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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
a51850c6fa3663dc53493b52d6f5f542e2953533 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/field_theory/splitting_field.lean | 7c8c6dd0ff687751b54c0cfe64921752ed5cd762 | [] | 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 | 20,837 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.ring... |
2e47e9f0d16d1346498822d4748efce32684d2e1 | aa3f8992ef7806974bc1ffd468baa0c79f4d6643 | /tests/lean/t12.lean | 9b9f2afcf9aed49b7f8d2c34dbaaacca763c0911 | [
"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 | 247 | lean | precedence `+` : 65
precedence `*` : 75
constant N : Type.{1}
check λ (f : N -> N -> N) (g : N → N → N) (infix + := f) (infix * := g) (x y : N), x+x*y
constant f : N → N → N
constant a : N
check a+a -- + notation is not available anymore
|
d47e13d3df04c1417e8621f110ffcf81e96999b2 | 64874bd1010548c7f5a6e3e8902efa63baaff785 | /tests/lean/inv_del.lean | 4cfca0bce85f8bb5fd40a6768869ad43bd99ee9f | [
"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 | 346 | lean | import logic
open nat
inductive vec (A : Type) : nat → Type :=
vnil : vec A zero,
vone : A → vec A (succ zero),
vtwo : A → A → vec A (succ (succ zero))
namespace vec
theorem eone {A : Type} {P : vec A (succ zero) → Type} (H : Π a, P (vone a)) (v : vec A (succ zero)) : P v :=
begin
cases v,
-- apply (H a)... |
6aa09d465a94a90112ccc8028fed0e0a5e1cbbc5 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/data/list/nat_antidiagonal.lean | 6b4875623f36b95f7ca275c509f3a0af6e7fb307 | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 2,298 | lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import data.list.range
/-!
# Antidiagonals in ℕ × ℕ as lists
This file defines the antidiagonals of ℕ × ℕ as lists: the `n`-th antidiagonal is the list of
pairs `(i... |
1d52343a987d7595e8255e2832300df815cec6a9 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Init/Meta.lean | dcd3471c7a24a7e4be6667c93c94889b75563803 | [
"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 | 47,328 | 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 and Sebastian Ullrich
Additional goodies for writing macros
-/
prelude
import Init.Data.Array.Basic
import Init.Data.Option.BasicAux
namespace Lean
@[extern... |
5a8c9e19bda491cecaeb515263b2f8a65a8847db | 761d983a78bc025071bac14a3facced881cf5e53 | /new_affine/test.lean | 4c70c41c7291807c44e0835ea74dc874ca0601d1 | [] | no_license | rohanrajnair/affine_lib | bcf22ff892cf74ccb36a95bc9b7fff8e0adb2d0d | 83076864245ac547b9d615bc6a23804b1b4a8f70 | refs/heads/master | 1,673,320,928,343 | 1,603,036,653,000 | 1,603,036,653,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 41 | lean | #check tactic.eval_expr
#check reflected |
c7e64b27f2338452f0174d732806748d2016a658 | 367134ba5a65885e863bdc4507601606690974c1 | /src/set_theory/cardinal_ordinal.lean | ae824d61c3d10977855c59177cbea6c095e8ec19 | [
"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 | 36,215 | 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, Floris van Doorn
-/
import set_theory.ordinal_arithmetic
import tactic.linarith
/-!
# Cardinals and ordinals
Relationships between cardinals and ordi... |
0cffdfb393926798646c746976a0eec7958973b7 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/preadditive/yoneda/injective.lean | cd5a64ba95c780b47fcad97d3d31b6a5ecb01cd1 | [
"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 | 1,822 | lean | /-
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Scott Morrison
-/
import category_theory.preadditive.yoneda.basic
import category_theory.preadditive.injective
import algebra.category.Group.epi_mono
import algebra.categ... |
8889c7d3dc8bc1ee503a481492bd95dd895b552a | acc85b4be2c618b11fc7cb3005521ae6858a8d07 | /data/num/lemmas.lean | 354738cd9ed3808efd13797c52cb906424a17f33 | [
"Apache-2.0"
] | permissive | linpingchuan/mathlib | d49990b236574df2a45d9919ba43c923f693d341 | 5ad8020f67eb13896a41cc7691d072c9331b1f76 | refs/heads/master | 1,626,019,377,808 | 1,508,048,784,000 | 1,508,048,784,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 19,823 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
Properties of the binary representation of integers.
-/
import data.num.basic data.num.bitwise
meta def unfold_coe : tactic unit :=
`[unfold coe lift_t has_lift_... |
4e8cb0e26432b40f5b7c3ae597b9b3679f25a308 | 274261f7150b4ed5f1962f172c9357591be8a2b5 | /src/lattices.lean | 0082e015d4be753d10b3b694717c56e71b9e52ef | [] | no_license | rspencer01/lean_representation_theory | 219ea1edf4b9897b2997226b54473e44e1538b50 | 2eef2b4b39d99d7ce71bec7bbc3dcc2f7586fcb5 | refs/heads/master | 1,588,133,157,029 | 1,571,689,957,000 | 1,571,689,957,000 | 175,835,785 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,083 | lean | import order.bounded_lattice
import order.order_iso
import order.complete_lattice
open lattice
variables {α β : Type} [bounded_lattice α] [bounded_lattice β]
@[simp]
def preserves_meet (f : α → β) := ∀ a₁ a₂, f(a₁ ⊓ a₂) = f(a₁) ⊓ f(a₂)
@[simp]
def preserves_join (f : α → β) := ∀ a₁ a₂, f(a₁ ⊔ a₂) = f(a₁) ⊔ f(a₂)
va... |
dedb9933b6b0ff3a0efc3fd5922211beef8d8fd9 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Init/Data/Array.lean | d478edb9a145ba905758b0004485d7eb56f288bd | [
"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 | 390 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner
-/
prelude
import Init.Data.Array.Basic
import Init.Data.Array.QSort
import Init.Data.Array.BinSearch
import Init.Data.Array.InsertionSort
import Init.Data.Array.D... |
1c7dc62457776da915bd21a7c99923bf52beeaaa | 367134ba5a65885e863bdc4507601606690974c1 | /src/category_theory/abelian/additive_functor.lean | 5f0526eb3cf8a77d3a1469aa1c4e9334076b4ba1 | [
"Apache-2.0"
] | permissive | kodyvajjha/mathlib | 9bead00e90f68269a313f45f5561766cfd8d5cad | b98af5dd79e13a38d84438b850a2e8858ec21284 | refs/heads/master | 1,624,350,366,310 | 1,615,563,062,000 | 1,615,563,062,000 | 162,666,963 | 0 | 0 | Apache-2.0 | 1,545,367,651,000 | 1,545,367,651,000 | null | UTF-8 | Lean | false | false | 2,126 | 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.preadditive
import category_theory.abelian.basic
/-!
# Additive Functors
A functor between two preadditive categories is called *additive*
provided ... |
bf4315fc124d7a76ef9615a64e943380662f63fa | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/category_theory/functor.lean | 771bc291a13739934f96e0dbf51731a252e84912 | [
"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 | 3,490 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tim Baumann, Stephen Morgan, Scott Morrison
Defines a functor between categories.
(As it is a 'bundled' object rather than the `is_functorial` typeclass parametrised
by the underlyin... |
0f2a44ce56acb83e122f74f47e67f353084bfe19 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/measure_theory/measure/measure_space.lean | ef343796071df602bad6c3570166b03813ad7954 | [
"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 | 180,748 | 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 measure_theory.measure.null_measurable
import measure_theory.measurable_space
import topology.algebra.order.liminf_limsup
/-!
# Measure spaces... |
f8b76553494e6536ee2f0a2b5dec96d6422f2d5b | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /src/Lean/Compiler/IR/SimpCase.lean | f8b36e07717d23899fe0b54c7597a8aebbc0072c | [
"Apache-2.0"
] | permissive | WojciechKarpiel/lean4 | 7f89706b8e3c1f942b83a2c91a3a00b05da0e65b | f6e1314fa08293dea66a329e05b6c196a0189163 | refs/heads/master | 1,686,633,402,214 | 1,625,821,189,000 | 1,625,821,258,000 | 384,640,886 | 0 | 0 | Apache-2.0 | 1,625,903,617,000 | 1,625,903,026,000 | null | UTF-8 | Lean | false | false | 2,214 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Compiler.IR.Basic
import Lean.Compiler.IR.Format
namespace Lean.IR
def ensureHasDefault (alts : Array Alt) : Array Alt :=
if alts.any Alt.is... |
118206c30c0fad2f34edd68bbd5dd1d8ccd43602 | 3dd1b66af77106badae6edb1c4dea91a146ead30 | /tests/lean/run/id.lean | 05f1ba8d27f1a8b88bc83a97bcf0508ef3c84b51 | [
"Apache-2.0"
] | permissive | silky/lean | 79c20c15c93feef47bb659a2cc139b26f3614642 | df8b88dca2f8da1a422cb618cd476ef5be730546 | refs/heads/master | 1,610,737,587,697 | 1,406,574,534,000 | 1,406,574,534,000 | 22,362,176 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 206 | lean | import standard
definition id {A : Type} (a : A) := a
check id id
set_option pp.universes true
check id id
check id Prop
check id num.num
check @id.{0}
check @id.{1}
check id num.zero
check @eq
check eq eq
|
f761b4c5faa82cfec9b961edd5a934ac4a5e2dea | 618003631150032a5676f229d13a079ac875ff77 | /src/data/equiv/encodable.lean | f38e21017253fbd14865f7e575a5adb07cd0f349 | [
"Apache-2.0"
] | permissive | awainverse/mathlib | 939b68c8486df66cfda64d327ad3d9165248c777 | ea76bd8f3ca0a8bf0a166a06a475b10663dec44a | refs/heads/master | 1,659,592,962,036 | 1,590,987,592,000 | 1,590,987,592,000 | 268,436,019 | 1 | 0 | Apache-2.0 | 1,590,990,500,000 | 1,590,990,500,000 | null | UTF-8 | Lean | false | false | 14,720 | 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, Mario Carneiro
Type class for encodable Types.
Note that every encodable Type is countable.
-/
import data.equiv.nat
import order.order_iso
open option list n... |
f62a97b4f865a79513577e95aa4e4485c561cb82 | a4673261e60b025e2c8c825dfa4ab9108246c32e | /tests/lean/resolveGlobalName.lean | 07fa54e1a8886b6b4d00c6a83cf6ef164f6ecb82 | [
"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 | 581 | lean | import Lean
def Boo.x := 1
def Foo.x := 2
def Foo.x.y := 3
def Bla.x := 4
namespace Test
export Bla (x)
end Test
open Lean
open Lean.Elab.Term
open Lean.Elab.Command
syntax[resolveKind] "#resolve " ident : command
@[commandElab resolveKind] def elabResolve : CommandElab :=
fun stx => liftTermElabM none do
let c... |
d16df2b76ed1e7fa9b51c4fb4facf69127b07c22 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/geometry/euclidean/sphere.lean | 1e616fde03c5cee427f57870e63034895bd3df20 | [
"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 | 5,645 | 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 geometry.euclidean.basic
/-!
# Spheres
This file proves basic geometrical results about distances and angles
in spheres in real inner product spaces and Eu... |
5e87ff07888d9fd6f166cf56376b4caca175fac1 | cb1829c15cd3d28210f93507f96dfb1f56ec0128 | /assets/code/indrec.lean | aca51f667bb87ffa2648dbfa272572c3d42d9580 | [] | no_license | williamdemeo/LEAN_wjd | 69f9f76e35092b89e4479a320be2fa3c18aed6fe | 13826c75c06ef435166a26a72e76fe984c15bad7 | refs/heads/master | 1,609,516,630,137 | 1,518,123,893,000 | 1,518,123,893,000 | 97,740,278 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 312 | lean | universe u
constant vec : Type u → ℕ → Type u
namespace vec
constant empty : Π α : Type u, vec α 0
constant cons :
Π (α : Type u) (n : ℕ), α → vec α n → vec α (n + 1)
constant append :
Π (α : Type u) (n m : ℕ), vec α m → vec α n → vec α (n + m)
end vec
#check vec
|
1be43ab34c5c18bc01237a55bb22f73fad187c8d | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/geometry/manifold/algebra/structures.lean | afb8cc7febbd38af3b2914e9f95bc6b1f0b52ed8 | [
"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 | 1,828 | lean | /-
Copyright © 2020 Nicolò Cavalleri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolò Cavalleri
-/
/-|
# Smooth structures
In this file we define smooth structures that build on Lie groups. We prefer using the term smooth
instead of Lie mainly because Lie ring ... |
71e49adf1b2d2a02e01a0e1f27255ed04f25f47e | 618003631150032a5676f229d13a079ac875ff77 | /src/linear_algebra/nonsingular_inverse.lean | 79a6847fdbece8aff7f5239a3dc958028baffc6b | [
"Apache-2.0"
] | permissive | awainverse/mathlib | 939b68c8486df66cfda64d327ad3d9165248c777 | ea76bd8f3ca0a8bf0a166a06a475b10663dec44a | refs/heads/master | 1,659,592,962,036 | 1,590,987,592,000 | 1,590,987,592,000 | 268,436,019 | 1 | 0 | Apache-2.0 | 1,590,990,500,000 | 1,590,990,500,000 | null | UTF-8 | Lean | false | false | 15,537 | lean | /-
Copyright (c) 2019 Tim Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Tim Baanen.
-/
import algebra.associated
import linear_algebra.determinant
import tactic.linarith
import tactic.ring_exp
/-!
# Nonsingular inverses
In this file, we define an inverse for ... |
9efe24d06cbd49dc3030444156a113fa6a7e9440 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/algebra/continued_fractions/computation/correctness_terminating.lean | 4c5df332680f3eec32edd9cf4c3a86b818cb80ce | [
"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 | 12,393 | lean | /-
Copyright (c) 2020 Kevin Kappelmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
-/
import algebra.continued_fractions.computation.translations
import algebra.continued_fractions.terminated_stable
import algebra.continued_fractions.continuants_re... |
588cc0aa62e734f9aac2af1cee09586d3aacbe8f | 4727251e0cd73359b15b664c3170e5d754078599 | /src/ring_theory/adjoin/basic.lean | b771859d492633ca029c8a4232bd33be59a1a895 | [
"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 | 14,597 | 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.tower
import linear_algebra.prod
import linear_algebra.finsupp
import algebra.algebra.operations
/-!
# Adjoining elements to form subalgebras
This file... |
4688860271aba3f247b4d9a091032f1381c3abc0 | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /03_Propositions_and_Proofs.org.15.lean | 562b5872e74285d5d5414e03a57423257c122003 | [] | 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 | 150 | lean | /- page 38 -/
import standard
variables p q r s : Prop
theorem t2 (H1 : q → r) (H2 : p → q) : p → r :=
assume H3 : p,
show r, from H1 (H2 H3)
|
074781e0b2c97aa02c42ab80d7ef6dd7c05402a9 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/category_theory/elements.lean | 9a8cb9b3f8d14050041119a8b8e6a9da50598f94 | [
"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 | 9,534 | 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.structured_arrow
import category_theory.groupoid
import category_theory.punit
/-!
# The category of elements
This file defines the category o... |
8a9011e484639d81103ab771d4a3b3dbcfd7ecc4 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/topology/instances/ereal.lean | fdc981a10009788b430faa15d6664a60b5b39665 | [
"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 | 13,264 | lean | /-
Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import topology.instances.ennreal
import topology.algebra.ordered.monotone_continuity
import data.real.ereal
/-!
# Topological structure on `ereal`
We endow `... |
0ab55f82a6339361d152fbf710322d373d566281 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/data/fintype/basic.lean | e4056cd670c4b8f740149b3f74e056638725efe7 | [
"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 | 100,063 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import data.array.lemmas
import data.finset.fin
import data.finset.option
import data.finset.pi
import data.finset.powerset
import data.finset.prod
import data.finset... |
8ec29bf0b2299efdf8ba5a0b7c972fea6ba31e64 | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/complex/is_R_or_C.lean | 4d93a91e08c6b7cd26312240385e996964e64037 | [
"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 | 32,036 | lean | /-
Copyright (c) 2020 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
import data.real.sqrt
import field_theory.tower
import analysis.normed_space.finite_dimension
/-!
# `is_R_or_C`: a typeclass for ℝ or ℂ
This file defines the type... |
34af70423f351126c458ff1d51d67658fe696bbe | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /stage0/src/Lean/Meta/Tactic/Induction.lean | 50592386940b9300f1b16a3861859b7841f574db | [
"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 | 11,487 | 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.Meta.RecursorInfo
import Lean.Meta.SynthInstance
import Lean.Meta.Tactic.Util
import Lean.Meta.Tactic.Revert
import Lean.Meta.Tactic.Intro
impor... |
c9ba6c9702152c0bfef084aa0a3b74e4409f82a8 | eb9357a70318e50e095b58730bebfe0cffee457f | /lean/love13_rational_and_real_numbers_demo.lean | ed8fe9d475c7d6b5d457507964755c6b33e4f9bb | [] | no_license | Vierkantor/logical_verification_2021 | 7485dd916953131d501760f023d5b30fbb74d36a | 9500b9c194e22a9ab4067321cfed7a1f445afcfc | refs/heads/main | 1,692,560,845,086 | 1,624,721,275,000 | 1,624,721,275,000 | 416,354,079 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,048 | lean | import .lovelib
/-! # LoVe Demo 13: Rational and Real Numbers
We review the construction of `ℚ` and `ℝ` as quotient types.
Our procedure to construct types with specific properties:
1. Create a new type that can represent all elements, but not necessarily in a
unique manner.
2. Quotient this representation, eq... |
65e564b461e701cca78ad0cd5f415bda872ed4c6 | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/equiv/transfer_instance.lean | 5ecca444b6024c6700f5ea1bd41076ee179f7593 | [
"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 | 10,896 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import data.equiv.basic
import algebra.field
import algebra.module
import algebra.algebra.basic
import algebra.group.type_tags
import ring_theory.ideal.basic
/-!
# T... |
abacd61644e1e2a9a07cdfeb27623dfac3f1161d | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/data/padics/padic_numbers.lean | b96f6107efb35df9342ee2bc38f7605154a99816 | [
"Apache-2.0"
] | permissive | rmitta/mathlib | 8d90aee30b4db2b013e01f62c33f297d7e64a43d | 883d974b608845bad30ae19e27e33c285200bf84 | refs/heads/master | 1,585,776,832,544 | 1,576,874,096,000 | 1,576,874,096,000 | 153,663,165 | 0 | 2 | Apache-2.0 | 1,544,806,490,000 | 1,539,884,365,000 | Lean | UTF-8 | Lean | false | false | 32,528 | lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis
-/
import data.real.cau_seq_completion topology.metric_space.cau_seq_filter
import data.padics.padic_norm algebra.archimedean analysis.normed_space.basic
import tact... |
a82c2c810a68a9ca75bc7102b28c3ef9c833263f | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/algebra/module/default.lean | ddb93422d3c0bab310dc3de2e55fe13fde839069 | [
"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 | 317 | lean | /-
Copyright (c) 2020 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import algebra.module.basic
import algebra.module.submodule
/-!
# Default file for module
This file imports `algebra.module.basic` and `algebra.module.submodule`.
-/
|
fcd02e82de6f87ca3182015c0ac0278815b94537 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/logic/lemmas.lean | 930d6d764eebc849e33706edb119642804c37054 | [
"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 | 2,766 | lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import tactic.congr
import tactic.protected
import tactic.rcases
import tactic.split_ifs
import logic.basic
/-!
# More basic logic properties
> THIS FILE IS SYNCHRONIZE... |
ab9e6b477a3695a71159941c03c11eb17e4911f7 | 6c56e3fbe5d7711b66a3b46f1810b44cfa109768 | /src/week2.lean | 2bac6642ace4c0ba04789b39714640608fe73606 | [] | no_license | kodyvajjha/lean-mmc2021 | 015e7ba9d2f43397582d42ad282e88c8ce876dc3 | cc774208f9dc041cad4def289357301b4a0a8173 | refs/heads/master | 1,689,416,888,246 | 1,630,161,054,000 | 1,630,161,054,000 | 384,140,257 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,418 | lean | /-
# Inductive Types
In this file, we will learn about induction and inductive types.
Along with dependent type theory, they form the core of Lean. We shall
also see how the natural numbers and integers are defined.
For more information, please refer to Theorem Proving in Lean :
https://leanprover.github.io/theorem... |
6bab09ec842208188d550d9e96b0dc9c72fd8d84 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/ring/units.lean | c80b6157c20003789e52ac0e30515d590f92a2a0 | [
"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 | 3,477 | 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, Yury Kudryashov, Neil Strickland
-/
import algebra.ring.inj_surj
import algebra.group.units
/-!
# Units in semirings and rings
> TH... |
bc3a1b6a273e471c96caeff185d215239a6e9370 | 95dcf8dea2baf2b4b0a60d438f27c35ae3dd3990 | /src/category_theory/adjunction.lean | 221f9aadd75323799e6341d6236a73e270f0ed71 | [
"Apache-2.0"
] | permissive | uniformity1/mathlib | 829341bad9dfa6d6be9adaacb8086a8a492e85a4 | dd0e9bd8f2e5ec267f68e72336f6973311909105 | refs/heads/master | 1,588,592,015,670 | 1,554,219,842,000 | 1,554,219,842,000 | 179,110,702 | 0 | 0 | Apache-2.0 | 1,554,220,076,000 | 1,554,220,076,000 | null | UTF-8 | Lean | false | false | 14,343 | lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Johan Commelin
-/
import category_theory.limits.preserves
import category_theory.whiskering
import category_theory.equivalence
namespace category_theory
open category
open ... |
806349701e2c6f7afbc6dee30929ec4d4fb4a065 | 5ae26df177f810c5006841e9c73dc56e01b978d7 | /src/topology/algebra/TopCommRing/default.lean | c88db3f92bc4df73f37d9279a0d6bcf37c91af27 | [
"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 | 42 | lean | import topology.algebra.TopCommRing.basic
|
36ed8bca0f2b6ecedb5988a7c6c22894d430798d | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/order/with_bot.lean | 61431d9664c9657abfec21c873ed30f8f17a8245 | [
"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 | 37,536 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import order.bounded_order
/-!
# `with_bot`, `with_top`
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> https://github.com/leanprover-community/mathlib4/pull/776
> Any... |
5ccc2f82d6b3090e5a9563fa6092713687f36bd9 | 2385ce0e3b60d8dbea33dd439902a2070cca7a24 | /tests/lean/induction_naming2.lean | ec92353dbbc6b9a3b3c35bb2fd7126d8f754ea18 | [
"Apache-2.0"
] | permissive | TehMillhouse/lean | 68d6fdd2fb11a6c65bc28dec308d70f04dad38b4 | 6bbf2fbd8912617e5a973575bab8c383c9c268a1 | refs/heads/master | 1,620,830,893,339 | 1,515,592,479,000 | 1,515,592,997,000 | 116,964,828 | 0 | 0 | null | 1,515,592,734,000 | 1,515,592,734,000 | null | UTF-8 | Lean | false | false | 208 | lean | inductive tree
| leaf : tree
| node (left : tree) (val : nat) (right : tree) : tree
constant foo : tree → tree
example (a : tree) : foo a = a :=
begin
induction a,
trace_state,
repeat { sorry }
end
|
9a37579d5aa7d738e03ec3a3c31c304ebb1b200c | c777c32c8e484e195053731103c5e52af26a25d1 | /src/algebra/category/Module/algebra.lean | 224baa250b67277edc2517081518b8629f134b5e | [
"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 | 1,954 | lean | /-
Copyright (c) 2022 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import algebra.algebra.restrict_scalars
import category_theory.linear.basic
import algebra.category.Module.basic
/-!
# Additional typeclass for modules over an algeb... |
c7150943a41e3dc34101772fb58c9e734f8b6958 | ae1e94c332e17c7dc7051ce976d5a9eebe7ab8a5 | /src/Init/Data/UInt.lean | 086b09060f98e08247537c0778e2782663c2197d | [
"Apache-2.0"
] | permissive | dupuisf/lean4 | d082d13b01243e1de29ae680eefb476961221eef | 6a39c65bd28eb0e28c3870188f348c8914502718 | refs/heads/master | 1,676,948,755,391 | 1,610,665,114,000 | 1,610,665,114,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 12,130 | 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.Data.Fin.Basic
import Init.System.Platform
open Nat
@[extern "lean_uint8_of_nat"]
def UInt8.ofNat (n : @& Nat) : UInt8 := ⟨Fin.ofNat n... |
b636b130506cf4dc4bffaf9c9b0768d23ad56729 | 75db7e3219bba2fbf41bf5b905f34fcb3c6ca3f2 | /library/data/finset/equiv.lean | 27a7d6caa93031cd8e9f80011983d57836cd98a1 | [
"Apache-2.0"
] | permissive | jroesch/lean | 30ef0860fa905d35b9ad6f76de1a4f65c9af6871 | 3de4ec1a6ce9a960feb2a48eeea8b53246fa34f2 | refs/heads/master | 1,586,090,835,348 | 1,455,142,203,000 | 1,455,142,277,000 | 51,536,958 | 1 | 0 | null | 1,455,215,811,000 | 1,455,215,811,000 | null | UTF-8 | Lean | false | false | 13,802 | 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.finset.card
open nat decidable
namespace finset
variable {A : Type}
protected definition to_nat (s : finset nat) : nat :=
finset.Sum s (λ n, 2^... |
0c8c7634ebee1f8ee9d765a8b33156e509885722 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/topology/metric_space/emetric_space.lean | c8aa5c127cf5a8e1a0d61a18a2cd94a06c17eae3 | [
"Apache-2.0"
] | permissive | AntoineChambert-Loir/mathlib | 64aabb896129885f12296a799818061bc90da1ff | 07be904260ab6e36a5769680b6012f03a4727134 | refs/heads/master | 1,693,187,631,771 | 1,636,719,886,000 | 1,636,719,886,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 45,881 | 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.nat.interval
import data.real.ennreal
import topology.uniform_space.pi
import topo... |
5ce5e66df5f5250c513feed7581198fa5923d0ba | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/init/meta/rec_util.lean | 94b5797dd349e74adce75f5bb9baf8378c900b3a | [] | 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 | 439 | 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
Helper tactic for showing that a type has decidable equality.
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.meta.tactic
import Mathlib.Lean3Lib.init.... |
58a2f8a2326f54cdf46bd8afdf3b7c5b30c2c7f7 | d436468d80b739ba7e06843c4d0d2070e43448e5 | /src/data/set/basic.lean | 78429032afd3b6531b94567b248f3cdd96aad152 | [
"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 | 57,179 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad, Leonardo de Moura
-/
import tactic.basic tactic.finish data.subtype logic.unique
open function
/- set coercion to a type -/
namespace set
instance {α : Type*} : has_coe_... |
f8107ac2a7fb6aec3e361f8f2c6605c636cb5be7 | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/nat/modeq.lean | 6a762a281e491247309e0ae62a16792f7e56619a | [
"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 | 14,072 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import data.int.gcd
import tactic.abel
import data.list.rotate
/-
# Congruences modulo a natural number
This file defines the equivalence relation `a ≡ b [MOD n]` on... |
9c0169b5819b027535e3dba87d950f2ae494cad1 | 07c76fbd96ea1786cc6392fa834be62643cea420 | /hott/hit/quotient.hlean | a124aeae91d3823d0436065f57730d33ece23afb | [
"Apache-2.0"
] | permissive | fpvandoorn/lean2 | 5a430a153b570bf70dc8526d06f18fc000a60ad9 | 0889cf65b7b3cebfb8831b8731d89c2453dd1e9f | refs/heads/master | 1,592,036,508,364 | 1,545,093,958,000 | 1,545,093,958,000 | 75,436,854 | 0 | 0 | null | 1,480,718,780,000 | 1,480,718,780,000 | null | UTF-8 | Lean | false | false | 11,880 | 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, Ulrik Buchholtz
Quotients. This is a quotient without truncation for an arbitrary type-valued binary relation.
See also .set_quotient
-/
/-
The hit quotient is ... |
7414aa1753509d9a0bad4cd2739c902a09b01d14 | efa51dd2edbbbbd6c34bd0ce436415eb405832e7 | /20161026_ICTAC_Tutorial/ex43.lean | 7cec0f75c5e32edd118862683dad56be3445a0a8 | [
"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 | 357 | lean | check eq.refl -- ∀ (a : ?M_1), a = a
check eq.symm -- ?M_2 = ?M_3 → ?M_3 = ?M_2
check eq.trans -- ?M_2 = ?M_3 → ?M_3 = ?M_4 → ?M_2 = ?M_4
variables (A : Type) (a b c d : A)
premises (hab : a = b) (hcb : c = b) (hcd : c = d)
example : a = d :=
eq.trans (eq.trans hab (eq.symm hcb)) hcd
example : a = d :=
(hab^... |
d28193c7c96942f3ef66de904090b7a8c570c270 | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/group_theory/semidirect_product.lean | 549b1f06d27338076e5660d346a1997b45f8dbd5 | [
"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 | 9,050 | lean | /-
Copyright (c) 2020 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import data.equiv.mul_add logic.function.basic group_theory.subgroup
/-!
# Semidirect product
This file defines semidirect products of groups, and the canonical maps in ... |
2145dfd1bec1be0d00922e55ddca054080ed333c | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/bench/qsort.lean | 225db4966e19aedf3cb4691b0e3e7d1eadbeb126 | [
"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 | 2,448 | lean | abbrev Elem := UInt32
def badRand (seed : Elem) : Elem :=
seed * 1664525 + 1013904223
def mkRandomArray : Nat → Elem → Array Elem → Array Elem
| 0, seed, as => as
| i+1, seed, as => mkRandomArray i (badRand seed) (as.push seed)
partial def checkSortedAux (a : Array Elem) : Nat → IO Unit
| i =>
if i < a.size - 1 ... |
1bfbd572858e0e74d1796bf372e2ef8f21f66d55 | 49bd2218ae088932d847f9030c8dbff1c5607bb7 | /src/analysis/specific_limits.lean | c48590f7edd9e616e13b63ef6e981f7995d939ef | [
"Apache-2.0"
] | permissive | FredericLeRoux/mathlib | e8f696421dd3e4edc8c7edb3369421c8463d7bac | 3645bf8fb426757e0a20af110d1fdded281d286e | refs/heads/master | 1,607,062,870,732 | 1,578,513,186,000 | 1,578,513,186,000 | 231,653,181 | 0 | 0 | Apache-2.0 | 1,578,080,327,000 | 1,578,080,326,000 | null | UTF-8 | Lean | false | false | 19,855 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
A collection of specific limit computations.
-/
import analysis.normed_space.basic algebra.geom_sum
import topology.instances.ennreal
noncomputable theory
open_locale ... |
e37a82d6876c3374e2bfa85863984bc67a64e7a8 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/category_theory/monoidal/limits.lean | b8d72308365e4a7200a7484171545d6d71d3d664 | [
"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 | 3,850 | 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 category_theory.monoidal.functorial
import category_theory.monoidal.functor_category
import category_theory.limits.has_limits
/-!
# `lim : (J ⥤ C) ⥤ C` is lax... |
7ee608d8fad4b4f5b8285387d0b815f94486f69f | f1a12d4db0f46eee317d703e3336d33950a2fe7e | /lia/cooper/main.lean | 7bfcd5a58c8e580e864b3a7554ecef9338dcdc07 | [
"Apache-2.0"
] | permissive | avigad/qelim | bce89b79c717b7649860d41a41a37e37c982624f | b7d22864f1f0a2d21adad0f4fb3fc7ba665f8e60 | refs/heads/master | 1,584,548,938,232 | 1,526,773,708,000 | 1,526,773,708,000 | 134,967,693 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,893 | lean | import .preprocess
open lia tactic
instance : decidable_eq (fm atom) :=
by mk_dec_eq_instance
def of_as_true_le {x y : int} (h₂ : as_true (has_le.le x y)) : (has_le.le x y) :=
match (int.decidable_le x y), h₂ with
| (is_true h_c), h₂ := h_c
| (is_false h_c), h₂ := false.elim h₂
end
def of_as_true_dvd {x y : int} (... |
c9f43a2a3acef9481c1c2433b2f0cfb0ba49ae8d | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/analysis/normed_space/enorm.lean | 308ed7b4aa52a63aad69e690350e17d938b836fb | [] | 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 | 8,963 | 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.normed_space.basic
import Mathlib.PostPort
universes u_1 u_2 l
namespace... |
2113f41a497f6e5170f51db35c889c986b47226a | 00de0c30dd1b090ed139f65c82ea6deb48c3f4c2 | /src/linear_algebra/basic.lean | 079e1a2f419aee1e9e0cb500bf1004468bf22a14 | [
"Apache-2.0"
] | permissive | paulvanwamelen/mathlib | 4b9c5c19eec71b475f3dd515cd8785f1c8515f26 | 79e296bdc9f83b9447dc1b81730d36f63a99f72d | refs/heads/master | 1,667,766,172,625 | 1,590,239,595,000 | 1,590,239,595,000 | 266,392,625 | 0 | 0 | Apache-2.0 | 1,590,257,277,000 | 1,590,257,277,000 | null | UTF-8 | Lean | false | false | 83,780 | 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.pi_instances
import data.finsupp
/-!
# Linear algebra
This file defines the basics of linear algebra.... |
96f32070eb9b50992e546a4222471d4cf70e16fc | 4950bf76e5ae40ba9f8491647d0b6f228ddce173 | /src/topology/instances/ennreal.lean | e2c90bf96a9dec4f58b09527cf63a7df2162dc21 | [
"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 | 41,821 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl
-/
import topology.instances.nnreal
/-!
# Extended non-negative reals
-/
noncomputable theory
open classical set filter metric
open_locale classical topological_space e... |
ada6150319e608f44ec216fd35508752982af19f | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/cc5.lean | 23093bc876aca5fe25da41d9fcd2a46ae0fcb545 | [
"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 | 2,575 | lean | constants (A : Type) (B : A → Type) (C : ∀ (a : A) (ba : B a), Type)
(D : ∀ (a : A) (ba : B a) (cba : C a ba), Type)
(E : ∀ (a : A) (ba : B a) (cba : C a ba) (dcba : D a ba cba), Type)
(F : ∀ (a : A) (ba : B a) (cba : C a ba) (dcba : D a ba cba) (edcba : E a ba cba dcba), Type)
(... |
8ded761c791cfbf478bd3387b4d1a8601e8828e4 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Elab/Tactic/Injection.lean | 7f6fe14757d0b3299202c83e5d1cbb786a81ea25 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 1,826 | 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.Meta.Tactic.Injection
import Lean.Meta.Tactic.Assumption
import Lean.Elab.Tactic.ElabTerm
namespace Lean.Elab.Tactic
-- optional (" with " >> m... |
15c1b73c0cc4234b7e32e49252557bb8fe347b62 | ca1ad81c8733787aba30f7a8d63f418508e12812 | /clfrags/src/hilbert/wr/proofs/ka.lean | 7c6a30810438039937d972c1c974d52ab02c5da4 | [] | no_license | greati/hilbert-classical-fragments | 5cdbe07851e979c8a03c621a5efd4d24bbfa333a | 18a21ac6b2e890060eb4ae65752fc0245394d226 | refs/heads/master | 1,591,973,117,184 | 1,573,822,710,000 | 1,573,822,710,000 | 194,334,439 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,917 | lean | import hilbert.wr.ka
namespace clfrags
namespace hilbert
namespace wr
namespace ka
theorem ka₀ {a b c : Prop} (h₁ : ka a b c) : a :=
have h₃ : ka (ka a b c) (ka a b c) a, from ka₁ h₁ h₁,
have h₄ : ka (ka a b c) a (ka a b c), from ka₃ h₃,
... |
c077bdf094057cd52a8d483bd9a23bff58166395 | fe84e287c662151bb313504482b218a503b972f3 | /src/algebra/dga.lean | 13a6f1d276f5fa21212acaaab4275e441309b9ff | [] | 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 | 912 | lean | import algebra.ring group_theory.subgroup.basic tactic.ring data.finsupp
variables (A : ℤ → Type*) [∀ n, add_comm_group (A n)]
def tot := Σ (n : ℤ), A n
variable {A}
def deg : tot A → ℤ := λ x, x.1
variable (A)
class dga' :=
(mul : tot A → tot A → tot A)
(deg_mul : ∀ a b, deg (mul a b) = deg a + deg b)
(mul_comm... |
edeffc69c830e1983c707e71c6167b15b170b7a8 | d642a6b1261b2cbe691e53561ac777b924751b63 | /src/topology/instances/nnreal.lean | f021d9dbbafdfab89658a561265353bd358b55f5 | [
"Apache-2.0"
] | permissive | cipher1024/mathlib | fee56b9954e969721715e45fea8bcb95f9dc03fe | d077887141000fefa5a264e30fa57520e9f03522 | refs/heads/master | 1,651,806,490,504 | 1,573,508,694,000 | 1,573,508,694,000 | 107,216,176 | 0 | 0 | Apache-2.0 | 1,647,363,136,000 | 1,508,213,014,000 | Lean | UTF-8 | Lean | false | false | 4,484 | lean | /-
Copyright (c) 2018 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
Nonnegative real numbers.
-/
import data.real.nnreal topology.instances.real topology.algebra.infinite_sum
noncomputable theory
open set topological_space metric
names... |
feb792fe25f6f7d2a4c36ead99b123fe4ac9df8e | 94e33a31faa76775069b071adea97e86e218a8ee | /src/field_theory/primitive_element.lean | b05a38b1f7129a17c486e25c0346031187e788b2 | [
"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 | 8,818 | lean | /-
Copyright (c) 2020 Thomas Browning, Patrick Lutz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning, Patrick Lutz
-/
import field_theory.adjoin
import field_theory.fixed
import field_theory.is_alg_closed.basic
import field_theory.separable
import ring_... |
efe902170d3ca6949d194027d50df03f40c9bcdc | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/data/finset/pairwise.lean | 47e14a48da52efbaba12e9c73b3a67168bf3fb5f | [
"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 | 3,965 | lean | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import data.finset.lattice
/-!
# Relations holding pairwise on finite sets
In this file we prove a few results about the interaction of `set.pairwise_disjoint` and `fin... |
c192bcfa8095101b700df8aeaadb549407735510 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/category_theory/limits/shapes/wide_equalizers.lean | 2cfd12efcb850e752ccaf52072f6d11085a13b50 | [
"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 | 27,871 | 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.epi_mono
import category_theory.limits.has_limits
import category_theory.limits.shapes.equalizers
/-!
# Wide equalizers and wide coequalizers
Thi... |
4b7867d7edce65b77a709a37c69bb7edfcfc1efa | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /src/Lean/Meta/Tactic/Simp/Types.lean | 677fa2a614b379d638a1724ac608d94249934f04 | [
"Apache-2.0"
] | permissive | WojciechKarpiel/lean4 | 7f89706b8e3c1f942b83a2c91a3a00b05da0e65b | f6e1314fa08293dea66a329e05b6c196a0189163 | refs/heads/master | 1,686,633,402,214 | 1,625,821,189,000 | 1,625,821,258,000 | 384,640,886 | 0 | 0 | Apache-2.0 | 1,625,903,617,000 | 1,625,903,026,000 | null | UTF-8 | Lean | false | false | 2,466 | 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.Meta.AppBuilder
import Lean.Meta.Tactic.Simp.SimpLemmas
import Lean.Meta.Tactic.Simp.CongrLemmas
namespace Lean.Meta
namespace Simp
structure ... |
8fe626a5f030becd50609fcb6d3c31dca6fc6599 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/xrewrite1.lean | a36137fdb5de5e83600ec7b71ee789e812d6a834 | [
"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 | 269 | lean | open nat tactic
constant zeroadd (a : nat) : 0 + a = a
meta definition xrewrite (th_name : name) : tactic unit :=
do th ← mk_const th_name,
rewrite_target th,
try reflexivity
example (a : nat) : (0 + a) + (0 + a) + (0 + a) = a + a + a :=
by xrewrite `zeroadd
|
c2e4e75646ea5bfa57cac03a0e185162ec585481 | bb31430994044506fa42fd667e2d556327e18dfe | /src/algebra/graded_monoid.lean | a0c0af93134a680002ef51a3fc29af73780634cb | [
"Apache-2.0"
] | permissive | sgouezel/mathlib | 0cb4e5335a2ba189fa7af96d83a377f83270e503 | 00638177efd1b2534fc5269363ebf42a7871df9a | refs/heads/master | 1,674,527,483,042 | 1,673,665,568,000 | 1,673,665,568,000 | 119,598,202 | 0 | 0 | null | 1,517,348,647,000 | 1,517,348,646,000 | null | UTF-8 | Lean | false | false | 22,002 | lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import algebra.group.inj_surj
import data.list.big_operators.basic
import data.list.fin_range
import group_theory.group_action.defs
import group_theory.submonoid.basic
impo... |
f904514522295fcae0fd831bdb0e5f2268c5dd28 | 206422fb9edabf63def0ed2aa3f489150fb09ccb | /src/analysis/normed_space/units.lean | c735c9e61f9f981432cf9cd10d80de514312bc83 | [
"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 | 11,024 | lean | /-
Copyright (c) 2020 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
import analysis.specific_limits
import analysis.asymptotics
/-!
# The group of units of a complete normed ring
This file contains the basic theory for the group o... |
164eb4bc5d414a61c713842337ae21dd2fac86e5 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/order/upper_lower.lean | 9cb3be7ba60e7878bf96b73cbe3f18f9222da24a | [
"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 | 7,670 | lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import algebra.order.group.defs
import data.set.pointwise.smul
import order.upper_lower
/-!
# Algebraic operations on upper/lower sets
Upper/lower sets are preserved un... |
16d2620ce84d62e742ec80c5f738ef18c20a052a | 1abd1ed12aa68b375cdef28959f39531c6e95b84 | /src/data/mv_polynomial/rename.lean | 509d6523625ff8248887540d189562f93886a699 | [
"Apache-2.0"
] | permissive | jumpy4/mathlib | d3829e75173012833e9f15ac16e481e17596de0f | af36f1a35f279f0e5b3c2a77647c6bf2cfd51a13 | refs/heads/master | 1,693,508,842,818 | 1,636,203,271,000 | 1,636,203,271,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,925 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
-/
import data.mv_polynomial.basic
/-!
# Renaming variables of polynomials
This file establishes the `rename` operation on multivariat... |
a35555bb516c49336e0a9d048a402e205a91becb | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/sec3.lean | b5920481a8470027d6cdd96a1e7471d782a0b659 | [
"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 | 110 | lean | section
parameter A : Type
definition tst (a : A) := a
set_option pp.universes true
check tst.{1}
end
|
e3f0f7d5a43e6d2755e816aa9ea6d8c674758ec3 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/polynomial/degree/definitions.lean | 895f51d0483e2ebd8133b27872f8e430e093aff7 | [
"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 | 50,414 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Scott Morrison, Jens Wagemaker
-/
import data.fintype.big_operators
import data.nat.with_bot
import data.polynomial.monomial
import data.polynomial.coeff
/... |
a4c039328d608ecfc1806119542b766566a13625 | 12dabd587ce2621d9a4eff9f16e354d02e206c8e | /world08/level01.lean | a068985671079fa27fb70616ff0bc434b5043ff9 | [] | no_license | abdelq/natural-number-game | a1b5b8f1d52625a7addcefc97c966d3f06a48263 | bbddadc6d2e78ece2e9acd40fa7702ecc2db75c2 | refs/heads/master | 1,668,606,478,691 | 1,594,175,058,000 | 1,594,175,058,000 | 278,673,209 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 99 | lean | theorem succ_inj' {a b : mynat} (hs : succ(a) = succ(b)) : a = b :=
begin
exact succ_inj(hs),
end
|
f3f3d00e1d183308c2abe92ce78dbc907f5b9bc2 | 1446f520c1db37e157b631385707cc28a17a595e | /tests/compiler/closure_bug4.lean | 316a1c52045565f582046a894c89fac44d35b3ba | [
"Apache-2.0"
] | permissive | bdbabiak/lean4 | cab06b8a2606d99a168dd279efdd404edb4e825a | 3f4d0d78b2ce3ef541cb643bbe21496bd6b057ac | refs/heads/master | 1,615,045,275,530 | 1,583,793,696,000 | 1,583,793,696,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 543 | lean | def f (x : Nat) : Nat × (Nat → String) :=
let x1 := x + 1;
let x2 := x + 2;
let x3 := x + 3;
let x4 := x + 4;
let x5 := x + 5;
let x6 := x + 6;
let x7 := x + 7;
let x8 := x + 8;
let x9 := x + 9;
let x10 := x + 10;
let x11 := x + 11;
let x12 := x + 12;
let x13 := x + 13;
let x14 := x + 14;
let x15 := x + 15;
let x16 := ... |
880c50d5ad3eec8613cbf4ae21a7ff22713b6ff3 | 217bb195841a8be2d1b4edd2084d6b69ccd62f50 | /library/init/core.lean | 5a77ccc565062b569532802039e4ac79f412ae0c | [
"Apache-2.0"
] | permissive | frank-lesser/lean4 | 717f56c9bacd5bf3a67542d2f5cea721d4743a30 | 79e2abe33f73162f773ea731265e456dbfe822f9 | refs/heads/master | 1,589,741,267,933 | 1,556,424,200,000 | 1,556,424,281,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 61,076 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
notation, basic datatypes and type classes
-/
prelude
notation `Prop` := Sort 0
notation f ` $ `:1 a:0 := f a
/- Logical operations and relations -/
reserv... |
fa4160cfa70415392b44aeceda449538ac55fdbe | b9a81ebb9de684db509231c4469a7d2c88915808 | /src/super/selection.lean | 06d99d4f5c5eebb89e6a0222597219140dc6c98c | [] | no_license | leanprover/super | 3dd81ce8d9ac3cba20bce55e84833fadb2f5716e | 47b107b4cec8f3b41d72daba9cbda2f9d54025de | refs/heads/master | 1,678,482,996,979 | 1,676,526,367,000 | 1,676,526,367,000 | 92,215,900 | 12 | 6 | null | 1,513,327,539,000 | 1,495,570,640,000 | Lean | UTF-8 | Lean | false | false | 3,717 | 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 .prover_state
open native
namespace super
meta def simple_selection_strategy (f : (expr → expr → bool) → clause → list ℕ) : selection_strategy :=
assume dc, ... |
e794ca671d4e7a13217d11f6e6a9ffad019cda29 | c3f2fcd060adfa2ca29f924839d2d925e8f2c685 | /tests/lean/var.lean | 1089a8bdd6de0e18c8ff18a5a507ce7ff0ac070d | [
"Apache-2.0"
] | permissive | respu/lean | 6582d19a2f2838a28ecd2b3c6f81c32d07b5341d | 8c76419c60b63d0d9f7bc04ebb0b99812d0ec654 | refs/heads/master | 1,610,882,451,231 | 1,427,747,084,000 | 1,427,747,429,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 115 | lean | import logic
context
variable A : Type
parameter a : A
end
section
variable A : Type
variable a : A
end
|
66caa0f93d1d9aed94bee2f694a2605f79101e57 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/measure_theory/measurable_space_def.lean | fcb813acb3d39ada7750a7d4ac7f8640e286e54a | [
"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 | 18,125 | 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 order.symm_diff
import order.disjointed
import order.conditionally_complete_lattice
import data.equiv.encodable.lattice
import data.set.countab... |
44a7ea2bac745cc7931e0681cd65c11423401ae8 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/run/meta1.lean | d15f8378121efbb1ca310e356f2efd8b3ea46d5c | [
"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 | 93 | lean | definition bla (a : nat) := a
meta_definition foo (a : nat) := bla a
meta_constant A : nat
|
b938b6d7e4b5fc50f9658d03a02749302f1fae52 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/open_namespaces.lean | b62b2f6fb4283824cc6b2136b553bba74d0734ee | [
"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 | 88 | lean | open nat
namespace foo
open int
run_cmd tactic.open_namespaces >>= tactic.trace
end foo
|
9dbcc28fdc7845f83c02b4b6f955c6a037d45e61 | 02005f45e00c7ecf2c8ca5db60251bd1e9c860b5 | /src/data/polynomial/degree/definitions.lean | c515c4029814e603415ce3ec4c6ddd6dbe75c2f1 | [
"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 | 37,980 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Scott Morrison, Jens Wagemaker
-/
import data.polynomial.coeff
import data.nat.with_bot
/-!
# Theory of univariate polynomials
The definitions include
`de... |
500be4c8c203942406f0eb0c6f94718269261092 | 6dc0c8ce7a76229dd81e73ed4474f15f88a9e294 | /stage0/src/Lean/Data/Json/Basic.lean | b99ffc1209ca43e48bd86c5c15f5482127846ed8 | [
"Apache-2.0"
] | permissive | williamdemeo/lean4 | 72161c58fe65c3ad955d6a3050bb7d37c04c0d54 | 6d00fcf1d6d873e195f9220c668ef9c58e9c4a35 | refs/heads/master | 1,678,305,356,877 | 1,614,708,995,000 | 1,614,708,995,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,726 | lean | /-
Copyright (c) 2019 Gabriel Ebner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner, Marc Huisinga
-/
import Std.Data.RBTree
namespace Lean
-- mantissa * 10^-exponent
structure JsonNumber where
mantissa : Int
exponent : Nat
deriving DecidableEq
n... |
0087f019ce859b7de581bfe9e787fd88a26e1151 | 9028d228ac200bbefe3a711342514dd4e4458bff | /src/tactic/interactive.lean | 1c31bbc3cb4ca12764bc9064836a3b3895eaa7cb | [
"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 | 40,713 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Simon Hudon, Sebastien Gouezel, Scott Morrison
-/
import tactic.lint
open lean
open lean.parser
local postfix `?`:9001 := optional
local postfix *:9001 := many
names... |
9fd68dab787a9fe01c156f667d3219062e5db370 | ee8cdbabf07f77e7be63a449b8483ce308d37218 | /lean/src/test/others-chickenmcnuggets.lean | bad8283795bc3edc77827f385637b46d2f994410 | [
"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 | 243 | 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 (n : ℕ) : ∃ i j, n + 152 = 9 * i + 20 * j :=
begin
sorry
end
|
94334a4bb4fbe3fc33fb4ce57f867cf877722639 | 1abd1ed12aa68b375cdef28959f39531c6e95b84 | /src/data/vector/basic.lean | a359346a3dea2891277576dc891d088b47484778 | [
"Apache-2.0"
] | permissive | jumpy4/mathlib | d3829e75173012833e9f15ac16e481e17596de0f | af36f1a35f279f0e5b3c2a77647c6bf2cfd51a13 | refs/heads/master | 1,693,508,842,818 | 1,636,203,271,000 | 1,636,203,271,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 20,385 | 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.vector
import data.list.nodup
import data.list.of_fn
import control.applicative
/-!
# Additional theorems and definitions about the `vector` type
This fi... |
c2401d572bba5feec0d2192cb230121535ba4737 | bb31430994044506fa42fd667e2d556327e18dfe | /src/order/rel_iso/basic.lean | f2bb56d77922799db9da7163d4cebe03ae253bd5 | [
"Apache-2.0"
] | permissive | sgouezel/mathlib | 0cb4e5335a2ba189fa7af96d83a377f83270e503 | 00638177efd1b2534fc5269363ebf42a7871df9a | refs/heads/master | 1,674,527,483,042 | 1,673,665,568,000 | 1,673,665,568,000 | 119,598,202 | 0 | 0 | null | 1,517,348,647,000 | 1,517,348,646,000 | null | UTF-8 | Lean | false | false | 25,962 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import data.fun_like.basic
import logic.embedding.basic
import order.rel_classes
/-!
# Relation homomorphisms, embeddings, isomorphisms
> THIS FILE IS SYNCHRONIZED ... |
d33a53ba470722774a93594ffbf7bc766bc0044b | e9078bde91465351e1b354b353c9f9d8b8a9c8c2 | /colimit/sequence.hlean | f04215d76896fbe603889159222f34289b6d91b3 | [
"Apache-2.0"
] | permissive | EgbertRijke/leansnippets | 09fb7a9813477471532fbdd50c99be8d8fe3e6c4 | 1d9a7059784c92c0281fcc7ce66ac7b3619c8661 | refs/heads/master | 1,610,743,957,626 | 1,442,532,603,000 | 1,442,532,603,000 | 41,563,379 | 0 | 0 | null | 1,440,787,514,000 | 1,440,787,514,000 | null | UTF-8 | Lean | false | false | 4,379 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Egbert Rijke
-/
import types.nat .move_to_lib
open nat eq equiv sigma sigma.ops is_equiv
namespace seq_colim
definition seq_diagram [class] (A : ℕ → Type) : T... |
3032febdf515825605ad812a040e2f869e82cbc7 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/int/absolute_value.lean | 754cf1b10bbb055a73438c8f8b58addd98b8b57f | [
"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 | 1,520 | lean | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import algebra.module.basic
import algebra.order.absolute_value
import data.int.cast.lemmas
import data.int.units
import group_theory.group_action.units
/-!
# Absolute val... |
b550f43675e300b23eb1eaf06326375b7e2c965b | 4a092885406df4e441e9bb9065d9405dacb94cd8 | /src/for_mathlib/submonoid.lean | bb1a19cfc7c4805d9c6c71671e29ccef0908ae1c | [
"Apache-2.0"
] | permissive | semorrison/lean-perfectoid-spaces | 78c1572cedbfae9c3e460d8aaf91de38616904d8 | bb4311dff45791170bcb1b6a983e2591bee88a19 | refs/heads/master | 1,588,841,765,494 | 1,554,805,620,000 | 1,554,805,620,000 | 180,353,546 | 0 | 1 | null | 1,554,809,880,000 | 1,554,809,880,000 | null | UTF-8 | Lean | false | false | 409 | lean | import group_theory.submonoid
section
variables {α : Type*} [monoid α]
@[to_additive is_add_submonoid.inter]
lemma is_submonoid.inter (s₁ s₂ : set α) [is_submonoid s₁] [is_submonoid s₂] :
is_submonoid (s₁ ∩ s₂) :=
{ one_mem := ⟨is_submonoid.one_mem _, is_submonoid.one_mem _⟩,
mul_mem := λ x y hx hy,
⟨is_submo... |
117df53154c4e906876db3cceba96db19edc117c | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/tactic/subtype_instance.lean | e8a1d7d53251f64a521af90e080c78b166e76d10 | [] | 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 | 918 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
Provides a `subtype_instance` tactic which builds instances for algebraic substructures
(sub-groups, sub-rings...).
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.def... |
c54fe79857fb49d0b0e1c4281d77ed72c19ffcd8 | 42ac672183d9c61794c6c07440ee0fa791296189 | /tests/examplefiles/test.lean | a7b7e261790fc6b66862144ace6af5413a9aea0a | [
"BSD-2-Clause"
] | permissive | pydanny/pygments-custom | c5f900dcb7e5cb73b01c8cbe787306c3310781aa | b2862e3e58c7e42028ec8363ae668f2f7efd6ccb | refs/heads/master | 1,693,251,820,507 | 1,497,475,453,000 | 1,497,475,453,000 | 93,273,976 | 2 | 3 | BSD-2-Clause | 1,628,615,457,000 | 1,496,524,001,000 | Python | UTF-8 | Lean | false | false | 6,921 | lean | /-
Theorems/Exercises from "Logical Investigations, with the Nuprl Proof Assistant"
by Robert L. Constable and Anne Trostle
http://www.nuprl.org/MathLibrary/LogicalInvestigations/
-/
import logic
-- 2. The Minimal Implicational Calculus
theorem thm1 {A B : Prop} : A → B → A :=
assume Ha Hb, Ha
theorem thm2 {A B C : P... |
667f1d41b3c75796e634663536a38b47f625a0b6 | 1cc8cf59a317bf12d71a5a8ed03bfc1948c66f10 | /src/cauchy.lean | a80804d3ed473db289c084915c8577ba2d7d755c | [
"Apache-2.0"
] | permissive | kckennylau/M1P1-lean | 1e4fabf513539669f86a439af6844aa078c239ad | c92e524f3e4e7aec5dc09e05fb8923cc9720dd34 | refs/heads/master | 1,587,503,976,663 | 1,549,715,955,000 | 1,549,715,955,000 | 169,875,735 | 1 | 0 | Apache-2.0 | 1,549,722,917,000 | 1,549,722,917,000 | null | UTF-8 | Lean | false | false | 856 | lean | import limits
noncomputable theory
local attribute [instance, priority 0] classical.prop_decidable
-- the maths starts here.
-- We introduce the usual mathematical notation for absolute value
local notation `|` x `|` := abs x
def is_cauchy (a : ℕ → ℝ) : Prop :=
∀ ε > 0, ∃ N, ∀ m ≥ N, ∀ n ≥ N, |a m - a n| < ε
-- i... |
116f3e8c79162b50e3192451ef55598bcf7c1d66 | 77c5b91fae1b966ddd1db969ba37b6f0e4901e88 | /src/order/order_dual.lean | 7fa02603f182a973b9c81b81ac2140c5ca2dc6aa | [
"Apache-2.0"
] | permissive | dexmagic/mathlib | ff48eefc56e2412429b31d4fddd41a976eb287ce | 7a5d15a955a92a90e1d398b2281916b9c41270b2 | refs/heads/master | 1,693,481,322,046 | 1,633,360,193,000 | 1,633,360,193,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,560 | lean | /-
Copyright (c) 2020 Johan Commelin, Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Damiano Testa
-/
import order.basic
import data.equiv.basic
/-!
# Initial lemmas to work with the `order_dual`
## Definitions
`to_dual` and `of_dual` t... |
dba627345d3ef6f547167fa5c975dbd1135c3ffc | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/finset_coe.lean | 7798bad384c0c013aaf25eb8ab1abc0aec47a8ed | [
"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 | 203 | lean | import data.finset data.set
open finset set
definition to_set [coercion] {A : Type} (s : finset A) : set A := λ a, a ∈ s
constant P {A : Type} (s : set A) : Prop
variable s : finset nat
check P s
|
1628c79516618284ecb37af99fedc51f470866f6 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/analysis/special_functions/log/deriv.lean | 8db6780d5370266080026b52df1d1e054ef10b4f | [
"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 | 12,628 | 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.log.basic
import analysis.special_functions.exp_deriv
/-!
# Derivative and series expan... |
a8de8e156ec24073f724312a2d0cd3f88bb20378 | 6094e25ea0b7699e642463b48e51b2ead6ddc23f | /library/data/list/perm.lean | 970917de44ed53246d3cb647850796e87e35dcf9 | [
"Apache-2.0"
] | permissive | gbaz/lean | a7835c4e3006fbbb079e8f8ffe18aacc45adebfb | a501c308be3acaa50a2c0610ce2e0d71becf8032 | refs/heads/master | 1,611,198,791,433 | 1,451,339,111,000 | 1,451,339,111,000 | 48,713,797 | 0 | 0 | null | 1,451,338,939,000 | 1,451,338,939,000 | null | UTF-8 | Lean | false | false | 40,956 | 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
List permutations.
-/
import data.list.basic data.list.set
open list setoid nat binary
variables {A B : Type}
inductive perm : list A → list A → Prop :=
| ni... |
f96612a220ab49fd6b885afdb94b51f83a6263c4 | 7571914d3f4d9677288f35ab1a53a2ad70a62bd7 | /library/init/meta/tactic.lean | dc9e54a0d92be4115827e0a42e6f8d52d6426429 | [
"Apache-2.0"
] | permissive | picrin/lean-1 | a395fed5287995f09a15a190bb24609919a0727f | b50597228b42a7eaa01bf8cb7a4fb1a98e7a8aab | refs/heads/master | 1,610,757,735,162 | 1,502,008,413,000 | 1,502,008,413,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 47,119 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.function init.data.option.basic init.util
import init.category.combinators init.category.monad init.category.alternative init.category.m... |
bbf527d87865559df62966bc8209da36fdaf5408 | 217bb195841a8be2d1b4edd2084d6b69ccd62f50 | /library/init/control/state.lean | 4c0ce33621d622b169d0cd71734726803befda4d | [
"Apache-2.0"
] | permissive | frank-lesser/lean4 | 717f56c9bacd5bf3a67542d2f5cea721d4743a30 | 79e2abe33f73162f773ea731265e456dbfe822f9 | refs/heads/master | 1,589,741,267,933 | 1,556,424,200,000 | 1,556,424,281,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,905 | 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.control.alternative init.control.lift
import init.control.id init.control.except
univer... |
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