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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
819bf0ecc6983790aefb36ac913ca9c9d52ec5c6 | 6b2a480f27775cba4f3ae191b1c1387a29de586e | /group_rep_2/Tools/matrix.lean | 6f6cb5ffe6f23d31d2853d697505f99f4d2dd2c5 | [] | no_license | Or7ando/group_representation | a681de2e19d1930a1e1be573d6735a2f0b8356cb | 9b576984f17764ebf26c8caa2a542d248f1b50d2 | refs/heads/master | 1,662,413,107,324 | 1,590,302,389,000 | 1,590,302,389,000 | 258,130,829 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 4,833 | lean | import linear_algebra.matrix
import Tools.matrix_tools
universe variables u v w t
open_locale big_operators matrix
open matrix linear_map
/--
Technical : `ite (x0 = x ∧ y0 = y) (1 : R) 0 = (ite (x0 = x) 1 0) * (ite (y0 = y) 1 0)`
-/
@[simp]lemma mul_ite_ite {X : Type u}[fintype X][decidable_eq X] {R : Type v} [com... |
a1680cadbd1aba3c3eb64f33342cd3eec578bbf6 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /stage0/src/Lean/Data/Lsp/LanguageFeatures.lean | b79aa82d5c4e635c3ef1c68e8fc3291406e7dff0 | [
"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 | 6,494 | lean | /-
Copyright (c) 2020 Wojciech Nawrocki. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wojciech Nawrocki
-/
import Lean.Data.Json
import Lean.Data.Lsp.Basic
namespace Lean
namespace Lsp
open Json
structure CompletionOptions where
triggerCharacters? : Option (A... |
a1f2e1b4f4545af2353bc9743106d9d72aa6767b | 8d65764a9e5f0923a67fc435eb1a5a1d02fd80e3 | /src/data/set/basic.lean | b9aa78996e1f4be46469f778a4f05941892fd9cd | [
"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 | 113,077 | lean | /-
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
-/
import logic.unique
import logic.relation
import order.boolean_algebra
/-!
# Basic properties of sets
Sets in Lean are homogeneous; all their eleme... |
be9e9d715025ec0336a72254381a24626c471d87 | 66a6486e19b71391cc438afee5f081a4257564ec | /spectrum/spectrification.hlean | 07b5053ab82559992e7171a57b7c6508f4934f62 | [
"Apache-2.0"
] | permissive | spiceghello/Spectral | c8ccd1e32d4b6a9132ccee20fcba44b477cd0331 | 20023aa3de27c22ab9f9b4a177f5a1efdec2b19f | refs/heads/master | 1,611,263,374,078 | 1,523,349,717,000 | 1,523,349,717,000 | 92,312,239 | 0 | 0 | null | 1,495,642,470,000 | 1,495,642,470,000 | null | UTF-8 | Lean | false | false | 11,827 | hlean | import .basic ..colimit.pointed
open eq pointed succ_str is_equiv equiv spectrum.smap seq_colim nat
namespace spectrum
/- Prespectrification -/
definition is_sconnected {N : succ_str} {X Y : gen_prespectrum N} (h : X →ₛ Y) : Type :=
Π (E : gen_spectrum N), is_equiv (λ g : Y →ₛ E, g ∘ₛ h)
-- We introduce a p... |
964a224fecd4382860010cb8f1b8ef2c8d03f3ba | 94e33a31faa76775069b071adea97e86e218a8ee | /src/group_theory/order_of_element.lean | 32b543e312ecf886b522b32bcdba4ae8b5d0d133 | [
"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 | 33,816 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Julian Kuelshammer
-/
import algebra.hom.iterate
import data.nat.modeq
import data.set.pointwise
import dynamics.periodic_pts
import group_theory.index
/-!
# Order of ... |
f8764b98e655616435a696de34151a1de09b9a40 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/topology/fiber_bundle/constructions.lean | a4d859c6166d302adaf2106d2dd244f55ddbc50b | [
"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 | 16,923 | lean | /-
Copyright © 2022 Nicolò Cavalleri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolò Cavalleri, Sébastien Gouëzel, Heather Macbeth, Floris van Doorn
-/
import topology.fiber_bundle.basic
/-!
# Standard constructions on fiber bundles
> THIS FILE IS SYNCHRONIZED... |
0f9802e180b371a5b85fefdf76dea274deb1a91b | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/algebra/tower.lean | bbc8bc168af954fb11f51b552a618f60f6043e88 | [
"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 | 11,297 | lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Anne Baanen
-/
import algebra.algebra.equiv
import linear_algebra.span
/-!
# Towers of algebras
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a... |
9b0c707db67dc143b3f97af27a6a8be6a04f6da9 | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/buffer/basic.lean | 660eb5cc666c28c89494040bd4ed1cde63ae3385 | [
"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 | 6,147 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
General utility functions for buffers.
-/
import data.buffer
import data.array.lemmas
import control.traversable.instances
namespace buffer
open function
variables {α : Ty... |
e8276661713ab20bf0bd0ba08cf8b0b8814082d8 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/mv_polynomial/rename.lean | 4988434d325025d19b2e498c578a7be546fe6211 | [] | 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 | 7,119 | 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
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.mv_polynomial.basic
import Mathlib.PostPort
universes... |
1e7151f02e4ada72eed37d0f5ecc95db26e306f1 | 5749d8999a76f3a8fddceca1f6941981e33aaa96 | /src/order/filter/lift.lean | 58e35ae78834c0dbdb539d7b686699e3e51db6bd | [
"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 | 16,568 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Lift filters along filter and set functions.
-/
import order.filter.basic
open lattice set
open_locale classical
namespace filter
variables {α : Type*} {β : Type*} {... |
6471759d4e3ea359efd76b369f70b75366e0c082 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/combinatorics/derangements/finite.lean | 3fe5af9fa252da6654ecc835b1b8d8e9aedc0ec7 | [
"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 | 4,732 | lean | /-
Copyright (c) 2021 Henry Swanson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Henry Swanson
-/
import combinatorics.derangements.basic
import data.fintype.card
import tactic.delta_instance
import tactic.ring
/-!
# Derangements on fintypes
This file contains lem... |
ea79faad9df70bdb497f3b607db5c343a6066756 | 761d983a78bc025071bac14a3facced881cf5e53 | /affine/aff_coord_basis.lean | 4d753fd524446cb6e58154ebbabb3a132085a299 | [] | no_license | rohanrajnair/affine_lib | bcf22ff892cf74ccb36a95bc9b7fff8e0adb2d0d | 83076864245ac547b9d615bc6a23804b1b4a8f70 | refs/heads/master | 1,673,320,928,343 | 1,603,036,653,000 | 1,603,036,653,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,125 | lean | import .aff_coord_space .affine .list_stuff data.real.basic
universes u v w x
variables (X : Type u) (K : Type v) (V : Type w) (n : ℕ) (k : K)
[inhabited K] [field K] [add_comm_group V] [vector_space K V] [affine_space X K V]
abbreviation zero := list.field_zero K n
def list.to_basis_vec : fin n → list K :... |
1058aeffe943c5d036ca799c4dfc22c94a35242d | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/sym_auto.lean | 8686b4991ad7a404e59fddd576ec1f3e02f2060d | [] | 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 | 4,895 | lean | /-
Copyright (c) 2020 Kyle Miller All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Kyle Miller.
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.multiset.basic
import Mathlib.data.vector2
import Mathlib.tactic.tidy
import Mathlib.PostPort... |
339d50a86556ce1972575f74f0600b21c39920ef | 1e3a43e8ba59c6fe1c66775b6e833e721eaf1675 | /src/data/nat/modeq.lean | 981efb5bf41a081cb978ffe78c0226c53053d131 | [
"Apache-2.0"
] | permissive | Sterrs/mathlib | ea6910847b8dfd18500486de9ab0ee35704a3f52 | d9327e433804004aa1dc65091bbe0de1e5a08c5e | refs/heads/master | 1,650,769,884,257 | 1,587,808,694,000 | 1,587,808,694,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 12,447 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
Modular equality relation.
-/
import data.int.gcd
import tactic.abel
import data.list.rotate
namespace nat
/-- Modular equality. `modeq n a b`, or `a ≡ b [MOD n]`, me... |
5088a26b0644f0320624bd4df2cb18e00ab9f0e4 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/category_theory/limits/shapes/pullbacks.lean | 15902cba45dce0d8da45e7c3b7f8a61aab0f8336 | [
"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 | 45,065 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Markus Himmel, Bhavik Mehta
-/
import category_theory.limits.shapes.wide_pullbacks
import category_theory.limits.shapes.binary_products
/-!
# Pullbacks
We define a ca... |
01f32147ab7c8fc5947c2cc9c5e740c99fb54655 | 33340b3a23ca62ef3c8a7f6a2d4e14c07c6d3354 | /dlo/main.lean | 3f077033cd71337dbb5245fb2f7fed10b5996032 | [] | no_license | lclem/cooper | 79554e72ced343c64fed24b2d892d24bf9447dfe | 812afc6b158821f2e7dac9c91d3b6123c7a19faf | refs/heads/master | 1,607,554,257,488 | 1,578,694,133,000 | 1,578,694,133,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 179 | lean | import .reify .reify' .eval_qe
meta def quant_elim : tactic unit :=
pexact ``(eval_qe.elim_left _)
meta def dlo : tactic unit :=
reify' >> quant_elim >> tactic.exact_dec_trivial |
9f81d1f6d011503c7cd4e6b6d8fa425880d9714d | 618003631150032a5676f229d13a079ac875ff77 | /src/field_theory/splitting_field.lean | 0360e462ce8a1fda902d840d1fafe9326353ffc6 | [
"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 | 8,883 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
Definition of splitting fields, and definition of homomorphism into any field that splits
-/
import data.polynomial
import ring_theory.principal_ideal_domain
universes u v... |
1a954aa0238f6d3eb82f63f5e40735fb4d5ee2fb | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/algebra/unitization.lean | a789b95747b4bde20974df3e9d1016d7c027be6b | [
"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 | 21,701 | lean | /-
Copyright (c) 2022 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import algebra.algebra.basic
import linear_algebra.prod
import algebra.hom.non_unital_alg
/-!
# Unitization of a non-unital algebra
> THIS FILE IS SYNCHRONIZED WITH ... |
b81075285f5ecdad859802bd7683296f8c2be734 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/topology/sheaves/abelian.lean | c63e2191cf07f56196c4d8b36bc157ff71fbd2d9 | [
"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 | 2,214 | lean | /-
Copyright (c) 2022 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz, Jujian Zhang
-/
import category_theory.abelian.functor_category
import category_theory.preadditive.additive_functor
import category_theory.preadditive.functor_category
import... |
7e25bdb7a607c4fa7d15904a12ff450e0f5ea120 | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/int/range.lean | 92b1f509c6bc81ff0401ec2a5ee3e3e9fee740dd | [
"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 | 1,797 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro and Kenny Lau
-/
import data.int.basic
import data.list.range
namespace int
local attribute [semireducible] int.nonneg
/-- List enumerating `[m, n)`. -/
def range (m n : ℤ... |
89d48f61a08b79337eb4ffab133c7f55964aa0c6 | 367134ba5a65885e863bdc4507601606690974c1 | /src/computability/turing_machine.lean | d9a989195cc3818bffd56ce498d2d9305da73c9a | [
"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 | 109,920 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
-/
import algebra.order
import data.fintype.basic
import data.pfun
import tactic.apply_fun
import logic.function.iterate
/-!
# Turing machines
This file defines a seque... |
015b363169cb44f6bbbe2184b9d72db222caece2 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/algebra/module/linear_map.lean | a6067dae5c0d5dfdb9c66ee7d24c15ba49603ac2 | [
"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 | 22,644 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nathaniel Thomas, Jeremy Avigad, Johannes Hölzl, Mario Carneiro, Anne Baanen
-/
import algebra.group.hom
import algebra.module.basic
import algebra.group_action_hom
/-!
# Linear maps and... |
c34337acd5863ef85e29350a161e95790963fe7a | 07c76fbd96ea1786cc6392fa834be62643cea420 | /hott/hit/two_quotient.hlean | 298025ba27806f256268ee028c9e0f64a85a018f | [
"Apache-2.0"
] | permissive | fpvandoorn/lean2 | 5a430a153b570bf70dc8526d06f18fc000a60ad9 | 0889cf65b7b3cebfb8831b8731d89c2453dd1e9f | refs/heads/master | 1,592,036,508,364 | 1,545,093,958,000 | 1,545,093,958,000 | 75,436,854 | 0 | 0 | null | 1,480,718,780,000 | 1,480,718,780,000 | null | UTF-8 | Lean | false | false | 31,471 | 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
open quotient eq circle sum sigma equiv function relation e_closure
/-
Thi... |
02d35c02c8e7acb10c369548a232884d3c60f3ff | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/category_theory/whiskering.lean | 6686581c13080794c7bd0bf64a7e27efa0ac6121 | [
"Apache-2.0"
] | permissive | gebner/mathlib | eab0150cc4f79ec45d2016a8c21750244a2e7ff0 | cc6a6edc397c55118df62831e23bfbd6e6c6b4ab | refs/heads/master | 1,625,574,853,976 | 1,586,712,827,000 | 1,586,712,827,000 | 99,101,412 | 1 | 0 | Apache-2.0 | 1,586,716,389,000 | 1,501,667,958,000 | Lean | UTF-8 | Lean | false | false | 5,943 | 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]
... |
69bd85bf806fdb76f7bd5e2eee4d8a1bd6a956fd | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/1779.lean | bf501903565ee681e4092d6de5a88ccce57ee2a7 | [
"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 | 475 | lean | section
variable [Coe Int R] [Neg R] (a : R) (n : Int)
#check a = -n
#check a = (-n : R)
#check -n = a
#check (-n : R) = a
end
section
variable [Coe Int R] [Add R] (a : R) (n : Int)
#check a = n + n
#check a = (n + n : R)
end
section
variable [Coe Int R] [OfNat R 0] [Sub R] (a : R) (n : Int)
#check a = 0 - n
#check a... |
b82f59d880ff0e1b932cf50a934e899ace6698e7 | de91c42b87530c3bdcc2b138ef1a3c3d9bee0d41 | /old/expressions/classical_hertz.lean | bbfa110127c8c2647f08febf76fb866652350560 | [] | no_license | kevinsullivan/lang | d3e526ba363dc1ddf5ff1c2f36607d7f891806a7 | e9d869bff94fb13ad9262222a6f3c4aafba82d5e | refs/heads/master | 1,687,840,064,795 | 1,628,047,969,000 | 1,628,047,969,000 | 282,210,749 | 0 | 1 | null | 1,608,153,830,000 | 1,595,592,637,000 | Lean | UTF-8 | Lean | false | false | 1,206 | lean | import ...phys.src.classical_hertz
namespace lang.classicalHertz
structure var : Type :=
mk :: (num : ℕ)
structure spaceVar extends var
def myvar : spaceVar := ⟨⟨2⟩⟩
def p : spaceVar := ⟨⟨1⟩⟩
inductive spaceExpr
| lit (v : classicalHertz)
| var (v : spaceVar)
abbreviation spaceEnv := spaceVar → classicalHertz
a... |
32ce7f2ebc45c765f35d810ebe56369234aee97c | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/1663.lean | 09576d833be1fa4552fe6ba4749b597ac11515d9 | [
"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 | 616 | lean | inductive statement : Type
| Sswitch : list (option ℤ × statement) → statement
open statement
mutual def find_label, find_label_ls
with find_label : statement → nat → option (statement × nat)
| (Sswitch sl) := λ k, find_label_ls sl k
with find_label_ls : list (option ℤ × statement) → nat → option (statement × nat)
... |
8c38b9f48dfe9234caebd53eeac3ebbb0068ddc1 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/topology/maps.lean | e9f61dbcc69a30fa0e2779b39b9d8c5e17e2c25f | [
"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 | 20,304 | 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 topology.order
/-!
# Specific classes of maps between topological spaces
This file introduces the following properties of a m... |
6f334ae977236632c47bbf0a09a1ab67f1c1641d | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/data/option/basic.lean | f31bfca6345d7c4d40191ea176e3b6a39aa26802 | [
"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 | 7,626 | 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 tactic.basic
namespace option
variables {α : Type*} {β : Type*} {γ : Type*}
lemma some_ne_none (x : α) : some x ≠ none := λ h, option.no_confusion h
@[simp]... |
adb8502f38c2c6f31075022910946d5ca1b96262 | d642a6b1261b2cbe691e53561ac777b924751b63 | /src/topology/dense_embedding.lean | 5e9be96b85887fe753a8912104815f3272733d7b | [
"Apache-2.0"
] | permissive | cipher1024/mathlib | fee56b9954e969721715e45fea8bcb95f9dc03fe | d077887141000fefa5a264e30fa57520e9f03522 | refs/heads/master | 1,651,806,490,504 | 1,573,508,694,000 | 1,573,508,694,000 | 107,216,176 | 0 | 0 | Apache-2.0 | 1,647,363,136,000 | 1,508,213,014,000 | Lean | UTF-8 | Lean | false | false | 13,596 | lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot
-/
import topology.separation
/-!
# Dense embeddings
This file defines three properties of functions:
`dense_range f` means `f` has ... |
78fbb6694de3aee26aaa5af9cc76c12c937b85ea | f1dc39e1c68f71465c8bf79910c4664d03824751 | /library/init/data/nat/lemmas.lean | f3460045884496c98f4f21cdeebdaf0acf065925 | [
"Apache-2.0"
] | permissive | kckennylau/lean-2 | 6504f45da07bc98b098d726b74130103be25885c | c9a9368bc0fd600d832bd56c5cb2124b8a523ef9 | refs/heads/master | 1,659,140,308,864 | 1,589,361,166,000 | 1,589,361,166,000 | 263,748,786 | 0 | 0 | null | 1,589,405,915,000 | 1,589,405,915,000 | null | UTF-8 | Lean | false | false | 49,459 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad
-/
prelude
import init.data.nat.basic init.data.nat.div init.meta init.algebra.functions
universes u
namespace nat
attribute [pre_smt] nat_zero... |
65ca1a87ebcdad845469699473771bd5bde63600 | 2d787ac9a5ab28a7d164cd13cee8a3cdc1e4680a | /src/my_exercises/04_exists.lean | 7dbe11ab0f752830acc4b722016e39cc3a3a7ea8 | [
"Apache-2.0"
] | permissive | paulzfm/lean3-tutorials | 8c113ec2c9494d401c8a877f094db93e5a631fd6 | f41baf1c62c251976ec8dd9ccae9e85ec4c4d336 | refs/heads/master | 1,679,267,488,532 | 1,614,782,461,000 | 1,614,782,461,000 | 344,157,026 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,947 | lean | import data.real.basic
import data.int.parity
/-
In this file, we learn how to handle the ∃ quantifier.
In order to prove `∃ x, P x`, we give some x₀ using tactic `use x₀` and
then prove `P x₀`. This x₀ can be an object from the local context
or a more complicated expression.
-/
example : ∃ n : ℕ, 8 = 2*n :=
begin
... |
fb716fbf45a32b68f8ab4cf7175a6cac14d897dc | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/ring_theory/non_zero_divisors.lean | 5c2c79a045708ee0cc7cfa57f4bb82ff5d0716ed | [
"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 | 3,769 | lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Devon Tuma
-/
import group_theory.submonoid.operations
import group_theory.submonoid.membership
/-!
# Non-zero divisors
In this file we define the submonoid `non_zero_divisors... |
70d81922534374a2595d690d3057e42492c0972d | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/tactic/group.lean | 1cfe207169a8e4df0794d6dab9d18fe060c1de42 | [
"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 | 3,834 | lean | /-
Copyright (c) 2020. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import tactic.ring
import tactic.doc_commands
import algebra.group.commutator
/-!
# `group`
Normalizes expressions in the language of groups. The basic idea is to use the simplifi... |
d8ee176f39ff3e28020feb800251060f0264846b | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/topology/algebra/uniform_group.lean | 0720c33d8c0119eda12637e7cf35c677d11a16de | [
"Apache-2.0"
] | permissive | dupuisf/mathlib | 62de4ec6544bf3b79086afd27b6529acfaf2c1bb | 8582b06b0a5d06c33ee07d0bdf7c646cae22cf36 | refs/heads/master | 1,669,494,854,016 | 1,595,692,409,000 | 1,595,692,409,000 | 272,046,630 | 0 | 0 | Apache-2.0 | 1,592,066,143,000 | 1,592,066,142,000 | null | UTF-8 | Lean | false | false | 19,552 | lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl
-/
import topology.uniform_space.uniform_embedding
import topology.uniform_space.complete_separated
import topology.algebra.group
import tactic.abel
/-!... |
da853a0b9bfb89d86b65d117a1fdaff10f7e0a42 | 23c79f5a2b724d0a6865a697f74bc337c40a1c17 | /verified-counting/src/elgamal_encryption.lean | ffbc6026289f5d29816b31e91bc76ac95adca185 | [] | no_license | mukeshtiwari/Puzzles | 145e679e637d1c36363c90863cba7c0fda0190b1 | 4a760e7dc6c65cab0fde86d0296d863c62fdda29 | refs/heads/master | 1,608,024,738,873 | 1,607,504,305,000 | 1,607,504,305,000 | 5,691,003 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,276 | lean | import data.zmod.basic data.nat.prime
number_theory.quadratic_reciprocity
tactic.find tactic.omega list_lemma
namespace encryption
variables
(p q k : ℕ) (g h pubkey : zmod p) (prikey : zmod q)
(Hk : 2 ≤ k) (Hp : fact (nat.prime p)) (Hq : fact (nat.prime q))
(Hdiv : p = q * k + 1) (H₁ : h ≠ 0) (H₂ : h^k... |
749c91b9e4fd394bbc2b66897a777248d6364b08 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/group_theory/specific_groups/quaternion.lean | 00cbba859b363c8c6fa21e252ced7af8d698dd98 | [
"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 | 9,214 | lean | /-
Copyright (c) 2021 Julian Kuelshammer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Kuelshammer
-/
import data.zmod.basic
import data.nat.basic
import tactic.interval_cases
import group_theory.specific_groups.dihedral
import group_theory.specific_groups.cyc... |
e835fd5d56ead7e8e9b969c5eff75bc6a025c9e3 | aa2345b30d710f7e75f13157a35845ee6d48c017 | /data/real/cau_seq_filter.lean | f2ee0a34566e3f7560b81f1521e90cd161a97278 | [
"Apache-2.0"
] | permissive | CohenCyril/mathlib | 5241b20a3fd0ac0133e48e618a5fb7761ca7dcbe | a12d5a192f5923016752f638d19fc1a51610f163 | refs/heads/master | 1,586,031,957,957 | 1,541,432,824,000 | 1,541,432,824,000 | 156,246,337 | 0 | 0 | Apache-2.0 | 1,541,434,514,000 | 1,541,434,513,000 | null | UTF-8 | Lean | false | false | 9,838 | lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis
Reconcile the filter notion of Cauchy-ness with the cau_seq notion on normed spaces.
-/
import analysis.topology.uniform_space analysis.normed_space data.real.cau_se... |
deecdbdd60092c01cf73babb0ee123b1c84c3210 | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /counterexamples/phillips.lean | e3b23b407547331a3a51c6a85678834b9d4cdaab | [
"Apache-2.0"
] | permissive | hikari0108/mathlib | b7ea2b7350497ab1a0b87a09d093ecc025a50dfa | a9e7d333b0cfd45f13a20f7b96b7d52e19fa2901 | refs/heads/master | 1,690,483,608,260 | 1,631,541,580,000 | 1,631,541,580,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 28,542 | lean | /-
Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import analysis.normed_space.hahn_banach
import measure_theory.measure.lebesgue
/-!
# A counterexample on Pettis integrability
There are several theories of i... |
2508603158dc732032c09715c8615c798fe5331e | 0cdf5dd5a0097eee7ab6414c7b09ec3384e83e30 | /library/init/data/int/basic.lean | dd0540ce8bc5aa3e6fa4967c46a2a2907dfa96e9 | [
"Apache-2.0"
] | permissive | palotasb/lean | 0304993115bb1877b336d434fcd578a410367f3a | 587540f11bcc92c8242c66ab910a3a3f548c70bd | refs/heads/master | 1,620,943,727,531 | 1,515,195,659,000 | 1,515,195,659,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 17,940 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
The integers, with addition, multiplication, and subtraction.
-/
prelude
import init.data.nat.lemmas init.data.nat.gcd init.meta.transfer init.data.list
open nat
/- the ... |
c4b0880fd099666d2d4fe816b1c3a69916e5cbc9 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/limits/yoneda_auto.lean | e03f7ec085851e72f660b0926b2c18b3edfca6fe | [] | 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 | 5,575 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Bhavik Mehta
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.category_theory.limits.limits
import Mathlib.category_theory.limits.functor_c... |
eda25f673516fc497bf24773436d13408b141c9b | ae1e94c332e17c7dc7051ce976d5a9eebe7ab8a5 | /stage0/src/Std/Data/HashMap.lean | 1a588a981313df9308de927d46b8b04ee41aabd4 | [
"Apache-2.0"
] | permissive | dupuisf/lean4 | d082d13b01243e1de29ae680eefb476961221eef | 6a39c65bd28eb0e28c3870188f348c8914502718 | refs/heads/master | 1,676,948,755,391 | 1,610,665,114,000 | 1,610,665,114,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,234 | lean | /-
Copyright (c) 2018 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
import Std.Data.AssocList
namespace Std
universes u v w
def HashMapBucket (α : Type u) (β : Type v) :=
{ b : Array (AssocList α β) // b.size > 0 }
def Ha... |
ab8a2a4a7b9b0c87ea826d7244569a6f2d119dea | 0c1546a496eccfb56620165cad015f88d56190c5 | /library/init/data/subtype/instances.lean | 641f94f9398452a8e113e68fde81bb271e8da4b0 | [
"Apache-2.0"
] | permissive | Solertis/lean | 491e0939957486f664498fbfb02546e042699958 | 84188c5aa1673fdf37a082b2de8562dddf53df3f | refs/heads/master | 1,610,174,257,606 | 1,486,263,620,000 | 1,486,263,620,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 388 | 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.meta.mk_dec_eq_instance init.data.subtype.basic
open tactic subtype
universe variables u
instance {α : Type u} {p : α → Prop} [decidable... |
f7ca7256f34975afdac849d6ec3d3be5f7770fb5 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /stage0/src/Lean/Meta/Constructions.lean | ec665b3d95db8e2abfc7bea2dcb55eac59fa2edb | [
"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 | 5,207 | 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
-/
import Lean.AuxRecursor
import Lean.Meta.AppBuilder
namespace Lean
@[extern "lean_mk_cases_on"] constant mkCasesOnImp (env : Environment) (declName : @& N... |
b9f1d5d2c7bf8bc43581152be841ccbab3bb8cfa | b70031c8e2c5337b91d7e70f1e0c5f528f7b0e77 | /src/topology/category/Compactum.lean | 60b0db1d7361cbcc1f9e058b921b144c278ac168 | [
"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 | 17,290 | lean | /-
Copyright (c) 2020 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz
-/
import category_theory.monad.types
import category_theory.monad.limits
import category_theory.equivalence
import topology.category.CompHaus
import data.set.constructions
/-... |
e1e1a746d8ba7cc02227bf3d08d4d313c7665cd4 | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/tactic/find.lean | 35148664ff655f455aa5e09f0305ad780c7b372d | [
"Apache-2.0"
] | permissive | fpvandoorn/mathlib | b21ab4068db079cbb8590b58fda9cc4bc1f35df4 | b3433a51ea8bc07c4159c1073838fc0ee9b8f227 | refs/heads/master | 1,624,791,089,608 | 1,556,715,231,000 | 1,556,715,231,000 | 165,722,980 | 5 | 0 | Apache-2.0 | 1,552,657,455,000 | 1,547,494,646,000 | Lean | UTF-8 | Lean | false | false | 2,396 | lean | /-
Copyright (c) 2017 Sebastian Ullrich. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Ullrich
-/
import tactic.basic
open expr
open interactive
open lean.parser
open tactic
private meta def match_subexpr (p : pattern) : expr → tactic (list expr)
| e := pr... |
08315485c0a133e02977b1e0892acc572f47c7e7 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /test/localized/localized.lean | 6d7e4030ebc252fe825b6de246b25fee4723d460 | [
"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 | 1,491 | lean | import tactic.localized
import algebra.group_power.lemmas
open tactic
local infix ` ⊹ `:59 := nat.mul
local infix ` ↓ `:59 := pow
local infix ` ⊖ `:59 := pow
example : 2 ⊹ 3 = 6 := rfl
example : 2 ↓ 3 = 8 := rfl
example : 2 ⊖ 3 = 8 := rfl
example {n m : ℕ} (h : n < m) : n ≤ m := by { success_if_fail { simp [h] }, exac... |
76c65f18d432499013587f8c25e12030d50df258 | 94637389e03c919023691dcd05bd4411b1034aa5 | /src/zzz_junk/temp.lean | cbe831dbbc1b0467250ba9a5be67105b224c68f3 | [] | no_license | kevinsullivan/complogic-s21 | 7c4eef2105abad899e46502270d9829d913e8afc | 99039501b770248c8ceb39890be5dfe129dc1082 | refs/heads/master | 1,682,985,669,944 | 1,621,126,241,000 | 1,621,126,241,000 | 335,706,272 | 0 | 38 | null | 1,618,325,669,000 | 1,612,374,118,000 | Lean | UTF-8 | Lean | false | false | 5,193 | lean | /-
Namespaces
-/
namespace hidden -- "hidden" has no special meaning
/-
Polymorphism
-/
/-
Polymorphic Functions
-/
-- A problem
def id_nat : nat → nat :=
λ n, n
def id_string : string → string :=
λ n, n
def id_bool : bool → bool :=
λ n, n
/- A solution
Parametric polymorphism means (1) one of
the... |
5f9a0c191202522d04dd743e3029558cc6fadc2f | 4727251e0cd73359b15b664c3170e5d754078599 | /src/analysis/convex/jensen.lean | a548eb26f0c6b08b9f1994f0c349b25e665f4d6b | [
"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 | 6,027 | lean | /-
Copyright (c) 2019 Alexander Bentkamp. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp, Yury Kudriashov
-/
import analysis.convex.combination
import analysis.convex.function
/-!
# Jensen's inequality and maximum principle for convex functions
In ... |
24add2074776237a9e6ad01f659d456831c4d4ce | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/order/conditionally_complete_lattice/basic.lean | 9d6897de353eaaf170dbd8dd6bc9d1584818eebc | [
"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 | 56,180 | lean | /-
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import order.bounds.basic
import order.well_founded
import data.set.intervals.basic
import data.set.lattice
/-!
# Theory of conditionally complete lattices.
A... |
009cc0b48f659db4b1f8c9186473ae9d05105abe | e447aba4f95cefc4e26736a59e4781640deafcc5 | /src/main.lean | cedf0739eb40704694da3b452b74553980b2a7a2 | [
"Unlicense"
] | permissive | Eloitor/four-squares-modular-forms | 45674978910900ac4b773316d2642774ecad3f7e | f1eaa559640b75371149f5fe819869babeb60aa2 | refs/heads/main | 1,677,012,829,783 | 1,611,628,491,000 | 1,611,628,491,000 | 321,801,679 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 118 | lean | import data.nat.basic
theorem nat.sum_four_squares (n : ℕ ):
∃ (a b c d : ℕ), a^2+b^2+c^2+d^2 = n :=
sorry
|
121799f3eee25bc6eeec391accd6b5ee17a9c551 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/category_theory/limits/cone_category.lean | 21da24abd0217436b85dfb4fc6bc26fc6fa9b022 | [
"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 | 8,861 | 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.adjunction.comma
import category_theory.limits.preserves.shapes.terminal
import category_theory.structured_arrow
import category_theory.limits.shapes... |
64a2db716df50307e4574933138d479b28d00dba | a726f88081e44db9edfd14d32cfe9c4393ee56a4 | /src/game/world7/level7.lean | 52650f424f325b15a486c3b34ccfd06e400b44f8 | [] | no_license | b-mehta/natural_number_game | 80451bf10277adc89a55dbe8581692c36d822462 | 9faf799d0ab48ecbc89b3d70babb65ba64beee3b | refs/heads/master | 1,598,525,389,186 | 1,573,516,674,000 | 1,573,516,674,000 | 217,339,684 | 0 | 0 | null | 1,571,933,100,000 | 1,571,933,099,000 | null | UTF-8 | Lean | false | false | 802 | lean | /-
# Advanced proposition world.
## Level 7: `or_symm`
Proving that $(P\lor Q)\implies(Q\lor P)$ involves an element of danger.
`intro h,` is the obvious start. But now,
even though the goal is an `∨` statement, both `left` and `right` put
you in a situation with an impossible goal. Fortunately, after `intro h,`
yo... |
09448afac966d76a514056f7fc943d61d82b02a6 | b29f946a2f0afd23ef86b9219116968babbb9f4f | /src/lean_format_tests/sandwich.lean | 699b90d9952f08dff59493412d6ab74be8717ff5 | [
"Apache-2.0"
] | permissive | ImperialCollegeLondon/M1P1-lean | 58be7394fded719d95e45e6b10e1ecf2ed3c7c4c | 3723468cc50f8bebd00a9811caf25224a578de17 | refs/heads/master | 1,587,063,867,779 | 1,572,727,164,000 | 1,572,727,164,000 | 165,845,802 | 14 | 4 | Apache-2.0 | 1,549,730,698,000 | 1,547,554,675,000 | Lean | UTF-8 | Lean | false | false | 2,258 | lean | -- begin header
import limits
namespace M1P1
-- end header
/- Section
The sandwich theorem
-/
/- Sub-section
Introduction
-/
/-
The sandwich theorem, or squeeze theorem, for real sequences is the statement that if $(a_n)$, $(b_n)$, and $(c_n)$ are three real-valued sequences satisfying $a_n≤ b_n≤ c_n$ for all $n$, ... |
404490109082cd20daf1005241b01b7c2e85bf54 | fe84e287c662151bb313504482b218a503b972f3 | /src/data/SL2N.lean | 4f8f134965367f1f1f6a54c4d82e8c6f3de9f295 | [] | 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 | 30,457 | lean | /-
Copyright (c) 2019 Neil Strickland. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Neil Strickland
This file defines the monoid SL₂(ℕ) of 2 × 2 matrices over ℕ with
determinant one. Various things about the Euclidean algorithm,
continued fractions and so on can be... |
0005987beecfd16eb7449668259b490311c3dc57 | 5fbbd711f9bfc21ee168f46a4be146603ece8835 | /lean/natural_number_game/tutorial/3.lean | b807d112bb152480bf53c3d2827a6543f542accb | [
"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 | 88 | lean | lemma example3 (a b : mynat) (h : succ a = b) : succ(succ(a)) = succ(b) :=
rwa h,
end
|
57db6f8bfc20aa2500a655aa9bf1beb4c9cdde3f | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /11_Tactic-Style_Proofs.org.44.lean | 0b96f5e2c02dad67c193ca65a984ea75b30822c2 | [] | no_license | cjmazey/lean-tutorial | ba559a49f82aa6c5848b9bf17b7389bf7f4ba645 | 381f61c9fcac56d01d959ae0fa6e376f2c4e3b34 | refs/heads/master | 1,610,286,098,832 | 1,447,124,923,000 | 1,447,124,923,000 | 43,082,433 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 209 | lean | import standard
import data.nat
open nat
-- BEGIN
variables (f : nat → nat → nat → nat) (a b : nat)
example (H₁ : a = b) (H₂ : f b a b = 0) : f a a a = 0 :=
by rewrite [H₁ at {1, 3}, H₂]
-- END
|
6e391324eb8e7fc73b4bee269b834503f06933ef | 968e2f50b755d3048175f176376eff7139e9df70 | /examples/prop_logic_theory/unnamed_1109.lean | f18badbe76aeff0ee6e8941b20373c54952efdce | [] | no_license | gihanmarasingha/mth1001_sphinx | 190a003269ba5e54717b448302a27ca26e31d491 | 05126586cbf5786e521be1ea2ef5b4ba3c44e74a | refs/heads/master | 1,672,913,933,677 | 1,604,516,583,000 | 1,604,516,583,000 | 309,245,750 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 116 | lean | variables p q r : Prop
-- BEGIN
theorem and_assoc1 : (p ∧ q) ∧ r → p ∧ (q ∧ r) :=
begin
sorry
end
-- END |
ee0d7bb1c317817d5715b201a3c0371f5c490f91 | 3dc4623269159d02a444fe898d33e8c7e7e9461b | /.github/workflows/geo/Yoneda.lean | 5d213ae31bbfdee2806b3b53804fa36067a291d4 | [] | no_license | Or7ando/lean | cc003e6c41048eae7c34aa6bada51c9e9add9e66 | d41169cf4e416a0d42092fb6bdc14131cee9dd15 | refs/heads/master | 1,650,600,589,722 | 1,587,262,906,000 | 1,587,262,906,000 | 255,387,160 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 115 | lean | import .global
import .Spec
universes u
local notation `Ring` := CommRing.{u}
local notation `Set` := Type u
|
b00a99a54b6e1b33af95ef8980df7aeb255ca9f6 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /tests/lean/run/methodsRetInhabited.lean | 5df0496087a24fef31a6ab54dbd56972a81994a4 | [
"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 | 347 | lean | open Lean
def exec (x : MacroM α) : Option α :=
match x {
mainModule := `Expander
currMacroScope := 0
ref := arbitrary
methods := arbitrary } { macroScope := 0 } with
| EStateM.Result.ok a s => a
| _ => none
def tst : MacroM String := do
let n ← Macro.getCurrNamespace
return toSt... |
38e478e8c0cd97a8f4fe77c151ea764d56aa76c7 | 856e2e1615a12f95b551ed48fa5b03b245abba44 | /src/computability/list_computable.lean | e0c7889c53b934be5f7740f46a05346647d3e8eb | [
"Apache-2.0"
] | permissive | pimsp/mathlib | 8b77e1ccfab21703ba8fbe65988c7de7765aa0e5 | 913318ca9d6979686996e8d9b5ebf7e74aae1c63 | refs/heads/master | 1,669,812,465,182 | 1,597,133,610,000 | 1,597,133,610,000 | 281,890,685 | 1 | 0 | null | 1,595,491,577,000 | 1,595,491,576,000 | null | UTF-8 | Lean | false | false | 6,452 | lean | import .encode_alphabet
import computability.turing_machine
import algebra.polynomial.basic
namespace tm2
section
parameters {K : Type} [decidable_eq K] -- Index type of stacks
parameters (k₀ k₁ : K) -- input and output stack
parameters (Γ : K → Type) -- Type of stack elements
parameters (Λ : Type) [inhabited Λ]
param... |
f4615ff7b02cbca111ab734b08d54ce0b6f950d0 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/section1.lean | 850f1c9d47a10877bbaefb016ff1ae3bf01d00e1 | [
"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 | 215 | lean | open tactic
section
set_option pp.universes true
set_option pp.implicit true
variable {A : Type}
variables {a b : A}
variable H : a = b
variables H1 H2 : b = a
#check H1
#check H
#check H2
end
|
10c0b218041a3153e93edcd1ada72424908f22bb | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /test/logic_inline.lean | 928407da674a535eea824e058799207b552ee686 | [
"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 | 549 | lean | /-
Copyright (c) 2019 Keeley Hoek. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Keeley Hoek, Floris van Doorn
-/
import logic.basic
meta def error_msg (s : string) : bool := @undefined_core bool $ s ++ ".decidable not inlined"
meta def examine (b : Prop) [decidable... |
5df41bc64b1906da2f1e79da5befbed44918c15b | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/doNotation1.lean | c1070c8991adb7c9f032789f8a20cb66a2279ad6 | [
"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 | 3,091 | lean | open Lean
def f : IO Nat :=
pure 0
def g (x : Nat) : IO Nat :=
pure (x + 1)
def g1 {α : Type} (x : α) : IO (α × α) :=
pure (x, x)
def g2 (p : Nat × Nat) : Nat :=
p.1
-- set_option trace.Elab.definition true
def h (x : Nat) : StateT Nat IO Nat := do
let s ← get
let a ← f -- liftM inserted here
let b ← g1 1 ... |
918bd05a3b378fb059547f45197e4e353c70ccef | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/algebra/module/pi.lean | c22df30f2ce255536579faf0c74f7381821ac5c2 | [
"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 | 9,070 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Patrick Massot
-/
import algebra.module.basic
import algebra.regular.smul
import algebra.ring.pi
/-!
# Pi instances for module and multiplicative actions
This file defines ... |
ddc3907a7fd704ff0d7fff62b4e515f5762de4ba | fe208a542cea7b2d6d7ff79f94d535f6d11d814a | /src/Logic/Alexandru_Bosinta.lean | 65f252285f812380e0baea723eab6517ffc473e9 | [] | no_license | ImperialCollegeLondon/M1F_room_342_questions | c4b98b14113fe900a7f388762269305faff73e63 | 63de9a6ab9c27a433039dd5530bc9b10b1d227f7 | refs/heads/master | 1,585,807,312,561 | 1,545,232,972,000 | 1,545,232,972,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,694 | lean | inductive fml
| atom (i : ℕ)
| imp (a b : fml)
| not (a : fml)
open fml
infixr ` →' `:50 := fml.imp -- right associative
prefix `¬' `:40 := fml.not
inductive prf : fml → Type
| axk (p q) : prf (p →' q →' p)
| axs (p q r) : prf $ (p →' q →' r) →' (p →' q) →' (p →' r)
| axX (p q) : prf $ ((¬' q) →' (¬' ... |
78299aede9e3044bf635a79bafceeeb0b7a964b6 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/analysis/normed_space/star/basic.lean | 0ee496043638a21fe1d363732a342a08b7edbe3e | [
"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 | 7,478 | lean | /-
Copyright (c) 2021 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
import analysis.normed.group.hom
import analysis.normed_space.basic
import analysis.normed_space.linear_isometry
import algebra.star.self_adjoint
import algebra.st... |
28dd76d0482e949bbab9c71a49a3233a417895b5 | 8b9f17008684d796c8022dab552e42f0cb6fb347 | /tests/lean/run/local_eqns2.lean | badd54c20ac3bedeeb0ce70b7b3689862fc648d3 | [
"Apache-2.0"
] | permissive | chubbymaggie/lean | 0d06ae25f9dd396306fb02190e89422ea94afd7b | d2c7b5c31928c98f545b16420d37842c43b4ae9a | refs/heads/master | 1,611,313,622,901 | 1,430,266,839,000 | 1,430,267,083,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 426 | lean | import data.fin
open fin nat
definition nz_cases_on {C : Π n, fin (succ n) → Type}
(H₁ : Π n, C n (fz n))
(H₂ : Π n (f : fin n), C n (fs f))
{n : nat}
(f : fin (succ n)) : C n f :=
begin
reverts [n, f],
show ∀ (n : nat) ... |
e18fc756a48c0f4674cd113b95911bdee17e250c | 737dc4b96c97368cb66b925eeea3ab633ec3d702 | /tests/lean/run/generalizeMany.lean | 846a3d2ba7007a5c80f6bb07e3d061fe1c44aaf8 | [
"Apache-2.0"
] | permissive | Bioye97/lean4 | 1ace34638efd9913dc5991443777b01a08983289 | bc3900cbb9adda83eed7e6affeaade7cfd07716d | refs/heads/master | 1,690,589,820,211 | 1,631,051,000,000 | 1,631,067,598,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 320 | lean | def Fin.succ (v : Fin n) : Fin n.succ :=
match v with
| ⟨v, h⟩ => ⟨v+1, Nat.succ_lt_succ h⟩
set_option pp.analyze false
example (p : (n : Nat) → Fin n → Prop)
(n : Nat)
(v : Fin n)
: p n.succ v.succ := by
generalize h₁ : n.succ = n', h₂ : v.succ = v'
traceState
admit
|
466fe0061b7b78a2a15a5f6eac8f1cdef617e7bf | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/field_theory/finite/trace.lean | b5c3451ff78b4fb0ae0a2d6c94b83943c3e616cb | [
"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 | 905 | lean | /-
Copyright (c) 2022 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
import ring_theory.trace
import field_theory.finite.galois_field
/-!
# The trace map for finite fields
We state the fact that the trace map from a finite field of
cha... |
0ebea47b2c2b67756b930618f035979ca08ae763 | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /tests/lean/run/KyleAlg.lean | 7175640b2155fa219c45cf6c2da320e07d4d1966 | [
"Apache-2.0"
] | permissive | collares/lean4 | 861a9269c4592bce49b71059e232ff0bfe4594cc | 52a4f535d853a2c7c7eea5fee8a4fa04c682c1ee | refs/heads/master | 1,691,419,031,324 | 1,618,678,138,000 | 1,618,678,138,000 | 358,989,750 | 0 | 0 | Apache-2.0 | 1,618,696,333,000 | 1,618,696,333,000 | null | UTF-8 | Lean | false | false | 8,405 | lean | import Lean
/- from core:
class OfNat (α : Type u) (n : Nat) where
ofNat : α
class Mul (α : Type u) where
mul : α → α → α
class Add (α : Type u) where
add : α → α → α
-/
class Inv (α : Type u) where
inv : α → α
postfix:max "⁻¹" => Inv.inv
class One (α : Type u) where
one : α
export One (one)
instance... |
69fde8f52498fe3d4e0408fc58b1c65916a3fd20 | e030b0259b777fedcdf73dd966f3f1556d392178 | /library/init/util.lean | 8e88dad089ae826694541da523fa3842ac3a1911 | [
"Apache-2.0"
] | permissive | fgdorais/lean | 17b46a095b70b21fa0790ce74876658dc5faca06 | c3b7c54d7cca7aaa25328f0a5660b6b75fe26055 | refs/heads/master | 1,611,523,590,686 | 1,484,412,902,000 | 1,484,412,902,000 | 38,489,734 | 0 | 0 | null | 1,435,923,380,000 | 1,435,923,379,000 | null | UTF-8 | Lean | false | false | 655 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.data.string.basic
/- This function has a native implementation that tracks time. -/
def timeit {α : Type} (s : string) (f : unit → α) :... |
5131927f394c71ddd55f758668e906b14b8b7dcc | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/normed_space/star/basic.lean | 722dd00fc35c30c991c0982c1ef881131f82375d | [
"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 | 10,668 | lean | /-
Copyright (c) 2021 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
import analysis.normed.group.hom
import analysis.normed_space.basic
import analysis.normed_space.linear_isometry
import algebra.star.self_adjoint
import algebra.st... |
fdcac6e6c841eabdabeb5b940973aaa02476382b | abd85493667895c57a7507870867b28124b3998f | /src/data/list/defs.lean | 1d2b0738a535a3fe312e35a23b1681dfbca99a0e | [
"Apache-2.0"
] | permissive | pechersky/mathlib | d56eef16bddb0bfc8bc552b05b7270aff5944393 | f1df14c2214ee114c9738e733efd5de174deb95d | refs/heads/master | 1,666,714,392,571 | 1,591,747,567,000 | 1,591,747,567,000 | 270,557,274 | 0 | 0 | Apache-2.0 | 1,591,597,975,000 | 1,591,597,974,000 | null | UTF-8 | Lean | false | false | 20,501 | lean | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
Extra definitions on lists.
-/
import data.option.defs
import logic.basic
import tactic.cache
n... |
60a99f1c3ceb35b26324a30abbe204dddb1b633f | 4fa161becb8ce7378a709f5992a594764699e268 | /src/category_theory/discrete_category.lean | cdab859e663432313127e05976e113326f0539b9 | [
"Apache-2.0"
] | permissive | laughinggas/mathlib | e4aa4565ae34e46e834434284cb26bd9d67bc373 | 86dcd5cda7a5017c8b3c8876c89a510a19d49aad | refs/heads/master | 1,669,496,232,688 | 1,592,831,995,000 | 1,592,831,995,000 | 274,155,979 | 0 | 0 | Apache-2.0 | 1,592,835,190,000 | 1,592,835,189,000 | null | UTF-8 | Lean | false | false | 3,630 | 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, Floris van Doorn
-/
import data.ulift
import data.fintype.basic
import category_theory.eq_to_hom
namespace category_theory
universes v₁ v₂ u₁ u₂ -- de... |
68b52549c80b0f624bf8c119aafbfd16c4c4bc31 | a0a027e4a00cdb315527e8922122f2a4411fd01c | /4.5-the-existential-quantifier.lean | 9d79e12990023babcf88884437f5cd35d1f86fcb | [] | no_license | spl/lean-tutorial | 96a1ef321d06b9b28d044eeb6bf1ff9a86761a6e | 35c0250004d75d8ae58f6192b649744545116022 | refs/heads/master | 1,610,250,012,890 | 1,454,259,122,000 | 1,454,259,122,000 | 49,971,362 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,837 | lean | open classical
variables (A : Type) (p : A → Prop)
example (H : ¬∀ x, ¬p x) : ∃ x, p x :=
by_contradiction
(assume Hnep : ¬∃ x, p x,
have Hanp : ∀ x, ¬p x, from
take x : A,
assume Hpx : p x,
have Hep : ∃ x, p x, from
exists.intro x Hpx,
show false, from Hnep Hep,
show fal... |
f5cc1ef3133251f7b0a6475620af75bf63a6a0c8 | 1d335ec6ac4181a0a762b12797936770cc9fcef9 | /imperative_DSL/physlang.lean | 42a4c749e2b4afa29d5d9840914010ac4fc182c8 | [] | no_license | rohanrajnair/lang | dbadcc3997e44245ca84d48dc1733cf09a2605a6 | 3beb4e29d8faa692983a55fa18acb6eb947134e8 | refs/heads/master | 1,672,640,379,424 | 1,597,948,771,000 | 1,597,948,771,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,862 | lean | import .environment
import ..eval.accelerationEval
import ..eval.geometryEval
import ..eval.timeEval
import ..eval.velocityEval
import ..expressions.classical_geometry
import ..expressions.classical_time
import ..expressions.classical_velocity
import ..expressions.classical_acceleration
import ..override.geomOverride
i... |
158891f46fc84c992292da66f18f1dd3ba8c0189 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/seq/computation.lean | d55639fc39a9ccb3a417fd79649c74bea41dc284 | [
"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 | 38,013 | 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.init
import tactic.basic
open function
universes u v w
/-
coinductive computation (α... |
544d47dbe4b10d747a3eef2934c02cec9de3a3c3 | 957a80ea22c5abb4f4670b250d55534d9db99108 | /tests/lean/run/nat_bug4.lean | 335e675c501e8dcfa4c3bc293054acc5dd75902d | [
"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 | 468 | lean |
namespace experiment
inductive nat : Type
| zero : nat
| succ : nat → nat
namespace nat
definition add (x y : nat) : nat := nat.rec x (λn r, succ r) y
infixl `+` := add
definition mul (n m : nat) : nat := nat.rec zero (fun m x, x + n) m
infixl `*` := mul
axiom mul_succ_right (n m : nat) : n * succ m = n * m + n
open ... |
31d216d9e9e08a78810e862d02713c649fdcbd02 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/inst_bug.lean | 2d07f7b96d8bdd810ba6cdc13662b16eb74c2c54 | [
"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 | 364 | lean | namespace test
class inductive {u} is_equiv (A B : Type u) (f : A → B) : Type u
definition inverse (A B : Type*) (f : A → B) [H : is_equiv A B f] := Type*
definition foo (A : Type*) (B : A → Type*) (h : A → A) (g : Π(a : A), B a → B a)
[H : Π(a : A), is_equiv _ _ (g a)] (x : A) : Type* :=
inverse (B (h x... |
fab606283a83dd487a4879c08626b5bbd65b4950 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/order/preorder_hom.lean | 1939b8a7ac8dc3c2927beb0e92fef5d32a354390 | [
"Apache-2.0"
] | permissive | abentkamp/mathlib | d9a75d291ec09f4637b0f30cc3880ffb07549ee5 | 5360e476391508e092b5a1e5210bd0ed22dc0755 | refs/heads/master | 1,682,382,954,948 | 1,622,106,077,000 | 1,622,106,077,000 | 149,285,665 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,046 | 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 logic.function.iterate
import order.basic
import order.bounded_lattice
import order... |
f52c5c8dc332a4b7a606c1c363e5f08aec75d87d | aa3f8992ef7806974bc1ffd468baa0c79f4d6643 | /library/algebra/category/functor.lean | aaf7eb124f38036341186f9bd045d1846a7edd2d | [
"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 | 5,299 | lean | -- Copyright (c) 2014 Floris van Doorn. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Author: Floris van Doorn
import .basic
import logic.cast
open function
open category eq eq.ops heq
inductive functor (C D : Category) : Type :=
mk : Π (obF : C → D) (homF : Π(a b : C)... |
74d7e25c2d57537334a98271312fa585b7f836a7 | 87d5955e1100ba73f6b56149b659e85116fa215b | /group_theory/perm.lean | ba02bfea401d140f38da080af33e3f806e5ba073 | [
"Apache-2.0"
] | permissive | avigad/leanproved | 4d15a05f8544a67b9f589c5e656358e1485aef3c | 3cf0f5dda3ace82f6b7cdc159528ce3ebaef159f | refs/heads/master | 1,611,368,103,158 | 1,433,589,072,000 | 1,433,589,072,000 | 36,843,899 | 0 | 0 | null | 1,433,385,918,000 | 1,433,385,918,000 | null | UTF-8 | Lean | false | false | 2,943 | lean | /-
Copyright (c) 2015 Haitao Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author : Haitao Zhang
-/
import algebra.group data .extra .finfun
open nat function list algebra
namespace group
open fintype
section perm
variable {A : Type}
variable [finA ... |
5da65ed02502e60e87f7bf6ac18df1b17f4fd2b7 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/topology/homeomorph.lean | f4c3d0a6f97584c650d75f0d6be779c2e15fe464 | [
"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 | 15,843 | lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Sébastien Gouëzel, Zhouhang Zhou, Reid Barton
-/
import topology.dense_embedding
/-!
# Homeomorphisms
This file defines homeomorphisms between two topolo... |
e379cef352e43d594338a5faefcc40afaaaa87e0 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/algebra/lie/weights.lean | f8ced446e4c8d6b40853655eb704bf86607c0bac | [
"Apache-2.0"
] | permissive | abentkamp/mathlib | d9a75d291ec09f4637b0f30cc3880ffb07549ee5 | 5360e476391508e092b5a1e5210bd0ed22dc0755 | refs/heads/master | 1,682,382,954,948 | 1,622,106,077,000 | 1,622,106,077,000 | 149,285,665 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 21,362 | 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.nilpotent
import algebra.lie.tensor_product
import algebra.lie.character
import algebra.lie.cartan_subalgebra
import linear_algebra.eigenspace
/-!
# Wei... |
6f0ab6a64e8eaa7c6252139324cc94e84aafcf33 | ba4794a0deca1d2aaa68914cd285d77880907b5c | /src/game/world3/level7.lean | b0e9b655fde5405fd5899f0f99a575b3096f9c8e | [
"Apache-2.0"
] | permissive | ChrisHughes24/natural_number_game | c7c00aa1f6a95004286fd456ed13cf6e113159ce | 9d09925424da9f6275e6cfe427c8bcf12bb0944f | refs/heads/master | 1,600,715,773,528 | 1,573,910,462,000 | 1,573,910,462,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,926 | lean | import game.world3.level6 -- hide
namespace mynat -- hide
/-
# Multiplication World
## Level 7: `add_mul`
We proved `mul_add` already, but because we don't have commutativity yet
we also need to prove `add_mul`. We have a bunch of tools now, so this won't
be too hard. You know what -- you can do this one by inductio... |
3b021605819d8b750661b5f24f5b8087f1651cae | aa3f8992ef7806974bc1ffd468baa0c79f4d6643 | /tests/lean/run/num.lean | b8b2f917b9c97a50824c6fcc8c720bdb09a6421e | [
"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 | 56 | lean | import standard
check 14
check 0
check 3
check 2
check 4 |
1dc126489baab5230e8ea7b3017e31abe1b2be08 | 01f6b345a06ece970e589d4bbc68ee8b9b2cf58a | /src/normed_valued.lean | a0fda3ca8fd43f017792086fb05b6f259744eb4c | [] | 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 | 7,017 | 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 rank_one_valuation
import ring_seminorm
import topology.algebra.valuation
/-!
# Correspondence between nontrivial nonarchimede... |
b9dc76577e0eaa1a387459c2ccbca0c9ce00b0a1 | 958488bc7f3c2044206e0358e56d7690b6ae696c | /lean/setoid.lean | 6ca9124c07865f658ebd838c3552a281495c99e5 | [] | no_license | possientis/Prog | a08eec1c1b121c2fd6c70a8ae89e2fbef952adb4 | d4b3debc37610a88e0dac3ac5914903604fd1d1f | refs/heads/master | 1,692,263,717,723 | 1,691,757,179,000 | 1,691,757,179,000 | 40,361,602 | 3 | 0 | null | 1,679,896,438,000 | 1,438,953,859,000 | Coq | UTF-8 | Lean | false | false | 2,936 | lean | universe u
class setoid2 (α : Sort u) : Sort (max 1 u) :=
(r : α → α → Prop) (iseqv : equivalence r)
--#check @setoid
--#check @setoid2
--#check (@setoid.iseqv α s).left
--#check @quot
def quotient2 {α : Sort u} (s : setoid α) := @quot α setoid.r
--#check @quotient
--#check @quotient2
--#check @quotient.mk
--#c... |
8e90ad296709624dcb51f6f309c440e222efdeba | e030b0259b777fedcdf73dd966f3f1556d392178 | /library/init/core.lean | 9896507346e87bb4076427ee24be34a573874382 | [
"Apache-2.0"
] | permissive | fgdorais/lean | 17b46a095b70b21fa0790ce74876658dc5faca06 | c3b7c54d7cca7aaa25328f0a5660b6b75fe26055 | refs/heads/master | 1,611,523,590,686 | 1,484,412,902,000 | 1,484,412,902,000 | 38,489,734 | 0 | 0 | null | 1,435,923,380,000 | 1,435,923,379,000 | null | UTF-8 | Lean | false | false | 16,930 | 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
notation, basic datatypes and type classes
-/
prelude
notation `Prop` := Type 0
notation `Type₂` := Type 2
notation `Type₃` := Type 3
/- Logical operations... |
cf3cce043b96885a84990ad169bcef2c61cd1bbd | ea5678cc400c34ff95b661fa26d15024e27ea8cd | /involution.lean | 836a7d8f4883dded05270af88af0ee6c035f1a3a | [] | 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 | 22,176 | lean | import data.fintype data.nat.modeq data.fintype data.set.finite data.nat.prime set_theory.cardinal algebra.ordered_ring
universe u
variable α : Type u
local attribute [instance,priority 0] classical.prop_decidable
noncomputable theory
open nat fintype
instance fintype_subtype_of_fintype (p : α → Prop) [fintype α] : fi... |
e65b258cdf5cec2e2d282ae50b118ac40838fbff | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/topology/category/Top/limits.lean | 2cd1ef52239c4ce612965a35d6ff9a2ce6a6cd0e | [
"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 | 2,767 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Scott Morrison, Mario Carneiro
-/
import topology.category.Top.basic
import category_theory.limits.types
import category_theory.limits.preserves
open topological_space... |
bef5e65b80b6487f07ba29b56ea71cd0bdbeedb4 | 6b2a480f27775cba4f3ae191b1c1387a29de586e | /group_rep1/terr.lean | cbdbe2360621f87109761b8a3ce64826aeeeb55d | [] | no_license | Or7ando/group_representation | a681de2e19d1930a1e1be573d6735a2f0b8356cb | 9b576984f17764ebf26c8caa2a542d248f1b50d2 | refs/heads/master | 1,662,413,107,324 | 1,590,302,389,000 | 1,590,302,389,000 | 258,130,829 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 298 | lean | import category_theory.category
open category_theory
universes v u
variables {C : Type u} [𝒞 : category.{v} C]
include 𝒞
local notation f `# ` A ` #` g := (f : _ ⟶ A) ≫ g
example {P Q R S : C} (f : P ⟶ Q) (g : Q ⟶ R) (h : R ⟶ S) : f ≫ g ≫ h = ((f ≫ g) ≫ h) :=
begin
end |
809dc1210fe21be57a824316f00135c1d914a43d | ae1e94c332e17c7dc7051ce976d5a9eebe7ab8a5 | /tests/lean/run/depElim1.lean | 6c0c9487da257af489d10980b6c55e66eaf8646a | [
"Apache-2.0"
] | permissive | dupuisf/lean4 | d082d13b01243e1de29ae680eefb476961221eef | 6a39c65bd28eb0e28c3870188f348c8914502718 | refs/heads/master | 1,676,948,755,391 | 1,610,665,114,000 | 1,610,665,114,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 13,770 | lean | import Lean.Meta.Match
open Lean
open Lean.Meta
open Lean.Meta.Match
/- Infrastructure for testing -/
universes u v
def check (x : Bool) : IO Unit := do
unless x do
throw $ IO.userError "check failed"
def inaccessible {α : Sort u} (a : α) : α := a
def val {α : Sort u} (a : α) : α := a
def As {α : Sort u} (v a : ... |
1cb5682468f9ea646cc1bf93282e91af17a3c189 | ce89339993655da64b6ccb555c837ce6c10f9ef4 | /na4zagin3/top23.lean | d4cc45274a27bafc2c7e1645d5cbf8c4871d754d | [] | no_license | zeptometer/LearnLean | ef32dc36a22119f18d843f548d0bb42f907bff5d | bb84d5dbe521127ba134d4dbf9559b294a80b9f7 | refs/heads/master | 1,625,710,824,322 | 1,601,382,570,000 | 1,601,382,570,000 | 195,228,870 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 924 | lean | inductive bin : nat -> Prop
| bin_epsilon : bin 0
| bin_0 : forall n, bin n -> bin (2 * n)
| bin_1 : forall n, bin n -> bin (2 * n + 1)
.
def is_expressible_in_binary_notation := bin.
#check nat.mod_lt
theorem top23 : forall n, is_expressible_in_binary_notation n :=
begin
intro n,
unfold is_expressible_in_bina... |
b3f3e9b6e6b6e8edbd8ba12464ae47c733b7e6bc | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/algebra/char_p/subring.lean | bb9b0b5beac0de26743f20966d4e787d33d748c5 | [
"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 | 1,038 | 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.char_p.basic
import ring_theory.subring
/-!
# Characteristic of subrings
-/
universes u v
namespace char_p
instance subsemiring (R : Type u) [semiring R] (p... |
467c479c2dcec287bf60dbe813e0bbfae1ee6b4a | eee9431f1775ed555dbf09e29e071194c6d586bf | /ACE/ex01.lean | 7ddc63d09312774674404f4ccff891f266a066d4 | [] | no_license | Paox2/myWorkInCollege | 0d60abceb28d0228576f87ceb9f0a0aaeb944144 | fadf8a93b27a56b2f5d8f0063087fdb71390cf93 | refs/heads/master | 1,679,972,166,761 | 1,617,740,970,000 | 1,617,740,970,000 | 256,950,200 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,661 | lean | /- id: 20126355 full name: Wendi Han -/
variables P Q R : Prop
theorem e01 : P → Q → P :=
begin
assume p,
assume q,
exact p,
end
theorem e02 : (P → Q → R) → (P → Q) → P → R :=
begin
assume pqr pq p,
apply pqr,
exact p,
apply pq,
exact p,
end
theorem e03 : (P → Q) → P ∧ R → Q ∧ R... |
53c2cb7d222940a1276cd7f4c4ed5a48e1fb2407 | d6124c8dbe5661dcc5b8c9da0a56fbf1f0480ad6 | /Papyrus/IR/ValueRef.lean | ef7d6291b87406c2430ea6419e85e474be8de4b4 | [
"Apache-2.0"
] | permissive | xubaiw/lean4-papyrus | c3fbbf8ba162eb5f210155ae4e20feb2d32c8182 | 02e82973a5badda26fc0f9fd15b3d37e2eb309e0 | refs/heads/master | 1,691,425,756,824 | 1,632,122,825,000 | 1,632,123,075,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,258 | lean | import Papyrus.Context
import Papyrus.IR.TypeRef
import Papyrus.IR.ValueKind
namespace Papyrus
/--
An opaque type representing an external LLVM
[Value](https://llvm.org/doxygen/classllvm_1_1Value.html).
-/
constant Llvm.Value : Type := Unit
/--
A reference to an external LLVM
[Value](https://llvm.org/doxygen... |
cc9427b289ac0b34ec270bef4c583166a3f831c3 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/topology/algebra/group.lean | 99590388a60ace608fd435e016b535526147f76f | [
"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 | 29,632 | 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 order.filter.pointwise
import group_theory.quotient_group
import topology.algebra.monoid
import topology.homeomorph
/-!
# The... |
04425826d5af30093312eb12eb1a0d1831fd3a82 | 5756a081670ba9c1d1d3fca7bd47cb4e31beae66 | /Mathport/Syntax/Translate/Notation.lean | d4784514296c740fb3ac2ca2de901ae7a9029d2c | [
"Apache-2.0"
] | permissive | leanprover-community/mathport | 2c9bdc8292168febf59799efdc5451dbf0450d4a | 13051f68064f7638970d39a8fecaede68ffbf9e1 | refs/heads/master | 1,693,841,364,079 | 1,693,813,111,000 | 1,693,813,111,000 | 379,357,010 | 27 | 10 | Apache-2.0 | 1,691,309,132,000 | 1,624,384,521,000 | Lean | UTF-8 | Lean | false | false | 8,067 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathport.Util.Json
import Mathport.Util.Misc
import Mathlib.Mathport.Syntax
import Std.Util.ExtendedBinder
import Std.Classes.SetNotation
import Mathlib... |
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