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922f63125f69a1755f56a058edb17b51d5fad841 | 8d65764a9e5f0923a67fc435eb1a5a1d02fd80e3 | /src/data/seq/computation.lean | ba5063ca8f30fc549b856d56ea54bec8b30adadf | [
"Apache-2.0"
] | permissive | troyjlee/mathlib | e18d4b8026e32062ab9e89bc3b003a5d1cfec3f5 | 45e7eb8447555247246e3fe91c87066506c14875 | refs/heads/master | 1,689,248,035,046 | 1,629,470,528,000 | 1,629,470,528,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 37,963 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
Coinductive formalization of unbounded computations.
-/
import data.stream
import tactic.basic
universes u v w
/-
coinductive computation (α : Type u) : Type u... |
3fcd4c4252d199534a3682776f110d5d43be10f5 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /library/init/unit.lean | 8a69ec30ab1150f56f9bb6e8f6143b6fa38d4718 | [
"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 | 503 | 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.logic
theorem unit_eq (a b : unit) : a = b :=
unit.rec_on a (unit.rec_on b rfl)
theorem unit_eq_unit (a : unit) : a = () :=
unit_eq a (... |
c907c3c462834a97ab3ca6e363d136d5e5b6d9bf | e00ea76a720126cf9f6d732ad6216b5b824d20a7 | /src/algebra/char_p.lean | 22f88d2b40c4878a90c1fe2cc32457eb1c6ca072 | [
"Apache-2.0"
] | permissive | vaibhavkarve/mathlib | a574aaf68c0a431a47fa82ce0637f0f769826bfe | 17f8340912468f49bdc30acdb9a9fa02eeb0473a | refs/heads/master | 1,621,263,802,637 | 1,585,399,588,000 | 1,585,399,588,000 | 250,833,447 | 0 | 0 | Apache-2.0 | 1,585,410,341,000 | 1,585,410,341,000 | null | UTF-8 | Lean | false | false | 8,674 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Kenny Lau, Joey van Langen, Casper Putz
Characteristic of semirings.
-/
import data.padics.padic_norm data.nat.choose data.fintype
import data.zmod.basic algebra.module
universes u v
/--... |
2e99c8031a2ff9190d0e9f245a7f1bda20b10fbb | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/topology/maps_auto.lean | 45939f644164bd199c0d768547e05b49f2d6f329 | [] | 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 | 19,231 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.topology.order
import Mathlib.PostPort
universes u_1 u_2 l... |
386d655405881ef7fab87936405b1c1f36b1eb27 | 367134ba5a65885e863bdc4507601606690974c1 | /src/algebra/homology/exact.lean | 25ab1bcecaa35749839f3f1c73e05fc69a4663e0 | [
"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 | 5,376 | 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 algebra.homology.image_to_kernel_map
/-!
# Exact sequences
In a category with zero morphisms, images, and equalizers we say that `f : A ⟶ B` and `g : B ⟶ C`
ar... |
200cb4bc2cc3875146e5c7b54917b6ed1e67a302 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/interactive/my_tac_class.lean | 1cdfd51e93b0e942c8d05ea96371fdc2911766f0 | [
"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 | 1,873 | lean | meta def mytac :=
state_t nat tactic
section
local attribute [reducible] mytac
meta instance : monad mytac := by apply_instance
meta instance : monad_state nat mytac := by apply_instance
meta instance : has_monad_lift tactic mytac := by apply_instance
end
meta instance (α : Type) : has_coe (tactic α) (mytac α) :=
⟨mo... |
583c43af0a69c015a99697b2211cf8b5bcb3711a | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/order/positive/field.lean | c5a955471ca015827b6d7353d8d5a63010b18b05 | [
"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 | 1,152 | lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import algebra.order.field.basic
import algebra.order.positive.ring
/-!
# Algebraic structures on the set of positive numbers
> THIS FILE IS SYNCHRONIZED WITH MAT... |
75a3a4157613f9a39a324370a9485448729fdb28 | c678b448c073e84fd00f1777ac278c36a7bb9a83 | /data/containers/utils/list.lean | 47c871b28743d57405abeda564e4676f0a4df751 | [] | no_license | GaloisInc/lean-containers | 9d714d9a355381d66f4bf9b686589a85ce7afcc4 | c3359c6e439a611926168e2c86496d0d90a67f9b | refs/heads/master | 1,587,884,399,036 | 1,548,187,422,000 | 1,548,187,422,000 | 173,382,186 | 0 | 0 | null | 1,551,483,637,000 | 1,551,483,637,000 | null | UTF-8 | Lean | false | false | 605 | lean | /- Additional theroems for list. -/
import data.list
import .option
namespace list
theorem find_append {α : Type _} (p : α → Prop) [decidable_pred p] (x y : list α)
: list.find p (x ++ y) = (list.find p x <|> list.find p y) :=
begin
induction x,
case list.nil {
simp [list.find, option.none_or_else],
},
ca... |
c6623323157ed7985775a1843085f3240af508dc | 9cba98daa30c0804090f963f9024147a50292fa0 | /old/src/classical_hertz.lean | 037a54e815c63fbd5948a5e61bbd35afb2385a5f | [] | 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 | 1,796 | lean | import .....math.affine.affine_coordinate_framed_space_lib
import .....math.affine.affine_coordinate_transform
import ..metrology.dimensions
import ..metrology.measurement
import data.real.basic
noncomputable theory
--open real_lib
open measurementSystem
open aff_fr
open aff_lib
open aff_trans
/-
add in a frame here... |
c1e8b359cd5c054d494329df08e43671f18f94a5 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/algebra/add_torsor_auto.lean | b5832aa1fb63a9a0d15193a7e7b1faeb15668095 | [] | 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 | 23,716 | lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers, Yury Kudryashov.
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebra.group.prod
import Mathlib.algebra.group.type_tags
import Mathlib.alge... |
007c96f82b4e444625d4f8f815c62a8e0f7bc3d2 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/analysis/complex/upper_half_plane/basic.lean | b9451fd70a07c1008961059f2cc93e21e845a85f | [
"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 | 11,469 | lean | /-
Copyright (c) 2021 Alex Kontorovich and Heather Macbeth and Marc Masdeu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Kontorovich, Heather Macbeth, Marc Masdeu
-/
import linear_algebra.special_linear_group
import analysis.complex.basic
import group_theory.gr... |
55e0200f84e495af015d3255c3794bc383343607 | 5e3548e65f2c037cb94cd5524c90c623fbd6d46a | /src_icannos_totilas/applications_lineaires/cpge_applin_16.lean | 5cccfde90ee519d90d02285c1874dacec51db60e | [] | no_license | ahayat16/lean_exos | d4f08c30adb601a06511a71b5ffb4d22d12ef77f | 682f2552d5b04a8c8eb9e4ab15f875a91b03845c | refs/heads/main | 1,693,101,073,585 | 1,636,479,336,000 | 1,636,479,336,000 | 415,000,441 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 356 | lean | import algebra.module.linear_map
import linear_algebra.basic
import data.real.basic
import algebra.module.submodule
theorem cpge_applin_16
(R : Type*) (E : Type*) (F : Type*)
[field R]
[add_comm_group E] [module R E]
(f g : linear_map R E E)
:
f.comp (g.comp f) = f ∧ g.comp (f.comp g) = g -> g.ker + ((⊤ : subm... |
ae2034385e36cb7fd1ae07204d84aa3c2c0c60b2 | b2e508d02500f1512e1618150413e6be69d9db10 | /src/topology/instances/nnreal.lean | 9cb60c61e0eef35aaa18ccc7c35fc67a7e4c7ffe | [
"Apache-2.0"
] | permissive | callum-sutton/mathlib | c3788f90216e9cd43eeffcb9f8c9f959b3b01771 | afd623825a3ac6bfbcc675a9b023edad3f069e89 | refs/heads/master | 1,591,371,888,053 | 1,560,990,690,000 | 1,560,990,690,000 | 192,476,045 | 0 | 0 | Apache-2.0 | 1,568,941,843,000 | 1,560,837,965,000 | Lean | UTF-8 | Lean | false | false | 4,508 | lean | /-
Copyright (c) 2018 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
Nonnegative real numbers.
-/
import data.real.nnreal topology.instances.real topology.algebra.infinite_sum
noncomputable theory
open set topological_space metric
names... |
73318d76d99ccbe08e99d2c2c739687f9c6cfd99 | 618003631150032a5676f229d13a079ac875ff77 | /src/data/list/sections.lean | ad6dc99d1e54d6efc98c216f1844975b21d41233 | [
"Apache-2.0"
] | permissive | awainverse/mathlib | 939b68c8486df66cfda64d327ad3d9165248c777 | ea76bd8f3ca0a8bf0a166a06a475b10663dec44a | refs/heads/master | 1,659,592,962,036 | 1,590,987,592,000 | 1,590,987,592,000 | 268,436,019 | 1 | 0 | Apache-2.0 | 1,590,990,500,000 | 1,590,990,500,000 | null | UTF-8 | Lean | false | false | 1,281 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import data.list.forall2
universes u v
open nat function
variables {α : Type u} {β : Type v}
namespace list
/- sections -/
theorem mem_sections {L : list (list α... |
173c541d2497504f3bfd9905cbdfbc13b2a62239 | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /tests/lean/run/subst.lean | 85179ffdf785599b2cb1d32280fa6d9d9e37ec67 | [
"Apache-2.0"
] | permissive | WojciechKarpiel/lean4 | 7f89706b8e3c1f942b83a2c91a3a00b05da0e65b | f6e1314fa08293dea66a329e05b6c196a0189163 | refs/heads/master | 1,686,633,402,214 | 1,625,821,189,000 | 1,625,821,258,000 | 384,640,886 | 0 | 0 | Apache-2.0 | 1,625,903,617,000 | 1,625,903,026,000 | null | UTF-8 | Lean | false | false | 2,262 | lean | universe u
def f1 (n m : Nat) (x : Fin n) (h : n = m) : Fin m :=
h ▸ x
def f2 (n m : Nat) (x : Fin n) (h : m = n) : Fin m :=
h ▸ x
theorem ex1 {α : Sort u} {a b c : α} (h₁ : a = b) (h₂ : b = c) : a = c :=
h₂ ▸ h₁
theorem ex2 {α : Sort u} {a b : α} (h : a = b) : b = a :=
h ▸ rfl
theorem ex3 {α : Sort u} {a b c : α}... |
49dff23bffa6dcb6a7555a716023f4d14cbae63a | 97f752b44fd85ec3f635078a2dd125ddae7a82b6 | /hott/algebra/group.hlean | f7c3cd08fc6b00f13a2ca955f593774263cc13ce | [
"Apache-2.0"
] | permissive | tectronics/lean | ab977ba6be0fcd46047ddbb3c8e16e7c26710701 | f38af35e0616f89c6e9d7e3eb1d48e47ee666efe | refs/heads/master | 1,532,358,526,384 | 1,456,276,623,000 | 1,456,276,623,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 25,368 | hlean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura
Various multiplicative and additive structures. Partially modeled on Isabelle's library.
-/
import algebra.binary algebra.priority
open eq eq.ops -... |
8bf845a10677ddc8907b7b68e99d6e97a60d2182 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/geometry/manifold/bump_function.lean | 80262412fa133ae6a0be63f316e8fee25d725e0d | [
"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 | 14,019 | lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import analysis.calculus.bump_function_findim
import geometry.manifold.cont_mdiff
/-!
# Smooth bump functions on a smooth manifold
In this file we define `smooth_... |
7aab4a9e22054442a866263d63389fd675cad518 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/linear_algebra/linear_pmap.lean | 671eb8c0f2a1ba0e350e1cbb6b13cff8963200d4 | [
"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 | 15,598 | lean | /-
Copyright (c) 2020 Yury Kudryashov All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import linear_algebra.basic
/-!
# Partially defined linear maps
A `linear_pmap R E F` is a linear map from a submodule of `E` to `F`. We define
a `semilattice_inf_... |
6a0cad30621f9ab115121ac1a7b2c845aa785ed9 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/seq/parallel_auto.lean | 115f7be266b75bf00b22c81c6de22603405aba6f | [] | 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 | 4,049 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
Parallel computation of a computable sequence of computations by
a diagonal enumeration.
The important theorems of this operation are proven as
terminates_paralle... |
1b95cb3d0e56155b5977e9e4631bb75501845036 | 01f6b345a06ece970e589d4bbc68ee8b9b2cf58a | /src/smoothing_seminorm.lean | bce3901cfeda032f35c37924d36e8bb8257ada98 | [] | no_license | mariainesdff/norm_extensions_journal_submission | 6077acb98a7200de4553e653d81d54fb5d2314c8 | d396130660935464fbc683f9aaf37fff8a890baa | refs/heads/master | 1,686,685,693,347 | 1,684,065,115,000 | 1,684,065,115,000 | 603,823,641 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 41,014 | lean | /-
Copyright (c) 2023 María Inés de Frutos-Fernández. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: María Inés de Frutos-Fernández
-/
import analysis.special_functions.pow
import limsup
import ring_seminorm
/-!
# smoothing_seminorm
In this file, we prove [BGR, Propo... |
df5489438e89f836043f2c5a430948fafb6e4dcc | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/linear_algebra/eigenspace.lean | ac3f5e43711fbc42570cabb4b42a2dad29323696 | [] | 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 | 12,205 | lean | /-
Copyright (c) 2020 Alexander Bentkamp. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Alexander Bentkamp.
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.field_theory.algebraic_closure
import Mathlib.linear_algebra.finsupp
import Mathlib... |
c3617cd98fd2ad10b3795c3ace0115773a76f1e5 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/number_theory/bernoulli_polynomials.lean | ff121baf16da2adedfc809de303d73a6ba4de9ba | [
"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 | 10,169 | lean | /-
Copyright (c) 2021 Ashvni Narayanan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ashvni Narayanan, David Loeffler
-/
import data.polynomial.algebra_map
import data.polynomial.derivative
import data.nat.choose.cast
import number_theory.bernoulli
/-!
# Bernoulli p... |
a1cc0dda467c6d08f17fe4a8f2eeaf4753cf96fb | 1b8f093752ba748c5ca0083afef2959aaa7dace5 | /src/category_theory/limits/limits.lean | 3e9a8c45402edce200ad070ccabcb3342ef00388 | [] | no_license | khoek/lean-category-theory | 7ec4cda9cc64a5a4ffeb84712ac7d020dbbba386 | 63dcb598e9270a3e8b56d1769eb4f825a177cd95 | refs/heads/master | 1,585,251,725,759 | 1,539,344,445,000 | 1,539,344,445,000 | 145,281,070 | 0 | 0 | null | 1,534,662,376,000 | 1,534,662,376,000 | null | UTF-8 | Lean | false | false | 10,374 | lean | -- Copyright (c) 2018 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Scott Morrison, Reid Barton, Mario Carneiro
import category_theory.limits.shape
import category_theory.filtered
import category_theory.functor_categories.whiskering
import categ... |
83918deb7409e64b1e193644a472f11d878b6b0e | ea5678cc400c34ff95b661fa26d15024e27ea8cd | /simple_group.lean | b712b7c689d0745a46b2e64664f8873644ae77eb | [] | no_license | ChrisHughes24/leanstuff | dca0b5349c3ed893e8792ffbd98cbcadaff20411 | 9efa85f72efaccd1d540385952a6acc18fce8687 | refs/heads/master | 1,654,883,241,759 | 1,652,873,885,000 | 1,652,873,885,000 | 134,599,537 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 23,006 | lean | import group_theory.perm group_theory.order_of_element data.set.finite
open equiv
example : (⟨1, rfl⟩ : {x : perm bool // x = 1}) = ⟨swap ff tt * swap ff tt, dec_trivial⟩ :=
subtype.eq dec_trivial
@[instance, priority 1000] def foo {α : Type*} [decidable_eq α] {P : α → Prop} :
decidable_eq (subtype P) :=
λ a b, de... |
534ab66ac77e38caa48bd4caa9f157e4159ef2fc | 92b50235facfbc08dfe7f334827d47281471333b | /library/logic/axioms/hilbert.lean | 70eaa0aa08202dc4e4b8a3d86a0884fda91664ff | [
"Apache-2.0"
] | permissive | htzh/lean | 24f6ed7510ab637379ec31af406d12584d31792c | d70c79f4e30aafecdfc4a60b5d3512199200ab6e | refs/heads/master | 1,607,677,731,270 | 1,437,089,952,000 | 1,437,089,952,000 | 37,078,816 | 0 | 0 | null | 1,433,780,956,000 | 1,433,780,955,000 | null | UTF-8 | Lean | false | false | 2,703 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad
Follows Coq.Logic.ClassicalEpsilon (but our definition of "inhabited" is the constructive one).
-/
import logic.quantifiers
import data.subtype... |
ee7a926baf9095f3a05903bba3501c9968590683 | 59a4b050600ed7b3d5826a8478db0a9bdc190252 | /src/category_theory/limits/shape.lean | ea24e5222b1a04cf23cb1abf8074252aa6bc5dc3 | [] | no_license | rwbarton/lean-category-theory | f720268d800b62a25d69842ca7b5d27822f00652 | 00df814d463406b7a13a56f5dcda67758ba1b419 | refs/heads/master | 1,585,366,296,767 | 1,536,151,349,000 | 1,536,151,349,000 | 147,652,096 | 0 | 0 | null | 1,536,226,960,000 | 1,536,226,960,000 | null | UTF-8 | Lean | false | false | 3,633 | lean | -- Copyright (c) 2018 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Scott Morrison, Reid Barton, Mario Carneiro
import category_theory.types
import category_theory.isomorphism
import category_theory.tactics.obviously
open category_theory
unive... |
90c2891003fcd7a3ded3a1bcae50fa1fb830fdcd | 94e33a31faa76775069b071adea97e86e218a8ee | /src/ring_theory/discriminant.lean | 71461eea136b9478be1596e2dd6f9f792c6ce92e | [
"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 | 16,452 | lean | /-
Copyright (c) 2021 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca
-/
import ring_theory.trace
import ring_theory.norm
import number_theory.number_field
/-!
# Discriminant of a family of vectors
Given an `A`-algebra `B` and `b`, an... |
9ff5de40e6867124a3b05083e5cf2b252b10ab0f | c777c32c8e484e195053731103c5e52af26a25d1 | /src/algebraic_geometry/projective_spectrum/scheme.lean | 4bfbcf04dcd7e442cec0f6b9099eefb0b52e4a56 | [
"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 | 22,508 | lean | /-
Copyright (c) 2022 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
import algebraic_geometry.projective_spectrum.structure_sheaf
import algebraic_geometry.Spec
import ring_theory.graded_algebra.radical
/-!
# Proj as a scheme
This file ... |
c523c9d063ea1fed1ce1b24382ca41d5287c2705 | 3863d2564418bccb1859e057bf5a4ef240e75fd7 | /hott/hit/two_quotient.hlean | baafed5b96ff9444436862ff01106ac0e4b01e2f | [
"Apache-2.0"
] | permissive | JacobGross/lean | 118bbb067ff4d4af48a266face2c7eb9868fa91c | eb26087df940c54337cb807b4bc6d345d1fc1085 | refs/heads/master | 1,582,735,011,532 | 1,462,557,826,000 | 1,462,557,826,000 | 46,451,196 | 0 | 0 | null | 1,462,557,826,000 | 1,447,885,161,000 | C++ | UTF-8 | Lean | false | false | 22,970 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import homotopy.circle eq2 algebra.e_closure cubical.squareover cubical.cube cubical.square2
open quotient eq circle sum sigma equiv function relation e_closur... |
04ab7aac10d048318d94e203a691f6f5a512934f | c777c32c8e484e195053731103c5e52af26a25d1 | /src/data/finset/sum.lean | 86d4f7ab8974f4f2e0e1e482daa1b602cdce09e9 | [
"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 | 3,269 | 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.multiset.sum
import data.finset.card
/-!
# Disjoint sum of finsets
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a correspon... |
2f54f903799d88c1e26d94de5b88ea946683573b | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/group_theory/abelianization.lean | ef4e9b2b8f415ef41a53a3eee4d88359b2deadee | [] | 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 | 2,688 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Michael Howes
The functor Grp → Ab which is the left adjoint
of the forgetful functor Ab → Grp.
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.gro... |
7ab8fee03a71fecdfc3e3d769c1734e85eed6bfe | ac2987d8c7832fb4a87edb6bee26141facbb6fa0 | /Mathlib/Data/Equiv/Basic.lean | 3e3562a9f2d5ef7da69fd69b32614eac348b25d3 | [
"Apache-2.0"
] | permissive | AurelienSaue/mathlib4 | 52204b9bd9d207c922fe0cf3397166728bb6c2e2 | 84271fe0875bafdaa88ac41f1b5a7c18151bd0d5 | refs/heads/master | 1,689,156,096,545 | 1,629,378,840,000 | 1,629,378,840,000 | 389,648,603 | 0 | 0 | Apache-2.0 | 1,627,307,284,000 | 1,627,307,284,000 | null | UTF-8 | Lean | false | false | 1,937 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Mario Carneiro
-/
import Mathlib.Logic.Function.Basic
/-!
# Equivalence between types
* `equiv α β` a.k.a. `α ≃ β`: a bijective map `α → β` bundled with its ... |
7dbcf8ccc0051333b00538a940e04d688f8c334c | 3c9dc4ea6cc92e02634ef557110bde9eae393338 | /stage0/src/Lean/MetavarContext.lean | 01980ccf572ea1f82a599cb3b2fac4899ab586a2 | [
"Apache-2.0"
] | permissive | shingtaklam1324/lean4 | 3d7efe0c8743a4e33d3c6f4adbe1300df2e71492 | 351285a2e8ad0cef37af05851cfabf31edfb5970 | refs/heads/master | 1,676,827,679,740 | 1,610,462,623,000 | 1,610,552,340,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 51,940 | 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.Util.MonadCache
import Lean.LocalContext
namespace Lean
/-
The metavariable context stores metavariable declarations and their
assignments. It... |
60491d8372befc791c87fe38140ffddb3a8bbfbd | 9d2e3d5a2e2342a283affd97eead310c3b528a24 | /src/solutions/tuesday/afternoon/logic.lean | 8ce46b63a15fb8de379738e666b0c4c7d3d62b21 | [] | permissive | Vtec234/lftcm2020 | ad2610ab614beefe44acc5622bb4a7fff9a5ea46 | bbbd4c8162f8c2ef602300ab8fdeca231886375d | refs/heads/master | 1,668,808,098,623 | 1,594,989,081,000 | 1,594,990,079,000 | 280,423,039 | 0 | 0 | MIT | 1,594,990,209,000 | 1,594,990,209,000 | null | UTF-8 | Lean | false | false | 6,427 | lean | /-
Lean for the Curious Mathematician
Tuesday, July 14, 2020
13:00 session
Happy Bastille Day!
-/
import data.real.basic
/-! ## Logic -/
/-!
### Agenda
- a quick overview of Lean's tactics for dealing with logical connectives
- continue with Patrick Massot's tutorial
After the overview, I will ask you to tell us h... |
58f8bc6d8e3a09e25a5713037ca76e09e69a2bc8 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/playground/parser/filemap.lean | 61f310c2a7637bf2fd459f58634173e9a20dcdc6 | [
"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 | 1,779 | lean | structure Position :=
(line : Nat := 1)
(column : Nat := 0)
instance : Inhabited Position :=
⟨{}⟩
structure FileMap :=
(source : String)
(positions : Array String.Pos)
(lines : Array Nat)
namespace FileMap
instance : Inhabited FileMap :=
⟨{ source := "", positions := Array.empty, lines := Array.empty }⟩
p... |
2f946cbcaf2e1ae586d9a338ae183610ab1ac8d4 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/field_theory/fixed.lean | 51765ca8db1cec9b183845ae87b202a41ced2cb9 | [] | 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 | 9,969 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebra.polynomial.group_ring_action
import Mathlib.deprecated.subfield
import Mathlib.field_theory.n... |
ef9fa96392b61f555d55183fd1ab6715b3c9b05e | 9028d228ac200bbefe3a711342514dd4e4458bff | /src/data/set/intervals/basic.lean | f7b81467d52d06506329ae2f11264ae19f00354e | [
"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 | 35,887 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot, Yury Kudryashov
-/
import algebra.ordered_group
import data.set.basic
/-!
# Intervals
In any preorder `α`, we define intervals (which ... |
3828afcba9d0a2b1319e3061a3f8fcb3baf08b93 | 56e5b79a7ab4f2c52e6eb94f76d8100a25273cf3 | /src/evaluation/bfs/gptf.lean | 42c97528eebbfbd75be59580dee080f97b1e1179 | [
"Apache-2.0"
] | permissive | DyeKuu/lean-tpe-public | 3a9968f286ca182723ef7e7d97e155d8cb6b1e70 | 750ade767ab28037e80b7a80360d213a875038f8 | refs/heads/master | 1,682,842,633,115 | 1,621,330,793,000 | 1,621,330,793,000 | 368,475,816 | 0 | 0 | Apache-2.0 | 1,621,330,745,000 | 1,621,330,744,000 | null | UTF-8 | Lean | false | false | 1,760 | lean | import evaluation_step
import backends.bfs.openai
section main
local notation `ENGINE_ID` := ""
local notation `OPENAI_API_KEY` := ""
meta def SEARCH_CORE
(req : openai.CompletionRequest)
(engine_id : string := ENGINE_ID) (api_key : string := OPENAI_API_KEY) (fuel : ℕ := 25) :
state_t BFSState tactic unit :=
... |
ca283b3d41654da1acec45055639b9b2ed0d79da | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/data/nat/lattice.lean | cdc59f7f06f1c756a1578fd8109473f197c64c2a | [
"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 | 6,839 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Floris van Doorn, Gabriel Ebner, Yury Kudryashov
-/
import order.conditionally_complete_lattice
/-!
# Conditionally complete linear order structure on `ℕ`
In this fil... |
c0cdac464a3648af9962c12402800f0e4ead5b06 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/category_theory/sites/closed.lean | 4680d4a99d38b33c1e5cfaf420f745e82e8a0b3e | [
"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 | 12,154 | lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import category_theory.sites.sheaf_of_types
import order.closure
/-!
# Closed sieves
A natural closure operator on sieves is a closure operator on `sieve X` for each `X... |
830123980255426662f2f9aa80c7aecae99af686 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/category_theory/whiskering.lean | f6e31b824e5d9d64c3965bd499bcbddf9d96bbf3 | [
"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 | 5,947 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.natural_isomorphism
namespace category_theory
universes u₁ v₁ u₂ v₂ u₃ v₃ u₄ v₄
section
variables {C : Type u₁} [𝒞 : category.{v₁} C]
... |
608e19b2f020e19652dd31864dcf837ade0eb621 | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/linear_algebra/nonsingular_inverse.lean | 18c08ff9cb23065f9e58544ba53f210bc841c776 | [
"Apache-2.0"
] | permissive | lacker/mathlib | f2439c743c4f8eb413ec589430c82d0f73b2d539 | ddf7563ac69d42cfa4a1bfe41db1fed521bd795f | refs/heads/master | 1,671,948,326,773 | 1,601,479,268,000 | 1,601,479,268,000 | 298,686,743 | 0 | 0 | Apache-2.0 | 1,601,070,794,000 | 1,601,070,794,000 | null | UTF-8 | Lean | false | false | 16,964 | lean | /-
Copyright (c) 2019 Tim Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Tim Baanen.
-/
import algebra.associated
import linear_algebra.determinant
import tactic.linarith
import tactic.ring_exp
/-!
# Nonsingular inverses
In this file, we define an inverse for ... |
5dcc8708e91f626fb6ea06f3ab0dcf6a4f24ff2f | 37da0369b6c03e380e057bf680d81e6c9fdf9219 | /hott/cubical/pathover2.hlean | 96c703819f66f7df29c8aa1f142eb6074d52cb3f | [
"Apache-2.0"
] | permissive | kodyvajjha/lean2 | 72b120d95c3a1d77f54433fa90c9810e14a931a4 | 227fcad22ab2bc27bb7471be7911075d101ba3f9 | refs/heads/master | 1,627,157,512,295 | 1,501,855,676,000 | 1,504,809,427,000 | 109,317,326 | 0 | 0 | null | 1,509,839,253,000 | 1,509,655,713,000 | C++ | UTF-8 | Lean | false | false | 6,415 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Floris van Doorn
Coherence conditions for operations on pathovers
-/
open function equiv
namespace eq
variables {A A' A'' : Type} {B B' : A → Type} {B'' : A' → Type} {C : Π⦃a⦄, ... |
f5cad2676c79986320928d1d38b5da738bb34ea9 | 5749d8999a76f3a8fddceca1f6941981e33aaa96 | /src/data/real/ennreal.lean | 0a842b1c2fa6cc41624333a6b6dcff3e0f242530 | [
"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 | 40,042 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl, Yury Kudryashov
Extended non-negative reals
-/
import data.real.nnreal order.bounds data.set.intervals tactic.norm_num
noncomputable theory
open classical set lattice
... |
6b0c308d0885b2a3b6484db740bfbee622ea56ba | 0ca0916cad8827b3daa8456cce211dc0a10b8886 | /benchmarks/sum_ints/sum_ints.lean | 6f2594cb20b4e17e82065d53902cfe5699f81509 | [] | no_license | jroesch/compiler-performance | d97e1e12de8b6e05c25261c5be5a24e305e48b56 | 0c4c860444148b4fc2d164baaa6553654b779bf4 | refs/heads/master | 1,591,852,191,453 | 1,481,253,759,000 | 1,481,253,759,000 | 75,999,260 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 537 | lean | import system.io
set_option native.library_path "/Users/jroesch/Git/lean/build/debug"
set_option native.include_path "/Users/jroesch/Git/lean_install/include/lean_ext"
-- This flag controls whether lean will automatically invoke C++
-- set_option native.emit_dwarf true
-- set_option native.dump "anf"
-- set_option tr... |
8947eac3e46c93995c21394e58c733d2c8c7ee07 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/linear_algebra/linear_independent.lean | b0baca789a72f6bf16ced4b5ce4db97ae5c58eaf | [
"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 | 57,494 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Alexander Bentkamp, Anne Baanen
-/
import algebra.big_operators.fin
import linear_algebra.finsupp
import linear_algebra.prod
import set_theory.cardinal.bas... |
069c1c55cd920190b80b31ea330eb3197f36c8fb | 3dd1b66af77106badae6edb1c4dea91a146ead30 | /tests/lean/run/coe5.lean | 0b0d7a868e5abaa1a80b8f73ba3717368eba2065 | [
"Apache-2.0"
] | permissive | silky/lean | 79c20c15c93feef47bb659a2cc139b26f3614642 | df8b88dca2f8da1a422cb618cd476ef5be730546 | refs/heads/master | 1,610,737,587,697 | 1,406,574,534,000 | 1,406,574,534,000 | 22,362,176 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,049 | lean | import standard
namespace setoid
inductive setoid : Type :=
| mk_setoid: Π (A : Type'), (A → A → Prop) → setoid
set_option pp.universes true
check setoid
definition test : Type.{2} := setoid.{0}
definition carrier (s : setoid)
:= setoid_rec (λ a eq, a) s
definition eqv {s : setoid} : carrier s → ca... |
93862227e554300e966772bc273d68eee259ffd5 | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /tests/lean/run/meta5.lean | 394e58137fe9afe62f4be13ffff05d9c7658ae5d | [
"Apache-2.0"
] | permissive | mhuisi/lean4 | 28d35a4febc2e251c7f05492e13f3b05d6f9b7af | dda44bc47f3e5d024508060dac2bcb59fd12e4c0 | refs/heads/master | 1,621,225,489,283 | 1,585,142,689,000 | 1,585,142,689,000 | 250,590,438 | 0 | 2 | Apache-2.0 | 1,602,443,220,000 | 1,585,327,814,000 | C | UTF-8 | Lean | false | false | 664 | lean | import Init.Lean.Meta
open Lean
open Lean.Meta
def tst1 : MetaM Unit :=
withLocalDecl `y (mkConst `Nat) BinderInfo.default $ fun y => do
withLetDecl `x (mkConst `Nat) (mkNatLit 0) $ fun x => do {
mvar ← mkFreshExprMVar (mkConst `Nat) Name.anonymous MetavarKind.syntheticOpaque;
trace! `Meta mvar;
r ← mkLambda #[y... |
0fee599f2c2bbec5263d9403fa78ca2161f78709 | 853df553b1d6ca524e3f0a79aedd32dde5d27ec3 | /src/ring_theory/subsemiring.lean | 3ea3a8ed3fc85d18897e9be1e80eb9d46af0f61e | [
"Apache-2.0"
] | permissive | DanielFabian/mathlib | efc3a50b5dde303c59eeb6353ef4c35a345d7112 | f520d07eba0c852e96fe26da71d85bf6d40fcc2a | refs/heads/master | 1,668,739,922,971 | 1,595,201,756,000 | 1,595,201,756,000 | 279,469,476 | 0 | 0 | null | 1,594,696,604,000 | 1,594,696,604,000 | null | UTF-8 | Lean | false | false | 24,642 | lean | /-
Copyright (c) 2020 Yury Kudryashov All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import ring_theory.prod
import group_theory.submonoid
import data.equiv.ring
/-!
# Bundled subsemirings
We define bundled subsemirings and some standard construct... |
fe5a484eba7fcb1ffdafe2062c2ec226902c5d51 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /tests/bench/liasolver.lean | 5183d2f9e777b6b568ee23c90ce6f682dc1ad1d7 | [
"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 | 13,885 | lean | /-
Linear Diophantine equation solver
Author: Marc Huisinga
-/
import Std.Data.HashMap
open Std
namespace Int
def roundedDiv (a b : Int) : Int := Id.run <| do
let mut div := a / b
let sgn := if a ≥ 0 ∧ b ≥ 0 ∨ a < 0 ∧ b < 0 then 1 else -1
let rest := (a % b).natAbs
if 2*rest ≥ b.n... |
0e2152a132c120bf4e9da7e299aa2a8554338a3b | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/data/real/ennreal.lean | 7b394591cf8dafa9e80271bd0538d857abcb80f0 | [
"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 | 75,273 | 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 data.real.nnreal
/-!
# Extended non-negative reals
We define `ennreal = ℝ≥0∞ := with_top ℝ≥0` to be the type of extended nonnegative real nu... |
b1c2e601e98125d21b4176030b8275cc3a1183ed | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/category_theory/single_obj.lean | 146f34a959481646d36499eec0f4c992c2d0246b | [
"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 | 5,351 | lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import category_theory.endomorphism
import category_theory.groupoid
import category_theory.category.Cat
import data.equiv.algebra
import algebra.category.Mon.basic... |
9369255b297382cc9f0cadb077abb188e9ce62b4 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/order/compactly_generated.lean | adbe8dca087c93720edac4a72922c10404102c15 | [
"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 | 20,370 | 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 data.finset.order
import order.atoms
import order.order_iso_nat
import order.zorn
import tactic.tfae
/-!
# Compactness properties for complete lattices
For complet... |
afe0095f3daf6419a5328af17ece52d350eb7687 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/number_theory/divisors_auto.lean | 862a87007dc9e3db2fea2129b5ada1658b6c02d2 | [] | 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 | 8,397 | lean | /-
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebra.big_operators.order
import Mathlib.tactic.default
import Mathlib.data.nat.prime
imp... |
87e39491b68d271750195d357b98a5840237d7f3 | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/interactive/t5.lean | f11ffd6859031dac98dab4d6ac64cc4ec6635751 | [
"Apache-2.0"
] | permissive | codyroux/lean0.1 | 1ce92751d664aacff0529e139083304a7bbc8a71 | 0dc6fb974aa85ed6f305a2f4b10a53a44ee5f0ef | refs/heads/master | 1,610,830,535,062 | 1,402,150,480,000 | 1,402,150,480,000 | 19,588,851 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 130 | lean | (* import("tactic.lua") *)
axiom magic (a : Bool) : a.
theorem T (a : Bool) : a.
apply magic.
done.
print environment 1. |
06d71e3825aa5dc61ee104cb4b9d77009751b28d | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/linear_algebra/affine_space/independent.lean | 47723cc191a7d85e83a27121549488ff83709575 | [
"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 | 24,228 | 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 data.finset.sort
import data.matrix.notation
import linear_algebra.affine_space.combination
import linear_algebra.basis
/-!
# Affine independence
This file defin... |
8377ab53a6457dbaab3102b06fc0086294334fb0 | bd12a817ba941113eb7fdb7ddf0979d9ed9386a0 | /src/tactic/core.lean | 545c5682458ab3e58f22847dc67f0f4e4f727eb5 | [
"Apache-2.0"
] | permissive | flypitch/mathlib | 563d9c3356c2885eb6cefaa704d8d86b89b74b15 | 70cd00bc20ad304f2ac0886b2291b44261787607 | refs/heads/master | 1,590,167,818,658 | 1,557,762,121,000 | 1,557,762,121,000 | 186,450,076 | 0 | 0 | Apache-2.0 | 1,557,762,289,000 | 1,557,762,288,000 | null | UTF-8 | Lean | false | false | 34,419 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Simon Hudon, Scott Morrison, Keeley Hoek
-/
import data.dlist.basic category.basic meta.expr meta.rb_map tactic.cache
namespace expr
open tactic
attribute [derive has... |
2d945907be030ed98157556838c6866f7080046b | e0f9ba56b7fedc16ef8697f6caeef5898b435143 | /src/data/polynomial.lean | eeda6d76945d08266eea68f02b897723cde81a2b | [
"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 | 106,572 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Scott Morrison, Jens Wagemaker
Theory of univariate polynomials, represented as `add_monoid_algebra R ℕ`, where `R` is a commutative semiring.
-/
import da... |
ef0cc04281e667ed7489616f8776c2acbed0e848 | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/topology/metric_space/closeds.lean | 9bc30dac9e67c7cb3c7086c9ec03bdb93b410de3 | [
"Apache-2.0"
] | permissive | lacker/mathlib | f2439c743c4f8eb413ec589430c82d0f73b2d539 | ddf7563ac69d42cfa4a1bfe41db1fed521bd795f | refs/heads/master | 1,671,948,326,773 | 1,601,479,268,000 | 1,601,479,268,000 | 298,686,743 | 0 | 0 | Apache-2.0 | 1,601,070,794,000 | 1,601,070,794,000 | null | UTF-8 | Lean | false | false | 21,403 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Sébastien Gouëzel
-/
import topology.metric_space.hausdorff_distance
import analysis.specific_limits
/-!
# Closed subsets
This file defines the metric and emetric space structure o... |
0a3257fe08515d2c2bade2ddec05d1263af7e2d1 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/bad_error4.lean | 5569189f20b3b41b15c603f696a5ff3d89326b61 | [
"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 | 79 | lean | structure foo :=
(f: unit -> unit)
definition bar : foo :=
{ f := λ a b, _ }
|
7b60ca7ce44bc8c8308b92e27b1de9dd1a239703 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/1337.lean | aa914ff820d5dcae2fc50917d455c9406f29ec9f | [
"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 | 377 | lean | theorem n_minus_one_le_n {n : Nat} : n > 0 → n - 1 < n := by
cases n with
| zero => simp []
| succ n =>
intros
rw [Nat.succ_eq_add_one, Nat.add_sub_cancel]
apply Nat.le.refl
partial def foo : Array Int → Int
| arr => Id.run do
let mut r : Int := 1
while h : arr.size > 0 do
r := r * arr[arr.... |
571e79c0260d863eca4452f3b21c4e01ca492c94 | c3f2fcd060adfa2ca29f924839d2d925e8f2c685 | /tests/lean/run/tree_height.lean | 74bc685932c1eb1b4c7bc1ed7ddad15f14c3e9c3 | [
"Apache-2.0"
] | permissive | respu/lean | 6582d19a2f2838a28ecd2b3c6f81c32d07b5341d | 8c76419c60b63d0d9f7bc04ebb0b99812d0ec654 | refs/heads/master | 1,610,882,451,231 | 1,427,747,084,000 | 1,427,747,429,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,090 | lean | import logic data.nat
open eq.ops nat
inductive tree (A : Type) :=
| leaf : A → tree A
| node : tree A → tree A → tree A
namespace tree
definition height {A : Type} (t : tree A) : nat :=
tree.rec_on t
(λ a, zero)
(λ t₁ t₂ h₁ h₂, succ (max h₁ h₂))
definition height_lt {A : Type} : tree A → tree A → Prop :=
inv_i... |
55371edf93e743f2b1e292f849f3ad1f671d0ff6 | e61a235b8468b03aee0120bf26ec615c045005d2 | /stage0/src/Init/Lean/Elab/Log.lean | 8811ff36e6a0fd06b3b71527baf1aeb334879253 | [
"Apache-2.0"
] | permissive | SCKelemen/lean4 | 140dc63a80539f7c61c8e43e1c174d8500ec3230 | e10507e6615ddbef73d67b0b6c7f1e4cecdd82bc | refs/heads/master | 1,660,973,595,917 | 1,590,278,033,000 | 1,590,278,033,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,761 | 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.Elab.Util
import Init.Lean.Elab.Exception
namespace Lean
namespace Elab
class MonadPosInfo (m : Type → Type) :=
(getFileMap : m... |
ee5fc585d2b9765173c900062afd5b9eaa3b0473 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /tests/lean/run/simp7.lean | 16964d3a511f37aec5d7c2be1edf67427f93f57a | [
"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 | 1,423 | lean | def f (x : α) := x
theorem ex1 (a : α) (b : List α) : f (a::b = []) = False :=
by simp [f]
def length : List α → Nat
| [] => 0
| a::as => length as + 1
theorem ex2 (a b c : α) (as : List α) : length (a :: b :: as) > length as := by
simp [length]
apply Nat.lt.step
apply Nat.lt_succ_self
def fact : Nat... |
4b34c2b088bb335e65c86f5ea31f92b46248ad56 | 6e41ee3ac9b96e8980a16295cc21f131e731884f | /tests/lean/run/e9.lean | 75d1f0fb063308b5e0500d48ce9fcb3ad6edd856 | [
"Apache-2.0"
] | permissive | EgbertRijke/lean | 3426cfa0e5b3d35d12fc3fd7318b35574cb67dc3 | 4f2e0c6d7fc9274d953cfa1c37ab2f3e799ab183 | refs/heads/master | 1,610,834,871,476 | 1,422,159,801,000 | 1,422,159,801,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 668 | lean | prelude
precedence `+`:65
namespace nat
constant nat : Type.{1}
constant add : nat → nat → nat
infixl + := add
end nat
namespace int
open nat (nat)
constant int : Type.{1}
constant add : int → int → int
infixl + := add
constant of_nat : nat → int
end int
namespace int_coercions
persistent attribute... |
ccc7f62ed126ac331dc04169a0b9afe4f4c054ad | 94e33a31faa76775069b071adea97e86e218a8ee | /src/topology/gluing.lean | 25543d9719b0b06f795ddd11a32d9dfa0675cc2a | [
"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 | 18,569 | lean | /-
Copyright (c) 2021 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import topology.category.Top
import category_theory.glue_data
import category_theory.concrete_category.elementwise
/-!
# Gluing Topological spaces
Given a family of gluin... |
44f936e5093ccc15b89a55239344ed30f2884c48 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/topology/extend_from.lean | 5653df35b3b89a145f9444ebcb8d8ebf155e0b13 | [
"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 | 4,050 | lean | /-
Copyright (c) 2020 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Anatole Dedecker
-/
import topology.separation
/-!
# Extending a function from a subset
The main definition of this file is `extend_from A f` where `f : X → Y`
and ... |
c99d3d68134ec4d611135fdf32c1ecfcc5f1d136 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/1081.lean | 7a8530018142d48ce2f86428efcda0453ad97ed2 | [
"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 | 1,280 | lean | def f : Nat → Nat → Nat
| 0, y => y
| x+1, y+1 => f (x-2) y
| x+1, 0 => 0
example : f 0 y = y :=
rfl -- Error, it does not hold by reflexivity since the recursion is on `y`
example : f 0 0 = 0 := rfl
example : f 0 (y+1) = y+1 := rfl
inductive Vector (α : Type u) : Nat → Type u where
| nil : Vector ... |
80804f59c97ea1b01b34db6813d1f4b20715e6b7 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/1074a.lean | 49451e8026e88aeb1ff9452ec659b7f9dc055509 | [
"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 | 420 | lean | inductive Term
| id2: Term -> Term -> Term
inductive Brx: Term -> Prop
| id2: Brx z -> Brx (Term.id2 n z)
def Brx.interp {a} (H: Brx a): Nat :=
match a with
| Term.id2 n z => by
let ⟨Hn, Hz⟩: True ∧ Brx z
:= by cases H <;> exact ⟨by simp, by assumption⟩;
exact Hz.interp
def Brx.interp_nil (H: Brx a... |
dabb9a1dde8d80b1e6ca42bb161ab6738c665216 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/order/filter/bases.lean | 25eba813bef2ba64da6d942b96c1d7f6646f1141 | [
"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 | 49,500 | lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Johannes Hölzl, Mario Carneiro, Patrick Massot
-/
import data.prod.pprod
import data.set.countable
import order.filter.prod
/-!
# Filter bases
> THIS FILE IS SYNCHR... |
1817b1605c88e77b968b9b7a133b7f89de890c65 | 206422fb9edabf63def0ed2aa3f489150fb09ccb | /src/analysis/hofer.lean | 9a872ce3bdb040615c1cedf42f5b744d7d987409 | [
"Apache-2.0"
] | permissive | hamdysalah1/mathlib | b915f86b2503feeae268de369f1b16932321f097 | 95454452f6b3569bf967d35aab8d852b1ddf8017 | refs/heads/master | 1,677,154,116,545 | 1,611,797,994,000 | 1,611,797,994,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,589 | lean | /-
Copyright (c) 2020 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import analysis.specific_limits
/-!
# Hofer's lemma
This is an elementary lemma about complete metric spaces. It is motivated by an
application to the bubbling-off... |
d9c834daf9a88e362da08412a1a22c475e1be41d | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/order/pfilter.lean | 14faa4e39f27c8527f27a33a28c9dd5b12704e52 | [
"Apache-2.0"
] | permissive | ilitzroth/mathlib | ea647e67f1fdfd19a0f7bdc5504e8acec6180011 | 5254ef14e3465f6504306132fe3ba9cec9ffff16 | refs/heads/master | 1,680,086,661,182 | 1,617,715,647,000 | 1,617,715,647,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,822 | lean | /-
Copyright (c) 2020 Mathieu Guay-Paquet. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mathieu Guay-Paquet
-/
import order.ideal
/-!
# Order filters
## Main definitions
Throughout this file, `P` is at least a preorder, but some sections
require more structure, su... |
bd65c3d89ab061fa4e0c59d38de5626371200f02 | 3dd1b66af77106badae6edb1c4dea91a146ead30 | /tests/lean/run/t7.lean | 7f16841467b9942ca3f82a6cbe038154f93386e1 | [
"Apache-2.0"
] | permissive | silky/lean | 79c20c15c93feef47bb659a2cc139b26f3614642 | df8b88dca2f8da1a422cb618cd476ef5be730546 | refs/heads/master | 1,610,737,587,697 | 1,406,574,534,000 | 1,406,574,534,000 | 22,362,176 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 70 | lean | variable A : Type.{1}
variable f : A → A → A
print raw f _ (f _ _) |
80909f94465b83d7411bfc0e068c6924ebbd86de | a4673261e60b025e2c8c825dfa4ab9108246c32e | /src/Lean/Syntax.lean | 896d46d4b7746af5a7877486ee352d82f37593e5 | [
"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 | 13,178 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Sebastian Ullrich, Leonardo de Moura
-/
import Lean.Data.Name
import Lean.Data.Format
namespace Lean
namespace SourceInfo
def updateTrailing (info : SourceInfo) (trailing : Opt... |
f0374dbebcc8e0feecff158a2583782d482f3536 | ce6917c5bacabee346655160b74a307b4a5ab620 | /src/ch2/ex0302.lean | b1b2e0512ef683140eb240e8cb4c89376edd372f | [] | 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 | 405 | lean | constants α β : Type
constants a1 a2 : α
constants b1 b2 : β
constant f : α → α
constant g : α → β
constant h : α → β → α
constant p : α → α → bool
#check fun x : α, f x
#check λ x : α, f x
#check λ x : α, f (f x)
#check λ x : α, h x b1
#check λ y : β, h a1 y
#check λ x : α, p (f (f x)) (h (f a1) b2)
#check λ (x : α)... |
16b40cc8369cd1c4ecca8c0b8f77c917c3da732a | 3f7026ea8bef0825ca0339a275c03b911baef64d | /src/category_theory/products/default.lean | fa90fdf826744331377878c075d0539a2e349928 | [
"Apache-2.0"
] | permissive | rspencer01/mathlib | b1e3afa5c121362ef0881012cc116513ab09f18c | c7d36292c6b9234dc40143c16288932ae38fdc12 | refs/heads/master | 1,595,010,346,708 | 1,567,511,503,000 | 1,567,511,503,000 | 206,071,681 | 0 | 0 | Apache-2.0 | 1,567,513,643,000 | 1,567,513,643,000 | null | UTF-8 | Lean | false | false | 6,918 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stephen Morgan, Scott Morrison
-/
import category_theory.functor_category
import category_theory.isomorphism
import tactic.interactive
namespace category_theory
universes v₁ v₂ v₃ v₄... |
bcdf0bd1e7c560156954979b89b2fe6a051663b1 | 61c3861020ef87c6c325fc3c3dcbabf5d6b07985 | /hit/quotient.lean | 313f3143ba52af3db2e70e5916cd99ad21b3110e | [
"Apache-2.0"
] | permissive | jonas-frey/hott3 | a623be2959e8a713c03fa1b0f34bf76a561dfa87 | a944051b4eb5919bdc70978ee15fcbb48a824811 | refs/heads/master | 1,628,408,720,559 | 1,510,267,042,000 | 1,510,267,042,000 | 106,760,764 | 0 | 0 | null | 1,507,856,238,000 | 1,507,856,238,000 | null | UTF-8 | Lean | false | false | 14,034 | lean | /-
Copyright (c) 2017 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Ulrik Buchholtz
Quotients. This is a quotient without truncation for an arbitrary type-valued binary relation.
See also .set_quotient
-/
/-
The hit quotient is ... |
a75b943b46d8e77e458783787b5965a82cb423eb | fe84e287c662151bb313504482b218a503b972f3 | /src/group_theory/elementary_two.lean | 96a97f384a5e42d5985d86146b180a0b63c3a002 | [] | no_license | NeilStrickland/lean_lib | 91e163f514b829c42fe75636407138b5c75cba83 | 6a9563de93748ace509d9db4302db6cd77d8f92c | refs/heads/master | 1,653,408,198,261 | 1,652,996,419,000 | 1,652,996,419,000 | 181,006,067 | 4 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 1,259 | lean | /-
Copyright (c) 2019 Neil Strickland. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Neil Strickland
If `G` is a group in which all elements `g` stisfy `g² = 1`, then
`G` is automatically abelian. We prove this, and encode the proof
as a typeclass instance.
-/
imp... |
6ea107db4af1dcc241ded65b36174a5f4e6c1e0d | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/data/finset/fold.lean | 31120d6e4bc95f553a930c8bca089bf2dab29107 | [
"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 | 8,692 | 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.finset.basic
import data.multiset.fold
/-!
# The fold operation for a commutative associative operation over a finset.
-/
namespace finset
open multiset... |
e7f9b782049fc7ec9094431b318576d53c7e8e33 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/category_theory/functor/flat.lean | 3a5480f6c52762f8bbfccf178e0f9fee5ef0ade8 | [
"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 | 15,576 | lean | /-
Copyright (c) 2021 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import category_theory.limits.filtered_colimit_commutes_finite_limit
import category_theory.limits.preserves.functor_category
import category_theory.limits.preserves.shapes... |
25479c170b6206492587d73c4e85e2ab1b56c43a | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/equation_with_values.lean | 1bb5e4423544ee2d1591c52eb74bb9032a6405ef | [
"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 | 940 | lean | def f : char → nat
| 'a' := 0
| 'b' := 1
| 'c' := 2
| 'd' := 3
| 'e' := 4
| _ := 5
#check f.equations._eqn_1
#check f.equations._eqn_2
#check f.equations._eqn_3
#check f.equations._eqn_4
#check f.equations._eqn_5
#check f.equations._eqn_6
def g : nat → nat
| 100000 := 0
| 200000 := 1
| 300000 := 2
| 400000 := 3
| ... |
b2b82e9e906a5014a189e20b90105597fa6f6ef4 | e38d5e91d30731bef617cc9b6de7f79c34cdce9a | /src/core/connection/both.lean | 0361a25058872dcbe72ec2450f09e3dd87fa3ac4 | [
"Apache-2.0"
] | permissive | bbentzen/cubicalean | 55e979c303fbf55a81ac46b1000c944b2498be7a | 3b94cd2aefdfc2163c263bd3fc6f2086fef814b5 | refs/heads/master | 1,588,314,875,258 | 1,554,412,699,000 | 1,554,412,699,000 | 177,333,390 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,447 | lean | /-
Copyright (c) 2019 Bruno Bentzen. All rights reserved.
Released under the Apache License 2.0 (see "License");
Author: Bruno Bentzen
-/
import .join
open interval
-- the meet-and-join connection
def both.horn {A : Type} (kan : has_hcom2 A)
(p q : I → A) (h : p i1 = q i0) : horn2 A :=
begin
fap... |
6e5eabe9220a18ba7b76a54497c67ec37eac6d62 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/symmetrized.lean | c335e5b9864c500cc1dbbe0a8ce0ff051ffa4385 | [
"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 | 9,913 | lean | /-
Copyright (c) 2021 Christopher Hoskin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Hoskin
-/
import algebra.jordan.basic
import algebra.module.basic
/-!
# Symmetrized algebra
A commutative multiplication on a real or complex space can be constructed... |
2d33bff453752367edfac6aef25c422f90b721ea | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/topology/algebra/floor_ring.lean | c8f8f9a744ccf38632fe8dbe28b7e75ff23668f1 | [] | 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 | 6,483 | lean | /-
Copyright (c) 2020 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
Basic topological facts (limits and continuity) about `floor`,
`ceil` and `fract` in a `floor_ring`.
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
... |
ccae884a18c9733c593d14cefb09749926947730 | 2f8bf12144551bc7d8087a6320990c4621741f3d | /library/init/lean/parser/declaration.lean | 40c6679a9d050443ab0e9cd9fb83a38879f72efd | [
"Apache-2.0"
] | permissive | jesse-michael-han/lean4 | eb63a12960e69823749edceb4f23fd33fa2253ce | fa16920a6a7700cabc567aa629ce4ae2478a2f40 | refs/heads/master | 1,589,935,810,594 | 1,557,177,860,000 | 1,557,177,860,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,344 | lean | /-
Copyright (c) 2018 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Sebastian Ullrich
Parsers for commands that declare things
-/
prelude
import init.lean.parser.term
namespace Lean
namespace Parser
open Combinators MonadParsec
open Parser.Ha... |
99ae66829bf5d7c88a1d6120208dfd3637fdd34a | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/category_theory/limits/presheaf.lean | b18e8cf46220c4ccb89f2ab8f678a2876c33e383 | [
"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 | 15,971 | lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import category_theory.adjunction.limits
import category_theory.adjunction.opposites
import category_theory.elements
import category_theory.limits.functor_category
import... |
2e186d4f16f6bd1436dbfa7a3d290d6c109ea425 | 6dc0c8ce7a76229dd81e73ed4474f15f88a9e294 | /tests/lean/run/withReducibleAndInstancesCrash.lean | c427a771ce47d4892ef41a23601e166838d0332b | [
"Apache-2.0"
] | permissive | williamdemeo/lean4 | 72161c58fe65c3ad955d6a3050bb7d37c04c0d54 | 6d00fcf1d6d873e195f9220c668ef9c58e9c4a35 | refs/heads/master | 1,678,305,356,877 | 1,614,708,995,000 | 1,614,708,995,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 468 | lean | import Lean
@[reducible] def foo (x : Nat) := x + 1
@[reducible] def bla (x y : Nat) := foo (foo x) + foo (foo x)
@[reducible] def boo (x y : Nat) := foo (bla (foo x) (foo y) * bla (foo y) (foo x) * bla (foo y) (foo x))
open Lean
open Lean.Meta
def tst : MetaM Unit := do
let c ← getConstInfo `boo
lambdaTelescope ... |
e899f35e722aac607bc211c90b9557bdabbee4b5 | dc253be9829b840f15d96d986e0c13520b085033 | /colimit/omega_compact.hlean | daa9a6ff6eb0a95d1da47b4dba6a1331ea55f0e8 | [
"Apache-2.0"
] | permissive | cmu-phil/Spectral | 4ce68e5c1ef2a812ffda5260e9f09f41b85ae0ea | 3b078f5f1de251637decf04bd3fc8aa01930a6b3 | refs/heads/master | 1,685,119,195,535 | 1,684,169,772,000 | 1,684,169,772,000 | 46,450,197 | 42 | 13 | null | 1,505,516,767,000 | 1,447,883,921,000 | Lean | UTF-8 | Lean | false | false | 6,583 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Egbert Rijke
-/
import .seq_colim types.unit
open eq nat is_equiv equiv is_trunc pi unit function prod unit sigma sigma.ops sum prod trunc fin
algebra
names... |
9531467f7c5ae1d76be1b41a76d9fd93efe6326a | 7cdf3413c097e5d36492d12cdd07030eb991d394 | /src/game/world3/level3.lean | c9e3e311e16232ea80dd4e84b6f56a5385e1c9af | [] | no_license | alreadydone/natural_number_game | 3135b9385a9f43e74cfbf79513fc37e69b99e0b3 | 1a39e693df4f4e871eb449890d3c7715a25c2ec9 | refs/heads/master | 1,599,387,390,105 | 1,573,200,587,000 | 1,573,200,691,000 | 220,397,084 | 0 | 0 | null | 1,573,192,734,000 | 1,573,192,733,000 | null | UTF-8 | Lean | false | false | 1,046 | lean | import game.world3.level2 -- hide
import mynat.mul -- hide
namespace mynat -- hide
/-
# Multiplication World
## Level 3: `one_mul`
Currently our tools for multiplication are the
following:
* `mul_zero m : m * 0 = 0`
* `zero_mul m : 0 * m = 0`
* `mul_succ a b : a * succ b = a * b + a`
* `mul_one m : m * 1 = 1`
We... |
c7ee30363aee6f900e290c4a91ce0c5791bc6697 | ecdf4e083eb363cd3a0d6880399f86e2cd7f5adb | /src/category_theory/basic.lean | d828dbaafc37803761cd93924aa911c47881cb46 | [] | no_license | fpvandoorn/formalabstracts | 29aa71772da418f18994c38379e2192a6ef361f7 | cea2f9f96d89ee1187d1b01e33f22305cdfe4d59 | refs/heads/master | 1,609,476,761,601 | 1,558,130,287,000 | 1,558,130,287,000 | 97,261,457 | 0 | 2 | null | 1,550,879,230,000 | 1,500,056,313,000 | Lean | UTF-8 | Lean | false | false | 132 | lean | import category_theory.category tactic.omitted
@[obviously] meta def obviously_omitted : tactic unit := tactic.interactive.omitted
|
35b380c9e9c8ca5c0202ee38880875b5c5801b28 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/topology/algebra/ordered/liminf_limsup.lean | b84ab16907e1060aedac360c815c2f1cbcc75177 | [
"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 | 8,437 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Yury Kudryashov
-/
import topology.algebra.ordered.basic
import order.liminf_limsup
/-!
# Lemmas about liminf and limsup in an order topology.
-/
open... |
06298f3ebc428f56e5d0bb8dddb5d95f349d4b52 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/struct_class.lean | 40fa376d084d5bec274aa4dde810bb8318c864d4 | [
"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 | 166 | lean | structure point [class] (A : Type) (B : Type) :=
mk :: (x : A) (y : B)
print classes
structure point2 (A : Type) (B : Type) :=
mk :: (x : A) (y : B)
print classes
|
2cad82846aea477c29ba45402cf91ddcc957f863 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/fieldAutoBound.lean | 847eab275e27ea8b3c05b99a6d4f52de387da401 | [
"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 | 316 | lean | namespace Test
open Function
class LawfulFunctor (f : Type u → Type v) [Functor f] : Prop where
map_const : (Functor.mapConst : α → f β → f α) = Functor.map ∘ const β
id_map (x : f α) : id <$> x = x
comp_map (g : α → β) (h : β → γ) (x : f α) : (h ∘ g) <$> x = h <$> g <$> x
end Test
|
e7a87caedf83c024548612316f0ce3ecb32a2d48 | 95dcf8dea2baf2b4b0a60d438f27c35ae3dd3990 | /src/category_theory/natural_transformation.lean | 197e0592034404051bae1f57c17bf63af998798b | [
"Apache-2.0"
] | permissive | uniformity1/mathlib | 829341bad9dfa6d6be9adaacb8086a8a492e85a4 | dd0e9bd8f2e5ec267f68e72336f6973311909105 | refs/heads/master | 1,588,592,015,670 | 1,554,219,842,000 | 1,554,219,842,000 | 179,110,702 | 0 | 0 | Apache-2.0 | 1,554,220,076,000 | 1,554,220,076,000 | null | UTF-8 | Lean | false | false | 4,348 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tim Baumann, Stephen Morgan, Scott Morrison
Defines natural transformations between functors.
Introduces notations
`F ⟹ G` for the type of natural transformations between functors ... |
f2c7c79ad3c8b137ad9f2cc7242537163d782349 | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/simp2.lean | 75e19991dc7b065b1a3a9a2a2a6337eee38371e6 | [
"Apache-2.0"
] | permissive | codyroux/lean0.1 | 1ce92751d664aacff0529e139083304a7bbc8a71 | 0dc6fb974aa85ed6f305a2f4b10a53a44ee5f0ef | refs/heads/master | 1,610,830,535,062 | 1,402,150,480,000 | 1,402,150,480,000 | 19,588,851 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,503 | lean | -- We can also use Lean simplifier to simplify proofs.
-- First, we prove some theorems about trans. All theorems are just using the fact that
-- we have proof irrelevance in Lean. That is, all proofs of a fact A are considered equal.
theorem trans_refl_right {A : TypeU} {a b : A} (Hab : a = b) (Hbb : b = b) : trans H... |
2df242ccd07607d716d28e3ae7d5bc82042121e8 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/red.lean | bdf39fe493f23cf0b8838817922d64e12ccd0c1a | [
"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 | 486 | lean | constant g : nat → nat
noncomputable definition f := g
example : f = g := rfl
attribute f [irreducible]
example : f = g := rfl -- Error
example (a : nat) (H : a = g a) : f a = a :=
eq.subst H rfl -- Error
attribute f [semireducible]
example (a : nat) (H : a = g a) : f a = a :=
eq.subst H rfl -- Error
example :... |
e9415290db5c07f8207698c158fb4e3dfad1ee12 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/const_choice.lean | 441421f9f00ae31b2829924b7bc78bba99efa1ae | [
"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 | 160 | lean | import data.nat.basic
open nat
definition pred (a : nat) : nat :=
nat.cases_on a
zero
(fun a₁, a₁)
example : pred 1 = 0 :=
rfl
print definition pred
|
81db85234a80389eb191c84194d5a28ba889b103 | cf39355caa609c0f33405126beee2739aa3cb77e | /library/init/meta/smt/rsimp.lean | f3950d262d01ab9ee51d089b014a62b17e47c247 | [
"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 | 6,588 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.meta.smt.smt_tactic init.meta.fun_info init.meta.rb_map
def tactic.id_tag.rsimp : unit := ()
open tactic
private meta def add_lemma (... |
3a318dd356f002c2fe7e53f9ad6d0a6a1cfc4301 | dc253be9829b840f15d96d986e0c13520b085033 | /homotopy/join_theorem.hlean | fdbc4b7a72dcaa76214e735cf5fde062d6c26f34 | [
"Apache-2.0"
] | permissive | cmu-phil/Spectral | 4ce68e5c1ef2a812ffda5260e9f09f41b85ae0ea | 3b078f5f1de251637decf04bd3fc8aa01930a6b3 | refs/heads/master | 1,685,119,195,535 | 1,684,169,772,000 | 1,684,169,772,000 | 46,450,197 | 42 | 13 | null | 1,505,516,767,000 | 1,447,883,921,000 | Lean | UTF-8 | Lean | false | false | 1,962 | hlean | /-- Authors: Clive, Egbert --/
import homotopy.connectedness homotopy.join
open eq sigma pi function join is_conn is_trunc equiv is_equiv
namespace retraction
variables {A B C : Type} (r2 : B → C) (r1 : A → B)
definition is_retraction_compose
[Hr2 : is_retraction r2] [Hr1 : is_retraction r1] :
is_retra... |
22bb1b1da6c6c0003f91466e1fe7140252959977 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/group_theory/free_abelian_group.lean | c8dabb2ed4ef1ad6d8fb67255b771f85eb317bc7 | [
"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 | 19,471 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import algebra.group.pi
import group_theory.free_group
import group_theory.abelianization
import algebra.module.basic -- we use the ℤ-module structure on an add_comm_group in ... |
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