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864 commits

Author SHA1 Message Date
Jeremy Avigad
dc8858d764 refactor(library/init/nat,library/): protect more nat theorems 2015-11-08 14:04:59 -08:00
Jeremy Avigad
7bb2ffb79a refactor(library/data/nat/*): protect some theorems in nat 2015-11-08 14:04:59 -08:00
Leonardo de Moura
4eafcfe945 chore(library/data/fintype/function): fix indentation 2015-11-08 14:04:58 -08:00
Leonardo de Moura
a10aef0792 fix(library/data/tuple): modify definition to make sure we can compile it using new type class resolution procedure 
The issue are universe level constraints that cannot be solved by the
new procedure.
 2015-11-08 14:04:58 -08:00
Leonardo de Moura
5468076400 refactor(library/data): cleanup proofs 2015-11-08 14:04:58 -08:00
Leonardo de Moura
bd41b6ea13 refactor(library/data/rat/basic): cleanup proof 2015-11-08 14:04:58 -08:00
Leonardo de Moura
ac01e9e352 refactor(library/data/int/basic): cleanup proof 2015-11-08 14:04:58 -08:00
Leonardo de Moura
bceac9ece5 refactor(library/data/nat/sub): cleanup nasty proofs 2015-11-08 14:04:58 -08:00
Leonardo de Moura
13ccbaa0d9 refactor(library/data/encodable): mark auxiliary theorems as private 2015-11-08 14:04:56 -08:00
Leonardo de Moura
f14d0523ec refactor(library/data/set/filter): add missing [instance] attribute 2015-11-08 14:04:56 -08:00
Leonardo de Moura
08c061e1fa refactor(library/data/set): remove [reducible] annotation from set operations 2015-11-08 14:04:56 -08:00
Leonardo de Moura
6df31d3406 refactor(library/data/nat/basic): mark some theorems as protected to avoid overloading 2015-11-08 14:04:56 -08:00
Leonardo de Moura
6779cb4fc6 refactor(library/data/real/division): make sure \sy and / notation for reals is available even when we do not open the namespace algebra 2015-11-08 14:04:56 -08:00
Leonardo de Moura
fa937395d9 fix(library/data/real): minor adjustments 2015-11-08 14:04:55 -08:00
Rob Lewis
670ac6ae19 fix(real/order): remove sorry 2015-11-08 14:04:55 -08:00
Rob Lewis
06c1a97259 feat(library/real): fix real.complete 2015-11-08 14:04:55 -08:00
Rob Lewis
0d0df0417d fix(library/real): fix real.division 2015-11-08 14:04:55 -08:00
Rob Lewis
f4e1f3bb1b feat(library/data/real): fix real.order 2015-11-08 14:04:55 -08:00
Leonardo de Moura
fbe80d48dc chore(library): remove "set_option pp.*" commands 2015-11-08 14:04:55 -08:00
Leonardo de Moura
ce21996635 feat(library): define custom recursors for nat, and minimize the use of krewrite 2015-11-08 14:04:55 -08:00
Leonardo de Moura
6e44a42779 refactor(library/data/int,library/data/rat): rename theorems: of_nat_zero, of_nat_one, of_int_zero, of_int_one 2015-11-08 14:04:55 -08:00
Leonardo de Moura
e8454fad26 fix(library/data/real/basic): remove obsolete notation declarations 2015-11-08 14:04:55 -08:00
Jeremy Avigad
7f88e9ad33 fix(library/data/real,library/theories/group_theory): group theory and real/basic 2015-11-08 14:04:55 -08:00
Leonardo de Moura
0eec984485 fix(library/data/equiv): minor adjustment 2015-11-08 14:04:55 -08:00
Leonardo de Moura
724aacb2c1 fix(library): remove "-[notations]" hack at "open -[notations] algebra" 2015-11-08 14:04:55 -08:00
Leonardo de Moura
26eb6fa849 feat(*): new numeral encoding 2015-11-08 14:04:55 -08:00
Leonardo de Moura
8ee214f133 checkpoint: new numeral encoding 2015-11-08 14:04:55 -08:00
Leonardo de Moura
8657ccfc04 fix(library/data/int/gcd): remove sorry 2015-11-08 14:04:55 -08:00
Leonardo de Moura
a9f5735bb5 fix(library/data/int/basic): remove sorry's 2015-11-08 14:04:55 -08:00
Leonardo de Moura
843e95ade6 fix(library/data/real/basic): some real theorems 2015-11-08 14:04:55 -08:00
Leonardo de Moura
c0990d1902 fix(library/data/pnat): pnat with type classes 2015-11-08 14:04:55 -08:00
Leonardo de Moura
a23c05549e fix(library/data/int/div): int div 2015-11-08 14:04:54 -08:00
Jeremy Avigad
1ffe62341b fix(library/data/int): more int problems 2015-11-08 14:04:54 -08:00
Leonardo de Moura
07b33ec75e fix(library/data/int,library/data/rat): int and rat 2015-11-08 14:04:54 -08:00
Leonardo de Moura
744d1cba3d feat(library,hott,frontends/lean): avoid keywords with hyphen 2015-11-08 14:04:54 -08:00
Leonardo de Moura
27b4eb2058 fix(library/data): hf, int, nat, pnat 2015-11-08 14:04:54 -08:00
Leonardo de Moura
3369152559 fix(library/data,library/theories): fin, bag, finset, hf, list, ... 2015-11-08 14:04:54 -08:00
Leonardo de Moura
e6d7e89419 fix(library/data/int,library/data/nat): nat and int 2015-11-08 14:04:54 -08:00
Leonardo de Moura
a618bd7d6c refactor(library): use type classes for encoding all arithmetic operations 
Before this commit we were using overloading for concrete structures and
type classes for abstract ones.

This is the first of series of commits that implement this modification
 2015-11-08 14:04:54 -08:00
Leonardo de Moura
5f967f40b2 fix(library/data/nat/basic): simplify two lemmas 2015-10-07 10:32:20 -07:00
Leonardo de Moura
ede23a3267 feat(hott,library): add additional spacing hints 2015-09-30 17:41:44 -07:00
Sebastian Ullrich
d1b5031dbd feat(library): add some spacing hints 2015-09-30 17:36:32 -07:00
Jeremy Avigad
719e9043cd feat(library/data/set/equinumerosity): add Cantor's theorem, Schroeder-Bernstein theorem 2015-09-25 09:32:28 -07:00
Jeremy Avigad
2c7526e1fc feat(library/*): add various theorems 2015-09-25 09:32:28 -07:00
Jeremy Avigad
9561e379c7 fix(library/data/set/basic): make set_of reducible 2015-09-20 19:54:46 -04:00
Rob Lewis
ee257a7c6c chore(library/data/{nat,real}): rename and move iterate function 2015-09-16 08:28:11 -07:00
Rob Lewis
f5dcb1e0a9 feat(library/algebra): add missing theorems to algebra library 2015-09-16 08:28:11 -07:00
Rob Lewis
4312f1e54b chore(library/data/real): clean and rename theorems in completeness proofs 2015-09-16 08:28:11 -07:00
Rob Lewis
f4fa38e365 chore(library/data/{rat, pnat}): move theorems from reals to more appropriate places 2015-09-16 08:28:11 -07:00
Jeremy Avigad
b48b33c412 feat(library/data/real/division): add useful rules for proving equalities 2015-09-12 21:46:09 -04:00
Jeremy Avigad
780c950414 refactor(library/data/int/order): use 'exists' instead of 'ex', 'least' instead of 'smallest', etc. 2015-09-12 21:46:09 -04:00
Jeremy Avigad
1affeec3c6 fix(library/algebra/ordered_filed): rename theorems 2015-09-12 21:46:09 -04:00
Jeremy Avigad
8db9afbf1c feat/refactor(data/real/complete): add another archimedean property, rename theorems 2015-09-12 21:46:09 -04:00
Jeremy Avigad
d9e166f77f feat/refactor(library/data/real/*): add / improve casts to real from nat, int, rat 2015-09-12 21:46:09 -04:00
Jeremy Avigad
de83a68667 refactor(library/data/{int,rat}/*): clean up casts between nat, int, and rat 2015-09-12 21:46:09 -04:00
Leonardo de Moura
3035dd7e66 refactor(library/data/finset/equiv): remove workarounds added by commit e9809a453d 
The workarounds were needed due to a bug at local_context class.
The problem has been fixed at df3100d2cd
 2015-09-12 17:19:49 -07:00
Leonardo de Moura
e9809a453d fix(library/data/finset/equiv): broken proof 
TODO: investigate why the proof has to be fixed
 2015-09-11 23:24:29 -07:00
Rob Lewis
8d1f449491 refactor(library/data/real): move and rename theorems 2015-09-11 08:52:53 -07:00
Rob Lewis
e722120e34 fix(library/data/rat/order): declare decidable_le an instance 2015-09-03 15:43:07 -07:00
Jeremy Avigad
2ab7928257 refactor(library/data/set/basic): standardize intro and elim theorem names 2015-09-03 15:38:27 -07:00
Jeremy Avigad
072971f3bb feat(library/data/finset/comb,library/data/set/basic): define set complement 2015-09-01 14:47:19 -07:00
Jeremy Avigad
840ef98829 refactor(library/init/nat): make \nat notation available at top level 2015-09-01 14:47:19 -07:00
Jeremy Avigad
7d72c9b6b5 refactor(library/algebra/{field,ordered_field}, library/*): more renaming, setting implicit arguments 
Many theorems for division rings and fields have stronger versions for discrete fields, where we
assume x / 0 = 0. Before, we used primes to distinguish the versions, but that has the downside
that e.g. for rat and real, all the theorems are equally present. Now, I qualified the weaker ones
with division_ring.foo or field.foo. Maybe that is not ideal, but let's try it.

I also set implicit arguments with the following convention: an argument to a theorem should be
explicit unless it can be inferred from the other arguments and hypotheses.
 2015-09-01 14:47:19 -07:00
Jeremy Avigad
93c2d1e9d0 refactor(library/algebra/ordered_field): rename theorems to maintain consistency with other parts of the library 2015-09-01 14:47:19 -07:00
Jeremy Avigad
92af727daf fix(library/data/real/{basic,division,order}: use notation for 0 and 1 
These changes were needed because e.g. real.add_zero was "x + zero = x", and rewrite
would not match it to a goal "t + 0".

The fix was a lot harder than I expected. At first, migrate failed with resource
errors. In the end, what worked was this: I defined the coercion from num to real
directly (rather than infer num -> nat -> int -> rat -> real).

I still don't understand what the issues are, though. There are subtle issues with
numerals and coercions and migrate.

(We are not alone. Isabelle also suffers from the fact that there are too many
"zero"s and "one"s.)
 2015-09-01 14:47:19 -07:00
Leonardo de Moura
3b19de1974 feat(library/data/num): show that num has decidable equality 2015-08-31 17:47:07 -10:00
Leonardo de Moura
63b93cf762 refactor(library/data/set/finite): make proof more robust 2015-08-31 17:26:24 -10:00
Leonardo de Moura
92716972c0 refactor(library/data/hf): add local attribute to make proofs more robust 2015-08-31 17:06:54 -10:00
Leonardo de Moura
f74d7fc266 refactor(library/data/real/basic): add extra step to help unifier 2015-08-31 16:56:05 -10:00
Leonardo de Moura
e01b155b2e refactor(library/data/int/basic): cleanup proof 
Proof was abusing the higher-order unifier
 2015-08-31 16:53:11 -10:00
Leonardo de Moura
ea05ce7fe9 fix(library/data/real/order): mark '2' as local notation 2015-08-31 15:03:18 -10:00
Leonardo de Moura
86b10ab184 feat(library/data): define perm as a special kind of equiv 
This commit also proves the basic permutation lemmas in the nominal isabelle library.
 2015-08-27 06:06:02 -10:00
Leonardo de Moura
3a72cd9621 fix(frontends/lean): rename multiword keyword "suffices to show" to "suffices" 2015-08-18 17:57:53 -07:00
Leonardo de Moura
3ce8c5d6f7 feat(frontends/lean): add "suffices to show A, from B, C" construct 2015-08-18 17:04:38 -07:00
Jeremy Avigad
7dda69fec7 feat/refactor(library/theories/number_theory/irrational_roots,library/*): show nth roots irrational, and add lots of missing theorems 2015-08-16 23:23:23 -04:00
Leonardo de Moura
a06b288deb fix(library/data/set/finite): the powerset notation has already been fixed 2015-08-16 18:47:20 -07:00
Leonardo de Moura
40ef589d8c fix(library/data/finset,library/data/list): fixes #799 
Make sure standard library - theories folder can be compiled with --to_axiom
 2015-08-15 09:49:40 -07:00
Jeremy Avigad
e416291135 feat(library/algebra/*,library/data/*): small additions and changes 2015-08-14 18:49:57 -07:00
Jeremy Avigad
4a36f843f7 refactor(library/algebra/group_power,library/*): change definition of pow 
I changed the definition of pow so that a^(succ n) reduces to a * a^n rather than a^n * a.

This has the nice effect that on nat and int, where multiplication is defined by recursion on the right,
a^1 reduces to a, and a^2 reduces to a * a.

The change was a pain in the neck, and in retrospect maybe not worth it, but oh, well.
 2015-08-14 18:49:57 -07:00
Jeremy Avigad
f9f4cd2197 feat(library/algebra/ordered_field,library/data/int/div): prove sign a = a / abs a 2015-08-14 18:49:57 -07:00
Jeremy Avigad
a56a7d2736 feat(library/data/rat/basic): prove numerator and denominator are coprime 2015-08-14 18:49:57 -07:00
Leonardo de Moura
49eb7166f0 refactor(library/data): rename fixed_list -> tuple 2015-08-13 16:45:34 -07:00
Leonardo de Moura
9bb778dc7c feat(library/data/hf): define head and tail for hf 2015-08-13 16:00:32 -07:00
Leonardo de Moura
a6b1c84874 feat(library/data/hf): add basic list functions to hf 2015-08-13 15:36:54 -07:00
Leonardo de Moura
50983c4573 feat(library/data/hf): prove that s₁ ⊆ s₂ → s₁ ≤ s₂ for hereditarily finite sets 2015-08-13 15:36:26 -07:00
Leonardo de Moura
aa2a417483 feat(library/data/hf): add induction and total order for hf 2015-08-13 14:11:44 -07:00
Leonardo de Moura
f4a81fdd73 fix(library/data): powerset notation 2015-08-13 09:04:00 -07:00
Leonardo de Moura
51c48277c8 feat(library/data/hf): add hf.powerset 2015-08-13 08:52:45 -07:00
Leonardo de Moura
6bec3ba58b feat(library/data/hf): add hf.image 2015-08-13 08:22:58 -07:00
Leonardo de Moura
bf65acb126 feat(library/data/rat): show that the rationals are encodable and countable 2015-08-12 21:31:24 -07:00
Leonardo de Moura
710b7b6e40 feat(library/data/int/countable): show that int is encodable, isomorphic to nat, and countable 2015-08-12 21:31:24 -07:00
Leonardo de Moura
52f902bc33 feat(library/data/encodable): show that the quotient A/R is encodable if A is encodable and R is decidable 2015-08-12 21:31:24 -07:00
Leonardo de Moura
d2eb99bf11 refactor(library/logic): move logic/choice.lean to init/classical.lean 
choice axiom is now in the classical namespace.
 2015-08-12 18:37:33 -07:00
Leonardo de Moura
cb9830beaf refactor(library/logic/choice): move prop_decidable instance into namespace 'classical' 2015-08-12 17:06:15 -07:00
Leonardo de Moura
b4024982a2 refactor(library/data): move vector as indexed family to examples folder 2015-08-12 15:05:14 -07:00
Leonardo de Moura
840c1a3693 refactor(library/data): rename vec to fixed_list 2015-08-12 14:38:21 -07:00
Leonardo de Moura
cee9d6b092 feat(library/data/hf): define Hereditarily finite sets 2015-08-11 16:56:06 -07:00
Leonardo de Moura
6fd3affeb1 feat(library/data/finset/equiv): show that (finset nat) is isomorphic to nat 2015-08-11 15:54:14 -07:00
Leonardo de Moura
1cacac2789 feat(library/data/nat/parity): add auxiliary lemma 2015-08-11 14:20:58 -07:00
Leonardo de Moura
a5615a6ea7 feat(library/data/finset/equiv): start bijection from (finset nat) to nat 2015-08-10 19:42:09 -07:00