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4283e22c0f6627ad84fbc49c0e2244b86948846f | 206422fb9edabf63def0ed2aa3f489150fb09ccb | /src/measure_theory/outer_measure.lean | 010f656c7375d37dcf868e224b4ee33a749f6c4b | [
"Apache-2.0"
] | permissive | hamdysalah1/mathlib | b915f86b2503feeae268de369f1b16932321f097 | 95454452f6b3569bf967d35aab8d852b1ddf8017 | refs/heads/master | 1,677,154,116,545 | 1,611,797,994,000 | 1,611,797,994,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 41,648 | 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
-/
import analysis.specific_limits
import measure_theory.measurable_space
import topology.algebra.infinite_sum
/-!
# Outer Measures
An outer measure is... |
b2b26ffd5f54c48af9577692cb6dc7bed87f721d | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/algebraic_geometry/presheafed_space.lean | 53ec251efcace6d2cdcaa3df258a1460c867d9df | [
"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 | 10,843 | 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 topology.sheaves.presheaf
/-!
# Presheafed spaces
Introduces the category of topological spaces equipped with a presheaf (taking values in an
arbitrary targe... |
5c79039deea34aaa7ed4d063cad76e05c9c56ede | c777c32c8e484e195053731103c5e52af26a25d1 | /src/geometry/euclidean/basic.lean | 543b4470efd8dbd0463913e17c30af5b924342cd | [
"Apache-2.0"
] | permissive | kbuzzard/mathlib | 2ff9e85dfe2a46f4b291927f983afec17e946eb8 | 58537299e922f9c77df76cb613910914a479c1f7 | refs/heads/master | 1,685,313,702,744 | 1,683,974,212,000 | 1,683,974,212,000 | 128,185,277 | 1 | 0 | null | 1,522,920,600,000 | 1,522,920,600,000 | null | UTF-8 | Lean | false | false | 31,947 | 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 algebra.quadratic_discriminant
/-!
# Euclidean spaces
This file makes some definitions and proves... |
c4eed629db78c7ba70b5a07884e2b2869bace617 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/init/data/string/default_auto.lean | 591bd959ff685238b4657f9feea94604540a78f1 | [] | 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 | 310 | 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
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.data.string.basic
import Mathlib.Lean3Lib.init.data.string.ops
namespace Mathlib
end Mathlib |
7637d1cd31381a93aaa6e15c77aff3897ab44f71 | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /tests/bench/binarytrees.lean | 8dde86c46fa86a582e376ee610a3e86fc1fd6209 | [
"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 | 1,702 | lean | inductive Tree
| Nil
| Node (l r : Tree) : Tree
open Tree
instance : Inhabited Tree := ⟨Nil⟩
-- This Function has an extra argument to suppress the
-- common sub-expression elimination optimization
partial def make' : UInt32 -> UInt32 -> Tree
| n, d =>
if d = 0 then Node Nil Nil
else Node (make' n (d - 1)) (make' ... |
3046d492b676d018a816c1d359564bb8485b4a7b | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/algebra/euclidean_domain.lean | f8b8b191b33ec6c7d3fa00727d7ebc0e34d901d7 | [
"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 | 13,773 | lean | /-
Copyright (c) 2018 Louis Carlin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Louis Carlin, Mario Carneiro
Euclidean domains and Euclidean algorithm (extended to come)
A lot is based on pre-existing code in mathlib for natural number gcds
-/
import data.int.basic... |
4d2c458e64dd11021c8a56c53c2f110dd31b14ce | 94e33a31faa76775069b071adea97e86e218a8ee | /src/topology/algebra/group.lean | e16da7f2165350cc394fae46ab15612ff9fa1579 | [
"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 | 61,161 | 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 group_theory.group_action.conj_act
import group_theory.group_action.quotient
import order.filter.pointwise
import topology.alge... |
89b53ee2fac8a46533630fe81dff9ef547b4ae15 | 5719a16e23dfc08cdea7a5bf035b81690f307965 | /src/Init/Lean/Meta/WHNF.lean | 8d79fc56e622b13762b96f8003e3979835548837 | [
"Apache-2.0"
] | permissive | postmasters/lean4 | 488b03969a371e1507e1e8a4df9ebf63c7cbe7ac | f3976fc53a883ac7606fc59357d43f4b51016ca7 | refs/heads/master | 1,655,582,707,480 | 1,588,682,595,000 | 1,588,682,595,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,891 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import Init.Lean.AuxRecursor
import Init.Lean.Util.WHNF
import Init.Lean.Meta.Basic
import Init.Lean.Meta.LevelDefEq
namespace Lean
namespace Meta
... |
8579487c4c4caedfd7b6e796168fb508760f0751 | efa51dd2edbbbbd6c34bd0ce436415eb405832e7 | /20150803_CADE/examples/ex3.lean | 24a8041fcc75b362891b85bc8608419691295311 | [
"Apache-2.0"
] | permissive | leanprover/presentations | dd031a05bcb12c8855676c77e52ed84246bd889a | 3ce2d132d299409f1de269fa8e95afa1333d644e | refs/heads/master | 1,688,703,388,796 | 1,686,838,383,000 | 1,687,465,742,000 | 29,750,158 | 12 | 9 | Apache-2.0 | 1,540,211,670,000 | 1,422,042,683,000 | Lean | UTF-8 | Lean | false | false | 338 | lean | open nat
inductive tree (A : Type) :=
| leaf : A → tree A
| node : tree A → tree A → tree A
check tree.leaf 10
check tree.leaf (10:nat)
open tree
check leaf 10
definition nleaves {A : Type} (t : tree A) : nat :=
tree.rec (λ a, 1) (λ n₁ n₂ r₁ r₂, r₁ + r₂) t
eval nleaves (node (leaf 10) (node (leaf 20) (leaf 30)))
|
b16c8a3d2f3e67ab4e178d0c61a707f5fb8eccf3 | d436468d80b739ba7e06843c4d0d2070e43448e5 | /src/tactic/finish.lean | f40f7b8b81259c242ff519652e91034782bb3af4 | [
"Apache-2.0"
] | permissive | roro47/mathlib | 761fdc002aef92f77818f3fef06bf6ec6fc1a28e | 80aa7d52537571a2ca62a3fdf71c9533a09422cf | refs/heads/master | 1,599,656,410,625 | 1,573,649,488,000 | 1,573,649,488,000 | 221,452,951 | 0 | 0 | Apache-2.0 | 1,573,647,693,000 | 1,573,647,692,000 | null | UTF-8 | Lean | false | false | 21,583 | lean | /-
Copyright (c) 2017 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Jesse Michael Han
These tactics do straightforward things: they call the simplifier, split conjunctive assumptions,
eliminate existential quantifiers on the left, and lo... |
79d3e0f965cb6a55e79f7ad84d3c7cf45324770e | 137c667471a40116a7afd7261f030b30180468c2 | /src/group_theory/perm/basic.lean | 02ee030a933d21a4cbb9017f2c37a62f60c7b351 | [
"Apache-2.0"
] | permissive | bragadeesh153/mathlib | 46bf814cfb1eecb34b5d1549b9117dc60f657792 | b577bb2cd1f96eb47031878256856020b76f73cd | refs/heads/master | 1,687,435,188,334 | 1,626,384,207,000 | 1,626,384,207,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 15,245 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Mario Carneiro
-/
import algebra.group.pi
import algebra.group_power
/-!
# The group of permutations (self-equivalences) of a type `α`
This file defines the... |
c228a810a26dbcf4bdb3119984be056f88f11e2c | e151e9053bfd6d71740066474fc500a087837323 | /src/hott/init/meta/simp.lean | 1db9de0310f7800bea1618a128200b937e09648e | [
"Apache-2.0"
] | permissive | daniel-carranza/hott3 | 15bac2d90589dbb952ef15e74b2837722491963d | 913811e8a1371d3a5751d7d32ff9dec8aa6815d9 | refs/heads/master | 1,610,091,349,670 | 1,596,222,336,000 | 1,596,222,336,000 | 241,957,822 | 0 | 0 | Apache-2.0 | 1,582,222,839,000 | 1,582,222,838,000 | null | UTF-8 | Lean | false | false | 4,676 | lean | /-
Copyright (c) 2017 Gabriel Ebner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner
-/
import .rewrite
open tactic expr
namespace hott
meta def simplify_plus_d (s : simp_lemmas) (to_unfold : list name := []) (e : expr) (cfg : simp_config := {}) (r : nam... |
0965c7a9823b15bee49d1fb60c0fd4ea315d20b6 | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/order/bounds.lean | 55345dcac06a0b311a3559fba536f56bf704db17 | [
"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 | 27,360 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yury Kudryashov
-/
import data.set.intervals.basic
/-!
# Upper / lower bounds
In this file we define:
* `upper_bounds`, `lower_bounds` : the set of upper bounds (res... |
b2a94389a4fe926ad9ff065b5789654a75c285e9 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/unification_hints1.lean | fe2025de479cee361f9490d9cf8dbedd5b74ee6a | [
"Apache-2.0"
] | permissive | leanprover-community/lean | 12b87f69d92e614daea8bcc9d4de9a9ace089d0e | cce7990ea86a78bdb383e38ed7f9b5ba93c60ce0 | refs/heads/master | 1,687,508,156,644 | 1,684,951,104,000 | 1,684,951,104,000 | 169,960,991 | 457 | 107 | Apache-2.0 | 1,686,744,372,000 | 1,549,790,268,000 | C++ | UTF-8 | Lean | false | false | 1,203 | lean | --
open list nat
namespace toy
constants (A : Type) (f h : A → A) (x y z : A)
attribute [irreducible]
noncomputable definition g (x y : A) : A := f z
#unify (g x y), (f z)
@[unify]
noncomputable definition toy_hint (x y : A) : unification_hint :=
{ pattern := g x y ≟ f z,
constraints := [] }
#unify (g x y), (f z)... |
b9479d1e71c2e8f14cf5405bc59ab351b680ab32 | 5412d79aa1dc0b521605c38bef9f0d4557b5a29d | /src/Lean/Elab.lean | 537b9c061b35ff26dc7854a5def77be48b28cdb2 | [
"Apache-2.0"
] | permissive | smunix/lean4 | a450ec0927dc1c74816a1bf2818bf8600c9fc9bf | 3407202436c141e3243eafbecb4b8720599b970a | refs/heads/master | 1,676,334,875,188 | 1,610,128,510,000 | 1,610,128,521,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 838 | 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.Import
import Lean.Elab.Exception
import Lean.Elab.Command
import Lean.Elab.Term
import Lean.Elab.App
import Lean.Elab.Binders
import Lean.... |
19359d7bb0ade8c891c47e881c164e7aa3b8de63 | a88f0086fb3e2025ebb21e0ba2f2725774c6979f | /src/topology/metric_space/basic.lean | 692685ba97a2a5752e312b4531d980eca4a2cc32 | [
"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 | 57,868 | lean | /-
Copyright (c) 2015, 2017 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Metric spaces.
Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
Many definitions and theorems expected on metric spaces are already introduced o... |
83da75e64c9087d8b13a9de51396186f1460ceb9 | 5ae26df177f810c5006841e9c73dc56e01b978d7 | /src/group_theory/subgroup.lean | f6a5f4983f6b0ff97d4b7e28af9588481eae22b4 | [
"Apache-2.0"
] | permissive | ChrisHughes24/mathlib | 98322577c460bc6b1fe5c21f42ce33ad1c3e5558 | a2a867e827c2a6702beb9efc2b9282bd801d5f9a | refs/heads/master | 1,583,848,251,477 | 1,565,164,247,000 | 1,565,164,247,000 | 129,409,993 | 0 | 1 | Apache-2.0 | 1,565,164,817,000 | 1,523,628,059,000 | Lean | UTF-8 | Lean | false | false | 36,164 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mitchell Rowett, Scott Morrison, Johan Commelin, Mario Carneiro,
Michael Howes
-/
import group_theory.submonoid
open set function
variables {α : Type*} {β : Type*} {... |
00a79fc0948932afad3198681118fd013c2ad79e | ac89c256db07448984849346288e0eeffe8b20d0 | /src/Init/Data/Nat/Basic.lean | efa755250cdb662a1efe2d0c945b0a3c16cf6b7d | [
"Apache-2.0"
] | permissive | chepinzhang/lean4 | 002cc667f35417a418f0ebc9cb4a44559bb0ccac | 24fe2875c68549b5481f07c57eab4ad4a0ae5305 | refs/heads/master | 1,688,942,838,326 | 1,628,801,942,000 | 1,628,801,995,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 13,911 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Leonardo de Moura
-/
prelude
import Init.SimpLemmas
universe u
namespace Nat
@[specialize] def foldAux {α : Type u} (f : Nat → α → α) (s : Nat) : Nat → α → α... |
cf90d99e45c4640e3266db13b1c51da7eb8ed509 | 30b012bb72d640ec30c8fdd4c45fdfa67beb012c | /analysis/normed_space.lean | 2c5fc983bf8374986c1f711edaa9feb724c916d3 | [
"Apache-2.0"
] | permissive | kckennylau/mathlib | 21fb810b701b10d6606d9002a4004f7672262e83 | 47b3477e20ffb5a06588dd3abb01fe0fe3205646 | refs/heads/master | 1,634,976,409,281 | 1,542,042,832,000 | 1,542,319,733,000 | 109,560,458 | 0 | 0 | Apache-2.0 | 1,542,369,208,000 | 1,509,867,494,000 | Lean | UTF-8 | Lean | false | false | 14,974 | lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Normed spaces.
Authors: Patrick Massot, Johannes Hölzl
-/
import algebra.pi_instances
import linear_algebra.basic
import analysis.nnreal
variables {α : Type*} {β : Type*} {γ : Type*} {ι : Typ... |
d3976fd5d79f9ae299871e955c4c91be66dbd39e | 4727251e0cd73359b15b664c3170e5d754078599 | /src/category_theory/sites/plus.lean | 0520c3b1c40aaac6e7e7abd348e87015740238e2 | [
"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 | 11,005 | lean | /-
Copyright (c) 2021 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz
-/
import category_theory.sites.sheaf
/-!
# The plus construction for presheaves.
This file contains the construction of `P⁺`, for a presheaf `P : Cᵒᵖ ⥤ D`
where `C` is endow... |
3e73763289fa515cb7de2243f01af7757b6ce973 | 32a2d1642d7519c99693bc1d3b24069e4853dd1f | /group_theory/free_group.lean | 93d6da13853f63b7de2ecf786401cf19009cd1e5 | [
"Apache-2.0"
] | permissive | Cedric0099/mathlib | 7edb81d5d68e280b4d21f6c0377dad1f9b8c0d71 | a97101d2df5d186848075a2d0452f6a04d8a13eb | refs/heads/master | 1,584,201,847,599 | 1,524,979,632,000 | 1,524,979,632,000 | 131,690,350 | 0 | 0 | null | 1,525,162,341,000 | 1,525,162,341,000 | null | UTF-8 | Lean | false | false | 28,912 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
Free groups as a quotient over the reduction relation `a * x * x⁻¹ * b = a * b`.
First we introduce the one step reduction relation
`free_group.red.step`: w * x * x⁻¹ * v ~... |
0592d6f1b4929565f9d6a075634b27cb85f719eb | dce2ec26258c35f21c8a5318a7a2ed297ddba7c6 | /src/Problems/1_4.lean | db1ff382eac2e9c4e8d8856f38da2802002c241e | [] | no_license | nedsu/lean-category-theory-pr | c151c4f95d58a2d3b33e8f38ff7734d85d82e5ee | 8d72f4645d83c72d15afaee7a2df781b952417e9 | refs/heads/master | 1,625,444,569,743 | 1,597,056,476,000 | 1,597,056,476,000 | 145,738,350 | 0 | 0 | null | 1,534,957,201,000 | 1,534,957,201,000 | null | UTF-8 | Lean | false | false | 5,953 | lean | import ncategory_theory.ndefs
open category_theory category_theory.functor function
universes u₁ v₁ u₂ v₂ u₃ v₃ u₄ v₄
--4a Show that any functor F : C ⥤ D can be factorised as L : C ⥤ E and R : E ⥤ D where L is bijective on objects, and R is full and faithful.
structure functor_decomp (C : Type u₁) [category.{v₁} C... |
1d1a09f35940245248a6f0b8e8363a6e760a7eca | 88892181780ff536a81e794003fe058062f06758 | /src/xena_challenge/challenge4.lean | 0a038049c5a5b19fc38df75b333d112a1b57893a | [] | no_license | AtnNn/lean-sandbox | fe2c44280444e8bb8146ab8ac391c82b480c0a2e | 8c68afbdc09213173aef1be195da7a9a86060a97 | refs/heads/master | 1,623,004,395,876 | 1,579,969,507,000 | 1,579,969,507,000 | 146,666,368 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 306 | lean | import tactic
import lib.attempt
open function
theorem challenge4 (X Y Z : Type) (f : X → Y) (g : Y → Z) : surjective (g ∘ f) → surjective g :=
attempt begin
unfold surjective,
intros h b,
cases h b with a hh,
use f a,
exact hh,
end $
λ h b, let ⟨ a, h ⟩ := h b in ⟨ f a, h ⟩
|
fb2d5d5140870d1bdcdc31e5494d08acebcf4488 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/group_theory/subgroup/simple.lean | b629a87b9ab547e286b4297b8bb955863000905a | [
"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 | 2,036 | lean | /-
Copyright (c) 2021 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import group_theory.subgroup.actions
/-!
# Simple groups
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathli... |
b0dea0c7d2d88f86431e1fdcee5429df26b712fa | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/finsupp/defs.lean | d21d60bc1202e143a3bef6296c2b85642dd20c7a | [
"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 | 41,256 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Scott Morrison
-/
import algebra.indicator_function
import group_theory.submonoid.basic
/-!
# Type of functions with finite support
> THIS FILE IS SYNCHRONIZED WITH M... |
8dcb215877ece47a1988b7b539666ed5f22445fb | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/topology/metric_space/partition_of_unity.lean | 22f30453a6e2bbebfc341fd669f3be68295ad006 | [
"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 | 8,200 | lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import topology.metric_space.emetric_paracompact
import analysis.convex.partition_of_unity
/-!
# Lemmas about (e)metric spaces that need partition of unity
The ma... |
677755e2b523ff8508be319c91daee558da4bec7 | 38bf3fd2bb651ab70511408fcf70e2029e2ba310 | /src/algebra/floor.lean | eade208b4e78c256a66157633765c7ecc950f74d | [
"Apache-2.0"
] | permissive | JaredCorduan/mathlib | 130392594844f15dad65a9308c242551bae6cd2e | d5de80376088954d592a59326c14404f538050a1 | refs/heads/master | 1,595,862,206,333 | 1,570,816,457,000 | 1,570,816,457,000 | 209,134,499 | 0 | 0 | Apache-2.0 | 1,568,746,811,000 | 1,568,746,811,000 | null | UTF-8 | Lean | false | false | 9,530 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Kevin Kappelmann
-/
import data.int.basic
import tactic.linarith tactic.abel
/-!
# Floor and Ceil
## Summary
We define `floor`, `ceil`, and `nat_ceil` functions on li... |
2abad4012dd1c5754b9d37a9c91f1f127a5eef85 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/analysis/special_functions/trigonometric/complex_deriv.lean | a8a78b04f7acb418fd4160e04f54a5eb4dc4b1dc | [
"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 | 2,604 | 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, Benjamin Davidson
-/
import analysis.special_functions.trigonometric.complex
import analysis.special_functions.trigonometric... |
e5b231bb1777c31dadf266b92593c540158a8d71 | 0f5090f82d527e0df5bf3adac9f9e2e1d81d71e2 | /src/michael/graph_induction.lean | 14cbd74fa9b83c36d64d823eb545b1c898dfe77d | [] | no_license | apurvanakade/mc2020-lean-projects | 36eb42c4baccc37183635c36f8e1b3afa4ec1230 | 02466225aa629ab1232043bcc0a053a099fdb939 | refs/heads/master | 1,688,791,717,534 | 1,597,874,092,000 | 1,597,874,092,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,273 | lean | import michael.simple_graph
noncomputable theory
open_locale classical
universes u
variables {V : Type u}
namespace simple_graph
def is_subgraph (H : simple_graph V) (G : simple_graph V) : Prop :=
∀ u v, H.adj u v → G.adj u v
variables (G : simple_graph V)
include G
@[refl] lemma is_subgraph_self : G.is_subg... |
14a06d20818e49a0123c5b18994a56e8b9f6cb01 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/computability/halting.lean | 2e8c47bebc624b37206915dadf1ce2d59e8ce711 | [
"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 | 13,293 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
More partial recursive functions using a universal program;
Rice's theorem and the halting problem.
-/
import computability.partrec_code
open encodable denumerable
nam... |
e669689544823dcb2cfb850f248e9e26037e87be | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/univInference.lean | 40b16d73fe2468208eacca25590dd32deec416d5 | [
"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 | 2,407 | lean |
universe w₁ w₂ w₃
namespace Struct
structure S1.{r, s} (α : Type s) : Type (max s r) :=
up :: (down : α)
def ex1.{u, v} (α : Type u) (σ : Type (max v u)) (h : σ = S1.{v, u} α) : True :=
trivial
structure S2.{u, v} (α : Sort u) (β : Sort v) :=
(a : α)
(b : β)
def ex2.{u, v} (α : Sort u) (β : Sort v) (σ : So... |
10609bb147241ff44963bc5a1f6b21802d73a847 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/category_theory/limits/shapes/zero_morphisms.lean | e74ed7ee776edea6ba372d914975d4e3e3197f9a | [
"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 | 19,793 | 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... |
36a222021e9346a4bbc30e40a28ef8b6c1c1d91d | f7315930643edc12e76c229a742d5446dad77097 | /hott/arity.hlean | cac814dbe148c3bad630b01884fd9f8015904d9c | [
"Apache-2.0"
] | permissive | bmalehorn/lean | 8f77b762a76c59afff7b7403f9eb5fc2c3ce70c1 | 53653c352643751c4b62ff63ec5e555f11dae8eb | refs/heads/master | 1,610,945,684,489 | 1,429,681,220,000 | 1,429,681,449,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,315 | hlean | /-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: init.path
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}... |
613c95bf9ef4d5f5196b35130854a037c38f27aa | a047a4718edfa935d17231e9e6ecec8c7b701e05 | /src/linear_algebra/dimension.lean | e8bcf41f0087a334d1798ecf07c0b7d73e459d1c | [
"Apache-2.0"
] | permissive | utensil-contrib/mathlib | bae0c9fafe5e2bdb516efc89d6f8c1502ecc9767 | b91909e77e219098a2f8cc031f89d595fe274bd2 | refs/heads/master | 1,668,048,976,965 | 1,592,442,701,000 | 1,592,442,701,000 | 273,197,855 | 0 | 0 | null | 1,592,472,812,000 | 1,592,472,811,000 | null | UTF-8 | Lean | false | false | 17,996 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro, Johannes Hölzl, Sander Dahmen
-/
import linear_algebra.basis
import set_theory.ordinal
/-!
# Dimension of modules and vector spaces
## Main definitions
* The dimension... |
4062029d49f747c5fddca046c7b1296769665719 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/notation7.lean | 309bbde50cb7994d8b77602bb6c970bf333f2bae | [
"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 | 201 | lean | --
open num
constant f : num → num
constant g : num → num → num
notation A `:+1`:100000 := f A
check g 0:+1:+1 (1:+1 + 2:+1):+1
set_option pp.notation false
check g 0:+1:+1 (1:+1 + 2:+1):+1
|
5230288acbb008df76d05907eaaa9e7d25c2ac13 | 08bd4ba4ca87dba1f09d2c96a26f5d65da81f4b4 | /src/Lean/Elab/PreDefinition/WF/Eqns.lean | 22605f3b8e3aafba458b60a6f1ee7a8e8a62ac8c | [
"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",
"Apache-2.0",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | gebner/lean4 | d51c4922640a52a6f7426536ea669ef18a1d9af5 | 8cd9ce06843c9d42d6d6dc43d3e81e3b49dfc20f | refs/heads/master | 1,685,732,780,391 | 1,672,962,627,000 | 1,673,459,398,000 | 373,307,283 | 0 | 0 | Apache-2.0 | 1,691,316,730,000 | 1,622,669,271,000 | Lean | UTF-8 | Lean | false | false | 9,981 | lean | /-
Copyright (c) 2022 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.Rewrite
import Lean.Meta.Tactic.Split
import Lean.Elab.PreDefinition.Basic
import Lean.Elab.PreDefinition.Eqns
namespace Lean.Elab.... |
2d404dc68aa6f093fd54ca97c294254ceb46e8d8 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/algebraic_topology/simplex_category.lean | 0e3ecfad0e8e725b9182194a1d3645601f2726ba | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 17,552 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Scott Morrison, Adam Topaz
-/
import category_theory.skeletal
import tactic.linarith
import data.fintype.sort
import order.category.NonemptyFinLinOrd
/-! # The simple... |
d732adab63359cf60fdcfdcc6ccf4662be78c91e | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/measure_theory/measure/vector_measure.lean | 89a8d7b274b667e0562fae0f43919dddf0509a69 | [
"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 | 50,114 | lean | /-
Copyright (c) 2021 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
import measure_theory.measure.measure_space
import analysis.complex.basic
/-!
# Vector valued measures
This file defines vector valued measures, which are σ-additive fun... |
71759b93091365e7b3a879b60b5f4ab78586ec13 | 02005f45e00c7ecf2c8ca5db60251bd1e9c860b5 | /src/analysis/special_functions/polynomials.lean | 7829d6f66e959f97b3318d0ceb5e956f96f44c18 | [
"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 | 6,146 | lean | /-
Copyright (c) 2020 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-/
import analysis.asymptotics.asymptotic_equivalent
import analysis.asymptotics.specific_asymptotics
import data.polynomial.erase_lead
/-!
# Limits related to poly... |
202710788f3a0bb9b68b93c296934dca4a33b214 | 33340b3a23ca62ef3c8a7f6a2d4e14c07c6d3354 | /lia/eval_sqe_core.lean | a1d4a3b366d4f1abbcb3de07ce296c5cdb66851e | [] | 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 | 20,011 | lean | import .sqe .qfree .wf --..equiv ..num .sqe
open list
def atom.unified (a : atom) : Prop :=
head_coeff a = -1 ∨ head_coeff a = 0 ∨ head_coeff a = 1
def unified (p : formula) : Prop := ∀ a ∈ p.atoms, (atom.unified a)
lemma eval_subst_iff {i ks xs} :
∀ {p}, nqfree p →
((subst i ks p).eval xs ↔ p.eval ((i + zn... |
021c0e53e2f09f78fa26af30d3595412252a1828 | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /stage0/src/Init/Data/Array/Basic.lean | b41dab9d48872f418f06e084fe94e62cd730de17 | [
"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 | 27,887 | lean | /-
Copyright (c) 2018 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import Init.WFTactics
import Init.Data.Nat.Basic
import Init.Data.Fin.Basic
import Init.Data.UInt
import Init.Data.Repr
import Init.Data.ToString.Ba... |
84243ccd6a7e3cd36344e282590951abfdc36d91 | 5ae26df177f810c5006841e9c73dc56e01b978d7 | /src/analysis/normed_space/basic.lean | d618455c5af409ffea7fe0ae76c3be8a5ee1eda1 | [
"Apache-2.0"
] | permissive | ChrisHughes24/mathlib | 98322577c460bc6b1fe5c21f42ce33ad1c3e5558 | a2a867e827c2a6702beb9efc2b9282bd801d5f9a | refs/heads/master | 1,583,848,251,477 | 1,565,164,247,000 | 1,565,164,247,000 | 129,409,993 | 0 | 1 | Apache-2.0 | 1,565,164,817,000 | 1,523,628,059,000 | Lean | UTF-8 | Lean | false | false | 23,906 | lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Normed spaces.
Authors: Patrick Massot, Johannes Hölzl
-/
import algebra.pi_instances
import linear_algebra.basic
import topology.instances.nnreal topology.instances.complex
import topology.a... |
9f8a8ac7fd4a3584f4a993403f857c0415265c84 | cf39355caa609c0f33405126beee2739aa3cb77e | /library/init/meta/interactive.lean | 71476dcf68789e93d86b95351157dd24e61491ef | [
"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 | 74,184 | 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, Jannis Limperg
-/
prelude
import init.meta.tactic init.meta.type_context init.meta.rewrite_tactic init.meta.simp_tactic
import init.meta.smt.congruence_closur... |
100127b34e09fffd5cbb072d563c03827b74c356 | e39f04f6ff425fe3b3f5e26a8998b817d1dba80f | /category_theory/const.lean | 4b08ed139cf9a39f995ce24d053ff1f66c59f406 | [
"Apache-2.0"
] | permissive | kristychoi/mathlib | c504b5e8f84e272ea1d8966693c42de7523bf0ec | 257fd84fe98927ff4a5ffe044f68c4e9d235cc75 | refs/heads/master | 1,586,520,722,896 | 1,544,030,145,000 | 1,544,031,933,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,630 | 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.functor_category
import category_theory.isomorphism
universes u₁ v₁ u₂ v₂ u₃ v₃
open category_theory
namespace category_theory.functor
... |
790be1686d6fb5ec64cb488c9457bb051e92aa36 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/computability/ackermann.lean | 779c3b679b7caf9dd1a0ded9ef101760495a3c15 | [
"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 | 13,395 | lean | /-
Copyright (c) 2022 Violeta Hernández Palacios. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Violeta Hernández Palacios
-/
import computability.primrec
import tactic.linarith
/-!
# Ackermann function
In this file, we define the two-argument Ackermann function `a... |
f3b8ef702d63fcc5285054439efdc08b8df3115c | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/topology/constructions.lean | bd3f4a4f17f770ac614900d9a4cf005a54133e13 | [
"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 | 58,879 | 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.maps
import topology.locally_finite
import order.filter.pi
import data.fin.tuple
/-!
# Constructions of new topologic... |
1cc727efb6c46ca3d59e1958da552f90af0352ed | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/1363.lean | 8fe0cd21655d62d1eaae5855cf6f58ca3945dbf1 | [
"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 | 516 | lean | import Lean.Data.Parsec
open Lean Parsec
@[macro_inline] -- Error
def f : Nat → Nat
| 0 => 0
| n + 1 => f n
@[macro_inline] -- Error
def g : Nat → Nat
| 0 => 0
| n + 1 => g n
termination_by g x => x
@[macro_inline] -- Error
def h : Nat → Nat → Nat
| 0, _ => 0
| n + 1, m => h n m
termination_by h x y => x... |
d5e72593ed7862855d4f0ef1397e3fa722b529e5 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/topology/metric_space/emetric_space.lean | 62e8c98cc21f6066a1476498b1be3e988c19bd05 | [
"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 | 37,519 | lean | /-
Copyright (c) 2015, 2017 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
-/
import data.real.ennreal
import data.finset.intervals
import topology.uniform_space.uniform_em... |
2e9ca4a564f1d37e4b7b0b6ebc2e95ea3d2ccde6 | 853df553b1d6ca524e3f0a79aedd32dde5d27ec3 | /src/analysis/convex/cone.lean | 9a9ffaf25b557c8b5eb263a8b40488954f47680a | [
"Apache-2.0"
] | permissive | DanielFabian/mathlib | efc3a50b5dde303c59eeb6353ef4c35a345d7112 | f520d07eba0c852e96fe26da71d85bf6d40fcc2a | refs/heads/master | 1,668,739,922,971 | 1,595,201,756,000 | 1,595,201,756,000 | 279,469,476 | 0 | 0 | null | 1,594,696,604,000 | 1,594,696,604,000 | null | UTF-8 | Lean | false | false | 18,746 | lean | /-
Copyright (c) 2020 Yury Kudryashov All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import linear_algebra.linear_pmap
import analysis.convex.basic
import order.zorn
/-!
# Convex cones
In a vector space `E` over `ℝ`, we define a convex cone as a su... |
223c3526e5e581fec8a3cad8c2c0237167752ab6 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /hott/algebra/category/constructions/functor.hlean | a115924fa86aeea10e7048dae7947940ad8e302f | [
"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 | 33,696 | 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, Jakob von Raumer
Functor precategory and category
-/
import .opposite ..functor.attributes
open eq category is_trunc nat_trans iso is_equiv category.hom trunc
n... |
86b43fc6064d93a57e4a989a4a22b65adfe60424 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/ring_theory/adjoin.lean | 483b3d414fbf67f153de9f095425bb85421542b8 | [
"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 | 7,921 | lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
Adjoining elements to form subalgebras.
-/
import ring_theory.algebra_operations ring_theory.polynomial ring_theory.principal_ideal_domain
import algebra.pointwise
universes u ... |
c7619f4cbfaabb62da2105518bc9088169ec5d56 | a4673261e60b025e2c8c825dfa4ab9108246c32e | /stage0/src/Lean/Meta/Tactic.lean | 0c2658c949ff3c69757fa71c67474fe32a623858 | [
"Apache-2.0"
] | permissive | jcommelin/lean4 | c02dec0cc32c4bccab009285475f265f17d73228 | 2909313475588cc20ac0436e55548a4502050d0a | refs/heads/master | 1,674,129,550,893 | 1,606,415,348,000 | 1,606,415,348,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 613 | 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.Meta.Tactic.Intro
import Lean.Meta.Tactic.Assumption
import Lean.Meta.Tactic.Apply
import Lean.Meta.Tactic.Revert
import Lean.Meta.Tactic.Clear
... |
4a31c95a0c6537e17e63da2d2af009e6a2f88cab | 64874bd1010548c7f5a6e3e8902efa63baaff785 | /hott/init/types/sum.hlean | 664a2b5e651835b68eab0da0f7e8fb10af76f4b8 | [
"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 | 460 | hlean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura, Jeremy Avigad
-/
prelude
import init.datatypes init.reserved_notation
namespace sum
notation A ⊎ B := sum A B
notation A + B := sum A B
namespace low_p... |
f11b19600f8f9c81735dfacac5e932bcb39c4056 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/ring_theory/adjoin/basic.lean | 1e8853cbe9fbf63869543500429fd5d2f50ae34e | [
"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 | 15,870 | lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import algebra.algebra.operations
import algebra.algebra.subalgebra.tower
import linear_algebra.prod
import linear_algebra.finsupp
/-!
# Adjoining elements to form subalgebras... |
622829f561d0f7b0b2be7fbd1e1be824b2358447 | 98000ddc36f1ec26addea0df1853c69fa0e71d67 | /fan.lean | a6c1dd6013c778bd900286a9d3ecf971e835b22a | [] | no_license | SCRK16/Intuitionism | 50b7b5ed780a75c4ff1339c3d36f1133b8acdfe3 | a3d9920ae056b39a66e37d1d0e03d246bca1e961 | refs/heads/master | 1,670,199,869,808 | 1,598,045,061,000 | 1,598,045,061,000 | 254,657,585 | 1 | 0 | null | 1,590,754,909,000 | 1,586,529,604,000 | Lean | UTF-8 | Lean | false | false | 1,914 | lean | /-
This file captures the notions:
* Spread laws and spreads
* Fan laws and fans
* Bars
* The fan theorem, introduced as an axiom
-/
-- Decide: Use def / structure / class
import ..Intuitionism.bcp
import ..Intuitionism.fin_seq
open fin_seq
def is_spread_law (σ : fin_seq → ℕ) : Prop :=
σ empty_seq = 0 ∧
(∀ ... |
6103b2e86199be0183ec375da4f5a2a15a4e5117 | bf532e3e865883a676110e756f800e0ddeb465be | /linear_algebra/multivariate_polynomial.lean | ec98978b6382e247db4d4e76bb3e1267c4cf9f88 | [
"Apache-2.0"
] | permissive | aqjune/mathlib | da42a97d9e6670d2efaa7d2aa53ed3585dafc289 | f7977ff5a6bcf7e5c54eec908364ceb40dafc795 | refs/heads/master | 1,631,213,225,595 | 1,521,089,840,000 | 1,521,089,840,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,572 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Multivariate Polynomial
-/
import data.finsupp linear_algebra.basic
noncomputable theory
open classical set function finsupp lattice
local attribute [instance] classic... |
92cea4d038c24212ea56b367b21c4fec5ecf420a | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/pkg/frontend/Frontend/Import2.lean | 605cc3688309a1dfea34e05476d209db94565172 | [
"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 | 31 | lean | import Frontend.RegisterOption
|
0a50a46a8c4b4d5b2eff15f62469085fad00d14a | d796eac6dc113f68ec6fc0579c13e8eae2bdef6c | /Resources/Code/Category+Theory-Github-Topic/monoidal-categories-reboot/src/monoidal_categories_reboot/monoidal_category.lean | 4f7d365d12383320d529930cb6a6c88e5c0cd772 | [
"Apache-2.0"
] | permissive | paddlelaw/functional-discipline-content-cats | 5a7e13e8adedd96b94f66b0b3cbf1847bc86d7f6 | d93b7aa849b343c384cec40c73ee84a9300004e8 | refs/heads/master | 1,675,541,859,508 | 1,607,251,766,000 | 1,607,251,766,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,695 | lean | -- Copyright (c) 2018 Michael Jendrusch. All rights reserved.
import category_theory.category
import category_theory.functor
import category_theory.products
import category_theory.natural_isomorphism
import category_theory.tactics.obviously -- Give ourselves access to `rewrite_search`
import .tensor_product
import tac... |
fcba8600b923e0e6196fcf7a059655bd90fd2cf1 | 19cc34575500ee2e3d4586c15544632aa07a8e66 | /src/field_theory/intermediate_field.lean | ba559c5047a587eb389683aff32e2c04f0d829cc | [
"Apache-2.0"
] | permissive | LibertasSpZ/mathlib | b9fcd46625eb940611adb5e719a4b554138dade6 | 33f7870a49d7cc06d2f3036e22543e6ec5046e68 | refs/heads/master | 1,672,066,539,347 | 1,602,429,158,000 | 1,602,429,158,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,361 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import field_theory.subfield
import ring_theory.algebra_tower
/-!
# Intermediate fields
Let `L / K` be a field extension, given as an instance `algebra K L`.
This file d... |
fe1fca4794ce969bfdeac4f14d8139b5fd8eb51d | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/logic/equiv/local_equiv.lean | d86e01abfeddcb6f893e4163910153d887f1b4ae | [
"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 | 34,490 | 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 data.set.function
import logic.equiv.defs
/-!
# Local equivalences
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corr... |
7c6c36b3dc654cfacd3c0f06501224e267ef6091 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/tactic/polyrith.lean | 5ff1c6072e44c6e64902e1cab2983e7059a55fc5 | [
"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 | 23,074 | lean | /-
Copyright (c) 2022 Dhruv Bhatia. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dhruv Bhatia, Eric Wieser
-/
import tactic.linear_combination
import data.buffer.parser.numeral
/-!
# polyrith Tactic
In this file, the `polyrith` tactic is created. This tactic, whi... |
727e515f0e029b644d8f70d8b1d6ef49d4809fd0 | 8eeb99d0fdf8125f5d39a0ce8631653f588ee817 | /src/topology/algebra/ordered.lean | a47f89c6002fdc72c055d105a8b6923cb342f411 | [
"Apache-2.0"
] | permissive | jesse-michael-han/mathlib | a15c58378846011b003669354cbab7062b893cfe | fa6312e4dc971985e6b7708d99a5bc3062485c89 | refs/heads/master | 1,625,200,760,912 | 1,602,081,753,000 | 1,602,081,753,000 | 181,787,230 | 0 | 0 | null | 1,555,460,682,000 | 1,555,460,682,000 | null | UTF-8 | Lean | false | false | 131,531 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Yury Kudryashov
-/
import tactic.linarith
import tactic.tfae
import algebra.archimedean
import algebra.group.pi
import algebra.ordered_ring
import order... |
5ed64d80bc4aced331b0b0c93b317dafe14aefa7 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/ring_theory/matrix_algebra.lean | c80879ea682024bd1da9e1e5954f4975790637b8 | [
"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 | 6,714 | 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 ring_theory.tensor_product
/-!
We provide the `R`-algebra structure on `matrix n n A` when `A` is an `R`-algebra,
and show `matrix n n A ≃ₐ[R] (A ⊗[R] matrix ... |
4ac4eac91b3947ce14265324d5722d3d2c49916e | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/limits/shapes/wide_equalizers.lean | 1ffed64a6845c00ba6461db287f44fd507e30163 | [
"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 | 28,004 | lean | /-
Copyright (c) 2021 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import category_theory.limits.has_limits
import category_theory.limits.shapes.equalizers
/-!
# Wide equalizers and wide coequalizers
> THIS FILE IS SYNCHRONIZED WITH MA... |
e13a94d9b5d0cce0ab7fdc3ece7ece9e30811e1e | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/640b.lean | 5e74dc2905f908e74f9a21a4fb7d792c14faffb8 | [
"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 | 50 | lean | abbreviation bar [parsing_only] := @eq
check @bar
|
f5edfff3159de0859afa43e00143ba510ef075ce | 94e33a31faa76775069b071adea97e86e218a8ee | /src/analysis/convex/exposed.lean | 565f0d6d47336f1797875c5982762ceb01ad2fba | [
"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 | 9,327 | lean | /-
Copyright (c) 2021 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
import analysis.convex.extreme
import analysis.convex.function
import analysis.normed_space.ordered
/-!
# Exposed sets
This file defines exp... |
103498a02a180a93f3cae2702a88d6d02f42928b | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/ring_theory/polynomial/eisenstein.lean | cf28fd70a6b874643988100978e1ceada02bd7b3 | [
"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 | 28,667 | lean | /-
Copyright (c) 2022 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca
-/
import ring_theory.eisenstein_criterion
import ring_theory.integrally_closed
import ring_theory.norm
import ring_theory.polynomial.cyclotomic.basic
/-!
# Eisenste... |
1369c8709962a9d76b64c8a85531f6f667d926cf | 957a80ea22c5abb4f4670b250d55534d9db99108 | /library/init/native/default.lean | 50bf17060583fb39d7150f665c1078b268b2d4e0 | [
"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 | 23,755 | lean | /-
Copyright (c) 2016 Jared Roesch. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jared Roesch
-/
prelude
import init.meta.format
import init.meta.expr
import init.category.state
import init.data.string
import init.data.list.instances
import init.native.ir
import in... |
d5ea65e1f97efc0cc631c1cd2ddafa3dd7a23268 | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/ring_theory/polynomial/rational_root.lean | fd2b0b8aef29a99878fdf3df1e2014cc302f1d37 | [
"Apache-2.0"
] | permissive | agjftucker/mathlib | d634cd0d5256b6325e3c55bb7fb2403548371707 | 87fe50de17b00af533f72a102d0adefe4a2285e8 | refs/heads/master | 1,625,378,131,941 | 1,599,166,526,000 | 1,599,166,526,000 | 160,748,509 | 0 | 0 | Apache-2.0 | 1,544,141,789,000 | 1,544,141,789,000 | null | UTF-8 | Lean | false | false | 5,002 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import ring_theory.polynomial.scale_roots
import ring_theory.localization
/-!
# Rational root theorem and integral root theorem
This file contains the rational root theo... |
9e8e735f9c4d7660374bd200641caa0209bd76e5 | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/real/golden_ratio.lean | 87f7c3e1e001a280eff8c5fa59909af307e6cdbc | [
"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 | 5,599 | lean | /-
Copyright (c) 2020 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker, Alexey Soloyev, Junyan Xu
-/
import data.real.irrational
import data.nat.fib
import data.matrix.notation
import tactic.ring_exp
import algebra.linear_recurrence
/-... |
7429d0bb1d59c2bfc68b6359c2ec23ebafd18806 | 76df16d6c3760cb415f1294caee997cc4736e09b | /lean/src/interp/sym/defs.lean | af051ebeb8acbd1b7d7cb73625a27fed495fa532 | [
"MIT"
] | permissive | uw-unsat/leanette-popl22-artifact | 70409d9cbd8921d794d27b7992bf1d9a4087e9fe | 80fea2519e61b45a283fbf7903acdf6d5528dbe7 | refs/heads/master | 1,681,592,449,670 | 1,637,037,431,000 | 1,637,037,431,000 | 414,331,908 | 6 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 2,969 | lean | import ...cs.sym
import ...cs.svm
namespace interp
open sym
open lang.exp
open sym.result
section interp
variables
{Model SymB SymV D O : Type}
[inhabited Model] [inhabited SymV]
(f : sym.factory Model SymB SymV D O)
-- The symbolic interpreter:
-- `interpS` consumes a `fuel`, an program `e`, a symbolic en... |
48249ee91e77c69ada8d72ceec24d6e697028b1b | 7b66d83f3b69dae0a3dfb684d7ebe5e9e3f3c913 | /src/solutions/friday/topology.lean | dbfdcbbc9d31cd8a9fa60b436825d650f2cf79ef | [] | permissive | dpochekutov/lftcm2020 | 58a09e10f0e638075b97884d3c2612eb90296adb | cdfbf1ac089f21058e523db73f2476c9c98ed16a | refs/heads/master | 1,669,226,265,076 | 1,594,629,725,000 | 1,594,629,725,000 | 279,213,346 | 1 | 0 | MIT | 1,594,622,757,000 | 1,594,615,843,000 | null | UTF-8 | Lean | false | false | 15,676 | lean | import topology.metric_space.basic
open_locale classical filter topological_space
namespace lftcm
open filter set
/-!
# Filters
## Definition of filters
-/
def principal {α : Type*} (s : set α) : filter α :=
{ sets := {t | s ⊆ t},
univ_sets := begin
-- sorry
tauto,
-- sorry
end,
sets_of_superset ... |
089c3a3fb856c5eba53499a8c6093e07fd0d9811 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Server/FileWorker.lean | c0ffdd37e178813af5553014c310a4728c0d52c8 | [
"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 | 23,984 | lean | /-
Copyright (c) 2020 Marc Huisinga. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Marc Huisinga, Wojciech Nawrocki
-/
import Init.System.IO
import Lean.Data.RBMap
import Lean.Environment
import Lean.Data.Lsp
import Lean.Data.Json.FromToJson
import Lean.Util.Paths... |
46f8108c4636722b1788d6fbeffe15771b888570 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/analysis/convex/integral_auto.lean | e4b8a5a326c0b4509d9aca25720e2342bd6773ed | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,464 | lean | /-
Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Yury G. Kudryashov
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.analysis.convex.basic
import Mathlib.measure_theory.set_integral
import Mathlib.Post... |
5bae55013470ce7045bba442b598f911a00ccece | 5ee26964f602030578ef0159d46145dd2e357ba5 | /src/for_mathlib/sheaves/sheaf.lean | 91a623f1631cb65122f7a3e0027fdcafc15cf6ce | [
"Apache-2.0"
] | permissive | fpvandoorn/lean-perfectoid-spaces | 569b4006fdfe491ca8b58dd817bb56138ada761f | 06cec51438b168837fc6e9268945735037fd1db6 | refs/heads/master | 1,590,154,571,918 | 1,557,685,392,000 | 1,557,685,392,000 | 186,363,547 | 0 | 0 | Apache-2.0 | 1,557,730,933,000 | 1,557,730,933,000 | null | UTF-8 | Lean | false | false | 1,561 | lean | /-
Sheaf (of types).
https://stacks.math.columbia.edu/tag/006S
Author: Ramon Fernandez Mir
-/
import for_mathlib.sheaves.covering
import for_mathlib.sheaves.presheaf
universes u v
open topological_space lattice
section sheaf_condition
variables {α : Type u} [topological_space α]
-- Restriction map f... |
93f4987d95ed3eafd9d33a295fb03fb93913fadd | 36c7a18fd72e5b57229bd8ba36493daf536a19ce | /library/data/finset/card.lean | a30964e3029b588925d6ab9d6a0fd9dc9db8c517 | [
"Apache-2.0"
] | permissive | YHVHvx/lean | 732bf0fb7a298cd7fe0f15d82f8e248c11db49e9 | 038369533e0136dd395dc252084d3c1853accbf2 | refs/heads/master | 1,610,701,080,210 | 1,449,128,595,000 | 1,449,128,595,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,463 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad
Cardinality calculations for finite sets.
-/
import .to_set .bigops data.set.function data.nat.power data.nat.bigops
open nat nat.finset eq.ops
open algebra
names... |
70f2ceb7035325422d8f675132ffde3f46fe1fa5 | df7bb3acd9623e489e95e85d0bc55590ab0bc393 | /lean/love07_metaprogramming_homework_sheet.lean | d9a26fcf5db70d90605004722e3d0ddb71d97984 | [] | no_license | MaschavanderMarel/logical_verification_2020 | a41c210b9237c56cb35f6cd399e3ac2fe42e775d | 7d562ef174cc6578ca6013f74db336480470b708 | refs/heads/master | 1,692,144,223,196 | 1,634,661,675,000 | 1,634,661,675,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,093 | lean | import .lovelib
/- # LoVe Homework 7: Metaprogramming
Homework must be done individually. -/
set_option pp.beta true
set_option pp.generalized_field_notation false
namespace LoVe
/- ## Question 1 (9 points): A `mindless` Tactic
We develop a tactic that automates some of the mindless `intro`/`apply`
proofs that... |
bb1bc10220d15aacbc949eda4c3d563951de378c | 31f556cdeb9239ffc2fad8f905e33987ff4feab9 | /stage0/src/Lean/PrettyPrinter/Formatter.lean | b3cadae89992d1db2a4d668ecc953d313e6c35af | [
"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 | tobiasgrosser/lean4 | ce0fd9cca0feba1100656679bf41f0bffdbabb71 | ebdbdc10436a4d9d6b66acf78aae7a23f5bd073f | refs/heads/master | 1,673,103,412,948 | 1,664,930,501,000 | 1,664,930,501,000 | 186,870,185 | 0 | 0 | Apache-2.0 | 1,665,129,237,000 | 1,557,939,901,000 | Lean | UTF-8 | Lean | false | false | 23,512 | lean | /-
Copyright (c) 2020 Sebastian Ullrich. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Ullrich
-/
import Lean.CoreM
import Lean.Parser.Extension
import Lean.Parser.StrInterpolation
import Lean.KeyedDeclsAttribute
import Lean.ParserCompiler.Attribute
import L... |
09c7bd1d06c7ff575067a543be6e1906411e185a | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/analysis/calculus/tangent_cone.lean | 07457bc9e4c354309f1be7ad13d4047fd0e0fca9 | [
"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 | 16,532 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import analysis.convex.basic analysis.normed_space.bounded_linear_maps analysis.specific_limits
/-!
# Tangent cone
In this file, we define two predicates `un... |
2dfc4bdf0b1cfaef737047ac7bcd892c232a5b87 | d0c6b2ba2af981e9ab0a98f6e169262caad4b9b9 | /stage0/src/Init/Data/List/Control.lean | 4770df21ee5abfb168589f72e60fd746d0b3ab64 | [
"Apache-2.0"
] | permissive | fizruk/lean4 | 953b7dcd76e78c17a0743a2c1a918394ab64bbc0 | 545ed50f83c570f772ade4edbe7d38a078cbd761 | refs/heads/master | 1,677,655,987,815 | 1,612,393,885,000 | 1,612,393,885,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,435 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
prelude
import Init.Control.Basic
import Init.Data.List.Basic
namespace List
universes u v w u₁ u₂
/-
Remark: we can define `mapM`, `mapM₂` and `forM` usin... |
e8927680bbd345a6830322b505e101b4ebae9fec | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /12_Axioms.org.34.lean | fc1f9a74e14b6801901ab1de4d8a84de41af5367 | [] | 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 | 177 | lean | import standard
import data.finset data.set
-- BEGIN
print axioms
print axioms nat.add
print axioms finset.union
print axioms set.empty_union
print axioms classical.some
-- END
|
05d272384b12fbd62bb459ac9e803c233296ade9 | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /tests/lean/run/localcoe.lean | e8f8a75145701194c3ebe71087a9bac2f35efba0 | [
"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 | 208 | lean | open nat
section
inductive NatA :=
| a : NatA
| s : NatA → NatA
open NatA
definition foo (n : nat) : NatA :=
nat.rec_on n a (λ n' r, s r)
local attribute foo [coercion]
check s 10
end
|
09782938952fb85089a22c9e467a295d57d4408a | 9ad8d18fbe5f120c22b5e035bc240f711d2cbd7e | /src/data/power_series.lean | 71c99201e314f8821121c7917c967642aac01365 | [] | no_license | agusakov/lean_lib | c0e9cc29fc7d2518004e224376adeb5e69b5cc1a | f88d162da2f990b87c4d34f5f46bbca2bbc5948e | refs/heads/master | 1,642,141,461,087 | 1,557,395,798,000 | 1,557,395,798,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,866 | lean | import algebra.ring algebra.pi_instances algebra.big_operators
import data.birange
universes u v
variables (α : Type u) (β : Type v)
def power_series := ℕ → α
namespace power_series
@[extensionality]
lemma ext {a b : power_series α} : a = b ↔ ∀ k, (a k) = (b k) :=
⟨λ e, congr_fun e,λ e,funext e⟩
section add_c... |
3b512f21478c6dd38c2429974710dfd5a7e168a6 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/jason1.lean | 0e1f132ffd0b2bd636a2121d691566b99b2f0b3b | [
"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 | 2,148 | lean | section
variable (G : Type) (T : Type) (Tm : Type)
(EG : G → G → Type) (ET : T → T → Type) (ETm : Tm → Tm → Type)
(getCtx : T → G) (getTy : Tm → T)
inductive CtxSyntaxLayer where
| emp : CtxSyntaxLayer
| snoc : (Γ : G) → (t : T) → EG Γ (getCtx t) → CtxSyntaxLayer
end
section
variable... |
6df5bd63ac2b1a513e904887d746baf35d0e5dd0 | ef39146fd8dfb387869d11b95feaab74afb75032 | /set_pairs/src/pairs.lean | f3868d82d3583d256b877526815282dba1f10900 | [] | no_license | reubenrowe/lean-experiments | a8192520dccd4a311cb4e47ec34b529cfe0b1a4b | 368760f0e49b674e124f95b18d2879b10ce7ff72 | refs/heads/master | 1,598,468,214,530 | 1,575,240,218,000 | 1,575,240,218,000 | 217,110,245 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 23,122 | lean | universe u
namespace or
section
parameters { p q r : Prop }
lemma right_neutral
{p : Prop} : p ∨ false ↔ p
:=
begin
split,
show p → p ∨ false, from or.intro_left false,
show p ∨ false → p, by {
assume : p ∨ false,
cases this,
case... |
f32d1ef17d95286b3cf9ccfd473720ca3651a036 | 6ae186a0c6ab366b39397ec9250541c9d5aeb023 | /src/category_theory/functor_categories/isomorphisms.lean | 11a95ff6f6d5a69341766f3770fe191b6d22fdfb | [] | no_license | ThanhPhamPhuong/lean-category-theory | 0d5c4fe1137866b4fe29ec2753d99aa0d0667881 | 968a29fe7c0b20e10d8a27e120aca8ddc184e1ea | refs/heads/master | 1,587,206,682,489 | 1,544,045,056,000 | 1,544,045,056,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,796 | lean | -- Copyright (c) 2017 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Stephen Morgan, Scott Morrison
import category_theory.isomorphism
import category_theory.whiskering
open category_theory
namespace category_theory.functor
universes u₁ v₁ u₂ ... |
658723ad3807702d784ce4a90665526cef6a0f8a | 9fbfc7e84d479e54de3c77b32724433407ea166b | /06_Negation/00_intro.lean | 0525bf2b76747ef9e57c7b41df92832213801279 | [] | no_license | ryangreen1234/cs-dm | 86843939250350455a45e5b508e9d6906e6d4ac9 | 2fed37a845894188ce855b277b7fecda9b0e097d | refs/heads/master | 1,585,441,631,595 | 1,537,270,760,000 | 1,537,270,760,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 20,923 | lean | /-
* proposition built using ¬
* the formal meaning of ¬
* proofs of inequalities, ¬a=b
* disjointness of constructors
* strategy: proof by negation
* inference rule: modus tollens
* principle: non-contradiction
* rule: negation elimination
* axiom: excluded middle
* classical vs constructive logic
* double-negatio... |
584c1c8400125ae0534ffc82302ed69d0eb2b686 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/meta_wf_error.lean | 944c4b8c14d5f9b94f5831f9ac8580eb10d5bde3 | [
"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 | 211 | lean | meta def Div : nat → nat → nat
| x y :=
if h : 0 < y ∧ y ≤ x
then
have x - y < x, from nat.sub_lt (nat.lt_of_lt_of_le h.left h.right) h.left,
Div (x - y) y + 1
else 0
using_well_founded {}
|
d77870c05de42744076ec26221241bdd8ab42670 | ee8cdbabf07f77e7be63a449b8483ce308d37218 | /lean/src/test/algebra-sqineq-at2malt1.lean | d3a61256424cd4e4f19fcb69de22a162006f9b94 | [
"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 | 318 | lean | /-
Copyright (c) 2021 OpenAI. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kunhao Zheng
-/
import data.real.basic
example (a : ℝ) : a * (2 - a) ≤ 1 :=
begin
suffices: 0 ≤ a^2 - 2*a + 1, nlinarith,
suffices: 0 ≤ (a - 1) ^ 2, nlinarith,
nlinarith,
end
|
918a9e2b76eb1129ab2855d08ce7d20cd7cba3e4 | 76c77df8a58af24dbf1d75c7012076a42244d728 | /futurama.lean | dbc3ad234cb39086bd7691f341383b544d0cbae8 | [] | no_license | kris-brown/theorem_proving_in_lean | 7a7a584ba2c657a35335dc895d49d991c997a0c9 | 774460c21bf857daff158210741bd88d1c8323cd | refs/heads/master | 1,668,278,123,743 | 1,593,445,161,000 | 1,593,445,161,000 | 265,748,924 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 8,826 | lean | import data.fintype.basic
import data.equiv.basic
import data.real.basic
import algebra.group.defs
import tactic
-- https://en.wikipedia.org/wiki/The_Prisoner_of_Benda#The_theorem
-- Perhaps this could be improved by using more from:
--https://leanprover-community.github.io/mathlib_docs/group_theory/perm/sign.html#... |
4c7325baab6826a462bae3e41073c275252b4b30 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/analysis/special_functions/trigonometric/angle.lean | f9013210363f8359a4beb369efedcba238f0a334 | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 5,742 | lean | /-
Copyright (c) 2019 Calle Sönne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Calle Sönne
-/
import analysis.special_functions.trigonometric.basic
/-!
# The type of angles
In this file we define `real.angle` to be the quotient group `ℝ/2πℤ` and prove a few simple... |
a66c4e680af36f6acc2b316c79bf457c88352c1f | 94e33a31faa76775069b071adea97e86e218a8ee | /src/algebra/field/basic.lean | c2c0d963c8dd23b4b7a09dee6a0f510c5d10cbdf | [
"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 | 17,571 | lean | /-
Copyright (c) 2014 Robert Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Lewis, Leonardo de Moura, Johannes Hölzl, Mario Carneiro
-/
import algebra.hom.ring
import data.rat.defs
/-!
# Division (semi)rings and (semi)fields
This file introduces fields ... |
475fda5404c8feb7af756699d9a6e29185233393 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/analysis/normed_space/completion.lean | ce76de757b24e296292bb58a8b21e45eb31ecc59 | [
"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 | 2,127 | lean | /-
Copyright (c) 2022 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import analysis.normed.group.completion
import analysis.normed_space.operator_norm
import topology.algebra.uniform_mul_action
/-!
# Normed space structure on... |
2eb82070ee682201182e82acce528fe02e4bb8f7 | 453dcd7c0d1ef170b0843a81d7d8caedc9741dce | /category_theory/functor_category.lean | 3f2c74d4b38636af1eee9acf6b83e459bf253ca5 | [
"Apache-2.0"
] | permissive | amswerdlow/mathlib | 9af77a1f08486d8fa059448ae2d97795bd12ec0c | 27f96e30b9c9bf518341705c99d641c38638dfd0 | refs/heads/master | 1,585,200,953,598 | 1,534,275,532,000 | 1,534,275,532,000 | 144,564,700 | 0 | 0 | null | 1,534,156,197,000 | 1,534,156,197,000 | null | UTF-8 | Lean | false | false | 2,419 | lean | -- Copyright (c) 2017 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Tim Baumann, Stephen Morgan, Scott Morrison
import .natural_transformation
namespace category_theory
universes u₁ v₁ u₂ v₂ u₃ v₃
open nat_trans
/--
`functor.category C D` gi... |
8e24867022a4c1b4d0f7bfcde52def4c01e72efc | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/topology/metric_space/pi_nat.lean | 5311742e8272fc211b26f04a92cc470732abff70 | [
"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 | 43,288 | lean | /-
Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import tactic.ring_exp
import topology.metric_space.hausdorff_distance
/-!
# Topological study of spaces `Π (n : ℕ), E n`
> THIS FILE IS SYNCHRONIZED WITH MAT... |
b1d4a496bdcaecdc3559486884df30e45a7ae09f | 856e2e1615a12f95b551ed48fa5b03b245abba44 | /src/topology/algebra/monoid.lean | ec716b983b1b35afdc7fb70f9504cc8b34f53429 | [
"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 | 5,741 | 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 algebra.pi_instances
open classical set filter topological_space
open_locale cl... |
51165b081e9bf47281561012bfef7ab3c620ff69 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/algebra/lie/skew_adjoint.lean | 308b77e9c393cf1f5f2a25e6a049c083ecb7db3f | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 7,193 | lean | /-
Copyright (c) 2020 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import algebra.lie.matrix
import linear_algebra.bilinear_form
/-!
# Lie algebras of skew-adjoint endomorphisms of a bilinear form
When a module carries a bilinear form, t... |
3644136f0b117c04050ff83ef11a97f0ddc2d4cc | 4fa118f6209450d4e8d058790e2967337811b2b5 | /src/continuous_valuations.lean | 8c6e72df114f5f7de5a313a7579ad1133ef595df | [
"Apache-2.0"
] | permissive | leanprover-community/lean-perfectoid-spaces | 16ab697a220ed3669bf76311daa8c466382207f7 | 95a6520ce578b30a80b4c36e36ab2d559a842690 | refs/heads/master | 1,639,557,829,139 | 1,638,797,866,000 | 1,638,797,866,000 | 135,769,296 | 96 | 10 | Apache-2.0 | 1,638,797,866,000 | 1,527,892,754,000 | Lean | UTF-8 | Lean | false | false | 6,016 | lean | import topology.algebra.ring
import valuation_spectrum
import valuation.valuation_field_completion
import for_mathlib.nonarchimedean.basic
/-!
# Continuous valuations
The general theory of valuations does not consider a topology on the ring.
However, in practice many rings are naturally topological rings: for exampl... |
3bc713c941bc054277a5e1f2053cb25191454abc | 90edd5cdcf93124fe15627f7304069fdce3442dd | /src/Lean/Aesop/DefaultRules.lean | 9572e6e74595c974ad353f88cc98d84e33acfd5e | [
"Apache-2.0"
] | permissive | JLimperg/lean4-aesop | 8a9d9cd3ee484a8e67fda2dd9822d76708098712 | 5c4b9a3e05c32f69a4357c3047c274f4b94f9c71 | refs/heads/master | 1,689,415,944,104 | 1,627,383,284,000 | 1,627,383,284,000 | 377,536,770 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,561 | lean | /-
Copyright (c) 2021 Jannis Limperg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jannis Limperg
-/
import Lean.Aesop.DefaultRules.SplitHyps
import Lean.Aesop.Config
open Lean.Elab
open Lean.Elab.Tactic
open Lean.Meta
namespace Lean.Aesop.DefaultRules
def assump... |
81d4372c1378e669f10a01dfe4363c1914e67766 | e39f04f6ff425fe3b3f5e26a8998b817d1dba80f | /category_theory/pempty.lean | 4fb3e6a83e39870a9c12eecb7f0a68f468ddd36e | [
"Apache-2.0"
] | permissive | kristychoi/mathlib | c504b5e8f84e272ea1d8966693c42de7523bf0ec | 257fd84fe98927ff4a5ffe044f68c4e9d235cc75 | refs/heads/master | 1,586,520,722,896 | 1,544,030,145,000 | 1,544,031,933,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 516 | 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.functor
universes u v
namespace category_theory
instance pempty_category : small_category pempty :=
{ hom := λ X Y, pempty,
id := b... |
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