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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
6acc166a8836cecd420c8f43c2178aeb876467f7 | d8f6c47921aa2f4f02b5272d2ed9c99f396d3858 | /lean/src/bv/basic.lean | de780f1054865cd0e19566b1eb62c804f3cdc698 | [] | no_license | hongyunnchen/jitterbug | cc94e01483cdb36f9007ab978f174e5df9a65fd2 | eb5d50ef17f78c430f9033ff18472972b3588aee | refs/heads/master | 1,670,909,198,044 | 1,599,154,934,000 | 1,599,154,934,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,680 | lean | import data.fin
import data.fintype.basic
import tactic.omega.main
/-!
# Fixed-size bitvectors
This file defines fixed-sized bitvectors following the SMT-LIB standard.
## References
* http://smtlib.cs.uiowa.edu/Theories/FixedSizeBitVectors.smt2
* http://smtlib.cs.uiowa.edu/Logics/QF_BV.smt2
-/
/--
The type of bitv... |
8c6aef20fb5bc2db9dc06e218cbe816a57f1d78e | a7eef317ddec01b9fc6cfbb876fe7ac00f205ac7 | /src/algebra/pointwise.lean | 8477da68cdeab8172f6c7913f57801d6d2285523 | [
"Apache-2.0"
] | permissive | kmill/mathlib | ea5a007b67ae4e9e18dd50d31d8aa60f650425ee | 1a419a9fea7b959317eddd556e1bb9639f4dcc05 | refs/heads/master | 1,668,578,197,719 | 1,593,629,163,000 | 1,593,629,163,000 | 276,482,939 | 0 | 0 | null | 1,593,637,960,000 | 1,593,637,959,000 | null | UTF-8 | Lean | false | false | 12,439 | lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import algebra.module
/-!
# Pointwise addition, multiplication, and scalar multiplication of sets.
This file defines `pointwise_mul`: for a type `α` with multiplic... |
28c16a779b14ee06a48fa896be2ee2d18422dd67 | 5fbbd711f9bfc21ee168f46a4be146603ece8835 | /lean/natural_number_game/advanced_addition/09.lean | 2b17fb099eeebf9ed8d58a8314ead119d5f35ca5 | [
"LicenseRef-scancode-warranty-disclaimer"
] | no_license | goedel-gang/maths | 22596f71e3fde9c088e59931f128a3b5efb73a2c | a20a6f6a8ce800427afd595c598a5ad43da1408d | refs/heads/master | 1,623,055,941,960 | 1,621,599,441,000 | 1,621,599,441,000 | 169,335,840 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 97 | lean | theorem succ_ne_zero (a : mynat) : succ a ≠ 0 :=
begin
symmetry,
exact zero_ne_succ a,
end
|
b85afa427188117ec061bc32a7b433b740e154b7 | 4aca55eba10c989f0d58647d3c2f371e7da44355 | /src/backup.lean | c7f8ef2d6deceeb0cb298d16ba723a7902ba1603 | [] | no_license | eric-wieser/l534zhan-my_project | f9fc75fb5454405e1a2fa9b56cf96c355f6f2336 | febc91e76b7b00fe2517f258ca04d27b7f35fcf3 | refs/heads/master | 1,689,218,910,420 | 1,630,439,440,000 | 1,630,439,440,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,459 | lean | /-
/-- `|{a : F // is_quad_residue a}| * 2 = |F| - 1` -/
theorem card_residues_mul_two_eq [decidable_eq F] (hp: p ≠ 2) :
fintype.card {a : F // is_quad_residue a} * 2 = q - 1 :=
by rwa [← card_units, card_units_eq_card_residues_mul_two F hp]
-/
/-
lemma residues_setcard_eq_fintype_card [decidable_eq F] :
set.card {a :... |
986fca081ba4ee4c7c2b85e518f6378d645f5e19 | b70031c8e2c5337b91d7e70f1e0c5f528f7b0e77 | /src/category_theory/abelian/non_preadditive.lean | 4b3c1c21aa4d03dabd9bd1e65034cc20196bb28d | [
"Apache-2.0"
] | permissive | molodiuc/mathlib | cae2ba3ef1601c1f42ca0b625c79b061b63fef5b | 98ebe5a6739fbe254f9ee9d401882d4388f91035 | refs/heads/master | 1,674,237,127,059 | 1,606,353,533,000 | 1,606,353,533,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 32,109 | lean | /-
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import category_theory.limits.shapes.finite_products
import category_theory.limits.shapes.kernels
import category_theory.limits.shapes.pullbacks
import category_theory.... |
876d15db27445d0a89e73fab976d429bc442e757 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/order/complete_lattice.lean | b82d56608ee027814159d8b38243f43af09f9518 | [
"Apache-2.0"
] | permissive | ramonfmir/mathlib | c5dc8b33155473fab97c38bd3aa6723dc289beaa | 14c52e990c17f5a00c0cc9e09847af16fabbed25 | refs/heads/master | 1,661,979,343,526 | 1,660,830,384,000 | 1,660,830,384,000 | 182,072,989 | 0 | 0 | null | 1,555,585,876,000 | 1,555,585,876,000 | null | UTF-8 | Lean | false | false | 55,643 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import data.bool.set
import data.nat.basic
import order.bounds
/-!
# Theory of complete lattices
## Main definitions
* `Sup` and `Inf` are the supremum and the inf... |
75b4269c2848a787532244b8d61b10f08f325f6e | a4673261e60b025e2c8c825dfa4ab9108246c32e | /src/Lean/Parser/Module.lean | af25a9f9730bab9120502485dd4b93085cac7ea5 | [
"Apache-2.0"
] | permissive | jcommelin/lean4 | c02dec0cc32c4bccab009285475f265f17d73228 | 2909313475588cc20ac0436e55548a4502050d0a | refs/heads/master | 1,674,129,550,893 | 1,606,415,348,000 | 1,606,415,348,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,551 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Sebastian Ullrich
-/
import Lean.Message
import Lean.Parser.Command
namespace Lean
namespace Parser
namespace Module
def «prelude» := parser! "prelude"
def... |
8b9bfa88216a25c067ad76ba4f5e78798816e534 | 9c1ad797ec8a5eddb37d34806c543602d9a6bf70 | /projects.lean | c680874e16e3182c80273d74f2cf6ec1fc7eef01 | [] | no_license | timjb/lean-category-theory | 816eefc3a0582c22c05f4ee1c57ed04e57c0982f | 12916cce261d08bb8740bc85e0175b75fb2a60f4 | refs/heads/master | 1,611,078,926,765 | 1,492,080,000,000 | 1,492,080,000,000 | 88,348,246 | 0 | 0 | null | 1,492,262,499,000 | 1,492,262,498,000 | null | UTF-8 | Lean | false | false | 734 | lean | -- PROJECTS
-- define Day convolution: the monoidal structure on FunctorCategory C D when D is monoidal.
-- is this known: a monoidal structure on monoidal functors from C to D when D is braided?
-- transporting structures along equivalences: e.g. given an equivalence of categories, transport a monoidal structure?
-- e... |
dc2f289889948e03f1a4bbc424289a001fc04132 | 74caf7451c921a8d5ab9c6e2b828c9d0a35aae95 | /library/init/data/list/instances.lean | ab7dcfb42fdd1d818e34b42663c31359e2ee201d | [
"Apache-2.0"
] | permissive | sakas--/lean | f37b6fad4fd4206f2891b89f0f8135f57921fc3f | 570d9052820be1d6442a5cc58ece37397f8a9e4c | refs/heads/master | 1,586,127,145,194 | 1,480,960,018,000 | 1,480,960,635,000 | 40,137,176 | 0 | 0 | null | 1,438,621,351,000 | 1,438,621,351,000 | null | UTF-8 | Lean | false | false | 792 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
prelude
import init.category.monad init.category.alternative init.data.list.basic
import init.meta.mk_dec_eq_instance
open list
universe variables u v
@[in... |
293a1148ba933b50e17e5f4193b2c5491e6787c1 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/matchApp.lean | 5b9faf42c70b1c6e02fe3df8194d0da5e9eaef26 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 328 | lean | def f (xs ys : List α) : Nat :=
match xs, ys with
| [], [] => 0
| _, [] => 1
| _, _ => 2
#check fun {α : Type} (motive : List α → List α → Type)
(h1 : Unit → motive [] [])
(h2 : (x : List α) → motive x [])
(h3 : (x x_1 : List α) → motive x x_1)
=> f.match_1 (motive := motive) [] [] h1 h2 h3
|
b1899da77dab0486356e5c493f5c98d9a8a4873f | 46125763b4dbf50619e8846a1371029346f4c3db | /src/algebra/category/Module/basic.lean | c6a83b1f52d7c3ff7b2674c477c4fac4df523d50 | [
"Apache-2.0"
] | permissive | thjread/mathlib | a9d97612cedc2c3101060737233df15abcdb9eb1 | 7cffe2520a5518bba19227a107078d83fa725ddc | refs/heads/master | 1,615,637,696,376 | 1,583,953,063,000 | 1,583,953,063,000 | 246,680,271 | 0 | 0 | Apache-2.0 | 1,583,960,875,000 | 1,583,960,875,000 | null | UTF-8 | Lean | false | false | 3,940 | lean | /-
Copyright (c) 2019 Robert A. Spencer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert A. Spencer, Markus Himmel
-/
import algebra.module
import algebra.punit_instances
import category_theory.concrete_category
import category_theory.limits.shapes.zero
import ca... |
7039a1701a1196661e12d096410a2b87dc0a73eb | 2d2554d724f667419148b06acf724e2702ada7c9 | /src/solve_theorems.lean | 03faacd4ac2d0c5a195ca5f1a99483e8b315c740 | [] | no_license | hediet/lean-linear-integer-equation-solver | 64591803a01d38dba8599c5bde3e88446a2dca28 | 1a83fa7935b4411618c4edcdee7edb5c4a6678a7 | refs/heads/master | 1,677,680,410,160 | 1,612,962,170,000 | 1,612,962,170,000 | 337,718,062 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,027 | lean | import .definitions
import data.bool
import data.int.gcd
import tactic
import .mod
import .solve
import .main
lemma divide_by_gcd'_correct (eqs eqs': Eqs)
(h1: divide_by_gcd' eqs = some eqs')
(x: list ℤ) (h2: x ∈ eqs):
(x ∈ eqs') ∧ (t eqs' ≤ t eqs) :=
begin
cases eqs,
cases eqs',
cases eqs_eqs;
unfold divide_by... |
3d87b5ff58b9b6b0c108f9b91d5f1b61161eeaed | 271e26e338b0c14544a889c31c30b39c989f2e0f | /stage0/src/Init/Lean/Meta/LevelDefEq.lean | 1e5b1157da32256affecef67747925b1bfeaed1f | [
"Apache-2.0"
] | permissive | dgorokho/lean4 | 805f99b0b60c545b64ac34ab8237a8504f89d7d4 | e949a052bad59b1c7b54a82d24d516a656487d8a | refs/heads/master | 1,607,061,363,851 | 1,578,006,086,000 | 1,578,006,086,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,792 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import Init.Lean.Meta.Basic
namespace Lean
namespace Meta
private partial def decAux? : Level → MetaM (Option Level)
| Level.zero _ => pure... |
1265e679ceeb75207e3b7a026c0ae3c312f1fbe9 | ce6917c5bacabee346655160b74a307b4a5ab620 | /src/ch4/ex0501.lean | 02b0c46a1c08bc03427668542f9312be45fae6de | [] | no_license | Ailrun/Theorem_Proving_in_Lean | ae6a23f3c54d62d401314d6a771e8ff8b4132db2 | 2eb1b5caf93c6a5a555c79e9097cf2ba5a66cf68 | refs/heads/master | 1,609,838,270,467 | 1,586,846,743,000 | 1,586,846,743,000 | 240,967,761 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 216 | lean | variable f : ℕ → ℕ
variable h : ∀ x : ℕ, f x ≤ f (x + 1)
example : f 0 ≤ f 3 :=
have f 0 ≤ f 1, from h 0,
have f 0 ≤ f 2, from le_trans this (h 1),
show f 0 ≤ f 3, from le_trans this (h 2)
|
c6ea78285cc9c79836d592326af6d37a55593fe9 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/json.lean | b504379d36475fd00781fc28dd3dc199eb08eda7 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 11,280 | lean | /-
Copyright (c) 2022 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import tactic.core
/-!
# Json serialization typeclass
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathlib4.
This ... |
e1529290b2b29e85b5d6fa03b687569abef4f6df | 976d2334b51721ddc405deb2e1754016d454286e | /src/game_files/sqrt2/sq_eq_zero1.lean | 72e929011477a926228baa8cea3f098fd06c8dac | [] | no_license | kbuzzard/lean-at-MC2020 | 11bb6ac9ec38a6caace9d5d9a1705d6794d9f477 | 1f7ca65a7ba5cc17eb49f525c02dc6b0e65d6543 | refs/heads/master | 1,668,496,422,317 | 1,594,131,838,000 | 1,594,131,838,000 | 277,877,735 | 0 | 0 | null | 1,594,142,006,000 | 1,594,142,005,000 | null | UTF-8 | Lean | false | false | 538 | lean | import tactic
import data.nat.basic
-- Level name : squares_to_zero
/-
Comment here
-/
/- Hint : title_of_the_hint
Content of the hint
-/
/- Tactic : ring
Normalizes expressions in commutative rings by applying lots of
distributivity, associativity, commutativity. Can prove equalities.
-/
example := nat.pow_two
/... |
3538667bf9ede43e9089d1c5af20598d705eb13e | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/measure_theory/lebesgue_measure_auto.lean | 5df65794b8ebd14b31158d7d7f91cfe9ebefbdd3 | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,801 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yury Kudryashov
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.measure_theory.pi
import Mathlib.PostPort
universes u_1
namespace Mathl... |
aac4aca00687ec74b1bebec01f294d51f2ae7754 | f1815407acd03d5e25cd9508eb98a28d9b42a66d | /src/helloworld.lean | 4fca867ae0ea59a0d14e33e7645422c36cacceb4 | [] | no_license | jesse-michael-han/lean-demo | 5856ea69873130a91bdc7d39e25e241bdf7c1ba9 | 4ec7af0d3933470030598cbb1c0c853792bd0b54 | refs/heads/master | 1,650,492,056,866 | 1,587,804,047,000 | 1,587,804,047,000 | 258,457,256 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,538 | lean | import tactic
import data.nat.parity
import system.io
section warm_up
variables {α β : Type} (p q : α → Prop) (r : α → β → Prop)
lemma exercise_1 : (∀ x, p x) ∧ (∀ x, q x) → ∀ x, p x ∧ q x :=
begin
intro H, intro x, refine ⟨_,_⟩,
cases H with Hp Hq, exact Hp x,
cases H with Hp Hq, exact Hq x
end
#check exerci... |
4ffc5dfa2e6a26203f5143fa41a98c1443bc24b2 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/measure_theory/measure/finite_measure_weak_convergence.lean | 0c2cc0f97382c6628d712e3ae29706f3aae8064e | [
"Apache-2.0"
] | permissive | AntoineChambert-Loir/mathlib | 64aabb896129885f12296a799818061bc90da1ff | 07be904260ab6e36a5769680b6012f03a4727134 | refs/heads/master | 1,693,187,631,771 | 1,636,719,886,000 | 1,636,719,886,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,328 | lean | /-
Copyright (c) 2021 Kalle Kytölä. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kalle Kytölä
-/
import measure_theory.measure.measure_space
/-!
# Weak convergence of (finite) measures
This file will define the topology of weak convergence of finite measures and pr... |
169fad6e8849d283b75e6924479b5cedabe945a0 | 48eee836fdb5c613d9a20741c17db44c8e12e61c | /src/algebra/theories/magma.lean | ebc83622f4ab57ddc3b4f92ebd0b1fc39500bc8a | [
"Apache-2.0"
] | permissive | fgdorais/lean-universal | 06430443a4abe51e303e602684c2977d1f5c0834 | 9259b0f7fb3aa83a9e0a7a3eaa44c262e42cc9b1 | refs/heads/master | 1,592,479,744,136 | 1,589,473,399,000 | 1,589,473,399,000 | 196,287,552 | 1 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 1,964 | lean | -- Copyright © 2019 François G. Dorais. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
import .basic
import .action
namespace algebra
signature magma (α : Type*) :=
(op : α → α → α)
namespace magma_sig
variables {α : Type*} (s : magma_sig α)
@[signature_instance]
defini... |
5d6506c331d4aa91e8775a4d5b6098a3b2d157a4 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/elab3.lean | 7d5be49ed26bb2634ef55b6413638b92b2e66be0 | [
"Apache-2.0"
] | permissive | soonhokong/lean-osx | 4a954262c780e404c1369d6c06516161d07fcb40 | 3670278342d2f4faa49d95b46d86642d7875b47c | refs/heads/master | 1,611,410,334,552 | 1,474,425,686,000 | 1,474,425,686,000 | 12,043,103 | 5 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 71 | lean | open tactic
set_option pp.all true
check trace_state >> trace_state
|
3acc91d6ee024dab48345efda0727bdf3d772940 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/set/sups.lean | a03506695192e237e5acc02299bea379f2c5863f | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 9,790 | lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import data.set.n_ary
import order.upper_lower.basic
/-!
# Set family operations
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresp... |
677df19251c5e5a95ad2353d16328b522611d92a | 54d7e71c3616d331b2ec3845d31deb08f3ff1dea | /library/init/meta/transfer.lean | 3d6ca447db4a65b1d9965bc284ba55cfcd3b0be8 | [
"Apache-2.0"
] | permissive | pachugupta/lean | 6f3305c4292288311cc4ab4550060b17d49ffb1d | 0d02136a09ac4cf27b5c88361750e38e1f485a1a | refs/heads/master | 1,611,110,653,606 | 1,493,130,117,000 | 1,493,167,649,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,598 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl (CMU)
-/
prelude
import init.meta.tactic init.meta.match_tactic init.relator init.meta.mk_dec_eq_instance
import init.data.list.instances
namespace transfer
open tactic ... |
e4654c2cc7407c557f4b36e4243c1d876715a065 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/group_theory/congruence.lean | 857995ec743300441fb90e1d20b4a2843cd50b2c | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 52,791 | lean | /-
Copyright (c) 2019 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
import algebra.group.prod
import algebra.hom.equiv.basic
import data.setoid.basic
import group_theory.submonoid.operations
/-!
# Congruence relations
> THIS F... |
319413b5fd56b6c2852b2b2c4b514852219cb7b7 | 9028d228ac200bbefe3a711342514dd4e4458bff | /src/data/nat/multiplicity.lean | 826c15136d5ee0d7a2a2165cefa705ed09a49048 | [
"Apache-2.0"
] | permissive | mcncm/mathlib | 8d25099344d9d2bee62822cb9ed43aa3e09fa05e | fde3d78cadeec5ef827b16ae55664ef115e66f57 | refs/heads/master | 1,672,743,316,277 | 1,602,618,514,000 | 1,602,618,514,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,464 | lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import data.nat.choose.dvd
import ring_theory.multiplicity
import data.nat.modeq
import algebra.gcd_monoid
import data.finset.intervals
/-!
# Natural number multiplicit... |
3d0ae448e6081d28e717de6115b08de4e95d5035 | 48eee836fdb5c613d9a20741c17db44c8e12e61c | /src/universal/compactness.lean | 2b934f3abede0223953ed03f75d0f2ab80c4feb4 | [
"Apache-2.0"
] | permissive | fgdorais/lean-universal | 06430443a4abe51e303e602684c2977d1f5c0834 | 9259b0f7fb3aa83a9e0a7a3eaa44c262e42cc9b1 | refs/heads/master | 1,592,479,744,136 | 1,589,473,399,000 | 1,589,473,399,000 | 196,287,552 | 1 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 3,629 | lean | import .basic
import .model
import .proof
namespace universal
variables {τ : Type} {σ : Type*} {sig : signature τ σ} {ι : Type} {ax : ι → identity sig}
namespace proof
variables {ι' : Type} {ax' : ι' → identity sig} (ht : Π (i : ι), proof ax' (ax i).lhs (ax i).rhs)
definition transfer {dom} : Π {cod} {t₁ t₂ : term s... |
855ab4e92dbe1d75dd9a2d935e654891b8cd388d | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/matrix/basis.lean | 276ed52bb3a49f47c99c715b3b65fe0d74a95e5d | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 5,484 | lean | /-
Copyright (c) 2020 Jalex Stark. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jalex Stark, Scott Morrison, Eric Wieser, Oliver Nash
-/
import data.matrix.basic
import linear_algebra.matrix.trace
/-!
# Matrices with a single non-zero element.
> THIS FILE IS SYNCHR... |
800912adbd7a9c96ea26e8b95becef2f77420397 | 097294e9b80f0d9893ac160b9c7219aa135b51b9 | /instructor/predicate_logic/intro_and_elim_rules/implies.lean | 233a882f1a52efdd887651ea2d4a00613f3c58e4 | [] | no_license | AbigailCastro17/CS2102-Discrete-Math | cf296251be9418ce90206f5e66bde9163e21abf9 | d741e4d2d6a9b2e0c8380e51706218b8f608cee4 | refs/heads/main | 1,682,891,087,358 | 1,621,401,341,000 | 1,621,401,341,000 | 368,749,959 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,894 | lean | /-
If you understand the introduction and elimination
rules for ∀, then you understand these rules for
proving, and using proofs of implications. Consider
an implication, P → Q. To construct a proof, pq, of
P → Q, you simply *assume* you're given an arbitrary
but specific value/proof of P and in this context you
must ... |
fd3549aa6b850d8c5fc70e9fd5320614654d67c1 | cc060cf567f81c404a13ee79bf21f2e720fa6db0 | /lean/list_examples.lean | 301d1052906508cbe8f011dac8143b53cf909832 | [
"Apache-2.0"
] | permissive | semorrison/proof | cf0a8c6957153bdb206fd5d5a762a75958a82bca | 5ee398aa239a379a431190edbb6022b1a0aa2c70 | refs/heads/master | 1,610,414,502,842 | 1,518,696,851,000 | 1,518,696,851,000 | 78,375,937 | 2 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 1,335 | lean | namespace hide
inductive list (A : Type) : Type :=
| nil {} : list A
| cons : A → list A → list A
namespace list
notation `[` l:(foldr `,` (h t, cons h t) nil) `]` := l
variable {A : Type}
notation h :: t := cons h t
definition append (s t : list A) : list A :=
list.rec_on s t (λ x l u, x::u)
notation s ++ t :=... |
ed86650bfe5de11b2423c013e2382c681938d8e5 | 9028d228ac200bbefe3a711342514dd4e4458bff | /src/geometry/euclidean/basic.lean | baabf8dc8f4dc015c992d4d8bab56d081fa5a7f7 | [
"Apache-2.0"
] | permissive | mcncm/mathlib | 8d25099344d9d2bee62822cb9ed43aa3e09fa05e | fde3d78cadeec5ef827b16ae55664ef115e66f57 | refs/heads/master | 1,672,743,316,277 | 1,602,618,514,000 | 1,602,618,514,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 48,476 | lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Joseph Myers.
-/
import analysis.normed_space.inner_product
import algebra.quadratic_discriminant
import analysis.normed_space.add_torsor
import data.matrix.notation
import linear_algebra... |
d99bd594a666c1ca879015e9d5de7088a06359b4 | 6b45072eb2b3db3ecaace2a7a0241ce81f815787 | /tools/tactic/tactic.lean | 5ef8d06e6aed93424bbe750b20190bc734d8a11d | [] | no_license | avigad/library_dev | 27b47257382667b5eb7e6476c4f5b0d685dd3ddc | 9d8ac7c7798ca550874e90fed585caad030bbfac | refs/heads/master | 1,610,452,468,791 | 1,500,712,839,000 | 1,500,713,478,000 | 69,311,142 | 1 | 0 | null | 1,474,942,903,000 | 1,474,942,902,000 | null | UTF-8 | Lean | false | false | 735 | lean | /-
Copyright (c) 2017 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
Some useful tactics.
-/
open expr tactic
namespace tactic
/- call (assert n t) with a fresh name n. -/
meta def assert_fresh (t : expr) : tactic expr :=
do n ← get_unus... |
934021461dcc2bcda5a233c56a61c96d2266f7e5 | 367134ba5a65885e863bdc4507601606690974c1 | /test/pi_simp.lean | 84e6bf92780232afef572c13d2f3fa423b065273 | [
"Apache-2.0"
] | permissive | kodyvajjha/mathlib | 9bead00e90f68269a313f45f5561766cfd8d5cad | b98af5dd79e13a38d84438b850a2e8858ec21284 | refs/heads/master | 1,624,350,366,310 | 1,615,563,062,000 | 1,615,563,062,000 | 162,666,963 | 0 | 0 | Apache-2.0 | 1,545,367,651,000 | 1,545,367,651,000 | null | UTF-8 | Lean | false | false | 648 | lean | /-
Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Yury G. Kudryashov
-/
import algebra.group.pi
/-!
Test if `simp` can use a lemma about `pi.has_one` to simplify `1` coming from `pi.group`
-/
variables {I : Type*} {f : Π i : I, T... |
0704e3760cae7ae63826a3c411c36251ce2f7e76 | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/topology/uniform_space/uniform_embedding.lean | e3d5d43229cbbe5c77bee93c59664ad22afcc9e7 | [
"Apache-2.0"
] | permissive | ayush1801/mathlib | 78949b9f789f488148142221606bf15c02b960d2 | ce164e28f262acbb3de6281b3b03660a9f744e3c | refs/heads/master | 1,692,886,907,941 | 1,635,270,866,000 | 1,635,270,866,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 22,508 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Sébastien Gouëzel, Patrick Massot
-/
import topology.uniform_space.cauchy
import topology.uniform_space.separation
import topology.dense_embedding
/-!
# Uniform embedd... |
bb909edee0f36d12e30c73540cdd8d9b12ad0c1d | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/number_theory/sum_four_squares.lean | c73110316dd857574e7a4a8ae204ea686d67be7e | [
"Apache-2.0"
] | permissive | agjftucker/mathlib | d634cd0d5256b6325e3c55bb7fb2403548371707 | 87fe50de17b00af533f72a102d0adefe4a2285e8 | refs/heads/master | 1,625,378,131,941 | 1,599,166,526,000 | 1,599,166,526,000 | 160,748,509 | 0 | 0 | Apache-2.0 | 1,544,141,789,000 | 1,544,141,789,000 | null | UTF-8 | Lean | false | false | 11,873 | lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
## Lagrange's four square theorem
The main result in this file is `sum_four_squares`,
a proof that every natural number is the sum of four square numbers.
# Implementatio... |
4afdc31863cb9b3542e3453f0402f9eacfaa9ab4 | fcf3ffa92a3847189ca669cb18b34ef6b2ec2859 | /src/world5/level7.lean | 991c65cd9b1b1ab2411cf460412175dfeee46e4d | [
"Apache-2.0"
] | permissive | nomoid/lean-proofs | 4a80a97888699dee42b092b7b959b22d9aa0c066 | b9f03a24623d1a1d111d6c2bbf53c617e2596d6a | refs/heads/master | 1,674,955,317,080 | 1,607,475,706,000 | 1,607,475,706,000 | 314,104,281 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 160 | lean | example (P Q F : Type) : (P → Q) → ((Q → F) → (P → F)) :=
begin
intro pq,
intro qf,
intro p,
apply qf,
apply pq,
exact p,
end
|
4300b716d47a1449727db2fb974f49e457b65727 | 5fbbd711f9bfc21ee168f46a4be146603ece8835 | /lean/natural_number_game/proposition/3.lean | 28146a6ab3dcac36b8b47b497991716e4c3273bd | [
"LicenseRef-scancode-warranty-disclaimer"
] | no_license | goedel-gang/maths | 22596f71e3fde9c088e59931f128a3b5efb73a2c | a20a6f6a8ce800427afd595c598a5ad43da1408d | refs/heads/master | 1,623,055,941,960 | 1,621,599,441,000 | 1,621,599,441,000 | 169,335,840 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 167 | lean | lemma maze (P Q R S T U: Prop)
(p : P)
(h : P → Q)
(i : Q → R)
(j : Q → T)
(k : S → T)
(l : T → U)
: U :=
begin
cc, -- instead of exact blah blah blah
end
|
33ca6bf83fbb6b1634b46254b893a3e6d5d8c0bb | e0b0b1648286e442507eb62344760d5cd8d13f2d | /tests/lean/rewrite.lean | 16d893a646cc70e9672673c4d7fb76725ceba7f6 | [
"Apache-2.0"
] | permissive | MULXCODE/lean4 | 743ed389e05e26e09c6a11d24607ad5a697db39b | 4675817a9e89824eca37192364cd47a4027c6437 | refs/heads/master | 1,682,231,879,857 | 1,620,423,501,000 | 1,620,423,501,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,403 | lean | axiom appendNil {α} (as : List α) : as ++ [] = as
axiom appendAssoc {α} (as bs cs : List α) : (as ++ bs) ++ cs = as ++ (bs ++ cs)
axiom reverseEq {α} (as : List α) : as.reverse.reverse = as
theorem ex1 {α} (as bs : List α) : as.reverse.reverse ++ [] ++ [] ++ bs ++ bs = as ++ (bs ++ bs) := by
rw [appendNil, appendNil... |
960927993550cc1e72241339accfaf878800f6d1 | e0f9ba56b7fedc16ef8697f6caeef5898b435143 | /src/tactic/derive_inhabited.lean | c7cd1307e78014f731d862be0a6ce63447408d44 | [
"Apache-2.0"
] | permissive | anrddh/mathlib | 6a374da53c7e3a35cb0298b0cd67824efef362b4 | a4266a01d2dcb10de19369307c986d038c7bb6a6 | refs/heads/master | 1,656,710,827,909 | 1,589,560,456,000 | 1,589,560,456,000 | 264,271,800 | 0 | 0 | Apache-2.0 | 1,589,568,062,000 | 1,589,568,061,000 | null | UTF-8 | Lean | false | false | 2,327 | lean | /-
Copyright (c) 2020 Gabriel Ebner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
-/
import logic.basic
/-!
# Derive handler for `inhabited` instances
This file introduces a derive handle to automatically generate `inhabited`
instances for structures and inductives. We also... |
9073c89dd281625105e75d69e1f41bc5085ca7cf | b7f22e51856f4989b970961f794f1c435f9b8f78 | /library/algebra/ordered_ring.lean | c349149dd4dd6d568911070b5636837857f0ed87 | [
"Apache-2.0"
] | permissive | soonhokong/lean | cb8aa01055ffe2af0fb99a16b4cda8463b882cd1 | 38607e3eb57f57f77c0ac114ad169e9e4262e24f | refs/heads/master | 1,611,187,284,081 | 1,450,766,737,000 | 1,476,122,547,000 | 11,513,992 | 2 | 0 | null | 1,401,763,102,000 | 1,374,182,235,000 | C++ | UTF-8 | Lean | false | false | 28,499 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
Here an "ordered_ring" is partially ordered ring, which is ordered with respect to both a weak
order and an associated strict order. Our numeric structures (int, rat, and... |
dbcb25c9d986b1d15f691405f4ef0fc308ecea33 | 35b83be3126daae10419b573c55e1fed009d3ae8 | /_target/deps/mathlib/algebra/order.lean | 2550e482d73a3235c98b309ad0ad2719f1adbfe4 | [] | no_license | AHassan1024/Lean_Playground | ccb25b72029d199c0d23d002db2d32a9f2689ebc | a00b004c3a2eb9e3e863c361aa2b115260472414 | refs/heads/master | 1,586,221,905,125 | 1,544,951,310,000 | 1,544,951,310,000 | 157,934,290 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,512 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
universe u
variables {α : Type u}
lemma not_le_of_lt [preorder α] {a b : α} (h : a < b) : ¬ b ≤ a :=
(le_not_le_of_lt h).right
lemma not_lt_of_le [preorder α] {a b... |
d47c9c80ce77b2cd47d7c21f69d5214065e5f55b | 5749d8999a76f3a8fddceca1f6941981e33aaa96 | /src/analysis/normed_space/finite_dimension.lean | 97d53088e2cbda6d3e5afeee8be4a2750fd52031 | [
"Apache-2.0"
] | permissive | jdsalchow/mathlib | 13ab43ef0d0515a17e550b16d09bd14b76125276 | 497e692b946d93906900bb33a51fd243e7649406 | refs/heads/master | 1,585,819,143,348 | 1,580,072,892,000 | 1,580,072,892,000 | 154,287,128 | 0 | 0 | Apache-2.0 | 1,540,281,610,000 | 1,540,281,609,000 | null | UTF-8 | Lean | false | false | 13,076 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import analysis.normed_space.operator_norm linear_algebra.finite_dimensional tactic.omega
/-!
# Finite dimensional normed spaces over complete fields
Over a ... |
b2bcb072a25d8f57d25e3d46dfa8219b49e73724 | 5df84495ec6c281df6d26411cc20aac5c941e745 | /src/formal_ml/set.lean | 6284a43824b9141429adf27df02b81716089ca25 | [
"Apache-2.0"
] | permissive | eric-wieser/formal-ml | e278df5a8df78aa3947bc8376650419e1b2b0a14 | 630011d19fdd9539c8d6493a69fe70af5d193590 | refs/heads/master | 1,681,491,589,256 | 1,612,642,743,000 | 1,612,642,743,000 | 360,114,136 | 0 | 0 | Apache-2.0 | 1,618,998,189,000 | 1,618,998,188,000 | null | UTF-8 | Lean | false | false | 12,617 | lean | /-
Copyright 2020 Google LLC
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
di... |
38414108a298384ccf4d2328016fcf9c819b619e | 47181b4ef986292573c77e09fcb116584d37ea8a | /src/valuations/bounded.lean | acc0e6c72876c8b26e96046d9c33e3df05f7797f | [
"MIT"
] | permissive | RaitoBezarius/berkovich-spaces | 87662a2bdb0ac0beed26e3338b221e3f12107b78 | 0a49f75a599bcb20333ec86b301f84411f04f7cf | refs/heads/main | 1,690,520,666,912 | 1,629,328,012,000 | 1,629,328,012,000 | 332,238,095 | 4 | 0 | MIT | 1,629,312,085,000 | 1,611,414,506,000 | Lean | UTF-8 | Lean | false | false | 5,759 | lean | import data.real.cau_seq
import algebra.big_operators.basic
import algebra.big_operators.ring
import valuations.basic
import for_mathlib.specific_limits
open is_absolute_value
open_locale classical big_operators
lemma absolute_value_units_bounded {α} [ring α] [nontrivial α]
(abv: α → ℝ) [is_absolute_value abv]
(... |
2e16aad890a490bc7a730b4e6e8f54e7880bf69d | 94e33a31faa76775069b071adea97e86e218a8ee | /src/topology/G_delta.lean | a33ee4ce59df610e9c60efa9cc998f0460624afc | [
"Apache-2.0"
] | permissive | urkud/mathlib | eab80095e1b9f1513bfb7f25b4fa82fa4fd02989 | 6379d39e6b5b279df9715f8011369a301b634e41 | refs/heads/master | 1,658,425,342,662 | 1,658,078,703,000 | 1,658,078,703,000 | 186,910,338 | 0 | 0 | Apache-2.0 | 1,568,512,083,000 | 1,557,958,709,000 | Lean | UTF-8 | Lean | false | false | 6,859 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Yury Kudryashov
-/
import topology.uniform_space.basic
import topology.separation
/-!
# `Gδ` sets
In this file we define `Gδ` sets and prove their basic propert... |
c826854572930d2d6809cf7084a1f09a173de87c | 37becf0efe4d7dede56551dfb45910cf3f9f579e | /src/ecff/euler_continued.lean | 74530b011652287ab7ddf07bd4bfc524d00362ed | [] | no_license | Pazzaz/lean-math | c66ff4ea9e99d4fbd9c3143e1a055f72a7bb936d | a61df645dcc7d91d1454129dd68833821ff02fb7 | refs/heads/master | 1,679,198,234,708 | 1,615,995,023,000 | 1,615,995,023,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 25,839 | lean | import algebra.continued_fractions
import data.real.basic
import algebra.continued_fractions.convergents_equiv
import tactic.unfold_cases
open generalized_continued_fraction as gcf
-- 1. Skriv ut theorem för \R
-- 1. använd convergents'
-- `sum_prod a_k n` = ∑_{i=1}^{n} (∏_{j=1}^{i} a_j)
def sum_prod {K : Type*... |
0dd5acd26ad8f342e38b4981cbf2f49e16b1b308 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/measure_theory/group/pointwise.lean | 86bbc5f745e233e26f9af8ac1b1d02e1298f8872 | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 1,656 | lean | /-
Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov, Alex J. Best
-/
import measure_theory.group.arithmetic
/-!
# Pointwise set operations on `measurable_set`s
In this file we prove several versions of the follo... |
9ac35aef61260f4079002527647b49043e38dfc8 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/ring_theory/algebraic.lean | 31e228c7132542522e9b1ad42af9c992ff5977cb | [
"Apache-2.0"
] | permissive | Lix0120/mathlib | 0020745240315ed0e517cbf32e738d8f9811dd80 | e14c37827456fc6707f31b4d1d16f1f3a3205e91 | refs/heads/master | 1,673,102,855,024 | 1,604,151,044,000 | 1,604,151,044,000 | 308,930,245 | 0 | 0 | Apache-2.0 | 1,604,164,710,000 | 1,604,163,547,000 | null | UTF-8 | Lean | false | false | 4,699 | lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import linear_algebra.finite_dimensional
import ring_theory.integral_closure
import data.polynomial.integral_normalization
/-!
# Algebraic elements and algebraic ex... |
5c776e5ff679da4f2e8757a072051f69e800bc31 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/category_theory/fin_category.lean | da22a25bbb1bd0ff3718ee4ae71cb1095d805e4c | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 4,183 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import data.fintype.basic
import category_theory.discrete_category
import category_theory.opposites
/-!
# Finite categories
A category is finite in this sense if it... |
8bae974c071c428ab447ebd9a5b53319377afd5e | c777c32c8e484e195053731103c5e52af26a25d1 | /archive/miu_language/decision_suf.lean | 257bea77baa2e8028183d563f5dbe8759d35d920 | [
"Apache-2.0"
] | permissive | kbuzzard/mathlib | 2ff9e85dfe2a46f4b291927f983afec17e946eb8 | 58537299e922f9c77df76cb613910914a479c1f7 | refs/heads/master | 1,685,313,702,744 | 1,683,974,212,000 | 1,683,974,212,000 | 128,185,277 | 1 | 0 | null | 1,522,920,600,000 | 1,522,920,600,000 | null | UTF-8 | Lean | false | false | 14,518 | lean | /-
Copyright (c) 2020 Gihan Marasingha. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gihan Marasingha
-/
import .decision_nec
import tactic.linarith
/-!
# Decision procedure - sufficient condition and decidability
We give a sufficient condition for a string to be d... |
0a1715d8be3daa9a4a57488c0ec70e946b4db5f5 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/analysis/normed_space/spectrum.lean | 10154a20b4e3688f29a61f00a4939ea006d72db6 | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 21,546 | lean | /-
Copyright (c) 2021 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import algebra.algebra.spectrum
import analysis.special_functions.pow
import analysis.special_functions.exponential
import analysis.complex.liouville
import analysis.an... |
0d83b9232d3246fb7c8f762144c603451d22634d | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/model_theory/syntax.lean | afa5ab848bd720285c5f0213687c9c06bedbe86b | [
"Apache-2.0"
] | permissive | ramonfmir/mathlib | c5dc8b33155473fab97c38bd3aa6723dc289beaa | 14c52e990c17f5a00c0cc9e09847af16fabbed25 | refs/heads/master | 1,661,979,343,526 | 1,660,830,384,000 | 1,660,830,384,000 | 182,072,989 | 0 | 0 | null | 1,555,585,876,000 | 1,555,585,876,000 | null | UTF-8 | Lean | false | false | 38,622 | lean | /-
Copyright (c) 2021 Aaron Anderson, Jesse Michael Han, Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson, Jesse Michael Han, Floris van Doorn
-/
import data.list.prod_sigma
import data.set.prod
import logic.equiv.fin
import model_theory.... |
861164cd9974fa2548d462317e6954fa7fe1bc48 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /src/Lean/Data/Lsp/Diagnostics.lean | 2f84efe0f1bdd1e5f8714dade74e87ee5ca34197 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | cipher1024/lean4 | 6e1f98bb58e7a92b28f5364eb38a14c8d0aae393 | 69114d3b50806264ef35b57394391c3e738a9822 | refs/heads/master | 1,642,227,983,603 | 1,642,011,696,000 | 1,642,011,696,000 | 228,607,691 | 0 | 0 | Apache-2.0 | 1,576,584,269,000 | 1,576,584,268,000 | null | UTF-8 | Lean | false | false | 3,016 | lean | /-
Copyright (c) 2020 Marc Huisinga. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Marc Huisinga, Wojciech Nawrocki
-/
import Lean.Data.Json
import Lean.Data.Lsp.Basic
import Lean.Data.Lsp.Utf16
import Lean.Message
/-! Definitions and functionality for emitting dia... |
6e2a5f432ae9810ed1652232efe8b48e2370f77f | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /archive/100-theorems-list/57_herons_formula.lean | a0fbf10fc921198818f4da5ef748d417370e7ee0 | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 2,831 | lean | /-
Copyright (c) 2021 Matt Kempster. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Matt Kempster
-/
import geometry.euclidean.triangle
import analysis.special_functions.trigonometric
/-!
# Freek № 57: Heron's Formula
This file proves Theorem 57 from the [100 Theorem... |
adba333ee753e4ec96f724fbec8af85cef1a14a3 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/measure_theory/function/simple_func_dense.lean | 43fbd7037f1a0fca605ae4a4597d93365da99d11 | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 7,466 | lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Yury Kudryashov, Heather Macbeth
-/
import measure_theory.integral.mean_inequalities
import topology.continuous_function.compact
import topology.metric_space.metrizable
... |
e7d8bec621057d0e522b960bd739acc942ebb8f5 | e0f9ba56b7fedc16ef8697f6caeef5898b435143 | /src/control/traversable/lemmas.lean | 782f17bb9e6b5b4d529f4e5d1ca8623d98b79d0d | [
"Apache-2.0"
] | permissive | anrddh/mathlib | 6a374da53c7e3a35cb0298b0cd67824efef362b4 | a4266a01d2dcb10de19369307c986d038c7bb6a6 | refs/heads/master | 1,656,710,827,909 | 1,589,560,456,000 | 1,589,560,456,000 | 264,271,800 | 0 | 0 | Apache-2.0 | 1,589,568,062,000 | 1,589,568,061,000 | null | UTF-8 | Lean | false | false | 3,655 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Simon Hudon
Lemmas about traversing collections.
Inspired by:
The Essence of the Iterator Pattern
Jeremy Gibbons and Bruno César dos Santos Oliveira
In Journal of Functional... |
8c2b1ca081512d9906742f38279bb69ab0c10d6b | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /doc/BoolExpr.lean | ae9d02cbd4b994623fb018dc1a3c6f51308db282 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 3,605 | lean | open Std
open Lean
inductive BoolExpr where
| var (name : String)
| val (b : Bool)
| or (p q : BoolExpr)
| not (p : BoolExpr)
deriving Repr, BEq, DecidableEq
def BoolExpr.isValue : BoolExpr → Bool
| val _ => true
| _ => false
instance : Inhabited BoolExpr where
default := BoolExpr.val false
nam... |
703feb3310b4ca8d486097d8d9d9ee75a6d2d837 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /src/Lean/Compiler/IR/LiveVars.lean | 1ef00ff1169469a8496750cc591d107b701d89fb | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | cipher1024/lean4 | 6e1f98bb58e7a92b28f5364eb38a14c8d0aae393 | 69114d3b50806264ef35b57394391c3e738a9822 | refs/heads/master | 1,642,227,983,603 | 1,642,011,696,000 | 1,642,011,696,000 | 228,607,691 | 0 | 0 | Apache-2.0 | 1,576,584,269,000 | 1,576,584,268,000 | null | UTF-8 | Lean | false | false | 6,963 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Compiler.IR.Basic
import Lean.Compiler.IR.FreeVars
namespace Lean.IR
/- Remark: in the paper "Counting Immutable Beans" the concepts of
fre... |
709614e1b451e14e5eb1f52b8c47e240537a3041 | 500f65bb93c499cd35c3254d894d762208cae042 | /src/data/mv_polynomial.lean | d8b8fd44bf88fdfe4a570aa5189a30309509d48b | [
"Apache-2.0"
] | permissive | PatrickMassot/mathlib | c39dc0ff18bbde42f1c93a1642f6e429adad538c | 45df75b3c9da159fe3192fa7f769dfbec0bd6bda | refs/heads/master | 1,623,168,646,390 | 1,566,940,765,000 | 1,566,940,765,000 | 115,220,590 | 0 | 1 | null | 1,514,061,524,000 | 1,514,061,524,000 | null | UTF-8 | Lean | false | false | 42,143 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
Multivariate Polynomial
-/
import algebra.ring
import data.finsupp data.polynomial data.equiv.algebra
open set function finsupp lattice... |
85fdbc0744675c7017efa903506b16419ded11c1 | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /tests/lean/run/autoboundIssues.lean | 1e88b98747dcb62ab44b0a4e7de0722808f2ac27 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | EdAyers/lean4 | 57ac632d6b0789cb91fab2170e8c9e40441221bd | 37ba0df5841bde51dbc2329da81ac23d4f6a4de4 | refs/heads/master | 1,676,463,245,298 | 1,660,619,433,000 | 1,660,619,433,000 | 183,433,437 | 1 | 0 | Apache-2.0 | 1,657,612,672,000 | 1,556,196,574,000 | Lean | UTF-8 | Lean | false | false | 246 | lean | example : n.succ = 1 → n = 0 := by
intros h; injection h; assumption
example (h : n.succ = 1) : n = 0 := by
injection h; assumption
opaque T : Type
opaque T.Pred : T → T → Prop
example {ρ} (hρ : ρ.Pred σ) : T.Pred ρ ρ := sorry
|
5631bb7fe0cecaed1ee4f3d8706b69bf9625edaf | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/field_theory/fixed.lean | 38726f7a0e04ac91255a922066bafb2e2913993a | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 14,456 | lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import algebra.polynomial.group_ring_action
import field_theory.normal
import field_theory.separable
import field_theory.tower
/-!
# Fixed field under a group action.
This i... |
b1699a5fdde4b961717e440219d5978a1e56fb9e | a047a4718edfa935d17231e9e6ecec8c7b701e05 | /src/category_theory/limits/shapes/binary_products.lean | 1fe884d892a7dcb72f5208822e5d949b5181fc82 | [
"Apache-2.0"
] | permissive | utensil-contrib/mathlib | bae0c9fafe5e2bdb516efc89d6f8c1502ecc9767 | b91909e77e219098a2f8cc031f89d595fe274bd2 | refs/heads/master | 1,668,048,976,965 | 1,592,442,701,000 | 1,592,442,701,000 | 273,197,855 | 0 | 0 | null | 1,592,472,812,000 | 1,592,472,811,000 | null | UTF-8 | Lean | false | false | 24,302 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Bhavik Mehta
-/
import category_theory.limits.shapes.terminal
/-!
# Binary (co)products
We define a category `walking_pair`, which is the index category
for a binary ... |
06f676719a300169a50d4f733345572a62f64137 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/bug6.lean | 479b942bd3f7dc6490ed3cea0c44a3414910b641 | [
"Apache-2.0"
] | permissive | leanprover-community/lean | 12b87f69d92e614daea8bcc9d4de9a9ace089d0e | cce7990ea86a78bdb383e38ed7f9b5ba93c60ce0 | refs/heads/master | 1,687,508,156,644 | 1,684,951,104,000 | 1,684,951,104,000 | 169,960,991 | 457 | 107 | Apache-2.0 | 1,686,744,372,000 | 1,549,790,268,000 | C++ | UTF-8 | Lean | false | false | 314 | lean | section
variable {A : Type}
theorem T {a b : A} (H : a = b) : b = a
:= symm H
variables x y : A
variable H : x = y
#check T H
#check T
end
section
variable {A : Type}
theorem T2 ⦃a b : A⦄ (H : a = b) : b = a
:= symm H
variables x y : A
variable H : x = y
#check T2 H
#check T2
end
|
85fc2ce85130192c09ded1e4d2ec78c718b3638d | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/empty_set_inside_quotations.lean | 915ac13a76b79459ab3732b167034c08f8d41578 | [
"Apache-2.0"
] | permissive | leanprover-community/lean | 12b87f69d92e614daea8bcc9d4de9a9ace089d0e | cce7990ea86a78bdb383e38ed7f9b5ba93c60ce0 | refs/heads/master | 1,687,508,156,644 | 1,684,951,104,000 | 1,684,951,104,000 | 169,960,991 | 457 | 107 | Apache-2.0 | 1,686,744,372,000 | 1,549,790,268,000 | C++ | UTF-8 | Lean | false | false | 480 | lean | instance {α} : has_union (set α) := ⟨λ s t, {a | a ∈ s ∨ a ∈ t}⟩
constant union_is_assoc {α} : is_associative (set α) (∪)
attribute [instance] union_is_assoc
#check ({} : set nat)
open tactic expr
meta def is_assoc_bin_app : expr → tactic (expr × expr)
| (app (app op a1) a2) := do h ← to_expr ``(is_associative.assoc... |
2382e98f1b36d314f73b20e8ebb6765147f4ea22 | 5121e95053e1e1895a377da05d0e2744fce6a5a9 | /src/sr.lean | 52ff1a56bf64183bbaba42683ac71ac3a5a295fe | [] | no_license | miguelraz/special_relativity | 4c9426202493c8c930dc3b8b56d05fa44c915e1b | c918f2a919a0c518d6a3bd2e5e2fa1a4f0307088 | refs/heads/master | 1,668,480,638,260 | 1,594,619,371,000 | 1,594,619,371,000 | 279,223,829 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,495 | lean | import data.real.basic tactic
noncomputable theory -- v4abs does not need to be computable, don't care about it.
local notation `⟨╯°□°⟩╯︵┻━┻` := sorry
structure v₄ : Type := (x y z t : ℝ)
#check (⟨ 0, 0, 0, 1⟩ : v₄)
def v₄abs (v : v₄ ) : ℝ := real.sqrt(v.x^2 + v.y^2 + v.z^2 + v.t^2)
notation `|`x`|` := v₄abs x... |
09ccdbf0af36be5f3d26b1ac76a015d56f43c6ce | 4d7079ae603c07560e99d1ce35876f769cbb3e24 | /src/monotonicity.lean | 6c58f86abf8d01baf27608a7a8459d78a58b765f | [] | no_license | chasenorman/Formalized-Voting | 72493a08aa09d98d0fb589731b842e2d08c991d0 | de04e630b83525b042db166670ba97f9952b5691 | refs/heads/main | 1,687,282,160,284 | 1,627,155,031,000 | 1,627,155,031,000 | 370,472,025 | 13 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,819 | lean | import main
import split_cycle
import algebra.linear_ordered_comm_group_with_zero
open_locale classical
variables {V X : Type}
def simple_lift : Prof V X → Prof V X → X → Prop :=
λ P' P x, (∀ (a ≠ x) (b ≠ x) i, P i a b ↔ P' i a b)
∧ ∀ a i, ((P i x a → P' i x a) ∧ (P' i a x → P i a x))
def monotonicity (F ... |
419bf26a8cb2e2c6ef2295fb5365a8ed42a93428 | 8cb37a089cdb4af3af9d8bf1002b417e407a8e9e | /library/init/data/list/lemmas.lean | 406718c0e4eb99a9e89a68037e9cd1068daad9d4 | [
"Apache-2.0"
] | permissive | kbuzzard/lean | ae3c3db4bb462d750dbf7419b28bafb3ec983ef7 | ed1788fd674bb8991acffc8fca585ec746711928 | refs/heads/master | 1,620,983,366,617 | 1,618,937,600,000 | 1,618,937,600,000 | 359,886,396 | 1 | 0 | Apache-2.0 | 1,618,936,987,000 | 1,618,936,987,000 | null | UTF-8 | Lean | false | false | 10,525 | lean | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn
-/
prelude
import init.data.list.basic init.function init.meta init.data.nat.lemmas
import init.meta.interactive i... |
ed8d91fddfeccf17e665046243e8bfb132845bf3 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/order/preorder_hom.lean | 6719c3fc0cf66181a73a74bc8b935a7a669b3cf3 | [
"Apache-2.0"
] | permissive | Lix0120/mathlib | 0020745240315ed0e517cbf32e738d8f9811dd80 | e14c37827456fc6707f31b4d1d16f1f3a3205e91 | refs/heads/master | 1,673,102,855,024 | 1,604,151,044,000 | 1,604,151,044,000 | 308,930,245 | 0 | 0 | Apache-2.0 | 1,604,164,710,000 | 1,604,163,547,000 | null | UTF-8 | Lean | false | false | 5,483 | lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
# Preorder homomorphisms
Bundled monotone functions, `x ≤ y → f x ≤ f y`.
-/
import order.basic
import order.bounded_lattice
import order.complete_lattice
import tact... |
5f95ff59c3202d77b46eedc15f438ff1756de0a7 | 947b78d97130d56365ae2ec264df196ce769371a | /src/Lean/Elab/ResolveName.lean | 856d935fcb2e3929cbcb224ab7dc25317f35ab28 | [
"Apache-2.0"
] | permissive | shyamalschandra/lean4 | 27044812be8698f0c79147615b1d5090b9f4b037 | 6e7a883b21eaf62831e8111b251dc9b18f40e604 | refs/heads/master | 1,671,417,126,371 | 1,601,859,995,000 | 1,601,860,020,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,269 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Sebastian Ullrich
-/
import Lean.Data.OpenDecl
import Lean.Hygiene
import Lean.Modifiers
import Lean.Elab.Alias
namespace Lean
namespace Elab
/- Global name... |
bfa4e55ecc45ef62cf0fd38196192b790a08323e | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/geometry/manifold/whitney_embedding.lean | 945d74a4860eeefbd8ad544e0c993aee3403e0ab | [
"Apache-2.0"
] | permissive | waynemunro/mathlib | e3fd4ff49f4cb43d4a8ded59d17be407bc5ee552 | 065a70810b5480d584033f7bbf8e0409480c2118 | refs/heads/master | 1,693,417,182,397 | 1,634,644,781,000 | 1,634,644,781,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,161 | lean | /-
Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import geometry.manifold.partition_of_unity
/-!
# Whitney embedding theorem
In this file we prove a version of the Whitney embedding theorem: for any compac... |
bed32ed189593daa47f4bcdbeb0b1fe3ef01fa3d | f5f7e6fae601a5fe3cac7cc3ed353ed781d62419 | /src/linear_algebra/determinant.lean | 465e36daf5c81a16c0ced97e2fdf9f1b43c513e5 | [
"Apache-2.0"
] | permissive | EdAyers/mathlib | 9ecfb2f14bd6caad748b64c9c131befbff0fb4e0 | ca5d4c1f16f9c451cf7170b10105d0051db79e1b | refs/heads/master | 1,626,189,395,845 | 1,555,284,396,000 | 1,555,284,396,000 | 144,004,030 | 0 | 0 | Apache-2.0 | 1,533,727,664,000 | 1,533,727,663,000 | null | UTF-8 | Lean | false | false | 5,516 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Chris Hughes
-/
import data.matrix
import group_theory.subgroup group_theory.perm.sign
universes u v
open equiv equiv.perm finset function
namespace matrix
variables {n : Type... |
57de94ebdce1ab23eefd8de135feca6e338f4519 | d7189ea2ef694124821b033e533f18905b5e87ef | /galois/word.lean | a711485d58c080716a9fe29a986a3b57bdee7c73 | [
"Apache-2.0"
] | permissive | digama0/lean-protocol-support | eaa7e6f8b8e0d5bbfff1f7f52bfb79a3b11b0f59 | cabfa3abedbdd6fdca6e2da6fbbf91a13ed48dda | refs/heads/master | 1,625,421,450,627 | 1,506,035,462,000 | 1,506,035,462,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,891 | lean | /- This defines a simple type for bytes. -/
import data.bitvec
-- A byte is a 8-bit bitvecotr
definition byte := bitvec 8
instance : has_zero byte := begin unfold byte, apply_instance end
instance : has_one byte := begin unfold byte, apply_instance end
instance : has_add byte := begin unfold byte, apply_instance en... |
f451ec5d14e4a6ffae1cde63443db2cd704f4e4d | d1a52c3f208fa42c41df8278c3d280f075eb020c | /src/Lean/Util/OccursCheck.lean | 203d26b9ce2af0b65f2b14e6da5c35c9fde244a5 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | cipher1024/lean4 | 6e1f98bb58e7a92b28f5364eb38a14c8d0aae393 | 69114d3b50806264ef35b57394391c3e738a9822 | refs/heads/master | 1,642,227,983,603 | 1,642,011,696,000 | 1,642,011,696,000 | 228,607,691 | 0 | 0 | Apache-2.0 | 1,576,584,269,000 | 1,576,584,268,000 | null | UTF-8 | Lean | false | false | 1,545 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.MetavarContext
namespace Lean
/--
Return true if `e` does **not** contain `mvarId` directly or indirectly
This function considers assigmen... |
e75c7dbc8129ba59211ab079d3c632e4c4caa91e | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/analysis/convex/exposed.lean | b451f90c60dac6e56cc07ef44ab83ad36894cb2f | [
"Apache-2.0"
] | permissive | stjordanis/mathlib | 51e286d19140e3788ef2c470bc7b953e4991f0c9 | 2568d41bca08f5d6bf39d915434c8447e21f42ee | refs/heads/master | 1,631,748,053,501 | 1,627,938,886,000 | 1,627,938,886,000 | 228,728,358 | 0 | 0 | Apache-2.0 | 1,576,630,588,000 | 1,576,630,587,000 | null | UTF-8 | Lean | false | false | 8,924 | lean | /-
Copyright (c) 2021 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
import analysis.convex.extreme
import analysis.normed_space.basic
/-!
# Exposed sets
This file defines exposed sets and exposed points for s... |
dc1cec7f7376e2b335b08c66c947590a0836f6e9 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/extra/rec.lean | e9b3aaa014cdf22251e5ac435729f7fcea7361b0 | [
"Apache-2.0"
] | permissive | leanprover-community/lean | 12b87f69d92e614daea8bcc9d4de9a9ace089d0e | cce7990ea86a78bdb383e38ed7f9b5ba93c60ce0 | refs/heads/master | 1,687,508,156,644 | 1,684,951,104,000 | 1,684,951,104,000 | 169,960,991 | 457 | 107 | Apache-2.0 | 1,686,744,372,000 | 1,549,790,268,000 | C++ | UTF-8 | Lean | false | false | 1,449 | lean | import data.examples.vector
open nat vector
definition fib : nat → nat,
fib 0 := 1,
fib 1 := 1,
fib (a+2) := (fib a ↓ lt.step (lt.base a)) + (fib (a+1) ↓ lt.base (a+1))
[wf] lt.wf
definition gcd : nat → nat → nat,
gcd 0 x := x,
gcd x 0 := x,
gcd (succ x) (succ y) := if y ≤ x
... |
1ddc5ab35004bc0fe773e527dc629dca20a10890 | 367134ba5a65885e863bdc4507601606690974c1 | /src/category_theory/limits/shapes/finite_products.lean | 7c6b9f6cfb31ae94ddcee81df1984235571f4bb0 | [
"Apache-2.0"
] | permissive | kodyvajjha/mathlib | 9bead00e90f68269a313f45f5561766cfd8d5cad | b98af5dd79e13a38d84438b850a2e8858ec21284 | refs/heads/master | 1,624,350,366,310 | 1,615,563,062,000 | 1,615,563,062,000 | 162,666,963 | 0 | 0 | Apache-2.0 | 1,545,367,651,000 | 1,545,367,651,000 | null | UTF-8 | Lean | false | false | 2,514 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.limits.shapes.finite_limits
import category_theory.limits.shapes.binary_products
import category_theory.limits.shapes.terminal
universes v u
... |
9b479a79dc2b7d55c8ff8cff0429b883295cf956 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/data/fintype/basic.lean | 33a5f9fad2d7367d75f8160916c12c1e29ff6a48 | [
"Apache-2.0"
] | permissive | urkud/mathlib | eab80095e1b9f1513bfb7f25b4fa82fa4fd02989 | 6379d39e6b5b279df9715f8011369a301b634e41 | refs/heads/master | 1,658,425,342,662 | 1,658,078,703,000 | 1,658,078,703,000 | 186,910,338 | 0 | 0 | Apache-2.0 | 1,568,512,083,000 | 1,557,958,709,000 | Lean | UTF-8 | Lean | false | false | 97,453 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import data.array.lemmas
import data.finset.fin
import data.finset.option
import data.finset.pi
import data.finset.powerset
import data.finset.prod
import data.finset... |
67bce0da61833edd59e33d1ecea7ad0ce1d7c89d | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/sites/sieves.lean | 0b439ab41467ac4d9b49169f8f3ef7ec9c26f0c6 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 25,158 | lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, E. W. Ayers
-/
import order.complete_lattice
import category_theory.over
import category_theory.yoneda
import category_theory.limits.shapes.pullbacks
import data.set.latti... |
6caaeff1ad51c07f139f5660cf1cd825e7b337de | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/tactic/lint/type_classes.lean | 275255a46aa3619624d258dc396ef1e959bdf7e5 | [
"Apache-2.0"
] | permissive | agjftucker/mathlib | d634cd0d5256b6325e3c55bb7fb2403548371707 | 87fe50de17b00af533f72a102d0adefe4a2285e8 | refs/heads/master | 1,625,378,131,941 | 1,599,166,526,000 | 1,599,166,526,000 | 160,748,509 | 0 | 0 | Apache-2.0 | 1,544,141,789,000 | 1,544,141,789,000 | null | UTF-8 | Lean | false | false | 16,981 | lean | /-
Copyright (c) 2020 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Robert Y. Lewis, Gabriel Ebner
-/
import tactic.lint.basic
/-!
# Linters about type classes
This file defines several linters checking the correct usage of type c... |
31d6267eb8e22a1bc08b345fb8cf74a3b800bdf1 | dd4e652c749fea9ac77e404005cb3470e5f75469 | /src/array2.lean | 06e1f17dd10caaa345be91fa6e35e8d311222d6b | [] | no_license | skbaek/cvx | e32822ad5943541539966a37dee162b0a5495f55 | c50c790c9116f9fac8dfe742903a62bdd7292c15 | refs/heads/master | 1,623,803,010,339 | 1,618,058,958,000 | 1,618,058,958,000 | 176,293,135 | 3 | 2 | null | null | null | null | UTF-8 | Lean | false | false | 1,521 | lean | import data.rat .string .array .vector
variables {α β : Type}
variables {k m n : nat}
open nat tactic
def array₂ (m n : nat) (α : Type) : Type := array m (array n α)
namespace array₂
def mk (m n : nat) (a : α) : array₂ m n α :=
mk_array m (mk_array n a)
def read : array₂ m n α → fin m → fin n → α
| A i j := arr... |
660b7e84c9e30fb052104938d44ca9c5c9d46ecd | 122543640bfbfedbcee1318bfdbd466ead2716a7 | /src/p1.lean | ba8384d760364b72a35f88ed6bd5cc6b63ba595c | [] | no_license | jsm28/bmo2-2020-lean | f038489093312c97b9cae3cdb9410b2683ccb11f | ff87ce51ed080d462e63c5549d5f2b377ad83204 | refs/heads/master | 1,692,783,059,184 | 1,689,807,657,000 | 1,689,807,657,000 | 239,362,030 | 9 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,096 | lean | -- BMO2 2020 problem 1.
-- Choices made for formalization: the original problem does not
-- specify a type for the terms of the sequence; we choose ℤ. We also
-- index the sequence starting at 0 rather than at 1 as in the
-- original problem.
import data.int.parity
import tactic.basic
import tactic.linarith
import t... |
f8676c5466c526123d6aaff5e0b528f07bcefcf4 | 19e65f097e49ef249bf10eb0d5cc0075bc4216a2 | /src/week08.lean | 917b1285d05e3c4fac70fe02bfac12c8fd759b70 | [] | no_license | UVM-M52/week-8-fgdorais | 6eccbcf373d9a872949d37e434e18b082cf6ae48 | 251579081a03fadedc1606bcda8004cabf217ac3 | refs/heads/master | 1,613,424,257,678 | 1,583,335,096,000 | 1,583,335,096,000 | 244,933,167 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,268 | lean | -- Math 52: Week 8
import .utils
open classical
definition is_even (n : ℤ) : Prop := ∃ (k : ℤ), n = 2 * k
definition is_odd (n : ℤ) : Prop := ∃ (k : ℤ), n = 2 * k + 1
-- We will prove these two basic facts later in the course.
axiom is_not_even_iff_is_odd (n : ℤ) : ¬ is_even n ↔ is_odd n
axiom is_not_odd_iff_is_eve... |
231aaccfb5f5dca5ad5bdcbb61af1feb9521feeb | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/geometry/manifold/instances/sphere.lean | f63a5beffe4c52451fce10f33cb5c360804cebe5 | [
"Apache-2.0"
] | permissive | ramonfmir/mathlib | c5dc8b33155473fab97c38bd3aa6723dc289beaa | 14c52e990c17f5a00c0cc9e09847af16fabbed25 | refs/heads/master | 1,661,979,343,526 | 1,660,830,384,000 | 1,660,830,384,000 | 182,072,989 | 0 | 0 | null | 1,555,585,876,000 | 1,555,585,876,000 | null | UTF-8 | Lean | false | false | 20,897 | lean | /-
Copyright (c) 2021 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
import analysis.complex.circle
import analysis.normed_space.ball_action
import analysis.inner_product_space.calculus
import analysis.inner_product_space.pi_L2
impor... |
fb1d392b1cbbb09542b3f3b420f1d8d6cdf2d11e | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/category_theory/adjunction/over.lean | 048eb4e5ac321d315c8e80a5225561d9dde3dc01 | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 1,626 | lean | /-
Copyright (c) 2021 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import category_theory.limits.shapes.binary_products
import category_theory.monad.products
import category_theory.over
/-!
# Adjunctions related to the over category
Co... |
2f7c9bba64b0b98ec2b1606248c0508d84df7cd8 | e514e8b939af519a1d5e9b30a850769d058df4e9 | /src/tactic/rewrite_search/core/debug.lean | 0b0a8f394ff59ad680393670e8620ff202ce59fd | [] | no_license | semorrison/lean-rewrite-search | dca317c5a52e170fb6ffc87c5ab767afb5e3e51a | e804b8f2753366b8957be839908230ee73f9e89f | refs/heads/master | 1,624,051,754,485 | 1,614,160,817,000 | 1,614,160,817,000 | 162,660,605 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 2,401 | lean | import .types
namespace tactic.rewrite_search
namespace search_state
variables {α β γ δ : Type} (g : search_state α β γ δ)
meta def trace_tactic {ε : Type} [has_to_tactic_format ε] (fn : tactic ε) : tactic unit :=
if g.conf.trace then do ev ← fn, tactic.trace ev else tactic.skip
meta def trace {ε : Type} [has_to_... |
7acb0ffc93f9dc9ca081ffdddf55bdbd8774d993 | 5ae26df177f810c5006841e9c73dc56e01b978d7 | /docs/tutorial/category_theory/calculating_colimits_in_Top.lean | f8fa88aa7150783212defdf65143b7904c25888b | [
"Apache-2.0"
] | permissive | ChrisHughes24/mathlib | 98322577c460bc6b1fe5c21f42ce33ad1c3e5558 | a2a867e827c2a6702beb9efc2b9282bd801d5f9a | refs/heads/master | 1,583,848,251,477 | 1,565,164,247,000 | 1,565,164,247,000 | 129,409,993 | 0 | 1 | Apache-2.0 | 1,565,164,817,000 | 1,523,628,059,000 | Lean | UTF-8 | Lean | false | false | 2,886 | lean | import topology.Top.limits
import category_theory.limits.shapes
import topology.instances.real
/- This file contains some demos of using the (co)limits API to do topology. -/
noncomputable theory
open category_theory
open category_theory.limits
def R : Top := Top.of ℝ
def I : Top := Top.of (set.Icc 0 1 : set ℝ)
def... |
75ffd4b9ebc4260a356b64caac810beb20cc243a | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/algebra/lie/solvable.lean | a8d3eb045c8937354e1541d2c4b047428a3f34ca | [
"Apache-2.0"
] | permissive | AntoineChambert-Loir/mathlib | 64aabb896129885f12296a799818061bc90da1ff | 07be904260ab6e36a5769680b6012f03a4727134 | refs/heads/master | 1,693,187,631,771 | 1,636,719,886,000 | 1,636,719,886,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,032 | lean | /-
Copyright (c) 2021 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import algebra.lie.ideal_operations
import algebra.lie.abelian
import order.preorder_hom
/-!
# Solvable Lie algebras
Like groups, Lie algebras admit a natural concept of ... |
22b3359af05903496963f53a984bb75ff1515917 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/tactic/nth_rewrite/basic_auto.lean | 484f7ccf636ef08234fd234efd00b7a90622c645 | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 414 | lean | /-
Copyright (c) 2018 Keeley Hoek. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Keeley Hoek, Scott Morrison
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.meta.expr_lens
import Mathlib.PostPort
namespace Mathlib
namesp... |
f3a4e6f66bbb15f359b04e99ac7efed5ed95802e | 6b10c15e653d49d146378acda9f3692e9b5b1950 | /examples/logic/unnamed_520.lean | 428fab798329975c386317cfc7d0c04f5c970d2b | [] | no_license | gebner/mathematics_in_lean | 3cf7f18767208ea6c3307ec3a67c7ac266d8514d | 6d1462bba46d66a9b948fc1aef2714fd265cde0b | refs/heads/master | 1,655,301,945,565 | 1,588,697,505,000 | 1,588,697,505,000 | 261,523,603 | 0 | 0 | null | 1,588,695,611,000 | 1,588,695,610,000 | null | UTF-8 | Lean | false | false | 552 | lean | import tactic
variables A B C : Prop
example : A ∧ (A → B) → A ∧ B :=
sorry
example : B → (A → B) :=
sorry
example (h : A ∧ B → C) : A → B → C :=
sorry
example (h : A → B → C) : A ∧ B → C :=
sorry
example : (A → B) ∧ (B → C) ∧ A → C :=
sorry
example : A → (A → B) → (A ∧ B → C) → C :=
sorry
-- use rcases
example... |
7c29f4e6753b271199b64d71a1d8eba69504aa6d | aa3f8992ef7806974bc1ffd468baa0c79f4d6643 | /tests/lean/inst.lean | 6a87d2a7073d8999af95aac12bdbb1c0ab371518 | [
"Apache-2.0"
] | permissive | codyroux/lean | 7f8dff750722c5382bdd0a9a9275dc4bb2c58dd3 | 0cca265db19f7296531e339192e9b9bae4a31f8b | refs/heads/master | 1,610,909,964,159 | 1,407,084,399,000 | 1,416,857,075,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 568 | lean | import logic data.prod priority
open priority
set_option pp.notation false
inductive C [class] (A : Type) :=
mk : A → C A
definition val {A : Type} (c : C A) : A :=
C.rec (λa, a) c
constant magic (A : Type) : A
definition C_magic [instance] [priority max] (A : Type) : C A :=
C.mk (magic A)
definition C_prop [instan... |
c077ab8c71af81ee6f61aed25e0fe8483dd78057 | 367134ba5a65885e863bdc4507601606690974c1 | /src/group_theory/perm/fin.lean | 7100dc598632b8374a3fde140953d6cbbe18401e | [
"Apache-2.0"
] | permissive | kodyvajjha/mathlib | 9bead00e90f68269a313f45f5561766cfd8d5cad | b98af5dd79e13a38d84438b850a2e8858ec21284 | refs/heads/master | 1,624,350,366,310 | 1,615,563,062,000 | 1,615,563,062,000 | 162,666,963 | 0 | 0 | Apache-2.0 | 1,545,367,651,000 | 1,545,367,651,000 | null | UTF-8 | Lean | false | false | 2,849 | lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Eric Wieser
-/
import group_theory.perm.option
import data.equiv.fin
/-!
# Permutations of `fin n`
-/
open equiv
/-- Permutations of `fin (n + 1)` are equivalent to fixing a single
`fin ... |
b861bc83fa4eba33c26bdc2f7005eadeae809d26 | c86b74188c4b7a462728b1abd659ab4e5828dd61 | /src/Init/Notation.lean | b99901f18cf817953bc67aff392ae5a31c31b7b4 | [
"Apache-2.0"
] | permissive | cwb96/lean4 | 75e1f92f1ba98bbaa6b34da644b3dfab2ce7bf89 | b48831cda76e64f13dd1c0edde7ba5fb172ed57a | refs/heads/master | 1,686,347,881,407 | 1,624,483,842,000 | 1,624,483,842,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,384 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
Notation for operators defined at Prelude.lean
-/
prelude
import Init.Prelude
-- DSL for specifying parser precedences and priorities
namespace Lean.Parser.... |
fdf84e1573dd1e35c6a630f55a042b8feccb41a8 | 957a80ea22c5abb4f4670b250d55534d9db99108 | /tests/lean/run/smt_array.lean | 03aca38f6a45321c176ab8dabfd99c6dfe664dc8 | [
"Apache-2.0"
] | permissive | GaloisInc/lean | aa1e64d604051e602fcf4610061314b9a37ab8cd | f1ec117a24459b59c6ff9e56a1d09d9e9e60a6c0 | refs/heads/master | 1,592,202,909,807 | 1,504,624,387,000 | 1,504,624,387,000 | 75,319,626 | 2 | 1 | Apache-2.0 | 1,539,290,164,000 | 1,480,616,104,000 | C++ | UTF-8 | Lean | false | false | 481 | lean | namespace hide
constant array : Type
constant read : array → nat → nat
constant write : array → nat → nat → array
axiom rw1 : ∀ a i v, read (: write a i v :) i = v
axiom rw2 : ∀ a i j v, i = j ∨ (: read (write a i v) j :) = read a j
attribute [ematch] rw1 rw2
lemma ex3 (a1 a2 a3 a4 a5 : array) (v : nat) :
a2 = write ... |
dc89931020f34c96eec95c983e15d8e94e81099f | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Elab/ComputedFields.lean | 2019d83ee1b388a650309ccb091d93d1918c365c | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 9,623 | lean | /-
Copyright (c) 2022 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner
-/
import Lean.Meta.Constructions
import Lean.Compiler.ImplementedByAttr
import Lean.Elab.PreDefinition.WF.Eqns
/-!
# Computed fields
Inductives can have compute... |
ef8f7c6029807bb0f5f5977938fa7ae19c5a1ee5 | 022547453607c6244552158ff25ab3bf17361760 | /src/analysis/mean_inequalities.lean | 4b4854e78f5ce27a7874bcff3d59d2f8ca8dd45a | [
"Apache-2.0"
] | permissive | 1293045656/mathlib | 5f81741a7c1ff1873440ec680b3680bfb6b7b048 | 4709e61525a60189733e72a50e564c58d534bed8 | refs/heads/master | 1,687,010,200,553 | 1,626,245,646,000 | 1,626,245,646,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 33,242 | lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Sébastien Gouëzel, Rémy Degenne
-/
import analysis.convex.specific_functions
import analysis.special_functions.pow
import data.real.conjugate_exponents
import tactic.... |
63aa64ea31c85cef70c685044d7e711b098f84af | 94e33a31faa76775069b071adea97e86e218a8ee | /src/data/bundle.lean | 5f9810be8eca69aefde0ec190120dae4d1aa38b7 | [
"Apache-2.0"
] | permissive | urkud/mathlib | eab80095e1b9f1513bfb7f25b4fa82fa4fd02989 | 6379d39e6b5b279df9715f8011369a301b634e41 | refs/heads/master | 1,658,425,342,662 | 1,658,078,703,000 | 1,658,078,703,000 | 186,910,338 | 0 | 0 | Apache-2.0 | 1,568,512,083,000 | 1,557,958,709,000 | Lean | UTF-8 | Lean | false | false | 5,133 | lean | /-
Copyright © 2021 Nicolò Cavalleri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolò Cavalleri
-/
import tactic.basic
import algebra.module.basic
/-!
# Bundle
Basic data structure to implement fiber bundles, vector bundles (maybe fibrations?), etc. This file
s... |
435c998d5736a07caf55ebebee6b9b1f057940c4 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/analysis/asymptotics/asymptotic_equivalent.lean | 16e0f02892359b3bab23e004152932d50f3540e5 | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 11,042 | lean | /-
Copyright (c) 2020 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-/
import analysis.asymptotics.asymptotics
import analysis.normed_space.ordered
import analysis.normed_space.bounded_linear_maps
/-!
# Asymptotic equivalence
In th... |
033e0d59cb85f96a40f9857890e4afc86ed2fe81 | f3ab5c6b849dd89e43f1fe3572fbed3fc1baaf0f | /lean/perm.lean | 886941b5ab8b9030b172c379f14e6ae7fc63dbc5 | [
"Apache-2.0",
"BSD-2-Clause",
"LicenseRef-scancode-unknown-license-reference"
] | permissive | ekmett/coda | 69fa7ac66924ea2cee12f7005b192c22baf9e03e | 3309ea70c31b58a3915b0ecc9140985c3a1ac565 | refs/heads/master | 1,670,616,044,398 | 1,619,020,702,000 | 1,619,020,702,000 | 100,850,826 | 170 | 15 | NOASSERTION | 1,670,434,088,000 | 1,503,220,814,000 | Haskell | UTF-8 | Lean | false | false | 4,675 | lean | open function
open nat
-- seeking some position i, currently at some position n.
-- todo: convert a cursor to a Prop
def cursor (n s i k: ℕ) := n + s * k = i ∧ s > 0
-- k = 0 → i = n
def start(i: ℕ) : cursor 0 1 i i := begin
-- apply (@cursor.mk 0 1 i i),
apply and.intro,
rw [zero_add, one_mul],
from nat.ze... |
b9b36d6c34a409acf45744d792e44d615e0e45f1 | 9cba98daa30c0804090f963f9024147a50292fa0 | /old/src/classical_time_test.lean | b1f3ff63c6886c52f8ea27f03d90fadb95b082e0 | [] | no_license | kevinsullivan/phys | dcb192f7b3033797541b980f0b4a7e75d84cea1a | ebc2df3779d3605ff7a9b47eeda25c2a551e011f | refs/heads/master | 1,637,490,575,500 | 1,629,899,064,000 | 1,629,899,064,000 | 168,012,884 | 0 | 3 | null | 1,629,644,436,000 | 1,548,699,832,000 | Lean | UTF-8 | Lean | false | false | 4,096 | lean | import .classical_time
/-
Instantiate two different physical time spaces,
to test that our design meets the requirement we
set out in the README file. Two unrelated spaces
modeling separate timelines.
-/
noncomputable def timeline1 := classicalTime.mk 0
noncomputable def timeline2 := classicalTime.mk 0
/-
Get the und... |
109bb6bc461ca26909a44e424c8f1eaff6cab800 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/order/conditionally_complete_lattice.lean | 004138b1974d9c08541bf5de88dd615c3139310c | [
"Apache-2.0"
] | permissive | rmitta/mathlib | 8d90aee30b4db2b013e01f62c33f297d7e64a43d | 883d974b608845bad30ae19e27e33c285200bf84 | refs/heads/master | 1,585,776,832,544 | 1,576,874,096,000 | 1,576,874,096,000 | 153,663,165 | 0 | 2 | Apache-2.0 | 1,544,806,490,000 | 1,539,884,365,000 | Lean | UTF-8 | Lean | false | false | 32,373 | lean | /-
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
Adapted from the corresponding theory for complete lattices.
Theory of conditionally complete lattices.
A conditionally complete lattice is a lattice in which ev... |
6e47caa038d5d17cba1c474687ae2d58dd314d0f | f29cd213e19220aedf7c72ee6ac95ba61a73f452 | /src/pullbacks.lean | 96ee08a6a68b5075faf850d6024bc5e3ee60acc8 | [] | no_license | EdAyers/topos | 1e42c2514272bc53379c6534643c6be0dc28ab9c | 349dac256403619869d01bc0f4c55048570cb61d | refs/heads/master | 1,610,003,311,636 | 1,582,115,034,000 | 1,582,115,034,000 | 241,615,626 | 0 | 0 | null | 1,582,115,125,000 | 1,582,115,124,000 | null | UTF-8 | Lean | false | false | 4,224 | lean | import category_theory.limits.shapes.pullbacks
namespace category_theory.limits
open category_theory
universes u v
variables {C : Type u} [𝒞 : category.{v} C]
variables {J K : Type v} [small_category J] [small_category K]
include 𝒞
lemma cone.ext {F : J ⥤ C} : Π (c₁ c₂: cone F), (c₁.X = c₂.X) → (c₁.π == c₂.π) → c₁ ... |
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