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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
913bac4c597cadea83f2202df17cbdcacdb5b756 | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /tests/lean/run/doNotation1.lean | a32deb8392d4b193c2422f1383c883ada3c3fca7 | [
"Apache-2.0"
] | permissive | walterhu1015/lean4 | b2c71b688975177402758924eaa513475ed6ce72 | 2214d81e84646a905d0b20b032c89caf89c737ad | refs/heads/master | 1,671,342,096,906 | 1,599,695,985,000 | 1,599,695,985,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,495 | lean | open Lean
partial def expandHash : Syntax → StateT Bool MacroM Syntax
| Syntax.node k args =>
if k == `doHash then do set true; `(←MonadState.get)
else do
args ← args.mapM expandHash;
pure $ Syntax.node k args
| stx => pure stx
@[macro Lean.Parser.Term.do] def expandDo : Macro :=
fun stx => do
(stx, exp... |
53ef91e7ba2a6c2373cbc8c969633127b9f23324 | 130c49f47783503e462c16b2eff31933442be6ff | /src/Lean/PrettyPrinter/Delaborator/TopDownAnalyze.lean | 1495c5ab198eee5a5b630a829be1b60b5974b1bd | [
"Apache-2.0"
] | permissive | Hazel-Brown/lean4 | 8aa5860e282435ffc30dcdfccd34006c59d1d39c | 79e6732fc6bbf5af831b76f310f9c488d44e7a16 | refs/heads/master | 1,689,218,208,951 | 1,629,736,869,000 | 1,629,736,896,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 26,230 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Daniel Selsam
-/
import Lean.Meta
import Lean.Util.FindMVar
import Lean.Util.FindLevelMVar
import Lean.Util.CollectLevelParams
import Lean.Util.ReplaceLevel
import Lean.PrettyPr... |
ad29defcf07eea771be0576d02261c0021cd3b76 | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /archive/imo/imo2005_q3.lean | 28a9ec832e870a2789372f36dfb80f45f3d01fe0 | [
"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 | 3,478 | lean | /-
Copyright (c) 2021 Manuel Candales. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Manuel Candales
-/
import data.real.basic
/-!
# IMO 2005 Q3
Let `x`, `y` and `z` be positive real numbers such that `xyz ≥ 1`. Prove that:
`(x^5 - x^2)/(x^5 + y^2 + z^2) + (y^5 - y^2... |
32de8ce3c2b46bcd8a46e5b78a83d73e1934a451 | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /11_Tactic-Style_Proofs.org.17.lean | 44af2b755a9c94fea84231106a99790f8a091d27 | [] | 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 | 383 | lean | import standard
import data.nat
open nat
variables x y z : ℕ
example : x = x :=
begin
generalize x, -- goal is x : ℕ ⊢ ∀ (x : ℕ), x = x
intro y, -- goal is x y : ℕ ⊢ y = y
apply rfl
end
example (H : x = y) : y = x :=
begin
generalize H, -- goal is x y : ℕ, H : x = y ⊢ y = x
intro H1, -- goal is x y : ℕ, H H... |
6626ca0ec521072caf704fed387d0b1062db6467 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/group_theory/group_action/defs.lean | 3911e71d457079a5e480d211d77992df11b1fd3a | [] | 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 | 8,645 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.equiv.basic
import Mathlib.algebra.group.defs
import Mathlib.algebra.group.hom
import Math... |
22a2987f1a353e8e0769d25ed539367bba57dff6 | a88f0086fb3e2025ebb21e0ba2f2725774c6979f | /src/data/int/basic.lean | ffc2db6b7a33e25963a865ffe5c0dc75fa34f74c | [
"Apache-2.0"
] | permissive | Kha/stdlib | b5a4456c35def0ca8f1bf2d32dbeebd7639cbc4d | e44b105c72ec77120f43a7a7dd1cd49867a65a41 | refs/heads/master | 1,609,528,111,500 | 1,572,963,395,000 | 1,572,963,395,000 | 98,516,307 | 0 | 1 | null | 1,501,146,352,000 | 1,501,146,352,000 | null | UTF-8 | Lean | false | false | 51,078 | 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.
-/
import data.nat.basic data.list.basic algebra.char_zero algebra.order_functions
open nat
namespace int
... |
9c58560a617fd1b088072fa96341728293e1c1da | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/linear_algebra/matrix/bilinear_form.lean | ea6878ba4f3d3f6ee5e489eff60deea10362822b | [
"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 | 22,779 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Kexing Ying
-/
import linear_algebra.matrix.basis
import linear_algebra.matrix.nondegenerate
import linear_algebra.matrix.nonsingular_inverse
import linear_algebra.matrix.to... |
9a514bb8b87e82bb38411a04631e2643b77c3ada | b7f22e51856f4989b970961f794f1c435f9b8f78 | /hott/types/pi.hlean | 9095e1d6cd95b0581059b0a541c692c3ae70832c | [
"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 | 14,316 | hlean | /-
Copyright (c) 2014-15 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Floris van Doorn
Partially ported from Coq HoTT
Theorems about pi-types (dependent function spaces)
-/
import types.sigma arity cubical.square
open eq equiv is_equiv funext sigm... |
db06f3c154d2d46795bc9e407337385a940b59c0 | fffbc47930dc6615e66ece42324ce57a21d5b64b | /src/topology/algebra/monoid.lean | 8f8bae5503c33f832479f76c303dd12ce5e42e56 | [
"Apache-2.0"
] | permissive | skbaek/mathlib | 3caae8ae413c66862293a95fd2fbada3647b1228 | f25340175631cdc85ad768a262433f968d0d6450 | refs/heads/master | 1,588,130,123,636 | 1,558,287,609,000 | 1,558,287,609,000 | 160,935,713 | 0 | 0 | Apache-2.0 | 1,544,271,146,000 | 1,544,271,146,000 | null | UTF-8 | Lean | false | false | 5,179 | 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
Theory of topological monoids.
TODO: generalize `topological_monoid` and `topological_add_monoid` to semigroups, or add a type class
`topological_opera... |
d9968ba540dbdad7f7579a8df312053fea42845c | 4727251e0cd73359b15b664c3170e5d754078599 | /src/linear_algebra/direct_sum/tensor_product.lean | 384cd8fc38511b3884c6071c3621b9b4c7258d8d | [
"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 | 2,183 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Mario Carneiro
-/
import linear_algebra.tensor_product
import algebra.direct_sum.module
/-!
# Tensor products of direct sums
This file shows that taking `tensor_product`s comm... |
6b21c43deaa044adffd884d8f7b2a889ddc1e2e4 | 92b50235facfbc08dfe7f334827d47281471333b | /hott/arity.hlean | f4be844c9bbb123803661cd0fd6ab042810cda37 | [
"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 | 10,918 | hlean | /-
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
Theorems about functions with multiple arguments
-/
variables {A U V W X Y Z : Type} {B : A → Type} {C : Πa, B a → Type} {D : Πa b, C a b → Type}
{E : Πa ... |
8c9e71cc76220fee3fc65665faa61a3334c3f3c4 | 9028d228ac200bbefe3a711342514dd4e4458bff | /src/algebraic_geometry/presheafed_space/has_colimits.lean | 6bc6c28c403272a603048f2de543ee541e218de8 | [
"Apache-2.0"
] | permissive | mcncm/mathlib | 8d25099344d9d2bee62822cb9ed43aa3e09fa05e | fde3d78cadeec5ef827b16ae55664ef115e66f57 | refs/heads/master | 1,672,743,316,277 | 1,602,618,514,000 | 1,602,618,514,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,841 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import algebraic_geometry.presheafed_space
import topology.category.Top.limits
import topology.sheaves.limits
import category_theory.limits.concrete_category
/-!
# `... |
258ba75502a85e750b449a8e9263f8f056c87435 | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /02_Dependent_Type_Theory.org.25.lean | a1c653cea04a7d1b91f3b4694d91abeedb5125a4 | [] | 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 | 247 | lean | /- page 23 -/
import standard
section useful
variables (A B C : Type)
variables (g : B → C) (f : A → B) (h : A → A)
variable x : A
definition compose := g (f x)
definition do_twice := h (h x)
definition do_thrice := h (h (h x))
end useful
|
0409378ba7b5777a311ff0e4693a4827a486e345 | fe84e287c662151bb313504482b218a503b972f3 | /src/exercises/loh/binomial_solution.lean | 8035eb44761999645ce6ff03d119a76a1d758bbb | [] | 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 | 525 | lean | import tactic
lemma binomial_solution (x : ℤ) : x ^ 2 - 2 * x + 1 = 0 ↔ x = 1 :=
begin
split; intro h,
{ have : (x - 1) ^ 2 = x ^ 2 - 2 * x + 1 := by {
rw[pow_two, pow_two, two_mul, mul_sub, mul_one, sub_mul, one_mul],
rw[← sub_add, sub_add_eq_sub_sub]
},
rw[← this] at h,
exact sub_eq_zero... |
f3ae2897665d2ef7a2afbd8fe278efe44c1ec5a2 | e9dbaaae490bc072444e3021634bf73664003760 | /src/Background/Array.lean | 93899468a5cb05d04ac51900684053a1294735fc | [
"Apache-2.0"
] | permissive | liaofei1128/geometry | 566d8bfe095ce0c0113d36df90635306c60e975b | 3dd128e4eec8008764bb94e18b932f9ffd66e6b3 | refs/heads/master | 1,678,996,510,399 | 1,581,454,543,000 | 1,583,337,839,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 162 | lean | import Geo.Background.List
namespace Array
universe u
variable {α : Type u}
def allP (xs : Array α) (p : α → Prop) : Prop :=
xs.toList.allP p
end Array
|
f2ed583a4df1e14603ccc4eb1b56bd7d34e55617 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/tactic/rewrite_search/types_auto.lean | ca717d7fd18453162788c563efb7bc9c6fd1ff3f | [] | 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 | 1,620 | lean | /-
Copyright (c) 2020 Kevin Lacker, Keeley Hoek, Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Lacker, Keeley Hoek, Scott Morrison
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.tactic.nth_rewrite.default
import Mat... |
9e9046984270c868c64d7afc081d7324fcae2f98 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebraic_geometry/gluing.lean | 18c770363b79aa6d549cda08e446b59401cbf93f | [
"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 | 17,355 | lean | /-
Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import algebraic_geometry.presheafed_space.gluing
/-!
# Gluing Schemes
Given a family of gluing data of schemes, we may glue them together.
## Main definitions
* `algeb... |
5efb3ebbbb62dec4e82d79c9aded5c193a2d2d25 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /library/data/set/card.lean | 05f3dcbbe656bb5ad86e0357a14f21d68c5021ec | [
"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 | 5,879 | lean | /-
Copyright (c) 2015 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad
Cardinality of finite sets.
-/
import .finite data.finset.card
open nat classical
namespace set
variable {A : Type}
noncomputable definition card (s : set A) := finset.... |
66168c175c640a1f866a2ca735b9298012033b54 | 4e3bf8e2b29061457a887ac8889e88fa5aa0e34c | /lean/love11_logical_foundations_of_mathematics_exercise_sheet.lean | 80665ac63ae3e2180b81a0fd3979c7ab3807cd70 | [] | no_license | mukeshtiwari/logical_verification_2019 | 9f964c067a71f65eb8884743273fbeef99e6503d | 16f62717f55ed5b7b87e03ae0134791a9bef9b9a | refs/heads/master | 1,619,158,844,208 | 1,585,139,500,000 | 1,585,139,500,000 | 249,906,380 | 0 | 0 | null | 1,585,118,728,000 | 1,585,118,727,000 | null | UTF-8 | Lean | false | false | 4,182 | lean | /- LoVe Exercise 11: Logical Foundations of Mathematics -/
import .love11_logical_foundations_of_mathematics_demo
namespace LoVe
universe variable u
set_option pp.beta true
/- Question 1: Subtypes -/
namespace my_vector
/- Recall the definition of vectors from the lecture: -/
#check vector
/- The following fu... |
a997060d5d8149eb14e17f45c206e501f27d1d0a | aa3f8992ef7806974bc1ffd468baa0c79f4d6643 | /library/data/nat/order.lean | 839e0844d57d1979ad2ee7c36572d8bec6bfa394 | [
"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 | 17,616 | 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, Leonardo de Moura
-- data.nat.order
-- ==============
--
-- The ordering on the natural numbers
import .basic
open eq.ops
namespace nat
-- Less than or... |
59328a80d441333dcc205a14928d3b6d68e595b6 | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /src/Lean/Elab/PreDefinition/WF/Rel.lean | d998d6b3980b560cbc766ba9dca7f4258b84fade | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | EdAyers/lean4 | 57ac632d6b0789cb91fab2170e8c9e40441221bd | 37ba0df5841bde51dbc2329da81ac23d4f6a4de4 | refs/heads/master | 1,676,463,245,298 | 1,660,619,433,000 | 1,660,619,433,000 | 183,433,437 | 1 | 0 | Apache-2.0 | 1,657,612,672,000 | 1,556,196,574,000 | Lean | UTF-8 | Lean | false | false | 7,710 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Meta.Tactic.Apply
import Lean.Meta.Tactic.Rename
import Lean.Meta.Tactic.Intro
import Lean.Elab.SyntheticMVars
import Lean.Elab.PreDefinition.Ba... |
00be56fc2249061bab190328d06796b06b2ff2d0 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/topology/algebra/order/compact.lean | 16b76cbd0680a93c7d3728f07039a1ea6f503c50 | [
"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 | 17,905 | lean | /-
Copyright (c) 2021 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Yury Kudryashov
-/
import topology.algebra.order.intermediate_value
/-!
# Compactness of a closed interval
In this file we prove that a closed interval in a condition... |
4a9dc62712624523dce2dbcf3cb6673e8284c1dc | 947b78d97130d56365ae2ec264df196ce769371a | /src/Init/Control/Except.lean | 7b40b0e9161b15a7b7921317fa556d10931635ff | [
"Apache-2.0"
] | permissive | shyamalschandra/lean4 | 27044812be8698f0c79147615b1d5090b9f4b037 | 6e7a883b21eaf62831e8111b251dc9b18f40e604 | refs/heads/master | 1,671,417,126,371 | 1,601,859,995,000 | 1,601,860,020,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,490 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jared Roesch, Sebastian Ullrich
The Except monad transformer.
-/
prelude
import Init.Data.ToString
import Init.Control.Alternative
import Init.Control.MonadControl
import Init.... |
86635dd0b816eede34605617836432e748502aa3 | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /library/algebra/complete_lattice.lean | d7e24a56f1d2d321331dcaa10ee911c94a45569b | [
"Apache-2.0"
] | permissive | davidmueller13/lean | 65a3ed141b4088cd0a268e4de80eb6778b21a0e9 | c626e2e3c6f3771e07c32e82ee5b9e030de5b050 | refs/heads/master | 1,611,278,313,401 | 1,444,021,177,000 | 1,444,021,177,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,967 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
Complete lattices
TODO: define dual complete lattice and simplify proof of dual theorems.
-/
import algebra.lattice data.set.basic
open set
namespace algebra... |
e6b1c88ce0a9a0553b620060e3127fcf71db0380 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/measure_theory/function/convergence_in_measure.lean | a641cdf84b018d24cdd66084edb460359e21c5bf | [
"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 | 16,852 | lean | /-
Copyright (c) 2022 Rémy Degenne, Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Kexing Ying
-/
import measure_theory.function.egorov
/-!
# Convergence in measure
We define convergence in measure which is one of the many notions of conve... |
7008d22b12284c8aeebd252de46f23bdd199dac8 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/group_theory/submonoid/membership.lean | b6e020331a6430a0a24caadcbda04d0430fd73e2 | [
"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 | 13,745 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau, Johan Commelin, Mario Carneiro, Kevin Buzzard,
Amelia Livingston, Yury Kudryashov
-/
import group_theory.submonoid.operations
import algebra.big_operators.ba... |
cd3ba710901f30f55b046693aaad469d9090b0c2 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/algebra/lie/quotient.lean | d387306e4bc65db801de83b4cd08f07e6b0ffdce | [
"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 | 6,553 | 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.submodule
import algebra.lie.of_associative
/-!
# Quotients of Lie algebras and Lie modules
Given a Lie submodule of a Lie module, the quotient carries... |
5bc87f3ab75444d2d7d412e6ceaa87109452d042 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/complex/upper_half_plane/manifold.lean | 0c070195cc5dda0274eeb69d30aaafc31aca3c6d | [
"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 | 1,199 | lean | /-
Copyright (c) 2022 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
import analysis.complex.upper_half_plane.topology
import geometry.manifold.cont_mdiff_mfderiv
/-!
# Manifold structure on the upper half plane.
> THIS FILE IS SYNCHR... |
5471d570c82e52cf66e467e240f93d40b154b531 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/special_functions/gamma/basic.lean | e8cdf1d2b63bab6f198c9363ed1ef300b73ef4cc | [
"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 | 24,387 | lean | /-
Copyright (c) 2022 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
import measure_theory.integral.exp_decay
import analysis.special_functions.improper_integrals
import analysis.mellin_transform
/-!
# The Gamma function
> THIS FILE ... |
2a12dcc58bbf3c184c59523d8609c911adac1ab1 | ee8cdbabf07f77e7be63a449b8483ce308d37218 | /lean/src/valid/mathd-numbertheory-32.lean | 7f8364d96bee46524e086068898a6c4f87a5fdfd | [
"MIT",
"Apache-2.0"
] | permissive | zeta1999/miniF2F | 6d66c75d1c18152e224d07d5eed57624f731d4b7 | c1ba9629559c5273c92ec226894baa0c1ce27861 | refs/heads/main | 1,681,897,460,642 | 1,620,646,361,000 | 1,620,646,361,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 374 | lean | /-
Copyright (c) 2021 OpenAI. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kunhao Zheng
-/
import algebra.big_operators.basic
import data.pnat.basic
import data.finset.basic
open_locale big_operators
example (h₀ : fintype { n : ℕ | n ∣ 36}) : ∑ k in { n : ℕ | n ∣ 36... |
b9f02b2d91621ff088d051bc9d9825e5df8a5b68 | e09201d437062e1f95e6e5360aab0c9f947901aa | /src/languages/basic.lean | a25b12547144cc8d9fed829dd830d1c57672bf03 | [] | no_license | VArtem/lean-regular-languages | 34f4b093f28ef2f09ba7e684e642a0f97c901560 | e877243188253d0ac17ccf0ae2da7bf608686ff0 | refs/heads/master | 1,683,590,111,306 | 1,622,307,234,000 | 1,622,307,234,000 | 284,232,653 | 7 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,979 | lean | import data.set
import logic.function.iterate
import algebra.group_power
import tactic.nth_rewrite
import data.list.basic
open set
namespace languages
variable {S : Type}
@[simp] def append_lang (L M: set (list S)) :=
{ w : list S | ∃ {left right}, left ∈ L ∧ right ∈ M ∧ w = left ++ right}
@[simp] lemma appe... |
003055323a57fe650fbf9c22700b73aa52bb3f34 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/implicitTypePos.lean | 5e071e238e23d523d0ab145954032d96274a1948 | [
"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 | 103 | lean | def f x y := 0
def g (x y z) := 0 + x + z
def h {α β} (a : α) := a
def r {{α β}} (a : α) := a
|
869fa47d80933e22908ed752c7c0090d89829c40 | f20db13587f4dd28a4b1fbd31953afd491691fa0 | /library/init/data/setoid.lean | f5bcbc14878643477c39c55b46335420e1a26acc | [
"Apache-2.0"
] | permissive | AHartNtkn/lean | 9a971edfc6857c63edcbf96bea6841b9a84cf916 | 0d83a74b26541421fc1aa33044c35b03759710ed | refs/heads/master | 1,620,592,591,236 | 1,516,749,881,000 | 1,516,749,881,000 | 118,697,288 | 1 | 0 | null | 1,516,759,470,000 | 1,516,759,470,000 | null | UTF-8 | Lean | false | false | 883 | 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
-/
prelude
import init.logic
universes u
class setoid (α : Sort u) :=
(r : α → α → Prop) (iseqv : equivalence r)
instance setoid_has_equiv {α : Sort u} [seto... |
ad28359340992579daa53bf337476c4c9a8d47c9 | 01ae0d022f2e2fefdaaa898938c1ac1fbce3b3ab | /categories/universal/complete/default.lean | 3ac2dff19693c448f49cd51fa27ed94f051d096b | [] | no_license | PatrickMassot/lean-category-theory | 0f56a83464396a253c28a42dece16c93baf8ad74 | ef239978e91f2e1c3b8e88b6e9c64c155dc56c99 | refs/heads/master | 1,629,739,187,316 | 1,512,422,659,000 | 1,512,422,659,000 | 113,098,786 | 0 | 0 | null | 1,512,424,022,000 | 1,512,424,022,000 | null | UTF-8 | Lean | false | false | 3,310 | lean | -- Copyright (c) 2017 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Scott Morrison
import ..instances
import ...discrete_category
open categories
open categories.functor
open categories.natural_transformation
open categories.functor_categories
... |
3a83ba6b46139a99a102071f61ca0e52f3d67483 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/module/submodule/basic.lean | 6b5d2175764bbebb6c594a02620ac387d6fe896b | [
"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 | 18,523 | lean | /-
Copyright (c) 2015 Nathaniel Thomas. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nathaniel Thomas, Jeremy Avigad, Johannes Hölzl, Mario Carneiro
-/
import algebra.module.linear_map
import algebra.module.equiv
import group_theory.group_action.sub_mul_action
import... |
5d8581f55e54a70da319c0c44756a8adaa3f19df | 94e33a31faa76775069b071adea97e86e218a8ee | /src/order/atoms.lean | d200acc5025f18a5532a0bca2715b059345af0a6 | [
"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 | 26,541 | 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 order.complete_boolean_algebra
import order.cover
import order.modular_lattice
import data.fintype.basic
/-!
# Atoms, Coatoms, and Simple Lattices
This modu... |
9d088b7e96ce1e89786ebfee8a6a51e0f688138c | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/linear_algebra/basic.lean | d4fb7038ff70eb811eacbd95a4620c0462738d7d | [
"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 | 115,771 | 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, Kevin Buzzard, Yury Kudryashov
-/
import algebra.big_operators.pi
import algebra.module.hom
import algebra.module.pi
import algebra.module.prod
import a... |
eb71c65a54bea91d87200d3136119e1a799e2ffa | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/algebra/gcd_monoid/basic.lean | b9d1989f192fc3da7be880e071b214b8e588e798 | [
"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 | 49,318 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jens Wagemaker
-/
import algebra.associated
import algebra.group_power.lemmas
/-!
# Monoids with normalization functions, `gcd`, and `lcm`
This file defines extra st... |
3865a4c416d28c85615377a24bba5b81c21c08c9 | 5c7fe6c4a9d4079b5457ffa5f061797d42a1cd65 | /src/exercises/src_40_sequences.lean | 6ae35d47ddbae3eee7898872b07bc997a54eef85 | [] | no_license | gihanmarasingha/mth1001_tutorial | 8e0817feeb96e7c1bb3bac49b63e3c9a3a329061 | bb277eebd5013766e1418365b91416b406275130 | refs/heads/master | 1,675,008,746,310 | 1,607,993,443,000 | 1,607,993,443,000 | 321,511,270 | 3 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,140 | lean | import data.real.basic
import data.set.basic
import tactic
namespace mth1001
/-
We'll only deal with real-valued sequences. Such a sequence is merely a function from `ℕ` to `ℝ`
We'll use the Lean built-in real number type rather than the type we've constructed.
-/
section convergence
-- `convergesto f a` means
def ... |
cf445dbeb86517516af47d2c0dc4019bd29ab75a | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/char_p/mixed_char_zero.lean | 0c17a7d83dc45c7f83bd877cefd5449b1da02c06 | [
"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 | 14,952 | lean | /-
Copyright (c) 2022 Jon Eugster. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jon Eugster
-/
import algebra.char_p.algebra
import algebra.char_p.local_ring
import ring_theory.ideal.quotient
import tactic.field_simp
/-!
# Equal and mixed characteristic
> THIS FILE... |
742157ef628063bcfdfc07e0f96347a72e3a3d28 | 02005f45e00c7ecf2c8ca5db60251bd1e9c860b5 | /src/algebra/ring/basic.lean | 9bacb50ec849feafd6ccabe53b22f6a87f475d11 | [
"Apache-2.0"
] | permissive | anthony2698/mathlib | 03cd69fe5c280b0916f6df2d07c614c8e1efe890 | 407615e05814e98b24b2ff322b14e8e3eb5e5d67 | refs/heads/master | 1,678,792,774,873 | 1,614,371,563,000 | 1,614,371,563,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 42,007 | 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, Floris van Doorn, Amelia Livingston, Yury Kudryashov,
Neil Strickland
-/
import algebra.divisibility
import data.set.basic
/-!
# Properties and homomo... |
1c445f3b8b023d9e12b1571911be19daffede1e1 | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /stage0/src/Init/Coe.lean | a97ca477ec571c291d7245414dcef1500bf20215 | [
"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 | 4,352 | 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
-/
prelude
import Init.HasCoe -- import legacy HasCoe
import Init.Core
universes u v w w'
class Coe (α : Sort u) (β : Sort v) :=
(coe : α → β)
/-- Auxiliary... |
42b1a13023a81edb3aed47e77b0443d7c8eaf142 | 82b86ba2ae0d5aed0f01f49c46db5afec0eb2bd7 | /src/Lean/Elab/Binders.lean | fb73ffbfc8b6ea2f57c54c4bd5eaeee6bd0cf4e8 | [
"Apache-2.0"
] | permissive | banksonian/lean4 | 3a2e6b0f1eb63aa56ff95b8d07b2f851072d54dc | 78da6b3aa2840693eea354a41e89fc5b212a5011 | refs/heads/master | 1,673,703,624,165 | 1,605,123,551,000 | 1,605,123,551,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 23,110 | 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.Elab.Term
import Lean.Elab.Quotation
namespace Lean.Elab.Term
open Meta
/--
Given syntax of the forms
a) (`:` term)?
b) `:` term
r... |
81634149fdac8e6f03937dc8ee6f5d1e8f43d23b | 11e28114d9553ecd984ac4819661ffce3068bafe | /src/examples/datatypes.lean | e32cc6c12d28c0cdfdf4cfb089203afdcf46be79 | [
"MIT"
] | permissive | EdAyers/lean-subtask | 9a26eb81f0c8576effed4ca94342ae1281445c59 | 04ac5a6c3bc3bfd190af4d6dcce444ddc8914e4b | refs/heads/master | 1,586,516,665,621 | 1,558,701,948,000 | 1,558,701,948,000 | 160,983,035 | 4 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 2,299 | lean | /- Author: E.W.Ayers © 2019 -/
import ..equate
open robot
section
universe u
open list
variables {α : Type u} {a h : α} {l t s : list α}
@[equate] def nil_append : [] ++ l = l := rfl
@[equate] def append_cons : (h::t) ++ l = h:: (t ++ l) := rfl
@[equate] def reverse_def : reverse l = reverse_cor... |
2e3b4c947b607100bac0a261a65cc7d34eeadb4d | 4950bf76e5ae40ba9f8491647d0b6f228ddce173 | /src/data/equiv/mul_add.lean | 9700fc1d5f6b1747c9caf9021bcc0086f5a98ae0 | [
"Apache-2.0"
] | permissive | ntzwq/mathlib | ca50b21079b0a7c6781c34b62199a396dd00cee2 | 36eec1a98f22df82eaccd354a758ef8576af2a7f | refs/heads/master | 1,675,193,391,478 | 1,607,822,996,000 | 1,607,822,996,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 15,428 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Callum Sutton, Yury Kudryashov
-/
import algebra.group.hom
import algebra.group.type_tags
import algebra.group.units_hom
/-!
# Multiplicative and additive equivs
In t... |
cf9320eee5ee7115ecfb2f4c3c9763fb9eb15d4f | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/geometry/euclidean/basic.lean | 2fd08526903dd49df9e56f9730813e82820b88ff | [
"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 | 57,380 | lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers, Manuel Candales
-/
import analysis.inner_product_space.projection
import analysis.special_functions.trigonometric.inverse
import algebra.quadratic_discriminant
import linea... |
4389c5d9eeaad5bc7a9dc01cfce7352d9e0d07b0 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/topology/maps.lean | b4eabe0a902c4fce373c558824017c27f1a9a115 | [
"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 | 15,956 | 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... |
a2a85c3dd7815887ee7e6ecbd7adce3c548da963 | e0f9ba56b7fedc16ef8697f6caeef5898b435143 | /src/linear_algebra/basis.lean | 681be77181c799bb9b9fc165bf886ed703313b09 | [
"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 | 52,472 | 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, Alexander Bentkamp
-/
import linear_algebra.finsupp
import order.zorn
import data.fintype.card
/-!
# Linear independence and bases
This file defines ... |
813988c20419873b29aac150bbbb58e0946cc92d | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/data/rat.lean | 96ecc5cac417d38b08a7e5d9ce6d1a8b9f62a3fc | [
"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 | 44,835 | 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
Introduces the rational numbers as discrete, linear ordered field.
-/
import
data.nat.gcd data.pnat data.int.sqrt data.equiv.encodable
algebra.grou... |
7c66e15a31e7db2832a4eec87ab699d9658d0550 | 02005f45e00c7ecf2c8ca5db60251bd1e9c860b5 | /src/linear_algebra/clifford_algebra.lean | 080934db03e9b76d0b849d2ff99f6b14d265c4e7 | [
"Apache-2.0"
] | permissive | anthony2698/mathlib | 03cd69fe5c280b0916f6df2d07c614c8e1efe890 | 407615e05814e98b24b2ff322b14e8e3eb5e5d67 | refs/heads/master | 1,678,792,774,873 | 1,614,371,563,000 | 1,614,371,563,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,218 | lean | /-
Copyright (c) 2020 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Utensil Song.
-/
import algebra.ring_quot
import linear_algebra.tensor_algebra
import linear_algebra.exterior_algebra
import linear_algebra.quadratic_form
/-!
# Clifford Al... |
369a6f09102f5720816bf304f0598af154f1a172 | 3c9dc4ea6cc92e02634ef557110bde9eae393338 | /tests/lean/run/typeclass_coerce.lean | b8f411312f20430c3951bf1ce270a368b722d5e3 | [
"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 | 3,808 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Daniel Selsam, Leonardo de Moura
Declare new, simpler coercion class without the special support for transitivity.
Test that new tabled typeclass resolution deals with loops an... |
70f87d8d315868cbd7a2a9ac5937cc3f7f1e6754 | e0b0b1648286e442507eb62344760d5cd8d13f2d | /stage0/src/Lean/Elab/Do.lean | 54349a16f1319988f10998a97499749777008c8a | [
"Apache-2.0"
] | permissive | MULXCODE/lean4 | 743ed389e05e26e09c6a11d24607ad5a697db39b | 4675817a9e89824eca37192364cd47a4027c6437 | refs/heads/master | 1,682,231,879,857 | 1,620,423,501,000 | 1,620,423,501,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 68,913 | 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.Elab.Term
import Lean.Elab.Binders
import Lean.Elab.Match
import Lean.Elab.Quotation.Util
import Lean.Parser.Do
namespace Lean.Elab.Term
open L... |
02bda7f9015380bc25c49e7352c904a77181aa46 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/autoBoundErrorMsg.lean | 91db72d8dc50cf17f2805f1774bed388d09ca5f6 | [
"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 | 48 | lean | example (h : {a b : α} → a = b) : a = b := _
|
b32cc03aaa0740f4954a30eed2a72ff731ccdb3d | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /archive/imo/imo1960_q1.lean | 63c74ee06bee4a85d7f48175c8b09a83d6901fff | [
"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 | 3,336 | lean | /-
Copyright (c) 2020 Kevin Lacker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Lacker
-/
import data.nat.digits
/-!
# IMO 1960 Q1
Determine all three-digit numbers $N$ having the property that $N$ is divisible by 11, and
$\dfrac{N}{11}$ is equal to the sum... |
cc3ba8f94e9f2b89e86d555937569c0a4158e24b | 969dbdfed67fda40a6f5a2b4f8c4a3c7dc01e0fb | /src/category_theory/limits/shapes/images.lean | da30e39b67f8e459f844ea7ced4a11d1d0586991 | [
"Apache-2.0"
] | permissive | SAAluthwela/mathlib | 62044349d72dd63983a8500214736aa7779634d3 | 83a4b8b990907291421de54a78988c024dc8a552 | refs/heads/master | 1,679,433,873,417 | 1,615,998,031,000 | 1,615,998,031,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 25,282 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Markus Himmel
-/
import category_theory.limits.shapes.equalizers
import category_theory.limits.shapes.pullbacks
import category_theory.limits.shapes.strong_epi
/-!
# C... |
6dca149fe23a555c66ca1add05f121d3f7490da5 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/ring_theory/valuation/valuation_ring.lean | ab9a3b5e97613aa7e9cdd9ee4506d6c1cc0884c2 | [
"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 | 17,207 | lean | /-
Copyright (c) 2022 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz
-/
import ring_theory.valuation.integers
import ring_theory.ideal.local_ring
import ring_theory.localization.fraction_ring
import ring_theory.localization.integer
import ring_th... |
e7cc422597e412e6c24464c65526e0ea2882aa13 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/category_theory/functor/fully_faithful.lean | 400658ba2ff001368faab523c3b0f0ab4def7efd | [
"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 | 12,634 | 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
import logic.equiv.defs
/-!
# Full and faithful functors
We define typeclasses `full` and `faithful`, decorating functors... |
2b05cd193267dd489a463a16051763bbae11f885 | e0b0b1648286e442507eb62344760d5cd8d13f2d | /stage0/src/Lean/Parser/Command.lean | d0c3749aeebea66b08831cd6744cb23d646a49a0 | [
"Apache-2.0"
] | permissive | MULXCODE/lean4 | 743ed389e05e26e09c6a11d24607ad5a697db39b | 4675817a9e89824eca37192364cd47a4027c6437 | refs/heads/master | 1,682,231,879,857 | 1,620,423,501,000 | 1,620,423,501,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,462 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Sebastian Ullrich
-/
import Lean.Parser.Term
import Lean.Parser.Do
namespace Lean
namespace Parser
/--
Syntax quotation for terms and (lists of) commands.... |
2ec298d99f55244b707290295c15e28e85f53278 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/run/congr_lemma1.lean | 993cfdf8cbe3125c5e189d5d742f4f3ec3b0efd7 | [
"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 | 223 | lean | open tactic
set_option pp.binder_types true
example : true :=
by do
ite ← mk_const `ite,
l ← mk_congr_simp ite,
trace (congr_lemma.type l),
l ← mk_hcongr ite,
trace (congr_lemma.type l),
constructor
|
8cad85c928f02e6add2db44593d31a3e8a946a49 | f3849be5d845a1cb97680f0bbbe03b85518312f0 | /tests/lean/run/1590.lean | 6fbb0a55ae269a202a8cee92fb2d2966b69be052 | [
"Apache-2.0"
] | permissive | bjoeris/lean | 0ed95125d762b17bfcb54dad1f9721f953f92eeb | 4e496b78d5e73545fa4f9a807155113d8e6b0561 | refs/heads/master | 1,611,251,218,281 | 1,495,337,658,000 | 1,495,337,658,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 65 | lean | #check `(true.intro)
#check λ (h : true) [reflected h], `(id h)
|
0c29a946adafeb42fe414e0421446829e7a41b2b | caa1512363b76923d0e9cdb716122a5c26c3c6bc | /src/eigenvectors/linear_independent_multiset.lean | a74c5e0a5758f9541dd3bf2b32e8fd65af912e1f | [] | no_license | apurvanakade/cvx | deb20e425ce478159a98e1ffc0d37f9c88a89280 | b47784831339df5a3e45f5cddd84edc545f95808 | refs/heads/master | 1,687,403,288,536 | 1,555,930,740,000 | 1,555,930,740,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,844 | lean |
import linear_algebra.basis
import data.finset
import algebra.module
local attribute [instance] classical.prop_decidable
variables (α : Type) {ι β : Type} [inhabited ι] [division_ring α] [decidable_eq β] [add_comm_group β] [module α β]
open function set finsupp
def linear_independent_family (s : ι → β) : Prop :=... |
70f362f21aacad711a2c15f81549a91c7439bd9c | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/lie/tensor_product.lean | 1512f182e6fbccf0351f5dc65fa1a6b0c75c1d2b | [
"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 | 8,983 | 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.abelian
/-!
# Tensor products of Lie modules
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathli... |
c7210b43dc397c25bb5d4e8b3c3bf2f6eec3dfc0 | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/data/dfinsupp.lean | 64b3c32d502824880a3cdafe5002ad3001c46119 | [
"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 | 33,031 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau
-/
import algebra.module.pi
import algebra.big_operators.basic
import data.set.finite
/-!
# Dependent functions with finite support
For a non-dependent version s... |
9d0ac0a738254848aef9d4bb3ce9deaab8dcf272 | 64874bd1010548c7f5a6e3e8902efa63baaff785 | /tests/lean/run/enum.lean | 06c8b44767e11f251b31af2ffa7dda579183c152 | [
"Apache-2.0"
] | permissive | tjiaqi/lean | 4634d729795c164664d10d093f3545287c76628f | d0ce4cf62f4246b0600c07e074d86e51f2195e30 | refs/heads/master | 1,622,323,796,480 | 1,422,643,069,000 | 1,422,643,069,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 390 | lean | import logic
inductive Three :=
zero : Three,
one : Three,
two : Three
namespace Three
theorem disj (a : Three) : a = zero ∨ a = one ∨ a = two :=
rec (or.inl rfl) (or.inr (or.inl rfl)) (or.inr (or.inr rfl)) a
example (a : Three) : a ≠ zero → a ≠ one → a = two :=
rec (λ h₁ h₂, absurd rfl h₁) (λ h₁ h₂, absu... |
8ec235468eea35dedeac7db594d9104e63d319ce | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Meta/RecursorInfo.lean | 824d069673a0176d11ac564cf1daa70e5a512721 | [
"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 | 13,468 | 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.Util.FindExpr
import Lean.Meta.Basic
namespace Lean.Meta
inductive RecursorUnivLevelPos where
| motive ... |
3e0da72e026eb5591e99a8df95a8f12c6caa6016 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/category_theory/limits/shapes/zero_morphisms.lean | 00d1e6267f0edeff59679cf94551f4c7f0f39cb3 | [
"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 | 19,952 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.limits.shapes.products
import category_theory.limits.shapes.images
import category_theory.isomorphism_classes
import category_theory.limits.sha... |
d55444e149debaa73926b20abcb2c00fdcac2c05 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/topology/metric_space/gluing.lean | c73ed5095126e378e104b271a79d61481525f372 | [
"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 | 23,741 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import topology.metric_space.isometry
/-!
# Metric space gluing
Gluing two metric spaces along a common subset. Formally, we are given
```
Φ
Z ---> X
... |
1db0370e1bf212b2a6e238a1684862ee6bcb3f96 | 367134ba5a65885e863bdc4507601606690974c1 | /src/field_theory/splitting_field.lean | 96e0501f876979f4bea76b78ce651627ce0ce230 | [
"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 | 35,919 | 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 ring_theory.adjoin_root
import ring_theory.algebra_tower
import ring_the... |
120fe9551871d039cb0bd3212faceeb57a347c79 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/run/e3.lean | e22f6d6b6026c1eb1e6fd7e03fe5b6a5fd391aea | [
"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 | 389 | lean | prelude
definition Prop := Type.{0}
definition false := ∀x : Prop, x
check false
theorem false.elim (C : Prop) (H : false) : C
:= H C
definition eq {A : Type} (a b : A)
:= ∀ {P : A → Prop}, P a → P b
check eq
infix `=`:50 := eq
theorem refl {A : Type} (a : A) : a = a
:= λ P H, H
theorem subst {A : Type} {P : A -... |
14a990fd5b42bfa11ee7396b84a0a3ad7b24f75f | 4727251e0cd73359b15b664c3170e5d754078599 | /src/topology/algebra/constructions.lean | d41da27532151857668b0fdc431ed51d4cb18e4e | [
"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 | 2,754 | lean | /-
Copyright (c) 2021 Nicolò Cavalleri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolò Cavalleri
-/
import topology.homeomorph
/-!
# Topological space structure on the opposite monoid and on the units group
In this file we define `topological_space` structure ... |
4e0ca48b51dbd2abb5347cfb65564b1e0a8e58c0 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/analysis/normed_space/bounded_linear_maps.lean | e3bdda58b3c51b3f026db338ffefee2656c61fce | [
"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 | 22,059 | 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 analysis.normed_space.multilinear
/-!
# Continuous linear maps
This file defines a class stating that a map between normed vector spaces is (... |
16711c77cfe778facdcc2faa004e1e8843967700 | d450724ba99f5b50b57d244eb41fef9f6789db81 | /src/instructor/lectures/lecture_23b.lean | b5047796dba12236b5325fedac24b504a45ef3ec | [] | no_license | jakekauff/CS2120F21 | 4f009adeb4ce4a148442b562196d66cc6c04530c | e69529ec6f5d47a554291c4241a3d8ec4fe8f5ad | refs/heads/main | 1,693,841,880,030 | 1,637,604,848,000 | 1,637,604,848,000 | 399,946,698 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,440 | lean | /-
A challenging example that we considered recently
was the question whether a relation {(1,2),(4,5)}
is transitive. It is because it is a model of the
constraint that defines transitivity: a universal
generalization of a conditional. For every three
possible objects, a, b, and c, if the pair (a,b)
is in the relation... |
41c675b481168858491a0b7d16783a9492a1a0c4 | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /13_More_Tactics.org.6.lean | 4e40fea0e515b8d9c816c34bf2f4e1f9ac242682 | [] | 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 | 184 | lean | import standard
import data.nat
open nat
example : ∃ x, x > 2 :=
by existsi 3; exact dec_trivial
example (B : ℕ → Type) (b : B 2) : Σ x : ℕ, B x :=
by existsi 2; assumption
|
2a8d2d762e7f67cddc4b8adab6870f777c4f386a | 947b78d97130d56365ae2ec264df196ce769371a | /src/Lean/Eval.lean | c15aa6655c79fb165f0b76b44eaaa4c98bf0a297 | [
"Apache-2.0"
] | permissive | shyamalschandra/lean4 | 27044812be8698f0c79147615b1d5090b9f4b037 | 6e7a883b21eaf62831e8111b251dc9b18f40e604 | refs/heads/master | 1,671,417,126,371 | 1,601,859,995,000 | 1,601,860,020,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 905 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Sebastian Ullrich
-/
import Lean.Environment
namespace Lean
universe u
/-- `HasEval` extension that gives access to the current environment & options.
... |
8ca28a8ff237143a37698551b9a994889bcb32b9 | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /src/Std/Data/HashMap.lean | e9cecaeb86efd8df11f67f7a2e3776989ef06082 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | EdAyers/lean4 | 57ac632d6b0789cb91fab2170e8c9e40441221bd | 37ba0df5841bde51dbc2329da81ac23d4f6a4de4 | refs/heads/master | 1,676,463,245,298 | 1,660,619,433,000 | 1,660,619,433,000 | 183,433,437 | 1 | 0 | Apache-2.0 | 1,657,612,672,000 | 1,556,196,574,000 | Lean | UTF-8 | Lean | false | false | 9,093 | 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
universe u v w
def HashMapBucket (α : Type u) (β : Type v) :=
{ b : Array (AssocList α β) // b.size > 0 }
def Has... |
36c273444b23e2c2496233ad034a704c5b18603f | 5d166a16ae129621cb54ca9dde86c275d7d2b483 | /leanpkg/leanpkg/proc.lean | 8ed73265c8da40cecd53b7c864138f74c6418cc6 | [
"Apache-2.0"
] | permissive | jcarlson23/lean | b00098763291397e0ac76b37a2dd96bc013bd247 | 8de88701247f54d325edd46c0eed57aeacb64baf | refs/heads/master | 1,611,571,813,719 | 1,497,020,963,000 | 1,497,021,515,000 | 93,882,536 | 1 | 0 | null | 1,497,029,896,000 | 1,497,029,896,000 | null | UTF-8 | Lean | false | false | 626 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Gabriel Ebner
-/
import system.io leanpkg.toml
open io io.proc
variable [io.interface]
namespace leanpkg
def exec_cmd (args : io.process.spawn_args) : io unit := do
let cmdstr ... |
d92a1a1307a4ef9283cf88aec5d006612ac34226 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/linear_algebra/affine_space/affine_map.lean | 49fe60c2c55c1852c25bc08d7cd96efc517bf852 | [
"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 | 23,585 | lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import algebra.add_torsor
import data.set.intervals.unordered_interval
import linear_algebra.affine_space.basic
import linear_algebra.bilinear_map
import linear_algebra.p... |
43db9ca6dc6706501adec7e1f44cdf324121c54e | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/linear_algebra/bilinear_map.lean | 2d9681ce2e4b984fc8280c8f0e0d60bb8afa9263 | [
"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 | 16,763 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Mario Carneiro
-/
import linear_algebra.basic
import linear_algebra.basis
/-!
# Basics on bilinear maps
This file provides basics on bilinear maps. The most general form consi... |
6de6d4839c73ed9b2629eb2b0c94f712d91fbc33 | 6fbf10071e62af7238f2de8f9aa83d55d8763907 | /src/2.5_logic_propositions.lean | baf568f6b164ceaffd980afa9ca9a325dab00d8a | [] | no_license | HasanMukati/uva-cs-dm-s19 | ee5aad4568a3ca330c2738ed579c30e1308b03b0 | 3e7177682acdb56a2d16914e0344c10335583dcf | refs/heads/master | 1,596,946,213,130 | 1,568,221,949,000 | 1,568,221,949,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 295 | lean | namespace Propositions.ex1
axioms (P Q : Prop)
axioms (p1 p2 : P)
axiom Cool : P → Prop
#check true
#check false
#check P
#check Q
#check p1 = p2
#check P ∧ Q
#check P → Q
#check P ↔ Q
#check P ∨ Q
#check ¬ P
#check ∀ p : P, Cool p
#check ∃ p : P, Cool p
end Propositions.ex1
|
bd033922a4dcf5b786bd3206dd5efcbae3433234 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /test/library_search/ordered_ring.lean | 244e01019986d4cb6d6f4a65915220d7d49722cd | [
"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 | 462 | 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 tactic.basic
import data.nat.basic
import algebra.ordered_ring
/- Turn off trace messages so they don't pollute the test build: -/
set_option trace.silence_li... |
0808bda4f357e856af3e610ec66d564ed028afe5 | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/tactic/ext.lean | d793bf656d7c331b126846139925fdc6cf4611da | [
"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 | 6,901 | lean |
import tactic.basic data.list.defs data.prod data.sum tactic.rcases
universes u₁ u₂
open interactive interactive.types
open lean.parser nat tactic
meta def get_ext_subject : expr → tactic name
| (expr.pi n bi d b) :=
do v ← mk_local' n bi d,
b' ← whnf $ b.instantiate_var v,
get_ext_subject b'
| (expr.ap... |
f9f7763c7e149ed78d5dac56715900aeb07ed479 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/analysis/special_functions/log/basic.lean | a4ffa13124f6f2618667c566bb136e9cc18c4e90 | [
"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 | 12,111 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne
-/
import analysis.special_functions.exp
import data.nat.factorization.basic
/-!
# Real logarithm
In this file we define `r... |
5697f5471a08a962d60cee1c2044aad291a7e1a4 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/topology/tietze_extension.lean | 5364e367cb487087cb314dcd64f4ab21b416e14f | [
"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 | 22,969 | lean | /-
Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import analysis.specific_limits.basic
import data.set.intervals.iso_Ioo
import topology.algebra.order.monotone_continuity
import topology.urysohns_bounded
/-... |
2ed217b779659cbf77df0ea3a3b4b17990d53395 | ce6917c5bacabee346655160b74a307b4a5ab620 | /src/ch5/ex0305.lean | fd62da6ab6130884702ae92a9515bed0a94dc401 | [] | 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 | 142 | lean | example (p q : ℕ → Prop) : (∃ x, p x) → ∃ x, p x ∨ q x :=
begin
intro h,
cases h with x hpx,
existsi x, left, exact hpx
end
|
07059608d89efd191f3becd5092ea59b7bee1f84 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/computability/turing_machine.lean | d4c5b816e3052d70effc3fbad4bc4a79c31618b7 | [
"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 | 109,947 | 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.fintype.basic
import data.pfun
import logic.function.iterate
import order.basic
import tactic.apply_fun
/-!
# Turing machines
This file defines a sequen... |
b4de676630d43c519d8fc9f1876135eb4fee1a93 | 37a833c924892ee3ecb911484775a6d6ebb8984d | /src/category_theory/examples/rings/others.lean | 4880b3729c1d897792eeaf53fc2c1f6f966a133f | [] | no_license | silky/lean-category-theory | 28126e80564a1f99e9c322d86b3f7d750da0afa1 | 0f029a2364975f56ac727d31d867a18c95c22fd8 | refs/heads/master | 1,589,555,811,646 | 1,554,673,665,000 | 1,554,673,665,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,498 | lean | -- import ring_theory.ideals
-- import linear_algebra.quotient_module
-- import ..rings
-- import category_theory.limits
-- import category_theory.filtered
-- universes u v w
-- namespace category_theory.examples
-- open category_theory
-- open category_theory.limits
-- variables {α : Type v}
-- def coequalizer_id... |
bb27fce4d13d7860a7d4a6be6a2af9ed11dcad99 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/346.lean | 2c1be478532454d37cf1d575d8b8e7f0a787bf32 | [
"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 | 144 | lean | inductive SomeType
| x : SomeType
namespace SomeType
def a : SomeType := SomeType.x
end SomeType
#eval SomeType.b
def f (x : Nat) :=
x.z
|
537b524da4186ef87c5ccd427070dcf6159bbb58 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/t5.lean | 750632b64f1819cdfdf92636f0dfc4c3b592ba8b | [
"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 | 287 | lean | constant N : Type.{1}
constant f : N → N
constant a : N
noncomputable definition g (a : N) : N := f a
check g
namespace foo
noncomputable definition h : N := f a
check h
private noncomputable definition q : N := f a
check q
end foo
check foo.h
check q -- Error q is now hidden
|
f7f3a9e3216497919c83db7ff3eb3f8a27798ba2 | f00cc9c04d77f9621aa57d1406d35c522c3ff82c | /library/init/data/nat/bitwise.lean | 8ceea3c316f7dcb55129435f35e7da6a446db773 | [
"Apache-2.0"
] | permissive | shonfeder/lean | 444c66a74676d74fb3ef682d88cd0f5c1bf928a5 | 24d5a1592d80cefe86552d96410c51bb07e6d411 | refs/heads/master | 1,619,338,440,905 | 1,512,842,340,000 | 1,512,842,340,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,847 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
-/
prelude
import init.data.nat.lemmas init.meta.well_founded_tactics
universe u
namespace nat
def bodd_div2 : ℕ → bool × ℕ
| 0 := (ff, 0)
| (succ n) :=... |
861e15ee8aa10f2c00d8667efd6e89cc40d3ff77 | 86f6f4f8d827a196a32bfc646234b73328aeb306 | /examples/basics/unnamed_293.lean | 24aa28c667e7146230479a539c81fe4089273a38 | [] | no_license | jamescheuk91/mathematics_in_lean | 09f1f87d2b0dce53464ff0cbe592c568ff59cf5e | 4452499264e2975bca2f42565c0925506ba5dda3 | refs/heads/master | 1,679,716,410,967 | 1,613,957,947,000 | 1,613,957,947,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 237 | lean | import data.real.basic
variables a b : ℝ
-- BEGIN
example : (a + b) * (a + b) = a * a + 2 * (a * b) + b * b :=
begin
rw [mul_add, add_mul, add_mul],
rw [←add_assoc, add_assoc (a * a)],
rw [mul_comm b a, ←two_mul]
end
-- END |
a4a30bd8ba137a8a04f5c27332a3c74b77604092 | 3618c6e11aa822fd542440674dfb9a7b9921dba0 | /scratch/coprod/coproduct.lean | 41bb53b659a53a026e99a1045ffa6383db3ddc56 | [] | no_license | ChrisHughes24/single_relation | 99ceedcc02d236ce46d6c65d72caa669857533c5 | 057e157a59de6d0e43b50fcb537d66792ec20450 | refs/heads/master | 1,683,652,062,698 | 1,683,360,089,000 | 1,683,360,089,000 | 279,346,432 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,495 | lean | import tactic.equiv_rw tactic group_theory.subgroup group_theory.semidirect_product
universes u v w x y z
def mul_left {G : Type*} [group G] : G →* equiv.perm G :=
{ to_fun := λ g,
{ to_fun := λ h, g * h,
inv_fun := λ h, g⁻¹ * h,
left_inv := λ _, by simp [mul_assoc],
right_inv := λ _, by simp [mul_assoc... |
da041628638028bc759b1055ff38e34472b6168a | a339bc2ac96174381fb610f4b2e1ba42df2be819 | /hott/types/unit.hlean | 31e4afd2ecf5ff9ae8811ddbb73096aeb804e881 | [
"Apache-2.0"
] | permissive | kalfsvag/lean2 | 25b2dccc07a98e5aa20f9a11229831f9d3edf2e7 | 4d4a0c7c53a9922c5f630f6f8ebdccf7ddef2cc7 | refs/heads/master | 1,610,513,122,164 | 1,483,135,198,000 | 1,483,135,198,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,384 | 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
Theorems about the unit type
-/
open is_equiv equiv option eq pointed is_trunc function
namespace unit
protected definition eta : Π(u : unit), ⋆ = u
| eta ⋆ ... |
8fda5a200afe212c251624beb708f777290de363 | 92e157ec9825b5e4597a6d715a8928703bc8e3b2 | /src/mywork/lecture_2.lean | 50b2b151d631e04e00f8f7ff7906e8db6e19296e | [] | no_license | exb3dg/cs2120f21 | 9e566bc508762573c023d3e70f83cb839c199ec8 | 319b8bf0d63bf96437bf17970ce0198d0b3525cd | refs/heads/main | 1,692,970,909,568 | 1,634,584,540,000 | 1,634,584,540,000 | 399,947,025 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,558 | lean | /-
INFERENCE RULE #1/2: EQUALITY IS REFLEXIVE
Everything is equal to itself. A bit more formally,
if one is given a type, T, and a value, t, of this
type, then you may have a proof of t = t "for free."
-/
axiom eq_refl :
∀ (T : Type) -- if T is any type (of thing)
(t : T), -- and t is thing of that type, T... |
93819382a6ca0b1b5cffcd8e36d4deeb9ac49d13 | 367134ba5a65885e863bdc4507601606690974c1 | /src/linear_algebra/direct_sum_module.lean | dad206486c9d4ad9abbbe9f5da7c5934fd7d0fed | [
"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 | 5,101 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
Direct sum of modules over commutative rings, indexed by a discrete type.
-/
import algebra.direct_sum
import linear_algebra.dfinsupp
/-!
# Direct sum of modules over commutativ... |
5c1130cd86de118f324cfc1c2b5ccf2bbb4c8f01 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /library/data/examples/depchoice.lean | 4dd12d1ffed899779d84c378002409bc537a7153 | [
"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 | 3,080 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
import data.encodable
open nat encodable
/-
In mathematics, the axiom of dependent choice is a weak form of the axiom of choice that is
sufficient to develo... |
09544934245b22bdbca4ebb82d9cbc4bafab4522 | 67190c9aacc0cac64fb4463d93e84c696a5be896 | /Lists of exercises/List 3/HAM-LucasDomingues.lean | c8a6e1a34a3c7263600140eb711d3a3e23e4e176 | [] | no_license | lucasresck/Discrete-Mathematics | ffbaf55943e7ce2c7bc50cef7e3ef66a0212f738 | 0a08081c5f393e5765259d3f1253c3a6dd043dac | refs/heads/master | 1,596,627,857,734 | 1,573,411,500,000 | 1,573,411,500,000 | 212,489,764 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,730 | lean | -- Reduction of Hamiltonian path to SAT problem
-- My graph is G = {(1, 2), (1, 3), (1, 4), (2, 3)}
-- x_ij means the ith position of Hamiltonian path is occupied by node j
variables x11 x12 x13 x14
x21 x22 x23 x24
x31 x32 x33 x34
x41 x42 x43 x44 : Prop
-- Any path:
variables pa... |
ce99fff3782a451049cf7d01b589fc2aa2f7f9ef | f10d66a159ce037d07005bd6021cee6bbd6d5ff0 | /to_comm_semiring.lean | eca54fdf98f726f4a0e0ec1688bb97a61d98cac1 | [] | no_license | johoelzl/mason-stother | 0c78bca183eb729d7f0f93e87ce073bc8cd8808d | 573ecfaada288176462c03c87b80ad05bdab4644 | refs/heads/master | 1,631,751,973,492 | 1,528,923,934,000 | 1,528,923,934,000 | 109,133,224 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 9,974 | lean | import data.finsupp
import algebra.ring
import .to_finset
import .to_multiset
import to_semiring
noncomputable theory
local infix ^ := monoid.pow
open classical multiset
local attribute [instance] prop_decidable
--can the priority be set better? Because now we often have to provide parentheses
local notation a `~ᵤ... |
5dcb265b9f851db4ba502b748c4294e9bbc39078 | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/topology/algebra/monoid.lean | 89342c880653dce5a248e9420b6c30f49948a6d8 | [
"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 | 6,131 | 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
Theory of topological monoids.
-/
import topology.continuous_on
import group_theory.submonoid.basic
import algebra.group.prod
open classical set filter... |
5e5e24813a420f422496c8c1035a77dc897c0c34 | bae21755a4a03bbe0a5c22e258db8633407711ad | /library/init/category/state.lean | 7c0f8cec3ffb2136115a0c8d19fcd79ac663b202 | [
"Apache-2.0"
] | permissive | nor-code/lean | f437357a8f85db0f06f186fa50fcb1bc75f6b122 | aa306af3d7c47de3c7937c98d3aa919eb8da6f34 | refs/heads/master | 1,662,613,329,886 | 1,586,696,014,000 | 1,586,696,014,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,779 | 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, Sebastian Ullrich
The state monad transformer.
-/
prelude
import init.category.alternative init.category.lift
import init.category.id init.category.except
un... |
00c85982192c3cea993965028e83b45a28694938 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/measure_theory/function/strongly_measurable_lp.lean | 44f3b46bf86ca34efe4de1952e808ff6231e9bd5 | [
"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 | 2,710 | lean | /-
Copyright (c) 2022 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
import measure_theory.function.simple_func_dense_lp
import measure_theory.function.strongly_measurable
/-!
# Finitely strongly measurable functions in `Lp`
Functions i... |
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