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values | content stringlengths 3 6.12M |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
5b8044ca493121e51bce984b03c8cfc895c9eab9 | 57fdc8de88f5ea3bfde4325e6ecd13f93a274ab5 | /data/real/cau_seq.lean | f39d51d814eb4da03b2b59883c7bec6768c46d98 | [
"Apache-2.0"
] | permissive | louisanu/mathlib | 11f56f2d40dc792bc05ee2f78ea37d73e98ecbfe | 2bd5e2159d20a8f20d04fc4d382e65eea775ed39 | refs/heads/master | 1,617,706,993,439 | 1,523,163,654,000 | 1,523,163,654,000 | 124,519,997 | 0 | 0 | Apache-2.0 | 1,520,588,283,000 | 1,520,588,283,000 | null | UTF-8 | Lean | false | false | 19,971 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
A basic theory of Cauchy sequences, used in the construction of the reals.
Where applicable, lemmas that will be reused in other contexts have
been stated in extra gene... |
1fda3dc56f2b539575a6953852aa16222b80af81 | 02005f45e00c7ecf2c8ca5db60251bd1e9c860b5 | /src/linear_algebra/basis.lean | 188e73be1e37f049b68f496eb27c3e680c1873a8 | [
"Apache-2.0"
] | permissive | anthony2698/mathlib | 03cd69fe5c280b0916f6df2d07c614c8e1efe890 | 407615e05814e98b24b2ff322b14e8e3eb5e5d67 | refs/heads/master | 1,678,792,774,873 | 1,614,371,563,000 | 1,614,371,563,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 20,659 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Alexander Bentkamp
-/
import linear_algebra.linear_independent
import linear_algebra.projection
import linear_algebra.linear_pmap
import data.fintype.ca... |
7d71d2c1d530fcfa057a4bdb212fea2183156099 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/1681.lean | 70db944cf01ec5479463713456664abd5700798f | [
"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 | 326 | lean | def prod.foo (s : bool × bool) (fst : bool) : bool × bool :=
match s with
(a, b) := (fst, b)
end
variable s : bool × bool
#check prod.foo s
#check prod.foo s tt
#check s.foo
#check s.foo tt
def prod.foo2 {α β} (s : α × β) (fst : α) : α × β :=
match s with
(a, b) := (fst, b)
end
#check s.foo2
#check s.foo2 tt
|
b512bf4c44b778a5434db800c711e27e52c62c66 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/sites/pretopology.lean | 8a3af8eeec0c79d5c3925b2040406547f90f9d11 | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,643 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.category_theory.sites.grothendieck
import Mathlib.PostPort
universes v u l
namespace Mathlib... |
4980570071b9e96b112ca66968ce85d0fb28bff9 | f083c4ed5d443659f3ed9b43b1ca5bb037ddeb58 | /tactic/basic.lean | e34e5e7f3c9c95d642fe42243f20fccdeea91770 | [
"Apache-2.0"
] | permissive | semorrison/mathlib | 1be6f11086e0d24180fec4b9696d3ec58b439d10 | 20b4143976dad48e664c4847b75a85237dca0a89 | refs/heads/master | 1,583,799,212,170 | 1,535,634,130,000 | 1,535,730,505,000 | 129,076,205 | 0 | 0 | Apache-2.0 | 1,551,697,998,000 | 1,523,442,265,000 | Lean | UTF-8 | Lean | false | false | 18,585 | 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
-/
import data.dlist.basic category.basic
namespace name
meta def deinternalize_field : name → name
| (name.mk_string s name.anonymous) :=... |
ef766e2bcccc2adffda2a24388073abfce206146 | 947b78d97130d56365ae2ec264df196ce769371a | /tests/lean/run/eval_unboxed_const.lean | 2229dacb8255a9fd7fcf9c1936043557d5f5fb57 | [
"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 | 480 | lean | import Lean
new_frontend
open Lean
def c1 : Bool := true
unsafe def tst1 : CoreM Unit := do
let env ← getEnv;
let v := env.evalConst Bool `c1;
IO.println v
#eval tst1 -- outputs incorrect value (ok false). Reason: the unboxed value `true` is `1`, but the boxed `false` value is also `1`.
def c2 : Bool := false
uns... |
6d9e7cd775f3862c6f74412ff779139152e267a6 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/set_theory/cardinal/finite.lean | 7e1708e1a028e65684a8c57323e1969529c91c59 | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 3,342 | lean | /-
Copyright (c) 2021 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import data.zmod.defs
import set_theory.cardinal.basic
/-!
# Finite Cardinality Functions
## Main Definitions
* `nat.card α` is the cardinality of `α` as a natural... |
1c88715723a6864d99a1c1812de81235de9b42dc | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/data/set/intervals/unordered_interval.lean | 9461ef2701ef57d1a39dce79b3dc33e57d20836a | [
"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 | 10,354 | lean | /-
Copyright (c) 2020 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou
-/
import order.bounds
import data.set.intervals.image_preimage
/-!
# Intervals without endpoints ordering
In any decidable linear order `α`, we define the set of elemen... |
0b325fd82ce537a692fc165275d2255b6e3237bc | 6dc0c8ce7a76229dd81e73ed4474f15f88a9e294 | /tests/lean/run/getline_crash.lean | a84b5db01ba151f3cb861b3be2289624b5312e26 | [
"Apache-2.0"
] | permissive | williamdemeo/lean4 | 72161c58fe65c3ad955d6a3050bb7d37c04c0d54 | 6d00fcf1d6d873e195f9220c668ef9c58e9c4a35 | refs/heads/master | 1,678,305,356,877 | 1,614,708,995,000 | 1,614,708,995,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,265 | lean |
def tstGetLine (str : String) : IO Unit := do
let path := "tmp_file";
IO.FS.withFile path IO.FS.Mode.write $ λ (h : IO.FS.Handle) =>
h.putStrLn str;
IO.FS.withFile path IO.FS.Mode.read $ λ (h : IO.FS.Handle) => do
let str' ← h.getLine;
IO.println str.length;
IO.println str'.length;
IO.print str';
«unless»... |
06447a00efba11a4167ee76db71c28b861296929 | 037dba89703a79cd4a4aec5e959818147f97635d | /src/2019/questions/sheet3.lean | f4c34597cc445e97f070986e6de7a26ecbd87729 | [] | no_license | ImperialCollegeLondon/M40001_lean | 3a6a09298da395ab51bc220a535035d45bbe919b | 62a76fa92654c855af2b2fc2bef8e60acd16ccec | refs/heads/master | 1,666,750,403,259 | 1,665,771,117,000 | 1,665,771,117,000 | 209,141,835 | 115 | 12 | null | 1,640,270,596,000 | 1,568,749,174,000 | Lean | UTF-8 | Lean | false | false | 6,117 | lean | /- Math40001 : Introduction to university mathematics.
Problem Sheet 3, October 2019.
This is a Lean file. It can be read with the Lean theorem prover.
You can work on this file online at
https://tinyurl.com/Lean-M40001-Example-Sheet-3
or you can install Lean and its maths library following the
instructions at
ht... |
79eb1057b70a22bbb26d28fdc75ce410a52cc0ec | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/data/nat/parity.lean | 3d1295b945eb9b8cabe26214e253e7d07061ecfb | [
"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 | 4,069 | lean | /-
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
The `even` predicate on the natural numbers.
-/
import data.nat.modeq
namespace nat
@[simp] theorem mod_two_ne_one {n : nat} : ¬ n % 2 = 1 ↔ n % 2 = 0 :=
by cases mod_t... |
b0324e7677e5cf09e579c3ff6b9ff924eae32b36 | 206422fb9edabf63def0ed2aa3f489150fb09ccb | /src/data/buffer/parser/basic.lean | 3db3e23db83f2c2e24abc0b8577dd8b996bdecd9 | [
"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 | 29,220 | 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
/-!
# Parsers
`parser α` is the type that describes a computation that can ingest a `char_buffer`
and output, if successful, a term of ty... |
7240444c8c9e787cf61bc51c1342f10f15feb522 | f3849be5d845a1cb97680f0bbbe03b85518312f0 | /library/init/data/quot.lean | 013553b3dd109df2730b8a90ed1a31ee103ea7c2 | [
"Apache-2.0"
] | permissive | bjoeris/lean | 0ed95125d762b17bfcb54dad1f9721f953f92eeb | 4e496b78d5e73545fa4f9a807155113d8e6b0561 | refs/heads/master | 1,611,251,218,281 | 1,495,337,658,000 | 1,495,337,658,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,374 | 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
Quotient types.
-/
prelude
/- We import propext here, otherwise we would need a quot.lift for propositions. -/
import init.data.sigma.basic init.logic init.pro... |
58361c6b6b1f3c09de454bf42cdbb242baac850d | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/1334a.lean | 847680c9f8d2d57a227c08f79ec3aa84c0e4a803 | [
"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 | 199 | lean | inductive nlist : Type
| atom : nlist
| mk : list nlist → nlist
open nlist list
def fn : nlist → nlist
| (mk l) := mk []
| _ := atom
#check fn.equations._eqn_1
#check fn.equations._eqn_2
|
89cc482f313ad829398941a1a732ba4d64b2c929 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/measure_theory/decomposition/jordan.lean | 6ac5fb5ee48ac4151cf1f1c0b9bd02da6b9f404a | [
"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 | 25,315 | lean | /-
Copyright (c) 2021 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
import measure_theory.decomposition.signed_hahn
import measure_theory.measure.mutually_singular
/-!
# Jordan decomposition
This file proves the existence and uniqueness o... |
8ee32773e008dee643e047f2dd0d6f3eab575ec4 | 618003631150032a5676f229d13a079ac875ff77 | /src/analysis/calculus/specific_functions.lean | f6f6a196e183bff6b585d1cb9fa988176083f5cd | [
"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 | 7,687 | 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.calculus.extend_deriv
import analysis.calculus.iterated_deriv
import analysis.special_functions.exp_log
/-!
# Smoothness of specific functions
... |
bc3f45506318a4bb2693ed8428f590fd011c80b2 | 31f556cdeb9239ffc2fad8f905e33987ff4feab9 | /stage0/src/Lean/Meta/Tactic/Generalize.lean | 462fe2faea66d449c9f9542bb567967e3ddb448a | [
"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 | 4,438 | 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.KAbstract
import Lean.Meta.Tactic.Util
import Lean.Meta.Tactic.Intro
import Lean.Meta.Tactic.FVarSubst
import Lean.Meta.Tactic.Revert
name... |
62f1d6938443399a0bcc73384ff3242d18d5d7e0 | 94637389e03c919023691dcd05bd4411b1034aa5 | /src/inClassNotes/higherOrderFunctions/option_mapTest.lean | 8374a6fcadfedc89bf8713bfe2c982255b3f78f6 | [] | no_license | kevinsullivan/complogic-s21 | 7c4eef2105abad899e46502270d9829d913e8afc | 99039501b770248c8ceb39890be5dfe129dc1082 | refs/heads/master | 1,682,985,669,944 | 1,621,126,241,000 | 1,621,126,241,000 | 335,706,272 | 0 | 38 | null | 1,618,325,669,000 | 1,612,374,118,000 | Lean | UTF-8 | Lean | false | false | 629 | lean | import ..type_library.option
namespace hidden
-- concrete example
def map_option_nat_nat :
(nat → nat) →
(option nat) →
option nat
| f option.none := option.none
<<<<<<< HEAD
| f (option.some v) := option.some (f v)
=======
| f (option.some v) := option.some (_)
-- by case analysis on the option argument
>... |
5da0d853ce7a0439c9eb936f7516db3b690d8223 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/data/multiset/basic.lean | 7b15c442460d7a2dc8b462b47247a6b438e2cadd | [
"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 | 90,278 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import data.bool.all_any
import data.list.perm
/-!
# Multisets
These are implemented as the quotient of a list by permutations.
## Notation
We define the glob... |
efc4172832ea23bcecdb1581e08f37f10ecef2bf | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/analysis/special_functions/complex/log.lean | 7f31c378c7dd4be9af0c01b3d2d17b9c0f1dfd1f | [
"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 | 8,369 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson
-/
import analysis.special_functions.complex.arg
import analysis.special_functions.log
/-!
# The complex ... |
c85e2c11965e5e0e3ca1fd85bc1b1c521c1f40ee | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/field_theory/splitting_field.lean | eea0b8e29a9b7d3add3fc8aa8deccf4563586d7d | [
"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 | 44,797 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import field_theory.minpoly
import ring_theory.adjoin_root
import linear_algebra.finite_dimensional
import algebra.polynomial.big_operators
import ring_theory.algebraic
i... |
00faf6d04911228264556feabd32828f3d047f03 | 8d65764a9e5f0923a67fc435eb1a5a1d02fd80e3 | /src/measure_theory/measure/vector_measure.lean | 8e58f333844117ecedfff302f3407c44f20df326 | [
"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 | 36,721 | lean | /-
Copyright (c) 2021 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
import measure_theory.integral.lebesgue
/-!
# Vector valued measures
This file defines vector valued measures, which are σ-additive functions from a set to a add monoid
... |
5a9ac7a987c0dba17cfe431ed5dddb50c68ccbcb | d26814d9437130e14d6d016c92d8c436b6dc62f3 | /my_prelude.hlean | 97221815aa32c776faece44b3cb527311b460626 | [] | no_license | jonas-frey/segal | 92fb5a556c164d4e9e864f2da1258be5a6482af8 | 64b4ec62ec5f293b781d5bbfea5a6b0997558c13 | refs/heads/master | 1,594,256,935,764 | 1,566,490,351,000 | 1,566,490,351,000 | 203,831,654 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,105 | hlean | import prop_trunc types.prod types.fin hit.pushout types.fiber
open funext eq trunc is_trunc prod sum pi function
is_equiv sigma sigma.ops equiv nat eq equiv
universe variables u v
notation `↑` := eq_of_homotopy -- type \u
notation `⇑` := eq_of_homotopy2 -- type \u
notation `⤊` := eq_of_homotopy3 -- what... |
d2d55362a8598476c5f22eec22c98a4cc4ffdde5 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/category_theory/monad/limits.lean | 16210718bf8b744a89f6f0482bd7133bb87182cc | [
"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 | 15,010 | 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.monad.adjunction
import category_theory.adjunction.limits
import category_theory.limits.preserves.shapes.terminal
/-!
# Limits a... |
184a5a4ebe87a60a6a1952ebc6546f2f03e272fb | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/category_theory/fin_category.lean | 11e88b62157beb97958f0fa38d8df8b2ec9a07f6 | [
"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 | 4,252 | 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 data.fintype.card
import category_theory.discrete_category
import category_theory.opposites
import category_theory.category.ulift
/-!
# Finite categories
A c... |
32cbaac38333a93f68586c4f9865c33ecb93b458 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Data/PersistentHashSet.lean | 0cbcfacb0712ea253fead62f05473c90e8088382 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 1,709 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
import Lean.Data.PersistentHashMap
namespace Lean
universe u v
structure PersistentHashSet (α : Type u) [BEq α] [Hashable α] where
(set : PersistentHashM... |
6e0db9e82f5e6349f33622e70b76cf1414d2d306 | 6e36ebd5594a0d512dea8bc6ffe78c71b5b5032d | /src/mywork/Practice/myLecture14.lean | 731617ac037730dbbe29ec47ecf525ae333bc2d0 | [] | no_license | wrw2ztk/cs2120f21 | cdc4b1b4043c8ae8f3c8c3c0e91cdacb2cfddb16 | f55df4c723d3ce989908679f5653e4be669334ae | refs/heads/main | 1,691,764,473,342 | 1,633,707,809,000 | 1,633,707,809,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 498 | lean | axioms
(Person : Type)
(Likes : Person → Person → Prop)
example :
¬ (∀ p : Person, Likes p p ) ↔
∃ p : Person, ¬ Likes p p :=
begin
apply iff.intro,
assume h,
have f := classical.em (∃ (p : Person), ¬Likes p p),
cases f,
exact f,
have contra : ∀ (p : Person), Likes p p := _,
contradiction,
... |
e2095c13611be2ffb8c823aa1f62c107c3f2107b | 94e33a31faa76775069b071adea97e86e218a8ee | /src/number_theory/legendre_symbol/gauss_eisenstein_lemmas.lean | bd60ea818edcfb50e3ff0351d4283c5f73b7fd71 | [
"Apache-2.0"
] | permissive | urkud/mathlib | eab80095e1b9f1513bfb7f25b4fa82fa4fd02989 | 6379d39e6b5b279df9715f8011369a301b634e41 | refs/heads/master | 1,658,425,342,662 | 1,658,078,703,000 | 1,658,078,703,000 | 186,910,338 | 0 | 0 | Apache-2.0 | 1,568,512,083,000 | 1,557,958,709,000 | Lean | UTF-8 | Lean | false | false | 13,769 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import field_theory.finite.basic
import data.zmod.basic
/-!
# Lemmas of Gauss and Eisenstein
This file contains code for the proof of the Lemmas of Gauss and Eisenstein... |
9f82a3f11953cf363cc254d98e5ebe2246a180bd | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/algebra/order.lean | 7df05b270ff28b98a88019369ca76ee079e825f0 | [
"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 | 10,711 | 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 tactic.alias
import tactic.lint
/-!
# Lemmas about inequalities
This file contains some lemmas about `≤`/`≥`/`<`/`>`, and `cmp`.
* We simplify `a ≥ b` and `... |
8138dba737d1a47679bae24fbe1ac70a2044eada | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/simp8.lean | 6088279c7d527b9cdfb3e6cf08f858e49994d5ba | [
"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 | 294 | lean | variables a b c d e f : Nat
rewrite_set simple
add_rewrite Nat::add_assoc Nat::add_comm Nat::add_left_comm Nat::distributer Nat::distributel : simple
(*
local t = parse_lean("f + (c + f + d) + (e * (a + c) + (d + a))")
local t2, pr = simplify(t, "simple")
print(t)
print("====>")
print(t2)
*)
|
990a97a05e543fd637dda422ae039c1e950bd8c7 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/analysis/calculus/specific_functions.lean | 23d6c720645a868a5330496b7b7407071c313900 | [
"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 | 18,898 | 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.calculus.iterated_deriv
import analysis.normed_space.euclidean_dist
/-!
# Infinitely smooth bump function
In this file we construct several in... |
33318a9e2152e4ccd4415695865e65f8cbc93e26 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/linear_algebra/sesquilinear_form.lean | 7f97ce4f11024f7cf6aa553aff70a5d6fa6cf644 | [
"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 | 8,673 | lean | /-
Copyright (c) 2018 Andreas Swerdlow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Andreas Swerdlow
-/
import algebra.module ring_theory.maps
/-!
# Sesquilinear form
This file defines a bilinear form over a module. The definition requires a ring antiautomorphism
... |
22a9c74f2203d64d07c9da5e09bf0fe0d1332613 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/doc_string5.lean | ff36e7cc76c501d98d69d3679de36303dcceb7c4 | [
"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 | 192 | lean | /--
Doc string for constants
-/
constant a : nat
/--
Doc string for axiom
-/
axiom ax : a = 0
/--
Doc string for meta constant
-/
meta constant v : tactic unit
/--
Doc string
-/
def x := 1
|
171695caebf5d4bc603fd2c34f15f128abf65e2f | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/data/finset/option.lean | 4f43df6ee3bfe280a2f764b42288eefbd4bf9115 | [
"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 | 4,388 | lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Mario Carneiro, Sean Leather
-/
import data.finset.basic
import order.preorder_hom
/-!
# Finite sets in `option α`
In this file we define
* `option.to_finset`: con... |
e5ca1f94b6739052869e427f912cfca010681cb7 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/analysis/constant_speed.lean | c6ac9e016baf75f195f51a382f897202e6507861 | [
"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 | 13,463 | lean | /-
Copyright (c) 2023 Rémi Bottinelli. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémi Bottinelli
-/
import data.set.function
import analysis.bounded_variation
import tactic.swap_var
/-!
# Constant speed
This file defines the notion of constant (and unit) speed fo... |
83c0f242137e472cd20c24e73b093d8f58612467 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/algebra/module/pi.lean | bb91f6ee2bcd9b807da3991b5410c624735c7b5f | [
"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 | 2,725 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Patrick Massot
-/
import algebra.module.basic
import algebra.regular.smul
import algebra.ring.pi
import group_theory.group_action.pi
/-!
# Pi instances for modules
This fil... |
ff8e9727bbc255e0a345426bd140b621aa1354b8 | 75c54c8946bb4203e0aaf196f918424a17b0de99 | /old/term-jesse.lean | e6c84710b1ef12e0385553fdc7338b45fdb4534a | [
"Apache-2.0"
] | permissive | urkud/flypitch | 261e2a45f1038130178575406df8aea78255ba77 | 2250f5eda14b6ef9fc3e4e1f4a9ac4005634de5c | refs/heads/master | 1,653,266,469,246 | 1,577,819,679,000 | 1,577,819,679,000 | 259,862,235 | 1 | 0 | Apache-2.0 | 1,588,147,244,000 | 1,588,147,244,000 | null | UTF-8 | Lean | false | false | 1,787 | lean | /-- Authors: Andrew Tindall, Jesse Han --/
structure Language :=
language :: (consts : Type) (relations : Π n : nat, Type) (functions : Π n : nat, Type)
variable L : Language
inductive term : ℕ → Type
| nil {} : term 0
| const : L.consts → term 1
| var : nat → term 1
| apply : ∀ (n : nat), ∀ (f : L.func... |
80456f991d73a753950c44a043cf36e94852bb78 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/data/setoid/basic.lean | 0ee7b3b8eadf0fbf77139574e5fe8eb7b8c47f43 | [
"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 | 18,387 | lean | /-
Copyright (c) 2019 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston, Bryan Gin-ge Chen
-/
import order.galois_connection
/-!
# Equivalence relations
This file defines the complete lattice of equivalence relations on a type, resul... |
d2a21e174ebfe95d6f6f3a89a688fdc3b4cb5455 | 05b503addd423dd68145d68b8cde5cd595d74365 | /src/algebra/group/prod.lean | df9c3df6b29bced5687613c118d54a36dd8ed520 | [
"Apache-2.0"
] | permissive | aestriplex/mathlib | 77513ff2b176d74a3bec114f33b519069788811d | e2fa8b2b1b732d7c25119229e3cdfba8370cb00f | refs/heads/master | 1,621,969,960,692 | 1,586,279,279,000 | 1,586,279,279,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,842 | lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Patrick Massot, Yury Kudryashov
-/
import algebra.group.hom
/-!
# Monoid, group etc structures on `M × N`
In this file we define one-binop (`monoid`, `group` etc) stru... |
7f729d0e2ad51389a3cc2aef05f74dc8b766e675 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/algebra/algebra/subalgebra/basic.lean | d5ff8a8c1a12b459bb894842413b36b25d9c7ad3 | [
"Apache-2.0"
] | permissive | urkud/mathlib | eab80095e1b9f1513bfb7f25b4fa82fa4fd02989 | 6379d39e6b5b279df9715f8011369a301b634e41 | refs/heads/master | 1,658,425,342,662 | 1,658,078,703,000 | 1,658,078,703,000 | 186,910,338 | 0 | 0 | Apache-2.0 | 1,568,512,083,000 | 1,557,958,709,000 | Lean | UTF-8 | Lean | false | false | 44,718 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Yury Kudryashov
-/
import algebra.algebra.basic
import data.set.Union_lift
/-!
# Subalgebras over Commutative Semiring
In this file we define `subalgebra`s and the usual operat... |
d0a020e49d0ccccf9fb904404f8a34ae690a0cea | 94e33a31faa76775069b071adea97e86e218a8ee | /src/analysis/convex/join.lean | 5255a3d07c2a6157592c388f6fc44d393ff34179 | [
"Apache-2.0"
] | permissive | urkud/mathlib | eab80095e1b9f1513bfb7f25b4fa82fa4fd02989 | 6379d39e6b5b279df9715f8011369a301b634e41 | refs/heads/master | 1,658,425,342,662 | 1,658,078,703,000 | 1,658,078,703,000 | 186,910,338 | 0 | 0 | Apache-2.0 | 1,568,512,083,000 | 1,557,958,709,000 | Lean | UTF-8 | Lean | false | false | 10,211 | 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 analysis.convex.combination
/-!
# Convex join
This file defines the convex join of two sets. The convex join of `s` and `t` is the union of the
segments with one... |
3ef8aa428541ff5c9c22afe3ec8dcd56456aa707 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /hott/hit/two_quotient.hlean | 0919efe0962036308d17f048037e47a5e921589f | [
"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 | 31,451 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import homotopy.circle eq2 algebra.e_closure cubical.squareover cubical.cube cubical.square2
open quotient eq circle sum sigma equiv function relation e_closu... |
f27e337280f264bd74886f3f5da21fb83e312aa6 | 957a80ea22c5abb4f4670b250d55534d9db99108 | /library/init/meta/rewrite_tactic.lean | 00c6bb22032dec88ce5b8f3af9002c1b2bff5fe8 | [
"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 | 1,909 | 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.relation_tactics init.meta.occurrences
namespace tactic
/-- Configuration options for the `rewrite` tactic. -/
structure rewrite_c... |
acc8d621339f6f4f436e1fb5e1c7b17dce92283d | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Init/Control/ExceptCps.lean | 7adc504f9a2d82e0506b2bf6a6d220774c311a27 | [
"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 | 3,030 | 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
-/
prelude
import Init.Control.Lawful
/-!
The Exception monad transformer using CPS style.
-/
def ExceptCpsT (ε : Type u) (m : Type u → Type v) (α : Type u) ... |
7b91724324a1bfedb54b1a2290fa0d9ae2761c7e | a721fe7446524f18ba361625fc01033d9c8b7a78 | /elaborate/add_comm.stripped.lean | f8d79a1b69b654140bb06fd21fa8862ca5e95260 | [] | 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 | 2,029 | lean | λ (m n : mynat), mynat.rec (eq.rec true.intro (eq.rec (eq.refl (m = add zero m)) (eq.rec (eq.rec (eq.refl (m = add zero m)) (eq.rec (eq.refl (add zero m)) (mynat.rec (eq.refl zero) (λ (m_n : mynat) (m_ih : add zero m_n = m_n), eq.rec m_ih (eq.rec (eq.refl (succ (add zero m_n) = succ m_n)) (eq.rec (eq.refl (succ (add ze... |
e038c9eb6c8941ccc7c0dc2aef89ea674c38c7c7 | 4b846d8dabdc64e7ea03552bad8f7fa74763fc67 | /library/init/meta/format.lean | edcfaea44b130e0e13962b5c29c9bafa847f4971 | [
"Apache-2.0"
] | permissive | pacchiano/lean | 9324b33f3ac3b5c5647285160f9f6ea8d0d767dc | fdadada3a970377a6df8afcd629a6f2eab6e84e8 | refs/heads/master | 1,611,357,380,399 | 1,489,870,101,000 | 1,489,870,101,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,577 | 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.options
universes u v
inductive format.color
| red | green | orange | blue | pink | cyan | grey
meta constant format : Type
meta... |
a226625f2e4cc947388ed7a03f4a4ee32f051ab4 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/logic/basic.lean | 11a8fec89c18436723e9594eb7e8910505f4df05 | [
"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 | 57,850 | 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... |
0288d2d259c940b0e9e6776dd72f75621e369f43 | 86f6f4f8d827a196a32bfc646234b73328aeb306 | /examples/sets_functions_and_relations/unnamed_480.lean | b028db2821875c0dc1ed04c24633d5be1a626c13 | [] | 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 | 133 | lean | import data.nat.prime data.nat.parity tactic
open set nat
example : { n | prime n } ∩ { n | n > 2} ⊆ { n | ¬ even n } :=
sorry |
5e56cba8d9da1da8b100bd385f403995a1d304f9 | ad0c7d243dc1bd563419e2767ed42fb323d7beea | /order/filter.lean | 4e3dcf6f4c1854fc41f888fd23c5d18b066d1e39 | [
"Apache-2.0"
] | permissive | sebzim4500/mathlib | e0b5a63b1655f910dee30badf09bd7e191d3cf30 | 6997cafbd3a7325af5cb318561768c316ceb7757 | refs/heads/master | 1,585,549,958,618 | 1,538,221,723,000 | 1,538,221,723,000 | 150,869,076 | 0 | 0 | Apache-2.0 | 1,538,229,323,000 | 1,538,229,323,000 | null | UTF-8 | Lean | false | false | 82,935 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Theory of filters on sets.
-/
import order.galois_connection order.zorn
import data.set.finite data.list
import category.applicative
open lattice set
universes u v w x... |
6fd217a84238a9b22c1a0ea96e34bb397c3c44b7 | 35b83be3126daae10419b573c55e1fed009d3ae8 | /_target/deps/mathlib/analysis/complex.lean | 0c79e75d0e7725a8b71ab42b6b1a145e3f65094d | [] | no_license | AHassan1024/Lean_Playground | ccb25b72029d199c0d23d002db2d32a9f2689ebc | a00b004c3a2eb9e3e863c361aa2b115260472414 | refs/heads/master | 1,586,221,905,125 | 1,544,951,310,000 | 1,544,951,310,000 | 157,934,290 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,146 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
Topology of the complex numbers.
-/
import data.complex.basic analysis.metric_space
noncomputable theory
open filter
namespace complex
-- TODO(Mario): these proofs ar... |
95ab75d7536c3a0c509e917a9a4522625bef2bdb | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/complex/removable_singularity.lean | 784b50e998e6db15df55dbc73db0f2bf1f96792f | [
"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 | 9,674 | 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 analysis.calculus.fderiv_analytic
import analysis.asymptotics.specific_asymptotics
import analysis.complex.cauchy_integral
/-!
# Removable singularity theor... |
5ff1d6418517e792125171fe7a5891371a274ee3 | 75db7e3219bba2fbf41bf5b905f34fcb3c6ca3f2 | /tests/lean/hott/531b.hlean | 1d85fa49bbf37d46286bd5493daf056396f6dfca | [
"Apache-2.0"
] | permissive | jroesch/lean | 30ef0860fa905d35b9ad6f76de1a4f65c9af6871 | 3de4ec1a6ce9a960feb2a48eeea8b53246fa34f2 | refs/heads/master | 1,586,090,835,348 | 1,455,142,203,000 | 1,455,142,277,000 | 51,536,958 | 1 | 0 | null | 1,455,215,811,000 | 1,455,215,811,000 | null | UTF-8 | Lean | false | false | 6,287 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: init.hit
Authors: Floris van Doorn
Declaration of hits
-/
structure diagram [class] :=
(Iob : Type)
(Ihom : Type)
(ob : Iob → Type)
(dom cod : Ihom → Iob)
(hom : Π(j : Ih... |
0a8cec312e7dc17a9f814b8f81956b377bf78316 | 75db7e3219bba2fbf41bf5b905f34fcb3c6ca3f2 | /hott/algebra/trunc_group.hlean | 969961d0a6ad736940573642c0e322c7faa3621c | [
"Apache-2.0"
] | permissive | jroesch/lean | 30ef0860fa905d35b9ad6f76de1a4f65c9af6871 | 3de4ec1a6ce9a960feb2a48eeea8b53246fa34f2 | refs/heads/master | 1,586,090,835,348 | 1,455,142,203,000 | 1,455,142,277,000 | 51,536,958 | 1 | 0 | null | 1,455,215,811,000 | 1,455,215,811,000 | null | UTF-8 | Lean | false | false | 2,485 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
truncating an ∞-group to a group
-/
import hit.trunc algebra.group
open eq is_trunc trunc
namespace algebra
section
parameters (A : Type) (mul : A → A → A) ... |
2b910cdac2c600795c78bf6f72a3641e40125091 | f4bff2062c030df03d65e8b69c88f79b63a359d8 | /src/game/max/max_API_test.lean | a33acb8f15622685396c86e955a7a29b9331b840 | [
"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 | 4,906 | lean | import tactic
open_locale classical -- def of max a b is "if a <= b then b else a"
noncomputable theory -- same reason
-- A linear order is a reflexive, transitive, antisymmetric and total relation `≤`
variables {X : Type} [linear_order X] {a b c : X}
-- Note in the below that sometimes we have to supply the variab... |
512faf8ed6807a1ffbd25247180d74872303e699 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/number_theory/sum_two_squares.lean | b4fd2731133e7aca4f6a1b655e6d3c253e3b3c66 | [] | 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 | 736 | lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Chris Hughes
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.zsqrtd.gaussian_int
import Mathlib.PostPort
namespace Mathlib
/-!
# Sums of two squares
... |
20fc61fd19080646e629c97009522ac11705092b | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/616.lean | ff3a8407bd6305dacd828fcdcaea8f5d7502250d | [
"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 | 109 | lean | def bug : Monad (λ α : Type _ => α → Prop) where
pure x := (.=x)
bind s f y := ∃ x, s x ∧ f x y
|
f937104febfdfff6c72b930527d63aa8420720e2 | efce24474b28579aba3272fdb77177dc2b11d7aa | /src/homotopy_theory/formal/cylinder/hep.lean | 9a93f3ab280a96e67a1422a66714b2ed3153ec25 | [
"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 | 5,059 | lean | import category_theory.colimits
import category_theory.isomorphism
import category_theory.preserves_colimits
import category_theory.replete
import .definitions
import category_theory.functor
open category_theory
open category_theory.category
local notation f ` ∘ `:80 g:80 := g ≫ f
universes v u
namespace homotopy_th... |
ff15180576a12f7c67526c587cc9173afd504354 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/probability/hitting_time.lean | 70924d70c016fce6715a076281d0904abe92ebeb | [
"Apache-2.0"
] | permissive | urkud/mathlib | eab80095e1b9f1513bfb7f25b4fa82fa4fd02989 | 6379d39e6b5b279df9715f8011369a301b634e41 | refs/heads/master | 1,658,425,342,662 | 1,658,078,703,000 | 1,658,078,703,000 | 186,910,338 | 0 | 0 | Apache-2.0 | 1,568,512,083,000 | 1,557,958,709,000 | Lean | UTF-8 | Lean | false | false | 8,767 | lean | /-
Copyright (c) 2022 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying, Rémy Degenne
-/
import probability.stopping
/-!
# Hitting time
Given a stochastic process, the hitting time provides the first time the process ``hits'' some
subset of the ... |
d438ecd96e5d83d0f6a2cfd26f861a8dac9c87e8 | c3e8fac5ab7ca328e55bccf82a0207a97f96678c | /lean/src/byte.lean | f9ee72054506eb553022522d599dd5a7e51e437b | [
"Unlicense"
] | permissive | Rotsor/brainfuck | 941bb33862ce3e9d61f0454db5ca02942f4b5775 | 3e6f30f298b8ba76d0bc71b8b5a47cedaf2f0b97 | refs/heads/master | 1,619,718,778,100 | 1,532,913,653,000 | 1,532,913,653,000 | 121,682,141 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 425 | lean | def byte := fin 256
instance : has_repr byte := ⟨ (λ ⟨ n, _ ⟩, repr (char.of_nat n) : (fin 256) → string) ⟩
namespace byte
instance : has_add(byte) := ⟨fin.add⟩
instance : has_one(byte) := ⟨(1 : fin 256)⟩
instance : has_zero(byte) := ⟨(0 : fin 256)⟩
def increment : byte -> byte :=
fin.add 1
def decreme... |
424724fe027b0166d222c228932f0f2dda189df9 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/linear_algebra/symplectic_group.lean | a9fab15586eb14f9f55bc42894cc932afaebbd2e | [
"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 | 6,354 | lean | /-
Copyright (c) 2022 Matej Penciak. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Matej Penciak, Moritz Doll, Fabien Clery
-/
import data.real.basic
import linear_algebra.matrix.nonsingular_inverse
/-!
# The Symplectic Group
This file defines the symplectic group ... |
c19e8f2683b233b0fc978ddae7c58d17ff48fb51 | b82c5bb4c3b618c23ba67764bc3e93f4999a1a39 | /src/formal_ml/analytic_function.lean | 402149cb1bccd2628ff2a5e5ec24c6d52f33af2f | [
"Apache-2.0"
] | permissive | nouretienne/formal-ml | 83c4261016955bf9bcb55bd32b4f2621b44163e0 | 40b6da3b6e875f47412d50c7cd97936cb5091a2b | refs/heads/master | 1,671,216,448,724 | 1,600,472,285,000 | 1,600,472,285,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 136,694 | 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... |
50da1ade12a8e893590930a42b3a7d28dd1afa06 | 2f8bf12144551bc7d8087a6320990c4621741f3d | /library/init/util.lean | ac38c9113e7acaa7f41bec5d2e89488236528078 | [
"Apache-2.0"
] | permissive | jesse-michael-han/lean4 | eb63a12960e69823749edceb4f23fd33fa2253ce | fa16920a6a7700cabc567aa629ce4ae2478a2f40 | refs/heads/master | 1,589,935,810,594 | 1,557,177,860,000 | 1,557,177,860,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 680 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.data.string.basic
universes u
/- debugging helper functions -/
@[extern cpp inline "lean::dbg_trace(#2, #3)"]
def dbgTrace {α : Type u}... |
ccfce9b11e8c20849d6d0abe06cf72cef71088f4 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/data/finset/n_ary.lean | b28c3a645e4be7a84e7f223ed48ba7b870d8600d | [
"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 | 15,539 | 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.finset.prod
/-!
# N-ary images of finsets
This file defines `finset.image₂`, the binary image of finsets. This is the finset version of
`set.image2`. This i... |
7d6b2bbf2a8b031e503e7177fff2c79bade40aeb | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/algebra/category/Semigroup/basic.lean | 2c2fa19ea2784ed4f183fe19a8695e1c9d629249 | [
"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 | 6,347 | lean | /-
Copyright (c) 2021 Julian Kuelshammer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Kuelshammer
-/
import category_theory.concrete_category.bundled_hom
import category_theory.concrete_category.reflects_isomorphisms
import algebra.pempty_instances
/-!
# Cat... |
97f2de8aab97b060386564751511259aa4a97215 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/category_theory/abelian/exact.lean | 894721d963c0ad78eebf33d747d730c84a500dfc | [
"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 | 6,492 | 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.basic
import algebra.homology.exact
import tactic.tfae
/-!
# Exact sequences in abelian categories
In an abelian category, we get sever... |
7f0eae2eaf831dd0a93d378c95f61780908409e8 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/priority_test2.lean | d19d508a4573a6e1eb159137a81c0129e34f4d6c | [
"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 | 714 | lean | open nat
structure foo [class] :=
(a : nat) (b : nat)
definition i1 [instance] [priority std.priority.default-2] : foo :=
foo.mk 1 1
example : foo.a = 1 :=
rfl
definition i2 [instance] [priority std.priority.default-1] : foo :=
foo.mk 2 2
example : foo.a = 2 :=
rfl
definition i3 [instance] : foo :=
foo.mk 3 3
ex... |
059eb1259df5acba99321f7ad00a87a539ae30c6 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/linear_algebra/matrix/reindex.lean | cb94fdbc88ff342ec64c4e9f6536ba443ff25f24 | [
"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 | 5,455 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
-/
import linear_algebra.matrix.determinant
/-!
# Changing the index type of a matrix
This file concerns the map `matrix.rei... |
e3d43b53df8529b6f1903fec5d5409c78cb2d957 | ba4794a0deca1d2aaa68914cd285d77880907b5c | /src/game/world10/level15.lean | f04caf0a923507a02aaaaaf1f1b07a996a541e9b | [
"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 | 925 | lean | --import mynat.lt -- definition of <
import game.world10.level14 -- hide
namespace mynat -- hide
/-
# Inequality world.
## Level 15: introducing `<`
To get the remaining collectibles in this world, we need to
give a definition of `<`. By default, the definition of `a < b`
in Lean, once `≤` is defined, is this:
`a... |
a17f05923f87d80f2a57cdc7007bc32cce88f207 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/number_theory/primorial.lean | 005aeef3847305e323073c17dc06f826e8163472 | [
"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 | 7,369 | lean | /-
Copyright (c) 2020 Patrick Stevens. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Stevens
-/
import tactic.ring_exp
import data.nat.parity
import data.nat.choose.sum
/-!
# Primorial
This file defines the primorial function (the product of primes less than... |
0f8e1b00ff1396283af72d0ed1627d953f2c4ccd | 1dd482be3f611941db7801003235dc84147ec60a | /src/data/complex/exponential.lean | 9b27b03bf571fbec578df5e1932134b95aeb4ff9 | [
"Apache-2.0"
] | permissive | sanderdahmen/mathlib | 479039302bd66434bb5672c2a4cecf8d69981458 | 8f0eae75cd2d8b7a083cf935666fcce4565df076 | refs/heads/master | 1,587,491,322,775 | 1,549,672,060,000 | 1,549,672,060,000 | 169,748,224 | 0 | 0 | Apache-2.0 | 1,549,636,694,000 | 1,549,636,694,000 | null | UTF-8 | Lean | false | false | 46,918 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import algebra.archimedean
import data.nat.choose data.complex.basic
import tactic.linarith
local attribute [instance, priority 0] classical.prop_decidable
loc... |
c8a9045e2d119ec7c4cf13bbb39f1580bef7320b | ae1e94c332e17c7dc7051ce976d5a9eebe7ab8a5 | /tests/lean/run/stuckMVarBug.lean | 0936f803a5206be2d16c8beaa4747ae5196cc1c8 | [
"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 | 480 | lean | class HasMulComm (α : Type u) [Mul α] : Prop where
mulComm : {a b : α} → a * b = b * a
class A (α : Type u) where
[Mul : Mul α]
attribute [instance] A.mk A.Mul
class B (α : Type u) where
[Mul : Mul α]
[HasMulComm : HasMulComm α]
attribute [instance] B.mk B.Mul B.HasMulComm
example [A α] [HasMulComm α... |
a6a829199ae616181cd5409443da70a86a28c21b | 86f6f4f8d827a196a32bfc646234b73328aeb306 | /examples/basics/unnamed_410.lean | 995b7f318de93cb1bac55619f7d7c0d0e9d83bee | [] | 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 | 282 | lean | import data.real.basic
variables a b c d : ℝ
-- BEGIN
example (a b c d : ℝ) (hyp : c = d * a + b) (hyp' : b = a * d) :
c = 2 * a * d :=
begin
rw hyp' at hyp,
rw mul_comm d a at hyp,
rw ← two_mul (a * d) at hyp,
rw ← mul_assoc 2 a d at hyp,
exact hyp
end
-- END |
44367b45834c735f0140bf02615f666a1cf0b3e2 | efa51dd2edbbbbd6c34bd0ce436415eb405832e7 | /20161026_ICTAC_Tutorial/ex35.lean | 2d17b5f3b3889bdbedf4f3f790bf7b8ae9f7266f | [
"Apache-2.0"
] | permissive | leanprover/presentations | dd031a05bcb12c8855676c77e52ed84246bd889a | 3ce2d132d299409f1de269fa8e95afa1333d644e | refs/heads/master | 1,688,703,388,796 | 1,686,838,383,000 | 1,687,465,742,000 | 29,750,158 | 12 | 9 | Apache-2.0 | 1,540,211,670,000 | 1,422,042,683,000 | Lean | UTF-8 | Lean | false | false | 414 | lean | /- Falsity
Elimination: anything follows from false. -/
variables p q : Prop
example (h : false) : p :=
false.elim h
example (h : false) : p :=
@false.elim p h
/- Negation -/
print not
/- If we have (h1 : not p) and (h2 : p) we can derive false -/
example (h1 : not p) (h2 : p) : false :=
h1 h2
example (h1 :... |
88073df3c79b159ab8237c60851dd38bc216ed45 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /archive/100-theorems-list/73_ascending_descending_sequences.lean | ce47545e5e0c296f53d96977f693fc2c16610439 | [
"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 | 8,024 | 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 data.fintype.powerset
/-!
# Erdős–Szekeres theorem
This file proves Theorem 73 from the [100 Theorems List](https://www.cs.ru.nl/~freek/100/), also
known as the ... |
2dd70e4c8470fa0ab3365301a365b03f4b5ad30f | d257837ee5f268fcb6e9b719129ff77f25de30a0 | /student_contributions/ellen_matrices.lean | b7b19934e14a0280f716f16dbb678e57db4b2980 | [] | no_license | pirocks/xena | a05a8a7da5d15b1cc28830eb84d370f3d60edbbf | 458a43f36964e5bb7d2d8ea74060d105519e331a | refs/heads/master | 1,620,756,281,811 | 1,516,097,784,000 | 1,516,097,784,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,413 | lean | import algebra.big_operators
definition matrix (R: Type) (n m : nat)[ring R] := fin n →( fin m → R )
namespace matrix
definition add ( R : Type) [ring R] {n m: nat }(A:matrix R m n) ( B : matrix R m n): (matrix R m n):=
begin
unfold matrix,
intros I J,
exact A I J + B I J
end
definition neg ( R : Type) [ring ... |
3c7dd3071b91821d46e0a48a089d512e65fbac20 | 94637389e03c919023691dcd05bd4411b1034aa5 | /src/inClassNotes/02_polymorphicTypes.lean | 6b8772bd8a1b146461c795321bc1fe83c564ddd4 | [] | no_license | kevinsullivan/complogic-s21 | 7c4eef2105abad899e46502270d9829d913e8afc | 99039501b770248c8ceb39890be5dfe129dc1082 | refs/heads/master | 1,682,985,669,944 | 1,621,126,241,000 | 1,621,126,241,000 | 335,706,272 | 0 | 38 | null | 1,618,325,669,000 | 1,612,374,118,000 | Lean | UTF-8 | Lean | false | false | 5,649 | lean | namespace hidden
/-
Inductive, aka algebraic, data types
- sum types
- product types and case analysis
- parametrically polymorphic
- sum of product types and destructuring
-/
/-
SUM TYPES
A value of such a type is "one of these OR
one of those OR one of something else." SUM
means OR in this sense.
-/
indu... |
e8b9c5ff306cb05887b691584959768560b9cd08 | e0f9ba56b7fedc16ef8697f6caeef5898b435143 | /src/linear_algebra/multilinear.lean | 8d53f14d661434717cded1c83b3e57bc64ed9fd0 | [
"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 | 33,006 | 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 tactic.omega
import data.fintype.card
/-!
# Multilinear maps
We define multilinear maps as maps from `Π(i : ι), M₁ i` to `M... |
5a6464e7cb54f5ded1e7329128965c089b08d3cd | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/order/compare.lean | 92fb96f856652557fece6a2f41da62a0636d3cf5 | [
"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 | 8,378 | 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.
> Any changes to this file require a corresponding PR to mathlib4.
This file provi... |
1ab71dac6794bf397605625c0ebd992367de9206 | 57fdc8de88f5ea3bfde4325e6ecd13f93a274ab5 | /algebra/ordered_group.lean | 5a2d54c461d7bcb6e76bc0c09b1f4cfb0742ce9a | [
"Apache-2.0"
] | permissive | louisanu/mathlib | 11f56f2d40dc792bc05ee2f78ea37d73e98ecbfe | 2bd5e2159d20a8f20d04fc4d382e65eea775ed39 | refs/heads/master | 1,617,706,993,439 | 1,523,163,654,000 | 1,523,163,654,000 | 124,519,997 | 0 | 0 | Apache-2.0 | 1,520,588,283,000 | 1,520,588,283,000 | null | UTF-8 | Lean | false | false | 15,283 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johannes Hölzl
Ordered monoids and groups.
-/
import algebra.group tactic
universe u
variable {α : Type u}
section old_structure_cmd
set_option old_structure_cmd tr... |
d4dd578985b42f98b45f5b6b0be5f5b9ffe556ed | a047a4718edfa935d17231e9e6ecec8c7b701e05 | /src/data/set/lattice.lean | 24e889c0508e6fe15414e5f3b0daf362d05c1eea | [
"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 | 35,235 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Johannes Hölzl, Mario Carneiro
-- QUESTION: can make the first argument in ∀ x ∈ a, ... implicit?
-/
import order.complete_boolean_algebra
import data... |
e1c1946b12306ba656250376d95c785c47a2ea59 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/set_theory/cardinal/divisibility.lean | 883d7bbabacfd3518e68c82ac73e10368fd9364a | [
"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 | 5,299 | lean | /-
Copyright (c) 2022 Eric Rodriguez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Rodriguez
-/
import algebra.is_prime_pow
import set_theory.cardinal.ordinal
/-!
# Cardinal Divisibility
We show basic results about divisibility in the cardinal numbers. This r... |
3440f602e7af26bac186991fe86e33c132a109f6 | c46a31beec236d29b6c02e7d7683691bcfbb3014 | /src/utils/real.lean | 2f81d1982c993ebb423d78c2c219905bf3fdfc39 | [] | no_license | UVM-M52/quiz-5-maddiestrauss | a88b9bfbdd486a521ee280f9b7b551bcb48f23c6 | 214529615e08bbcdd3d6600c89432ec985e6ba3a | refs/heads/master | 1,617,897,187,103 | 1,584,922,038,000 | 1,584,922,038,000 | 248,787,429 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 431 | lean |
import .cmp
attribute [instance, priority 10] classical.prop_decidable
axiom ℝ : Type
@[instance]
axiom real_field : discrete_linear_ordered_field ℝ
axiom sup (s : ℕ → ℝ) : (∀ n, s n ≤ s (n+1)) → (∃ b, ∀ n, s n ≤ b) → ℝ
axiom sup_spec (s : ℕ → ℝ) (hm : ∀ n, s n ≤ s (n+1)) (hb : ∃ b, ∀ n, s n ≤ b) : (∀ n, s n ≤ su... |
6aeaca6e1f9c6a996e0da0d01b46bb01177ffefc | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/compiler/closure_bug2.lean | ca586cfb3086bbc806b255afb39b80f5d380a72f | [
"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 | 539 | lean |
def f (x : Nat) : Nat × (Nat → String) :=
let x1 := x + 1
let x2 := x + 2
let x3 := x + 3
let x4 := x + 4
let x5 := x + 5
let x6 := x + 6
let x7 := x + 7
let x8 := x + 8
let x9 := x + 9
let x10 := x + 10
let x11 := x + 11
let x12 := x + 12
let x13 := x + 13
let x14 := x + 14
let x15 := x + 15
let x16 := x + 16
let x17... |
b862fd719ebe0ec88f21cfb5520429f5736947b5 | f5f7e6fae601a5fe3cac7cc3ed353ed781d62419 | /src/algebra/pointwise.lean | 0fa274f434b02fecd8dedd5bb5309383db8a200b | [
"Apache-2.0"
] | permissive | EdAyers/mathlib | 9ecfb2f14bd6caad748b64c9c131befbff0fb4e0 | ca5d4c1f16f9c451cf7170b10105d0051db79e1b | refs/heads/master | 1,626,189,395,845 | 1,555,284,396,000 | 1,555,284,396,000 | 144,004,030 | 0 | 0 | Apache-2.0 | 1,533,727,664,000 | 1,533,727,663,000 | null | UTF-8 | Lean | false | false | 7,545 | lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
Pointwise addition and multiplication of sets
-/
import data.set.finite
import data.set.lattice
import algebra.group
import group_theory.subgroup
namespace set
open f... |
4a3cde25b4942dac8ba4e94a6ca7ee611a4f2834 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/inductive1.lean | e86facc3340caf0ab12799c390076ea7303021fc | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 1,641 | lean | inductive L1.{u} (α : Type u)
| nil
| cons : α → L1 α → L1 α
#check L1
#check @L1.cons
inductive L2.{u} (α : Type u)
| nil
| cons (head : α) (tail : L2 α)
#check @L2.cons
universe u v
variable (α : Type u)
inductive A (β : Type v)
| nil
| protected cons : α → β → A β → A β
#check @A.cons
#check A.nil (α := Nat) (... |
77e04105f6bfeb3f42877cd5689f88d2d6609f08 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/category_theory/whiskering.lean | 3983f85813602f553a10740fa94d387cb6bb313f | [
"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 | 8,473 | 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.isomorphism
import category_theory.functor.category
import category_theory.functor.fully_faithful
/-!
# Whiskering
Given a functor `F : C ⥤ ... |
5e03d3035bfe98867f4d49a346e08bc9504a033f | 4727251e0cd73359b15b664c3170e5d754078599 | /src/data/fintype/card_embedding.lean | 4b8b24fcdc02e5f4f06e8a8dbfd57221b033192a | [
"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 | 1,905 | lean | /-
Copyright (c) 2021 Eric Rodriguez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Rodriguez
-/
import data.fintype.card
import logic.equiv.fin
import logic.equiv.embedding
/-!
# Number of embeddings
This file establishes the cardinality of `α ↪ β` in full gen... |
9c44ce9acb671426b2b378e6f70429f4627bdda4 | 2c443ed3c09d98edcad40e5d286e53bc5a2ae838 | /src/category_theory_stuff/solutions/chapter_1/section_2.lean | fe4a4f6e9ad090929f670264e9ce83384e9308a9 | [] | no_license | agusakov/riehl-solutions | f8be5e0bbd9b4d691cb8a45b6e4f4cc06aaf6c17 | 3cba620de377649e9269c53e17a65cfccd7db651 | refs/heads/master | 1,668,377,179,927 | 1,593,744,143,000 | 1,593,744,143,000 | 275,534,049 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,172 | lean | import category_theory.category category_theory.epi_mono tactic-- this transitively imports
open category_theory
universes v u
variables (C : Type u) [category.{v} C]
/-Prove Lemma 1.2.11 by proving either (i) or (i') and either (ii) or (i'),
then arguing by duality. Conclude that the monomorphisms in any category... |
22227d30d7e4c0fed3900d4aeebb80fb85f24c36 | 947b78d97130d56365ae2ec264df196ce769371a | /tests/lean/lvl1.lean | b4ed09fc87b2fb961c32b9ff4dc952cbd02d0852 | [
"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 | 1,345 | lean | import Lean.Level
new_frontend
namespace Lean
namespace Level
def mkMax (xs : Array Level) : Level :=
xs.foldlFrom mkLevelMax (xs.get! 0) 1
#eval toString $ normalize $ mkLevelSucc $ mkLevelSucc $ mkMax #[levelZero, mkLevelParam `w, mkLevelSucc (mkLevelSucc (mkLevelSucc (mkLevelParam `z))), levelOne, mkLevelSucc (mkL... |
e00ccb5bbd3b6daba8a7e706df5b80972edbfa6f | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/mv_polynomial/equiv_auto.lean | 3482cee86c706db3dc83cd2975510f8b6a1fbc0f | [] | 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 | 10,407 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.mv_polynomial.rename
import Mathlib.data.equiv.fin
imp... |
9161b5339fa042dbbd2385c820a08d4da1db58d4 | fecda8e6b848337561d6467a1e30cf23176d6ad0 | /src/category_theory/limits/limits.lean | 8b1da2ee8beef896a644948ad2f2ab9366c0515f | [
"Apache-2.0"
] | permissive | spolu/mathlib | bacf18c3d2a561d00ecdc9413187729dd1f705ed | 480c92cdfe1cf3c2d083abded87e82162e8814f4 | refs/heads/master | 1,671,684,094,325 | 1,600,736,045,000 | 1,600,736,045,000 | 297,564,749 | 1 | 0 | null | 1,600,758,368,000 | 1,600,758,367,000 | null | UTF-8 | Lean | false | false | 61,554 | 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.adjunction.basic
import category_theory.limits.cones
import category_theory.reflects_isomorphism... |
04d64b2aee93605fde3329bb6ad3afe4e764dd9f | 86f6f4f8d827a196a32bfc646234b73328aeb306 | /examples/basics/unnamed_1408.lean | 9cf4e941b3388c846ba9532fc87b227a554e4269 | [] | 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 | 136 | lean | import data.real.basic tactic
variables a b : ℝ
-- BEGIN
example : abs (a*b) ≤ (a^2 + b^2) / 2 :=
sorry
#check abs_le'.mpr
-- END |
918544d596981941323838d1a7ccdae909470650 | 0845ae2ca02071debcfd4ac24be871236c01784f | /tests/playground/task_test2.lean | a97e1bca7c751007b5456bebb3198a1d0a904fa0 | [
"Apache-2.0"
] | permissive | GaloisInc/lean4 | 74c267eb0e900bfaa23df8de86039483ecbd60b7 | 228ddd5fdcd98dd4e9c009f425284e86917938aa | refs/heads/master | 1,643,131,356,301 | 1,562,715,572,000 | 1,562,715,572,000 | 192,390,898 | 0 | 0 | null | 1,560,792,750,000 | 1,560,792,749,000 | null | UTF-8 | Lean | false | false | 430 | lean | def run1 (i : Nat) (n : Nat) (xs : List Nat) : Nat :=
n.repeat (λ r,
dbgTrace (">> [" ++ toString i ++ "] " ++ toString r) $ λ _,
xs.foldl (+) r)
0
def main (xs : List String) : IO UInt32 :=
let ys := (List.replicate xs.head.toNat 1) in
let ts : List (Task Nat) := (List.iota 10).map (λ i, Task.mk $ λ _, run1 (i+1)... |
6e847a8c18f7b7951dab4c15f2b8e889801cff61 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/control/fold.lean | a57e90247f3237baec23d95b83b8fde16c00a8bf | [
"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 | 14,962 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Sean Leather
-/
import algebra.free_monoid
import algebra.opposites
import control.traversable.instances
import control.traversable.lemmas
import category_theory.category
imp... |
7c90fb6924c3250abf3ba271179f90f8656f18f8 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/1901.lean | 0a6e7dfabb392e2596acfba891f2b7619184a905 | [
"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 | 586 | lean | class Funny (F : Type _) (A B : outParam (Type _)) where
toFun : F → A → B
instance [Funny F A B] : CoeFun F fun _ => A → B where coe := Funny.toFun
class MulHomClass (F) (A B : outParam _) [Mul A] [Mul B] extends Funny F A B
class Monoid (M) extends Mul M
instance [Mul A] : Mul (Id A) := ‹_›
#check Funny.toFun
#c... |
31d5eade6118966aae03e2cd09ef550f3ab2c14a | 0845ae2ca02071debcfd4ac24be871236c01784f | /library/init/lean/class.lean | 4342066b6c5da461a4bd318adb6be320cf7b34c0 | [
"Apache-2.0"
] | permissive | GaloisInc/lean4 | 74c267eb0e900bfaa23df8de86039483ecbd60b7 | 228ddd5fdcd98dd4e9c009f425284e86917938aa | refs/heads/master | 1,643,131,356,301 | 1,562,715,572,000 | 1,562,715,572,000 | 192,390,898 | 0 | 0 | null | 1,560,792,750,000 | 1,560,792,749,000 | null | UTF-8 | Lean | false | false | 5,101 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.lean.attributes
namespace Lean
inductive ClassEntry
| «class» (name : Name) (hasOutParam : Bool)
| «instance» (name : Name) (ofClas... |
cac23d0bb68b60b85254401bd0719ee078073898 | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/topology/bases.lean | 40e7781020cff7d08553eb123fd565d1c2238f36 | [
"Apache-2.0"
] | permissive | hikari0108/mathlib | b7ea2b7350497ab1a0b87a09d093ecc025a50dfa | a9e7d333b0cfd45f13a20f7b96b7d52e19fa2901 | refs/heads/master | 1,690,483,608,260 | 1,631,541,580,000 | 1,631,541,580,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 26,170 | 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.continuous_on
import topology.constructions
/-!
# Bases of topologies. Countability axioms.
A topological basis on a topological sp... |
13f17c3d4099c41b6af861a98617f732c04a26b4 | 6b02ce66658141f3e0aa3dfa88cd30bbbb24d17b | /src/Lean/Meta/Basic.lean | dee91fae30fab894201ce223b19ab7dd501b0ebc | [
"Apache-2.0"
] | permissive | pbrinkmeier/lean4 | d31991fd64095e64490cb7157bcc6803f9c48af4 | 32fd82efc2eaf1232299e930ec16624b370eac39 | refs/heads/master | 1,681,364,001,662 | 1,618,425,427,000 | 1,618,425,427,000 | 358,314,562 | 0 | 0 | Apache-2.0 | 1,618,504,558,000 | 1,618,501,999,000 | null | UTF-8 | Lean | false | false | 45,653 | 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.Data.LOption
import Lean.Environment
import Lean.Class
import Lean.ReducibilityAttrs
import Lean.Util.Trace
import Lean.Util.RecDepth
import Lea... |
d3b8f0a8744590f0f1dfca8a788117b62262ad35 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/measure_theory/measure/finite_measure.lean | 2f56da55396ca5bff7f65dc043fb1649a2b8df3a | [
"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 | 33,195 | 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 topology.continuous_function.bounded
import topology.algebra.module.weak_dual
import measure_theory.integral.bochner
/-!
# Finite measures
This file defines the ... |
4ba2bb6b6d85511c8c6e5c0f2cfee21b2677aff2 | 43390109ab88557e6090f3245c47479c123ee500 | /src/M1F/problem_bank/0501/Q0501.lean | fc0bdf671781754a693e4d6d812dd7b2bde666fa | [
"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 | 1,192 | lean | import algebra.group_power tactic.norm_num algebra.big_operators
def Fib : ℕ → ℕ
| 0 := 0
| 1 := 1
| (n+2) := Fib n + Fib (n+1)
def is_even (n : ℕ) : Prop := ∃ k, n=2*k
def is_odd (n : ℕ) : Prop := ∃ k, n=2*k+1
lemma even_of_even_add_even (a b : ℕ) : is_even a → is_even b → is_even (a+b) :=
begin
intros Ha Hb,
cases... |
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