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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
62dd7a5c68b0e9cac300c73cddfcacb6f74b409a | 076f5040b63237c6dd928c6401329ed5adcb0e44 | /instructor-notes/2019.10.01..poly/boxed_test.lean | 9c893ba202a6c9979b280c10f123fd85e44a108c | [] | no_license | kevinsullivan/uva-cs-dm-f19 | 0f123689cf6cb078f263950b18382a7086bf30be | 09a950752884bd7ade4be33e9e89a2c4b1927167 | refs/heads/master | 1,594,771,841,541 | 1,575,853,850,000 | 1,575,853,850,000 | 205,433,890 | 4 | 9 | null | 1,571,592,121,000 | 1,567,188,539,000 | Lean | UTF-8 | Lean | false | false | 214 | lean | import .boxed
#check boxed
open boxed
def b2 : boxed nat := box 3
def b3 := box 3
def b4 := box tt
def b5 := box "I love polymorphism"
#check b3
#check b4
#check b5
#eval unbox b3
#eval unbox b4
#eval unbox b5 |
5382c3af2372ec53b61ee717ce68b470eda02b91 | 6f510b1ed724f95a55b7d26a8dcd13e1264123dd | /src/talk.lean | 66f151104f562a871ba95b21b4af09af704c8d1b | [] | no_license | jcommelin/oberharmersbach2019 | adaf2e54ba4eff7c178c933978055ff4d6b0593b | d2cdf780a10baa8502a9b0cae01c7efa318649a6 | refs/heads/master | 1,587,558,516,731 | 1,550,558,213,000 | 1,550,558,213,000 | 170,372,753 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 625 | lean | /- 2019-02-19, Oberharmersbach
Interactive theorem proving with a computer
— my experience
-- _
-- | | ___ __ _ _ __
-- | |/ _ \/ _` | '_ \
-- | | __| (_| | | | |
-- |_|\___|\__,_|_| |_|
--
A rose-colored introduction
-... |
5ac03266a63a530eb5f6a8c583a052aa1681b904 | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/ring_theory/derivation.lean | 1d64d3fd8baa71b71f2451f89d5451366c4cc22f | [
"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 | 8,071 | lean | /-
Copyright © 2020 Nicolò Cavalleri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Nicolò Cavalleri.
-/
import algebra.lie_algebra
import ring_theory.algebra_tower
import tactic
/-!
# Derivations
This file defines derivation. A derivation `D` from the `R`-algebra `... |
65838ee762a9db3e8bb88feaf95495b73d916863 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/order/compare.lean | edd8b1beed6deb56835859be2ba3f1074ce610cb | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 8,438 | 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 order.synonym
/-!
# Comparison
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> https://github.com/leanprover-community/mathlib4/pull/569
> Any changes to this f... |
e0a07544f26d7853f075be184277739edddaebe2 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/tactic/linarith/preprocessing.lean | ae700421d8eeb229362ec671da5171880b2d3682 | [
"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 | 12,639 | lean | /-
Copyright (c) 2020 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis
-/
import data.prod.lex
import tactic.cancel_denoms
import tactic.linarith.datatypes
import tactic.zify
/-!
# Linarith preprocessing
This file contains methods used ... |
851494441f29e91226237851f151e1f097ef76f7 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/rewriter7.lean | fa00de66710b0333864dde54b92de0d52ac4d6bb | [
"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 | 258 | lean | import data.int
open int
constant f : int → int
definition double (x : int) := x + x
theorem tst1 (x y : int) (H1 : double x = 0) (H2 : double y = 0) (H3 : f (double y) = 0) (H4 : y > 0) : f (x + x) = 0 :=
by rewrite [↑double at H1, H1, H2 at H3, H3]
|
139ca8f24e3aebb3a519b7b4dd2ca590c6981c64 | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/data/buffer/parser/basic.lean | a841794f62207b7968c6c89ee74a823fdcb23fd5 | [
"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 | 73,364 | lean | /-
Copyright (c) 2020 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
import data.string.basic
import data.buffer.basic
/-!
# Parsers
`parser α` is the type that describes a computation that can ingest a `char_buffer`
and output, if... |
306d0b818277a499e272619eeb6ef3a1420d971a | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/order/filter/basic.lean | 85569c1cc42f06208bd3a6035bf3ad79317d936a | [
"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 | 107,569 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jeremy Avigad
-/
import control.traversable.instances
import data.set.finite
import order.copy
import tactic.monotonicity
/-!
# Theory of filters on sets
## Main defi... |
e12dd0eb4b479da6c7d5efc06cf0fa0ab9e8ea59 | 1e561612e7479c100cd9302e3fe08cbd2914aa25 | /mathlib4_experiments/Data/Notation.lean | 8663078093f39538a4c8598295b4cfc1fb897435 | [
"Apache-2.0"
] | permissive | kbuzzard/mathlib4_experiments | 8de8ed7193f70748a7529e05d831203a7c64eedb | 87cb879b4d602c8ecfd9283b7c0b06015abdbab1 | refs/heads/master | 1,687,971,389,316 | 1,620,336,942,000 | 1,620,336,942,000 | 353,994,588 | 7 | 4 | Apache-2.0 | 1,622,410,748,000 | 1,617,361,732,000 | Lean | UTF-8 | Lean | false | false | 532 | lean | set_option autoBoundImplicitLocal false
universes u₁ u₂ v
/-
In Lean 3 mathlib, the `≃` notation is defined specifically for `equiv`.
This is a more flexible version using a type class for overloading support.
In the instance defined in `Data.Equiv.Basic`, `α` `β` and `γ` are all `Sort _`.
`γ` needs to be bundled b... |
9f59c2b21fbd94efbcd8bc6e222619e13a9e1e79 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /hott/algebra/category/constructions/pushout.hlean | 7f7afc0332ca6f760178cbc53ded34b051a988da | [
"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 | 21,442 | hlean | /-
Copyright (c) 2016 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
The pushout of categories
The morphisms in the pushout of two categories is defined as a quotient on lists of composable
morphisms. For this we use the notion of ... |
9e52f1b4e9e750f076376f0567bae868feaf5312 | f618aea02cb4104ad34ecf3b9713065cc0d06103 | /src/category_theory/instances/measurable_space.lean | 2b0d56562cd192af755ef51dd0e8bc77f58aaa82 | [
"Apache-2.0"
] | permissive | joehendrix/mathlib | 84b6603f6be88a7e4d62f5b1b0cbb523bb82b9a5 | c15eab34ad754f9ecd738525cb8b5a870e834ddc | refs/heads/master | 1,589,606,591,630 | 1,555,946,393,000 | 1,555,946,393,000 | 182,813,854 | 0 | 0 | null | 1,555,946,309,000 | 1,555,946,308,000 | null | UTF-8 | Lean | false | false | 876 | lean | /- Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Basic setup for measurable spaces.
-/
import category_theory.instances.Top
import measure_theory.borel_space
open category_theory
universes u v
namespace category_th... |
69a8c66465510227c0a6b3bfa905cb2c94c94334 | aa3f8992ef7806974bc1ffd468baa0c79f4d6643 | /tests/lean/run/ftree_brec.lean | 5edbf08c0a17dce357090728498f2fb79b9c3118 | [
"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 | 4,919 | lean | import data.unit data.prod
inductive ftree (A : Type) (B : Type) : Type :=
leafa : ftree A B,
node : (A → B → ftree A B) → (B → ftree A B) → ftree A B
set_option pp.universes true
check @ftree
namespace ftree
namespace manual
definition below.{l l₁ l₂} {A : Type.{l₁}} {B : Type.{l₂}} (C : ftree A B → Type.{l+1}) (... |
ae1dc59a6c638620c51f0d6e35edbe1992968479 | 9dd3f3912f7321eb58ee9aa8f21778ad6221f87c | /tests/lean/run/600c.lean | 4b5f618e3d5aacc1615708d7fa70b7a78865bad4 | [
"Apache-2.0"
] | permissive | bre7k30/lean | de893411bcfa7b3c5572e61b9e1c52951b310aa4 | 5a924699d076dab1bd5af23a8f910b433e598d7a | refs/heads/master | 1,610,900,145,817 | 1,488,006,845,000 | 1,488,006,845,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 98 | lean | /- /- -/ -/
/- - /--/-/
/-/-/--/-/-/
/- -/
/- -----------/
/- --/
/- ---/
/-
-/
----/
print "ok"
|
8b3dfd5795820cfbda2faa3f299ce0d3493febc3 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/analysis/convex/jensen.lean | a39c01298cb181f42b7c0fc5b77163f44f41b88c | [
"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 | 6,055 | lean | /-
Copyright (c) 2019 Alexander Bentkamp. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp, Yury Kudriashov
-/
import analysis.convex.combination
import analysis.convex.function
/-!
# Jensen's inequality and maximum principle for convex functions
In ... |
ee7b30cff9cf431c569d5fa333136ea1f83de475 | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /stage0/src/Lean/ProjFns.lean | fa5f827a3d027d03d71dc9302b0e2932f65e17aa | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | EdAyers/lean4 | 57ac632d6b0789cb91fab2170e8c9e40441221bd | 37ba0df5841bde51dbc2329da81ac23d4f6a4de4 | refs/heads/master | 1,676,463,245,298 | 1,660,619,433,000 | 1,660,619,433,000 | 183,433,437 | 1 | 0 | Apache-2.0 | 1,657,612,672,000 | 1,556,196,574,000 | Lean | UTF-8 | Lean | false | false | 2,487 | 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.Environment
namespace Lean
/--
Given a structure `S`, Lean automatically creates an auxiliary definition (projection function)
for each field.... |
cf3800642ef0bd372f7334e3c86afa94cee99637 | 2a70b774d16dbdf5a533432ee0ebab6838df0948 | /_target/deps/mathlib/src/data/mv_polynomial/basic.lean | 9e529a0cff8c92b502abe4e35bd0e8ec5240c205 | [
"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 | 35,787 | 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.polynomial.eval
/-!
# Multivariate polynomials
This file defines polynomial rings over a base ring (or even semiring),
... |
5d14f193e4bda87e3c33b5f6c392e641048cc42c | 8d65764a9e5f0923a67fc435eb1a5a1d02fd80e3 | /src/topology/connected.lean | 3da1549fcbb49e22f92b2f5fecf5437c3e5e84a5 | [
"Apache-2.0"
] | permissive | troyjlee/mathlib | e18d4b8026e32062ab9e89bc3b003a5d1cfec3f5 | 45e7eb8447555247246e3fe91c87066506c14875 | refs/heads/master | 1,689,248,035,046 | 1,629,470,528,000 | 1,629,470,528,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 41,500 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Yury Kudryashov
-/
import topology.subset_properties
/-!
# Connected subsets of topological spaces
In this file we define connected subsets of a topol... |
f8623daa3e4869f36b98860e350698e6ad60c11e | df7bb3acd9623e489e95e85d0bc55590ab0bc393 | /lean/love10_denotational_semantics_exercise_solution.lean | bd5ba7d4665eaf31adfa51e6116715db90e6778a | [] | no_license | MaschavanderMarel/logical_verification_2020 | a41c210b9237c56cb35f6cd399e3ac2fe42e775d | 7d562ef174cc6578ca6013f74db336480470b708 | refs/heads/master | 1,692,144,223,196 | 1,634,661,675,000 | 1,634,661,675,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,228 | lean | import .love10_denotational_semantics_demo
/- # LoVe Exercise 10: Denotational Semantics -/
set_option pp.beta true
set_option pp.generalized_field_notation false
namespace LoVe
/- ## Question 1: Monotonicity
1.1. Prove the following lemma from the lecture. -/
lemma monotone_comp {α β : Type} [partial_order α]... |
2ae7b42657fb3169b77b7ff81e8beaf2f0348c8e | b1e80085f6d9158c0b431ffc4fa9d0d53cbac8e4 | /src/result.lean | c6e94fc086a7d73ea0128fc5aa3aeb50be7cca22 | [] | no_license | dwarn/nielsen-schreier-2 | d73c20e4d2a8ae537fe4f8063272d0b72c58276a | e51a8c6511d374dc584698c7fa236a5be47e7dbe | refs/heads/master | 1,679,911,740,113 | 1,615,656,058,000 | 1,615,656,058,000 | 344,111,212 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 411 | lean | import arborescence contract connected covering
noncomputable theory
open category_theory
instance end_is_free {G} [groupoid G] [inhabited G] [preconnected_groupoid G] [is_free_groupoid G] :
is_free_group (End (default G)) :=
contract (geodesic_subgraph _)
instance subgroup_is_free {G} [group G] [is_free_group G]... |
f5f9193a031b07efaa67ceec766779f76f161288 | 206422fb9edabf63def0ed2aa3f489150fb09ccb | /src/algebra/char_p/basic.lean | 97a0dbb0c37d4742830ef42c9b42520624647460 | [
"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 | 15,181 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Kenny Lau, Joey van Langen, Casper Putz
-/
import data.fintype.basic
import data.nat.choose
import data.int.modeq
import algebra.module.basic
import algebra.iterate_hom
import group_theory.... |
c62d82840526d06d57f6a4fa486300e8b71f3e8e | ebf7140a9ea507409ff4c994124fa36e79b4ae35 | /src/demos/category_theory.lean | 35041a0ac94751bae8d9f8b1217596f668b10b44 | [] | no_license | fundou/lftcm2020 | 3e88d58a92755ea5dd49f19c36239c35286ecf5e | 99d11bf3bcd71ffeaef0250caa08ecc46e69b55b | refs/heads/master | 1,685,610,799,304 | 1,624,070,416,000 | 1,624,070,416,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 12,549 | lean | import category_theory.category
import category_theory.functor
import category_theory.functor_category
import algebra.category.CommRing
import algebra.category.Group.images
import algebra.category.Group.colimits
import algebra.category.Group.abelian
import algebra.category.Module.monoidal
import category_theory.abeli... |
20bd8b24d1ec0b78f6cf97a2a87e23d7f24bcd7e | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/linear_algebra/finsupp.lean | 25dfcbdc81be68c63625ea3f07f0d1faf7acf5ac | [
"Apache-2.0"
] | permissive | dupuisf/mathlib | 62de4ec6544bf3b79086afd27b6529acfaf2c1bb | 8582b06b0a5d06c33ee07d0bdf7c646cae22cf36 | refs/heads/master | 1,669,494,854,016 | 1,595,692,409,000 | 1,595,692,409,000 | 272,046,630 | 0 | 0 | Apache-2.0 | 1,592,066,143,000 | 1,592,066,142,000 | null | UTF-8 | Lean | false | false | 18,950 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl
Linear structures on function with finite support `α →₀ M`.
-/
import data.monoid_algebra
noncomputable theory
open set linear_map submodule
open_locale classical
na... |
5f80a00a69bb4647008083630420c0966c5354a4 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/is_def_eq_perf_bug.lean | 013efee25adcfba832cd1d65b1414cadfffc5a04 | [
"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 | 166 | lean | definition f (n : nat) : nat :=
if n = 100000 then 1 else 0
open tactic
example (n : nat) : f 100000 = (if (100000 : nat) = 100000 then 1 else 0) :=
by reflexivity
|
2fce27c7cdbbc6533e1c9d269e109268d66d91bc | 2731214ea32f2a1a985300e281fb3117640a16c3 | /portmanteau_comeonlean_lemmas.lean | bd8bb74e4aaadf3c5edbb34c13585a7e6641203f | [
"Apache-2.0"
] | permissive | kkytola/lean_portmanteau | 5d6a156db959974ebc4f5bed9118a7a2438a33fa | ac55eb4e24be43032cbc082e2b68d8fb8bd63f22 | refs/heads/main | 1,686,107,117,334 | 1,625,177,052,000 | 1,625,177,052,000 | 381,514,032 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 31,091 | lean | /-
Copyright (c) 2021 Kalle Kytölä. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kalle Kytölä
-/
import measure_theory.integration
import topology.metric_space.basic
import topology.instances.real
import topology.instances.ennreal
import topology.instances.nnreal
imp... |
0c596fc32156954c54a3623cb4dc751b3ccecd41 | 618003631150032a5676f229d13a079ac875ff77 | /src/data/rat/cast.lean | 25eee5d801070f0ce6bcfc7288fd4fe108f4d054 | [
"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 | 11,300 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import data.rat.order
/-!
# Casts for Rational Numbers
## Summary
We define the canonical injection from ℚ into an arbitrary division ring and prove... |
1adcc3289a128430c651a6453ed80b73cdcff1af | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/category/Mon/basic.lean | 33350da6a4ec43f6be974d1a82271ce7965c960b | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 8,310 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.concrete_category.bundled_hom
import algebra.punit_instances
import category_theory.functor.reflects_isomorphisms
/-!
# Category instances for... |
36655d7a15f52eb460ce36d2a85b763b245e58f0 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/modeq.lean | 68291700694b08632641d4a5e0ba7dada8d223f0 | [
"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 | 9,247 | lean | /-
Copyright (c) 2023 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import data.int.modeq
import group_theory.quotient_group
/-!
# Equality modulo an element
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require ... |
1a64c5364260787d8f992acafc62b5242106a135 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/data/mv_polynomial/basic.lean | 01173043ffae56cc323ee79b1f15e81fd1023b62 | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 49,601 | 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 ring_theory.adjoin.basic
import data.finsupp.antidiagonal
import algebra.monoid_algebra.support
import order.symm_diff
/-!
# ... |
6bb22247ba9a060462e6a594d4772f6a977365b2 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/category_theory/abelian/pseudoelements.lean | d5d62d6bbe91143e6e4ff9dc89ba314f10fec759 | [
"Apache-2.0"
] | permissive | waynemunro/mathlib | e3fd4ff49f4cb43d4a8ded59d17be407bc5ee552 | 065a70810b5480d584033f7bbf8e0409480c2118 | refs/heads/master | 1,693,417,182,397 | 1,634,644,781,000 | 1,634,644,781,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 18,858 | lean | /-
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import category_theory.abelian.exact
import category_theory.over
/-!
# Pseudoelements in abelian categories
A *pseudoelement* of an object `X` in an abelian category ... |
1089bd59f891520f28424b1c24c6d66b8263252a | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/category_theory/abelian/transfer.lean | a6aae2229c07791d3c7558d964fd7dd9e42e6433 | [
"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 | 8,592 | 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 category_theory.preadditive.additive_functor
import category_theory.abelian.basic
import category_theory.limits.preserves.shapes.kernels
import category_theory... |
a422db98da407a82a681ef0772c10216bcb1467d | d7189ea2ef694124821b033e533f18905b5e87ef | /galois/option.lean | 8b9bc8b925dfdd852ea549693848891185781ef9 | [
"Apache-2.0"
] | permissive | digama0/lean-protocol-support | eaa7e6f8b8e0d5bbfff1f7f52bfb79a3b11b0f59 | cabfa3abedbdd6fdca6e2da6fbbf91a13ed48dda | refs/heads/master | 1,625,421,450,627 | 1,506,035,462,000 | 1,506,035,462,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,070 | lean | /- This module defines lemmas for option -/
import data.option
universe variables u v
run_cmd mk_simp_attr `simp_option
namespace option
variables {α : Type u} {β : Type u}
@[simp_option]
theorem is_some_none : is_some (none : option α) = ff := rfl
@[simp_option]
theorem is_some_some {α : Type} (x : α) : option.... |
0be8aa554fcf485f78eecf9faf248be975c49aac | 87d5955e1100ba73f6b56149b659e85116fa215b | /group_theory/finsubg.lean | 9b1edc1225aa4124cfb5a2b31e725b4370ef13b0 | [
"Apache-2.0"
] | permissive | avigad/leanproved | 4d15a05f8544a67b9f589c5e656358e1485aef3c | 3cf0f5dda3ace82f6b7cdc159528ce3ebaef159f | refs/heads/master | 1,611,368,103,158 | 1,433,589,072,000 | 1,433,589,072,000 | 36,843,899 | 0 | 0 | null | 1,433,385,918,000 | 1,433,385,918,000 | null | UTF-8 | Lean | false | false | 4,593 | lean | /-
Copyright (c) 2015 Haitao Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author : Haitao Zhang
-/
-- develop the concept of finite subgroups based on finsets so that the properties
-- can be used directly without translating from the set based theory first
... |
d1637ee07685c729ee7741333822b1aeb74e7824 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/order/complete_lattice_intervals.lean | 370a5b8330f7ca512d52765b9f9ea0a37689d8f7 | [
"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 | 6,015 | lean | /-
Copyright (c) 2022 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
import order.conditionally_complete_lattice.basic
import data.set.intervals.ord_connected
/-! # Subtypes of conditionally complete linear orders
> THIS FILE IS SY... |
1a4a6ca86b548300c8a5e47fafa9c69295df8cb2 | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/exists1.lean | d830f00ca5f7b394f211823200a7a986327994c8 | [
"Apache-2.0"
] | permissive | codyroux/lean0.1 | 1ce92751d664aacff0529e139083304a7bbc8a71 | 0dc6fb974aa85ed6f305a2f4b10a53a44ee5f0ef | refs/heads/master | 1,610,830,535,062 | 1,402,150,480,000 | 1,402,150,480,000 | 19,588,851 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 152 | lean | import Int.
variable a : Int
variable P : Int -> Int -> Bool
axiom H : P a a
theorem T : exists x : Int, P a a := exists_intro a H.
print environment 1. |
9cb65ffb43cffab9de19a4a2306c03d74ccc6fd1 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/ring_theory/local_properties.lean | 70b0e5931f8522755b00e70ac91bdff2c6cfc329 | [
"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 | 30,216 | lean | /-
Copyright (c) 2021 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import ring_theory.finite_type
import ring_theory.localization.at_prime
import ring_theory.localization.away
import ring_theory.localization.integer
import ring_theory.loca... |
a046cc2ce3139cc3903da66ec0bc3c2d0c26ea96 | 957a80ea22c5abb4f4670b250d55534d9db99108 | /tests/lean/run/inst_bug.lean | 2041c270d4323544f27fbf47483c5463451216b6 | [
"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 | 340 | lean | class inductive {u} is_equiv (A B : Type u) (f : A → B) : Type u
definition inverse (A B : Type*) (f : A → B) [H : is_equiv A B f] := Type*
definition foo (A : Type*) (B : A → Type*) (h : A → A) (g : Π(a : A), B a → B a)
[H : Π(a : A), is_equiv _ _ (g a)] (x : A) : Type* :=
inverse (B (h x)) (B (h x)) (g... |
6fa77a175a3dd1022a33320fca9f9cd6514705ae | 9028d228ac200bbefe3a711342514dd4e4458bff | /src/field_theory/tower.lean | b2c6c5966a46335618374b83eafbcb213ae4539b | [
"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 | 5,263 | lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import ring_theory.algebra_tower
import linear_algebra.matrix
/-!
# Tower of field extensions
In this file we prove the tower law for arbitrary extensions and finite extensi... |
0038555ab8d17fa673c9fb3e92fdda6ed142ff9d | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /tests/pkg/user_ext/UserExt/BlaExt.lean | 5284117fe934c6afb76aa37d99edd693f9d53a8d | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | EdAyers/lean4 | 57ac632d6b0789cb91fab2170e8c9e40441221bd | 37ba0df5841bde51dbc2329da81ac23d4f6a4de4 | refs/heads/master | 1,676,463,245,298 | 1,660,619,433,000 | 1,660,619,433,000 | 183,433,437 | 1 | 0 | Apache-2.0 | 1,657,612,672,000 | 1,556,196,574,000 | Lean | UTF-8 | Lean | false | false | 755 | lean | import Lean
open Lean
initialize blaExtension : SimplePersistentEnvExtension Name NameSet ←
registerSimplePersistentEnvExtension {
name := `blaExt
addEntryFn := NameSet.insert
addImportedFn := fun es => mkStateFromImportedEntries NameSet.insert {} es
}
syntax (name := insertBla) "insert_b... |
93091f41c0b6f25935cd3bbb2b01ebb45241aa30 | 86f6f4f8d827a196a32bfc646234b73328aeb306 | /examples/introduction/unnamed_174.lean | 82a06068234261a3c841de5eb197dbaa623b0579 | [] | no_license | jamescheuk91/mathematics_in_lean | 09f1f87d2b0dce53464ff0cbe592c568ff59cf5e | 4452499264e2975bca2f42565c0925506ba5dda3 | refs/heads/master | 1,679,716,410,967 | 1,613,957,947,000 | 1,613,957,947,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 230 | lean | import data.nat.parity
open nat
example : ∀ m n : nat, even n → even (m * n) :=
assume m n ⟨k, (hk : n = 2 * k)⟩,
have hmn : m * n = 2 * (m * k),
by rw [hk, mul_left_comm],
show ∃ l, m * n = 2 * l,
from ⟨_, hmn⟩ |
4a9ec00cab409566239c23c5c90a93c130541216 | 48eee836fdb5c613d9a20741c17db44c8e12e61c | /src/algebra/theories/semiring.lean | 508e8adb9d7e648f3051fe292d054fc2536c7bbd | [
"Apache-2.0"
] | permissive | fgdorais/lean-universal | 06430443a4abe51e303e602684c2977d1f5c0834 | 9259b0f7fb3aa83a9e0a7a3eaa44c262e42cc9b1 | refs/heads/master | 1,592,479,744,136 | 1,589,473,399,000 | 1,589,473,399,000 | 196,287,552 | 1 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 3,089 | lean | -- Copyright © 2019 François G. Dorais. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
import .basic
import .group
import .monoid
set_option default_priority 0
namespace algebra
signature semiring (α : Type*) :=
(mul : α → α → α)
(one : α)
(add : α → α → α)
(zero : α)
... |
8e09df77fb40d90ea85e0bd557712c568928d06a | bb31430994044506fa42fd667e2d556327e18dfe | /src/data/real/golden_ratio.lean | 8e9c3be8a18df1a9e971a76e57478c2c61119b7f | [
"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 | 5,674 | lean | /-
Copyright (c) 2020 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker, Alexey Soloyev, Junyan Xu
-/
import data.real.irrational
import data.nat.fib
import data.nat.prime_norm_num
import data.fin.vec_notation
import tactic.ring_exp
impo... |
802c7b3fff84e5d03d195574a43368bbf2479b1e | 0c1546a496eccfb56620165cad015f88d56190c5 | /library/init/category/alternative.lean | c63686e0712963d1051331a2f8ab1b3b7ac76ff1 | [
"Apache-2.0"
] | permissive | Solertis/lean | 491e0939957486f664498fbfb02546e042699958 | 84188c5aa1673fdf37a082b2de8562dddf53df3f | refs/heads/master | 1,610,174,257,606 | 1,486,263,620,000 | 1,486,263,620,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 788 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
prelude
import init.logic init.category.applicative
universe variables u v
class alternative (f : Type u → Type v) extends applicative f : Type (max u+1 v) ... |
2d75dd4846fb39d13ac82338641ba43473b4d267 | d5ecf6c46a2f605470a4a7724909dc4b9e7350e0 | /number_theory/pell.lean | 99ed81ebc4e9c06437e24059f2ee3dbd5f9dfec4 | [
"Apache-2.0"
] | permissive | MonoidMusician/mathlib | 41f79df478987a636b735c338396813d2e8e44c4 | 72234ef1a050eea3a2197c23aeb345fc13c08ff3 | refs/heads/master | 1,583,672,205,771 | 1,522,892,143,000 | 1,522,892,143,000 | 128,144,032 | 0 | 0 | Apache-2.0 | 1,522,892,144,000 | 1,522,890,892,000 | Lean | UTF-8 | Lean | false | false | 62,380 | 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 data.nat.prime data.nat.modeq
/-- The ring of integers adjoined with a square root of `d`.
These have the form `a + b √d` where `a b : ℤ`. Th... |
fb0c81fb02dd07499a027e85a29ccd05b8eb110d | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/lie/character.lean | 1d85a4465fa2ac2b924fb7f767e352f8524b0b39 | [
"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 | 2,382 | lean | /-
Copyright (c) 2021 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import algebra.lie.abelian
import algebra.lie.solvable
import linear_algebra.dual
/-!
# Characters of Lie algebras
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any change... |
43a3fe4bfff14f4b12b8e08a2bf2759a4e89c100 | e0f9ba56b7fedc16ef8697f6caeef5898b435143 | /src/logic/basic.lean | 01cf7ee746fb7d8f7e5baec39639a000336da510 | [
"Apache-2.0"
] | permissive | anrddh/mathlib | 6a374da53c7e3a35cb0298b0cd67824efef362b4 | a4266a01d2dcb10de19369307c986d038c7bb6a6 | refs/heads/master | 1,656,710,827,909 | 1,589,560,456,000 | 1,589,560,456,000 | 264,271,800 | 0 | 0 | Apache-2.0 | 1,589,568,062,000 | 1,589,568,061,000 | null | UTF-8 | Lean | false | false | 37,483 | 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
/-!
# Basic logic properties
This file is one of the earliest imports in mathlib.
## Implementation notes
Theorems tha... |
e73d37a166c4d17083420982808418f655aa15f6 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/linear_algebra/affine_space/ordered.lean | a282d1f4badc5976c6444f9d6fd1a90ad245c251 | [
"Apache-2.0"
] | permissive | waynemunro/mathlib | e3fd4ff49f4cb43d4a8ded59d17be407bc5ee552 | 065a70810b5480d584033f7bbf8e0409480c2118 | refs/heads/master | 1,693,417,182,397 | 1,634,644,781,000 | 1,634,644,781,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 15,938 | lean | /-
Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import linear_algebra.affine_space.midpoint
import algebra.module.ordered
import tactic.field_simp
/-!
# Ordered modules as affine spaces
In this file we de... |
4f04ff8646434e1fd1534a6036fd51e56a771648 | a537b538f2bea3181e24409d8a52590603d1ddd9 | /test/rewrite_search_vs_ring.lean | bd744ca941f4d57ff2223beb6e57e1efa6286422 | [] | no_license | rwbarton/lean-tidy | 6134813ded72b275d19d4d32514dba80c21708e3 | fe1125d32adb60decda7a77d0f679614ba9f6fbb | refs/heads/master | 1,585,549,718,705 | 1,538,120,619,000 | 1,538,120,624,000 | 150,864,330 | 0 | 0 | null | 1,538,225,790,000 | 1,538,225,790,000 | null | UTF-8 | Lean | false | false | 2,002 | lean | import tactic.ring
import tidy.rewrite_search
open tidy.rewrite_search.metric
open tidy.rewrite_search.strategy
open tidy.rewrite_search.tracer
namespace tidy.rewrite_search.vs_ring
@[suggest] private def use_arithmetic := `arithmetic
constants a b c d e : ℚ
lemma test3 : (a * (b + c)) * d = a * (b * d) + a * (c *... |
6199dd15eb2fc2722d8a4ab48a49799e64272a03 | aa3f8992ef7806974bc1ffd468baa0c79f4d6643 | /library/data/int/basic.lean | e6d48957240e12c61cd2420d6d193952a826c0a7 | [
"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 | 28,318 | lean | -- Copyright (c) 2014 Floris van Doorn. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Floris van Doorn, Jeremy Avigad
-- int.basic
-- =========
-- The integers, with addition, multiplication, and subtraction.
import data.nat.basic data.nat.order data.nat.sub ... |
967257a51fa29a4f7ee0a56cd7961d5f741afd7e | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/logic/relator.lean | 4806a5966e105359314a2bb17c22bac4425e894e | [
"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 | 4,261 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Relator for functions, pairs, sums, and lists.
-/
import tactic.reserved_notation
namespace relator
universe variables u₁ u₂ v₁ v₂
/- TODO(johoelzl):
* should we in... |
b264243dab14be889c55b8f26082004ccc5b1bb6 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /tests/lean/StxQuot.lean | 0af82cda0d06eef986279d90c424c03a5b2b95de | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | cipher1024/lean4 | 6e1f98bb58e7a92b28f5364eb38a14c8d0aae393 | 69114d3b50806264ef35b57394391c3e738a9822 | refs/heads/master | 1,642,227,983,603 | 1,642,011,696,000 | 1,642,011,696,000 | 228,607,691 | 0 | 0 | Apache-2.0 | 1,576,584,269,000 | 1,576,584,268,000 | null | UTF-8 | Lean | false | false | 4,494 | lean | import Lean
open Lean
open Lean.Elab
def run {α} [ToString α] : Unhygienic α → String := toString ∘ Unhygienic.run
#eval run `()
#eval run `(Nat.one)
#eval run `($Syntax.missing)
namespace Lean.Syntax
#eval run `($missing)
#eval run `($(missing))
#eval run `($(id Syntax.missing) + 1)
#eval run $ let id := Syntax.mis... |
46792ecacd7ee5258192fbb920d44f9162e76e57 | 61c3861020ef87c6c325fc3c3dcbabf5d6b07985 | /hit/trunc.lean | c9d89fce2fb176809c581f5c19326cb7cf302505 | [
"Apache-2.0"
] | permissive | jonas-frey/hott3 | a623be2959e8a713c03fa1b0f34bf76a561dfa87 | a944051b4eb5919bdc70978ee15fcbb48a824811 | refs/heads/master | 1,628,408,720,559 | 1,510,267,042,000 | 1,510,267,042,000 | 106,760,764 | 0 | 0 | null | 1,507,856,238,000 | 1,507,856,238,000 | null | UTF-8 | Lean | false | false | 5,969 | lean | /-
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
n-truncation of types.
Ported from Coq HoTT
-/
/- The hit n-truncation is primitive, declared in init.hit. -/
import types.sigma types.pointed
universes u v w
ho... |
5ddfc84ddb0a05c679f955db7b6a80093460f558 | cf39355caa609c0f33405126beee2739aa3cb77e | /library/init/meta/json.lean | 3892e33b5c6a6f5e5c4b260ed5b9e0603547a563 | [
"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 | 2,208 | lean | /-
Copyright (c) E.W.Ayers 2020. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: E.W.Ayers
-/
prelude
import init.data
import init.meta.float
meta inductive json : Type
| of_string : string → json
| of_int : int → json
| of_float : native.float → json
| of_bool : bool ... |
95b0d0d49183a1fd11ebf80bef44aeda882283fe | 1b8f093752ba748c5ca0083afef2959aaa7dace5 | /src/category_theory/enriched.lean | 71487f9f378022b03f8a4e9737598c648744b10f | [] | no_license | khoek/lean-category-theory | 7ec4cda9cc64a5a4ffeb84712ac7d020dbbba386 | 63dcb598e9270a3e8b56d1769eb4f825a177cd95 | refs/heads/master | 1,585,251,725,759 | 1,539,344,445,000 | 1,539,344,445,000 | 145,281,070 | 0 | 0 | null | 1,534,662,376,000 | 1,534,662,376,000 | null | UTF-8 | Lean | false | false | 1,206 | lean | import category_theory.limits
import category_theory.universal.continuous
import category_theory.universal.types
import category_theory.embedding
open category_theory.limits
universes u v
namespace category_theory
variables {C : Type u} [𝒞 : category.{u v} C]
variables (V : Type (v+1)) [𝒱 : large_category V]
... |
3f75afd68078234394647dc9549a732a572026ac | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/pnat/xgcd.lean | eadc47c825a899d719e40fbb5e679b946bfad25b | [
"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 | 13,728 | lean | /-
Copyright (c) 2019 Neil Strickland. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Neil Strickland
-/
import tactic.ring
import data.pnat.prime
/-!
# Euclidean algorithm for ℕ
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a correspo... |
8e68a5dc9321ad94151b5700dbf97684b0cef478 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/abelian/non_preadditive.lean | 13f11f13ec1a972f9cc81991aca09605fc38090a | [
"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 | 17,369 | lean | /-
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import category_theory.limits.shapes.finite_products
import category_theory.limits.shapes.kernels
import category_theory.limits.shapes.normal_mono.equalizers
import cat... |
ef631689960630f961fd0dee82d2da9ad0e88539 | 31f556cdeb9239ffc2fad8f905e33987ff4feab9 | /src/Init/Data/Nat/Basic.lean | ac5ff5584e0a75f6674d5b1fff0973127eb52f1e | [
"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 | 26,370 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Leonardo de Moura
-/
prelude
import Init.SimpLemmas
universe u
namespace Nat
@[specialize] def fold {α : Type u} (f : Nat → α → α) : (n : Nat) → (init : α) →... |
354d988559a1c0dba6f48478cb8e10c4e3e151a9 | e0e64c424bf126977aef10e58324934782979062 | /src/wk1/Exercises/groups.lean | aef0a130725a1d03e1a24705155ca93b6e2bf59f | [] | no_license | jamesa9283/LiaLeanTutor | 34e9e133a4f7dd415f02c14c4a62351bb9fd8c21 | c7ac1400f26eb2992f5f1ee0aaafb54b74665072 | refs/heads/master | 1,686,146,337,422 | 1,625,227,392,000 | 1,625,227,392,000 | 373,130,175 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,489 | lean | import tactic
/-!
# Groups
Definition and basic properties of a group.
-/
-- Technical note: We work in a namespace `xena` because Lean already has groups.
namespace xena
-- Now our definition of a group will really be called `xena.group`.
/-
## Definition of a group
The `group` class will extend `has_mul`, `has_on... |
7ef348c185bbaca73c2e50ac9eea84a5f56a01db | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/ring_theory/jacobson.lean | a7e37cf47d1cdf81ebec78929416e4e0a9329152 | [
"Apache-2.0"
] | permissive | dupuisf/mathlib | 62de4ec6544bf3b79086afd27b6529acfaf2c1bb | 8582b06b0a5d06c33ee07d0bdf7c646cae22cf36 | refs/heads/master | 1,669,494,854,016 | 1,595,692,409,000 | 1,595,692,409,000 | 272,046,630 | 0 | 0 | Apache-2.0 | 1,592,066,143,000 | 1,592,066,142,000 | null | UTF-8 | Lean | false | false | 4,579 | lean | /-
Copyright (c) 2020 Devon Tuma. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Devon Tuma
-/
import data.mv_polynomial
import ring_theory.ideals
import ring_theory.ideal_operations
import ring_theory.jacobson_ideal
/-!
# Jacobson Rings
The following conditions are ... |
15ee7f82c42d1ffd0772dd22d8e617797b5d0c92 | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /stage0/src/Lean/Elab/DeclUtil.lean | 848bffe5d2212304b90ac1780dfa2313c9bdc696 | [
"Apache-2.0"
] | permissive | collares/lean4 | 861a9269c4592bce49b71059e232ff0bfe4594cc | 52a4f535d853a2c7c7eea5fee8a4fa04c682c1ee | refs/heads/master | 1,691,419,031,324 | 1,618,678,138,000 | 1,618,678,138,000 | 358,989,750 | 0 | 0 | Apache-2.0 | 1,618,696,333,000 | 1,618,696,333,000 | null | UTF-8 | Lean | false | false | 3,826 | 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, Sebastian Ullrich
-/
import Lean.Meta.ExprDefEq
namespace Lean.Meta
def forallTelescopeCompatibleAux {α} (k : Array Expr → Expr → Expr → MetaM α) : Nat → Ex... |
f7d76099181127cd7e4ab80b46b57d751021746f | f4bff2062c030df03d65e8b69c88f79b63a359d8 | /src/game/functions/composition_surjective.lean | 0cb1e3dcacd944432d2af7b377b50793cd811d1e | [
"Apache-2.0"
] | permissive | adastra7470/real-number-game | 776606961f52db0eb824555ed2f8e16f92216ea3 | f9dcb7d9255a79b57e62038228a23346c2dc301b | refs/heads/master | 1,669,221,575,893 | 1,594,669,800,000 | 1,594,669,800,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 478 | lean | import data.real.basic
open function
/-
# Chapter 6 : Functions
## Level 6
A classical result in composition of functions.
Now going the other way around.
-/
/- Lemma
If composition of $f$ and $g$ is surjective, then $g$ is injective.
-/
theorem composition_surjective
(X Y Z : set ℝ) (f : X → Y) (g : Y → Z) : ... |
84f8dd55fddfc2da16b668b080fc710d9c495309 | efce24474b28579aba3272fdb77177dc2b11d7aa | /src/homotopy_theory/topological_spaces/smush.lean | 626e8b21e8cb19c5ebef87dd646dba520218d1aa | [
"Apache-2.0"
] | permissive | rwbarton/lean-homotopy-theory | cff499f24268d60e1c546e7c86c33f58c62888ed | 39e1b4ea1ed1b0eca2f68bc64162dde6a6396dee | refs/heads/lean-3.4.2 | 1,622,711,883,224 | 1,598,550,958,000 | 1,598,550,958,000 | 136,023,667 | 12 | 6 | Apache-2.0 | 1,573,187,573,000 | 1,528,116,262,000 | Lean | UTF-8 | Lean | false | false | 8,421 | lean | import algebra.module
import topology.instances.real
import tactic.ring
/-
Construction of a homeomorphism of pairs
(Dⁿ, Sⁿ⁻¹) ⊗ (I, {0}) ≅ (Dⁿ, ∅) ⊗ (I, {0}).
See [tom Dieck, Algebraic Topology, Example 2.3.6].
Rather than specialize in ℝⁿ, we work in an arbitrary normed ℝ-linear
space V. Normed linear spaces are n... |
8cd7e8858c62ac523697c26583bba5ef17fcd949 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/analysis/normed_space/pi_Lp.lean | eb189829977ab110d5f70cc7e42df1cb3e3db542 | [
"Apache-2.0"
] | permissive | stjordanis/mathlib | 51e286d19140e3788ef2c470bc7b953e4991f0c9 | 2568d41bca08f5d6bf39d915434c8447e21f42ee | refs/heads/master | 1,631,748,053,501 | 1,627,938,886,000 | 1,627,938,886,000 | 228,728,358 | 0 | 0 | Apache-2.0 | 1,576,630,588,000 | 1,576,630,587,000 | null | UTF-8 | Lean | false | false | 21,950 | 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 analysis.mean_inequalities
import analysis.normed_space.inner_product
/-!
# `L^p` distance on finite products of metric spaces
Given finitely many metri... |
8344d1e3471d1b241ff439d01643b57f37774569 | b70031c8e2c5337b91d7e70f1e0c5f528f7b0e77 | /src/ring_theory/algebra_tower.lean | face41bcd26755c3d677a2a9aa68a37f84cc35da | [
"Apache-2.0"
] | permissive | molodiuc/mathlib | cae2ba3ef1601c1f42ca0b625c79b061b63fef5b | 98ebe5a6739fbe254f9ee9d401882d4388f91035 | refs/heads/master | 1,674,237,127,059 | 1,606,353,533,000 | 1,606,353,533,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 20,349 | lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import algebra.invertible
import ring_theory.adjoin
import linear_algebra.basis
import algebra.algebra.basic
/-!
# Towers of algebras
We set up the basic theory of algebra t... |
ba67bb831dc928bdc8d5f942b8d8b8f054b352bd | 206422fb9edabf63def0ed2aa3f489150fb09ccb | /src/topology/subset_properties.lean | e93f6de7e20ce8b2f082d2b6d41590e896b481b6 | [
"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 | 69,384 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Yury Kudryashov
-/
import topology.bases
import data.finset.order
/-!
# Properties of subsets of topological spaces
In this file we define various pro... |
999bfea93a972abe2c9ef40b8b75eb00da355c99 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/computability/tm_computable.lean | 45b5ada4d01335258a108cc0d7a20716477036f4 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 11,716 | lean | /-
Copyright (c) 2020 Pim Spelier, Daan van Gent. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Pim Spelier, Daan van Gent
-/
import computability.encoding
import computability.turing_machine
import data.polynomial.basic
import data.polynomial.eval
/-!
# Computable ... |
4908fbbcea3cfd77ddddc968c889da437dc359be | 92b50235facfbc08dfe7f334827d47281471333b | /library/data/real/division.lean | 08ade03eea1969859969791b51b2ce1e0acfb4bd | [
"Apache-2.0"
] | permissive | htzh/lean | 24f6ed7510ab637379ec31af406d12584d31792c | d70c79f4e30aafecdfc4a60b5d3512199200ab6e | refs/heads/master | 1,607,677,731,270 | 1,437,089,952,000 | 1,437,089,952,000 | 37,078,816 | 0 | 0 | null | 1,433,780,956,000 | 1,433,780,955,000 | null | UTF-8 | Lean | false | false | 22,620 | lean | /-
Copyright (c) 2015 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Robert Y. Lewis
The real numbers, constructed as equivalence classes of Cauchy sequences of rationals.
This construction follows Bishop and Bridges (1985).
At this point, we no longer... |
210f8f804ad139688770508006f52f3e199b4f4c | e514e8b939af519a1d5e9b30a850769d058df4e9 | /src/tactic/rewrite_search/discovery/suggest.lean | 02140982169bff81ba903ce57217364b3e4889dd | [] | no_license | semorrison/lean-rewrite-search | dca317c5a52e170fb6ffc87c5ab767afb5e3e51a | e804b8f2753366b8957be839908230ee73f9e89f | refs/heads/master | 1,624,051,754,485 | 1,614,160,817,000 | 1,614,160,817,000 | 162,660,605 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 2,134 | lean | import lib.tactic
import .bundle
namespace tactic.rewrite_search.discovery
open tactic
private meta def suggest_fail {α : Type} : format → tactic α := atrr_fail "suggest"
-- Reads the name of a list/single annotated with `[suggest]`.
meta def read_suggestion (n : name) : tactic (list name) := do
n ← mk_const n,
... |
59d41fca41f99ccb25a95750d49e52b646ac56a0 | a726f88081e44db9edfd14d32cfe9c4393ee56a4 | /src/game/world7/level6.lean | b879e7d5bda558bea67f65d26b7bf49318fb7d0c | [] | no_license | b-mehta/natural_number_game | 80451bf10277adc89a55dbe8581692c36d822462 | 9faf799d0ab48ecbc89b3d70babb65ba64beee3b | refs/heads/master | 1,598,525,389,186 | 1,573,516,674,000 | 1,573,516,674,000 | 217,339,684 | 0 | 0 | null | 1,571,933,100,000 | 1,571,933,099,000 | null | UTF-8 | Lean | false | false | 1,166 | lean | /-
# Advanced proposition world.
## Level 6: Or, and the `left` and `right` tactics.
`P ∨ Q` means "$P$ or $Q$". So to prove it, you
need to choose one of `P` or `Q`, and prove that one.
If `⊢ P ∨ Q` is your goal, then `left` changes this
goal to `⊢ P`, and `right` changes it to `⊢ Q`.
Note that you can take a wron... |
0f6c68afaf6a49a329046c6d30cda2f7dfa0dc05 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/data/list/zip.lean | 3a54aaf338928034239a3edfe1bfa515787e5c4a | [
"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 | 7,748 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Kenny Lau
-/
import data.list.basic
universes u v w z
variables {α : Type u} {β : Type v} {γ : Type w} {δ : Type z}
open nat
namespace list
/- zip & unzip -/
@[si... |
a41cd690e380828c5460a2d39b0abd94ef6a72d0 | d8820d2c92be8052d13f9c8f8c483a6e15c5f566 | /src/M40002/M40002_C6.lean | 70072e3e765cc5e765ba693f34615d1eb3c78cdc | [] | no_license | JasonKYi/M4000x_LEAN_formalisation | 4a19b84f6d0fe2e214485b8532e21cd34996c4b1 | 6e99793f2fcbe88596e27644f430e46aa2a464df | refs/heads/master | 1,599,755,414,708 | 1,589,494,604,000 | 1,589,494,604,000 | 221,759,483 | 8 | 1 | null | 1,589,494,605,000 | 1,573,755,201,000 | Lean | UTF-8 | Lean | false | false | 4,048 | lean | -- M40002 (Analysis I) Chapter 6. Differentiation
import M40002.M40002_C5
namespace M40002
-- Definition of a function being differntiable at a point
def is_derivative (f : ℝ → ℝ) (a l : ℝ) := func_converges_to (λ x : ℝ, (f x - f a) / (x - a)) a l
def differentiable_at (f : ℝ → ℝ) (a : ℝ) := ∃ l : ℝ, is_derivative f... |
b4f0469574ff175cee5fdd613680370fd1ad2490 | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /tests/lean/run/measurable.lean | 95b6c9af456101b6d9fe4ac7e7d8142b4d344408 | [
"Apache-2.0"
] | permissive | davidmueller13/lean | 65a3ed141b4088cd0a268e4de80eb6778b21a0e9 | c626e2e3c6f3771e07c32e82ee5b9e030de5b050 | refs/heads/master | 1,611,278,313,401 | 1,444,021,177,000 | 1,444,021,177,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 207 | lean | open prod nat
example (a b : nat) : size_of (a, true, bool.tt, (λ c d : nat, c + d), option.some b) = a + b :=
rfl
example : size_of (pair (pair (pair 2 true) (λ a : nat, a)) (option.some 3)) = 5 :=
rfl
|
b5983b527e135730c9b17acccc45a29aa48e0bcd | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/combinatorics/simple_graph/regularity/equitabilise.lean | 35531993e576742b319a403ce01e96c61714083f | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 10,801 | lean | /-
Copyright (c) 2022 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
import order.partition.equipartition
/-!
# Equitabilising a partition
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file ... |
874f00f1238ae4a1e8b40618e47d08b15ceb956f | 4950bf76e5ae40ba9f8491647d0b6f228ddce173 | /src/data/real/irrational.lean | 233fd9b5b02fdc45078931296e9a154974a488fb | [
"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 | 9,303 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Yury Kudryashov.
-/
import data.real.basic
import data.rat.sqrt
import ring_theory.int.basic
import data.polynomial.eval... |
974ed711a38a27e634fe321ae74a4441881cb48e | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/blast_cc7.lean | eff36e900455f28e136c24d65dda8d220699582f | [
"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 | 527 | lean | set_option blast.strategy "cc"
example (a b c d : Prop)
[d₁ : decidable a] [d₂ : decidable b] [d₃ : decidable c] [d₄ : decidable d]
: (a ↔ b) → (c ↔ d) → ((if (a ∧ c) then true else false) ↔ (if (b ∧ d) then true else false)) :=
by blast
example (a b c d : Prop) (x y z : nat)
[d₁ : decidable a] [d₂ : dec... |
517496dc8ede3942683a0589227e163c9852519b | b3fced0f3ff82d577384fe81653e47df68bb2fa1 | /src/category_theory/limits/limits.lean | f47249a07ce4dff6beb3487a9ff19bfdc6b23ac9 | [
"Apache-2.0"
] | permissive | ratmice/mathlib | 93b251ef5df08b6fd55074650ff47fdcc41a4c75 | 3a948a6a4cd5968d60e15ed914b1ad2f4423af8d | refs/heads/master | 1,599,240,104,318 | 1,572,981,183,000 | 1,572,981,183,000 | 219,830,178 | 0 | 0 | Apache-2.0 | 1,572,980,897,000 | 1,572,980,896,000 | null | UTF-8 | Lean | false | false | 36,697 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Mario Carneiro, Scott Morrison, Floris van Doorn
-/
import category_theory.whiskering
import category_theory.yoneda
import category_theory.limits.cones
import category_the... |
4cf563b2c6dda94d3e45314d8c1aeaab0f3eaaa9 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/field_theory/galois.lean | bda2410f5a67cc4165467b159608b27c79b7af31 | [
"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 | 18,437 | 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.normal
import field_theory.primitive_element
import field_theory.fixed
import ring_theory.power_basis
import group_... |
600517e2169a03f72af0a785fc6001b8ad41f344 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/analysis/calculus/darboux.lean | abd969a7dac0bcacd41f6241cb1986c20f6292b8 | [
"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 | 4,818 | lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import analysis.calculus.mean_value
/-!
# Darboux's theorem
In this file we prove that the derivative of a differentiable function on an interval takes all
interm... |
58d5a0322a7046961a85a842625cd03e2e2558d6 | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/algebra/group/hom_instances.lean | edb9f6f1c2d25c78f39302cc409f4f2fb0d52878 | [
"Apache-2.0"
] | permissive | ayush1801/mathlib | 78949b9f789f488148142221606bf15c02b960d2 | ce164e28f262acbb3de6281b3b03660a9f744e3c | refs/heads/master | 1,692,886,907,941 | 1,635,270,866,000 | 1,635,270,866,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,856 | lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Kevin Buzzard, Scott Morrison, Johan Commelin, Chris Hughes,
Johannes Hölzl, Yury Kudryashov
-/
import algebra.group_power.basic
/-!
# Instances on spaces of monoid... |
b9cd3a757b2b88e0906e4306cbdc114ca2d7a026 | 5fbbd711f9bfc21ee168f46a4be146603ece8835 | /lean/natural_number_game/multiplication/5.lean | 6ef58b2844900f93d56f4bcf379852c5ecdc035c | [
"LicenseRef-scancode-warranty-disclaimer"
] | no_license | goedel-gang/maths | 22596f71e3fde9c088e59931f128a3b5efb73a2c | a20a6f6a8ce800427afd595c598a5ad43da1408d | refs/heads/master | 1,623,055,941,960 | 1,621,599,441,000 | 1,621,599,441,000 | 169,335,840 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 165 | lean | lemma mul_assoc (a b c : mynat) : (a * b) * c = a * (b * c) :=
induction c with n hn,
repeat {rw mul_zero},
repeat {rw mul_succ},
rw hn,
rwa mul_add,
end
|
9f8c38536aa8643fd5a25b1ee59ff7134d977614 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/category_theory/preadditive/additive_functor.lean | 5c510d005408d2fb192fecb9c31771df0b68ada9 | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 5,217 | lean | /-
Copyright (c) 2021 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz, Scott Morrison
-/
import category_theory.preadditive
import category_theory.limits.shapes.biproducts
/-!
# Additive Functors
A functor between two preadditive categories is c... |
dc6cad500c70eb57b2bf6a86cd14dd892761b7ac | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/linear_algebra/finsupp_vector_space.lean | 86698215cc2f0e089f66923dacd75f2a487b6b30 | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 7,449 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import linear_algebra.dimension
import linear_algebra.finite_dimensional
import linear_algebra.std_basis
/-!
# Linear structures on function with finite support `ι ... |
f0e421415fa0c0a82b37f8a89a80a31d18bead1f | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/topology/sequences_auto.lean | 7f9ba753f806e5d89617abebb827cedf36ee6b56 | [] | 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 | 13,389 | lean | /-
Copyright (c) 2018 Jan-David Salchow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jan-David Salchow, Patrick Massot
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.topology.bases
import Mathlib.topology.subset_properties
import Mathl... |
34332643061cbea3ab28b2294b7ea8f809880f59 | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/complex/basic.lean | 68677207c9992bd5a34b9b8c5fa206baec34f3db | [
"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 | 26,704 | lean | /-
Copyright (c) 2017 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Mario Carneiro
-/
import data.real.sqrt
/-!
# The complex numbers
The complex numbers are modelled as ℝ^2 in the obvious way and it is shown that they form a field
of c... |
f1748f0726fd0899383ca24657581d5246c16cf5 | 1a61aba1b67cddccce19532a9596efe44be4285f | /library/data/real/complete.lean | 20d9fa70b9614b159c2cd405043bdeb416b1641e | [
"Apache-2.0"
] | permissive | eigengrau/lean | 07986a0f2548688c13ba36231f6cdbee82abf4c6 | f8a773be1112015e2d232661ce616d23f12874d0 | refs/heads/master | 1,610,939,198,566 | 1,441,352,386,000 | 1,441,352,494,000 | 41,903,576 | 0 | 0 | null | 1,441,352,210,000 | 1,441,352,210,000 | null | UTF-8 | Lean | false | false | 33,621 | lean | /-
Copyright (c) 2015 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Robert Y. Lewis
The real numbers, constructed as equivalence classes of Cauchy sequences of rationals.
This construction follows Bishop and Bridges (1985).
At this point, we no longer... |
ed99d427893e8d4bb362cc42ed3c516f91b046e3 | 969dbdfed67fda40a6f5a2b4f8c4a3c7dc01e0fb | /src/geometry/euclidean/basic.lean | ba7c64e2313942a1be5a2c35b41f4d5ef6d5e4fb | [
"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 | 45,259 | lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Joseph Myers.
-/
import analysis.normed_space.inner_product
import algebra.quadratic_discriminant
import analysis.normed_space.add_torsor
import data.matrix.notation
import linear_algebra... |
6bfd6f768356abe11adafe3e1d340e7da1dc6c33 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/category/basic.lean | 6a119b1d4800e529053e69ff4b0a7a40a0f26299 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 11,073 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stephen Morgan, Scott Morrison, Johannes Hölzl, Reid Barton
-/
import combinatorics.quiver.basic
/-!
# Categories
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this fil... |
021ef6f872ec6830cd1574366b21203f62c009ec | 46125763b4dbf50619e8846a1371029346f4c3db | /src/linear_algebra/basic.lean | 81dff4c3ad682182be78ebf78076267b1a350cd7 | [
"Apache-2.0"
] | permissive | thjread/mathlib | a9d97612cedc2c3101060737233df15abcdb9eb1 | 7cffe2520a5518bba19227a107078d83fa725ddc | refs/heads/master | 1,615,637,696,376 | 1,583,953,063,000 | 1,583,953,063,000 | 246,680,271 | 0 | 0 | Apache-2.0 | 1,583,960,875,000 | 1,583,960,875,000 | null | UTF-8 | Lean | false | false | 74,515 | 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
-/
import algebra.pi_instances data.finsupp data.equiv.algebra order.order_iso
/-!
# Linear algebra
This file defines the basics of lin... |
7689f02ba476fdd28bd3ae2e17dd22a0980a77b1 | e5169dbb8b1bea3ec2a32737442bc91a4a94b46a | /library/data/list/comb.lean | d3c47c565ad75bfe13a810cef54a97cb07992278 | [
"Apache-2.0"
] | permissive | pazthor/lean | 733b775e3123f6bbd2c4f7ccb5b560b467b76800 | c923120db54276a22a75b12c69765765608a8e76 | refs/heads/master | 1,610,703,744,289 | 1,448,419,395,000 | 1,448,419,703,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 21,429 | lean | /-
Copyright (c) 2015 Leonardo de Moura. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Haitao Zhang, Floris van Doorn
List combinators.
-/
import data.list.basic data.equiv
open nat prod decidable function helper_tactics algebra
namespace list
var... |
b9f23c909a065eac7d21d7b41338c965e0f88ac5 | f4bff2062c030df03d65e8b69c88f79b63a359d8 | /src/game/max/level09.lean | adb160a5bac49a9ac47c345e8140e11abd882a16 | [
"Apache-2.0"
] | permissive | adastra7470/real-number-game | 776606961f52db0eb824555ed2f8e16f92216ea3 | f9dcb7d9255a79b57e62038228a23346c2dc301b | refs/heads/master | 1,669,221,575,893 | 1,594,669,800,000 | 1,594,669,800,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 764 | lean | import game.max.level08 -- hide
open_locale classical -- hide
noncomputable theory -- hide
namespace xena -- hide
/-
# Chapter ? : Max
## Level 9
We've done `max_le_iff`; here is `le_max_iff`.
-/
/- Lemma
If $a$, $b$, $c$ are real numbers,
then $a\leq\max(b,c)$ iff ($a\leq b$ or $a\leq c$).
-/
theorem le_max_i... |
6b3e3d2f345cf40c20051952d247069739b90d51 | f1a12d4db0f46eee317d703e3336d33950a2fe7e | /lia/cooper/preprocess.lean | c335aa6b14cacb66227de3a46c9209a064ed9313 | [
"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 | 8,098 | lean | import .correctness ...common.tauto ...common.algebra ...common.int ...common.tactic
open lia tactic
meta instance : has_reflect (fm atom) :=
by mk_has_reflect_instance
meta def get_lhs : tactic expr :=
do `(%%lhs = _) ← target, return lhs
meta def get_rhs : tactic expr :=
do `(_ = %%rhs) ← target, return rhs
... |
2252a940ed80ad8d4fafd47605df7c4e3ceac16e | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/tactic/fresh_names.lean | 2406d6040176977de256f77e115e96d5b10581f3 | [
"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 | 5,087 | 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 data.sum
import meta.rb_map
import tactic.dependencies
/-!
# Tactics for giving hypotheses fresh names
When introducing hypotheses, we often want to make su... |
e2fbfc405f85b2ab50acf356ae4c4a83545f375a | 9cb9db9d79fad57d80ca53543dc07efb7c4f3838 | /src/polyhedral_lattice/pseudo_normed_group.lean | c934e1b15eaeee5ef4106d256cf7bf971d75dd27 | [] | no_license | mr-infty/lean-liquid | 3ff89d1f66244b434654c59bdbd6b77cb7de0109 | a8db559073d2101173775ccbd85729d3a4f1ed4d | refs/heads/master | 1,678,465,145,334 | 1,614,565,310,000 | 1,614,565,310,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,552 | lean | import polyhedral_lattice.basic
import normed_group.pseudo_normed_group
import pseudo_normed_group.with_Tinv
import for_mathlib.topological_group
import for_mathlib.topology
import facts
noncomputable theory
open_locale nnreal
namespace polyhedral_lattice
open pseudo_normed_group normed_group
variables (Λ : Type*... |
e902f12545f5e74023a8e042cca8a97ccebae192 | 43390109ab88557e6090f3245c47479c123ee500 | /src/M1P2/sheet_6.lean | 4014cb6291af1824ee45b476552830a41a368fc3 | [
"Apache-2.0"
] | permissive | Ja1941/xena-UROP-2018 | 41f0956519f94d56b8bf6834a8d39473f4923200 | b111fb87f343cf79eca3b886f99ee15c1dd9884b | refs/heads/master | 1,662,355,955,139 | 1,590,577,325,000 | 1,590,577,325,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,768 | lean | import algebra.order data.fintype group_theory.subgroup data.set.basic data.rat
variables {G : Type*} [group G]
variables (H K : set G)
variables [is_subgroup H] [is_subgroup K]
definition is_cyclic (G : Type*) [group G] := ∃ x : G, gpowers x = set.univ
-- 1. Let G be a group. For each of the following statements, sa... |
767c92ff7b1cbb038d0e5da64f08293fc55f3f3a | e151e9053bfd6d71740066474fc500a087837323 | /src/hott/cubical/square.lean | 138ca600e9552d55deea4556fd4365493cd21821 | [
"Apache-2.0"
] | permissive | daniel-carranza/hott3 | 15bac2d90589dbb952ef15e74b2837722491963d | 913811e8a1371d3a5751d7d32ff9dec8aa6815d9 | refs/heads/master | 1,610,091,349,670 | 1,596,222,336,000 | 1,596,222,336,000 | 241,957,822 | 0 | 0 | Apache-2.0 | 1,582,222,839,000 | 1,582,222,838,000 | null | UTF-8 | Lean | false | false | 38,309 | lean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Jakob von Raumer
Squares in a type
-/
import hott.types.eq
universes u v w
hott_theory
namespace hott
open eq hott.equiv hott.is_equiv
namespace eq
variables... |
7ecf576bfd029e5e970a864e0f86219f5ac79c13 | 432d948a4d3d242fdfb44b81c9e1b1baacd58617 | /src/linear_algebra/bilinear_form.lean | a643f5354a5edce0717699a7a805566211b4c042 | [
"Apache-2.0"
] | permissive | JLimperg/aesop3 | 306cc6570c556568897ed2e508c8869667252e8a | a4a116f650cc7403428e72bd2e2c4cda300fe03f | refs/heads/master | 1,682,884,916,368 | 1,620,320,033,000 | 1,620,320,033,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 63,069 | lean | /-
Copyright (c) 2018 Andreas Swerdlow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andreas Swerdlow, Kexing Ying
-/
import linear_algebra.matrix
import linear_algebra.tensor_product
import linear_algebra.nonsingular_inverse
/-!
# Bilinear form
This file defines ... |
e9fa142737441e8d7dcbb1d46fb8b21703ca34d0 | 07c6143268cfb72beccd1cc35735d424ebcb187b | /src/topology/algebra/group_completion.lean | 766fd8cba47509cf599caa6737dd8d3ffec94f0b | [
"Apache-2.0"
] | permissive | khoek/mathlib | bc49a842910af13a3c372748310e86467d1dc766 | aa55f8b50354b3e11ba64792dcb06cccb2d8ee28 | refs/heads/master | 1,588,232,063,837 | 1,587,304,803,000 | 1,587,304,803,000 | 176,688,517 | 0 | 0 | Apache-2.0 | 1,553,070,585,000 | 1,553,070,585,000 | null | UTF-8 | Lean | false | false | 4,157 | 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
Completion of topological groups:
-/
import topology.uniform_space.completion topology.algebra.uniform_group
noncomputable theory
section group
open un... |
f126b9124459c9c9bfc43ee7ad5939e05206a19a | 43390109ab88557e6090f3245c47479c123ee500 | /src/M3P14/kronecker_sym.lean | e099708def0801d4d9d71b7e52c46e4432a1f775 | [
"Apache-2.0"
] | permissive | Ja1941/xena-UROP-2018 | 41f0956519f94d56b8bf6834a8d39473f4923200 | b111fb87f343cf79eca3b886f99ee15c1dd9884b | refs/heads/master | 1,662,355,955,139 | 1,590,577,325,000 | 1,590,577,325,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,009 | lean | /- Generalisation of the Jacobi symbol which is itself a generalisation of the Legendre symbol
ROADMAP:
- Write the mathematical definition of the Kronecker symbol
- Write the algorithm that computes any kronecker symbol a b
- Prove the 2 above definitions are equal
- Prove the relationship between th... |
794a57c2cef5a5191d2f8858babcd35e6e524b53 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/combinatorics/quiver/arborescence.lean | 72b384ba9854bae94a329cd1e4b487c4e7d81e9f | [
"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 | 4,872 | lean | /-
Copyright (c) 2021 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn
-/
import order.well_founded
import data.nat.basic
import combinatorics.quiver.subquiver
import combinatorics.quiver.path
/-!
# Arborescences
A quiver `V` is an arborescence (... |
fd89cb5b01dc199bb586941d405ca9121ba3de31 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/order/ideal.lean | f5a9afc2dca0ad94196010cb5a0225b0164a075e | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 16,388 | lean | /-
Copyright (c) 2020 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn
-/
import logic.encodable.basic
import order.atoms
import order.upper_lower.basic
/-!
# Order ideals, cofinal sets, and the Rasiowa–Sikorski lemma
> THIS FILE IS SYNCHRONIZED ... |
edeb66fb0e04a52c9ddf331bdf6a0d4b2b741922 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/ring_theory/valuation/integral.lean | 50ed4e6f915fe6fae54242fadc3dcd48d4bb5652 | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 2,103 | lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import ring_theory.integrally_closed
import ring_theory.valuation.integers
/-!
# Integral elements over the ring of integers of a valution
The ring of integers is integrally... |
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