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Author SHA1 Message Date
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
65b367ddff feat(fin): port more parts of fin from the standard library 2016-03-03 10:13:20 -08:00
Floris van Doorn
bf403e124a feat(nat/div): port to HoTT library 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
Jakob von Raumer
1104537d02 chore(hott) adjust to new naming for pointed types and truncated types 2016-03-01 13:52:53 -08:00
Jakob von Raumer
2b13777bbe feat(hott) add type functors, maybe they should be changed to be un-funexted. 2016-03-01 13:52:53 -08:00
Jakob von Raumer
11458f64fe feat(hott/algebra) add order categories 2016-03-01 13:52:53 -08:00
Leonardo de Moura
fbe5188480 refactor(frontends/lean): remove 'by+' and 'begin+' tokens 2016-02-29 13:45:43 -08:00
Leonardo de Moura
faa0031d4e refactor(library,hott): remove 'by+' and 'begin+' 2016-02-29 13:15:48 -08:00
Leonardo de Moura
b41c65f549 feat(frontends/lean): remove '[visible]' annotation, remove 'is_visible' tracking 2016-02-29 12:31:23 -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
101cf1ec4c feat(frontends/lean): remove difference between 'have' and 'assert' 2016-02-29 11:28:20 -08:00
Leonardo de Moura
5a4dd3f237 feat(library/reducible): remove [quasireducible] annotation 2016-02-25 17:42:44 -08:00
Leonardo de Moura
d501295ec1 refactor(algebra/binary): remove unnecessary annotations 2016-02-25 15:11:52 -08:00
Leonardo de Moura
768ba1c363 refactor(library/hott): remove more unnecessary annotations 2016-02-25 14:30:00 -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
Leonardo de Moura
1924b2884c refactor(library/tactic): remove 'append' and 'interleave' tacticals 
Preparation for major refactoring in the tactic framework.
 2016-02-24 16:02:16 -08:00
Sebastian Ullrich
3de216d302 chore(*.md): fix/remove broken links 2016-02-23 10:11:24 -08:00
Floris van Doorn
6cdbc0f79f feat(pointed/equiv): add more theorems 
The theorems are mostly about the interaction between pointed equivalences and pointed homotopies
Some of these theorems were missing for (unpointed) equivalences, so I also added them there
 2016-02-22 11:15:39 -08:00
Floris van Doorn
eea2a1ac91 feat(hott): add some more abstracts 2016-02-22 11:15:39 -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
Floris van Doorn
7f09ba328e feat(hott): small changes 2016-02-22 11:15:38 -08:00
Floris van Doorn
78092af27f feat(hott): add some attributes 2016-02-22 11:15:38 -08:00
Floris van Doorn
cd74b6bff0 fix(hott): abstract some equivalence proofs 
Note: this is important. I proved a quite complicated equivalence with calc, by chaining these
equivalences. Now if I want to know the underlying function of this composite equivalence, I have to
unfold all these instances. Without the abstracts, this took 14 seconds, and afterwards, it took 2
seconds.
 2016-02-22 11:15:38 -08:00
Floris van Doorn
42b78962f9 feat(init/wf): simplify definition acc.drec 2016-02-09 10:03:48 -08:00
Floris van Doorn
e14d4a4c0c feat(init/wf): port from standard library to HoTT library 
After this commit we need some more advanced theorems in init/wf, notably function extenstionality.
For this reason I had to refactor the init folder a little bit.
To keep the init folders in both libraries similar, I did the same refactorization in the standard library, even though that was not required for the standard library
 2016-02-09 10:03:48 -08:00
Jakob von Raumer
c0abcc7722 chore(hott): fix signature of previous lemma 2016-02-09 09:59:03 -08:00
Jakob von Raumer
3c7536cff8 chore(hott): clean up cancellability proof a bit 2016-02-09 09:58:57 -08:00
Jakob von Raumer
4d6c516c01 feat(hott): add lemma: equivalent fin sets come from equal numbers, sums with fin sets are cancellable 2016-02-09 09:58:52 -08:00
Jakob von Raumer
4edb6d7765 feat(hott): finish cancelling law for sums with unit 2016-02-09 09:58:31 -08:00
Jakob von Raumer
0ad8131985 feat(hott): start cancellation proof for sums 2016-02-09 09:58:24 -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
1042f6c29d feat(hott): port finite ordinal sets from the std library, with all things related to nat.mod and to fintype still missing. 
create a logic.hlean file for further extension of the logic theory in the prelude. add distributivity lemmas for products and sums.
 2016-02-09 09:58:10 -08:00
Jakob von Raumer
cb3bc1a311 feat(hott): add another constructor for pointed equivalences 2016-02-09 09:57:59 -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
Floris van Doorn
ec38ee8df8 fix(hott/init/tactic): add replace 2016-02-07 14:06:28 -08:00
Leonardo de Moura
30d6853ffd refactor(hott,tests): make sure HoTT library and tests still work if we introduce checkpoints in have-expressions 2016-02-04 16:58:32 -08:00
Leonardo de Moura
42fbc63bb6 fix(library/tc_multigraph): avoid name collisions 
@avigad, @fpvandoorn, @rlewis1988, @dselsam

I changed how transitive instances are named.
The motivation is to avoid a naming collision problem found by Daniel.
Before this commit, we were getting an error on the following file
tests/lean/run/collision_bug.lean.

Now, transitive instances contain the prefix "_trans_".
It makes it clear this is an internal definition and it should not be used
by users.

This change also demonstrates (again) how the `rewrite` tactic is
fragile. The problem is that the matching procedure used by it has
very little support for solving matching constraints that involving type
class instances. Eventually, we will need to reimplement `rewrite`
using the new unification procedure used in blast.

In the meantime, the workaround is to use `krewrite` (as usual).
 2016-02-04 13:15:42 -08:00
Ulrik Buchholtz
dcb35008e1 feat(hott/homotopy): general connectivity elimination and the wedge connectivity lemma 2016-02-04 11:07:22 -08:00
Floris van Doorn
29c84aad19 fix(book.md): add types.arrow to 2.9 
closes #976
 2016-01-26 20:40:22 -08:00
Floris van Doorn
3409deecdb chore(hott): update md files, move port.md 2016-01-24 16:34:45 -08:00
Floris van Doorn
8eab58f41a fix(choice): make some style changes 2016-01-24 16:34:45 -08:00
seulbaek
92d6806073 refactor(hott/choice): rename 3.8.5 2016-01-24 16:34:35 -08:00
seulbaek
107550238b refactor(hott/choice): rename lemmas for 3.8.2 2016-01-24 16:34:23 -08:00
seulbaek
d42f3d313f feat(hott): add choice.hlean 2016-01-24 16:34:12 -08:00
seulbaek
2c81c93d69 feat(hott/types/equiv): add is_trunc_equiv to equiv.hlean 2016-01-24 16:33:59 -08:00
Jakob von Raumer
aa5e188179 feat(hott): add symmetry of pushouts and pointed pushouts 2016-01-24 16:30:26 -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
Jakob von Raumer
664132b845 feat(hott): add calc lemmas for pointed equivalences, make pinl and pinr constructors 2016-01-24 16:30:16 -08:00
Jakob von Raumer
8d22e454e7 feat(hott): add theory about pointed pushouts 2016-01-24 16:30:12 -08:00
Leonardo de Moura
66a722ff5a feat(library/unifier): remove "eager delta hack", use is_def_eq when delta-constraint does not have metavariables anymore 
The "eager-delta hack" was added to minimize problems in the interaction
between coercions and delta-constraints.
 2016-01-03 12:39:32 -08:00
Leonardo de Moura
b117a10f82 refactor(library/blast/simplifier): use priority_queue to store simp/congr lemmas, use name convention used at forward/backward lemmas, normalize lemmas when blast starts, cache get_simp_lemmas 2015-12-28 17:52:57 -08:00
Leonardo de Moura
f177082c3b refactor(*): normalize metaclass names 
@avigad and @fpvandoorn, I changed the metaclasses names. They
were not uniform:
- The plural was used in some cases (e.g., [coercions]).
- In other cases a cryptic name was used (e.g., [brs]).

Now, I tried to use the attribute name as the metaclass name whenever
possible. For example, we write

   definition foo [coercion] ...
   definition bla [forward] ...

and

  open [coercion] nat
  open [forward] nat

It is easier to remember and is uniform.
 2015-12-28 10:39:15 -08:00
Ulrik Buchholtz
b09fdc8c61 feat(hott/hit): flattening lemmas for coeq and pushout 2015-12-28 09:06:13 -08:00
Ulrik Buchholtz
f3b2c7010f feat(hott): functoriality of quotients 2015-12-28 09:06:13 -08:00
Leonardo de Moura
128b557d37 refactor(frontends/lean): use attribute_manager to simplify decl_attributes 2015-12-17 22:28:53 -08:00
Floris van Doorn
74366aa061 fix(hott): change some theorems to definitions 
This ensures that the HoTT library compiles with the option --to_axiom
 2015-12-17 12:46:16 -08:00
Floris van Doorn
c852f7bc71 feat(hott): use the induction tactic for trunc at some places 2015-12-17 12:46:16 -08:00
Floris van Doorn
da5f10ce63 feat(hott): minor fixes. allow the usage of numerals for trunc_index 2015-12-17 12:46:16 -08:00
Leonardo de Moura
61ecf018e9 feat(frontends/lean,library/tactic): add easy tactic parsing support for at ... and with ... 2015-12-17 12:18:32 -08:00
Leonardo de Moura
c824a0e050 chore(library,hott): enforce naming conventions 2015-12-17 11:36:58 -08:00
Leonardo de Moura
13419d1561 chore(hott/library): cleanup 2015-12-17 11:31:07 -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
Leonardo de Moura
e3a35ba4fd feat(frontends/lean): add 'with_attributes' tactical 
closes #494
 2015-12-13 18:27:44 -08:00
Leonardo de Moura
d4e49a8434 feat(library/tactic/intros_tactic): intro without argument should introduce a single variable 
see #695
 2015-12-13 16:28:39 -08:00
Floris van Doorn
4ef58f1ba5 chore(hott): more cleanup. 
Make zero and one reducible (see algebra/port.md)
Change some theorems which need to compute into definitions
 2015-12-10 10:42:16 -08:00
Floris van Doorn
c968f920ba chore(hott): cleanup 2015-12-10 10:42:16 -08:00
Floris van Doorn
65c93b180d fix(types.md): add num 2015-12-09 12:36:11 -08:00
Floris van Doorn
2325d23f68 feat(hott): port nat and int from the standard library 2015-12-09 12:36:11 -08:00
Floris van Doorn
46739c8b70 feat(hott/algebra): port abstract structures 2015-12-09 12:34:06 -08:00
Floris van Doorn
14a2c8e444 fix(init/nat): add spaces around inequalities 2015-12-09 12:34:06 -08:00
Floris van Doorn
377755e5ab feat(types/sigma): add lemma 2015-12-09 12:34:06 -08:00
Leonardo de Moura
6404c3c014 chore(hott/types/nat/order): remove occurrence of "migrate" command 2015-12-08 15:37:13 -08:00
Leonardo de Moura
85379b7706 feat(library/blast/actions/simple_actions): make sure contradiction action works even if classical logic support is not enabled 
not (not (not a)) -> not a
 2015-12-07 09:30:14 -08:00
Jakob von Raumer
cc8a5581d6 chore(hott/cubical): add lost space hints around square concatenations 2015-12-02 23:13:25 -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
1d68d57bb9 chore(hott/cubical): adapt cubovers to new order of faces 2015-12-02 23:13:07 -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
1b52ae8858 feat(hott/cubical): add cube concatenations 2015-12-02 23:12:54 -08:00
Jakob von Raumer
3f1cf3835f chore(hott/cubical): change order of visible arguments in cube 2015-12-02 23:12:50 -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
2bc45f4de1 feat(hott/cubical): add cubes which are degenerate in one dimension 2015-12-02 23:12:37 -08:00
Jakob von Raumer
bba6ab5a6d feat(hott/cubical): add fillers and other little lemmas for squares and cubes 2015-12-02 23:12:34 -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
fe8a858d79 feat(hott): add recursor to refl_quotient 2015-11-22 18:29:37 -08:00
Floris van Doorn
ae92e8c94d feat(hit/two_quotient): give dependent eliminator for two_quotients 2015-11-22 18:29:37 -08:00
Floris van Doorn
0537ef2bd9 chore(*): add me as author to files where I made nontrivial contributions 2015-11-22 14:21:26 -08:00
Floris van Doorn
74aff044ef feat(group): port three more theorems from the standard library 2015-11-22 14:21:26 -08:00
Floris van Doorn
482c68b387 feat(*/list): add some computation rules for lists in both libraries 2015-11-22 14:21:26 -08:00
Floris van Doorn
93283a4cf8 feat(list): also port part of list.comb 2015-11-22 14:21:26 -08:00
Floris van Doorn
cc03ca9c6d fix(reserved_notation): make :: bind stronger than ++ 
this allows us to write l1 ++ a :: l2 without parentheses
 2015-11-22 14:21:26 -08:00
Floris van Doorn
5abc450fad feat(list): port list.basic from the standard library 2015-11-22 14:21:26 -08:00
Floris van Doorn
88a62f8e74 feat(algebra|types): small additions 
add to markdown file for algebra, and add some definitions in types/
 2015-11-22 14:21:25 -08:00
Floris van Doorn
5328486d49 feat(hit): add elimination rule to propositions 2015-11-22 14:21:25 -08:00
Floris van Doorn
5b8486a34f feat(set_quotient): add some properties for set_quotients 2015-11-22 14:21:25 -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
Leonardo de Moura
491c7c55e1 feat(library/simplifier/simp_rule_set): add priorities for simp and congr rules 2015-11-16 22:34:06 -08:00
Floris van Doorn
9e492a8771 feat(category): more about adjoint functors 
This commit has multiple unfinished proofs (commented out)
 2015-11-16 21:32:09 -08:00
Floris van Doorn
f866f71491 feat(algebra/e_closure): add some support for dependent elimination of two_quotients 2015-11-16 21:32:09 -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
Floris van Doorn
d402b67d25 feat(hott/function): show that a function is embedding iff it has propositional fibers 2015-11-16 21:32:09 -08:00
Floris van Doorn
5c1bf1e777 fix(hott): delete empty file 2015-11-16 21:32:09 -08:00
Floris van Doorn
e00ccff6de fix(hott): make sure the HoTT library compiles with --to_axiom 2015-11-16 21:32:09 -08:00
Leonardo de Moura
4d68e2a520 feat(library,hott): add eq.mpr and eq.mp lemmas 2015-11-14 15:40:47 -08:00
Leonardo de Moura
5ceac83b6a feat(frontends/lean/elaborator): restrict the number of places where coercions are considered 
We do not consider coercions around meta-variables anymore.
 2015-11-11 12:37:19 -08:00
Leonardo de Moura
9bedbbb739 refactor(library,hott): remove coercions between algebraic structures 
They are classes, and mixing coercion with type class resolution is a
recipe for disaster (aka counterintuitive behavior).
 2015-11-11 11:57:44 -08:00
Ulrik Buchholtz
0eb070e183 fix(hott/book.md): align with previous commit 2015-11-08 14:21:27 -08:00
Ulrik Buchholtz
aebb88d42b feat(hott/homotopy): connectedness, including HoTT Thm 8.2.1 2015-11-08 14:21:16 -08:00
Leonardo de Moura
a07598a3ec feat(hott/init/logic): congr_fun was missing in the HoTT library, blast assumes it is part of the environment 2015-11-08 14:05:03 -08:00
Leonardo de Moura
01259a2d1c feat(library/app_builder): add helper functions for creating eq.rec applications 2015-11-08 14:05:01 -08:00
Floris van Doorn
4828afa781 fix(hott): small fixes after rebasing 2015-11-08 14:04:59 -08:00
Floris van Doorn
5e4441cb43 fix(functor.equivalence): comment out sorry's 2015-11-08 14:04:59 -08:00
Floris van Doorn
49cb516c71 feat(category.limit): prove that the limit functor is right adjoint to the diagonal map 2015-11-08 14:04:59 -08:00
Floris van Doorn
36dfb61a3e feat(category.limits): prove that yoneda preserves limits 2015-11-08 14:04:59 -08:00
Floris van Doorn
46dba4ee5e refactor(category): move some files to subfolders, and create file with basic functors 2015-11-08 14:04:59 -08:00
Floris van Doorn
e14754a337 feat(category): start on proof of yoneda preserves limits and limit functor is left adjoint 2015-11-08 14:04:59 -08:00
Floris van Doorn
a99a99f047 feat(hit/quotient): prove the flattening lemma 2015-11-08 14:04:59 -08:00
Floris van Doorn
aa9f32a3bd fix(init/equiv): make transport not an instance 2015-11-08 14:04:59 -08:00
Floris van Doorn
f2d07ca23c feat(category): various small changes in category theory 2015-11-08 14:04:59 -08:00
Floris van Doorn
de1c47eda9 feat(categories): add exponential laws for categories 
also give nicer rules to construct equalities between (pre)categories
 2015-11-08 14:04:59 -08:00
Floris van Doorn
0e7b7af1da refactor(category): add new folder functor, split adjoint file into separate files 2015-11-08 14:04:59 -08:00
Floris van Doorn
3f0d8c0a8c feat(category.adjoint): prove more about functors 2015-11-08 14:04:58 -08:00
Floris van Doorn
18ec5f8b85 feat(categories): prove introduction rule for equivalences 2015-11-08 14:04:58 -08:00
Floris van Doorn
448178a045 feat(category.functor2): prove that the category of functors is complete and cocomplete if the codomain is 2015-11-08 14:04:58 -08:00
Floris van Doorn
3b7afad6ad feat(category.hset): prove that the category of sets is cocomplete 2015-11-08 14:04:58 -08:00
Floris van Doorn
c7fd29f854 feat(category): start with the introduction rule for equivalences 2015-11-08 14:04:58 -08:00
Leonardo de Moura
50186e2db3 feat(library/class_instance_resolution): add old type class resolution procedure back to be able to compile HoTT library 2015-11-08 14:04:58 -08:00