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HITs-Examples
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151 Commits

Author SHA1 Message Date
Niels 41b952e0d0 Added alternative definition of k-finite via subobjects 2017-08-18 11:34:04 +02:00
Niels 29f3f31cec Improved lattice hints 2017-08-18 11:18:37 +02:00
Dan Frumin da60017367 Interval is K-finite 2017-08-17 22:46:47 +02:00
Niels 8ff54def39 Removed View_rec2 2017-08-17 17:18:57 +02:00
Dan Frumin ae60ac0146 LEM <~> all K-finite hsets are projective 
and LEMoo -> all K-finite objects (not just hsets) are projective
 2017-08-16 17:37:12 +02:00
Dan Frumin 56d6207d07 Circle is Kuratowski-finite 2017-08-16 17:13:08 +02:00
Dan Frumin 809382ba13 Every Bishop-finite set is Kuratowski-finite 2017-08-16 17:01:25 +02:00
Dan Frumin 99dfd73b5a K-finite objects are closed under surjections 2017-08-16 16:07:51 +02:00
Dan Frumin 57a4535f87 B-fin => K-fin if the underlying type has decidable paths 2017-08-16 16:00:21 +02:00
Niels 920fdd91ab further simplifications 2017-08-15 22:26:26 +02:00
Niels e1bc900abc Further simplifications in interface 2017-08-15 22:05:31 +02:00
Niels e29e978218 Improved interface.v 2017-08-15 20:08:16 +02:00
Niels 06701dcdf8 Simplified proof of extensionalty and proofs in interface.v 2017-08-14 21:38:50 +02:00
Niels b274fcddfc Simplified proof of extensionality 2017-08-14 16:39:20 +02:00
Niels 0f6e98a377 Strengthened mere choice 2017-08-14 12:43:15 +02:00
Niels bf0b9f8771 Added simplified proof of extensionality 2017-08-11 14:17:47 +02:00
Niels 5766024f95 path_ishprop now in extensionality 2017-08-11 13:15:31 +02:00
Niels 89808c7297 Added proof: Bishop finite => Kuratowski finite 2017-08-10 17:33:56 +02:00
Dan Frumin 33808928db Clean up trailing whitespaces and an unused definition. 2017-08-09 18:05:58 +02:00
Dan Frumin 31e08af1d1 Prove that the quotient of an implementation is isomorphic to FSet 
Formally, `View A <~> FSet A`
 2017-08-09 17:59:11 +02:00
Niels bd2ca9a0aa Added separation as operation 2017-08-09 17:03:51 +02:00
Dan Frumin f08918b60c Move the B-finiteness proofs and simplify them a bit 2017-08-09 16:01:54 +02:00
Niels cb0af9a36a Added min function with proof of its specification 2017-08-09 15:11:14 +02:00
Niels 5233fc6de9 Added proof that the finite sets in HoTTlibrary have no intersection and union 2017-08-09 12:07:43 +02:00
Niels c358ef1659 Added notation in Sub.v 2017-08-08 19:56:39 +02:00
Dan Frumin dad6686c4c Make everything work with the new notation 2017-08-08 17:44:27 +02:00
Dan Frumin 80dabe3162 Get a quotient from an implementation 2017-08-08 17:31:23 +02:00
Niels 3cda0d9bf2 Completely fixed notation 2017-08-08 17:00:30 +02:00
Niels 92bc50d79f Improved notation to unicode 2017-08-08 15:30:12 +02:00
Niels 2bdec415d9 Improved notatio 2017-08-08 15:29:50 +02:00
Niels de335c3955 Added join-semilattice 2017-08-08 13:45:27 +02:00
Niels c1dfef3cc1 Separated lemmas for extensionality for properties, added tactic toHProp 2017-08-08 13:35:28 +02:00
Dan Frumin 4ade6e60cc Clean up the interface.v proofs 2017-08-08 13:18:45 +02:00
Niels 4a98d84cbc Added separation 2017-08-08 00:41:27 +02:00
Niels 76fe6faff2 Small improvements 2017-08-07 23:27:53 +02:00
Niels 30004e1c8b Added membership of product 2017-08-07 23:15:25 +02:00
Niels e498b93f16 Added product 2017-08-07 22:13:42 +02:00
Niels 8c10ab1c0c More cleaning 2017-08-07 16:57:21 +02:00
Niels 1e373364b2 Some cleaning in notation 2017-08-07 16:49:46 +02:00
Niels 1bab2206a3 Some cleaning 2017-08-07 16:22:55 +02:00
Niels a0844f6be4 Some simplifications in proofs, extra proofs for implementation 2017-08-07 15:39:01 +02:00
Niels d5585f32c6 Added basis for reflection in interface 2017-08-07 14:55:07 +02:00
Niels d9cde16f5a Added interface of finite stes 2017-08-07 12:20:43 +02:00
Dan Frumin 6f016d1b7f Remove a useless vernacular command 2017-08-03 23:25:25 +02:00
Dan Frumin 90d795b708 Correspondence between enumerated subobjects and k-finite subobjects 2017-08-03 23:22:36 +02:00
Niels f106be08de Added merely decidable equality => LEM 2017-08-03 23:01:57 +02:00
Dan Frumin 6d3d0eda9f Construct a mapping from [FSet] to enumerated subobjects 2017-08-03 18:06:39 +02:00
Dan Frumin 69b4b6d7a5 Fix the implicit arguments for lattice operations 2017-08-03 17:09:10 +02:00
Dan Frumin 72ce66f833 Make [enumerated A] an hProp & show that Kf => enumerated 2017-08-03 17:00:02 +02:00
Dan Frumin c7e12d6d25 Enumerated implies Kurarowski-finite 2017-08-03 15:16:47 +02:00
Dan Frumin 31889d4e48 A short lemma [FSet A = FSetC A] 2017-08-03 15:10:45 +02:00
Niels 9cdfc671dc Added structure to k_finite sts 2017-08-03 15:07:53 +02:00
Niels 0bdf0b79fe Added k_finite in coq project 2017-08-03 13:54:02 +02:00
Dan Frumin efce779b06 Simplify some proofs and barely improve the compilation time 2017-08-03 12:49:15 +02:00
Niels 241f5ea377 Added subobjects 2017-08-03 12:27:43 +02:00
Niels fec00177ad Merge branch 'master' of https://github.com/nmvdw/HITs-Examples 2017-08-03 12:24:39 +02:00
Niels 7d74b45fc3 Changed lattice 2017-08-03 12:21:34 +02:00
Dan Frumin 8a65852d1b Fix compilation 2017-08-02 15:45:12 +02:00
Niels 77a449e68b Added lattice constructions 2017-08-02 14:21:12 +02:00
Dan Frumin 4141f9d456 Finalize the definition of K-finite (sub)objects 2017-08-02 14:14:14 +02:00
Niels fa076f5f41 k-finiteness 2017-08-02 13:30:25 +02:00
Niels 2ccece3225 Splitted cons_repr 2017-08-02 11:40:03 +02:00
Niels 5ee7053631 Removed bad hints 2017-08-01 17:35:23 +02:00
Niels e6bf0f9d5d Fixed NeutralL and NeutralR 2017-08-01 17:25:57 +02:00
Niels b3b3e5b6c2 HProp is a lattice 2017-08-01 17:12:32 +02:00
Niels 0de37d6cea Split the development into different directories 2017-08-01 15:41:53 +02:00
Niels bae04a6d2b Lowercase enumerated 2017-08-01 15:20:17 +02:00
Niels 1eec9628ce Lowercase files 2017-08-01 15:18:07 +02:00
Niels fed9546d11 Some cleanup 2017-08-01 15:18:07 +02:00
Dan Frumin 37e3017cfc Basic properties of enumerated sets 2017-07-31 17:39:01 +02:00
Niels b06c59339b Small fix 2017-07-31 14:54:20 +02:00
Niels 8ff9089d3d Added disjunction. 2017-07-31 14:52:41 +02:00
Dan Frumin f4d89f810c Proof that the trunctation is really needed 
If there is no 0-truncation then the resulting type is not an h-set.
 2017-06-21 14:10:59 +02:00
Dan Frumin ab48ab4a75 Decidable equality on FSets 2017-06-21 11:22:56 +02:00
Dan Frumin 1a3bb2cb5a Use the [Functorish] instance from the HoTT library 2017-06-21 11:07:22 +02:00
Niels 3274bed4e0 Lists and finite sets 2017-06-20 17:33:35 +02:00
Niels c8a84349b1 Further work on lists (simple implementation) 2017-06-20 15:08:52 +02:00
Niels 8c31e4d382 Lists implement finite sets 2017-06-20 13:54:42 +02:00
Dan Frumin a95ddea6ca FSet is a strong powerset monad 2017-06-20 11:34:09 +02:00
Dan Frumin 47a38b3568 Separate the lattice properties proofs, get rid of the admits and general cleanup 2017-06-19 21:32:55 +02:00
Dan Frumin 8e6ab4c340 Separate the extensionality proof 
and fix some tactics
 2017-06-19 21:06:17 +02:00
Niels 229df7b270 Shortened proofs 2017-06-19 17:54:44 +02:00
Niels 5f4c834cbe Proofs of the lattice properties (via extensionality) 2017-06-19 17:08:56 +02:00
Leon Gondelman 57d8ee9d55 cons representation of finite sets 2017-06-19 16:06:04 +02:00
Dan Frumin 490980db0f Some cleanup for the extensionality proof 2017-06-19 12:24:57 +02:00
Dan Frumin dce70f517f Minor cleanup of some proofs 2017-06-16 13:24:54 +02:00
Dan Frumin 6971697c09 Add the difference operation 2017-06-14 18:06:16 +02:00
Dan Frumin 036d1599b2 Merge branch 'bloop' 2017-06-14 13:09:52 +02:00
Dan Frumin abec9ecd00 Comment out the long min fn 2017-06-14 13:08:41 +02:00
Dan Frumin a1a6912cb2 Use equiv_iff_hprop_curried from HoTT 2017-06-14 13:00:20 +02:00
Leon Gondelman 0d210cae04 first step toward cons-union iso: construction of min function for FSet A, where A is Totally Ordered. To construct min, various lemmas about empty set are needed. This min function is constructed in a very inefficient way w.r.t. proofs of assoc, comm, etc. 2017-06-03 00:08:12 +02:00
Leon Gondelman f8ed41e5fe trailing white spaces 2017-05-26 12:28:07 +02:00
Leon Gondelman 140b02e9f4 subset 2017-05-24 18:28:24 +02:00
Dan Frumin 826b6ba233 Port the FiniteSets library to HitTactics 2017-05-24 13:54:00 +02:00
Niels 6ffbbb440f More absorbtion 2017-05-24 12:10:39 +02:00
Niels 565fecec30 Changed names, further work on distributive laws 2017-05-24 11:47:30 +02:00
Niels e63f1b8bf5 One absorption law 2017-05-23 23:24:22 +02:00
Niels 2f7840c494 Associativity of intersection. 2017-05-23 22:58:35 +02:00
Niels 0bdbcdfc6c Recursion rule is now defined via induction. 2017-05-23 21:50:26 +02:00
Niels 6bb5e8b690 Added idempotency of the intersection 2017-05-23 21:31:45 +02:00