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Author SHA1 Message Date
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
Leonardo de Moura
0e98f10c96 feat(library/data/nat/div): add div_div_eq_div_mul theorem for nat 2015-08-10 19:30:00 -07:00
Leonardo de Moura
de3d0e4162 feat(library/data/list/comb): show that (list A) is isomorphic to A if A is isomorphic to nat 2015-08-10 16:04:02 -07:00
Leonardo de Moura
303e9031d6 feat(library/data/encodable): add encodable subtypes 2015-08-10 09:54:48 -07:00
Leonardo de Moura
56e2e0c0a5 feat(library/data/encodable): show that (finset A) is encodable when A is encodable 2015-08-10 07:47:00 -07:00
Leonardo de Moura
70bd95d931 feat(library/data/list): show that (sort R l1 = sort R l2) when R is a decidable total order and l1 is a permutation of l2 2015-08-09 23:36:08 -07:00
Leonardo de Moura
2a22c75e52 feat(library/data/list/sort): prove that (sort R l) is strongly_sorted 2015-08-09 23:36:07 -07:00
Leonardo de Moura
5ca37dace0 fix(library/data/nat/order): fixes #786 2015-08-09 23:36:07 -07:00
Leonardo de Moura
f9b2b93f7a refactor(library/algebra/complete_lattice): add alternative definitions of complete_lattice and convertions between them 2015-08-09 20:40:07 -07:00
Jeremy Avigad
d17f72eb7c fix(library/data/set/filter): adapt to change in complete_lattice structure 2015-08-09 22:36:04 -04:00
Jeremy Avigad
b130a144c8 feat(library/data/set/filter): add filters, show they form a complete lattice 2015-08-09 22:14:25 -04:00
Jeremy Avigad
244052b413 refactor(library/data/set/*): rename setext to ext 2015-08-09 22:14:25 -04:00
Jeremy Avigad
209d7b07aa feat(library/data/set/basic): add a few theorems 2015-08-09 22:13:18 -04:00
Leonardo de Moura
276771e6ca feat(library/data/list/sort): add sort for lists 
TODO: prove the result is sorted, prove that l1 ~ l2 -> sort R l1 = sort R l2
 2015-08-09 14:23:09 -07:00
Leonardo de Moura
b4828283fa feat(library/data/list/sorted): add locally_sorted, sorted and strongly_sorted predicates for lists 2015-08-09 10:28:41 -07:00