..R@A.....@@..@. | ||
| 000032a0:· | 000032a0:·b390·0501·5ea0·9021·74b0·c005·016e·4e01··....^..!t....nN. | ||
| 000032b0:·c00 | 000032b0:·02ca·0102·dfc0·0501·6f4e·0102·ca01·02e0··........oN...... | ||
| 000032c0:·0 | 000032c0:·4040·c0b3·0409·4090·4002·05f5·e100·4001··@@....@.@.....@. | ||
| 000032d0:·0 | 000032d0:·0316·0411·b004·0604·0540·40d0·b390·0501··.........@@..... | ||
| Max diff block lines reached; 17102/140914 bytes (12.14%) of diff not shown. | |||
| Offset 1, 2430 lines modified | Offset 1, 2430 lines modified | ||
| 00000000:·4361·6d6c·3139·3939·5430·3330·8495·a6be··Caml1999T030.... | 00000000:·4361·6d6c·3139·3939·5430·3330·8495·a6be··Caml1999T030.... | ||
| 00000010:·0000·97b | 00000010:·0000·97b4·0000·19c3·0000·6d09·0000·6ad7··..........m...j. | ||
| 00000020:·0800·0034·0028·4861·7368·636f·6e73·91b0··...4.(Hashcons.. | 00000020:·0800·0034·0028·4861·7368·636f·6e73·91b0··...4.(Hashcons.. | ||
| 00000030:·a0b0·98d0·b12e·4861·7368·636f·6e73·6564··......Hashconsed | 00000030:·a0b0·98d0·b12e·4861·7368·636f·6e73·6564··......Hashconsed | ||
| 00000040:·5479·7065·0056·43a0·0402·b0c0·3063·6c69··Type.VC.....0cli | 00000040:·5479·7065·0056·43a0·0402·b0c0·3063·6c69··Type.VC.....0cli | ||
| 00000050:·622f·6861·7368·636f·6e73·2e6d·6c59·0105··b/hashcons.mlY.. | 00000050:·622f·6861·7368·636f·6e73·2e6d·6c59·0105··b/hashcons.mlY.. | ||
| 00000060:·0e01·051a·c004·0259·0105·0e01·0528·4090··.......Y.....(@. | 00000060:·0e01·051a·c004·0259·0105·0e01·0528·4090··.......Y.....(@. | ||
| 00000070:·d091·b0a0·b0a1·41a0·0800·0028·00b1·2174··......A....(..!t | 00000070:·d091·b0a0·b0a1·41a0·0800·0028·00b1·2174··......A....(..!t | ||
| 00000080:·0051·41a0·0402·b0c0·0410·5b01·0531·0105··.QA.......[..1.. | 00000080:·0051·41a0·0402·b0c0·0410·5b01·0531·0105··.QA.......[..1.. | ||
| 00000090:·3ac0·0411·5b01·0531·0105·3b40·4008·0000··:...[..1..;@@... | 00000090:·3ac0·0411·5b01·0531·0105·3b40·4008·0000··:...[..1..;@@... | ||
| 000000a0:·3800·4040·4041·4040·4040·40b0·c004·145b··8.@@@A@@@@@....[ | 000000a0:·3800·4040·4041·4040·4040·40b0·c004·145b··8.@@@A@@@@@....[ | ||
| 000000b0:·0105·3101·0535·0404·4040·4040·a104·2140··..1..5..@@@@..!@ | 000000b0:·0105·3101·0535·0404·4040·4040·a104·2140··..1..5..@@@@..!@ | ||
| 000000c0:·4040·4140·0403·4040·0800·0030·00a0·4040··@@A@..@@...0..@@ | 000000c0:·4040·4140·0403·4040·0800·0030·00a0·4040··@@A@..@@...0..@@ | Diff chunk too large, falling back to line-by-line diff (2209 lines added, 2209 lines removed) | |
| 000000d0:·0401·0401·0401·0401·0401·0401·0401·40ab··..............@. | 000000d0:·0401·0401·0401·0401·0401·0401·0401·40ab··..............@. | ||
| 000000e0:·a | 000000e0:·a7b1·b2b2·b2b2·b2b2·b2b2·b2b2·b2b2·b1b1··................ | ||
| 000000f0:·b1b1·b1b1·b1b1·b1b1·b1b1·b1b1·b1b1· | 000000f0:·b1b1·b1b1·b1b1·b1b1·b1b1·b1b1·b1b1·40a3··..............@. | ||
| 00000100:· | 00000100:·2a66·6c6f·6174·6172·7261·7951·0800·0038··*floatarrayQ...8 | ||
| 00000110:· | 00000110:·0040·4040·4140·4040·4040·b0c0·265f·6e6f··.@@@A@@@@@..&_no | ||
| 00000120:·6 | 00000120:·6e65·5f40·4000·ff04·0241·4040·4092·0406··ne_@@....A@@@... | ||
| 00000130:· | 00000130:·a335·6578·7465·6e73·696f·6e5f·636f·6e73··.5extension_cons | ||
| 00000140:·7 | 00000140:·7472·7563·746f·7250·0800·0038·0040·4040··tructorP...8.@@@ | ||
| 00000150:·4 | 00000150:·4140·4040·4040·0407·4040·4092·0403·a323··A@@@@@..@@@....# | ||
| 00000160:· | 00000160:·696e·7441·0800·0038·0040·4040·4140·4040··intA...8.@@@A@@@ | ||
| 00000170:·4040· | 00000170:·4040·040b·4041·4092·0403·a324·6368·6172··@@..@A@....$char | ||
| 00000180:· | 00000180:·4208·0000·3800·4040·4041·4040·4040·4004··B...8.@@@A@@@@@. | ||
| 00000190:·040 | 00000190:·0f40·4140·9204·03a3·2673·7472·696e·674f··.@A@....&stringO | ||
| 000001a0:· | 000001a0:·0800·0038·0040·4040·4140·4040·4040·0413··...8.@@@A@@@@@.. | ||
| 000001b0:· | 000001b0:·4040·4092·0403·a325·666c·6f61·7444·0800··@@@....%floatD.. | ||
| 000001c0:·00 | 000001c0:·0038·0040·4040·4140·4040·4040·0417·4040··.8.@@@A@@@@@..@@ | ||
| 000001d0:·40 | 000001d0:·4092·0403·a324·626f·6f6c·4508·0000·3800··@....$boolE...8. | ||
| 000001e0:· | 000001e0:·4040·a1a0·e0a3·2566·616c·7365·5e90·4040··@@....%false^.@@ | ||
| 000001f0:· | 000001f0:·0421·4092·0403·a0e0·a324·7472·7565·5f90··.!@......$true_. | ||
| 00000200:· | 00000200:·4040·0427·4092·0403·4040·4140·4040·4040··@@.'@...@@A@@@@@ | ||
| 00000210:· | 00000210:·0428·4041·4092·0410·a324·756e·6974·4608··.(@A@....$unitF. | ||
| 00000220:·0 | 00000220:·0000·3800·4040·a1a0·e0a3·2228·2960·9040··..8.@@...."()`.@ | ||
| 00000230:·40 | 00000230:·4004·3240·9204·0340·4041·4040·4040·4004··@.2@...@@A@@@@@. | ||
| 00000240:· | 00000240:·3340·4140·9204·0aa3·2365·786e·4708·0000··3@A@....#exnG... | ||
| 00000250:· | 00000250:·3800·4040·4141·4040·4040·4004·3740·4040··8.@@AA@@@@@.7@@@ | ||
| 00000260:· | 00000260:·9204·03a3·2561·7272·6179·4808·0000·3800··....%arrayH...8. | ||
| 00000270:· | 00000270:·a0c0·9040·0205·f5e1·0040·4f40·4140·4140··...@.....@O@A@A@ | ||
| 00000280:· | 00000280:·a000·7f40·a040·4040·4004·4040·4040·9204··...@.@@@@.@@@@.. | ||
| 00000290:·0 | 00000290:·08a3·246c·6973·7449·0800·0038·00a0·c004··..$listI...8.... | ||
| 000002a0:·0 | 000002a0:·0902·05f5·e100·4050·4041·a1a0·e0a3·225b··......@P@A...."[ | ||
| 000002b0:·5 | 000002b0:·5d61·9040·4004·4c40·9204·03a0·e0a3·223a··]a.@@.L@......": | ||
| 000002c0:·3a | 000002c0:·3a62·90a0·040e·a0c0·b390·0416·a004·1340··:b.............@ | ||
| 000002d0:· | 000002d0:·9040·0205·f5e1·0040·5140·4004·5940·9204··.@.....@Q@@.Y@.. | ||
| 000002e0:·040 | 000002e0:·0a40·4041·40a0·5940·a040·4040·4004·5c40··.@@A@.Y@.@@@@.\@ | ||
| 000002f0:·4040· | 000002f0:·4040·9204·1ba3·266f·7074·696f·6e4a·0800··@@....&optionJ.. | ||
| 00000300:·00 | 00000300:·0038·00a0·c004·2502·05f5·e100·4053·4041··.8....%.....@S@A | ||
| 00000310:· | 00000310:·a1a0·e0a3·244e·6f6e·6563·9040·4004·6840··....$Nonec.@@.h@ | ||
| 00000320:· | 00000320:·9204·03a0·e0a3·2453·6f6d·6564·90a0·040e··......$Somed.... | ||
| 00000330:· | 00000330:·4040·046f·4092·0404·4040·4140·a059·40a0··@@.o@...@@A@.Y@. | ||
| 00000340:· | 00000340:·4040·4040·0472·4040·4092·0415·a326·6c61··@@@@.r@@@....&la | ||
| 00000350:· | 00000350:·7a79·5f74·4e08·0000·3800·a0c0·043b·0205··zy_tN...8....;.. | ||
| 00000360:· | 00000360:·f5e1·0040·5540·4140·4140·a059·40a0·4040··...@U@A@A@.Y@.@@ | ||
| 00000370:·4040· | 00000370:·4040·047a·4040·4092·0407·a329·6e61·7469··@@.z@@@....)nati | ||
| 00000380:· | 00000380:·7665·696e·744b·0800·0038·0040·4040·4140··veintK...8.@@@A@ | ||
| 00000390:·4040·4040· | 00000390:·4040·4040·047e·4040·4092·0403·a325·696e··@@@@.~@@@....%in | ||
| 000003a0:· | 000003a0:·7433·324c·0800·0038·0040·4040·4140·4040··t32L...8.@@@A@@@ | ||
| 000003b0:·4040· | 000003b0:·4040·0482·4040·4092·0403·a325·696e·7436··@@..@@@....%int6 | ||
| 000003c0:·3 | 000003c0:·344d·0800·0038·0040·4040·4140·4040·4040··4M...8.@@@A@@@@@ | ||
| 000003d0:· | 000003d0:·0486·4040·4092·0403·a33a·556e·6465·6669··..@@@....:Undefi | ||
| 000003e0:·6 | 000003e0:·6e65·645f·7265·6375·7273·6976·655f·6d6f··ned_recursive_mo | ||
| 000003f0:·6 | 000003f0:·6475·6c65·5d08·0000·2000·9004·5740·90a0··dule]...·...W@.. | ||
| 00000400:· | 00000400:·c092·a0c0·b390·0483·4090·4002·05f5·e100··........@.@..... | ||
| 00000410:· | 00000410:·404a·a0c0·b390·0490·4090·4002·05f5·e100··@J......@.@..... | ||
| 00000420:· | 00000420:·4040·a004·0540·0205·f5e1·0040·5640·4041··@@...@.....@V@@A | ||
| 00000430:· | 00000430:·049a·a0b0·a03d·6f63·616d·6c2e·7761·726e··.....=ocaml.warn | ||
| 00000440:· | 00000440:·5f6f·6e5f·6c69·7465·7261·6c5f·7061·7474··_on_literal_patt | ||
| 00000450:· | 00000450:·6572·6e04·9e04·6104·9e40·9204·17a3·2e41··ern...a..@.....A | ||
| 00000460:· | 00000460:·7373·6572·745f·6661·696c·7572·655c·0800··ssert_failure\.. | ||
| 00000470:·00 | 00000470:·0020·0004·1840·90a0·c092·a004·17a0·0413··.·...@.......... | ||
| 00000480:· | 00000480:·a004·1440·0205·f5e1·0040·5840·4041·04a9··...@.....@X@@A.. | ||
| 00000490:·a | 00000490:·a0b0·a004·0f04·ac04·6f04·ac40·9204·0da3··........o..@.... | ||
| 000004a0:· | 000004a0:·3044·6976·6973·696f·6e5f·6279·5f7a·6572··0Division_by_zer | ||
| 000004b0:· | 000004b0:·6f59·0800·0020·0004·2640·9040·4041·04b1··oY...·..&@.@@A.. | ||
| 000004c0:· | 000004c0:·a0b0·a004·1704·b404·7704·b440·9204·07a3··........w..@.... | ||
| 000004d0:· | 000004d0:·2b45·6e64·5f6f·665f·6669·6c65·5808·0000··+End_of_fileX... | ||
| 000004e0:· | 000004e0:·2000·042e·4090·4040·4104·b9a0·b0a0·041f···...@.@@A....... | ||
| 000004f0:· | 000004f0:·04bc·047f·04bc·4092·0407·a329·5379·735f··......@....)Sys_ | ||
| 00000500:· | 00000500:·6572·726f·7257·0800·0020·0004·3640·90a0··errorW...·..6@.. | ||
| 00000510:· | 00000510:·0432·4040·4104·c2a0·b0a0·0428·04c5·0488··.2@@A......(.... | ||
| 00000520:· | 00000520:·04c5·4092·0408·a32e·5379·735f·626c·6f63··..@.....Sys_bloc | ||
| 00000530:·6 | 00000530:·6b65·645f·696f·5b08·0000·2000·043f·4090··ked_io[...·..?@. | ||
| 00000540:· | 00000540:·4040·4104·caa0·b0a0·0430·04cd·0490·04cd··@@A......0...... | ||
| 00000550:· | 00000550:·4092·0407·a329·4e6f·745f·666f·756e·6456··@....)Not_foundV | ||
| 00000560:· | 00000560:·0800·0020·0004·4740·9040·4041·04d2·a0b0··...·..G@.@@A.... | ||
| 00000570:· | 00000570:·a004·3804·d504·9804·d540·9204·07a3·2746··..8......@....'F | ||
| 00000580:· | 00000580:·6169·6c75·7265·5508·0000·2000·044f·4090··ailureU...·..O@. | ||
| 00000590:· | 00000590:·a004·4b40·4041·04db·a0b0·a004·4104·de04··..K@@A......A... | ||
| 000005a0:· | 000005a0:·a104·de40·9204·08a3·3049·6e76·616c·6964··...@....0Invalid | ||
| 000005b0:· | 000005b0:·5f61·7267·756d·656e·7454·0800·0020·0004··_argumentT...·.. | ||
| 000005c0:· | 000005c0:·5840·90a0·0454·4040·4104·e4a0·b0a0·044a··X@...T@@A......J | ||
| 000005d0:· | 000005d0:·04e7·04aa·04e7·4092·0408·a32e·5374·6163··......@.....Stac | ||
| 000005e0:·6 | 000005e0:·6b5f·6f76·6572·666c·6f77·5a08·0000·2000··k_overflowZ...·. | ||
| 000005f0:·0 | 000005f0:·0461·4090·4040·4104·eca0·b0a0·0452·04ef··.a@.@@A......R.. | ||
| 00000600:· | 00000600:·04b2·04ef·4092·0407·a32d·4f75·745f·6f66··....@....-Out_of | ||
| 00000610:· | 00000610:·5f6d·656d·6f72·7953·0800·0020·0004·6940··_memoryS...·..i@ | ||
| 00000620:· | 00000620:·9040·4041·04f4·a0b0·a004·5a04·f704·ba04··.@@A......Z..... | ||
| 00000630:· | 00000630:·f740·9204·07a3·2d4d·6174·6368·5f66·6169··.@....-Match_fai | ||
| 00000640:·6 | 00000640:·6c75·7265·5208·0000·2000·0471·4090·a0c0··lureR...·..q@... | ||
| 00000650:· | 00000650:·92a0·0470·a004·6ca0·046d·4002·05f5·e100··...p..l..m@..... | ||
| 00000660:· | 00000660:·4063·4040·4105·0102·a0b0·a004·6805·0105··@c@@A.......h... | ||
| 00000670:·0 | 00000670:·04c8·0501·0540·9204·0da3·2562·7974·6573··.....@....%bytes | ||
| 00000680:· | 00000680:·4308·0000·3800·4040·4041·4040·4040·4005··C...8.@@@A@@@@@. | ||
| 00000690:·0 | 00000690:·0109·4040·4092·0403·9092·2653·7464·6c69··..@@@.....&Stdli | ||
| 000006a0:·6 | 000006a0:·6292·264f·7074·696f·6e40·41b0·0501·3605··b.&Option@A...6. | ||
| 000006b0:· | 000006b0:·0139·40a0·b0a1·41a0·0800·0028·00b1·2175··.9@...A....(..!u | ||
| 000006c0:·00 | 000006c0:·0052·42a0·0402·b0c0·0501·535c·0105·3c01··.RB.......S\..<. | ||
| 000006d0:·5 | 000006d0:·0545·c005·0154·5c01·053c·0105·4640·4008··.E...T\..<..F@@. | ||
| 000006e0:·0 | 000006e0:·0000·3800·4040·4041·4040·4040·40b0·c005··..8.@@@A@@@@@... | ||
| 000006f0:· | 000006f0:·0157·5c01·053c·0105·4004·0440·4040·40a1··.W\..<..@..@@@@. | ||
| 00000700:·0 | 00000700:·0501·6441·4040·4140·0403·4040·0800·0030··..dA@@A@..@@...0 | ||
| 00000710:· | 00000710:·0005·0143·0501·4305·0143·0501·4305·0143··...C..C..C..C..C | ||
| 00000720:·0501·4 | 00000720:·0501·4305·0143·0501·4340·b105·0143·0501··..C..C..C@...C.. | ||
| 00000730:· | 00000730:·4f05·0149·4041·b004·0504·0840·a0b0·90f0··O..I@A.....@.... | ||
| 00000740:· | 00000740:·a028·6861·7368·636f·6e73·0053·a004·02b0··.(hashcons.S.... | ||
| 00000750:·005 | 00000750:·c005·0164·5d01·0547·0105·4fc0·0501·655d··...d]..G..O...e] | ||
| 00000760:· | 00000760:·0105·4701·0557·40d0·b140·d0b3·9004·1ca0··..G..W@..@...... | ||
| 00000770:· | 00000770:·9021·75b0·c005·016f·5d01·0547·0105·5bc0··.!u....o]..G..[. | ||
| 00000780:·05 | 00000780:·0501·705d·0105·4701·055c·4040·c0b3·0409··..p]..G..\@@.... | ||
| 00000790:·40 | 00000790:·4090·4002·05f5·e100·4001·0315·0800·0030··@.@.....@......0 | ||
| 000007a0:·0 | 000007a0:·0005·015e·0501·5e05·015e·0501·5e05·015e··...^..^..^..^..^ | ||
| 000007b0:·0501· | 000007b0:·0501·5e05·015e·0501·5e40·b104·1c04·2704··..^..^..^@....'. | ||
| 000007c0:· | 000007c0:·2140·41b0·0408·0407·4040·d0b1·40d0·b390··!@A.....@@..@... | ||
| 000007d0:· | 000007d0:·0501·70a0·9021·74b0·c005·0180·5d01·0547··..p..!t.....]..G | ||
| Max diff block lines reached; 27858/333826 bytes (8.35%) of diff not shown. | |||
| Offset 1, 1924 lines modified | Offset 1, 1924 lines modified | ||
| 00000000:·4361·6d6c·3139·3939·5430·3330·8495·a6be··Caml1999T030.... | 00000000:·4361·6d6c·3139·3939·5430·3330·8495·a6be··Caml1999T030.... | ||
| 00000010:·0000·781 | 00000010:·0000·7811·0000·1527·0000·5854·0000·56cc··..x....'..XT..V. | ||
| 00000020:·0800·0034·0024·4865·6170·91b0·a0b0·98d0··...4.$Heap...... | 00000020:·0800·0034·0024·4865·6170·91b0·a0b0·98d0··...4.$Heap...... | ||
| 00000030:·b127·4f72·6465·7265·6400·5342·a004·02b0··.'Ordered.SB.... | 00000030:·b127·4f72·6465·7265·6400·5342·a004·02b0··.'Ordered.SB.... | ||
| 00000040:·c02c·636c·6962·2f68·6561·702e·6d6c·4d01··.,clib/heap.mlM. | 00000040:·c02c·636c·6962·2f68·6561·702e·6d6c·4d01··.,clib/heap.mlM. | ||
| 00000050:·02b2·0102·bec0·0402·4d01·02b2·0102·c540··........M......@ | 00000050:·02b2·0102·bec0·0402·4d01·02b2·0102·c540··........M......@ | ||
| 00000060:·90d0·91b0·a0b0·a141·a008·0000·2800·b121··.......A....(..! | 00000060:·90d0·91b0·a0b0·a141·a008·0000·2800·b121··.......A....(..! | ||
| 00000070:·7400·5141·a004·02b0·c004·104e·0102·cc01··t.QA.......N.... | 00000070:·7400·5141·a004·02b0·c004·104e·0102·cc01··t.QA.......N.... | ||
| 00000080:·02d3·c004·114e·0102·cc01·02d4·4040·0800··.....N......@@.. | 00000080:·02d3·c004·114e·0102·cc01·02d4·4040·0800··.....N......@@.. | ||
| 00000090:·0038·0040·4040·4140·4040·4040·b0c0·0414··.8.@@@A@@@@@.... | 00000090:·0038·0040·4040·4140·4040·4040·b0c0·0414··.8.@@@A@@@@@.... | ||
| 000000a0:·4e01·02cc·0102·ce04·0440·4040·40a1·0421··N........@@@@..! | 000000a0:·4e01·02cc·0102·ce04·0440·4040·40a1·0421··N........@@@@..! | ||
| 000000b0:·4040·4041·4004·0340·4008·0000·3000·a040··@@@A@..@@...0..@ | 000000b0:·4040·4041·4004·0340·4008·0000·3000·a040··@@@A@..@@...0..@ | Diff chunk too large, falling back to line-by-line diff (1748 lines added, 1748 lines removed) | |
| 000000c0:·4004·0104·0104·0104·0104·0104·0104·0140··@..............@ | 000000c0:·4004·0104·0104·0104·0104·0104·0104·0140··@..............@ | ||
| 000000d0:·aba | 000000d0:·aba7·b1b2·b2b2·b2b2·b2b2·b2b2·b2b2·b2b1··................ | ||
| 000000e0:·b1b1·b1b1·b1b1·b1b1·b1b1·b1b1·b1b1·b1 | 000000e0:·b1b1·b1b1·b1b1·b1b1·b1b1·b1b1·b1b1·b140··...............@ | ||
| 000000f0:· | 000000f0:·a32a·666c·6f61·7461·7272·6179·5108·0000··.*floatarrayQ... | ||
| 00000100:· | 00000100:·3800·4040·4041·4040·4040·40b0·c026·5f6e··8.@@@A@@@@@..&_n | ||
| 00000110:·6 | 00000110:·6f6e·655f·4040·00ff·0402·4140·4040·9204··one_@@....A@@@.. | ||
| 00000120:·0 | 00000120:·06a3·3565·7874·656e·7369·6f6e·5f63·6f6e··..5extension_con | ||
| 00000130:· | 00000130:·7374·7275·6374·6f72·5008·0000·3800·4040··structorP...8.@@ | ||
| 00000140:·404 | 00000140:·4041·4040·4040·4004·0740·4040·9204·03a3··@A@@@@@..@@@.... | ||
| 00000150:· | 00000150:·2369·6e74·4108·0000·3800·4040·4041·4040··#intA...8.@@@A@@ | ||
| 00000160:·4040·40 | 00000160:·4040·4004·0b40·4140·9204·03a3·2463·6861··@@@..@A@....$cha | ||
| 00000170:· | 00000170:·7242·0800·0038·0040·4040·4140·4040·4040··rB...8.@@@A@@@@@ | ||
| 00000180:· | 00000180:·040f·4041·4092·0403·a326·7374·7269·6e67··..@A@....&string | ||
| 00000190:· | 00000190:·4f08·0000·3800·4040·4041·4040·4040·4004··O...8.@@@A@@@@@. | ||
| 000001a0:· | 000001a0:·1340·4040·9204·03a3·2566·6c6f·6174·4408··.@@@....%floatD. | ||
| 000001b0:·0 | 000001b0:·0000·3800·4040·4041·4040·4040·4004·1740··..8.@@@A@@@@@..@ | ||
| 000001c0:·4040· | 000001c0:·4040·9204·03a3·2462·6f6f·6c45·0800·0038··@@....$boolE...8 | ||
| 000001d0:· | 000001d0:·0040·40a1·a0e0·a325·6661·6c73·655e·9040··.@@....%false^.@ | ||
| 000001e0:·40 | 000001e0:·4004·2140·9204·03a0·e0a3·2474·7275·655f··@.!@......$true_ | ||
| 000001f0:· | 000001f0:·9040·4004·2740·9204·0340·4041·4040·4040··.@@.'@...@@A@@@@ | ||
| 00000200:·40 | 00000200:·4004·2840·4140·9204·10a3·2475·6e69·7446··@.(@A@....$unitF | ||
| 00000210:· | 00000210:·0800·0038·0040·40a1·a0e0·a322·2829·6090··...8.@@...."()`. | ||
| 00000220:· | 00000220:·4040·0432·4092·0403·4040·4140·4040·4040··@@.2@...@@A@@@@@ | ||
| 00000230:· | 00000230:·0433·4041·4092·040a·a323·6578·6e47·0800··.3@A@....#exnG.. | ||
| 00000240:·00 | 00000240:·0038·0040·4041·4140·4040·4040·0437·4040··.8.@@AA@@@@@.7@@ | ||
| 00000250:·40 | 00000250:·4092·0403·a325·6172·7261·7948·0800·0038··@....%arrayH...8 | ||
| 00000260:· | 00000260:·00a0·c090·4002·05f5·e100·404f·4041·4041··....@.....@O@A@A | ||
| 00000270:·4 | 00000270:·40a0·007f·40a0·4040·4040·0440·4040·4092··@...@.@@@@.@@@@. | ||
| 00000280:· | 00000280:·0408·a324·6c69·7374·4908·0000·3800·a0c0··...$listI...8... | ||
| 00000290:· | 00000290:·0409·0205·f5e1·0040·5040·41a1·a0e0·a322··.......@P@A...." | ||
| 000002a0:· | 000002a0:·5b5d·6190·4040·044c·4092·0403·a0e0·a322··[]a.@@.L@......" | ||
| 000002b0:· | 000002b0:·3a3a·6290·a004·0ea0·c0b3·9004·16a0·0413··::b............. | ||
| 000002c0:· | 000002c0:·4090·4002·05f5·e100·4051·4040·0459·4092··@.@.....@Q@@.Y@. | ||
| 000002d0:· | 000002d0:·040a·4040·4140·a059·40a0·4040·4040·045c··..@@A@.Y@.@@@@.\ | ||
| 000002e0:· | 000002e0:·4040·4092·041b·a326·6f70·7469·6f6e·4a08··@@@....&optionJ. | ||
| 000002f0:·0 | 000002f0:·0000·3800·a0c0·0425·0205·f5e1·0040·5340··..8....%.....@S@ | ||
| 00000300:·4 | 00000300:·41a1·a0e0·a324·4e6f·6e65·6390·4040·0468··A....$Nonec.@@.h | ||
| 00000310:· | 00000310:·4092·0403·a0e0·a324·536f·6d65·6490·a004··@......$Somed... | ||
| 00000320:·040 | 00000320:·0e40·4004·6f40·9204·0440·4041·40a0·5940··.@@.o@...@@A@.Y@ | ||
| 00000330:· | 00000330:·a040·4040·4004·7240·4040·9204·15a3·266c··.@@@@.r@@@....&l | ||
| 00000340:·6 | 00000340:·617a·795f·744e·0800·0038·00a0·c004·3b02··azy_tN...8....;. | ||
| 00000350:·0 | 00000350:·05f5·e100·4055·4041·4041·40a0·5940·a040··....@U@A@A@.Y@.@ | ||
| 00000360:·4040·40 | 00000360:·4040·4004·7a40·4040·9204·07a3·296e·6174··@@@.z@@@....)nat | ||
| 00000370:· | 00000370:·6976·6569·6e74·4b08·0000·3800·4040·4041··iveintK...8.@@@A | ||
| 00000380:·4 | 00000380:·4040·4040·4004·7e40·4040·9204·03a3·2569··@@@@@.~@@@....%i | ||
| 00000390:·6 | 00000390:·6e74·3332·4c08·0000·3800·4040·4041·4040··nt32L...8.@@@A@@ | ||
| 000003a0:·4040·40 | 000003a0:·4040·4004·8240·4040·9204·03a3·2569·6e74··@@@..@@@....%int | ||
| 000003b0:· | 000003b0:·3634·4d08·0000·3800·4040·4041·4040·4040··64M...8.@@@A@@@@ | ||
| 000003c0:·40 | 000003c0:·4004·8640·4040·9204·03a3·3a55·6e64·6566··@..@@@....:Undef | ||
| 000003d0:·6 | 000003d0:·696e·6564·5f72·6563·7572·7369·7665·5f6d··ined_recursive_m | ||
| 000003e0:·6 | 000003e0:·6f64·756c·655d·0800·0020·0090·0457·4090··odule]...·...W@. | ||
| 000003f0:· | 000003f0:·a0c0·92a0·c0b3·9004·8340·9040·0205·f5e1··.........@.@.... | ||
| 00000400:· | 00000400:·0040·4aa0·c0b3·9004·9040·9040·0205·f5e1··.@J......@.@.... | ||
| 00000410:· | 00000410:·0040·40a0·0405·4002·05f5·e100·4056·4040··.@@...@.....@V@@ | ||
| 00000420:·404 | 00000420:·4104·9aa0·b0a0·3d6f·6361·6d6c·2e77·6172··A.....=ocaml.war | ||
| 00000430:· | 00000430:·6e5f·6f6e·5f6c·6974·6572·616c·5f70·6174··n_on_literal_pat | ||
| 00000440:·74 | 00000440:·7465·726e·049e·0461·049e·4092·0417·a32e··tern...a..@..... | ||
| 00000450:· | 00000450:·4173·7365·7274·5f66·6169·6c75·7265·5c08··Assert_failure\. | ||
| 00000460:·0 | 00000460:·0000·2000·0418·4090·a0c0·92a0·0417·a004··..·...@......... | ||
| 00000470:· | 00000470:·13a0·0414·4002·05f5·e100·4058·4040·4104··....@.....@X@@A. | ||
| 00000480:· | 00000480:·a9a0·b0a0·040f·04ac·046f·04ac·4092·040d··.........o..@... | ||
| 00000490:· | 00000490:·a330·4469·7669·7369·6f6e·5f62·795f·7a65··.0Division_by_ze | ||
| 000004a0:· | 000004a0:·726f·5908·0000·2000·0426·4090·4040·4104··roY...·..&@.@@A. | ||
| 000004b0:· | 000004b0:·b1a0·b0a0·0417·04b4·0477·04b4·4092·0407··.........w..@... | ||
| 000004c0:· | 000004c0:·a32b·456e·645f·6f66·5f66·696c·6558·0800··.+End_of_fileX.. | ||
| 000004d0:·00 | 000004d0:·0020·0004·2e40·9040·4041·04b9·a0b0·a004··.·...@.@@A...... | ||
| 000004e0:· | 000004e0:·1f04·bc04·7f04·bc40·9204·07a3·2953·7973··.......@....)Sys | ||
| 000004f0:· | 000004f0:·5f65·7272·6f72·5708·0000·2000·0436·4090··_errorW...·..6@. | ||
| 00000500:· | 00000500:·a004·3240·4041·04c2·a0b0·a004·2804·c504··..2@@A......(... | ||
| 00000510:· | 00000510:·8804·c540·9204·08a3·2e53·7973·5f62·6c6f··...@.....Sys_blo | ||
| 00000520:·6 | 00000520:·636b·6564·5f69·6f5b·0800·0020·0004·3f40··cked_io[...·..?@ | ||
| 00000530:· | 00000530:·9040·4041·04ca·a0b0·a004·3004·cd04·9004··.@@A......0..... | ||
| 00000540:· | 00000540:·cd40·9204·07a3·294e·6f74·5f66·6f75·6e64··.@....)Not_found | ||
| 00000550:· | 00000550:·5608·0000·2000·0447·4090·4040·4104·d2a0··V...·..G@.@@A... | ||
| 00000560:· | 00000560:·b0a0·0438·04d5·0498·04d5·4092·0407·a327··...8......@....' | ||
| 00000570:· | 00000570:·4661·696c·7572·6555·0800·0020·0004·4f40··FailureU...·..O@ | ||
| 00000580:· | 00000580:·90a0·044b·4040·4104·dba0·b0a0·0441·04de··...K@@A......A.. | ||
| 00000590:· | 00000590:·04a1·04de·4092·0408·a330·496e·7661·6c69··....@....0Invali | ||
| 000005a0:·6 | 000005a0:·645f·6172·6775·6d65·6e74·5408·0000·2000··d_argumentT...·. | ||
| 000005b0:·0 | 000005b0:·0458·4090·a004·5440·4041·04e4·a0b0·a004··.X@...T@@A...... | ||
| 000005c0:· | 000005c0:·4a04·e704·aa04·e740·9204·08a3·2e53·7461··J......@.....Sta | ||
| 000005d0:·6 | 000005d0:·636b·5f6f·7665·7266·6c6f·775a·0800·0020··ck_overflowZ...· | ||
| 000005e0:· | 000005e0:·0004·6140·9040·4041·04ec·a0b0·a004·5204··..a@.@@A......R. | ||
| 000005f0:· | 000005f0:·ef04·b204·ef40·9204·07a3·2d4f·7574·5f6f··.....@....-Out_o | ||
| 00000600:·6 | 00000600:·665f·6d65·6d6f·7279·5308·0000·2000·0469··f_memoryS...·..i | ||
| 00000610:· | 00000610:·4090·4040·4104·f4a0·b0a0·045a·04f7·04ba··@.@@A......Z.... | ||
| 00000620:· | 00000620:·04f7·4092·0407·a32d·4d61·7463·685f·6661··..@....-Match_fa | ||
| 00000630:·6 | 00000630:·696c·7572·6552·0800·0020·0004·7140·90a0··ilureR...·..q@.. | ||
| 00000640:· | 00000640:·c092·a004·70a0·046c·a004·6d40·0205·f5e1··....p..l..m@.... | ||
| 00000650:· | 00000650:·0040·6340·4041·0501·02a0·b0a0·0468·0501··.@c@@A.......h.. | ||
| 00000660:·0 | 00000660:·0504·c805·0105·4092·040d·a325·6279·7465··......@....%byte | ||
| 00000670:· | 00000670:·7343·0800·0038·0040·4040·4140·4040·4040··sC...8.@@@A@@@@@ | ||
| 00000680:· | 00000680:·0501·0940·4040·9204·0390·9226·5374·646c··...@@@.....&Stdl | ||
| 00000690:·6 | 00000690:·6962·9226·4f70·7469·6f6e·4041·b005·0136··ib.&Option@A...6 | ||
| 000006a0:· | 000006a0:·0501·3940·a0b0·90f0·a027·636f·6d70·6172··..9@.....'compar | ||
| 000006b0:·6 | 000006b0:·6500·52a0·0402·b0c0·0501·524f·0102·d501··e.R.......RO.... | ||
| 000006c0:· | 000006c0:·02db·c005·0153·4f01·02d5·0102·e240·d0b1··.....SO......@.. | ||
| 000006d0:·0 | 000006d0:·40d0·b390·0501·4da0·9021·74b0·c005·015d··@.....M..!t....] | ||
| 000006e0:· | 000006e0:·4f01·02d5·0102·e5c0·0501·5e4f·0102·d501··O.........^O.... | ||
| 000006f0:· | 000006f0:·02e6·4040·c0b3·0409·4090·4002·05f5·e100··..@@....@.@..... | ||
| 00000700:·400 | 00000700:·4001·0315·0800·0030·0005·014c·0501·4c05··@......0...L..L. | ||
| 00000710:·014 | 00000710:·014c·0501·4c05·014c·0501·4c05·014c·0501··.L..L..L..L..L.. | ||
| 00000720:·4 | 00000720:·4c40·b105·014c·0501·5805·0152·4041·b004··L@...L..X..R@A.. | ||
| 00000730:·0 | 00000730:·0804·0740·40d0·b140·d0b3·9005·015e·a090··...@@..@.....^.. | ||
| 00000740:· | 00000740:·2174·b0c0·0501·6e4f·0102·d501·02ea·c005··!t....nO........ | ||
| 00000750:· | 00000750:·016f·4f01·02d5·0102·eb40·40c0·b304·0940··.oO......@@....@ | ||
| 00000760:· | 00000760:·9040·0205·f5e1·0040·0103·1604·11b0·0406··.@.....@........ | ||
| 00000770:· | 00000770:·0405·4040·d0b3·9005·0135·a090·2369·6e74··..@@.....5..#int | ||
| 00000780:· | 00000780:·b0c0·0501·7b4f·0102·d501·02ef·c005·017c··....{O.........| | ||
| 00000790:· | 00000790:·4f01·02d5·0102·f240·40c0·b304·0940·9040··O......@@....@.@ | ||
| 000007a0:· | 000007a0:·0205·f5e1·0040·0103·1704·1eb0·0406·0405··.....@.......... | ||
| 000007b0:· | 000007b0:·4040·c0c1·4004·1304·0640·0205·f5e1·0040··@@..@....@.....@ | ||
| 000007c0:·0 | 000007c0:·0103·1804·21b0·0416·0408·4040·c0c1·4004··....!.....@@..@. | ||
| 000007d0:· | 000007d0:·2704·0540·0205·f5e1·0040·0103·1904·24b0··'..@.....@....$. | ||
| Max diff block lines reached; 21849/264130 bytes (8.27%) of diff not shown. | |||
| Offset 1, 1866 lines modified | Offset 1, 1866 lines modified | ||
| 00000000:·4361·6d6c·3139·3939·5430·3330·8495·a6be··Caml1999T030.... | 00000000:·4361·6d6c·3139·3939·5430·3330·8495·a6be··Caml1999T030.... | ||
| 00000010:·0000·747 | 00000010:·0000·7471·0000·14cc·0000·56aa·0000·557f··..tq......V...U. | ||
| 00000020:·0800·0034·0027·4953·7472·6561·6d91·b0a0··...4.'IStream... | 00000020:·0800·0034·0027·4953·7472·6561·6d91·b0a0··...4.'IStream... | ||
| 00000030:·b0a3·41a0·0800·0028·00b1·246e·6f64·6500··..A....(..$node. | 00000030:·b0a3·41a0·0800·0028·00b1·246e·6f64·6500··..A....(..$node. | ||
| 00000040:·5141·a004·02b0·c02f·636c·6962·2f69·5374··QA...../clib/iSt | 00000040:·5141·a004·02b0·c02f·636c·6962·2f69·5374··QA...../clib/iSt | ||
| 00000050:·7265·616d·2e6d·6c4b·0102·a401·02ac·c004··ream.mlK........ | 00000050:·7265·616d·2e6d·6c4b·0102·a401·02ac·c004··ream.mlK........ | ||
| 00000060:·024b·0102·a401·02b0·40a0·a0d0·9021·61c0··.K......@....!a. | 00000060:·024b·0102·a401·02b0·40a0·a0d0·9021·61c0··.K......@....!a. | ||
| 00000070:·9090·0404·0205·f5e1·0040·0103·1808·0000··.........@...... | 00000070:·9090·0404·0205·f5e1·0040·0103·1808·0000··.........@...... | Diff chunk too large, falling back to line-by-line diff (1767 lines added, 1767 lines removed) | |
| 00000080:·3000·a040·4004·0104·0104·0104·0104·0104··0..@@........... | 00000080:·3000·a040·4004·0104·0104·0104·0104·0104··0..@@........... | ||
| 00000090:·0104·0140·b1b1·aba | 00000090:·0104·0140·b1b1·aba7·b1b2·b2b2·b2b2·b2b2··...@............ | ||
| 000000a0:·b2b2·b2b2·b2b | 000000a0:·b2b2·b2b2·b2b1·b1b1·b1b1·b1b1·b1b1·b1b1··................ | ||
| 000000b0:·b1b1·b1b1·b1 | 000000b0:·b1b1·b1b1·b140·a32a·666c·6f61·7461·7272··.....@.*floatarr | ||
| 000000c0:· | 000000c0:·6179·5108·0000·3800·4040·4041·4040·4040··ayQ...8.@@@A@@@@ | ||
| 000000d0:·40 | 000000d0:·40b0·c026·5f6e·6f6e·655f·4040·00ff·0402··@..&_none_@@.... | ||
| 000000e0:· | 000000e0:·4140·4040·9204·06a3·3565·7874·656e·7369··A@@@....5extensi | ||
| 000000f0:·6 | 000000f0:·6f6e·5f63·6f6e·7374·7275·6374·6f72·5008··on_constructorP. | ||
| 00000100:·0 | 00000100:·0000·3800·4040·4041·4040·4040·4004·0740··..8.@@@A@@@@@..@ | ||
| 00000110:·4040· | 00000110:·4040·9204·03a3·2369·6e74·4108·0000·3800··@@....#intA...8. | ||
| 00000120:· | 00000120:·4040·4041·4040·4040·4004·0b40·4140·9204··@@@A@@@@@..@A@.. | ||
| 00000130:·0 | 00000130:·03a3·2463·6861·7242·0800·0038·0040·4040··..$charB...8.@@@ | ||
| 00000140:·4 | 00000140:·4140·4040·4040·040f·4041·4092·0403·a326··A@@@@@..@A@....& | ||
| 00000150:· | 00000150:·7374·7269·6e67·4f08·0000·3800·4040·4041··stringO...8.@@@A | ||
| 00000160:·4 | 00000160:·4040·4040·4004·1340·4040·9204·03a3·2566··@@@@@..@@@....%f | ||
| 00000170:·6 | 00000170:·6c6f·6174·4408·0000·3800·4040·4041·4040··loatD...8.@@@A@@ | ||
| 00000180:·4040·40 | 00000180:·4040·4004·1740·4040·9204·03a3·2462·6f6f··@@@..@@@....$boo | ||
| 00000190:·6 | 00000190:·6c45·0800·0038·0040·40a1·a0e0·a325·6661··lE...8.@@....%fa | ||
| 000001a0:·6 | 000001a0:·6c73·655e·9040·4004·2140·9204·03a0·e0a3··lse^.@@.!@...... | ||
| 000001b0:· | 000001b0:·2474·7275·655f·9040·4004·2740·9204·0340··$true_.@@.'@...@ | ||
| 000001c0:·404 | 000001c0:·4041·4040·4040·4004·2840·4140·9204·10a3··@A@@@@@.(@A@.... | ||
| 000001d0:· | 000001d0:·2475·6e69·7446·0800·0038·0040·40a1·a0e0··$unitF...8.@@... | ||
| 000001e0:· | 000001e0:·a322·2829·6090·4040·0432·4092·0403·4040··."()`.@@.2@...@@ | ||
| 000001f0:·4 | 000001f0:·4140·4040·4040·0433·4041·4092·040a·a323··A@@@@@.3@A@....# | ||
| 00000200:· | 00000200:·6578·6e47·0800·0038·0040·4041·4140·4040··exnG...8.@@AA@@@ | ||
| 00000210:·4040· | 00000210:·4040·0437·4040·4092·0403·a325·6172·7261··@@.7@@@....%arra | ||
| 00000220:· | 00000220:·7948·0800·0038·00a0·c090·4002·05f5·e100··yH...8....@..... | ||
| 00000230:· | 00000230:·404f·4041·4041·40a0·007f·40a0·4040·4040··@O@A@A@...@.@@@@ | ||
| 00000240:·4 | 00000240:·0440·4040·4092·0408·a324·6c69·7374·4908··.@@@@....$listI. | ||
| 00000250:·0 | 00000250:·0000·3800·a0c0·0409·0205·f5e1·0040·5040··..8..........@P@ | ||
| 00000260:·4 | 00000260:·41a1·a0e0·a322·5b5d·6190·4040·044c·4092··A...."[]a.@@.L@. | ||
| 00000270:· | 00000270:·0403·a0e0·a322·3a3a·6290·a004·0ea0·c0b3··....."::b....... | ||
| 00000280:· | 00000280:·9004·16a0·0413·4090·4002·05f5·e100·4051··......@.@.....@Q | ||
| 00000290:· | 00000290:·4040·0459·4092·040a·4040·4140·a059·40a0··@@.Y@...@@A@.Y@. | ||
| 000002a0:· | 000002a0:·4040·4040·045c·4040·4092·041b·a326·6f70··@@@@.\@@@....&op | ||
| 000002b0:·7 | 000002b0:·7469·6f6e·4a08·0000·3800·a0c0·0425·0205··tionJ...8....%.. | ||
| 000002c0:· | 000002c0:·f5e1·0040·5340·41a1·a0e0·a324·4e6f·6e65··...@S@A....$None | ||
| 000002d0:·6 | 000002d0:·6390·4040·0468·4092·0403·a0e0·a324·536f··c.@@.h@......$So | ||
| 000002e0:·6 | 000002e0:·6d65·6490·a004·0e40·4004·6f40·9204·0440··med....@@.o@...@ | ||
| 000002f0:·404 | 000002f0:·4041·40a0·5940·a040·4040·4004·7240·4040··@A@.Y@.@@@@.r@@@ | ||
| 00000300:· | 00000300:·9204·15a3·266c·617a·795f·744e·0800·0038··....&lazy_tN...8 | ||
| 00000310:· | 00000310:·00a0·c004·3b02·05f5·e100·4055·4041·4041··....;.....@U@A@A | ||
| 00000320:·4 | 00000320:·40a0·5940·a040·4040·4004·7a40·4040·9204··@.Y@.@@@@.z@@@.. | ||
| 00000330:·0 | 00000330:·07a3·296e·6174·6976·6569·6e74·4b08·0000··..)nativeintK... | ||
| 00000340:· | 00000340:·3800·4040·4041·4040·4040·4004·7e40·4040··8.@@@A@@@@@.~@@@ | ||
| 00000350:· | 00000350:·9204·03a3·2569·6e74·3332·4c08·0000·3800··....%int32L...8. | ||
| 00000360:· | 00000360:·4040·4041·4040·4040·4004·8240·4040·9204··@@@A@@@@@..@@@.. | ||
| 00000370:·0 | 00000370:·03a3·2569·6e74·3634·4d08·0000·3800·4040··..%int64M...8.@@ | ||
| 00000380:·404 | 00000380:·4041·4040·4040·4004·8640·4040·9204·03a3··@A@@@@@..@@@.... | ||
| 00000390:· | 00000390:·3a55·6e64·6566·696e·6564·5f72·6563·7572··:Undefined_recur | ||
| 000003a0:·7 | 000003a0:·7369·7665·5f6d·6f64·756c·655d·0800·0020··sive_module]...· | ||
| 000003b0:· | 000003b0:·0090·0457·4090·a0c0·92a0·c0b3·9004·8340··...W@..........@ | ||
| 000003c0:· | 000003c0:·9040·0205·f5e1·0040·4aa0·c0b3·9004·9040··.@.....@J......@ | ||
| 000003d0:· | 000003d0:·9040·0205·f5e1·0040·40a0·0405·4002·05f5··.@.....@@...@... | ||
| 000003e0:· | 000003e0:·e100·4056·4040·4104·9aa0·b0a0·3d6f·6361··..@V@@A.....=oca | ||
| 000003f0:·6 | 000003f0:·6d6c·2e77·6172·6e5f·6f6e·5f6c·6974·6572··ml.warn_on_liter | ||
| 00000400:· | 00000400:·616c·5f70·6174·7465·726e·049e·0461·049e··al_pattern...a.. | ||
| 00000410:· | 00000410:·4092·0417·a32e·4173·7365·7274·5f66·6169··@.....Assert_fai | ||
| 00000420:·6 | 00000420:·6c75·7265·5c08·0000·2000·0418·4090·a0c0··lure\...·...@... | ||
| 00000430:· | 00000430:·92a0·0417·a004·13a0·0414·4002·05f5·e100··..........@..... | ||
| 00000440:· | 00000440:·4058·4040·4104·a9a0·b0a0·040f·04ac·046f··@X@@A..........o | ||
| 00000450:· | 00000450:·04ac·4092·040d·a330·4469·7669·7369·6f6e··..@....0Division | ||
| 00000460:· | 00000460:·5f62·795f·7a65·726f·5908·0000·2000·0426··_by_zeroY...·..& | ||
| 00000470:· | 00000470:·4090·4040·4104·b1a0·b0a0·0417·04b4·0477··@.@@A..........w | ||
| 00000480:· | 00000480:·04b4·4092·0407·a32b·456e·645f·6f66·5f66··..@....+End_of_f | ||
| 00000490:·6 | 00000490:·696c·6558·0800·0020·0004·2e40·9040·4041··ileX...·...@.@@A | ||
| 000004a0:· | 000004a0:·04b9·a0b0·a004·1f04·bc04·7f04·bc40·9204··.............@.. | ||
| 000004b0:·0 | 000004b0:·07a3·2953·7973·5f65·7272·6f72·5708·0000··..)Sys_errorW... | ||
| 000004c0:· | 000004c0:·2000·0436·4090·a004·3240·4041·04c2·a0b0···..6@...2@@A.... | ||
| 000004d0:· | 000004d0:·a004·2804·c504·8804·c540·9204·08a3·2e53··..(......@.....S | ||
| 000004e0:· | 000004e0:·7973·5f62·6c6f·636b·6564·5f69·6f5b·0800··ys_blocked_io[.. | ||
| 000004f0:·00 | 000004f0:·0020·0004·3f40·9040·4041·04ca·a0b0·a004··.·..?@.@@A...... | ||
| 00000500:· | 00000500:·3004·cd04·9004·cd40·9204·07a3·294e·6f74··0......@....)Not | ||
| 00000510:· | 00000510:·5f66·6f75·6e64·5608·0000·2000·0447·4090··_foundV...·..G@. | ||
| 00000520:· | 00000520:·4040·4104·d2a0·b0a0·0438·04d5·0498·04d5··@@A......8...... | ||
| 00000530:· | 00000530:·4092·0407·a327·4661·696c·7572·6555·0800··@....'FailureU.. | ||
| 00000540:·00 | 00000540:·0020·0004·4f40·90a0·044b·4040·4104·dba0··.·..O@...K@@A... | ||
| 00000550:· | 00000550:·b0a0·0441·04de·04a1·04de·4092·0408·a330··...A......@....0 | ||
| 00000560:· | 00000560:·496e·7661·6c69·645f·6172·6775·6d65·6e74··Invalid_argument | ||
| 00000570:· | 00000570:·5408·0000·2000·0458·4090·a004·5440·4041··T...·..X@...T@@A | ||
| 00000580:· | 00000580:·04e4·a0b0·a004·4a04·e704·aa04·e740·9204··......J......@.. | ||
| 00000590:·0 | 00000590:·08a3·2e53·7461·636b·5f6f·7665·7266·6c6f··...Stack_overflo | ||
| 000005a0:· | 000005a0:·775a·0800·0020·0004·6140·9040·4041·04ec··wZ...·..a@.@@A.. | ||
| 000005b0:· | 000005b0:·a0b0·a004·5204·ef04·b204·ef40·9204·07a3··....R......@.... | ||
| 000005c0:· | 000005c0:·2d4f·7574·5f6f·665f·6d65·6d6f·7279·5308··-Out_of_memoryS. | ||
| 000005d0:·0 | 000005d0:·0000·2000·0469·4090·4040·4104·f4a0·b0a0··..·..i@.@@A..... | ||
| 000005e0:· | 000005e0:·045a·04f7·04ba·04f7·4092·0407·a32d·4d61··.Z......@....-Ma | ||
| 000005f0:· | 000005f0:·7463·685f·6661·696c·7572·6552·0800·0020··tch_failureR...· | ||
| 00000600:· | 00000600:·0004·7140·90a0·c092·a004·70a0·046c·a004··..q@......p..l.. | ||
| 00000610:· | 00000610:·6d40·0205·f5e1·0040·6340·4041·0501·02a0··m@.....@c@@A.... | ||
| 00000620:· | 00000620:·b0a0·0468·0501·0504·c805·0105·4092·040d··...h........@... | ||
| 00000630:· | 00000630:·a325·6279·7465·7343·0800·0038·0040·4040··.%bytesC...8.@@@ | ||
| 00000640:·4 | 00000640:·4140·4040·4040·0501·0940·4040·9204·0390··A@@@@@...@@@.... | ||
| 00000650:·9 | 00000650:·9226·5374·646c·6962·9226·4f70·7469·6f6e··.&Stdlib.&Option | ||
| 00000660:· | 00000660:·0501·4408·0000·3800·a0c0·9040·0205·f5e1··..D...8....@.... | ||
| 00000670:· | 00000670:·0040·0103·1540·4140·4140·a047·40a0·4240··.@...@A@A@.G@.B@ | ||
| 00000680:· | 00000680:·4040·b0c0·0501·474b·0102·a401·02a4·c005··@@....GK........ | ||
| 00000690:· | 00000690:·0148·4d01·02bb·0102·d040·4040·40a1·0501··.HM......@@@@... | ||
| 000006a0:· | 000006a0:·5640·b121·7400·5241·0800·0038·00a0·c004··V@.!t.RA...8.... | ||
| 000006b0:·0 | 000006b0:·0c02·05f5·e100·4001·0317·4041·4041·90c0··......@...@A@A.. | ||
| 000006c0:· | 000006c0:·96c0·b390·040b·a0c0·9040·4240·0103·7840··.........@B@..x@ | ||
| 000006d0:·4240·0103·7 | 000006d0:·9040·4240·0103·7942·4001·0316·a047·40a0··.@B@..yB@....G@. | ||
| 000006e0:· | 000006e0:·4240·4040·b0c0·0501·5c4f·0102·d201·02d2··B@@@....\O...... | ||
| 000006f0:·01 | 000006f0:·c005·015d·4f01·02d2·0102·eb40·4040·40a1··...]O......@@@@. | ||
| 00000700:· | 00000700:·0501·6b41·4040·b0c0·0501·604b·0102·a401··..kA@@....`K.... | ||
| 00000710:· | 00000710:·02a9·c005·0161·4b01·02a4·0102·ab40·40a0··.....aK......@@. | ||
| 00000720:· | 00000720:·4241·4008·0000·3800·a005·015d·4041·a1a0··BA@...8....]@A.. | ||
| 00000730:· | 00000730:·e0a0·234e·696c·0053·9040·40b0·c005·016c··..#Nil.S.@@....l | ||
| 00000740:·4 | 00000740:·4c01·02b3·0102·b5c0·0501·6d4c·0102·b301··L.........mL.... | ||
| 00000750:· | 00000750:·02ba·4040·a105·017b·42a0·e0a0·2443·6f6e··..@@...{B...$Con | ||
| 00000760:· | 00000760:·7300·5490·a0c0·9605·016f·4340·0103·19a0··s.T......oC@.... | ||
| 00000770:· | 00000770:·c0b3·9004·31a0·c096·0501·7643·4001·031b··....1.....vC@... | ||
| 00000780:· | 00000780:·4090·d041·0406·0408·c096·c0b3·a1a1·044b··@..A...........K | ||
| 00000790:· | 00000790:·244c·617a·7921·74a0·c0b3·9005·0190·a0c0··$Lazy!t......... | ||
| 000007a0:·9 | 000007a0:·9605·0187·0205·f5e1·0040·0109·d840·9091··.........@...@.. | ||
| 000007b0:·0 | 000007b0:·0413·0205·f5e1·0040·0109·da40·90d0·4104··.......@...@..A. | ||
| 000007c0:· | 000007c0:·0f04·11c0·96c0·b3a1·9092·3043·616d·6c69··..........0Camli | ||
| 000007d0:· | 000007d0:·6e74·6572·6e61·6c4c·617a·7921·74a0·c096··nternalLazy!t... | ||
| Max diff block lines reached; 11775/256402 bytes (4.59%) of diff not shown. | |||
| Offset 1, 3143 lines modified | Offset 1, 3142 lines modified | ||
| 00000000:·4361·6d6c·3139·3939·5430·3330·8495·a6be··Caml1999T030.... | 00000000:·4361·6d6c·3139·3939·5430·3330·8495·a6be··Caml1999T030.... | ||
| 00000010:·0000·c44 | 00000010:·0000·c440·0000·2143·0000·8aec·0000·8830··...@..!C.......0 | ||
| 00000020:·0800·0034·0025·4d6f·6e61·6491·b0a0·b09d··...4.%Monad..... | 00000020:·0800·0034·0025·4d6f·6e61·6491·b0a0·b09d··...4.%Monad..... | ||
| 00000030:·b0a0·2a6f·6361·6d6c·2e74·6578·74b0·c026··..*ocaml.text..& | 00000030:·b0a0·2a6f·6361·6d6c·2e74·6578·74b0·c026··..*ocaml.text..& | ||
| 00000040:·5f6e·6f6e·655f·4040·00ff·0402·4190·a0a0··_none_@@....A... | 00000040:·5f6e·6f6e·655f·4040·00ff·0402·4190·a0a0··_none_@@....A... | ||
| 00000050:·a0c0·91b2·0926·2043·6f6d·6269·6e61·746f··.....&·Combinato | 00000050:·a0c0·91b2·0926·2043·6f6d·6269·6e61·746f··.....&·Combinato | ||
| 00000060:·7273·206f·6e20·6d6f·6e61·6469·6320·636f··rs·on·monadic·co | 00000060:·7273·206f·6e20·6d6f·6e61·6469·6320·636f··rs·on·monadic·co | ||
| 00000070:·6d70·7574·6174·696f·6e73·2e20·b0c0·2d63··mputations.·..-c | 00000070:·6d70·7574·6174·696f·6e73·2e20·b0c0·2d63··mputations.·..-c | ||
| 00000080:·6c69·622f·6d6f·6e61·642e·6d6c·4c01·02a5··lib/monad.mlL... | 00000080:·6c69·622f·6d6f·6e61·642e·6d6c·4c01·02a5··lib/monad.mlL... | ||
| 00000090:·0102·a5c0·0402·4c01·02a5·0102·d040·4004··......L......@@. | 00000090:·0102·a5c0·0402·4c01·02a5·0102·d040·4004··......L......@@. | ||
| 000000a0:·0440·4040·0404·4004·0404·0408·0000·3000··.@@@..@.......0. | 000000a0:·0440·4040·0404·4004·0404·0408·0000·3000··.@@@..@.......0. | Diff chunk too large, falling back to line-by-line diff (2918 lines added, 2918 lines removed) | |
| 000000b0:·a040·4004·0104·0104·0104·0104·0104·0104··.@@............. | 000000b0:·a040·4004·0104·0104·0104·0104·0104·0104··.@@............. | ||
| 000000c0:·0140·aba | 000000c0:·0140·aba7·b1b2·b2b2·b2b2·b2b2·b2b2·b2b2··.@.............. | ||
| 000000d0:·b2b | 000000d0:·b2b1·b1b1·b1b1·b1b1·b1b1·b1b1·b1b1·b1b1··................ | ||
| 000000e0:·b1 | 000000e0:·b140·a32a·666c·6f61·7461·7272·6179·5108··.@.*floatarrayQ. | ||
| 000000f0:·0 | 000000f0:·0000·3800·4040·4041·4040·4040·4004·3340··..8.@@@A@@@@@.3@ | ||
| 00000100:·4040· | 00000100:·4040·9204·03a3·3565·7874·656e·7369·6f6e··@@....5extension | ||
| 00000110:· | 00000110:·5f63·6f6e·7374·7275·6374·6f72·5008·0000··_constructorP... | ||
| 00000120:· | 00000120:·3800·4040·4041·4040·4040·4004·3740·4040··8.@@@A@@@@@.7@@@ | ||
| 00000130:· | 00000130:·9204·03a3·2369·6e74·4108·0000·3800·4040··....#intA...8.@@ | ||
| 00000140:·404 | 00000140:·4041·4040·4040·4004·3b40·4140·9204·03a3··@A@@@@@.;@A@.... | ||
| 00000150:· | 00000150:·2463·6861·7242·0800·0038·0040·4040·4140··$charB...8.@@@A@ | ||
| 00000160:·4040·4040· | 00000160:·4040·4040·043f·4041·4092·0403·a326·7374··@@@@.?@A@....&st | ||
| 00000170:·7 | 00000170:·7269·6e67·4f08·0000·3800·4040·4041·4040··ringO...8.@@@A@@ | ||
| 00000180:·4040·40 | 00000180:·4040·4004·4340·4040·9204·03a3·2566·6c6f··@@@.C@@@....%flo | ||
| 00000190:·6 | 00000190:·6174·4408·0000·3800·4040·4041·4040·4040··atD...8.@@@A@@@@ | ||
| 000001a0:·40 | 000001a0:·4004·4740·4040·9204·03a3·2462·6f6f·6c45··@.G@@@....$boolE | ||
| 000001b0:· | 000001b0:·0800·0038·0040·40a1·a0e0·a325·6661·6c73··...8.@@....%fals | ||
| 000001c0:· | 000001c0:·655e·9040·4004·5140·9204·03a0·e0a3·2474··e^.@@.Q@......$t | ||
| 000001d0:·7 | 000001d0:·7275·655f·9040·4004·5740·9204·0340·4041··rue_.@@.W@...@@A | ||
| 000001e0:·4 | 000001e0:·4040·4040·4004·5840·4140·9204·10a3·2475··@@@@@.X@A@....$u | ||
| 000001f0:· | 000001f0:·6e69·7446·0800·0038·0040·40a1·a0e0·a322··nitF...8.@@...." | ||
| 00000200:·2 | 00000200:·2829·6090·4040·0462·4092·0403·4040·4140··()`.@@.b@...@@A@ | ||
| 00000210:·4040·4040· | 00000210:·4040·4040·0463·4041·4092·040a·a323·6578··@@@@.c@A@....#ex | ||
| 00000220:· | 00000220:·6e47·0800·0038·0040·4041·4140·4040·4040··nG...8.@@AA@@@@@ | ||
| 00000230:· | 00000230:·0467·4040·4092·0403·a325·6172·7261·7948··.g@@@....%arrayH | ||
| 00000240:· | 00000240:·0800·0038·00a0·c090·4002·05f5·e100·404f··...8....@.....@O | ||
| 00000250:·4 | 00000250:·4041·4041·40a0·007f·40a0·4040·4040·0470··@A@A@...@.@@@@.p | ||
| 00000260:· | 00000260:·4040·4092·0408·a324·6c69·7374·4908·0000··@@@....$listI... | ||
| 00000270:· | 00000270:·3800·a0c0·0409·0205·f5e1·0040·5040·41a1··8..........@P@A. | ||
| 00000280:·a | 00000280:·a0e0·a322·5b5d·6190·4040·047c·4092·0403··..."[]a.@@.|@... | ||
| 00000290:· | 00000290:·a0e0·a322·3a3a·6290·a004·0ea0·c0b3·9004··..."::b......... | ||
| 000002a0:· | 000002a0:·16a0·0413·4090·4002·05f5·e100·4051·4040··....@.@.....@Q@@ | ||
| 000002b0:· | 000002b0:·0489·4092·040a·4040·4140·a059·40a0·4040··..@...@@A@.Y@.@@ | ||
| 000002c0:·4040· | 000002c0:·4040·048c·4040·4092·041b·a326·6f70·7469··@@..@@@....&opti | ||
| 000002d0:·6 | 000002d0:·6f6e·4a08·0000·3800·a0c0·0425·0205·f5e1··onJ...8....%.... | ||
| 000002e0:· | 000002e0:·0040·5340·41a1·a0e0·a324·4e6f·6e65·6390··.@S@A....$Nonec. | ||
| 000002f0:· | 000002f0:·4040·0498·4092·0403·a0e0·a324·536f·6d65··@@..@......$Some | ||
| 00000300:·6 | 00000300:·6490·a004·0e40·4004·9f40·9204·0440·4041··d....@@..@...@@A | ||
| 00000310:·4 | 00000310:·40a0·5940·a040·4040·4004·a240·4040·9204··@.Y@.@@@@..@@@.. | ||
| 00000320:· | 00000320:·15a3·266c·617a·795f·744e·0800·0038·00a0··..&lazy_tN...8.. | ||
| 00000330:· | 00000330:·c004·3b02·05f5·e100·4055·4041·4041·40a0··..;.....@U@A@A@. | ||
| 00000340:· | 00000340:·5940·a040·4040·4004·aa40·4040·9204·07a3··Y@.@@@@..@@@.... | ||
| 00000350:· | 00000350:·296e·6174·6976·6569·6e74·4b08·0000·3800··)nativeintK...8. | ||
| 00000360:· | 00000360:·4040·4041·4040·4040·4004·ae40·4040·9204··@@@A@@@@@..@@@.. | ||
| 00000370:·0 | 00000370:·03a3·2569·6e74·3332·4c08·0000·3800·4040··..%int32L...8.@@ | ||
| 00000380:·404 | 00000380:·4041·4040·4040·4004·b240·4040·9204·03a3··@A@@@@@..@@@.... | ||
| 00000390:· | 00000390:·2569·6e74·3634·4d08·0000·3800·4040·4041··%int64M...8.@@@A | ||
| 000003a0:·4 | 000003a0:·4040·4040·4004·b640·4040·9204·03a3·3a55··@@@@@..@@@....:U | ||
| 000003b0:· | 000003b0:·6e64·6566·696e·6564·5f72·6563·7572·7369··ndefined_recursi | ||
| 000003c0:· | 000003c0:·7665·5f6d·6f64·756c·655d·0800·0020·0090··ve_module]...·.. | ||
| 000003d0:· | 000003d0:·0457·4090·a0c0·92a0·c0b3·9004·8340·9040··.W@..........@.@ | ||
| 000003e0:· | 000003e0:·0205·f5e1·0040·4aa0·c0b3·9004·9040·9040··.....@J......@.@ | ||
| 000003f0:· | 000003f0:·0205·f5e1·0040·40a0·0405·4002·05f5·e100··.....@@...@..... | ||
| 00000400:· | 00000400:·4056·4040·4104·caa0·b0a0·3d6f·6361·6d6c··@V@@A.....=ocaml | ||
| 00000410:· | 00000410:·2e77·6172·6e5f·6f6e·5f6c·6974·6572·616c··.warn_on_literal | ||
| 00000420:· | 00000420:·5f70·6174·7465·726e·04ce·0461·04ce·4092··_pattern...a..@. | ||
| 00000430:· | 00000430:·0417·a32e·4173·7365·7274·5f66·6169·6c75··....Assert_failu | ||
| 00000440:·7 | 00000440:·7265·5c08·0000·2000·0418·4090·a0c0·92a0··re\...·...@..... | ||
| 00000450:· | 00000450:·0417·a004·13a0·0414·4002·05f5·e100·4058··........@.....@X | ||
| 00000460:· | 00000460:·4040·4104·d9a0·b0a0·040f·04dc·046f·04dc··@@A..........o.. | ||
| 00000470:· | 00000470:·4092·040d·a330·4469·7669·7369·6f6e·5f62··@....0Division_b | ||
| 00000480:· | 00000480:·795f·7a65·726f·5908·0000·2000·0426·4090··y_zeroY...·..&@. | ||
| 00000490:· | 00000490:·4040·4104·e1a0·b0a0·0417·04e4·0477·04e4··@@A..........w.. | ||
| 000004a0:· | 000004a0:·4092·0407·a32b·456e·645f·6f66·5f66·696c··@....+End_of_fil | ||
| 000004b0:·6 | 000004b0:·6558·0800·0020·0004·2e40·9040·4041·04e9··eX...·...@.@@A.. | ||
| 000004c0:· | 000004c0:·a0b0·a004·1f04·ec04·7f04·ec40·9204·07a3··...........@.... | ||
| 000004d0:· | 000004d0:·2953·7973·5f65·7272·6f72·5708·0000·2000··)Sys_errorW...·. | ||
| 000004e0:·0 | 000004e0:·0436·4090·a004·3240·4041·04f2·a0b0·a004··.6@...2@@A...... | ||
| 000004f0:· | 000004f0:·2804·f504·8804·f540·9204·08a3·2e53·7973··(......@.....Sys | ||
| 00000500:· | 00000500:·5f62·6c6f·636b·6564·5f69·6f5b·0800·0020··_blocked_io[...· | ||
| 00000510:· | 00000510:·0004·3f40·9040·4041·04fa·a0b0·a004·3004··..?@.@@A......0. | ||
| 00000520:· | 00000520:·fd04·9004·fd40·9204·07a3·294e·6f74·5f66··.....@....)Not_f | ||
| 00000530:·6 | 00000530:·6f75·6e64·5608·0000·2000·0447·4090·4040··oundV...·..G@.@@ | ||
| 00000540:·4 | 00000540:·4105·0102·a0b0·a004·3805·0105·0498·0501··A.......8....... | ||
| 00000550:·0 | 00000550:·0540·9204·07a3·2746·6169·6c75·7265·5508··.@....'FailureU. | ||
| 00000560:·0 | 00000560:·0000·2000·044f·4090·a004·4b40·4041·0501··..·..O@...K@@A.. | ||
| 00000570:·0 | 00000570:·0ba0·b0a0·0441·0501·0e04·a105·010e·4092··.....A........@. | ||
| 00000580:· | 00000580:·0408·a330·496e·7661·6c69·645f·6172·6775··...0Invalid_argu | ||
| 00000590:· | 00000590:·6d65·6e74·5408·0000·2000·0458·4090·a004··mentT...·..X@... | ||
| 000005a0:· | 000005a0:·5440·4041·0501·14a0·b0a0·044a·0501·1704··T@@A.......J.... | ||
| 000005b0:· | 000005b0:·aa05·0117·4092·0408·a32e·5374·6163·6b5f··....@.....Stack_ | ||
| 000005c0:· | 000005c0:·6f76·6572·666c·6f77·5a08·0000·2000·0461··overflowZ...·..a | ||
| 000005d0:· | 000005d0:·4090·4040·4105·011c·a0b0·a004·5205·011f··@.@@A.......R... | ||
| 000005e0:· | 000005e0:·04b2·0501·1f40·9204·07a3·2d4f·7574·5f6f··.....@....-Out_o | ||
| 000005f0:·6 | 000005f0:·665f·6d65·6d6f·7279·5308·0000·2000·0469··f_memoryS...·..i | ||
| 00000600:· | 00000600:·4090·4040·4105·0124·a0b0·a004·5a05·0127··@.@@A..$....Z..' | ||
| 00000610:· | 00000610:·04ba·0501·2740·9204·07a3·2d4d·6174·6368··....'@....-Match | ||
| 00000620:· | 00000620:·5f66·6169·6c75·7265·5208·0000·2000·0471··_failureR...·..q | ||
| 00000630:· | 00000630:·4090·a0c0·92a0·0470·a004·6ca0·046d·4002··@......p..l..m@. | ||
| 00000640:·0 | 00000640:·05f5·e100·4063·4040·4105·0132·a0b0·a004··....@c@@A..2.... | ||
| 00000650:· | 00000650:·6805·0135·04c8·0501·3540·9204·0da3·2562··h..5....5@....%b | ||
| 00000660:· | 00000660:·7974·6573·4308·0000·3800·4040·4041·4040··ytesC...8.@@@A@@ | ||
| 00000670:·4040·40 | 00000670:·4040·4005·0139·4040·4092·0403·9092·2653··@@@..9@@@.....&S | ||
| 00000680:· | 00000680:·7464·6c69·6292·264f·7074·696f·6e40·40a0··tdlib.&Option@@. | ||
| 00000690:· | 00000690:·b098·d0b1·2344·6566·0056·42a0·0402·b0c0··....#Def.VB..... | ||
| 000006a0:· | 000006a0:·0501·3b51·0103·2d01·0339·c005·013c·5101··..;Q..-..9...<Q. | ||
| 000006b0:· | 000006b0:·032d·0103·3c40·90d0·91b0·a0b0·a141·a008··.-..<@.......A.. | ||
| 000006c0:· | 000006c0:·0000·2800·b121·7400·5141·a004·02b0·c005··..(..!t.QA...... | ||
| 000006d0:· | 000006d0:·014a·5301·0344·0103·4fc0·0501·4b53·0103··.JS..D..O...KS.. | ||
| 000006e0:· | 000006e0:·4401·0350·40a0·a0d0·9021·61c0·9090·0404··D..P@....!a..... | ||
| 000006f0:· | 000006f0:·0205·f5e1·0040·0103·1608·0000·3000·0501··.....@......0... | ||
| 00000700:· | 00000700:·5105·0151·0501·5105·0151·0501·5105·0151··Q..Q..Q..Q..Q..Q | ||
| 00000710:·0501·5 | 00000710:·0501·5105·0151·40b1·0501·5104·1008·0000··..Q..Q@...Q..... | ||
| 00000720:· | 00000720:·3800·a0c0·9040·0205·f5e1·0040·0103·1540··8....@.....@...@ | ||
| 00000730:· | 00000730:·4140·4140·a047·40a0·4240·4040·b0c0·0501··A@A@.G@.B@@@.... | ||
| 00000740:· | 00000740:·5d53·0103·4401·0346·0413·4040·4040·a105··]S..D..F..@@@@.. | ||
| 00000750:· | 00000750:·0174·4040·41b0·c005·0160·5301·0344·0103··.t@@A....`S..D.. | ||
| 00000760:· | 00000760:·4cc0·0501·6153·0103·4401·034e·4040·a040··L...aS..D..N@@.@ | ||
| 00000770:· | 00000770:·4140·0800·0038·00a0·0414·4041·4041·40a0··A@...8....@A@A@. | ||
| 00000780:·4 | 00000780:·4140·a042·4040·4004·0b40·4040·0409·4040··A@.B@@@..@@@..@@ | ||
| 00000790:·4 | 00000790:·4140·040b·4040·0800·0030·0005·0164·0501··A@..@@...0...d.. | ||
| 000007a0:· | 000007a0:·6405·0164·0501·6405·0164·0501·6405·0164··d..d..d..d..d..d | ||
| 000007b0:·0501·6 | 000007b0:·0501·6440·0501·6340·41b0·040c·041e·40a0··..d@..c@A.....@. | ||
| 000007c0:· | 000007c0:·b090·f0a0·2672·6574·7572·6e00·52a0·0402··....&return.R... | ||
| 000007d0:· | 000007d0:·b0c0·0501·7154·0103·5101·0357·c005·0172··....qT..Q..W...r | ||
| Max diff block lines reached; 28694/432366 bytes (6.64%) of diff not shown. | |||
| Offset 1, 1090 lines modified | Offset 1, 1090 lines modified | ||
| 00000000:·4361·6d6c·3139·3939·5430·3330·8495·a6be··Caml1999T030.... | 00000000:·4361·6d6c·3139·3939·5430·3330·8495·a6be··Caml1999T030.... | ||
| 00000010:·0000·4 | 00000010:·0000·43fa·0000·0bf9·0000·3224·0000·313d··..C.......2$..1= | ||
| 00000020:·0800·0034·0026·4e65·4c69·7374·91b0·a0b0··...4.&NeList.... | 00000020:·0800·0034·0026·4e65·4c69·7374·91b0·a0b0··...4.&NeList.... | ||
| 00000030:·a341·a008·0000·2800·b121·7400·5141·a004··.A....(..!t.QA.. | 00000030:·a341·a008·0000·2800·b121·7400·5141·a004··.A....(..!t.QA.. | ||
| 00000040:·02b0·c02e·636c·6962·2f6e·654c·6973·742e··....clib/neList. | 00000040:·02b0·c02e·636c·6962·2f6e·654c·6973·742e··....clib/neList. | ||
| 00000050:·6d6c·4b01·02a4·0102·acc0·0402·4b01·02a4··mlK.........K... | 00000050:·6d6c·4b01·02a4·0102·acc0·0402·4b01·02a4··mlK.........K... | ||
| 00000060:·0102·ad40·a0a0·d090·2161·c090·9004·0402··...@....!a...... | 00000060:·0102·ad40·a0a0·d090·2161·c090·9004·0402··...@....!a...... | ||
| 00000070:·05f5·e100·4001·0317·0800·0030·00a0·4040··....@......0..@@ | 00000070:·05f5·e100·4001·0317·0800·0030·00a0·4040··....@......0..@@ | Diff chunk too large, falling back to line-by-line diff (990 lines added, 990 lines removed) | |
| 00000080:·0401·0401·0401·0401·0401·0401·0401·40b1··..............@. | 00000080:·0401·0401·0401·0401·0401·0401·0401·40b1··..............@. | ||
| 00000090:·aba | 00000090:·aba7·b1b2·b2b2·b2b2·b2b2·b2b2·b2b2·b2b1··................ | ||
| 000000a0:·b1b1·b1b1·b1b1·b1b1·b1b1·b1b1·b1b1·b1 | 000000a0:·b1b1·b1b1·b1b1·b1b1·b1b1·b1b1·b1b1·b140··...............@ | ||
| 000000b0:· | 000000b0:·a32a·666c·6f61·7461·7272·6179·5108·0000··.*floatarrayQ... | ||
| 000000c0:· | 000000c0:·3800·4040·4041·4040·4040·40b0·c026·5f6e··8.@@@A@@@@@..&_n | ||
| 000000d0:·6 | 000000d0:·6f6e·655f·4040·00ff·0402·4140·4040·9204··one_@@....A@@@.. | ||
| 000000e0:·0 | 000000e0:·06a3·3565·7874·656e·7369·6f6e·5f63·6f6e··..5extension_con | ||
| 000000f0:· | 000000f0:·7374·7275·6374·6f72·5008·0000·3800·4040··structorP...8.@@ | ||
| 00000100:·404 | 00000100:·4041·4040·4040·4004·0740·4040·9204·03a3··@A@@@@@..@@@.... | ||
| 00000110:· | 00000110:·2369·6e74·4108·0000·3800·4040·4041·4040··#intA...8.@@@A@@ | ||
| 00000120:·4040·40 | 00000120:·4040·4004·0b40·4140·9204·03a3·2463·6861··@@@..@A@....$cha | ||
| 00000130:· | 00000130:·7242·0800·0038·0040·4040·4140·4040·4040··rB...8.@@@A@@@@@ | ||
| 00000140:· | 00000140:·040f·4041·4092·0403·a326·7374·7269·6e67··..@A@....&string | ||
| 00000150:· | 00000150:·4f08·0000·3800·4040·4041·4040·4040·4004··O...8.@@@A@@@@@. | ||
| 00000160:· | 00000160:·1340·4040·9204·03a3·2566·6c6f·6174·4408··.@@@....%floatD. | ||
| 00000170:·0 | 00000170:·0000·3800·4040·4041·4040·4040·4004·1740··..8.@@@A@@@@@..@ | ||
| 00000180:·4040· | 00000180:·4040·9204·03a3·2462·6f6f·6c45·0800·0038··@@....$boolE...8 | ||
| 00000190:· | 00000190:·0040·40a1·a0e0·a325·6661·6c73·655e·9040··.@@....%false^.@ | ||
| 000001a0:·40 | 000001a0:·4004·2140·9204·03a0·e0a3·2474·7275·655f··@.!@......$true_ | ||
| 000001b0:· | 000001b0:·9040·4004·2740·9204·0340·4041·4040·4040··.@@.'@...@@A@@@@ | ||
| 000001c0:·40 | 000001c0:·4004·2840·4140·9204·10a3·2475·6e69·7446··@.(@A@....$unitF | ||
| 000001d0:· | 000001d0:·0800·0038·0040·40a1·a0e0·a322·2829·6090··...8.@@...."()`. | ||
| 000001e0:· | 000001e0:·4040·0432·4092·0403·4040·4140·4040·4040··@@.2@...@@A@@@@@ | ||
| 000001f0:· | 000001f0:·0433·4041·4092·040a·a323·6578·6e47·0800··.3@A@....#exnG.. | ||
| 00000200:·00 | 00000200:·0038·0040·4041·4140·4040·4040·0437·4040··.8.@@AA@@@@@.7@@ | ||
| 00000210:·40 | 00000210:·4092·0403·a325·6172·7261·7948·0800·0038··@....%arrayH...8 | ||
| 00000220:· | 00000220:·00a0·c090·4002·05f5·e100·404f·4041·4041··....@.....@O@A@A | ||
| 00000230:·4 | 00000230:·40a0·007f·40a0·4040·4040·0440·4040·4092··@...@.@@@@.@@@@. | ||
| 00000240:· | 00000240:·0408·a324·6c69·7374·4908·0000·3800·a0c0··...$listI...8... | ||
| 00000250:· | 00000250:·0409·0205·f5e1·0040·5040·41a1·a0e0·a322··.......@P@A...." | ||
| 00000260:· | 00000260:·5b5d·6190·4040·044c·4092·0403·a0e0·a322··[]a.@@.L@......" | ||
| 00000270:· | 00000270:·3a3a·6290·a004·0ea0·c0b3·9004·16a0·0413··::b............. | ||
| 00000280:· | 00000280:·4090·4002·05f5·e100·4051·4040·0459·4092··@.@.....@Q@@.Y@. | ||
| 00000290:· | 00000290:·040a·4040·4140·a059·40a0·4040·4040·045c··..@@A@.Y@.@@@@.\ | ||
| 000002a0:· | 000002a0:·4040·4092·041b·a326·6f70·7469·6f6e·4a08··@@@....&optionJ. | ||
| 000002b0:·0 | 000002b0:·0000·3800·a0c0·0425·0205·f5e1·0040·5340··..8....%.....@S@ | ||
| 000002c0:·4 | 000002c0:·41a1·a0e0·a324·4e6f·6e65·6390·4040·0468··A....$Nonec.@@.h | ||
| 000002d0:· | 000002d0:·4092·0403·a0e0·a324·536f·6d65·6490·a004··@......$Somed... | ||
| 000002e0:·040 | 000002e0:·0e40·4004·6f40·9204·0440·4041·40a0·5940··.@@.o@...@@A@.Y@ | ||
| 000002f0:· | 000002f0:·a040·4040·4004·7240·4040·9204·15a3·266c··.@@@@.r@@@....&l | ||
| 00000300:·6 | 00000300:·617a·795f·744e·0800·0038·00a0·c004·3b02··azy_tN...8....;. | ||
| 00000310:·0 | 00000310:·05f5·e100·4055·4041·4041·40a0·5940·a040··....@U@A@A@.Y@.@ | ||
| 00000320:·4040·40 | 00000320:·4040·4004·7a40·4040·9204·07a3·296e·6174··@@@.z@@@....)nat | ||
| 00000330:· | 00000330:·6976·6569·6e74·4b08·0000·3800·4040·4041··iveintK...8.@@@A | ||
| 00000340:·4 | 00000340:·4040·4040·4004·7e40·4040·9204·03a3·2569··@@@@@.~@@@....%i | ||
| 00000350:·6 | 00000350:·6e74·3332·4c08·0000·3800·4040·4041·4040··nt32L...8.@@@A@@ | ||
| 00000360:·4040·40 | 00000360:·4040·4004·8240·4040·9204·03a3·2569·6e74··@@@..@@@....%int | ||
| 00000370:· | 00000370:·3634·4d08·0000·3800·4040·4041·4040·4040··64M...8.@@@A@@@@ | ||
| 00000380:·40 | 00000380:·4004·8640·4040·9204·03a3·3a55·6e64·6566··@..@@@....:Undef | ||
| 00000390:·6 | 00000390:·696e·6564·5f72·6563·7572·7369·7665·5f6d··ined_recursive_m | ||
| 000003a0:·6 | 000003a0:·6f64·756c·655d·0800·0020·0090·0457·4090··odule]...·...W@. | ||
| 000003b0:· | 000003b0:·a0c0·92a0·c0b3·9004·8340·9040·0205·f5e1··.........@.@.... | ||
| 000003c0:· | 000003c0:·0040·4aa0·c0b3·9004·9040·9040·0205·f5e1··.@J......@.@.... | ||
| 000003d0:· | 000003d0:·0040·40a0·0405·4002·05f5·e100·4056·4040··.@@...@.....@V@@ | ||
| 000003e0:·404 | 000003e0:·4104·9aa0·b0a0·3d6f·6361·6d6c·2e77·6172··A.....=ocaml.war | ||
| 000003f0:· | 000003f0:·6e5f·6f6e·5f6c·6974·6572·616c·5f70·6174··n_on_literal_pat | ||
| 00000400:·74 | 00000400:·7465·726e·049e·0461·049e·4092·0417·a32e··tern...a..@..... | ||
| 00000410:· | 00000410:·4173·7365·7274·5f66·6169·6c75·7265·5c08··Assert_failure\. | ||
| 00000420:·0 | 00000420:·0000·2000·0418·4090·a0c0·92a0·0417·a004··..·...@......... | ||
| 00000430:· | 00000430:·13a0·0414·4002·05f5·e100·4058·4040·4104··....@.....@X@@A. | ||
| 00000440:· | 00000440:·a9a0·b0a0·040f·04ac·046f·04ac·4092·040d··.........o..@... | ||
| 00000450:· | 00000450:·a330·4469·7669·7369·6f6e·5f62·795f·7a65··.0Division_by_ze | ||
| 00000460:· | 00000460:·726f·5908·0000·2000·0426·4090·4040·4104··roY...·..&@.@@A. | ||
| 00000470:· | 00000470:·b1a0·b0a0·0417·04b4·0477·04b4·4092·0407··.........w..@... | ||
| 00000480:· | 00000480:·a32b·456e·645f·6f66·5f66·696c·6558·0800··.+End_of_fileX.. | ||
| 00000490:·00 | 00000490:·0020·0004·2e40·9040·4041·04b9·a0b0·a004··.·...@.@@A...... | ||
| 000004a0:· | 000004a0:·1f04·bc04·7f04·bc40·9204·07a3·2953·7973··.......@....)Sys | ||
| 000004b0:· | 000004b0:·5f65·7272·6f72·5708·0000·2000·0436·4090··_errorW...·..6@. | ||
| 000004c0:· | 000004c0:·a004·3240·4041·04c2·a0b0·a004·2804·c504··..2@@A......(... | ||
| 000004d0:· | 000004d0:·8804·c540·9204·08a3·2e53·7973·5f62·6c6f··...@.....Sys_blo | ||
| 000004e0:·6 | 000004e0:·636b·6564·5f69·6f5b·0800·0020·0004·3f40··cked_io[...·..?@ | ||
| 000004f0:· | 000004f0:·9040·4041·04ca·a0b0·a004·3004·cd04·9004··.@@A......0..... | ||
| 00000500:· | 00000500:·cd40·9204·07a3·294e·6f74·5f66·6f75·6e64··.@....)Not_found | ||
| 00000510:· | 00000510:·5608·0000·2000·0447·4090·4040·4104·d2a0··V...·..G@.@@A... | ||
| 00000520:· | 00000520:·b0a0·0438·04d5·0498·04d5·4092·0407·a327··...8......@....' | ||
| 00000530:· | 00000530:·4661·696c·7572·6555·0800·0020·0004·4f40··FailureU...·..O@ | ||
| 00000540:· | 00000540:·90a0·044b·4040·4104·dba0·b0a0·0441·04de··...K@@A......A.. | ||
| 00000550:· | 00000550:·04a1·04de·4092·0408·a330·496e·7661·6c69··....@....0Invali | ||
| 00000560:·6 | 00000560:·645f·6172·6775·6d65·6e74·5408·0000·2000··d_argumentT...·. | ||
| 00000570:·0 | 00000570:·0458·4090·a004·5440·4041·04e4·a0b0·a004··.X@...T@@A...... | ||
| 00000580:· | 00000580:·4a04·e704·aa04·e740·9204·08a3·2e53·7461··J......@.....Sta | ||
| 00000590:·6 | 00000590:·636b·5f6f·7665·7266·6c6f·775a·0800·0020··ck_overflowZ...· | ||
| 000005a0:· | 000005a0:·0004·6140·9040·4041·04ec·a0b0·a004·5204··..a@.@@A......R. | ||
| 000005b0:· | 000005b0:·ef04·b204·ef40·9204·07a3·2d4f·7574·5f6f··.....@....-Out_o | ||
| 000005c0:·6 | 000005c0:·665f·6d65·6d6f·7279·5308·0000·2000·0469··f_memoryS...·..i | ||
| 000005d0:· | 000005d0:·4090·4040·4104·f4a0·b0a0·045a·04f7·04ba··@.@@A......Z.... | ||
| 000005e0:· | 000005e0:·04f7·4092·0407·a32d·4d61·7463·685f·6661··..@....-Match_fa | ||
| 000005f0:·6 | 000005f0:·696c·7572·6552·0800·0020·0004·7140·90a0··ilureR...·..q@.. | ||
| 00000600:· | 00000600:·c092·a004·70a0·046c·a004·6d40·0205·f5e1··....p..l..m@.... | ||
| 00000610:· | 00000610:·0040·6340·4041·0501·02a0·b0a0·0468·0501··.@c@@A.......h.. | ||
| 00000620:·0 | 00000620:·0504·c805·0105·4092·040d·a325·6279·7465··......@....%byte | ||
| 00000630:· | 00000630:·7343·0800·0038·0040·4040·4140·4040·4040··sC...8.@@@A@@@@@ | ||
| 00000640:· | 00000640:·0501·0940·4040·9204·0390·9226·5374·646c··...@@@.....&Stdl | ||
| 00000650:·6 | 00000650:·6962·9226·4f70·7469·6f6e·0501·4308·0000··ib.&Option..C... | ||
| 00000660:· | 00000660:·3800·a0c0·9040·0205·f5e1·0040·0103·1640··8....@.....@...@ | ||
| 00000670:· | 00000670:·4140·4190·c096·c0b3·9005·014d·a0c0·9040··A@A........M...@ | ||
| 00000680:·01 | 00000680:·4240·0103·1d40·9040·4240·0103·1e42·4001··B@...@.@B@...B@. | ||
| 00000690:·0 | 00000690:·0315·a047·40a0·4240·4040·b0c0·0501·504b··...G@.B@@@....PK | ||
| 000006a0:· | 000006a0:·0102·a401·02a4·c005·0151·4b01·02a4·0102··.........QK..... | ||
| 000006b0:·4 | 000006b0:·bc40·4040·40a1·0501·5f40·4040·b0c0·0501··.@@@@..._@@@.... | ||
| 000006c0:· | 000006c0:·544b·0102·a401·02a9·c005·0155·4b01·02a4··TK.........UK... | ||
| 000006d0:·01 | 000006d0:·0102·ab40·40a0·4241·4008·0000·3800·a005··...@@.BA@...8... | ||
| 000006e0:·0 | 000006e0:·0151·4041·4041·90c0·92a0·c096·0501·5743··.Q@A@A........WC | ||
| 000006f0:· | 000006f0:·4001·0318·a0c0·b390·04f2·a004·0740·9040··@............@.@ | ||
| 00000700:· | 00000700:·0205·f5e1·0040·0103·1a40·0205·f5e1·0040··.....@...@.....@ | ||
| 00000710:·0 | 00000710:·0103·1ba0·5940·a040·4040·4004·1840·4040··....Y@.@@@@..@@@ | ||
| 00000720:· | 00000720:·0415·4040·4190·d092·a0d0·9021·6104·1105··..@@A......!a... | ||
| 00000730:· | 00000730:·0163·b0c0·0501·6f4b·0102·a401·02b0·c005··.c....oK........ | ||
| 00000740:· | 00000740:·0170·4b01·02a4·0102·b240·40a0·d0b3·0412··.pK......@@..... | ||
| 00000750:· | 00000750:·a090·246c·6973·74b0·c005·0178·4b01·02a4··..$list....xK... | ||
| 00000760:·01 | 00000760:·0102·b804·2840·a0d0·9021·6104·2005·0172··....(@...!a.·..r | ||
| 00000770:· | 00000770:·b0c0·0501·7e4b·0102·a401·02b5·c005·017f··....~K.......... | ||
| 00000780:· | 00000780:·4b01·02a4·0102·b740·4040·0420·0501·75b0··K......@@@.·..u. | ||
| 00000790:·04 | 00000790:·0403·0430·4040·4004·2705·0176·b004·1304··...0@@@.'..v.... | ||
| 000007a0:· | 000007a0:·3140·4004·3340·40b0·0433·0432·4008·0000··1@@.3@@..3.2@... | ||
| 000007b0:· | 000007b0:·3000·0501·7805·0178·0501·7805·0178·0501··0...x..x..x..x.. | ||
| 000007c0:·7 | 000007c0:·7805·0178·0501·7805·0178·4005·0176·4040··x..x..x..x@..v@@ | ||
| 000007d0:· | 000007d0:·a0b0·a140·a0c0·e0a0·a024·6865·6164·0052··...@.....$head.R | ||
| Max diff block lines reached; 11931/149332 bytes (7.99%) of diff not shown. | |||
| Offset 1, 9 lines modified | Offset 1, 9 lines modified | ||
| 00000000:·4361·6d6c·3139·3939·5430·3330·8495·a6be··Caml1999T030.... | 00000000:·4361·6d6c·3139·3939·5430·3330·8495·a6be··Caml1999T030.... | ||
| 00000010:·0000·da | 00000010:·0000·da0c·0000·2313·0000·972b·0000·9394··......#....+.... | ||
| 00000020:·0800·0034·0026·4f70·7469·6f6e·91b0·a0b0··...4.&Option.... | 00000020:·0800·0034·0026·4f70·7469·6f6e·91b0·a0b0··...4.&Option.... | ||
| 00000030:·9db0·a02a·6f63·616d·6c2e·7465·7874·b0c0··...*ocaml.text.. | 00000030:·9db0·a02a·6f63·616d·6c2e·7465·7874·b0c0··...*ocaml.text.. | ||
| 00000040:·265f·6e6f·6e65·5f40·4000·ff04·0241·90a0··&_none_@@....A.. | 00000040:·265f·6e6f·6e65·5f40·4000·ff04·0241·90a0··&_none_@@....A.. | ||
| 00000050:·a0a0·c091·b20a·0000·0124·204d·6f64·756c··.........$·Modul | 00000050:·a0a0·c091·b20a·0000·0124·204d·6f64·756c··.........$·Modul | ||
| 00000060:·6520·696d·706c·656d·656e·7469·6e67·2062··e·implementing·b | 00000060:·6520·696d·706c·656d·656e·7469·6e67·2062··e·implementing·b | ||
| 00000070:·6173·6963·2063·6f6d·6269·6e61·746f·7273··asic·combinators | 00000070:·6173·6963·2063·6f6d·6269·6e61·746f·7273··asic·combinators | ||
| 00000080:·2066·6f72·204f·4361·6d6c·206f·7074·696f···for·OCaml·optio | 00000080:·2066·6f72·204f·4361·6d6c·206f·7074·696f···for·OCaml·optio |
| 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, 9 lines modified | Offset 1, 9 lines modified | ||
| 00000000:·4361·6d6c·3139·3939·5430·3330·8495·a6be··Caml1999T030.... | 00000000:·4361·6d6c·3139·3939·5430·3330·8495·a6be··Caml1999T030.... | ||
| 00000010:·0000·a32 | 00000010:·0000·a328·0000·1c2d·0000·759a·0000·7250··...(...-..u...rP | ||
| 00000020:·0800·0034·002b·5365·676d·656e·7474·7265··...4.+Segmenttre | 00000020:·0800·0034·002b·5365·676d·656e·7474·7265··...4.+Segmenttre | ||
| 00000030:·6591·b0a0·b09d·b0a0·2a6f·6361·6d6c·2e74··e.......*ocaml.t | 00000030:·6591·b0a0·b09d·b0a0·2a6f·6361·6d6c·2e74··e.......*ocaml.t | ||
| 00000040:·6578·74b0·c026·5f6e·6f6e·655f·4040·00ff··ext..&_none_@@.. | 00000040:·6578·74b0·c026·5f6e·6f6e·655f·4040·00ff··ext..&_none_@@.. | ||
| 00000050:·0402·4190·a0a0·a0c0·91b2·09ba·2054·6869··..A.........·Thi | 00000050:·0402·4190·a0a0·a0c0·91b2·09ba·2054·6869··..A.........·Thi | ||
| 00000060:·7320·6d6f·6475·6c65·2069·7320·6120·7665··s·module·is·a·ve | 00000060:·7320·6d6f·6475·6c65·2069·7320·6120·7665··s·module·is·a·ve | ||
| 00000070:·7279·2073·696d·706c·6520·696d·706c·656d··ry·simple·implem | 00000070:·7279·2073·696d·706c·6520·696d·706c·656d··ry·simple·implem | ||
| 00000080:·656e·7461·7469·6f6e·206f·6620·2273·6567··entation·of·"seg | 00000080:·656e·7461·7469·6f6e·206f·6620·2273·6567··entation·of·"seg |
| Offset 1, 9 lines modified | Offset 1, 9 lines modified | ||
| 00000000:·4361·6d6c·3139·3939·5430·3330·8495·a6be··Caml1999T030.... | 00000000:·4361·6d6c·3139·3939·5430·3330·8495·a6be··Caml1999T030.... | ||
| 00000010:·0000·4d6 | 00000010:·0000·4d63·0000·0d74·0000·386a·0000·3729··..Mc...t..8j..7) | ||
| 00000020:·0800·0034·0025·5374·6f72·6591·b0a0·b09d··...4.%Store..... | 00000020:·0800·0034·0025·5374·6f72·6591·b0a0·b09d··...4.%Store..... | ||
| 00000030:·b0a0·2a6f·6361·6d6c·2e74·6578·74b0·c026··..*ocaml.text..& | 00000030:·b0a0·2a6f·6361·6d6c·2e74·6578·74b0·c026··..*ocaml.text..& | ||
| 00000040:·5f6e·6f6e·655f·4040·00ff·0402·4190·a0a0··_none_@@....A... | 00000040:·5f6e·6f6e·655f·4040·00ff·0402·4190·a0a0··_none_@@....A... | ||
| 00000050:·a0c0·91b2·0993·2054·6869·7320·6d6f·6475··......·This·modu | 00000050:·a0c0·91b2·0993·2054·6869·7320·6d6f·6475··......·This·modu | ||
| 00000060:·6c65·2069·6d70·6c65·6d65·6e74·7320·616e··le·implements·an | 00000060:·6c65·2069·6d70·6c65·6d65·6e74·7320·616e··le·implements·an | ||
| 00000070:·2022·756e·7479·7065·6420·7374·6f72·6522···"untyped·store" | 00000070:·2022·756e·7479·7065·6420·7374·6f72·6522···"untyped·store" | ||
| 00000080:·2c20·696e·2074·6869·7320·7061·7274·6963··,·in·this·partic | 00000080:·2c20·696e·2074·6869·7320·7061·7274·6963··,·in·this·partic |
| Offset 1, 9 lines modified | Offset 1, 9 lines modified | ||
| 00000000:·4361·6d6c·3139·3939·5430·3330·8495·a6be··Caml1999T030.... | 00000000:·4361·6d6c·3139·3939·5430·3330·8495·a6be··Caml1999T030.... | ||
| 00000010:·0001·8bb | 00000010:·0001·8bb4·0000·4b68·0001·2db7·0001·2a78··......Kh..-...*x | ||
| 00000020:·0800·0034·0028·5465·726d·696e·616c·91b0··...4.(Terminal.. | 00000020:·0800·0034·0028·5465·726d·696e·616c·91b0··...4.(Terminal.. | ||
| 00000030:·a0b0·a341·a008·0000·2800·b125·636f·6c6f··...A....(..%colo | 00000030:·a0b0·a341·a008·0000·2800·b125·636f·6c6f··...A....(..%colo | ||
| 00000040:·7200·5141·a004·02b0·c030·636c·6962·2f74··r.QA.....0clib/t | 00000040:·7200·5141·a004·02b0·c030·636c·6962·2f74··r.QA.....0clib/t | ||
| 00000050:·6572·6d69·6e61·6c2e·6d6c·4b01·02a4·0102··erminal.mlK..... | 00000050:·6572·6d69·6e61·6c2e·6d6c·4b01·02a4·0102··erminal.mlK..... | ||
| 00000060:·a9c0·0402·4b01·02a4·0102·ae40·4008·0000··....K......@@... | 00000060:·a9c0·0402·4b01·02a4·0102·ae40·4008·0000··....K......@@... | ||
| 00000070:·3800·4040·4041·90c0·98e0·a0a0·2a4c·4947··8.@@@A......*LIG | 00000070:·3800·4040·4041·90c0·98e0·a0a0·2a4c·4947··8.@@@A......*LIG | ||
| 00000080:·4854·5f43·5941·4e90·40a0·a025·494e·4445··HT_CYAN.@..%INDE | 00000080:·4854·5f43·5941·4e90·40a0·a025·494e·4445··HT_CYAN.@..%INDE |
| Offset 1, 2836 lines modified | Offset 1, 2835 lines modified | ||
| 00000000:·4361·6d6c·3139·3939·5430·3330·8495·a6be··Caml1999T030.... | 00000000:·4361·6d6c·3139·3939·5430·3330·8495·a6be··Caml1999T030.... | ||
| 00000010:·0000·b1 | 00000010:·0000·b10c·0000·202b·0000·82e6·0000·8159··......·+.......Y | ||
| 00000020:·0800·0034·0024·5472·6965·91b0·a0b0·98d0··...4.$Trie...... | 00000020:·0800·0034·0024·5472·6965·91b0·a0b0·98d0··...4.$Trie...... | ||
| 00000030:·b121·5300·5b44·a004·02b0·c02c·636c·6962··.!S.[D.....,clib | 00000030:·b121·5300·5b44·a004·02b0·c02c·636c·6962··.!S.[D.....,clib | ||
| 00000040:·2f74·7269·652e·6d6c·4b01·02a4·0102·b0c0··/trie.mlK....... | 00000040:·2f74·7269·652e·6d6c·4b01·02a4·0102·b0c0··/trie.mlK....... | ||
| 00000050:·0402·4b01·02a4·0102·b140·90d0·91b0·a0b0··..K......@...... | 00000050:·0402·4b01·02a4·0102·b140·90d0·91b0·a0b0··..K......@...... | ||
| 00000060:·a141·a008·0000·2800·b125·6c61·6265·6c00··.A....(..%label. | 00000060:·a141·a008·0000·2800·b125·6c61·6265·6c00··.A....(..%label. | ||
| 00000070:·5141·a004·02b0·c004·104d·0102·b801·02bf··QA.......M...... | 00000070:·5141·a004·02b0·c004·104d·0102·b801·02bf··QA.......M...... | ||
| 00000080:·c004·114d·0102·b801·02c4·4040·0800·0038··...M......@@...8 | 00000080:·c004·114d·0102·b801·02c4·4040·0800·0038··...M......@@...8 | ||
| 00000090:·0040·4040·4140·4040·4040·b0c0·0414·4d01··.@@@A@@@@@....M. | 00000090:·0040·4040·4140·4040·4040·b0c0·0414·4d01··.@@@A@@@@@....M. | ||
| 000000a0:·02b8·0102·ba04·0440·4040·40a1·0421·4040··.......@@@@..!@@ | 000000a0:·02b8·0102·ba04·0440·4040·40a1·0421·4040··.......@@@@..!@@ | Diff chunk too large, falling back to line-by-line diff (2723 lines added, 2723 lines removed) | |
| 000000b0:·4041·4004·0340·4008·0000·3000·a040·4004··@A@..@@...0..@@. | 000000b0:·4041·4004·0340·4008·0000·3000·a040·4004··@A@..@@...0..@@. | ||
| 000000c0:·0104·0104·0104·0104·0104·0104·0140·aba | 000000c0:·0104·0104·0104·0104·0104·0104·0140·aba7··.............@.. | ||
| 000000d0:· | 000000d0:·b1b2·b2b2·b2b2·b2b2·b2b2·b2b2·b2b1·b1b1··................ | ||
| 000000e0:·b1b1·b1b1·b1b1·b1b1·b1b1·b1b1·b1 | 000000e0:·b1b1·b1b1·b1b1·b1b1·b1b1·b1b1·b140·a32a··.............@.* | ||
| 000000f0:· | 000000f0:·666c·6f61·7461·7272·6179·5108·0000·3800··floatarrayQ...8. | ||
| 00000100:· | 00000100:·4040·4041·4040·4040·40b0·c026·5f6e·6f6e··@@@A@@@@@..&_non | ||
| 00000110:·6 | 00000110:·655f·4040·00ff·0402·4140·4040·9204·06a3··e_@@....A@@@.... | ||
| 00000120:· | 00000120:·3565·7874·656e·7369·6f6e·5f63·6f6e·7374··5extension_const | ||
| 00000130:·7 | 00000130:·7275·6374·6f72·5008·0000·3800·4040·4041··ructorP...8.@@@A | ||
| 00000140:·4 | 00000140:·4040·4040·4004·0740·4040·9204·03a3·2369··@@@@@..@@@....#i | ||
| 00000150:·6 | 00000150:·6e74·4108·0000·3800·4040·4041·4040·4040··ntA...8.@@@A@@@@ | ||
| 00000160:·40 | 00000160:·4004·0b40·4140·9204·03a3·2463·6861·7242··@..@A@....$charB | ||
| 00000170:· | 00000170:·0800·0038·0040·4040·4140·4040·4040·040f··...8.@@@A@@@@@.. | ||
| 00000180:· | 00000180:·4041·4092·0403·a326·7374·7269·6e67·4f08··@A@....&stringO. | ||
| 00000190:·0 | 00000190:·0000·3800·4040·4041·4040·4040·4004·1340··..8.@@@A@@@@@..@ | ||
| 000001a0:·4040· | 000001a0:·4040·9204·03a3·2566·6c6f·6174·4408·0000··@@....%floatD... | ||
| 000001b0:· | 000001b0:·3800·4040·4041·4040·4040·4004·1740·4040··8.@@@A@@@@@..@@@ | ||
| 000001c0:· | 000001c0:·9204·03a3·2462·6f6f·6c45·0800·0038·0040··....$boolE...8.@ | ||
| 000001d0:·40 | 000001d0:·40a1·a0e0·a325·6661·6c73·655e·9040·4004··@....%false^.@@. | ||
| 000001e0:· | 000001e0:·2140·9204·03a0·e0a3·2474·7275·655f·9040··!@......$true_.@ | ||
| 000001f0:·40 | 000001f0:·4004·2740·9204·0340·4041·4040·4040·4004··@.'@...@@A@@@@@. | ||
| 00000200:· | 00000200:·2840·4140·9204·10a3·2475·6e69·7446·0800··(@A@....$unitF.. | ||
| 00000210:·00 | 00000210:·0038·0040·40a1·a0e0·a322·2829·6090·4040··.8.@@...."()`.@@ | ||
| 00000220:· | 00000220:·0432·4092·0403·4040·4140·4040·4040·0433··.2@...@@A@@@@@.3 | ||
| 00000230:· | 00000230:·4041·4092·040a·a323·6578·6e47·0800·0038··@A@....#exnG...8 | ||
| 00000240:· | 00000240:·0040·4041·4140·4040·4040·0437·4040·4092··.@@AA@@@@@.7@@@. | ||
| 00000250:· | 00000250:·0403·a325·6172·7261·7948·0800·0038·00a0··...%arrayH...8.. | ||
| 00000260:· | 00000260:·c090·4002·05f5·e100·404f·4041·4041·40a0··..@.....@O@A@A@. | ||
| 00000270:· | 00000270:·007f·40a0·4040·4040·0440·4040·4092·0408··..@.@@@@.@@@@... | ||
| 00000280:· | 00000280:·a324·6c69·7374·4908·0000·3800·a0c0·0409··.$listI...8..... | ||
| 00000290:·0 | 00000290:·0205·f5e1·0040·5040·41a1·a0e0·a322·5b5d··.....@P@A...."[] | ||
| 000002a0:· | 000002a0:·6190·4040·044c·4092·0403·a0e0·a322·3a3a··a.@@.L@......":: | ||
| 000002b0:· | 000002b0:·6290·a004·0ea0·c0b3·9004·16a0·0413·4090··b.............@. | ||
| 000002c0:· | 000002c0:·4002·05f5·e100·4051·4040·0459·4092·040a··@.....@Q@@.Y@... | ||
| 000002d0:· | 000002d0:·4040·4140·a059·40a0·4040·4040·045c·4040··@@A@.Y@.@@@@.\@@ | ||
| 000002e0:·40 | 000002e0:·4092·041b·a326·6f70·7469·6f6e·4a08·0000··@....&optionJ... | ||
| 000002f0:· | 000002f0:·3800·a0c0·0425·0205·f5e1·0040·5340·41a1··8....%.....@S@A. | ||
| 00000300:·a | 00000300:·a0e0·a324·4e6f·6e65·6390·4040·0468·4092··...$Nonec.@@.h@. | ||
| 00000310:· | 00000310:·0403·a0e0·a324·536f·6d65·6490·a004·0e40··.....$Somed....@ | ||
| 00000320:·40 | 00000320:·4004·6f40·9204·0440·4041·40a0·5940·a040··@.o@...@@A@.Y@.@ | ||
| 00000330:·4040·40 | 00000330:·4040·4004·7240·4040·9204·15a3·266c·617a··@@@.r@@@....&laz | ||
| 00000340:·7 | 00000340:·795f·744e·0800·0038·00a0·c004·3b02·05f5··y_tN...8....;... | ||
| 00000350:· | 00000350:·e100·4055·4041·4041·40a0·5940·a040·4040··..@U@A@A@.Y@.@@@ | ||
| 00000360:·40 | 00000360:·4004·7a40·4040·9204·07a3·296e·6174·6976··@.z@@@....)nativ | ||
| 00000370:· | 00000370:·6569·6e74·4b08·0000·3800·4040·4041·4040··eintK...8.@@@A@@ | ||
| 00000380:·4040·40 | 00000380:·4040·4004·7e40·4040·9204·03a3·2569·6e74··@@@.~@@@....%int | ||
| 00000390:· | 00000390:·3332·4c08·0000·3800·4040·4041·4040·4040··32L...8.@@@A@@@@ | ||
| 000003a0:·40 | 000003a0:·4004·8240·4040·9204·03a3·2569·6e74·3634··@..@@@....%int64 | ||
| 000003b0:· | 000003b0:·4d08·0000·3800·4040·4041·4040·4040·4004··M...8.@@@A@@@@@. | ||
| 000003c0:· | 000003c0:·8640·4040·9204·03a3·3a55·6e64·6566·696e··.@@@....:Undefin | ||
| 000003d0:·6 | 000003d0:·6564·5f72·6563·7572·7369·7665·5f6d·6f64··ed_recursive_mod | ||
| 000003e0:· | 000003e0:·756c·655d·0800·0020·0090·0457·4090·a0c0··ule]...·...W@... | ||
| 000003f0:· | 000003f0:·92a0·c0b3·9004·8340·9040·0205·f5e1·0040··.......@.@.....@ | ||
| 00000400:·4 | 00000400:·4aa0·c0b3·9004·9040·9040·0205·f5e1·0040··J......@.@.....@ | ||
| 00000410:·40 | 00000410:·40a0·0405·4002·05f5·e100·4056·4040·4104··@...@.....@V@@A. | ||
| 00000420:· | 00000420:·9aa0·b0a0·3d6f·6361·6d6c·2e77·6172·6e5f··....=ocaml.warn_ | ||
| 00000430:· | 00000430:·6f6e·5f6c·6974·6572·616c·5f70·6174·7465··on_literal_patte | ||
| 00000440:· | 00000440:·726e·049e·0461·049e·4092·0417·a32e·4173··rn...a..@.....As | ||
| 00000450:·73 | 00000450:·7365·7274·5f66·6169·6c75·7265·5c08·0000··sert_failure\... | ||
| 00000460:· | 00000460:·2000·0418·4090·a0c0·92a0·0417·a004·13a0···...@........... | ||
| 00000470:· | 00000470:·0414·4002·05f5·e100·4058·4040·4104·a9a0··..@.....@X@@A... | ||
| 00000480:· | 00000480:·b0a0·040f·04ac·046f·04ac·4092·040d·a330··.......o..@....0 | ||
| 00000490:· | 00000490:·4469·7669·7369·6f6e·5f62·795f·7a65·726f··Division_by_zero | ||
| 000004a0:· | 000004a0:·5908·0000·2000·0426·4090·4040·4104·b1a0··Y...·..&@.@@A... | ||
| 000004b0:· | 000004b0:·b0a0·0417·04b4·0477·04b4·4092·0407·a32b··.......w..@....+ | ||
| 000004c0:· | 000004c0:·456e·645f·6f66·5f66·696c·6558·0800·0020··End_of_fileX...· | ||
| 000004d0:· | 000004d0:·0004·2e40·9040·4041·04b9·a0b0·a004·1f04··...@.@@A........ | ||
| 000004e0:· | 000004e0:·bc04·7f04·bc40·9204·07a3·2953·7973·5f65··.....@....)Sys_e | ||
| 000004f0:· | 000004f0:·7272·6f72·5708·0000·2000·0436·4090·a004··rrorW...·..6@... | ||
| 00000500:· | 00000500:·3240·4041·04c2·a0b0·a004·2804·c504·8804··2@@A......(..... | ||
| 00000510:· | 00000510:·c540·9204·08a3·2e53·7973·5f62·6c6f·636b··.@.....Sys_block | ||
| 00000520:·6 | 00000520:·6564·5f69·6f5b·0800·0020·0004·3f40·9040··ed_io[...·..?@.@ | ||
| 00000530:·404 | 00000530:·4041·04ca·a0b0·a004·3004·cd04·9004·cd40··@A......0......@ | ||
| 00000540:· | 00000540:·9204·07a3·294e·6f74·5f66·6f75·6e64·5608··....)Not_foundV. | ||
| 00000550:·0 | 00000550:·0000·2000·0447·4090·4040·4104·d2a0·b0a0··..·..G@.@@A..... | ||
| 00000560:· | 00000560:·0438·04d5·0498·04d5·4092·0407·a327·4661··.8......@....'Fa | ||
| 00000570:·6 | 00000570:·696c·7572·6555·0800·0020·0004·4f40·90a0··ilureU...·..O@.. | ||
| 00000580:· | 00000580:·044b·4040·4104·dba0·b0a0·0441·04de·04a1··.K@@A......A.... | ||
| 00000590:· | 00000590:·04de·4092·0408·a330·496e·7661·6c69·645f··..@....0Invalid_ | ||
| 000005a0:· | 000005a0:·6172·6775·6d65·6e74·5408·0000·2000·0458··argumentT...·..X | ||
| 000005b0:· | 000005b0:·4090·a004·5440·4041·04e4·a0b0·a004·4a04··@...T@@A......J. | ||
| 000005c0:· | 000005c0:·e704·aa04·e740·9204·08a3·2e53·7461·636b··.....@.....Stack | ||
| 000005d0:· | 000005d0:·5f6f·7665·7266·6c6f·775a·0800·0020·0004··_overflowZ...·.. | ||
| 000005e0:· | 000005e0:·6140·9040·4041·04ec·a0b0·a004·5204·ef04··a@.@@A......R... | ||
| 000005f0:· | 000005f0:·b204·ef40·9204·07a3·2d4f·7574·5f6f·665f··...@....-Out_of_ | ||
| 00000600:· | 00000600:·6d65·6d6f·7279·5308·0000·2000·0469·4090··memoryS...·..i@. | ||
| 00000610:· | 00000610:·4040·4104·f4a0·b0a0·045a·04f7·04ba·04f7··@@A......Z...... | ||
| 00000620:· | 00000620:·4092·0407·a32d·4d61·7463·685f·6661·696c··@....-Match_fail | ||
| 00000630:· | 00000630:·7572·6552·0800·0020·0004·7140·90a0·c092··ureR...·..q@.... | ||
| 00000640:· | 00000640:·a004·70a0·046c·a004·6d40·0205·f5e1·0040··..p..l..m@.....@ | ||
| 00000650:· | 00000650:·6340·4041·0501·02a0·b0a0·0468·0501·0504··c@@A.......h.... | ||
| 00000660:· | 00000660:·c805·0105·4092·040d·a325·6279·7465·7343··....@....%bytesC | ||
| 00000670:· | 00000670:·0800·0038·0040·4040·4140·4040·4040·0501··...8.@@@A@@@@@.. | ||
| 00000680:·0 | 00000680:·0940·4040·9204·0390·9226·5374·646c·6962··.@@@.....&Stdlib | ||
| 00000690:· | 00000690:·9226·4f70·7469·6f6e·4041·b005·0136·0501··.&Option@A...6.. | ||
| 000006a0:· | 000006a0:·3940·a0b0·a141·a008·0000·2800·b124·6461··9@...A....(..$da | ||
| 000006b0:· | 000006b0:·7461·0052·42a0·0402·b0c0·0501·534e·0102··ta.RB.......SN.. | ||
| 000006c0:· | 000006c0:·c501·02cc·c005·0154·4e01·02c5·0102·d040··.......TN......@ | ||
| 000006d0:· | 000006d0:·4008·0000·3800·4040·4041·4040·4040·40b0··@...8.@@@A@@@@@. | ||
| 000006e0:· | 000006e0:·c005·0157·4e01·02c5·0102·c704·0440·4040··...WN........@@@ | ||
| 000006f0:· | 000006f0:·40a1·0501·6441·4040·4140·0403·4040·0800··@...dA@@A@..@@.. | ||
| 00000700:·0 | 00000700:·0030·0005·0143·0501·4305·0143·0501·4305··.0...C..C..C..C. | ||
| 00000710:·014 | 00000710:·0143·0501·4305·0143·0501·4340·b105·0143··.C..C..C..C@...C | ||
| 00000720:· | 00000720:·0501·4f05·0149·4041·b004·0504·0840·a0b0··..O..I@A.....@.. | ||
| 00000730:· | 00000730:·a141·a008·0000·2800·b121·7400·5343·a004··.A....(..!t.SC.. | ||
| 00000740:· | 00000740:·02b0·c005·0165·4f01·02d1·0102·d8c0·0501··.....eO......... | ||
| 00000750:·0102·d | 00000750:·664f·0102·d101·02d9·4040·0800·0038·0040··fO......@@...8.@ | ||
| 00000760:· | 00000760:·4040·4140·4040·4040·b0c0·0501·694f·0102··@@A@@@@@....iO.. | ||
| 00000770:· | 00000770:·d101·02d3·0404·4040·4040·a105·0176·4240··......@@@@...vB@ | ||
| 00000780:· | 00000780:·4041·4004·0340·4008·0000·3000·0501·5505··@A@..@@...0...U. | ||
| 00000790:· | 00000790:·0155·0501·5505·0155·0501·5505·0155·0501··.U..U..U..U..U.. | ||
| 000007a0:·5 | 000007a0:·5505·0155·40b1·0413·041e·0418·4041·b004··U..U@.......@A.. | ||
| 000007b0:·0 | 000007b0:·0504·0840·a0b0·90f0·a025·656d·7074·7900··...@.....%empty. | ||
| 000007c0:· | 000007c0:·54a0·0402·b0c0·0501·7650·0102·da01·02e0··T.......vP...... | ||
| 000007d0:· | 000007d0:·c005·0177·5001·02da·0102·e540·d0b3·9004··...wP......@.... | ||
| Max diff block lines reached; 13161/389923 bytes (3.38%) of diff not shown. | |||
| Offset 1, 12816 lines modified | Offset 1, 12817 lines modified | ||
| 00000000:·4361·6d6c·3139·3939·5430·3330·8495·a6be··Caml1999T030.... | 00000000:·4361·6d6c·3139·3939·5430·3330·8495·a6be··Caml1999T030.... | ||
| 00000010:·0003·20 | 00000010:·0003·20e2·0000·9e5b·0002·7ac8·0002·75a1··..·....[..z...u. | ||
| 00000020:·0800·0034·0027·556e·6963·6f64·6591·b0a0··...4.'Unicode... | 00000020:·0800·0034·0027·556e·6963·6f64·6591·b0a0··...4.'Unicode... | ||
| 00000030:·b09d·b0a0·2a6f·6361·6d6c·2e74·6578·74b0··....*ocaml.text. | 00000030:·b09d·b0a0·2a6f·6361·6d6c·2e74·6578·74b0··....*ocaml.text. | ||
| 00000040:·c026·5f6e·6f6e·655f·4040·00ff·0402·4190··.&_none_@@....A. | 00000040:·c026·5f6e·6f6e·655f·4040·00ff·0402·4190··.&_none_@@....A. | ||
| 00000050:·a0a0·a0c0·91b2·3320·556e·6963·6f64·6520··......3·Unicode· | 00000050:·a0a0·a0c0·91b2·3320·556e·6963·6f64·6520··......3·Unicode· | ||
| 00000060:·7574·696c·6974·6965·7320·b0c0·2f63·6c69··utilities·../cli | 00000060:·7574·696c·6974·6965·7320·b0c0·2f63·6c69··utilities·../cli | ||
| 00000070:·622f·756e·6963·6f64·652e·6d6c·4b01·02a4··b/unicode.mlK... | 00000070:·622f·756e·6963·6f64·652e·6d6c·4b01·02a4··b/unicode.mlK... | ||
| 00000080:·0102·a4c0·0402·4b01·02a4·0102·bc40·4004··......K......@@. | 00000080:·0102·a4c0·0402·4b01·02a4·0102·bc40·4004··......K......@@. | ||
| 00000090:·0440·4040·0404·4004·0404·0408·0000·3000··.@@@..@.......0. | 00000090:·0440·4040·0404·4004·0404·0408·0000·3000··.@@@..@.......0. | Diff chunk too large, falling back to line-by-line diff (12327 lines added, 12327 lines removed) | |
| 000000a0:·a040·4004·0104·0104·0104·0104·0104·0104··.@@............. | 000000a0:·a040·4004·0104·0104·0104·0104·0104·0104··.@@............. | ||
| 000000b0:·0140·aba | 000000b0:·0140·abab·a7b1·b2b2·b2b2·b2b2·b2b2·b2b2··.@.............. | ||
| 000000c0:·b2b | 000000c0:·b2b2·b1b1·b1b1·b1b1·b1b1·b1b1·b1b1·b1b1··................ | ||
| 000000d0:·b140 | 000000d0:·b1b1·40a3·2a66·6c6f·6174·6172·7261·7951··..@.*floatarrayQ | ||
| 000000e0:·0 | 000000e0:·0800·0038·0040·4040·4140·4040·4040·0434··...8.@@@A@@@@@.4 | ||
| 000000f0:·4040·9204 | 000000f0:·4040·4092·0403·a335·6578·7465·6e73·696f··@@@....5extensio | ||
| 00000100:·5f63 | 00000100:·6e5f·636f·6e73·7472·7563·746f·7250·0800··n_constructorP.. | ||
| 00000110:· | 00000110:·0038·0040·4040·4140·4040·4040·0438·4040··.8.@@@A@@@@@.8@@ | ||
| 00000120:·9204 | 00000120:·4092·0403·a323·696e·7441·0800·0038·0040··@....#intA...8.@ | ||
| 00000130:·404 | 00000130:·4040·4140·4040·4040·043c·4041·4092·0403··@@A@@@@@.<@A@... | ||
| 00000140:·2463 | 00000140:·a324·6368·6172·4208·0000·3800·4040·4041··.$charB...8.@@@A | ||
| 00000150:·4040·4040·04 | 00000150:·4040·4040·4004·4040·4140·9204·03a3·2673··@@@@@.@@A@....&s | ||
| 00000160:·7269 | 00000160:·7472·696e·674f·0800·0038·0040·4040·4140··tringO...8.@@@A@ | ||
| 00000170:·4040·40 | 00000170:·4040·4040·0444·4040·4092·0403·a325·666c··@@@@.D@@@....%fl | ||
| 00000180:·6174 | 00000180:·6f61·7444·0800·0038·0040·4040·4140·4040··oatD...8.@@@A@@@ | ||
| 00000190:·40 | 00000190:·4040·0448·4040·4092·0403·a324·626f·6f6c··@@.H@@@....$bool | ||
| 000001a0:·0800 | 000001a0:·4508·0000·3800·4040·a1a0·e0a3·2566·616c··E...8.@@....%fal | ||
| 000001b0:·655e | 000001b0:·7365·5e90·4040·0452·4092·0403·a0e0·a324··se^.@@.R@......$ | ||
| 000001c0:·7275 | 000001c0:·7472·7565·5f90·4040·0458·4092·0403·4040··true_.@@.X@...@@ | ||
| 000001d0:·4 | 000001d0:·4140·4040·4040·0459·4041·4092·0410·a324··A@@@@@.Y@A@....$ | ||
| 000001e0:·6e69 | 000001e0:·756e·6974·4608·0000·3800·4040·a1a0·e0a3··unitF...8.@@.... | ||
| 000001f0:·2829 | 000001f0:·2228·2960·9040·4004·6340·9204·0340·4041··"()`.@@.c@...@@A | ||
| 00000200:·4040·4040·04 | 00000200:·4040·4040·4004·6440·4140·9204·0aa3·2365··@@@@@.d@A@....#e | ||
| 00000210:·6e47 | 00000210:·786e·4708·0000·3800·4040·4141·4040·4040··xnG...8.@@AA@@@@ | ||
| 00000220:·046 | 00000220:·4004·6840·4040·9204·03a3·2561·7272·6179··@.h@@@....%array | ||
| 00000230:·0800 | 00000230:·4808·0000·3800·a0c0·9040·0205·f5e1·0040··H...8....@.....@ | ||
| 00000240:·4 | 00000240:·4f40·4140·4140·a000·7f40·a040·4040·4004··O@A@A@...@.@@@@. | ||
| 00000250:·4040 | 00000250:·7140·4040·9204·08a3·246c·6973·7449·0800··q@@@....$listI.. | ||
| 00000260:·38 | 00000260:·0038·00a0·c004·0902·05f5·e100·4050·4041··.8..........@P@A | ||
| 00000270:·a0e0 | 00000270:·a1a0·e0a3·225b·5d61·9040·4004·7d40·9204··...."[]a.@@.}@.. | ||
| 00000280:·a0e0 | 00000280:·03a0·e0a3·223a·3a62·90a0·040e·a0c0·b390··...."::b........ | ||
| 00000290:·16a0 | 00000290:·0416·a004·1340·9040·0205·f5e1·0040·5140··.....@.@.....@Q@ | ||
| 000002a0:·04 | 000002a0:·4004·8a40·9204·0a40·4041·40a0·5940·a040··@..@...@@A@.Y@.@ | ||
| 000002b0:·4040·048 | 000002b0:·4040·4004·8d40·4040·9204·1ba3·266f·7074··@@@..@@@....&opt | ||
| 000002c0:·6f6e | 000002c0:·696f·6e4a·0800·0038·00a0·c004·2502·05f5··ionJ...8....%... | ||
| 000002d0:·0040 | 000002d0:·e100·4053·4041·a1a0·e0a3·244e·6f6e·6563··..@S@A....$Nonec | ||
| 000002e0:· | 000002e0:·9040·4004·9940·9204·03a0·e0a3·2453·6f6d··.@@..@......$Som | ||
| 000002f0:·6490 | 000002f0:·6564·90a0·040e·4040·04a0·4092·0404·4040··ed....@@..@...@@ | ||
| 00000300:·40a0 | 00000300:·4140·a059·40a0·4040·4040·04a3·4040·4092··A@.Y@.@@@@..@@@. | ||
| 00000310:·15a3 | 00000310:·0415·a326·6c61·7a79·5f74·4e08·0000·3800··...&lazy_tN...8. | ||
| 00000320:·c004 | 00000320:·a0c0·043b·0205·f5e1·0040·5540·4140·4140··...;.....@U@A@A@ | ||
| 00000330:·5940· | 00000330:·a059·40a0·4040·4040·04ab·4040·4092·0407··.Y@.@@@@..@@@... | ||
| 00000340:·296e | 00000340:·a329·6e61·7469·7665·696e·744b·0800·0038··.)nativeintK...8 | ||
| 00000350:· | 00000350:·0040·4040·4140·4040·4040·04af·4040·4092··.@@@A@@@@@..@@@. | ||
| 00000360:·03a3 | 00000360:·0403·a325·696e·7433·324c·0800·0038·0040··...%int32L...8.@ | ||
| 00000370:·404 | 00000370:·4040·4140·4040·4040·04b3·4040·4092·0403··@@A@@@@@..@@@... | ||
| 00000380:·2569 | 00000380:·a325·696e·7436·344d·0800·0038·0040·4040··.%int64M...8.@@@ | ||
| 00000390:·4 | 00000390:·4140·4040·4040·04b7·4040·4092·0403·a33a··A@@@@@..@@@....: | ||
| 000003a0:·6e64 | 000003a0:·556e·6465·6669·6e65·645f·7265·6375·7273··Undefined_recurs | ||
| 000003b0:·7665 | 000003b0:·6976·655f·6d6f·6475·6c65·5d08·0000·2000··ive_module]...·. | ||
| 000003c0:·0457 | 000003c0:·9004·5740·90a0·c092·a0c0·b390·0483·4090··..W@..........@. | ||
| 000003d0:·0205 | 000003d0:·4002·05f5·e100·404a·a0c0·b390·0490·4090··@.....@J......@. | ||
| 000003e0:·0205 | 000003e0:·4002·05f5·e100·4040·a004·0540·0205·f5e1··@.....@@...@.... | ||
| 000003f0:·4056 | 000003f0:·0040·5640·4041·04cb·a0b0·a03d·6f63·616d··.@V@@A.....=ocam | ||
| 00000400:·2e | 00000400:·6c2e·7761·726e·5f6f·6e5f·6c69·7465·7261··l.warn_on_litera | ||
| 00000410:·5f70 | 00000410:·6c5f·7061·7474·6572·6e04·cf04·6104·cf40··l_pattern...a..@ | ||
| 00000420:·0417 | 00000420:·9204·17a3·2e41·7373·6572·745f·6661·696c··.....Assert_fail | ||
| 00000430:·7265 | 00000430:·7572·655c·0800·0020·0004·1840·90a0·c092··ure\...·...@.... | ||
| 00000440:·0417 | 00000440:·a004·17a0·0413·a004·1440·0205·f5e1·0040··.........@.....@ | ||
| 00000450:·4040 | 00000450:·5840·4041·04da·a0b0·a004·0f04·dd04·6f04··X@@A..........o. | ||
| 00000460:·4092 | 00000460:·dd40·9204·0da3·3044·6976·6973·696f·6e5f··.@....0Division_ | ||
| 00000470:·795f | 00000470:·6279·5f7a·6572·6f59·0800·0020·0004·2640··by_zeroY...·..&@ | ||
| 00000480:· | 00000480:·9040·4041·04e2·a0b0·a004·1704·e504·7704··.@@A..........w. | ||
| 00000490:·4092 | 00000490:·e540·9204·07a3·2b45·6e64·5f6f·665f·6669··.@....+End_of_fi | ||
| 000004a0:·6 | 000004a0:·6c65·5808·0000·2000·042e·4090·4040·4104··leX...·...@.@@A. | ||
| 000004b0:·a0b0 | 000004b0:·eaa0·b0a0·041f·04ed·047f·04ed·4092·0407··............@... | ||
| 000004c0:·2953 | 000004c0:·a329·5379·735f·6572·726f·7257·0800·0020··.)Sys_errorW...· | ||
| 000004d0:·0436 | 000004d0:·0004·3640·90a0·0432·4040·4104·f3a0·b0a0··..6@...2@@A..... | ||
| 000004e0:·2804 | 000004e0:·0428·04f6·0488·04f6·4092·0408·a32e·5379··.(......@.....Sy | ||
| 000004f0:·5f62 | 000004f0:·735f·626c·6f63·6b65·645f·696f·5b08·0000··s_blocked_io[... | ||
| 00000500:·000 | 00000500:·2000·043f·4090·4040·4104·fba0·b0a0·0430···..?@.@@A......0 | ||
| 00000510:·f | 00000510:·04fe·0490·04fe·4092·0407·a329·4e6f·745f··......@....)Not_ | ||
| 00000520:·6f75 | 00000520:·666f·756e·6456·0800·0020·0004·4740·9040··foundV...·..G@.@ | ||
| 00000530:·4105 | 00000530:·4041·0501·03a0·b0a0·0438·0501·0604·9805··@A.......8...... | ||
| 00000540:·0 | 00000540:·0106·4092·0407·a327·4661·696c·7572·6555··..@....'FailureU | ||
| 00000550:·0000 | 00000550:·0800·0020·0004·4f40·90a0·044b·4040·4105··...·..O@...K@@A. | ||
| 00000560:·0 | 00000560:·010c·a0b0·a004·4105·010f·04a1·0501·0f40··......A........@ | ||
| 00000570:·0408 | 00000570:·9204·08a3·3049·6e76·616c·6964·5f61·7267··....0Invalid_arg | ||
| 00000580:·6d65 | 00000580:·756d·656e·7454·0800·0020·0004·5840·90a0··umentT...·..X@.. | ||
| 00000590:·5440 | 00000590:·0454·4040·4105·0115·a0b0·a004·4a05·0118··.T@@A.......J... | ||
| 000005a0:·aa05 | 000005a0:·04aa·0501·1840·9204·08a3·2e53·7461·636b··.....@.....Stack | ||
| 000005b0:·6f76 | 000005b0:·5f6f·7665·7266·6c6f·775a·0800·0020·0004··_overflowZ...·.. | ||
| 000005c0:·4090 | 000005c0:·6140·9040·4041·0501·1da0·b0a0·0452·0501··a@.@@A.......R.. | ||
| 000005d0:·04b2 | 000005d0:·2004·b205·0120·4092·0407·a32d·4f75·745f···....·@....-Out_ | ||
| 000005e0:·665f | 000005e0:·6f66·5f6d·656d·6f72·7953·0800·0020·0004··of_memoryS...·.. | ||
| 000005f0:·4090 | 000005f0:·6940·9040·4041·0501·25a0·b0a0·045a·0501··i@.@@A..%....Z.. | ||
| 00000600:·04ba | 00000600:·2804·ba05·0128·4092·0407·a32d·4d61·7463··(....(@....-Matc | ||
| 00000610:·5f | 00000610:·685f·6661·696c·7572·6552·0800·0020·0004··h_failureR...·.. | ||
| 00000620:·4090 | 00000620:·7140·90a0·c092·a004·70a0·046c·a004·6d40··q@......p..l..m@ | ||
| 00000630:·05f5 | 00000630:·0205·f5e1·0040·6340·4041·0501·33a0·b0a0··.....@c@@A..3... | ||
| 00000640:·6805 | 00000640:·0468·0501·3604·c805·0136·4092·040d·a325··.h..6....6@....% | ||
| 00000650:·7974 | 00000650:·6279·7465·7343·0800·0038·0040·4040·4140··bytesC...8.@@@A@ | ||
| 00000660:·4040·400 | 00000660:·4040·4040·0501·3a40·4040·9204·0390·9226··@@@@..:@@@.....& | ||
| 00000670:·7464 | 00000670:·5374·646c·6962·9223·496e·7492·264f·7074··Stdlib.#Int.&Opt | ||
| 00000680:·b0a3·41a0·0800·0028·00b1 | 00000680:·696f·6e40·40a0·b0a3·41a0·0800·0028·00b1··ion@@...A....(.. | ||
| 00000690:·7300·5141·a004·02b0·c005 | 00000690:·2673·7461·7475·7300·5141·a004·02b0·c005··&status.QA...... | ||
| 000006a0:·01 | 000006a0:·013f·4d01·02be·0102·c3c0·0501·404d·0102··.?M.........@M.. | ||
| 000006b0:· | 000006b0:·be01·02c9·4040·0800·0038·0040·40a1·a0e0··....@@...8.@@... | ||
| 000006c0:·6572·0052·9040·40b0·c005 | 000006c0:·a026·4c65·7474·6572·0052·9040·40b0·c005··.&Letter.R.@@... | ||
| 000006d0:·01 | 000006d0:·0149·4d01·02be·0102·ccc0·0501·4a4d·0102··.IM.........JM.. | ||
| 000006e0:· | 000006e0:·be01·02d2·4040·a105·0161·41a0·e0a0·2949··....@@...aA...)I | ||
| 000006f0:·7274·0053·9040·40b0·c005· | 000006f0:·6465·6e74·5061·7274·0053·9040·40b0·c005··dentPart.S.@@... | ||
| 00000700:·01 | 00000700:·0152·4d01·02be·0102·d3c0·0501·534d·0102··.RM.........SM.. | ||
| 00000710:·a105·016 | 00000710:·be01·02de·4040·a105·016a·42a0·e0a0·2653··....@@...jB...&S | ||
| 00000720:· | 00000720:·796d·626f·6c00·5490·4040·b0c0·0501·5b4d··ymbol.T.@@....[M | ||
| 00000730:· | 00000730:·0102·be01·02df·c005·015c·4d01·02be·0102··.........\M..... | ||
| 00000740:·7043·a0e0·a028·4964·656e | 00000740:·e740·40a1·0501·7343·a0e0·a028·4964·656e··.@@...sC...(Iden | ||
| 00000750:· | 00000750:·7453·6570·0055·9040·40b0·c005·0164·4d01··tSep.U.@@....dM. | ||
| 00000760:·0 | 00000760:·02be·0102·e8c0·0501·654d·0102·be01·02f2··........eM...... | ||
| 00000770:·44a0·e0a0·2755·6e6b·6e6f | 00000770:·4040·a105·017c·44a0·e0a0·2755·6e6b·6e6f··@@...|D...'Unkno | ||
| 00000780:· | 00000780:·776e·0056·9040·40b0·c005·016d·4d01·02be··wn.V.@@....mM... | ||
| 00000790:· | 00000790:·0102·f3c0·0501·6e4d·0102·be01·02fc·4040··......nM......@@ | ||
| 000007a0:· | 000007a0:·a105·0185·4540·4041·4040·4040·40b0·c005··....E@@A@@@@@... | ||
| 000007b0:·01 | 000007b0:·0171·4d01·02be·0102·be04·0440·4041·40a1··.qM........@@A@. | ||
| 000007c0:· | 000007c0:·0501·8840·4090·a0e0·0431·a004·31b0·042f··...@@....1..1../ | ||
| 000007d0:·04 | 000007d0:·042e·4090·4040·0431·40a0·e004·2da0·042d··..@.@@.1@...-..- | ||
| Max diff block lines reached; 65256/1767303 bytes (3.69%) of diff not shown. | |||
| Offset 1, 2519 lines modified | Offset 1, 2518 lines modified | ||
| 00000000:·4361·6d6c·3139·3939·5430·3330·8495·a6be··Caml1999T030.... | 00000000:·4361·6d6c·3139·3939·5430·3330·8495·a6be··Caml1999T030.... | ||
| 00000010:·0000·9d | 00000010:·0000·9d3e·0000·1b00·0000·7152·0000·6f2c··...>......qR..o, | ||
| 00000020:·0800·0034·0029·556e·696f·6e66·696e·6491··...4.)Unionfind. | 00000020:·0800·0034·0029·556e·696f·6e66·696e·6491··...4.)Unionfind. | ||
| 00000030:·b0a0·b09d·b0a0·2a6f·6361·6d6c·2e74·6578··......*ocaml.tex | 00000030:·b0a0·b09d·b0a0·2a6f·6361·6d6c·2e74·6578··......*ocaml.tex | ||
| 00000040:·74b0·c026·5f6e·6f6e·655f·4040·00ff·0402··t..&_none_@@.... | 00000040:·74b0·c026·5f6e·6f6e·655f·4040·00ff·0402··t..&_none_@@.... | ||
| 00000050:·4190·a0a0·a0c0·91b2·093b·2041·6e20·696d··A........;·An·im | 00000050:·4190·a0a0·a0c0·91b2·093b·2041·6e20·696d··A........;·An·im | ||
| 00000060:·7065·7261·7469·7665·2069·6d70·6c65·6d65··perative·impleme | 00000060:·7065·7261·7469·7665·2069·6d70·6c65·6d65··perative·impleme | ||
| 00000070:·6e74·6174·696f·6e20·6f66·2070·6172·7469··ntation·of·parti | 00000070:·6e74·6174·696f·6e20·6f66·2070·6172·7469··ntation·of·parti | ||
| 00000080:·7469·6f6e·7320·7669·6120·556e·696f·6e2d··tions·via·Union- | 00000080:·7469·6f6e·7320·7669·6120·556e·696f·6e2d··tions·via·Union- | ||
| 00000090:·4669·6e64·20b0·c031·636c·6962·2f75·6e69··Find·..1clib/uni | 00000090:·4669·6e64·20b0·c031·636c·6962·2f75·6e69··Find·..1clib/uni | ||
| 000000a0:·6f6e·6669·6e64·2e6d·6c4b·0102·a401·02a4··onfind.mlK...... | 000000a0:·6f6e·6669·6e64·2e6d·6c4b·0102·a401·02a4··onfind.mlK...... | ||
| 000000b0:·c004·024b·0102·a401·02e4·4040·0404·4040··...K......@@..@@ | 000000b0:·c004·024b·0102·a401·02e4·4040·0404·4040··...K......@@..@@ | ||
| 000000c0:·4004·0440·0404·0404·0800·0030·00a0·4040··@..@.......0..@@ | 000000c0:·4004·0440·0404·0404·0800·0030·00a0·4040··@..@.......0..@@ | Diff chunk too large, falling back to line-by-line diff (2349 lines added, 2349 lines removed) | |
| 000000d0:·0401·0401·0401·0401·0401·0401·0401·40ab··..............@. | 000000d0:·0401·0401·0401·0401·0401·0401·0401·40ab··..............@. | ||
| 000000e0:·a | 000000e0:·a7b1·b2b2·b2b2·b2b2·b2b2·b2b2·b2b2·b1b1··................ | ||
| 000000f0:·b1b1·b1b1·b1b1·b1b1·b1b1·b1b1·b1b1· | 000000f0:·b1b1·b1b1·b1b1·b1b1·b1b1·b1b1·b1b1·40a3··..............@. | ||
| 00000100:· | 00000100:·2a66·6c6f·6174·6172·7261·7951·0800·0038··*floatarrayQ...8 | ||
| 00000110:· | 00000110:·0040·4040·4140·4040·4040·0433·4040·4092··.@@@A@@@@@.3@@@. | ||
| 00000120:· | 00000120:·0403·a335·6578·7465·6e73·696f·6e5f·636f··...5extension_co | ||
| 00000130:·6 | 00000130:·6e73·7472·7563·746f·7250·0800·0038·0040··nstructorP...8.@ | ||
| 00000140:·4040·4 | 00000140:·4040·4140·4040·4040·0437·4040·4092·0403··@@A@@@@@.7@@@... | ||
| 00000150:· | 00000150:·a323·696e·7441·0800·0038·0040·4040·4140··.#intA...8.@@@A@ | ||
| 00000160:·4040·4040· | 00000160:·4040·4040·043b·4041·4092·0403·a324·6368··@@@@.;@A@....$ch | ||
| 00000170:·6 | 00000170:·6172·4208·0000·3800·4040·4041·4040·4040··arB...8.@@@A@@@@ | ||
| 00000180:·40 | 00000180:·4004·3f40·4140·9204·03a3·2673·7472·696e··@.?@A@....&strin | ||
| 00000190:·6 | 00000190:·674f·0800·0038·0040·4040·4140·4040·4040··gO...8.@@@A@@@@@ | ||
| 000001a0:· | 000001a0:·0443·4040·4092·0403·a325·666c·6f61·7444··.C@@@....%floatD | ||
| 000001b0:· | 000001b0:·0800·0038·0040·4040·4140·4040·4040·0447··...8.@@@A@@@@@.G | ||
| 000001c0:·4 | 000001c0:·4040·4092·0403·a324·626f·6f6c·4508·0000··@@@....$boolE... | ||
| 000001d0:· | 000001d0:·3800·4040·a1a0·e0a3·2566·616c·7365·5e90··8.@@....%false^. | ||
| 000001e0:· | 000001e0:·4040·0451·4092·0403·a0e0·a324·7472·7565··@@.Q@......$true | ||
| 000001f0:· | 000001f0:·5f90·4040·0457·4092·0403·4040·4140·4040··_.@@.W@...@@A@@@ | ||
| 00000200:·4040· | 00000200:·4040·0458·4041·4092·0410·a324·756e·6974··@@.X@A@....$unit | ||
| 00000210:· | 00000210:·4608·0000·3800·4040·a1a0·e0a3·2228·2960··F...8.@@...."()` | ||
| 00000220:· | 00000220:·9040·4004·6240·9204·0340·4041·4040·4040··.@@.b@...@@A@@@@ | ||
| 00000230:·40 | 00000230:·4004·6340·4140·9204·0aa3·2365·786e·4708··@.c@A@....#exnG. | ||
| 00000240:·0 | 00000240:·0000·3800·4040·4141·4040·4040·4004·6740··..8.@@AA@@@@@.g@ | ||
| 00000250:·4040· | 00000250:·4040·9204·03a3·2561·7272·6179·4808·0000··@@....%arrayH... | ||
| 00000260:· | 00000260:·3800·a0c0·9040·0205·f5e1·0040·4f40·4140··8....@.....@O@A@ | ||
| 00000270:·4 | 00000270:·4140·a000·7f40·a040·4040·4004·7040·4040··A@...@.@@@@.p@@@ | ||
| 00000280:· | 00000280:·9204·08a3·246c·6973·7449·0800·0038·00a0··....$listI...8.. | ||
| 00000290:· | 00000290:·c004·0902·05f5·e100·4050·4041·a1a0·e0a3··........@P@A.... | ||
| 000002a0:· | 000002a0:·225b·5d61·9040·4004·7c40·9204·03a0·e0a3··"[]a.@@.|@...... | ||
| 000002b0:· | 000002b0:·223a·3a62·90a0·040e·a0c0·b390·0416·a004··"::b............ | ||
| 000002c0:· | 000002c0:·1340·9040·0205·f5e1·0040·5140·4004·8940··.@.@.....@Q@@..@ | ||
| 000002d0:· | 000002d0:·9204·0a40·4041·40a0·5940·a040·4040·4004··...@@A@.Y@.@@@@. | ||
| 000002e0:· | 000002e0:·8c40·4040·9204·1ba3·266f·7074·696f·6e4a··.@@@....&optionJ | ||
| 000002f0:· | 000002f0:·0800·0038·00a0·c004·2502·05f5·e100·4053··...8....%.....@S | ||
| 00000300:· | 00000300:·4041·a1a0·e0a3·244e·6f6e·6563·9040·4004··@A....$Nonec.@@. | ||
| 00000310:· | 00000310:·9840·9204·03a0·e0a3·2453·6f6d·6564·90a0··.@......$Somed.. | ||
| 00000320:· | 00000320:·040e·4040·049f·4092·0404·4040·4140·a059··..@@..@...@@A@.Y | ||
| 00000330:· | 00000330:·40a0·4040·4040·04a2·4040·4092·0415·a326··@.@@@@..@@@....& | ||
| 00000340:· | 00000340:·6c61·7a79·5f74·4e08·0000·3800·a0c0·043b··lazy_tN...8....; | ||
| 00000350:· | 00000350:·0205·f5e1·0040·5540·4140·4140·a059·40a0··.....@U@A@A@.Y@. | ||
| 00000360:· | 00000360:·4040·4040·04aa·4040·4092·0407·a329·6e61··@@@@..@@@....)na | ||
| 00000370:· | 00000370:·7469·7665·696e·744b·0800·0038·0040·4040··tiveintK...8.@@@ | ||
| 00000380:·4 | 00000380:·4140·4040·4040·04ae·4040·4092·0403·a325··A@@@@@..@@@....% | ||
| 00000390:· | 00000390:·696e·7433·324c·0800·0038·0040·4040·4140··int32L...8.@@@A@ | ||
| 000003a0:·4040·4040· | 000003a0:·4040·4040·04b2·4040·4092·0403·a325·696e··@@@@..@@@....%in | ||
| 000003b0:· | 000003b0:·7436·344d·0800·0038·0040·4040·4140·4040··t64M...8.@@@A@@@ | ||
| 000003c0:·4040· | 000003c0:·4040·04b6·4040·4092·0403·a33a·556e·6465··@@..@@@....:Unde | ||
| 000003d0:·6 | 000003d0:·6669·6e65·645f·7265·6375·7273·6976·655f··fined_recursive_ | ||
| 000003e0:· | 000003e0:·6d6f·6475·6c65·5d08·0000·2000·9004·5740··module]...·...W@ | ||
| 000003f0:· | 000003f0:·90a0·c092·a0c0·b390·0483·4090·4002·05f5··..........@.@... | ||
| 00000400:· | 00000400:·e100·404a·a0c0·b390·0490·4090·4002·05f5··..@J......@.@... | ||
| 00000410:· | 00000410:·e100·4040·a004·0540·0205·f5e1·0040·5640··..@@...@.....@V@ | ||
| 00000420:·404 | 00000420:·4041·04ca·a0b0·a03d·6f63·616d·6c2e·7761··@A.....=ocaml.wa | ||
| 00000430:· | 00000430:·726e·5f6f·6e5f·6c69·7465·7261·6c5f·7061··rn_on_literal_pa | ||
| 00000440:· | 00000440:·7474·6572·6e04·ce04·6104·ce40·9204·17a3··ttern...a..@.... | ||
| 00000450:· | 00000450:·2e41·7373·6572·745f·6661·696c·7572·655c··.Assert_failure\ | ||
| 00000460:· | 00000460:·0800·0020·0004·1840·90a0·c092·a004·17a0··...·...@........ | ||
| 00000470:· | 00000470:·0413·a004·1440·0205·f5e1·0040·5840·4041··.....@.....@X@@A | ||
| 00000480:· | 00000480:·04d9·a0b0·a004·0f04·dc04·6f04·dc40·9204··..........o..@.. | ||
| 00000490:·0 | 00000490:·0da3·3044·6976·6973·696f·6e5f·6279·5f7a··..0Division_by_z | ||
| 000004a0:· | 000004a0:·6572·6f59·0800·0020·0004·2640·9040·4041··eroY...·..&@.@@A | ||
| 000004b0:· | 000004b0:·04e1·a0b0·a004·1704·e404·7704·e440·9204··..........w..@.. | ||
| 000004c0:·0 | 000004c0:·07a3·2b45·6e64·5f6f·665f·6669·6c65·5808··..+End_of_fileX. | ||
| 000004d0:·0 | 000004d0:·0000·2000·042e·4090·4040·4104·e9a0·b0a0··..·...@.@@A..... | ||
| 000004e0:· | 000004e0:·041f·04ec·047f·04ec·4092·0407·a329·5379··........@....)Sy | ||
| 000004f0:·7 | 000004f0:·735f·6572·726f·7257·0800·0020·0004·3640··s_errorW...·..6@ | ||
| 00000500:· | 00000500:·90a0·0432·4040·4104·f2a0·b0a0·0428·04f5··...2@@A......(.. | ||
| 00000510:· | 00000510:·0488·04f5·4092·0408·a32e·5379·735f·626c··....@.....Sys_bl | ||
| 00000520:·6 | 00000520:·6f63·6b65·645f·696f·5b08·0000·2000·043f··ocked_io[...·..? | ||
| 00000530:· | 00000530:·4090·4040·4104·faa0·b0a0·0430·04fd·0490··@.@@A......0.... | ||
| 00000540:· | 00000540:·04fd·4092·0407·a329·4e6f·745f·666f·756e··..@....)Not_foun | ||
| 00000550:·6 | 00000550:·6456·0800·0020·0004·4740·9040·4041·0501··dV...·..G@.@@A.. | ||
| 00000560:·0 | 00000560:·02a0·b0a0·0438·0501·0504·9805·0105·4092··.....8........@. | ||
| 00000570:· | 00000570:·0407·a327·4661·696c·7572·6555·0800·0020··...'FailureU...· | ||
| 00000580:· | 00000580:·0004·4f40·90a0·044b·4040·4105·010b·a0b0··..O@...K@@A..... | ||
| 00000590:· | 00000590:·a004·4105·010e·04a1·0501·0e40·9204·08a3··..A........@.... | ||
| 000005a0:· | 000005a0:·3049·6e76·616c·6964·5f61·7267·756d·656e··0Invalid_argumen | ||
| 000005b0:· | 000005b0:·7454·0800·0020·0004·5840·90a0·0454·4040··tT...·..X@...T@@ | ||
| 000005c0:·4 | 000005c0:·4105·0114·a0b0·a004·4a05·0117·04aa·0501··A.......J....... | ||
| 000005d0:· | 000005d0:·1740·9204·08a3·2e53·7461·636b·5f6f·7665··.@.....Stack_ove | ||
| 000005e0:· | 000005e0:·7266·6c6f·775a·0800·0020·0004·6140·9040··rflowZ...·..a@.@ | ||
| 000005f0:·404 | 000005f0:·4041·0501·1ca0·b0a0·0452·0501·1f04·b205··@A.......R...... | ||
| 00000600:·0 | 00000600:·011f·4092·0407·a32d·4f75·745f·6f66·5f6d··..@....-Out_of_m | ||
| 00000610:·6 | 00000610:·656d·6f72·7953·0800·0020·0004·6940·9040··emoryS...·..i@.@ | ||
| 00000620:·404 | 00000620:·4041·0501·24a0·b0a0·045a·0501·2704·ba05··@A..$....Z..'... | ||
| 00000630:·0 | 00000630:·0127·4092·0407·a32d·4d61·7463·685f·6661··.'@....-Match_fa | ||
| 00000640:·6 | 00000640:·696c·7572·6552·0800·0020·0004·7140·90a0··ilureR...·..q@.. | ||
| 00000650:· | 00000650:·c092·a004·70a0·046c·a004·6d40·0205·f5e1··....p..l..m@.... | ||
| 00000660:· | 00000660:·0040·6340·4041·0501·32a0·b0a0·0468·0501··.@c@@A..2....h.. | ||
| 00000670:· | 00000670:·3504·c805·0135·4092·040d·a325·6279·7465··5....5@....%byte | ||
| 00000680:· | 00000680:·7343·0800·0038·0040·4040·4140·4040·4040··sC...8.@@@A@@@@@ | ||
| 00000690:· | 00000690:·0501·3940·4040·9204·0390·9226·5374·646c··..9@@@.....&Stdl | ||
| 000006a0:·6 | 000006a0:·6962·9226·4f70·7469·6f6e·4040·a0b0·9db0··ib.&Option@@.... | ||
| 000006b0:· | 000006b0:·0501·4590·a0a0·a0c0·91b2·0a00·0001·2920··..E...........)· | ||
| 000006c0:· | 000006c0:·5061·7468·7320·6172·6520·636f·6d70·7265··Paths·are·compre | ||
| 000006d0:· | 000006d0:·7373·6564·2069·6d70·6572·6174·6976·656c··ssed·imperativel | ||
| 000006e0:· | 000006e0:·7920·6174·2065·6163·6820·6c6f·6f6b·7570··y·at·each·lookup | ||
| 000006f0:· | 000006f0:·206f·6620·610a·2020·2020·6361·6e6f·6e69···of·a.····canoni | ||
| 00000700:·6361·6 | 00000700:·6361·6c20·7265·7072·6573·656e·7461·7469··cal·representati | ||
| 00000710:· | 00000710:·7665·2e20·4561·6368·2075·6e69·6f6e·2061··ve.·Each·union·a | ||
| 00000720:·6 | 00000720:·6c73·6f20·6d6f·6469·6669·6573·2069·6e2d··lso·modifies·in- | ||
| 00000730:· | 00000730:·706c·6163·650a·2020·2020·7468·6520·7061··place.····the·pa | ||
| 00000740:·7 | 00000740:·7274·6974·696f·6e20·7374·7275·6374·7572··rtition·structur | ||
| 00000750:· | 00000750:·652e·0a0a·2020·2020·4e6f·7461·3a20·466f··e...····Nota:·Fo | ||
| 00000760:·7 | 00000760:·7220·7468·6520·6d6f·6d65·6e74·2077·6520··r·the·moment·we· | ||
| 00000770:· | 00000770:·7573·6520·5065·7276·6173·6976·6527·7320··use·Pervasive's· | ||
| 00000780:·6 | 00000780:·636f·6d70·6172·6973·6f6e·2066·6f72·0a20··comparison·for.· | ||
| 00000790:·20 | 00000790:·2020·2063·686f·6f73·696e·6720·7468·6520·····choosing·the· | ||
| 000007a0:· | 000007a0:·736d·616c·6c65·7374·206f·626a·6563·7420··smallest·object· | ||
| 000007b0:·6 | 000007b0:·6173·2072·6570·7265·7365·6e74·6174·6976··as·representativ | ||
| 000007c0:·6 | 000007c0:·652e·2054·6869·7320·636f·756c·640a·2020··e.·This·could.·· | ||
| 000007d0:· | 000007d0:·2020·6265·206d·6164·6520·6d6f·7265·2067····be·made·more·g | ||
| Max diff block lines reached; 20755/346043 bytes (6.00%) 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·····2836·2022-11-29·08:28:08.000000·control.tar.xz | 2 | -rw-r--r--···0········0········0·····2836·2022-11-29·08:28:08.000000·control.tar.xz |
| 3 | -rw-r--r--···0········0········0·225 | 3 | -rw-r--r--···0········0········0·22551636·2022-11-29·08:28:08.000000·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)····42928·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/boot/boot.cmxs | 9 | -rw-r--r--···0·root·········(0)·root·········(0)····42928·2022-11-29·08:28:08.000000·./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)··1463 | 11 | -rw-r--r--···0·root·········(0)·root·········(0)··1463396·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/clib.cma |
| 12 | -rw-r--r--···0·root·········(0)·root·········(0)··1448400·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/clib/clib.cmxs | 12 | -rw-r--r--···0·root·········(0)·root·········(0)··1448400·2022-11-29·08:28:08.000000·./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)····16992·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/config/config.cmxs | 15 | -rw-r--r--···0·root·········(0)·root·········(0)····16992·2022-11-29·08:28:08.000000·./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)··1097128·2022-11-29·08:28:08.000000·./usr/lib/ocaml/coq-core/engine/engine.cmxs | 18 | -rw-r--r--···0·root·········(0)·root·········(0)··1097128·2022-11-29·08:28:08.000000·./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·3139·3939·4130·3330·0012·4421··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····4 | 2 | -rw-r--r--···0········0········0····48032·2022-11-29·08:28:08.000000·control.tar.xz |
| 3 | -rw-r--r--···0········0········0·2147 | 3 | -rw-r--r--···0········0········0·21476944·2022-11-29·08:28:08.000000·data.tar.xz |
| Offset 1, 13 lines modified | Offset 1, 13 lines modified | ||
| 1 | Package:·libcoq-stdlib | 1 | Package:·libcoq-stdlib |
| 2 | Source:·coq | 2 | Source:·coq |
| 3 | Version:·8.16.1+dfsg-1 | 3 | Version:·8.16.1+dfsg-1 |
| 4 | Architecture:·amd64 | 4 | Architecture:·amd64 |
| 5 | Maintainer:·Debian·OCaml·Maintainers·<debian-ocaml-maint@lists.debian.org> | 5 | Maintainer:·Debian·OCaml·Maintainers·<debian-ocaml-maint@lists.debian.org> |
| 6 | Installed-Size:·13978 | 6 | Installed-Size:·139786 |
| 7 | Recommends:·coq·(>=·8.0) | 7 | Recommends:·coq·(>=·8.0) |
| 8 | Breaks:·coq-doc·(<=·8.0pl1.0-2),·coq-libs·(<<·8.2.pl1),·coq-theories | 8 | Breaks:·coq-doc·(<=·8.0pl1.0-2),·coq-libs·(<<·8.2.pl1),·coq-theories |
| 9 | Replaces:·coq-libs·(<<·8.2.pl1),·coq-theories | 9 | Replaces:·coq-libs·(<<·8.2.pl1),·coq-theories |
| 10 | Provides:·coq-theories·(=·8.16.1+dfsg-1),·libcoq-stdlib-ewsr6 | 10 | Provides:·coq-theories·(=·8.16.1+dfsg-1),·libcoq-stdlib-ewsr6 |
| 11 | Section:·math | 11 | Section:·math |
| 12 | Priority:·optional | 12 | Priority:·optional |
| 13 | Homepage:·http://coq.inria.fr/ | 13 | Homepage:·http://coq.inria.fr/ |
| Offset 1239, 35 lines modified | Offset 1239, 35 lines modified | ||
| 1239 | -rw-r--r--···0·root·········(0)·root·········(0)······269·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/NEWS.Debian.gz | 1239 | -rw-r--r--···0·root·········(0)·root·········(0)······269·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/NEWS.Debian.gz |
| 1240 | -rw-r--r--···0·root·········(0)·root·········(0)·····2173·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/README.md.gz | 1240 | -rw-r--r--···0·root·········(0)·root·········(0)·····2173·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/README.md.gz |
| 1241 | -rw-r--r--···0·root·········(0)·root·········(0)·····3892·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/changelog.Debian.gz | 1241 | -rw-r--r--···0·root·········(0)·root·········(0)·····3892·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/changelog.Debian.gz |
| 1242 | -rw-r--r--···0·root·········(0)·root·········(0)·····8290·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/copyright | 1242 | -rw-r--r--···0·root·········(0)·root·········(0)·····8290·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/copyright |
| 1243 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/ | 1243 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/ |
| 1244 | -rw-r--r--···0·root·········(0)·root·········(0)·····3005·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Arith.html | 1244 | -rw-r--r--···0·root·········(0)·root·········(0)·····3005·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Arith.html |
| 1245 | -rw-r--r--···0·root·········(0)·root·········(0)·····6691·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Arith_base.html | 1245 | -rw-r--r--···0·root·········(0)·root·········(0)·····6691·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Arith_base.html |
| 1246 | -rw-r--r--···0·root·········(0)·root·········(0)···1021 | 1246 | -rw-r--r--···0·root·········(0)·root·········(0)···102180·2022-11-29·08:28:08.000000·./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)····18068·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Le.html |
| 1259 | -rw-r--r--···0·root·········(0)·root·········(0)····24 | 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)····1594 | 1260 | -rw-r--r--···0·root·········(0)·root·········(0)····15942·2022-11-29·08:28:08.000000·./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)····17406·2022-11-29·08:28:08.000000·./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)····4154 | 1266 | -rw-r--r--···0·root·········(0)·root·········(0)····41549·2022-11-29·08:28:08.000000·./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 |
| 1272 | -rw-r--r--···0·root·········(0)·root·········(0)····27420·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Bool.Bvector.html | 1272 | -rw-r--r--···0·root·········(0)·root·········(0)····27420·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Bool.Bvector.html |
| 1273 | -rw-r--r--···0·root·········(0)·root·········(0)····10524·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Bool.DecBool.html | 1273 | -rw-r--r--···0·root·········(0)·root·········(0)····10524·2022-11-29·08:28:08.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Bool.DecBool.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="lab | 49 | <a·id="lab1273"></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="lab | 57 | <a·id="lab1274"></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="lab | 59 | <a·id="lab1275"></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="lab1290"></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="lab1255"></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="lab1236"></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="lab1237"></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="lab1284"></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="lab1285"></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="lab1244"></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="lab1245"></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="lab1246"></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="lab | 49 | <a·id="lab1276"></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="lab1254"></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="lab1277"></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="lab1278"></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="lab1279"></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="lab1223"></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="lab1224"></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="lab1225"></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="lab1226"></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="lab1227"></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="lab1228"></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="lab1229"></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="lab1259"></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="lab | 53 | <a·id="lab1215"></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="lab1216"></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="lab957"></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="lab958"></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="lab954"></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="lab863"></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="lab854"></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="lab864"></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="lab862"></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="lab867"></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="lab856"></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="lab858"></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="lab859"></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="lab871"></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="lab861"></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:·6c61·6238·3638·223e·3c2f·613e·3c68·3120··lab868"></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="lab857"></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="lab852"></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="lab853"></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="lab872"></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="lab767"></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="lab658"></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="lab690"></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="lab652"></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="lab676"></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="lab689"></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="lab755"></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="lab651"></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="lab705"></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="lab708"></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="lab709"></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="lab727"></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="lab650"></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="lab743"></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="lab747"></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="lab688"></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="lab713"></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="lab703"></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="lab704"></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="lab766"></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="lab357"></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="lab356"></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="lab362"></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="lab363"></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="lab364"></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="lab358"></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="lab359"></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="lab388"></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="lab382"></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="lab403"></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="lab4 | 49 | <a·id="lab405"></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, 16 lines modified | Offset 158, 16 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 | ||
| 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·6120·6964·3d22·6c61·6233··oc">.<a·id="lab3 | ||
| 00000a50:·3 | 00000a50:·3736·223e·3c2f·613e·3c68·3120·636c·6173··76"></a><h1·clas | ||
| 00000a60:·733d·2273·6563·7469·6f6e·223e·5072·6f70··s="section">Prop | 00000a60:·733d·2273·6563·7469·6f6e·223e·5072·6f70··s="section">Prop | ||
| 00000a70:·6f73·6974·696f·6e61·6c20·636f·6e6e·6563··ositional·connec | 00000a70:·6f73·6974·696f·6e61·6c20·636f·6e6e·6563··ositional·connec | ||
| 00000a80:·7469·7665·733c·2f68·313e·0a0a·3c64·6976··tives</h1>..<div | 00000a80:·7469·7665·733c·2f68·313e·0a0a·3c64·6976··tives</h1>..<div | ||
| 00000a90:·2063·6c61·7373·3d22·7061·7261·6772·6170···class="paragrap | 00000a90:·2063·6c61·7373·3d22·7061·7261·6772·6170···class="paragrap | ||
| 00000aa0:·6822·3e20·3c2f·6469·763e·0a0a·203c·7370··h">·</div>..·<sp | 00000aa0:·6822·3e20·3c2f·6469·763e·0a0a·203c·7370··h">·</div>..·<sp | ||
| 00000ab0:·616e·2063·6c61·7373·3d22·696e·6c69·6e65··an·class="inline | 00000ab0:·616e·2063·6c61·7373·3d22·696e·6c69·6e65··an·class="inline | ||
| 00000ac0:·636f·6465·223e·3c73·7061·6e20·636c·6173··code"><span·clas | 00000ac0:·636f·6465·223e·3c73·7061·6e20·636c·6173··code"><span·clas |
| Offset 50, 15 lines modified | Offset 50, 15 lines modified | ||
| 50 | <span·class="id"·title="keyword">Require</span>·<a·class="idref"·href="Coq.Init.Decimal.html#"><span·class="id"·title="library">Decimal</span></a>·<a·class="idref"·href="Coq.Init.Hexadecimal.html#"><span·class="id"·title="library">Hexadecimal</span></a>·<a·class="idref"·href="Coq.Init.Number.html#"><span·class="id"·title="library">Number</span></a>.<br/> | 50 | <span·class="id"·title="keyword">Require</span>·<a·class="idref"·href="Coq.Init.Decimal.html#"><span·class="id"·title="library">Decimal</span></a>·<a·class="idref"·href="Coq.Init.Hexadecimal.html#"><span·class="id"·title="library">Hexadecimal</span></a>·<a·class="idref"·href="Coq.Init.Number.html#"><span·class="id"·title="library">Number</span></a>.<br/> |
| 51 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">nat_scope</span>.<br/> | 51 | <span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">nat_scope</span>.<br/> |
| 52 | <br/> | 52 | <br/> |
| 53 | </div> | 53 | </div> |
| 54 | <div·class="doc"> | 54 | <div·class="doc"> |
| 55 | <a·id="lab | 55 | <a·id="lab389"></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="lab4 | 49 | <a·id="lab404"></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="lab374"></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="lab381"></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="lab380"></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="lab8 | 56 | <a·id="lab873"></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="lab905"></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="lab904"></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="lab258"></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="lab254"></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="lab | 113 | <a·id="lab336"></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="lab287"></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="lab333"></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="lab | 87 | <a·id="lab255"></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="lab | 106 | <a·id="lab329"></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="lab253"></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="lab | 176 | <a·id="lab291"></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="lab | 118 | <a·id="lab350"></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="lab | 49 | <a·id="lab290"></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="lab | 49 | <a·id="lab355"></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="lab | 49 | <a·id="lab1111"></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="lab1145"></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="lab1062"></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="lab1203"></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="lab | 49 | <a·id="lab1084"></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="lab | 49 | <a·id="lab1077"></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="lab1057"></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="lab1063"></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="lab1161"></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="lab1"></a><h1·class="section">Finite·sets·library·:·conversion·to·old·<span·class="inlinecode"><span·class="id"·title="var">Finite_sets</span></span></h1> | 49 | <a·id="lab1213"></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="lab2"></a><h1·class="section">Going·from·<span·class="inlinecode"><span·class="id"·title="var">MSets</span></span>·with·usual·Leibniz·equality</h1> | 58 | <a·id="lab1214"></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="lab12 | 49 | <a·id="lab1208"></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="lab4 | 56 | <a·id="lab408"></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="lab4 | 58 | <a·id="lab410"></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="lab4 | 68 | <a·id="lab411"></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="lab4 | 76 | <a·id="lab412"></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="lab4 | 86 | <a·id="lab413"></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="lab4 | 53 | <a·id="lab406"></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="lab5"></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="lab1"></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="lab51"></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="lab50"></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="lab63"></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="lab54"></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="lab53"></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="lab76"></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="lab77"></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="lab52"></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="lab18"></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="lab14"></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="lab13"></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="lab4 | 49 | <a·id="lab4"></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="lab6"></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="lab29"></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="lab16"></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="lab17"></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="lab4 | 49 | <a·id="lab49"></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="lab47"></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="lab2"></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="lab19"></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="lab3"></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="lab4 | 49 | <a·id="lab48"></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="lab20"></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="lab15"></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="lab41 | 472 | <a·id="lab41"></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="lab32"></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="lab4 | 53 | <a·id="lab42"></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="lab36"></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="lab31"></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="lab4 | 53 | <a·id="lab40"></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="lab4 | 70 | <a·id="lab46"></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="lab3 | 56 | <a·id="lab30"></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="lab26"></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="lab22"></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="lab25"></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="lab21"></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="lab9"></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="lab8"></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="lab7"></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="lab12"></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="lab975"></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="lab10 | 49 | <a·id="lab1030"></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="lab972"></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="lab252"></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="lab445"></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="lab439"></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="lab438"></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="lab444"></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="lab442"></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="lab419"></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="lab420"></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="lab421"></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="lab422"></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="lab423"></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="lab131"></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="lab203"></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:·6964·3d22·6c61·6232·3034·223e·3c2f·613e··id="lab204"></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="lab205"></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="lab78"></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, 31907 lines modified | Offset 102, 31906 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· | Diff chunk too large, falling back to line-by-line diff (31899 lines added, 31900 lines removed) | |
| 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:·6964·3d22·6c61·6238·3922·3e3c·2f61·3e3c··id="lab89"></a>< | ||
| 000006d0:· | 000006d0:·6831·2063·6c61·7373·3d22·7365·6374·696f··h1·class="sectio | ||
| 000006e0:·6 | 000006e0:·6e22·3e42·6173·6963·206c·656d·6d61·7320··n">Basic·lemmas· | ||
| 000006f0:· | 000006f0:·666f·7220·7468·6520·636c·6173·7369·6361··for·the·classica | ||
| 00000700:·6 | 00000700:·6c20·7265·616c·206e·756d·6265·7273·3c2f··l·real·numbers</ | ||
| 00000710:· | 00000710:·6831·3e0a·0a3c·2f64·6976·3e0a·3c64·6976··h1>..</div>.<div | ||
| 00000720:· | 00000720:·2063·6c61·7373·3d22·636f·6465·223e·0a0a···class="code">.. | ||
| 00000730:· | 00000730:·3c62·722f·3e0a·3c73·7061·6e20·636c·6173··<br/>.<span·clas | ||
| 00000740:·73 | 00000740:·733d·2269·6422·2074·6974·6c65·3d22·6b65··s="id"·title="ke | ||
| 00000750:· | 00000750:·7977·6f72·6422·3e52·6571·7569·7265·3c2f··yword">Require</ | ||
| 00000760:· | 00000760:·7370·616e·3e20·3c73·7061·6e20·636c·6173··span>·<span·clas | ||
| 00000770:·73 | 00000770:·733d·2269·6422·2074·6974·6c65·3d22·6b65··s="id"·title="ke | ||
| 00000780:· | 00000780:·7977·6f72·6422·3e49·6d70·6f72·743c·2f73··yword">Import</s | ||
| 00000790:·7 | 00000790:·7061·6e3e·203c·6120·636c·6173·733d·2269··pan>·<a·class="i | ||
| 000007a0:·6 | 000007a0:·6472·6566·2220·6872·6566·3d22·436f·712e··dref"·href="Coq. | ||
| 000007b0:· | 000007b0:·5265·616c·732e·4361·7563·6879·2e43·6f6e··Reals.Cauchy.Con | ||
| 000007c0:· | 000007c0:·7374·7275·6374·6976·6543·6175·6368·7952··structiveCauchyR | ||
| 000007d0:· | 000007d0:·6561·6c73·2e68·746d·6c23·223e·3c73·7061··eals.html#"><spa | ||
| 000007e0:·6 | 000007e0:·6e20·636c·6173·733d·2269·6422·2074·6974··n·class="id"·tit | ||
| 000007f0:· | 000007f0:·6c65·3d22·6c69·6272·6172·7922·3e43·6f6e··le="library">Con | ||
| 00000800:· | 00000800:·7374·7275·6374·6976·6543·6175·6368·7952··structiveCauchyR | ||
| 00000810:· | 00000810:·6561·6c73·3c2f·7370·616e·3e3c·2f61·3e2e··eals</span></a>. | ||
| 00000820:· | 00000820:·3c62·722f·3e0a·3c73·7061·6e20·636c·6173··<br/>.<span·clas | ||
| 00000830:·73 | 00000830:·733d·2269·6422·2074·6974·6c65·3d22·6b65··s="id"·title="ke | ||
| 00000840:· | 00000840:·7977·6f72·6422·3e52·6571·7569·7265·3c2f··yword">Require</ | ||
| 00000850:· | 00000850:·7370·616e·3e20·3c73·7061·6e20·636c·6173··span>·<span·clas | ||
| 00000860:·73 | 00000860:·733d·2269·6422·2074·6974·6c65·3d22·6b65··s="id"·title="ke | ||
| 00000870:· | 00000870:·7977·6f72·6422·3e49·6d70·6f72·743c·2f73··yword">Import</s | ||
| 00000880:·7 | 00000880:·7061·6e3e·203c·6120·636c·6173·733d·2269··pan>·<a·class="i | ||
| 00000890:·6 | 00000890:·6472·6566·2220·6872·6566·3d22·436f·712e··dref"·href="Coq. | ||
| 000008a0:· | 000008a0:·5265·616c·732e·4361·7563·6879·2e43·6f6e··Reals.Cauchy.Con | ||
| 000008b0:· | 000008b0:·7374·7275·6374·6976·6543·6175·6368·7952··structiveCauchyR | ||
| 000008c0:· | 000008c0:·6561·6c73·4d75·6c74·2e68·746d·6c23·223e··ealsMult.html#"> | ||
| 000008d0:·3 | 000008d0:·3c73·7061·6e20·636c·6173·733d·2269·6422··<span·class="id" | ||
| 000008e0:·2 | 000008e0:·2074·6974·6c65·3d22·6c69·6272·6172·7922···title="library" | ||
| 000008f0:· | 000008f0:·3e43·6f6e·7374·7275·6374·6976·6543·6175··>ConstructiveCau | ||
| 00000900:· | 00000900:·6368·7952·6561·6c73·4d75·6c74·3c2f·7370··chyRealsMult</sp | ||
| 00000910:· | 00000910:·616e·3e3c·2f61·3e2e·3c62·722f·3e0a·3c73··an></a>.<br/>.<s | ||
| 00000920:·7 | 00000920:·7061·6e20·636c·6173·733d·2269·6422·2074··pan·class="id"·t | ||
| 00000930:· | 00000930:·6974·6c65·3d22·6b65·7977·6f72·6422·3e52··itle="keyword">R | ||
| 00000940:· | 00000940:·6571·7569·7265·3c2f·7370·616e·3e20·3c73··equire</span>·<s | ||
| 00000950:·7 | 00000950:·7061·6e20·636c·6173·733d·2269·6422·2074··pan·class="id"·t | ||
| 00000960:· | 00000960:·6974·6c65·3d22·6b65·7977·6f72·6422·3e45··itle="keyword">E | ||
| 00000970:· | 00000970:·7870·6f72·743c·2f73·7061·6e3e·203c·6120··xport</span>·<a· | ||
| 00000980:· | 00000980:·636c·6173·733d·2269·6472·6566·2220·6872··class="idref"·hr | ||
| 00000990:· | 00000990:·6566·3d22·436f·712e·5265·616c·732e·5261··ef="Coq.Reals.Ra | ||
| 000009a0:· | 000009a0:·7869·6f6d·732e·6874·6d6c·2322·3e3c·7370··xioms.html#"><sp | ||
| 000009b0:· | 000009b0:·616e·2063·6c61·7373·3d22·6964·2220·7469··an·class="id"·ti | ||
| 000009c0:· | 000009c0:·746c·653d·226c·6962·7261·7279·223e·5261··tle="library">Ra | ||
| 000009d0:· | 000009d0:·7869·6f6d·733c·2f73·7061·6e3e·3c2f·613e··xioms</span></a> | ||
| 000009e0:· | 000009e0:·2e3c·6272·2f3e·0a3c·7370·616e·2063·6c61··.<br/>.<span·cla | ||
| 000009f0:· | 000009f0:·7373·3d22·6964·2220·7469·746c·653d·226b··ss="id"·title="k | ||
| 00000a00:·6 | 00000a00:·6579·776f·7264·223e·5265·7175·6972·653c··eyword">Require< | ||
| 00000a10:· | 00000a10:·2f73·7061·6e3e·203c·7370·616e·2063·6c61··/span>·<span·cla | ||
| 00000a20:· | 00000a20:·7373·3d22·6964·2220·7469·746c·653d·226b··ss="id"·title="k | ||
| 00000a30:·6 | 00000a30:·6579·776f·7264·223e·496d·706f·7274·3c2f··eyword">Import</ | ||
| 00000a40:· | 00000a40:·7370·616e·3e20·3c61·2063·6c61·7373·3d22··span>·<a·class=" | ||
| 00000a50:· | 00000a50:·6964·7265·6622·2068·7265·663d·2243·6f71··idref"·href="Coq | ||
| 00000a60:· | 00000a60:·2e52·6561·6c73·2e52·706f·775f·6465·662e··.Reals.Rpow_def. | ||
| 00000a70:· | 00000a70:·6874·6d6c·2322·3e3c·7370·616e·2063·6c61··html#"><span·cla | ||
| 00000a80:· | 00000a80:·7373·3d22·6964·2220·7469·746c·653d·226c··ss="id"·title="l | ||
| 00000a90:·6 | 00000a90:·6962·7261·7279·223e·5270·6f77·5f64·6566··ibrary">Rpow_def | ||
| 00000aa0:· | 00000aa0:·3c2f·7370·616e·3e3c·2f61·3e2e·3c62·722f··</span></a>.<br/ | ||
| 00000ab0:· | 00000ab0:·3e0a·3c73·7061·6e20·636c·6173·733d·2269··>.<span·class="i | ||
| 00000ac0:·6 | 00000ac0:·6422·2074·6974·6c65·3d22·6b65·7977·6f72··d"·title="keywor | ||
| 00000ad0:· | 00000ad0:·6422·3e52·6571·7569·7265·3c2f·7370·616e··d">Require</span | ||
| 00000ae0:· | 00000ae0:·3e20·3c73·7061·6e20·636c·6173·733d·2269··>·<span·class="i | ||
| 00000af0:·6 | 00000af0:·6422·2074·6974·6c65·3d22·6b65·7977·6f72··d"·title="keywor | ||
| 00000b00:· | 00000b00:·6422·3e49·6d70·6f72·743c·2f73·7061·6e3e··d">Import</span> | ||
| 00000b10:· | 00000b10:·203c·6120·636c·6173·733d·2269·6472·6566···<a·class="idref | ||
| 00000b20:· | 00000b20:·2220·6872·6566·3d22·436f·712e·5a41·7269··"·href="Coq.ZAri | ||
| 00000b30:· | 00000b30:·7468·2e5a·706f·7765·722e·6874·6d6c·2322··th.Zpower.html#" | ||
| 00000b40:· | 00000b40:·3e3c·7370·616e·2063·6c61·7373·3d22·6964··><span·class="id | ||
| 00000b50:· | 00000b50:·2220·7469·746c·653d·226c·6962·7261·7279··"·title="library | ||
| 00000b60:· | 00000b60:·223e·5a70·6f77·6572·3c2f·7370·616e·3e3c··">Zpower</span>< | ||
| 00000b70:· | 00000b70:·2f61·3e2e·3c62·722f·3e0a·3c73·7061·6e20··/a>.<br/>.<span· | ||
| 00000b80:· | 00000b80:·636c·6173·733d·2269·6422·2074·6974·6c65··class="id"·title | ||
| 00000b90:· | 00000b90:·3d22·6b65·7977·6f72·6422·3e52·6571·7569··="keyword">Requi | ||
| 00000ba0:· | 00000ba0:·7265·3c2f·7370·616e·3e20·3c73·7061·6e20··re</span>·<span· | ||
| 00000bb0:· | 00000bb0:·636c·6173·733d·2269·6422·2074·6974·6c65··class="id"·title | ||
| 00000bc0:· | 00000bc0:·3d22·6b65·7977·6f72·6422·3e45·7870·6f72··="keyword">Expor | ||
| 00000bd0:·7 | 00000bd0:·743c·2f73·7061·6e3e·203c·6120·636c·6173··t</span>·<a·clas | ||
| 00000be0:·73 | 00000be0:·733d·2269·6472·6566·2220·6872·6566·3d22··s="idref"·href=" | ||
| 00000bf0:· | 00000bf0:·436f·712e·7365·746f·6964·5f72·696e·672e··Coq.setoid_ring. | ||
| 00000c00:· | 00000c00:·5a41·7269·7468·5269·6e67·2e68·746d·6c23··ZArithRing.html# | ||
| 00000c10:·2 | 00000c10:·223e·3c73·7061·6e20·636c·6173·733d·2269··"><span·class="i | ||
| 00000c20:·6 | 00000c20:·6422·2074·6974·6c65·3d22·6c69·6272·6172··d"·title="librar | ||
| 00000c30:·7 | 00000c30:·7922·3e5a·4172·6974·6852·696e·673c·2f73··y">ZArithRing</s | ||
| 00000c40:·7 | 00000c40:·7061·6e3e·3c2f·613e·2e3c·6272·2f3e·0a3c··pan></a>.<br/>.< | ||
| 00000c50:· | 00000c50:·7370·616e·2063·6c61·7373·3d22·6964·2220··span·class="id"· | ||
| 00000c60:· | 00000c60:·7469·746c·653d·226b·6579·776f·7264·223e··title="keyword"> | ||
| 00000c70:· | 00000c70:·5265·7175·6972·653c·2f73·7061·6e3e·203c··Require</span>·< | ||
| 00000c80:· | 00000c80:·7370·616e·2063·6c61·7373·3d22·6964·2220··span·class="id"· | ||
| 00000c90:· | 00000c90:·7469·746c·653d·226b·6579·776f·7264·223e··title="keyword"> | ||
| 00000ca0:· | 00000ca0:·496d·706f·7274·3c2f·7370·616e·3e20·3c61··Import</span>·<a | ||
| 00000cb0:· | 00000cb0:·2063·6c61·7373·3d22·6964·7265·6622·2068···class="idref"·h | ||
| 00000cc0:· | 00000cc0:·7265·663d·2243·6f71·2e6d·6963·726f·6d65··ref="Coq.microme | ||
| 00000cd0:·6 | 00000cd0:·6761·2e5a·7461·632e·6874·6d6c·2322·3e3c··ga.Ztac.html#">< | ||
| 00000ce0:· | 00000ce0:·7370·616e·2063·6c61·7373·3d22·6964·2220··span·class="id"· | ||
| 00000cf0:· | 00000cf0:·7469·746c·653d·226c·6962·7261·7279·223e··title="library"> | ||
| 00000d00:· | 00000d00:·5a74·6163·3c2f·7370·616e·3e3c·2f61·3e2e··Ztac</span></a>. | ||
| 00000d10:· | 00000d10:·3c62·722f·3e0a·3c73·7061·6e20·636c·6173··<br/>.<span·clas | ||
| 00000d20:·73 | 00000d20:·733d·2269·6422·2074·6974·6c65·3d22·6b65··s="id"·title="ke | ||
| 00000d30:· | 00000d30:·7977·6f72·6422·3e52·6571·7569·7265·3c2f··yword">Require</ | ||
| 00000d40:· | 00000d40:·7370·616e·3e20·3c73·7061·6e20·636c·6173··span>·<span·clas | ||
| 00000d50:·73 | 00000d50:·733d·2269·6422·2074·6974·6c65·3d22·6b65··s="id"·title="ke | ||
| 00000d60:· | 00000d60:·7977·6f72·6422·3e45·7870·6f72·743c·2f73··yword">Export</s | ||
| 00000d70:·7 | 00000d70:·7061·6e3e·203c·6120·636c·6173·733d·2269··pan>·<a·class="i | ||
| 00000d80:·6 | 00000d80:·6472·6566·2220·6872·6566·3d22·436f·712e··dref"·href="Coq. | ||
| 00000d90:· | 00000d90:·7365·746f·6964·5f72·696e·672e·5265·616c··setoid_ring.Real | ||
| 00000da0:· | 00000da0:·4669·656c·642e·6874·6d6c·2322·3e3c·7370··Field.html#"><sp | ||
| 00000db0:· | 00000db0:·616e·2063·6c61·7373·3d22·6964·2220·7469··an·class="id"·ti | ||
| 00000dc0:· | 00000dc0:·746c·653d·226c·6962·7261·7279·223e·5265··tle="library">Re | ||
| 00000dd0:·6 | 00000dd0:·616c·4669·656c·643c·2f73·7061·6e3e·3c2f··alField</span></ | ||
| 00000de0:· | 00000de0:·613e·2e3c·6272·2f3e·0a0a·3c62·722f·3e0a··a>.<br/>..<br/>. | ||
| 00000df0:· | 00000df0:·3c73·7061·6e20·636c·6173·733d·2269·6422··<span·class="id" | ||
| 00000e00:·2 | 00000e00:·2074·6974·6c65·3d22·6b65·7977·6f72·6422···title="keyword" | ||
| 00000e10:· | 00000e10:·3e4c·6f63·616c·204f·7065·6e3c·2f73·7061··>Local·Open</spa | ||
| 00000e20:·6 | 00000e20:·6e3e·203c·7370·616e·2063·6c61·7373·3d22··n>·<span·class=" | ||
| Max diff block lines reached; -1/4402635 bytes (-0.00%) of diff not shown. | |||
| 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="lab248"></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="lab140"></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="lab171"></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="lab142"></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="lab134"></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·6162·3137·3822··>.<a·id="lab178" | ||
| 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:·6964·3d22·6c61·6231·3739·223e·3c2f·613e··id="lab179"></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="lab231"></a><h1·class="section">Field·operations</h1> |
| 71 | <div·class="paragraph">·</div> | 71 | <div·class="paragraph">·</div> |
| 72 | <a·id="lab | 72 | <a·id="lab232"></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="lab210"></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="lab173"></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="lab164"></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="lab227"></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="lab240"></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="lab126"></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="lab216"></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="lab219"></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="lab57 | 77 | <a·id="lab157"></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="lab162"></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="lab213"></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="lab245"></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="lab175"></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="lab221"></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="lab | 49 | <a·id="lab827"></a><h1·class="section">Some·properties·of·the·operators·on·relations</h1> |
| 50 | <a·id="lab | 50 | <a·id="lab828"></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="lab831"></a><h1·class="section">Some·operators·on·relations</h1> |
| 50 | <a·id="lab | 50 | <a·id="lab832"></a><h1·class="section">Initial·authors:·Bruno·Barras,·Cristina·Cornes</h1> |
| 51 | <a·id="lab | 51 | <a·id="lab833"></a><h1·class="section">···································································</h1> |
| 52 | <a·id="lab | 52 | <a·id="lab834"></a><h1·class="section">Some·of·the·initial·definitions·were·taken·from·:</h1> |
| 53 | <a·id="lab | 53 | <a·id="lab835"></a><h1·class="section">Constructing·Recursion·Operators·in·Type·Theory</h1> |
| 54 | <a·id="lab | 54 | <a·id="lab836"></a><h1·class="section">L.·Paulson··JSC·(1986)·2,·325-355</h1> |
| 55 | <a·id="lab | 55 | <a·id="lab837"></a><h1·class="section">···································································</h1> |
| 56 | <a·id="lab | 56 | <a·id="lab838"></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="lab839"></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="lab812"></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="lab813"></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="lab814"></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="lab824"></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="lab823"></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="lab943"></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="lab946"></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="lab504"></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="lab505"></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="lab506"></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="lab | 58 | <a·id="lab515"></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="lab485"></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="lab486"></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="lab507"></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="lab | 53 | <a·id="lab473"></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="lab | 55 | <a·id="lab474"></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="lab464"></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="lab482"></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="lab463"></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="lab466"></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="lab498"></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="lab499"></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="lab500"></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="lab | 57 | <a·id="lab516"></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="lab509"></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="lab483"></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="lab494"></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 5776, 4051 lines modified | Offset 5776, 4051 lines modified | ||
| 000168f0:·6c61·7373·3d22·6964·7265·6622·2068·7265··lass="idref"·hre | 000168f0:·6c61·7373·3d22·6964·7265·6622·2068·7265··lass="idref"·hre | ||
| 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 | Diff chunk too large, falling back to line-by-line diff (4044 lines added, 4044 lines removed) | |
| 00016950:·3e0a·0a3c·6469·7620·636c·6173·733d·2264··>..<div·class="d | 00016950:·3e0a·0a3c·6469·7620·636c·6173·733d·2264··>..<div·class="d | ||
| 00016960:·6f63·223e·0a3c·6120·6964·3d22·6c61·623 | 00016960:·6f63·223e·0a3c·6120·6964·3d22·6c61·6239··oc">.<a·id="lab9 | ||
| 00016970:·303 | 00016970:·3036·223e·3c2f·613e·3c68·3120·636c·6173··06"></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= | ||
| Max diff block lines reached; -1/558569 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="lab | 83 | <a·id="lab908"></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="lab592"></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="lab527"></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="lab520"></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="lab562"></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="lab517"></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="lab576"></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="lab584"></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="lab585"></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="lab640"></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="lab578"></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="lab580"></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="lab564"></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="lab524"></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="lab525"></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="lab632"></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="lab635"></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="lab565"></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="lab566"></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="lab575"></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="lab555"></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="lab581"></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="lab557"></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="lab579"></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="lab850"></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="lab934"></a><h1·class="section">Disclaimer:·trying·to·obtain·efficient·certified·programs</h1> |
| 64 | <a·id="lab | 64 | <a·id="lab935"></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="lab936"></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="lab928"></a><h1·class="section">Disclaimer:·trying·to·obtain·efficient·certified·programs</h1> |
| 64 | <a·id="lab | 64 | <a·id="lab929"></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="lab930"></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="lab918"></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="lab919"></a><h1·class="section">into·equivalent·versions·in·Haskell's·Prelude·that·are·defined</h1> |
| 49 | <a·id="lab | 49 | <a·id="lab920"></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="lab921"></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="lab922"></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="lab937"></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="lab931"></a><h1·class="section">Disclaimer:·trying·to·obtain·efficient·certified·programs</h1> |
| 64 | <a·id="lab | 64 | <a·id="lab932"></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="lab933"></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="lab923"></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="lab924"></a><h1·class="section">into·equivalent·versions·in·Haskell's·Prelude·that·are·defined</h1> |
| 49 | <a·id="lab | 49 | <a·id="lab925"></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="lab926"></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="lab927"></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="lab251"></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 |