Ulrik Buchholtz
bd9e47c82c
feat(hott): functoriality of pushout; connectedness in is_conn namespace
...
other changes:
- move result about connectedness of susp to homotopy.susp
- improved definition of circle multiplication
- improved the interface to join
2016-03-23 09:22:55 -07:00
Floris van Doorn
003c11c917
feat(connectedness): is_conn_map -> is_conn_fun, and unbundle the P in elimination principles
2016-03-06 13:03:31 -05:00
Floris van Doorn
671ef077b9
feat(hott): additions, mostly to types.trunc
2016-03-06 13:03:31 -05:00
Floris van Doorn
5cacebcf86
feat(hott): replace assert by have and merge namespace equiv.ops into equiv
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The coercion A ≃ B -> (A -> B) is now in namespace equiv. The notation ⁻¹ for symmetry of equivalences is not supported anymore. Use ⁻¹ᵉ
2016-03-03 10:13:21 -08:00
Floris van Doorn
058000f61d
feat(homotopy/homotopy_group): add theorems in section 8.3 of the HoTT book
2016-03-03 10:13:21 -08:00
Floris van Doorn
1903601ba5
refactor(trunc): rename namespace is_trunc.trunc_index to trunc_index
2016-03-03 10:13:20 -08:00
Floris van Doorn
af4ba3d2fb
feat(hott): prove that the (n+1)-sphere is n-connected
2016-03-03 10:13:20 -08:00
Floris van Doorn
e515875464
feat(hott): various additions
2016-03-03 10:13:20 -08:00
Floris van Doorn
c6e628da12
feat(hott): more computation rules for trunc_index and use nats for Lemma 8.6.2
2016-03-03 10:13:20 -08:00
Floris van Doorn
e5d5ef9d55
feat(hott/library): various changes and additions.
...
Most notably:
Give le.refl the attribute [refl]. This simplifies tactic proofs in various places.
Redefine the order of trunc_index, and instantiate it as weak order.
Add more about pointed equivalences.
2016-03-03 10:13:20 -08:00
Floris van Doorn
4238fdd3d8
fix(hott): add missing links to markdown files
2016-03-03 10:13:20 -08:00
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
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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
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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
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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
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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
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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
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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
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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
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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
