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HITs-Examples
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209 Commits

Author SHA1 Message Date
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
Niels 2273ecaae0 Merge remote-tracking branch 'origin/leon' into properties 2017-06-06 11:15:13 +02:00
Niels a98c56d154 changes 2017-06-06 11:15:01 +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
Niels 2a561d4983 Finished proof of extensionality 2017-05-25 22:21:19 +02:00
Niels 01e4cb982f Finished proof of extensionality 2017-05-25 22:20:46 +02:00
Niels 954c273ddf Merge remote-tracking branch 'origin/bloop' into properties 2017-05-25 21:51:27 +02:00
Dan Frumin 06dc8a0acd A proof of subset_isIn 2017-05-25 18:59:18 +02:00
Dan Frumin 294f818b07 Add [eq_subset] equivalence 
X = Y <~> X ⊂ Y /\ Y ⊂ X
 2017-05-25 16:28:09 +02:00
Dan Frumin 9202c6489d Speed up the compilation of properties.v a little bit 2017-05-25 15:11:41 +02:00
Leon Gondelman 140b02e9f4 subset 2017-05-24 18:28:24 +02:00
Niels 74cd449f7b Elements of union 2017-05-24 14:52:52 +02:00
Dan Frumin 826b6ba233 Port the FiniteSets library to HitTactics 2017-05-24 13:54:00 +02:00
Dan Frumin 25d1e1c969 Merge hrecursion into master 2017-05-24 13:00:56 +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
Leon Gondelman 13737556c6 Setup for finite sets library. 2017-05-23 16:30:31 +02:00
Dan Frumin 5abf0acf06 Switch to the DecidablePaths typeclass 2017-05-23 12:12:22 +02:00
Dan Frumin ebdaab4de0 Merge Leon's changes into hrecursion 2017-05-23 12:02:06 +02:00
Dan Frumin 9d9b7a4713 Prettify FinSets 2017-05-23 11:58:09 +02:00
Leon Gondelman afdc4a3e6b intersection_comm 2017-05-23 11:50:52 +02:00
Dan Frumin 2f68e833af Finish the comprehension_idem proof with functional extensionality 2017-05-23 00:17:33 +02:00
Niels c024e27338 Further work on associativity of union. 2017-05-22 23:05:43 +02:00
Dan Frumin f23d4aeacb Replace the canonical structures mechanism for recursion with type classes 
See changes in HitTactics.v
 2017-05-22 21:06:13 +02:00
Niels 6340f4cd77 Work on finite sets 2017-05-22 18:11:47 +02:00
Dan Frumin 5e594d10f0 Some modifications to the finset module 2017-05-22 17:01:19 +02:00
Niels b85976a96d Added Agda code for some HITs 2017-05-22 16:46:58 +02:00
Niels 27d78e1e75 Better gitignore 2017-05-22 16:45:51 +02:00
Dan Frumin 399fab467b Package both the induction and recursion principles in the same record 2017-05-20 14:05:46 +02:00
Dan Frumin 75120ba602 Update the README 2017-05-18 17:46:00 +02:00
Dan Frumin 44da34d72f Add a general hit recursion tactic. 
The tactic resolves the induction principle for a HIT
using Canonical Structures, following the suggestion of @gallais
 2017-05-18 17:43:19 +02:00
Dan Frumin e81986a920 Add .gitignore and remove the makefile 2017-05-18 17:12:42 +02:00
Dan Frumin f4bfeb98ca Add a _CoqProject and a makefile 2017-05-01 19:25:27 +02:00
Niels van der Weide 16f1ab86cb Expressions 2017-05-01 17:27:49 +02:00
leon-gondelman 14cf6c1031 Add files via upload 2017-04-19 17:16:17 +02:00
nmvdw 0cc0ecfd48 added proof that two reps of Z are iso (if everything set) 2017-01-10 23:46:50 +01:00
nmvdw 21120740b9 Delete HITs.pdf 2017-01-02 13:47:45 +01:00