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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
7c11f448fda1e35e565cf935579ac408f65861f8 | d1bbf1801b3dcb214451d48214589f511061da63 | /src/data/finset/basic.lean | 532db7e0851cd1c394293fd428212b71f60c5ca8 | [
"Apache-2.0"
] | permissive | cheraghchi/mathlib | 5c366f8c4f8e66973b60c37881889da8390cab86 | f29d1c3038422168fbbdb2526abf7c0ff13e86db | refs/heads/master | 1,676,577,831,283 | 1,610,894,638,000 | 1,610,894,638,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 104,328 | 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, Jeremy Avigad, Minchao Wu, Mario Carneiro
-/
import data.multiset.finset_ops
import tactic.monotonicity
import tactic.apply
import tactic.nth_rewrite
/-!
# F... |
41b0fda86d57dc6882fc843852ef07e4de2862b2 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/data/int/cast.lean | 8a0be11ecfbf3a9984790fcefa3e0a5dc4d91294 | [
"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 | 13,474 | 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.basic
import data.nat.cast
/-!
# Cast of integers
This file defines the *canonical* homomorphism from the integers into a type `α` with `0`,
`1`, `+... |
fbf53d3d0af5dc130de9c15745cc3cc5b6bafbb6 | 853df553b1d6ca524e3f0a79aedd32dde5d27ec3 | /src/topology/uniform_space/cauchy.lean | 16ef072110ea3a42907189ba9163b4fb3645c5e0 | [
"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 | 25,884 | 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 topology.uniform_space.basic
import topology.bases
import data.set.intervals
/-!
# Theory of Cauchy filters in uniform spaces. Complete uniform... |
c940c2725c4c8e07caf59c03f1fa0a30e8b184e6 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/number_theory/class_number/finite.lean | c1014c786715da08a482be94c249b5fb5085407d | [
"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 | 17,810 | 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 analysis.special_functions.pow
import linear_algebra.free_module.pid
import linear_algebra.matrix.absolute_value
import number_theory.class_number.admissible_absolu... |
59439c428b1a968adccfe6fdcf37e0cd7267d7fc | 31f556cdeb9239ffc2fad8f905e33987ff4feab9 | /stage0/src/Lean/Elab/Tactic/Conv/Congr.lean | 0c78c1e167407c8e159a5f6a1f7ad455a8feb946 | [
"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 | 8,079 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Meta.Tactic.Simp.Main
import Lean.Meta.Tactic.Congr
import Lean.Elab.Tactic.Conv.Basic
namespace Lean.Elab.Tactic.Conv
open Meta
private def c... |
48fa20fe576b72a289fb50be96422914f9abca1d | b328e8ebb2ba923140e5137c83f09fa59516b793 | /stage0/src/Lean/Environment.lean | 9fa22fc296737b49e2b1d26a4d48b982b619a993 | [
"Apache-2.0"
] | permissive | DrMaxis/lean4 | a781bcc095511687c56ab060e816fd948553e162 | 5a02c4facc0658aad627cfdcc3db203eac0cb544 | refs/heads/master | 1,677,051,517,055 | 1,611,876,226,000 | 1,611,876,226,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 30,213 | 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 Std.Data.HashMap
import Lean.Data.SMap
import Lean.Declaration
import Lean.LocalContext
import Lean.Util.Path
import Lean.Util.FindExpr
import Lean.U... |
5a45c9ab26d2898e54a5a7965dc1aa5a6702000a | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/manyAritySyntax.lean | e7897a54fb9b659f53ee8785d56a35af738f8e4b | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 144 | lean | syntax "enum'" ident " where " ("|" ident)* : command
macro_rules
| `(enum' $id where $[| $ids ]*) =>`(inductive $id where $[| $ids:ident ]*)
|
1dad86d06f2268382b5ae44d0f500c25b6360c56 | 26ac254ecb57ffcb886ff709cf018390161a9225 | /src/group_theory/semidirect_product.lean | 17c7dea6c1de7c48a354702d26a544ced6611a1c | [
"Apache-2.0"
] | permissive | eric-wieser/mathlib | 42842584f584359bbe1fc8b88b3ff937c8acd72d | d0df6b81cd0920ad569158c06a3fd5abb9e63301 | refs/heads/master | 1,669,546,404,255 | 1,595,254,668,000 | 1,595,254,668,000 | 281,173,504 | 0 | 0 | Apache-2.0 | 1,595,263,582,000 | 1,595,263,581,000 | null | UTF-8 | Lean | false | false | 7,564 | 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 ... |
32cc5f2d66c4b001de6dcad1ccd6bdb9f4ab4924 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/ring_theory/graded_algebra/homogeneous_localization.lean | f311442ab436fad067ee3bee9bc91b4f251e92e0 | [
"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 | 20,922 | lean | /-
Copyright (c) 2022 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang, Eric Wieser
-/
import ring_theory.localization.at_prime
import ring_theory.graded_algebra.basic
/-!
# Homogeneous Localization
## Notation
- `ι` is a commutative monoid;
... |
6f38d21899b0ad02c3ad76341f8da3b4765fc362 | 92e157ec9825b5e4597a6d715a8928703bc8e3b2 | /src/exams/exam1.lean | 9d4c195b3b9b097f9c56b8de667ca8791c0d0e46 | [] | no_license | exb3dg/cs2120f21 | 9e566bc508762573c023d3e70f83cb839c199ec8 | 319b8bf0d63bf96437bf17970ce0198d0b3525cd | refs/heads/main | 1,692,970,909,568 | 1,634,584,540,000 | 1,634,584,540,000 | 399,947,025 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 12,113 | lean | /-
*******************************
PART 1 of 2: AXIOMS [50 points]
*******************************
-/
/-
Explain the inference (introduction and
elimination) rules of predicate logic as
directed below. To give you guidance on
how to answer these questions we include
answers for some questions.
-/
-- ------... |
cfb497bb2acdb6cf32d46a0023bedcdf5772db96 | 74caf7451c921a8d5ab9c6e2b828c9d0a35aae95 | /library/init/category/state.lean | fe5d420a282c23124bdf411c1933f0469fe2f8dc | [
"Apache-2.0"
] | permissive | sakas--/lean | f37b6fad4fd4206f2891b89f0f8135f57921fc3f | 570d9052820be1d6442a5cc58ece37397f8a9e4c | refs/heads/master | 1,586,127,145,194 | 1,480,960,018,000 | 1,480,960,635,000 | 40,137,176 | 0 | 0 | null | 1,438,621,351,000 | 1,438,621,351,000 | null | UTF-8 | Lean | false | false | 1,970 | 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.logic init.category.monad
def state (σ : Type) (α : Type) : Type :=
σ → α × σ
section
variables {σ : Type} {α β : Type}
@[inline] def... |
323a9a7dc6a1b3b125e4987c75ed130c13593c73 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/order/concept.lean | 0327b0d58dc015aef46ccc2c1f260c55ca8b715e | [
"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 | 10,901 | lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import data.set.lattice
/-!
# Formal concept analysis
This file defines concept lattices. A concept of a relation `r : α → β → Prop` is a pair of sets
`s : set α` and `... |
c9f24b41e0293e8730278533d8eb4ef1e212b467 | a047a4718edfa935d17231e9e6ecec8c7b701e05 | /src/tactic/default.lean | 810e0393021501835858d8d402cf192c71580d77 | [
"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 | 923 | lean | /-
This file imports many useful tactics ("the kitchen sink").
You can use `import tactic` at the beginning of your file to get everything.
(Although you may want to strip things down when you're polishing.)
Because this file imports some complicated tactics, it has many transitive dependencies
(which of course may n... |
db19812ca55cbab4435e8166851794f133b1a317 | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/geometry/euclidean/triangle.lean | 18881979d87b9a9df5cc40b4fd2085d38ac7547c | [
"Apache-2.0"
] | permissive | ilitzroth/mathlib | ea647e67f1fdfd19a0f7bdc5504e8acec6180011 | 5254ef14e3465f6504306132fe3ba9cec9ffff16 | refs/heads/master | 1,680,086,661,182 | 1,617,715,647,000 | 1,617,715,647,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 17,005 | lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import geometry.euclidean.basic
import tactic.interval_cases
noncomputable theory
open_locale big_operators
open_locale classical
open_locale real
open_locale real_inner... |
8bdb3de0ce247974400a9651fd812eab22f879a4 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/analysis/subadditive.lean | afda32b190afabd5688d60de6075ecd531f8bbbf | [
"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 | 4,729 | 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.real
import order.filter.archimedean
/-!
# Convergence of subadditive sequences
A subadditive sequence `u : ℕ → ℝ` is a sequence sat... |
8812129aa28f7ddb73de30487c1db397c233a3d8 | b561a44b48979a98df50ade0789a21c79ee31288 | /stage0/src/Init/Core.lean | 9d90ef8611ba46d0a5c18a65ce1e3180bbf2f5bd | [
"Apache-2.0"
] | permissive | 3401ijk/lean4 | 97659c475ebd33a034fed515cb83a85f75ccfb06 | a5b1b8de4f4b038ff752b9e607b721f15a9a4351 | refs/heads/master | 1,693,933,007,651 | 1,636,424,845,000 | 1,636,424,845,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 35,784 | 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
import Init.Prelude
import Init.SizeOf
universe u v w
def inline {α : Sort u} (a : α) : α := a
@[inli... |
1a9848f4e7d310f5bc9507cd460d6561e191b3d5 | c1a29ca460720df88ab68dc42d9a1a02e029d505 | /examples/introduction/unnamed_192.lean | 193cdb06897a1a157eba5ff59d6ecf7424ef9952 | [] | no_license | agusakov/mathematics_in_lean | acb5b3d659e4522ae4b4836ea550527f03f6546c | 2539562e4d91c858c73dbecb5b282ce1a7d38b6d | refs/heads/master | 1,665,963,365,241 | 1,592,080,022,000 | 1,592,080,022,000 | 272,078,062 | 0 | 0 | null | 1,592,078,772,000 | 1,592,078,772,000 | null | UTF-8 | Lean | false | false | 160 | lean | import data.nat.parity tactic
open nat
example : ∀ m n, even n → even (m * n) :=
begin
rintros m n ⟨k, hk⟩,
use m * k,
rw [hk, mul_left_comm]
end |
0a368f492670643f2e45bf3e76b52cec823f2d1e | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /counterexamples/canonically_ordered_comm_semiring_two_mul.lean | 52afa207c84de4555077c532c82ad00d1887fe02 | [
"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 | 9,670 | lean | /-
Copyright (c) 2021 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
import data.zmod.basic
import ring_theory.subsemiring
import algebra.ordered_monoid
/-!
A `canonically_ordered_comm_semiring` with two different elements `a` and `b` s... |
69262f6396db60ef341f66b93ba6c969e9707f3e | ae1e94c332e17c7dc7051ce976d5a9eebe7ab8a5 | /src/Lean/Elab/Declaration.lean | 1003aaeb84971c6f7b67149b36c69215530ed8a5 | [
"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 | 11,781 | 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, Sebastian Ullrich
-/
import Lean.Util.CollectLevelParams
import Lean.Elab.DeclUtil
import Lean.Elab.DefView
import Lean.Elab.Inductive
import Lean.Elab.Struct... |
09751399710b5823c576e4e2bcb20ae106ed26b6 | 08bd4ba4ca87dba1f09d2c96a26f5d65da81f4b4 | /src/Lean/Parser/Extra.lean | 6b2bdc2697315b823cfa1db2cb593e44d1ccb0de | [
"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 | 10,104 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Sebastian Ullrich
-/
import Lean.Parser.Extension
-- necessary for auto-generation
import Lean.PrettyPrinter.Parenthesizer
import Lean.PrettyPrinter.Formatter... |
6e5729986418bd1611dbb05c95e0aa25520f09a7 | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /08_Building_Theories_and_Proofs.org.20.lean | 7b9c5073c89b13c76f90e9b3a16ab56fc3502c2d | [] | 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 | 39 | lean | import standard
set_option pp.all true
|
465c9d6f03a899fa2442b329be2c872a44b3d313 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/measure_theory/function/conditional_expectation/real.lean | 1d5a8929a2e18cfb92e6871bbe66f60a43163431 | [
"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 | 19,696 | lean | /-
Copyright (c) 2022 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Kexing Ying
-/
import measure_theory.function.conditional_expectation.indicator
import measure_theory.function.uniform_integrable
import measure_theory.decomposition.radon... |
63ae75ff2665c9c6143cb983817987be7a42ed86 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/data/zmod/algebra.lean | 65f3f96fc884fa32992c277189cc1b3f3340ef76 | [
"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 | 1,189 | lean | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import data.zmod.basic
import algebra.algebra.basic
/-!
# The `zmod n`-algebra structure on rings whose characteristic divides `n`
> THIS FILE IS SYNCHRONIZED WITH... |
b44829fe60b4581b49c4065ccf7a49629537a7de | 205f0fc16279a69ea36e9fd158e3a97b06834ce2 | /src/14.Inductive_Definitions/study-guide-inductive.lean | da4125eb13237b03c2306d9f971d2d117f852ae9 | [] | no_license | kevinsullivan/cs-dm-lean | b21d3ca1a9b2a0751ba13fcb4e7b258010a5d124 | a06a94e98be77170ca1df486c8189338b16cf6c6 | refs/heads/master | 1,585,948,743,595 | 1,544,339,346,000 | 1,544,339,346,000 | 155,570,767 | 1 | 3 | null | 1,541,540,372,000 | 1,540,995,993,000 | Lean | UTF-8 | Lean | false | false | 5,034 | lean | /-
===================================================
Inductive types, functions, properties, and proofs.
====================================================
-/
/-
Simple inductive types.
-----------------------
-/
/-
1.
Define a new type called day having
these seven constant constructors:
sunday, monday, tuesda... |
5c061d32b7fcc3e76384c89598a7361878a3b686 | d642a6b1261b2cbe691e53561ac777b924751b63 | /src/data/real/hyperreal.lean | 0e7c266e6a33e7261ff9be61a89bdf77065b026b | [
"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 | 36,600 | lean | /-
Copyright (c) 2019 Abhimanyu Pallavi Sudhir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Abhimanyu Pallavi Sudhir
Construction of the hyperreal numbers as an ultraproduct of real sequences.
-/
import data.real.basic algebra.field order.filter.filter_product anal... |
2e55540a93c09c15523b3dba317fc243fd09e9b6 | 969dbdfed67fda40a6f5a2b4f8c4a3c7dc01e0fb | /src/topology/algebra/multilinear.lean | ba17c3a5ed1811e28bef6a4aa3f7dd417ab22bb6 | [
"Apache-2.0"
] | permissive | SAAluthwela/mathlib | 62044349d72dd63983a8500214736aa7779634d3 | 83a4b8b990907291421de54a78988c024dc8a552 | refs/heads/master | 1,679,433,873,417 | 1,615,998,031,000 | 1,615,998,031,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 16,163 | lean | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import topology.algebra.module
import linear_algebra.multilinear
/-!
# Continuous multilinear maps
We define continuous multilinear maps as maps from `Π(i : ι... |
1b96fa0a9a80786bc86e27d76a72a01d0d35a446 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/category_theory/monad/kleisli.lean | 9aef0b22dba5f032fb75c92bd463c3c392492523 | [
"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 | 3,059 | lean | /-
Copyright (c) 2020 Wojciech Nawrocki. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wojciech Nawrocki, Bhavik Mehta
-/
import category_theory.adjunction.basic
import category_theory.monad.basic
/-! # Kleisli category on a monad
This file defines the Kleisli cate... |
2e0301a7afe228da37b30b45c129485ba9c1180f | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/tactic/alias.lean | a5a9ecac9177314af17459af9f1a3fd272adb1cd | [
"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 | 4,424 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
This file defines an alias command, which can be used to create copies
of a theorem or definition with different names.
Syntax:
/ -- doc string - /
alias my_theorem ←... |
c8410d7b1c5fe7a15c74172a4bf52837aa41a574 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/algebraic_topology/dold_kan/n_comp_gamma.lean | 52bdb21046dc0ef15e825d56f13d64c46b97ef9a | [
"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 | 10,843 | lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import algebraic_topology.dold_kan.gamma_comp_n
import algebraic_topology.dold_kan.n_reflects_iso
/-!
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file re... |
96fdd58f3cb74f237827403c5796033476b3286a | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/tactic/derive_inhabited.lean | a774f595656d2f922db4a93553a57aab25a8eaf3 | [
"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 | 2,329 | lean | /-
Copyright (c) 2020 Gabriel Ebner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
-/
import logic.basic
/-!
# Derive handler for `inhabited` instances
This file introduces a derive handler to automatically generate `inhabited`
instances for structures and inductives. We als... |
3537de7806fae561b3934fb96bd89f502ca14ba8 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/tactic/algebra.lean | 48a13789e8dcce686294f3da90753ae32518ac8b | [
"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 | 1,722 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import tactic.core
open lean.parser
namespace tactic
section performance -- see Note [user attribute parameters]
local attribute [semireducible] reflected
local attrib... |
028e6564c3904b2ee98aa46aeb8c26ddf6719205 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/linear_algebra/multilinear/basic.lean | 0b2e9306c5a1395a0c11c7f10cd892d4bf1262ee | [
"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 | 52,896 | lean | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import linear_algebra.basic
import algebra.algebra.basic
import algebra.big_operators.order
import algebra.big_operators.ring
import data.fintype.card
import da... |
3fa1f4532f5458088ed59a02f8260a1b92fdb544 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/topology/algebra/monoid.lean | 5886701a9a683a4c1d5a3654cde3eb3c479f2558 | [
"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 | 25,775 | 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 algebra.big_operators.finprod
import data.set.pointwise
import topology.algebra.mul_action
import algebra.big_operators.pi
/-!
# Theory of top... |
684dbf43faa909d6ae968a50f095a2ab003979ac | 947b78d97130d56365ae2ec264df196ce769371a | /stage0/src/Lean/Meta/Match/MatchPatternAttr.lean | 0db8032b632f6c2f780761c9c433d3084ed66eac | [
"Apache-2.0"
] | permissive | shyamalschandra/lean4 | 27044812be8698f0c79147615b1d5090b9f4b037 | 6e7a883b21eaf62831e8111b251dc9b18f40e604 | refs/heads/master | 1,671,417,126,371 | 1,601,859,995,000 | 1,601,860,020,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 648 | 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.Attributes
namespace Lean
def mkMatchPatternAttr : IO TagAttribute :=
registerTagAttribute `matchPattern "mark that a definition can be used i... |
78714865acf93069dff0e6fe33bbde6968b01def | 874a8d2247ab9a4516052498f80da2e32d0e3a48 | /triIneq.lean | 7cae0958e31e7d2da4980236b40f8fe5219d8e0f | [] | no_license | AlexKontorovich/Spring2020Math492 | 378b36c643ee029f5ab91c1677889baa591f5e85 | 659108c5d864ff5c75b9b3b13b847aa5cff4348a | refs/heads/master | 1,610,780,595,457 | 1,588,174,859,000 | 1,588,174,859,000 | 243,017,788 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 495 | lean | import tactic
import data.int.basic
universe u
--local attribute [instance] classical.prop_decidable
def absVal (a : ℤ) : ℤ := if a < 0 then -a else a
theorem triIneqInt (a : ℤ) (b : ℤ)
: (absVal(b - a) ≤ absVal(a) + absVal(b)) :=
begin
rw absVal,
rw absVal,
rw absVal,
split_ifs,
linarith,
linarith,
... |
7137f3f195c7c34444c3fad792f343efbf1a3589 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/invertible.lean | 9e64de20e92cb019363fe223234b888bf7e8f304 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 14,240 | 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 algebra.group.units
import algebra.group_with_zero.units.lemmas
import algebra.ring.defs
/-!
# Invertible elements
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> An... |
5e11d48bd6f9aad00cc90ff69effaec918b006cf | ba4794a0deca1d2aaa68914cd285d77880907b5c | /src/game/world8/level8.lean | 087601f8fb000858e2b4faa6220ad11726e23087 | [
"Apache-2.0"
] | permissive | ChrisHughes24/natural_number_game | c7c00aa1f6a95004286fd456ed13cf6e113159ce | 9d09925424da9f6275e6cfe427c8bcf12bb0944f | refs/heads/master | 1,600,715,773,528 | 1,573,910,462,000 | 1,573,910,462,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 663 | lean | import game.world8.level7 -- hide
namespace mynat -- hide
/-
# Advanced Addition World
## Level 8: `eq_zero_of_add_right_eq_self`
The lemma you're about to prove will be useful when we want to prove that $\leq$ is antisymmetric.
There are some wrong paths that you can take with this one.
-/
/- Lemma
If $a$ and $b$... |
c48e26f550a8f89b82393ee924729d895d21d36f | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/algebra/category/CommRing/limits.lean | c905d4e7d6c059877c8d864594917c985283c321 | [
"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 | 14,505 | 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 algebra.ring.pi
import algebra.category.CommRing.basic
import algebra.category.Group.limits
import ring_theory.subring
/-!
# The category of (commutative) rin... |
3f408e3cc53326af3446a0b17b2f9248af9b2484 | 618003631150032a5676f229d13a079ac875ff77 | /src/category_theory/equivalence.lean | 869dbe61665b5586179bab4881442b23953d8b3e | [
"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 | 14,742 | 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, Floris van Doorn
-/
import category_theory.fully_faithful
import category_theory.whiskering
import tactic.slice
namespace category_theory
... |
9020f4221e9afb218da0a3b05f51bd4dabc1cfa9 | 9028d228ac200bbefe3a711342514dd4e4458bff | /src/data/fin.lean | b7c88f3341e532cb9c5a85ab74a22f8e38783d6e | [
"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 | 42,014 | lean | /-
Copyright (c) 2017 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Keeley Hoek
-/
import data.nat.cast
import tactic.localized
import logic.embedding
/-!
# The finite type with `n` elements
`fin n` is the type whose elements are nat... |
e8b13cc4581df1e71c03ee3502dd9768af52e64b | 88fb7558b0636ec6b181f2a548ac11ad3919f8a5 | /tests/lean/run/default_param2.lean | 1f09d011b0961803cd68ece4c3432516dc47dc04 | [
"Apache-2.0"
] | permissive | moritayasuaki/lean | 9f666c323cb6fa1f31ac597d777914aed41e3b7a | ae96ebf6ee953088c235ff7ae0e8c95066ba8001 | refs/heads/master | 1,611,135,440,814 | 1,493,852,869,000 | 1,493,852,869,000 | 90,269,903 | 0 | 0 | null | 1,493,906,291,000 | 1,493,906,291,000 | null | UTF-8 | Lean | false | false | 1,057 | lean | universe variable u
def f (a : nat) (o : nat := 5) :=
a + o
example : f 1 = f 1 5 :=
rfl
#check f 1
structure config :=
(v1 := 10)
(v2 := 20)
(flag := tt)
(ps := ["hello", "world"])
def g (a : nat) (c : config := {}) : nat :=
if c^.flag then a + c^.v1 else a + c^.v2
example : g 1 = 11 :=
rfl
example : g 1 ... |
0a41c9060c2087135899f2b6a85e53d9d6481a6a | 61ccc57f9d72048e493dd6969b56ebd7f0a8f9e8 | /src/category_theory/limits/concrete_category.lean | 93472af687ec1157105fb8d93051be632266e810 | [
"Apache-2.0"
] | permissive | jtristan/mathlib | 375b3c8682975df28f79f53efcb7c88840118467 | 8fa8f175271320d675277a672f59ec53abd62f10 | refs/heads/master | 1,651,072,765,551 | 1,588,255,641,000 | 1,588,255,641,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,731 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.limits.cones
import category_theory.concrete_category.bundled_hom
/-!
# Facts about limits of functors into concrete categories
-/
universes ... |
5402a60558a906be928382e52b251620b72b63a7 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/category_theory/limits/shapes/binary_products.lean | bd0df3c4db86917051ec84eab084490201b0287c | [
"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 | 38,602 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Bhavik Mehta
-/
import category_theory.limits.shapes.terminal
import category_theory.discrete_category
import category_theory.epi_mono
import category_theory.over
/-!
... |
93d8aed354d602d60a1fb2dba0a6fde27bddbee2 | 07c76fbd96ea1786cc6392fa834be62643cea420 | /hott/types/nat/div.hlean | bca121dca2260f01f3a2d461574d01eec337ec8f | [
"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 | 25,928 | hlean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura
Definitions prod properties of div prod mod. Much of the development follows Isabelle's library.
-/
import .sub
open eq eq.ops well_founded decidable p... |
b7a9df92ba763158f2da5c87c5c783a14d37b00e | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/geometry/euclidean/default.lean | a79e5c08e564b06cbd302c35b946a9467be8c874 | [
"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 | 144 | lean | import geometry.euclidean.basic
import geometry.euclidean.circumcenter
import geometry.euclidean.monge_point
import geometry.euclidean.triangle
|
d7ea58300eb573263b4e7a5898a566c3ce51393b | 367134ba5a65885e863bdc4507601606690974c1 | /src/topology/uniform_space/basic.lean | d2b63a880b87cdd7c582d280cc6bbe7b349197eb | [
"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 | 70,768 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot
-/
import order.filter.lift
import topology.separation
/-!
# Uniform spaces
Uniform spaces are a generalization of metric spaces and top... |
f8b9ecec9c6058e8a78d50bca02eefb4efb73c67 | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/tactic/basic.lean | ebe5e8a325c97561e832a6a4436c0f65a61c602a | [
"Apache-2.0"
] | permissive | fpvandoorn/mathlib | b21ab4068db079cbb8590b58fda9cc4bc1f35df4 | b3433a51ea8bc07c4159c1073838fc0ee9b8f227 | refs/heads/master | 1,624,791,089,608 | 1,556,715,231,000 | 1,556,715,231,000 | 165,722,980 | 5 | 0 | Apache-2.0 | 1,552,657,455,000 | 1,547,494,646,000 | Lean | UTF-8 | Lean | false | false | 34,300 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Simon Hudon, Scott Morrison, Keeley Hoek
-/
import data.dlist.basic category.basic meta.expr meta.rb_map
namespace expr
open tactic
attribute [derive has_reflect] bin... |
21e381f3c1fb97135c9d901cbbe0fb1483387ee7 | ae9f8bf05de0928a4374adc7d6b36af3411d3400 | /src/formal_ml/pac_bounds.lean | 3c7f1c5efaf80d21a8b5521503e98ecd051ff07d | [
"Apache-2.0"
] | permissive | NeoTim/formal-ml | bc42cf6beba9cd2ed56c1cd054ab4eb5402ed445 | c9cbad2837104160a9832a29245471468748bb8d | refs/heads/master | 1,671,549,160,900 | 1,601,362,989,000 | 1,601,362,989,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 19,061 | lean | /-
Copyright 2020 Google LLC
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
di... |
4531705f3f38c258488b0be640aa96de6c37b97c | c777c32c8e484e195053731103c5e52af26a25d1 | /src/geometry/manifold/vector_bundle/pullback.lean | c65bc33987d0132d2b56cc6d8c09495f16bb3a77 | [
"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 | 2,196 | lean | /-
Copyright (c) 2023 Floris van Doorn, Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Heather Macbeth
-/
import geometry.manifold.cont_mdiff_map
import geometry.manifold.vector_bundle.basic
/-! # Pullbacks of smooth vector bundles
... |
18c52d460c4f3b678b3c8c859e6084972b37ef9e | 2a70b774d16dbdf5a533432ee0ebab6838df0948 | /_target/deps/mathlib/src/logic/basic.lean | 06d188c708d20117000142c146142123befa974f | [
"Apache-2.0"
] | permissive | hjvromen/lewis | 40b035973df7c77ebf927afab7878c76d05ff758 | 105b675f73630f028ad5d890897a51b3c1146fb0 | refs/heads/master | 1,677,944,636,343 | 1,676,555,301,000 | 1,676,555,301,000 | 327,553,599 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 51,635 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura
-/
import tactic.doc_commands
import tactic.reserved_notation
/-!
# Basic logic properties
This file is one of the earliest imports in mathlib.
## Im... |
af104eba5b6787484847d9360e8fe31050646098 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/175.lean | 712fd0c3791061433e56719763707fc82b8691c8 | [
"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 | 479 | lean | import Lean
namespace Foo
open Lean.Elab.Term
syntax (name := fooKind) "foo!" term : term
@[term_elab fooKind] def elabFoo : TermElab :=
fun stx expectedType? => elabTerm (stx.getArg 1) expectedType?
#check foo! 10
end Foo
namespace Lean
namespace Elab
namespace Tactic
open Meta
@[builtin_tactic clear] def myEv... |
b354f4d2c028016fc2e38da9c977d899d061cc8c | f1b7aef72be2a36b67a39b031ced3d630bb38742 | /src/quiz04.lean | 2f7cdbf012a33f9786dbcacf50f1335b857a94ab | [] | no_license | UVM-M52/quiz-4-ftclark3 | 47e01ae9e9b087fca3ddbde269de219982332b10 | feb44e4cf27ee98f6c7404e4220fcf59e170175d | refs/heads/master | 1,612,578,611,358 | 1,583,098,673,000 | 1,583,098,673,000 | 243,865,365 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,165 | lean | -- Math 52: Quiz 5
-- Open this file in a folder that contains 'utils'.
import utils
definition divides (a b : ℤ) : Prop := ∃ (k : ℤ), b = a * k
local infix ∣ := divides
axiom not_3_divides : ∀ (m : ℤ), ¬ (3 ∣ m) ↔ 3 ∣ m - 1 ∨ 3 ∣ m + 1
theorem main : ∀ (n : ℤ), ¬ (3 ∣ n) → 3 ∣ n * n - 1 :=
begin
intro n,
rw not_3_... |
e335c7df45031e7d594ad9d5c41ed2974d59cb30 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/rand_tst.lean | 12aebf32339858f137c88e637c4de2a7645c32e1 | [
"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 | 412 | lean | import system.io
universes u
open io
def prg (seed : nat): io unit :=
do put_str_ln ("Generating random numbers using seed: " ++ to_string seed),
set_rand_gen (mk_std_gen seed),
iterate 20 $ λ i,
if i > 0 then
do { n ← rand 0 18446744073709551616,
put_str_ln $ to_string n,
ret... |
5909969e47978ddf06c7cf87e5904c929eabb2e5 | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/category_theory/limits/connected.lean | c65f8ad9396ff22a68de81e21a6475ee6aa3df89 | [
"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 | 3,613 | lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import category_theory.limits.shapes.pullbacks
import category_theory.limits.shapes.equalizers
import category_theory.limits.preserves.basic
import category_theory.connec... |
6b70c7188eb628da26594a9c97073e119f824485 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/eta.lean | 8ebea64881ab62c505c39b8afe6d671eaa821a6c | [
"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 | 460 | lean | import Lean
open Lean in
open Lean.Meta in
def tst (declName : Name) : MetaM Unit := do
let info ← getConstInfo declName
trace[Meta.debug] ">> {info.value!.eta}"
def aux1 := fun (x : Nat) y z => Nat.add y z
def aux2 := fun y z => Nat.add y z
def aux3 := (1+.)
def aux4 := fun (x : Nat) y z => Nat.add z y
def aux5 ... |
15f3ae4f4181636b67bcf422b7d1cb5d47655953 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/logic/small.lean | ae110d8e29457b2c5d9db58b53e4e9de1e6f24a0 | [
"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 | 5,237 | lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import data.vector.basic
/-!
# Small types
A type is `w`-small if there exists an equivalence to some `S : Type w`.
We provide a noncomputable model `shrink α : Ty... |
5bfbc3ecb7fdeb92b65041991d32e1585c99b0d6 | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /12_Axioms.org.5.lean | 5d10e2f45982606444b7baccfae977228a6de432 | [] | 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 | 884 | lean | import standard
import standard
import logic
open eq.ops
namespace hide
definition set (X : Type) := X → Prop
namespace set
variable {X : Type}
definition mem [reducible] (x : X) (a : set X) := a x
notation e ∈ a := mem e a
theorem setext {a b : set X} (H : ∀ x, x ∈ a ↔ x ∈ b) : a = b :=
funext (take x, propext (... |
3175a445c3a69229389f6d7c361ae6ace661f9a7 | dfbb669f3f58ceb57cb207dcfab5726a07425b03 | /vscode-lean4/test/test-fixtures/multi/foo/Main.lean | f428f8277c652e6e6cbeb4dc642eea5621310cb8 | [
"Apache-2.0"
] | permissive | leanprover/vscode-lean4 | 8bcf7f06867b3c1d42007fe6da863a7a17444dbb | 6ef0bfa668bdeaad0979e6df10551d42fcc01094 | refs/heads/master | 1,692,247,771,767 | 1,691,608,804,000 | 1,691,608,804,000 | 325,845,305 | 64 | 24 | Apache-2.0 | 1,694,176,429,000 | 1,609,435,614,000 | TypeScript | UTF-8 | Lean | false | false | 78 | lean | import Foo
def main : IO Unit :=
IO.println s!"Hello, {hello}!"
#eval main |
67f664cbea892131502df271261fc89d1642b79f | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/category_theory/limits/shapes/wide_pullbacks.lean | 3aa364ea977270f2cf51352a1e99b45fc42aa31b | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 16,833 | lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Jakob von Raumer
-/
import category_theory.limits.has_limits
import category_theory.thin
/-!
# Wide pullbacks
We define the category `wide_pullback_shape`, (resp. `wide_p... |
a492ca5d5138bbd5d5977936cf28fe17d5e8195a | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/tactic/interactive_expr.lean | 5c57203a552bc165e205b960e2c8f50e587b6684 | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,109 | lean | /-
Copyright (c) 2020 E.W.Ayers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: E.W.Ayers
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.PostPort
namespace Mathlib
/-!
# Widgets used for tactic state and term-mode goal display
The vsco... |
d46e7e5c36b59afee8b57bc470f82f9a4efd033a | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/topology/algebra/uniform_field.lean | d751bca617980a68cdd595137accec0f3ebc1622 | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 6,563 | lean | /-
Copyright (c) 2019 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import topology.algebra.uniform_ring
import topology.algebra.field
/-!
# Completion of topological fields
The goal of this file is to prove the main part of Proposi... |
814d606b31e310ab7dd0dea1904c0c39f8ddcb1f | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/category_theory/linear/default.lean | 49491eac099635edab3ff861dbb3575913b1e044 | [
"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 | 4,322 | lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.preadditive
import algebra.module.linear_map
import algebra.invertible
import linear_algebra.basic
import algebra.algebra.basic
/-!
# Linear c... |
28df5806d308651eaf3b0052f5ee94ec3a3ffeba | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/tactic/by_contra.lean | d661c442a104ca9a92a8122e9cd133304573a780 | [
"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 | 2,297 | lean | /-
Copyright (c) 2021 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import tactic.core
import tactic.push_neg
/-!
# by_contra'
`by_contra'` is a tactic for proving propositions by contradiction.
It is similar to `by_contra` except ... |
a078f40e86b0f4dcb39d24577b680d292777a0a0 | 6f1049e897f569e5c47237de40321e62f0181948 | /src/exercises/01_equality_rewriting.lean | c89e472ac3f73b0a0443e0a5c32c1a77c26dd89e | [
"Apache-2.0"
] | permissive | anrddh/tutorials | f654a0807b9523608544836d9a81939f8e1dceb8 | 3ba43804e7b632201c494cdaa8da5406f1a255f9 | refs/heads/master | 1,655,542,921,827 | 1,588,846,595,000 | 1,588,846,595,000 | 262,330,134 | 0 | 0 | null | 1,588,944,346,000 | 1,588,944,345,000 | null | UTF-8 | Lean | false | false | 4,819 | lean | import data.real.basic
/-
One of the earliest kind of proofs one encounters while learning mathematics is proving by
a calculation. It may not sound like a proof, but this is actually using lemmas expressing
properties of operations on numbers. It also uses the fundamental property of equality: if two
mathematical ob... |
8d71c3273c47102b1949a3911021f5f9c4ff264e | 4fa161becb8ce7378a709f5992a594764699e268 | /src/tactic/basic.lean | d7a46cb7f406325bd8d8ba5487b4b7f5c0135ced | [
"Apache-2.0"
] | permissive | laughinggas/mathlib | e4aa4565ae34e46e834434284cb26bd9d67bc373 | 86dcd5cda7a5017c8b3c8876c89a510a19d49aad | refs/heads/master | 1,669,496,232,688 | 1,592,831,995,000 | 1,592,831,995,000 | 274,155,979 | 0 | 0 | Apache-2.0 | 1,592,835,190,000 | 1,592,835,189,000 | null | UTF-8 | Lean | false | false | 650 | lean | import tactic.alias
import tactic.clear
import tactic.converter.apply_congr
import tactic.elide
import tactic.explode
import tactic.find
import tactic.generalizes
import tactic.generalize_proofs
import tactic.lift
import tactic.lint
import tactic.localized
import tactic.mk_iff_of_inductive_prop
import tactic.push_neg
i... |
7a70d49530bcd56e8fa161434bfce78714baec1c | 0d107d7abd6ae235d586830f8e09b1b30e7eef0b | /src/real_fibonacci/Solution.lean | d327036cb7aca53075d0cda8053f4622585165e4 | [] | no_license | ukikagi/codewars-lean | 6b9a83ebbb159e7eebf8551b745a1c4d450e747f | 1912f2a4e25e917abfce70d65c0469cfac19dc93 | refs/heads/master | 1,672,948,190,244 | 1,603,361,004,000 | 1,603,795,841,000 | 303,746,208 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,322 | lean | import .Preloaded data.nat.fib
import tactic
lemma lt_wrap {n m: nat} {h: n < m}: n.lt m
:= by assumption
lemma ind2 {C: ℕ → Prop} {n: ℕ}:
C 0 → C 1 → (∀ k: ℕ, C k → C (k + 1) → C (k + 2)) → C n
:=
begin
intros h0 h1 hstep,
apply nat.lt_wf.induction,
intros n ih,
rcases n with _ | _ | n,
assumption',
... |
a4f971308dbd15c7bc1188f7e7c2cf8212868fef | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/set_theory/game/ordinal.lean | 34baa6c2abfb39afc5d17fb271478b59ffee0d62 | [
"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 | 6,449 | 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 set_theory.game.basic
import set_theory.ordinal.natural_ops
/-!
# Ordinals as games
We define the canonical map `ordinal → pgame`, w... |
df4141c48a1b8a8a2b50b98686e69d6e85d85491 | 969dbdfed67fda40a6f5a2b4f8c4a3c7dc01e0fb | /src/linear_algebra/determinant.lean | 854faee2076e01449835c2e4c1bf6a388412de57 | [
"Apache-2.0"
] | permissive | SAAluthwela/mathlib | 62044349d72dd63983a8500214736aa7779634d3 | 83a4b8b990907291421de54a78988c024dc8a552 | refs/heads/master | 1,679,433,873,417 | 1,615,998,031,000 | 1,615,998,031,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 16,554 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Chris Hughes, Tim Baanen
-/
import data.matrix.pequiv
import data.fintype.card
import group_theory.perm.sign
import algebra.algebra.basic
import tactic.ring
import linear_algebra... |
627dac8b31a0485e22e80cecc7f01850e96d92e4 | 4376c25f060c13471bb89cdb12aeac1d53e53876 | /src/espaces-metriques/custom/si_sequence.lean | 4d5917c8c9928b3f2542ab8e3a91ef73e5419a54 | [
"MIT"
] | permissive | RaitoBezarius/projet-maths-lean | 8fa7df563d64c256561ab71893c523fc1424b85c | 42356e980e021a20c3468f5ca1639fec01bb934f | refs/heads/master | 1,613,002,128,339 | 1,589,289,282,000 | 1,589,289,282,000 | 244,431,534 | 0 | 1 | MIT | 1,584,312,574,000 | 1,583,169,883,000 | TeX | UTF-8 | Lean | false | false | 5,350 | lean | import tactic
import data.set
import order.conditionally_complete_lattice
import .defs
import .sequences
noncomputable theory
open_locale classical
section suites
variables {X: Type} [conditionally_complete_linear_order X]
def suite_st_croissante {S: set X}
(Hinf: set.infinite S)
(Hset: (∀ M ⊆ S, M.nonempty → is... |
01d64ef5a6481bf4eda9b82484332d6575494434 | 56e5b79a7ab4f2c52e6eb94f76d8100a25273cf3 | /src/basic/list.lean | b406b6ca5e0c917db57c69abeac09735c7023e0c | [
"Apache-2.0"
] | permissive | DyeKuu/lean-tpe-public | 3a9968f286ca182723ef7e7d97e155d8cb6b1e70 | 750ade767ab28037e80b7a80360d213a875038f8 | refs/heads/master | 1,682,842,633,115 | 1,621,330,793,000 | 1,621,330,793,000 | 368,475,816 | 0 | 0 | Apache-2.0 | 1,621,330,745,000 | 1,621,330,744,000 | null | UTF-8 | Lean | false | false | 6,546 | lean | /- Author: E.W.Ayers © 2019.
Some additional helpers for working with lists.
I suspect that I have duplicated some functionality here.
-/
import data.list .control
universe u
namespace list
variables {α β : Type u} {T : Type u → Type u}
def mmapi_core [applicative T] (f : nat → α → T β) : nat → list α → T (list β)... |
2a9aefc114e2e07ab1c1f05a2df137cdda0cd9c3 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/homology/flip.lean | 310b4ac89443a5fbe4561b972aae3824df5e920c | [
"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 | 3,509 | lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import algebra.homology.homological_complex
/-!
# Flip a complex of complexes
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corres... |
63a2e6f39245732033c9662beece622647c5cacb | 64874bd1010548c7f5a6e3e8902efa63baaff785 | /library/algebra/ordered_group.lean | a6b07b281e857790e884fad4ab36799b990dc160 | [
"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 | 20,355 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.ordered_group
Authors: Jeremy Avigad
Partially ordered additive groups, modeled on Isabelle's library. We could refine the structures,
but we would have to declare more inherit... |
7c32ab87d868630f1c78de501bfc12edebefa1f1 | bdb33f8b7ea65f7705fc342a178508e2722eb851 | /analysis/measure_theory/measurable_space.lean | cd3976b125caa8d648a6e787af9527bf5fd6fd2d | [
"Apache-2.0"
] | permissive | rwbarton/mathlib | 939ae09bf8d6eb1331fc2f7e067d39567e10e33d | c13c5ea701bb1eec057e0a242d9f480a079105e9 | refs/heads/master | 1,584,015,335,862 | 1,524,142,167,000 | 1,524,142,167,000 | 130,614,171 | 0 | 0 | Apache-2.0 | 1,548,902,667,000 | 1,524,437,371,000 | Lean | UTF-8 | Lean | false | false | 27,021 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Measurable spaces -- σ-algberas
-/
import data.set data.set.disjointed data.finset order.galois_connection data.set.countable
open classical set lattice
local attribute... |
37d410c04d7de55f85bb92fe11a8f095ad9e6288 | a721fe7446524f18ba361625fc01033d9c8b7a78 | /src/principia/myint/dvd.lean | 7b5ba2bc3bd9f8d5d2a677ccf90f7295b9f83efe | [] | no_license | Sterrs/leaning | 8fd80d1f0a6117a220bb2e57ece639b9a63deadc | 3901cc953694b33adda86cb88ca30ba99594db31 | refs/heads/master | 1,627,023,822,744 | 1,616,515,221,000 | 1,616,515,221,000 | 245,512,190 | 2 | 0 | null | 1,616,429,050,000 | 1,583,527,118,000 | Lean | UTF-8 | Lean | false | false | 3,022 | lean | import ..mynat.dvd
import .max
import .le
namespace hidden
namespace myint
open myring
open ordered_myring
def dvd (m n : myint) := ∃ k : myint, n = k * m
instance: has_dvd myint := ⟨dvd⟩
def coprime (m n : myint) := ∀ k: myint, k ∣ m → k ∣ n → (k = 1 ∨ k = -1)
variables m n k : myint
theorem int_dvd_iff_abs_dvd ... |
71ab83f25c1d9bd8156fb3ea241744923e8b0c75 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/data/nat/enat.lean | 7a2e3ea1593668dbabdd9a7640a3152b72f39a29 | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 2,511 | 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 data.nat.lattice
import data.nat.succ_pred
/-!
# Definition and basic properties of extended natural numbers
In this file we define `enat` (notation: `ℕ∞`)... |
c439ec64cd11c98a58f879334292419082d36398 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/tactic/unify_equations.lean | ba29592f4743cc392c9fbdc0ee0b1ad14bb0ce8d | [
"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 | 14,556 | lean | /-
Copyright (c) 2020 Jannis Limperg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jannis Limperg
-/
import tactic.core
/-!
# The `unify_equations` tactic
This module defines `unify_equations`, a first-order unification tactic that
unifies one or more equations in ... |
d4c42c74af1e032a2cee15b55a55e93bf2003866 | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/algebraic_geometry/Scheme.lean | d20d46e416c230402ca14a6925b4e8c78d0714e6 | [
"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 | 3,164 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import algebraic_geometry.Spec
/-!
# The category of schemes
A scheme is a locally ringed space such that every point is contained in some open set
where there is a... |
d63e8e3d4e3037bcf7d248da8e76fa439de9532a | 38bf3fd2bb651ab70511408fcf70e2029e2ba310 | /test/solve_by_elim.lean | 97ffb5893a65923c1212e6beee3336ead3c59a6b | [
"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 | 2,553 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Scott Morrison
-/
import tactic.solve_by_elim
example {a b : Prop} (h₀ : a → b) (h₁ : a) : b :=
begin
apply_assumption,
apply_assumption,
end
example {X : Type} (x : X)... |
0a7ccd24f75ec42a9a2d6bbd2beb7ee273d148fd | 4bcaca5dc83d49803f72b7b5920b75b6e7d9de2d | /src/Lean/Meta/Tactic/Simp/Rewrite.lean | d41f7e48dd589522d0c07fbf21cc6ea3aad47239 | [
"Apache-2.0"
] | permissive | subfish-zhou/leanprover-zh_CN.github.io | 30b9fba9bd790720bd95764e61ae796697d2f603 | 8b2985d4a3d458ceda9361ac454c28168d920d3f | refs/heads/master | 1,689,709,967,820 | 1,632,503,056,000 | 1,632,503,056,000 | 409,962,097 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,101 | 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.SynthInstance
import Lean.Meta.Tactic.Simp.Types
namespace Lean.Meta.Simp
def synthesizeArgs (lemmaName : Nam... |
f3af04860c4fd12d68503dc70669dfa7f4861d5c | 8b9f17008684d796c8022dab552e42f0cb6fb347 | /library/logic/funext.lean | ba27712610bbae778b7062a476b9965022ce3146 | [
"Apache-2.0"
] | permissive | chubbymaggie/lean | 0d06ae25f9dd396306fb02190e89422ea94afd7b | d2c7b5c31928c98f545b16420d37842c43b4ae9a | refs/heads/master | 1,611,313,622,901 | 1,430,266,839,000 | 1,430,267,083,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,021 | 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
Basic theorems for functions
-/
import logic.cast algebra.function data.sigma
open function eq.ops
namespace function
variables {A B C D: Type}
theorem ... |
f3bb8d66752ad63847a6bad2ae773c7034cc5903 | 74caf7451c921a8d5ab9c6e2b828c9d0a35aae95 | /library/init/meta/interactive.lean | 4bfe6aaee6eb5c6337add2a598eb375b85f07bbe | [
"Apache-2.0"
] | permissive | sakas--/lean | f37b6fad4fd4206f2891b89f0f8135f57921fc3f | 570d9052820be1d6442a5cc58ece37397f8a9e4c | refs/heads/master | 1,586,127,145,194 | 1,480,960,018,000 | 1,480,960,635,000 | 40,137,176 | 0 | 0 | null | 1,438,621,351,000 | 1,438,621,351,000 | null | UTF-8 | Lean | false | false | 14,841 | 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.meta.tactic init.meta.rewrite_tactic init.meta.simp_tactic
namespace tactic
namespace interactive
namespace types
/- The parser treats ... |
5a4c9218b8ee95a760239908703fa16bcc480b0d | 54d7e71c3616d331b2ec3845d31deb08f3ff1dea | /library/data/buffer.lean | 9f1a1ddbe97bd5712c4c432dd948ce024b260c69 | [
"Apache-2.0"
] | permissive | pachugupta/lean | 6f3305c4292288311cc4ab4550060b17d49ffb1d | 0d02136a09ac4cf27b5c88361750e38e1f485a1a | refs/heads/master | 1,611,110,653,606 | 1,493,130,117,000 | 1,493,167,649,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,600 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
universes u w
def buffer (α : Type u) := Σ n, array α n
def mk_buffer {α : Type u} : buffer α :=
⟨0, {data := λ i, fin.elim0 i}⟩
def array.to_buffer {α :... |
b255bd656a03801fb1c0c47f0a1824b49edf1907 | 98beff2e97d91a54bdcee52f922c4e1866a6c9b9 | /src/equalizers.lean | 6eb8e58b9e13c66a4fc7cfbee2d115536df38198 | [] | no_license | b-mehta/topos | c3fc43fb04ba16bae1965ce5c26c6461172e5bc6 | c9032b11789e36038bc841a1e2b486972421b983 | refs/heads/master | 1,629,609,492,867 | 1,609,907,263,000 | 1,609,907,263,000 | 240,943,034 | 43 | 3 | null | 1,598,210,062,000 | 1,581,877,668,000 | Lean | UTF-8 | Lean | false | false | 2,845 | lean | import category_theory.limits.preserves.limits
import category_theory.limits.shapes.equalizers
namespace category_theory
open category_theory category_theory.category category_theory.limits
universes v u u₂
noncomputable theory
variables (C : Type u) [category.{v} C]
def of_iso_point {J : Type v} [small_category ... |
0c4693adcc5e1d32487fc3c9f6bf58792a2b85ed | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /10_Structures_and_Records.org.20.lean | 72f3576ddbeb9e39770b2c80e0652ddb41a1e501 | [] | 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 | 438 | lean | import standard
structure has_mul [class] (A : Type) :=
mk :: (mul : A → A → A)
infixl `*` := has_mul.mul
structure semigroup [class] (A : Type) extends has_mul A :=
mk :: (assoc : ∀ a b c, mul (mul a b) c = mul a (mul b c))
-- BEGIN
section
variables (A : Type) (s : semigroup A) (a b : A)
set_option pp.implicit ... |
cf685c891e9acbd840d8f4128bc0601f630e510c | e4a7c8ab8b68ca0e53d2c21397320ea590fa01c6 | /src/tactic/default.lean | b1ebad6b3beca1f8fa1d44e3e554a21b91fcd089 | [] | no_license | lean-forward/field | 3ff5dc5f43de40f35481b375f8c871cd0a07c766 | 7e2127ad485aec25e58a1b9c82a6bb74a599467a | refs/heads/master | 1,590,947,010,909 | 1,563,811,881,000 | 1,563,811,881,000 | 190,415,651 | 1 | 0 | null | 1,563,643,371,000 | 1,559,746,688,000 | Lean | UTF-8 | Lean | false | false | 14 | lean | import .polya
|
61b4ba01381b621e102b89febc2fd2fb54ccb8b3 | 83c8119e3298c0bfc53fc195c41a6afb63d01513 | /tests/lean/run/bin_tree.lean | f0aca6ebe98a4d56a5ce10fcea896faac92d64bc | [
"Apache-2.0"
] | permissive | anfelor/lean | 584b91c4e87a6d95f7630c2a93fb082a87319ed0 | 31cfc2b6bf7d674f3d0f73848b842c9c9869c9f1 | refs/heads/master | 1,610,067,141,310 | 1,585,992,232,000 | 1,585,992,232,000 | 251,683,543 | 0 | 0 | Apache-2.0 | 1,585,676,570,000 | 1,585,676,569,000 | null | UTF-8 | Lean | false | false | 1,030 | lean | namespace Ex
local attribute [simp] add_comm add_left_comm
def pairs_with_sum' : Π (m n) {d}, m + n = d → list {p : ℕ × ℕ // p.1 + p.2 = d}
| 0 n d h := [⟨(0, n), h⟩]
| (m+1) n d h := ⟨(m+1, n), h⟩ :: pairs_with_sum' m (n+1) (by simp at h; simp [h])
def pairs_with_sum (n) : list {p : ℕ × ℕ // p.1 + p.2 = n} :=
pai... |
27413e285c0f435ec0d707dd0e02648d3a7c972c | 85a51a7a118db552510ddb311e53e7a8bba7b477 | /src/complements/germ.lean | f7611cf64327b088e11d0da7b2ef40534133513e | [] | no_license | ADedecker/nonstandard | f0c1cac7482bb0dd48d2f2eb092f5262ff0fa2dc | c32f5e1d87cc9e6410d66cf3080fd8c4a47cf5e4 | refs/heads/master | 1,686,549,196,023 | 1,626,129,788,000 | 1,626,129,788,000 | 382,594,533 | 3 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,509 | lean | import order.filter.germ
import for_mathlib.filter_basic
/-! # Complements on filter germs -/
open filter function
namespace filter.germ
variables {ι α β : Type*} (l : filter ι)
local notation `∀*` binders `, ` r:(scoped p, filter.eventually p l) := r
local notation `α*` := l.germ α
local notation `β*` := l.germ β... |
a3ddd3c966951a4f0ea97e7163ed6b41c2d96e7b | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/algebraic_geometry/sheafed_space.lean | 4f183b3004843ac6bf456dbc19e1da71c31f0778 | [
"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 | 4,673 | 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 algebraic_geometry.presheafed_space
import topology.sheaves.sheaf
/-!
# Sheafed spaces
Introduces the category of topological spaces equipped with a sheaf (t... |
652471b851d361a735d79a24145d2a1066f088f9 | 957a80ea22c5abb4f4670b250d55534d9db99108 | /library/init/data/array/slice.lean | 05e73806dfb4c066b3946830d769f828cb098474 | [
"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 | 1,305 | 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.nat init.data.array.basic init.data.nat.lemmas
universes u
variables {α : Type u} {n : nat}
namespace array
def slice (a : array α n)... |
6e6578d13541fb5ae332859c003acd00d9f5293f | 957a80ea22c5abb4f4670b250d55534d9db99108 | /tests/lean/run/set1.lean | 8eba655b78765d82ee8d4b609bb65dff7b1307e4 | [
"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 | 156 | lean | variables A : Type
example (s₁ s₂ s₃ : set A) : s₁ ⊆ s₂ → s₂ ⊆ s₃ → s₁ ⊆ s₃ :=
assume h₁ h₂ a ains₁,
h₂ (h₁ ains₁)
|
f53ae19d5b62884ebc4ad9609965fde64ff7990c | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/module/localized_module.lean | ac588db9262ab1fbe3086175651b227ce0f4bdde | [
"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 | 39,836 | lean | /-
Copyright (c) 2022 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang, Jujian Zhang
-/
import group_theory.monoid_localization
import ring_theory.localization.basic
import algebra.algebra.restrict_scalars
/-!
# Localized Module
Given a commu... |
e54aef76c7982cb801ed184c135438874a19c0e8 | 853df553b1d6ca524e3f0a79aedd32dde5d27ec3 | /src/category_theory/functor.lean | f72da2d20abc9c327e63edf2db741e503d71e860 | [
"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 | 3,212 | 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... |
5353d1ce2dda09d4c306fd0462a7e6aa42e7f02c | e37bb385769d6f4ac9931236fd07b708397e086b | /src/library/src_field_lemmas.lean | 5c845d422ec08ba66a9f858841bf2d8819bf6bd1 | [] | no_license | gihanmarasingha/ems_reals | 5f5d5b9d9dfb5a10da465046336d74995132dff6 | 9df527742db69d0a389add44b506538fdb4d0800 | refs/heads/master | 1,675,327,747,064 | 1,608,036,820,000 | 1,608,036,820,000 | 315,825,726 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,624 | lean | import .src_field tactic
namespace mth1001
namespace myreal
section grouplaws
variables {R : Type} [comm_group R]
lemma add_comm (x y : R) : x + y = y + x := comm_group.add_comm x y
lemma add_assoc (x y z : R) : (x + y) + z = x + (y + z) := comm_group.add_assoc x y z
lemma add_zero (x : R) : x + 0 = x := comm_grou... |
b2444c26df348e72dd49ceb6eff4b6c62dfb6613 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/analysis/normed_space/basic.lean | d8e6ec8648b660f4ef78c68cbe3c59af664b0f08 | [
"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 | 40,282 | lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl
-/
import algebra.pi_instances
import linear_algebra.basic
import topology.instances.nnreal topology.instances.complex
import topology.algebra.module
im... |
42a09d87f610d8e2535491cf9a0413f3fac4866c | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/measure_theory/group.lean | fba67a66feb349a858c829177953671b04b63938 | [
"Apache-2.0"
] | permissive | ilitzroth/mathlib | ea647e67f1fdfd19a0f7bdc5504e8acec6180011 | 5254ef14e3465f6504306132fe3ba9cec9ffff16 | refs/heads/master | 1,680,086,661,182 | 1,617,715,647,000 | 1,617,715,647,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,305 | lean | /-
Copyright (c) 2020 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import measure_theory.integration
/-!
# Measures on Groups
We develop some properties of measures on (topological) groups
* We define properties on measures: l... |
333ef99ad9d8cb52dc06fa1c3bdd4d2e1c366dff | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/order/ring/with_top.lean | 5483f53ec6f3f18fc3cc0ca7bc6e5d6d2c29ebaa | [
"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 | 10,289 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro
-/
import algebra.hom.ring
import algebra.order.monoid.with_top
import algebra.order.ring.canonical
/-! # Structures involving `*` and ... |
20f108b39449857e04f9d87d9d8a791a4cdb3cf0 | dc253be9829b840f15d96d986e0c13520b085033 | /homotopy/smash_adjoint.hlean | 560a2dd0ac7b6df45dc3cc16ce9a4b2115ebc29b | [
"Apache-2.0"
] | permissive | cmu-phil/Spectral | 4ce68e5c1ef2a812ffda5260e9f09f41b85ae0ea | 3b078f5f1de251637decf04bd3fc8aa01930a6b3 | refs/heads/master | 1,685,119,195,535 | 1,684,169,772,000 | 1,684,169,772,000 | 46,450,197 | 42 | 13 | null | 1,505,516,767,000 | 1,447,883,921,000 | Lean | UTF-8 | Lean | false | false | 32,699 | hlean | -- Authors: Floris van Doorn
-- informal proofs in collaboration with Egbert, Stefano, Robin, Ulrik
/- the adjunction between the smash product and pointed maps -/
import .smash .susp ..pointed_pi ..pyoneda
open bool pointed eq equiv is_equiv sum bool prod unit circle cofiber prod.ops wedge is_trunc
function uni... |
d39102ab6776825bc5ced90658a8e56b5694d518 | 618003631150032a5676f229d13a079ac875ff77 | /src/category_theory/graded_object.lean | b99272bfa46926c7a246cad159c749b01784c7f0 | [
"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 | 6,810 | 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.shift
import category_theory.concrete_category
/-!
# The category of graded objects
For any type `β`, a `β`-graded object over some category ... |
0a8163d4747dc9e7e2802887888c663578866e75 | 618003631150032a5676f229d13a079ac875ff77 | /test/transport/basic.lean | 8f42e417334ed21e3b514c9825cf9ffd6940e0af | [
"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 | 2,909 | lean | import tactic.transport
import order.bounded_lattice
import algebra.lie_algebra
-- We verify that `transport` can move a `semiring` across an equivalence.
-- Note that we've never even mentioned the idea of addition or multiplication to `transport`.
def semiring.map {α : Type} [semiring α] {β : Type} (e : α ≃ β) : sem... |
3915c0b7715d626025aadccd4f8d6ab8c132f9d9 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/bad_index.lean | 9074e4ecd70170282a1b43d086307b3535714190 | [
"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 | 183 | lean | inductive foo1 : Type -> Type
| mk : foo1 (list (foo1 poly_unit)) -> foo1 (list (foo1 poly_unit))
inductive foo2 : Type -> Type
| mk : foo2 (foo2 poly_unit) -> foo2 (foo2 poly_unit)
|
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