Leonardo de Moura
cc8d9bc7ff
refactor(hott): replace 'assert'-expr with 'have'-expr
2016-02-29 12:11:17 -08:00
Leonardo de Moura
510168a387
refactor(library,hott): remove unnecessary annotations
2016-02-25 12:26:20 -08:00
Leonardo de Moura
146edde5b3
feat(library/class): mark instances as quasireducible by default
...
quasireducible are also known as lazyreducible.
There is a lot of work to be done.
We still need to revise blast, and add a normalizer for type class
instances. This commit worksaround that by eagerly unfolding
quasireducible.
2016-02-25 12:11:29 -08:00
Floris van Doorn
facd94a1b4
feat(hott): various changes
...
more about pointed truncated types, including pointed sets.
also increase the priority of some basic instances that nat/num/pos_num/trunc_index have 0, 1 and + (in both libraries)
also move the notation + for sum into the namespace sum, to (sometimes) avoid overloading with add
2016-02-22 11:15:38 -08:00
Floris van Doorn
087c44d614
style(hott): rename instances of pType using pfoo instead of Foo
...
For example, the pointed suspension operation was called Susp before this commit, but now is called psusp
2016-02-22 11:15:38 -08:00
Floris van Doorn
c64e5a114c
feat(circle): add missing facts that the circle is 1-truncated and 0-connected
2016-02-22 11:15:38 -08:00
Floris van Doorn
bac6d99cc7
style(hott): rename Pointed to pType
...
also rename sigma_equiv_sigma_id to sigma_equiv_sigma_right and similarly for pi
2016-02-22 11:15:38 -08:00
Floris van Doorn
43cf2ad23d
style(hott): replace all other occurrences of hprop/hset
...
They are replaced by either Prop/Set or prop/set
2016-02-22 11:15:38 -08:00
Floris van Doorn
4e2cc66061
style(*): rename is_hprop/is_hset to is_prop/is_set
2016-02-22 11:15:38 -08:00
Floris van Doorn
816237315c
feat(hott): various additions, especially for pointed maps/homotopies/equivalences
2016-02-22 11:15:38 -08:00
Floris van Doorn
ecc141779a
feat(init.path): update init.path to use tactics, also some additions
...
Now the file hardly uses eq.rec explicitly anymore.
Also add the fact that horizontal and vertical inverses of paths are equal
Make one more argument explicit in eq.cancel_left and eq.cancel_right (to make it nicer to write 'apply cancel_right p')
2016-02-22 11:15:38 -08:00
Jakob von Raumer
62e1431f04
chore(hott): delay lemmas about smash product until I have more ideas on how to tackle the coherence there.
2016-02-09 09:58:17 -08:00
Jakob von Raumer
23dec19aa7
feat(hott): start lemma about smashing with bool
2016-02-09 09:57:52 -08:00
Jakob von Raumer
8bc4206c62
feat(hott): add custom recursors for cofiber type
2016-02-09 09:57:47 -08:00
Jakob von Raumer
31e2653e58
feat(hott): add lemma: cofiber of terminal morphism is suspension
2016-02-09 09:57:39 -08:00
Jakob von Raumer
7e02ea6cab
feat(hott): add smash product of pointed types
2016-02-09 09:57:33 -08:00
Jakob von Raumer
ce8ca64771
feat(hott): adjust small things in wedge theory
2016-02-09 09:57:27 -08:00
Jakob von Raumer
56cd88267c
feat(hott): add cofiber of a function, prove lemma that cofibers of equivalences are contractible
2016-02-09 09:57:21 -08:00
Ulrik Buchholtz
dcb35008e1
feat(hott/homotopy): general connectivity elimination and the wedge connectivity lemma
2016-02-04 11:07:22 -08:00
Jakob von Raumer
d8d3b0c0b2
feat(hott): add wedge sum of pointed types, neutrality of wedging with the unit type
2016-01-24 16:30:21 -08:00
Sebastian Ullrich
2185ee7e95
feat(library/tactic): make let tactic transparent, introduce new opaque note tactic
...
The new let tactic is semantically equivalent to let terms, while `note`
preserves its old opaque behavior.
2015-12-14 10:14:02 -08:00
Floris van Doorn
2325d23f68
feat(hott): port nat and int from the standard library
2015-12-09 12:36:11 -08:00
Jakob von Raumer
68901c7788
feat(hott/homotopy): complete join associativity proof, helper lemmas for squares
2015-12-02 23:13:21 -08:00
Jakob von Raumer
bd064ef9c8
feat(hott/homotopy): prove missing helper lemmas up to cube massaging
2015-12-02 23:13:17 -08:00
Jakob von Raumer
811f3067ff
feat(hott): join associativity proof done up to small auxiliary lemmas, add transposition, inversion of cubes
2015-12-02 23:13:12 -08:00
Jakob von Raumer
e481e541a2
feat(hott/homotopy): more progress on join associativity
2015-12-02 23:13:03 -08:00
Jakob von Raumer
6c6dde7e48
feat(hott/homotopy): progress on join associativity, many coherence lemmas about square operations needed
2015-12-02 23:12:59 -08:00
Jakob von Raumer
54b1d1a9fe
feat(hott/homotopy): more steps towards join associativity, cube composition
2015-12-02 23:12:46 -08:00
Jakob von Raumer
e1e8680474
feat(hott/homotopy): continue defining squares for join associativity
2015-12-02 23:12:41 -08:00
Jakob von Raumer
12a498d411
feat(hott/homotopy): add join switch and derive associativity from switch
2015-12-02 23:12:29 -08:00
Jakob von Raumer
149e5fff9f
feat(hott/homotopy): add commutativity proof for join
2015-12-02 23:12:24 -08:00
Jakob von Raumer
eea219e33f
feat(hott/homotopy): start associativity proof for join
2015-12-02 23:12:19 -08:00
Floris van Doorn
c44ad80e4e
feat(homotopy/torus): give recursion and induction principle for the torus
...
also change the surface of the torus to a square instead of an equality between paths
2015-11-22 18:29:37 -08:00
Floris van Doorn
45d808ce7f
feat(homotopy/circle): give all higher homotopy groups of the circle
2015-11-22 14:21:25 -08:00
Floris van Doorn
810a399699
style(homotopy/circle): clean-up encode-decode proof
2015-11-22 14:21:25 -08:00
Floris van Doorn
206bcd4b2a
feat(algebra/homotopy_group): define homotopy groups
2015-11-16 21:32:09 -08:00
Floris van Doorn
47be1e3a15
feat(types/pointed): change definition of loop space
2015-11-16 21:32:09 -08:00
Ulrik Buchholtz
aebb88d42b
feat(hott/homotopy): connectedness, including HoTT Thm 8.2.1
2015-11-08 14:21:16 -08:00
Floris van Doorn
18ec5f8b85
feat(categories): prove introduction rule for equivalences
2015-11-08 14:04:58 -08:00
Jakob von Raumer
d508ceccec
feat(hott/homotpy) add join operator, and prove two basic lemmas
2015-10-13 09:59:24 -07:00
Floris van Doorn
3c4c722afd
feat(hott): port more from chapters 4 and 6 of the book
2015-09-28 09:09:21 -07:00
Ulrik Buchholtz
c6f3f6f3f4
feat(hott): prove HoTT book 7.5.4 and 7.5.5
2015-09-28 09:09:21 -07:00
Ulrik Buchholtz
ed1029641a
fix(hott/*): update book.md and clean up homotopy.connectedness
2015-09-28 09:09:21 -07:00
Leonardo de Moura
4a6ff8058d
fix(hott): import commands (some files have been moved to different directories)
2015-09-25 09:39:45 -07:00
Ulrik Buchholtz
384a366e0f
refactor(hott): move homotopy hits to new homotopy folder
2015-09-24 22:52:33 -04:00
