Jeremy Avigad
352a906ba2
feat(library/theories/{metric_space,real_limit}): define metric spaces, limits, instantiate reals
2015-09-12 21:46:09 -04:00
Jeremy Avigad
948cdee366
feat(library/algebra/ordered_group): add variant of triangle inequality
2015-09-12 21:46:09 -04:00
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
Jeremy Avigad
20f6b4c6bd
feat(library/logic/quantifiers): add 'the'
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
Leonardo de Moura
3c1d6ec67a
feat(library/algebra/algebra): add link to complete lattices module
2015-09-04 13:04:36 -07:00
Sebastian Reuße
f8a773be11
chore(library/algebra): remove obsolete link.
2015-09-04 09:41:34 +02:00
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
Floris van Doorn
9a439d4a4e
feat(library.md): update reference to classical axiom
2015-09-01 15:17:46 -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
51e0d31304
refactor(library/algebra/ordered_ring,ordered_field): move theorems from ordered_field to ordered_ring
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
c83d592c17
feat(library/theories/number_theory/square_root_irrational): add proof that sqrt 2 is irrational
2015-08-14 18:49:57 -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
