blob_id stringlengths 40 40 | directory_id stringlengths 40 40 | path stringlengths 7 139 | content_id stringlengths 40 40 | detected_licenses listlengths 0 16 | license_type stringclasses 2
values | repo_name stringlengths 7 55 | snapshot_id stringlengths 40 40 | revision_id stringlengths 40 40 | branch_name stringclasses 6
values | visit_date int64 1,471B 1,694B | revision_date int64 1,378B 1,694B | committer_date int64 1,378B 1,694B | github_id float64 1.33M 604M β | star_events_count int64 0 43.5k | fork_events_count int64 0 1.5k | gha_license_id stringclasses 6
values | gha_event_created_at int64 1,402B 1,695B β | gha_created_at int64 1,359B 1,637B β | gha_language stringclasses 19
values | src_encoding stringclasses 2
values | language stringclasses 1
value | is_vendor bool 1
class | is_generated bool 1
class | length_bytes int64 3 6.4M | extension stringclasses 4
values | content stringlengths 3 6.12M |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
3de45f5a57d4c3c71cee3bf2f6fb690aab51eb87 | 4da0c8e61fcd6ec3f3be47ee14a038850c03d0c3 | /src/s5/syntax/lemmas.lean | 1be99fddd283a965fa748deaf7a5882678eb9ae2 | [
"Apache-2.0"
] | permissive | bbentzen/mpl | fcbea60204bc8fd64667e0f76a5cebf4b67fb6ca | bb5066ec51fa11a4b66f440c4f6c9a3d8fb2e0de | refs/heads/master | 1,625,175,849,308 | 1,624,207,634,000 | 1,624,207,634,000 | 142,774,375 | 9 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 13,073 | lean | /-
Copyright (c) 2018 Bruno Bentzen. All rights reserved.
Released under the Apache License 2.0 (see "License");
Author: Bruno Bentzen
-/
import .basic
open prf
variable {Ο : nat}
namespace prf
/- identity implication -/
lemma id {p : form Ο} {Ξ : ctx Ο} :
Ξ β’ββ
p β p :=
mp (mp (@pl2 Ο Ξ p (p ... |
3cc48a194414135c18ad0bea66fa3317296ce1f0 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/DocString.lean | e77e76b27eb3959363b8780dc348b5f6c02c5fc3 | [
"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 | 3,889 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.DeclarationRange
import Lean.MonadEnv
namespace Lean
private builtin_initialize builtinDocStrings : IO.Ref (NameMap String) β IO.mkRef {}
priv... |
e51702954e61a4d62994bb0a05fb96e230b093d4 | 64874bd1010548c7f5a6e3e8902efa63baaff785 | /library/algebra/function.lean | 4bb598290dea04a2fe7fc6096444d6239de10571 | [
"Apache-2.0"
] | permissive | tjiaqi/lean | 4634d729795c164664d10d093f3545287c76628f | d0ce4cf62f4246b0600c07e074d86e51f2195e30 | refs/heads/master | 1,622,323,796,480 | 1,422,643,069,000 | 1,422,643,069,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,444 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.function
Author: Leonardo de Moura
General operations on functions.
-/
namespace function
variables {A : Type} {B : Type} {C : Type} {D : Type} {E : Type}
definition ... |
80b6d7e0f58f2dd7f8933a85a29d33e33a665a32 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /test/matrix.lean | 96416488c08580bd7684d8ec8c8dfe8f405f3542 | [
"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 | 5,015 | lean | import data.matrix.notation
import linear_algebra.matrix.determinant
import group_theory.perm.fin
import tactic.norm_swap
variables {Ξ± Ξ² : Type} [semiring Ξ±] [ring Ξ²]
namespace matrix
open_locale matrix
/-! Test that the dimensions are inferred correctly, even for empty matrices -/
section dimensions
set_option pp... |
2d6a9c1c88a01e7d98bda02ecf811ef37a407cd2 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/data/real/irrational.lean | ce41461f9adefa76009a4087da5557815e6e22cf | [
"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 | 17,722 | 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 SΓΆnne, Yury Kudryashov
-/
import data.real.sqrt
import tactic.interval_cases
import ring_theory.algebraic
import data.rat.sqrt
... |
4bd52279a15dc1666ce09eb8e73a33b60e989c60 | 958488bc7f3c2044206e0358e56d7690b6ae696c | /lean/list.lean | cbb7e4d01864d72beeb42bf96084c2173b66f1a7 | [] | no_license | possientis/Prog | a08eec1c1b121c2fd6c70a8ae89e2fbef952adb4 | d4b3debc37610a88e0dac3ac5914903604fd1d1f | refs/heads/master | 1,692,263,717,723 | 1,691,757,179,000 | 1,691,757,179,000 | 40,361,602 | 3 | 0 | null | 1,679,896,438,000 | 1,438,953,859,000 | Coq | UTF-8 | Lean | false | false | 1,168 | lean | namespace hidden1
universe u
constant list : Type u β Type u
constant cons : Ξ Ξ± : Type u, Ξ± β list Ξ± β list Ξ±
constant nil : Ξ Ξ± : Type u, list Ξ±
constant head : Ξ Ξ± : Type u, list Ξ± β Ξ±
constant tail : Ξ Ξ± : Type u, list Ξ± β list Ξ±
constant append : Ξ Ξ± : Type u, list Ξ± β list Ξ± β list Ξ±
end hidden1
op... |
ab7d526d1fa2046d7ca7287d5e66e7f0456d1560 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/category_theory/closed/cartesian.lean | 4c08ac952be4092469f0419800e9209bee6c2e28 | [
"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 | 14,896 | lean | /-
Copyright (c) 2020 Bhavik Mehta, Edward Ayers, Thomas Read. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Edward Ayers, Thomas Read
-/
import category_theory.limits.shapes.finite_products
import category_theory.limits.preserves.shapes.binary_products... |
6fc3dd18275f1c3017cc216764e0ab5abb094b55 | 692af846429926968acf45e9b67f76f7e7e41e1b | /systemF/chap23.lean | ab5b77a759b41a27eceec797cddc62be1a15755f | [] | no_license | NeM-T/Formalizing-TaPL | 6f5b176511362e195015d99a45d69342621014b3 | 2a4dba29d0850a7494c7fd52c0daf4bbb3879691 | refs/heads/master | 1,679,067,987,954 | 1,615,393,646,000 | 1,615,393,646,000 | 270,350,760 | 3 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,015 | lean | open nat bool
def leb : β β β β bool
| 0 _ := true
| (succ n) 0 := false
| (succ n) (succ m) := (leb n m)
lemma ltb_lt : β n m,
leb n m = true β n <= m := sorry
inductive ty : Type
| tyvar : β β ty
| arrow : ty β ty β ty
| tyall : ty β ty
open ty
def shift_type : β β β β ty β ty
| d c (tyvar n) := if (leb c n) t... |
69a5a3c64bc97e6147676a3d2a64973de0c1f171 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/1860.lean | ddd6a65efde0c7767aff1508ae78074082a6960b | [
"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 | 65 | lean | run_cmd tactic.trace $ let let_val := (2 : β) in `(id let_val)
|
6278b0cea1eb3bbb938a22f456aacb12d10fa482 | 5d166a16ae129621cb54ca9dde86c275d7d2b483 | /tests/lean/run/smt_destruct.lean | bb05b9425e8293589ceccc39ad6aeb14d7d5f5af | [
"Apache-2.0"
] | permissive | jcarlson23/lean | b00098763291397e0ac76b37a2dd96bc013bd247 | 8de88701247f54d325edd46c0eed57aeacb64baf | refs/heads/master | 1,611,571,813,719 | 1,497,020,963,000 | 1,497,021,515,000 | 93,882,536 | 1 | 0 | null | 1,497,029,896,000 | 1,497,029,896,000 | null | UTF-8 | Lean | false | false | 1,656 | lean | open smt_tactic
lemma ex1 (p q : Prop) : p β¨ q β p β¨ Β¬q β Β¬p β¨ q β Β¬p β¨ Β¬q β false :=
by using_smt $ do
intros,
trace_state,
a_1 β tactic.get_local `a_1,
destruct a_1,
repeat close
lemma ex2 (p q : Prop) : p β¨ q β p β¨ Β¬q β Β¬p β¨ q β Β¬p β¨ Β¬q β false :=
begin [smt]
intros,
assert h : p β¨ q,
destr... |
2002307026606216918bb2d0da4d1aaf3087a981 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/category_theory/types.lean | fc0e8d08d7cffb4f32dffa49b1b7521d1ef5680f | [
"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 | 9,575 | 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 HΓΆlzl
-/
import category_theory.functor_category
import category_theory.fully_faithful
import data.equiv.basic
/-!
# The category `Type`.
In ... |
b6e1a381dc129de2c9c28249ad4114dbcb79d0d2 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/algebra/category/Group/basic.lean | 48fb228f751a5e36aad85f3fd205b76b1d8bd8ee | [
"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 | 9,004 | lean | /-
Copyright (c) 2018 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import algebra.punit_instances
import algebra.category.Mon.basic
import category_theory.endomorphism
import category_theory.epi_mono
/-!
# Category instances for gr... |
73883d0df166e9d14a715db7727ae871f876b0e2 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/linear_algebra/quotient.lean | ec9f11661724d05e902ea9d5960fcf229a1f0b53 | [
"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 | 14,353 | lean | /-
Copyright (c) 2017 Johannes HΓΆlzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes HΓΆlzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov
-/
import linear_algebra.basic
/-!
# Quotients by submodules
* If `p` is a submodule of `M`, `submodule.quotient p` is ... |
22172bfa5e7630c66cd3c68f76cf1a5fd5345d72 | 361e951bc2e4c19795ad24240d87a079b5c0a5fb | /src/nikodym.lean | c6511c4313a9eaf8fbbd08217137a1d7a0e08d20 | [] | no_license | anshula/nikodym-lean | 9abf1883901b6d3abc576f7995b9f18a2f8f6849 | 1e53a9f09e7e7960835a9c5d30623527ea73b93e | refs/heads/master | 1,689,462,835,063 | 1,630,600,088,000 | 1,630,600,088,000 | 402,488,023 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,567 | lean |
import
field_theory.finite.polynomial
import data.nat.basic
open mv_polynomial
open polynomial
section polys
set_option class.instance_max_depth 200
parameters {Ξ± : Type} [field Ξ±] [fintype Ξ±] [decidable_eq Ξ±] [nonempty Ξ±]
parameters {Ο : Type*} [decidable_eq Ο]
parameters {Ο : Type*} [decidable_eq Ο]
... |
13aeddfeec76c9cc2bb5857c8217841678e8b807 | 02fbe05a45fda5abde7583464416db4366eedfbf | /library/init/data/list/lemmas.lean | 226beffa0b1d3e82f2b599f8a3814cfffa21c7ed | [
"Apache-2.0"
] | permissive | jasonrute/lean | cc12807e11f9ac6b01b8951a8bfb9c2eb35a0154 | 4be962c167ca442a0ec5e84472d7ff9f5302788f | refs/heads/master | 1,672,036,664,637 | 1,601,642,826,000 | 1,601,642,826,000 | 260,777,966 | 0 | 0 | Apache-2.0 | 1,588,454,819,000 | 1,588,454,818,000 | null | UTF-8 | Lean | false | false | 10,520 | lean | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn
-/
prelude
import init.data.list.basic init.function init.meta init.data.nat.lemmas
import init.meta.interactive i... |
5ed302eedb4c824dc8c4aeba56197764659d8ddd | df7bb3acd9623e489e95e85d0bc55590ab0bc393 | /lean/love04_functional_programming_exercise_sheet.lean | 8e65d7647dd0a6dc5ac3814f09f867b34b71a633 | [] | 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 | 5,498 | lean | import .love03_forward_proofs_demo
/- # LoVe Exercise 4: Functional Programming -/
set_option pp.beta true
set_option pp.generalized_field_notation false
namespace LoVe
/- ## Question 1: Reverse of a List
We define a new accumulator-based version of `reverse`. The first argument,
`as`, serves as the accumulator... |
dc52a9abe89f7252b5f4b8b228f499c4af1582e8 | 93366ecea09eebeeb0b320567c6f71715434c3f0 | /src/bum/configparser.lean | 68c36d850165c1b8df8863b4d948b99372b9d830 | [
"LicenseRef-scancode-mit-taylor-variant",
"LicenseRef-scancode-warranty-disclaimer"
] | permissive | o89/bum | 9c1286cedb878c1e14c618e81b33d365f62c8a8a | 18ffb2b46932ba767c50758a93cc99846ef1b46a | refs/heads/master | 1,670,171,693,018 | 1,669,086,393,000 | 1,669,086,393,000 | 205,409,352 | 8 | 6 | null | null | null | null | UTF-8 | Lean | false | false | 1,214 | lean | import bum.types
import bum.parser
def whitespace := sat Char.isWhitespace
def strSat := str β sat
def reserved := ",[]{} \n\t\""
def quote := Char.ofNat 34
def tok :=
(do ch quote; let str β strSat (not β BEq.beq quote);
ch quote; pure str) <|>
strSat (not β reserved.contains)
def gappy {Ξ± : Type} (p : Parser ... |
ecce4b67e162c4317121a41a37ff224da37ed6da | 25adb3ce35902d6e9c57e494fe055c47c9881db4 | /metrology/dimensions.lean | dc1c5ef8d8f753bc23acfe554204aef563b8da0c | [] | no_license | rohanrajnair/phys | fefb5e430f8e4b61c2acbaecb9d1c6702495ef87 | 0172c81b24bc94e2df5e32904c9f6904d8f24da7 | refs/heads/master | 1,673,021,045,568 | 1,603,474,638,000 | 1,603,474,638,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,012 | lean | import .....math.new_affine.real_affine_space
import data.real.basic
/-
The abstraction implemented in this component supports SI-like
physical dimensions and measurement systems, including SI and
Imperial. Kevin believe it's not quite right, insofar as the
SI system isn't based on the right abstractions. For examp... |
314f537bb41f3011a1bf406fe462f14f99663dc2 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/algebra/category/fgModule/basic.lean | c439cce1df2ee9f1e023597a0c7fe742ba38a010 | [
"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 | 7,079 | lean | /-
Copyright (c) 2021 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer
-/
import category_theory.monoidal.rigid.basic
import category_theory.monoidal.subcategory
import linear_algebra.coevaluation
import linear_algebra.free_module.finit... |
e589bc47114e3ea0d6bb8da628012d60ad2f4b27 | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/tactic/congr.lean | e23fe29379d7131d7691724cef08d7a3849c8548 | [
"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 | 8,645 | lean | /-
Copyright (c) 2020 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import tactic.lint
import tactic.ext
/-!
# Congruence and related tactics
This file contains the tactic `congr'`, which is an extension of `congr`, and various ... |
96370f887f02d1fd6f85a2e220f4ea75ba31d8b6 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/linear_algebra/dimension.lean | fd541f9ab08c18f3c4354caf4b77183403f97957 | [
"Apache-2.0"
] | permissive | AntoineChambert-Loir/mathlib | 64aabb896129885f12296a799818061bc90da1ff | 07be904260ab6e36a5769680b6012f03a4727134 | refs/heads/master | 1,693,187,631,771 | 1,636,719,886,000 | 1,636,719,886,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 52,775 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johannes HΓΆlzl, Sander Dahmen, Scott Morrison
-/
import linear_algebra.dfinsupp
import linear_algebra.std_basis
import linear_algebra.isomorphisms
import set_theory.cof... |
d72a6fe4ee87e08ea55894bb571983d92c862744 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/measure_theory/integral/interval_integral.lean | 5e7fbf3cc0745ddfc4373ab878eb789297b94c20 | [
"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 | 141,801 | 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, Patrick Massot, SΓ©bastien GouΓ«zel
-/
import analysis.normed_space.dual
import data.set.intervals.disjoint
import measure_theory.measure.haar_lebesgue
import mea... |
02471af00a9cf6b5025c5b48a35709450c33c1e0 | 968e2f50b755d3048175f176376eff7139e9df70 | /examples/pred_logic/unnamed_690.lean | 9e898237d827846f528441261bdce25722e94e82 | [] | no_license | gihanmarasingha/mth1001_sphinx | 190a003269ba5e54717b448302a27ca26e31d491 | 05126586cbf5786e521be1ea2ef5b4ba3c44e74a | refs/heads/master | 1,672,913,933,677 | 1,604,516,583,000 | 1,604,516,583,000 | 309,245,750 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,007 | lean | import tactic.interactive
variables {U : Type*} {P : U β Prop}
namespace hidden
-- BEGIN
theorem not_forall : Β¬(β x, P x) β β x, Β¬P x :=
begin
-- By iff intro., it suffices to prove 1. `Β¬(β x, P x) β β x, Β¬P x` and 2. `β x, Β¬P x β Β¬(β x, P x)`
split,
{ intro hβ, -- Case 1. Assume `hβ : Β¬(β x, P x)`. It suffices t... |
e7faabf46bf21d6035cf2121de00c56c61dc31c1 | d744d97b07fc1e61b0ebea192b2d624125898128 | /test/polymorphism_test.lean | f4417c600ea63171eeead2ce94eb77975b8a44f6 | [
"MIT"
] | permissive | parkersullivan/leanstuff | 019c757848dd8f5db185e6973969141aee6fef7c | 3da132c44d365ecd933de64fa04ba66b9e620683 | refs/heads/master | 1,599,036,040,845 | 1,573,316,625,000 | 1,573,316,625,000 | 219,181,711 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 926 | lean | import ..src.list
open my_private
/-testing partially evaluation with polymorphic lists-/
#check pol_list
#check @pol_list.cons
#check @pol_list.cons β
#check @pol_list.cons β 7
/-creating some list instances-/
def pl0 : (pol_list nat) := pol_list.nil
def pl1 : (pol_list nat) := pol_list.cons 1 pl0
def pl2 : (pol_li... |
87ef8a73b7f7ca6a134eec66432c25b4d219052a | d1a52c3f208fa42c41df8278c3d280f075eb020c | /src/Lean/Widget/InteractiveGoal.lean | f5064d6f86b9df4350f4d346e904cab4935202dd | [
"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 | 5,338 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wojciech Nawrocki
-/
import Lean.Meta.PPGoal
import Lean.Widget.InteractiveCode
/-! RPC procedures for retrieving tactic and term goals with embedded `CodeWithInfos`. -/
name... |
cee540c7d8b3720aae105315d74cf428978489a6 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /hott/algebra/category/constructions/cone.hlean | 1eaf4b82f31888a35ce515ab8121b5c9a44401f8 | [
"Apache-2.0"
] | permissive | soonhokong/lean-osx | 4a954262c780e404c1369d6c06516161d07fcb40 | 3670278342d2f4faa49d95b46d86642d7875b47c | refs/heads/master | 1,611,410,334,552 | 1,474,425,686,000 | 1,474,425,686,000 | 12,043,103 | 5 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 7,330 | 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
Cones of a diagram in a category
-/
import ..nat_trans ..category
open functor nat_trans eq equiv is_trunc is_equiv iso sigma sigma.ops pi
namespace category
... |
3c907d14dfb73fe16e4e86a1311d2eca959a65ce | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/invalidNamedArgs.lean | 0310bbe72732bd8f39d4c45e7dd90fb20f2b896c | [
"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 | 185 | lean |
def ex1 (xs : List Nat) : Nat :=
xs.foldl (b := 0) fun sum x => sum + x
def f (a : Nat) (flag := true) : Nat :=
a + if flag then 1 else 0
def g (a : Nat) : Nat :=
f a (flg := false)
|
b3e425aa781a8ed14b1fa4d5cd54bab3d3651feb | 9028d228ac200bbefe3a711342514dd4e4458bff | /src/deprecated/subfield.lean | 561372247d1842a0184b28196a15486dfe871e14 | [
"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 | 5,141 | lean | /-
Copyright (c) 2018 Andreas Swerdlow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andreas Swerdlow
-/
import deprecated.subring
import algebra.group_with_zero_power
variables {F : Type*} [field F] (S : set F)
class is_subfield extends is_subring S : Prop :=
(inv... |
bc2c5521e560e8d0084d9ea4f0a551c3e6a65903 | 969dbdfed67fda40a6f5a2b4f8c4a3c7dc01e0fb | /src/analysis/calculus/times_cont_diff.lean | 95bf7aed8a2177e131e3f874135e4878657cab9e | [
"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 | 138,582 | lean | /-
Copyright (c) 2019 SΓ©bastien GouΓ«zel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: SΓ©bastien GouΓ«zel
-/
import analysis.calculus.mean_value
import analysis.calculus.formal_multilinear_series
/-!
# Higher differentiability
A function is `C^1` on a domain if it is... |
af746777a7df6e135dd22bef65f62b01c7761317 | e6b8240a90527fd55d42d0ec6649253d5d0bd414 | /src/algebra/order_functions.lean | a844f88b891812edba617e1cd9de65d0f46eb1cd | [
"Apache-2.0"
] | permissive | mattearnshaw/mathlib | ac90f9fb8168aa642223bea3ffd0286b0cfde44f | d8dc1445cf8a8c74f8df60b9f7a1f5cf10946666 | refs/heads/master | 1,606,308,351,137 | 1,576,594,130,000 | 1,576,594,130,000 | 228,666,195 | 0 | 0 | Apache-2.0 | 1,576,603,094,000 | 1,576,603,093,000 | null | UTF-8 | Lean | false | false | 12,704 | 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 algebra.ordered_group order.lattice
open lattice
universes u v
variables {Ξ± : Type u} {Ξ² : Type v}
attribute [simp] max_eq_left max_eq_right min_eq_left min... |
1381835962cfb084364b7d596e7792e40b03327b | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/algebra/non_unital_alg_hom.lean | 029d11977935d99801c2986bc3f9813f6a8e6e4b | [
"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 | 7,758 | 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.algebra.basic
/-!
# Morphisms of non-unital algebras
This file defines morphisms between two types, each of which carries:
* an addition,
* an additive z... |
0beaecdced0f74c8a6cf98fcb00431092ae233cb | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/special_functions/japanese_bracket.lean | 6108b5d2321393796acd4887fbe65bc7315abdab | [
"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 | 8,166 | lean | /-
Copyright (c) 2022 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll
-/
import measure_theory.measure.lebesgue.eq_haar
import measure_theory.integral.layercake
/-!
# Japanese Bracket
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to... |
2b711c223e17c3156bc81593f0c44383b9211864 | 46125763b4dbf50619e8846a1371029346f4c3db | /src/category_theory/discrete_category.lean | 6e1dcec8b25a7766efb6a2412aecae887186f021 | [
"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 | 3,186 | 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, Floris van Doorn
-/
import data.ulift
import data.fintype
import category_theory.opposites category_theory.equivalence
namespace category_theory
unive... |
cb951299f04b461dc5b8b009107edb4ed5d92f4a | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/constFun2.lean | 47078dec082e21b8be1db188fcb4990f50c63abb | [
"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 | 436 | lean | structure ConstantFunction (Ξ± Ξ² : Type) where
f : Ξ± β Ξ²
h : β a b, f a = f b
instance : CoeFun (ConstantFunction Ξ± Ξ²) (fun _ => Ξ± β Ξ²) where
coe s := s.f
instance : Coe (ConstantFunction Ξ± Ξ²) (Ξ± β Ξ²) where
coe s := s.f
def zeroNatNat : ConstantFunction Nat Nat where
f x := 0
h a b := rfl
def tst1 (x... |
fc5a4c8d3537fe9977b64bccfd48c7abd0a0da3d | a4673261e60b025e2c8c825dfa4ab9108246c32e | /stage0/src/Lean.lean | 8af268eb5634913570c2b1374e2e11d1d50e12d4 | [
"Apache-2.0"
] | permissive | jcommelin/lean4 | c02dec0cc32c4bccab009285475f265f17d73228 | 2909313475588cc20ac0436e55548a4502050d0a | refs/heads/master | 1,674,129,550,893 | 1,606,415,348,000 | 1,606,415,348,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 687 | 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.Data
import Lean.Compiler
import Lean.Environment
import Lean.Modifiers
import Lean.ProjFns
import Lean.Runtime
import Lean.ResolveName
import L... |
4b0aa67b4aacac77f4ab7ba30a8caa09ed39dc42 | ce89339993655da64b6ccb555c837ce6c10f9ef4 | /ukikagi/top23.lean | 7fada8b52c5a25f5abcae9238a3666a5fb9a7397 | [] | no_license | zeptometer/LearnLean | ef32dc36a22119f18d843f548d0bb42f907bff5d | bb84d5dbe521127ba134d4dbf9559b294a80b9f7 | refs/heads/master | 1,625,710,824,322 | 1,601,382,570,000 | 1,601,382,570,000 | 195,228,870 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,426 | lean | inductive bin : nat -> Prop
| bin_epsilon : bin 0
| bin_0 : β n, bin n -> bin (2 * n)
| bin_1 : β n, bin n -> bin (2 * n + 1)
definition is_expressible_in_binary_notation := bin.
lemma zero_or_one {n} (h: n < 2): n = 0 β¨ n = 1
:=
begin
cases h,
right, trivial,
left,
apply nat.eq_zero_of_le_zero,
exact nat.l... |
1d8844354995ce4cafb6e6572fb9d80d1d797f4e | 07c6143268cfb72beccd1cc35735d424ebcb187b | /src/measure_theory/bochner_integration.lean | 816b7f4748ea1821ae824b368db583e34f971f6d | [
"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 | 55,222 | lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou
-/
import measure_theory.simple_func_dense
import analysis.normed_space.bounded_linear_maps
/-!
# Bochner integral
The Bochner integral extends the definition of the Le... |
028e649bc77ac592b4fb1e30aee19ab1b83ce051 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/limits/shapes/kernel_pair.lean | aea26e543051c0ce1aaeec167768e8dbd4ebcf56 | [
"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 | 9,432 | lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import category_theory.limits.shapes.equalizers
import category_theory.limits.shapes.comm_sq
import category_theory.limits.shapes.regular_mono
/-!
# Kernel pairs
> THIS... |
be4e6e114c72a20693ade8545cdae543f9b04dba | 367134ba5a65885e863bdc4507601606690974c1 | /src/measure_theory/outer_measure.lean | 940e0b9d15173aa32834903c2fc40d9ec1b29fe3 | [
"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 | 41,821 | lean | /-
Copyright (c) 2017 Johannes HΓΆlzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes HΓΆlzl, Mario Carneiro
-/
import analysis.specific_limits
import measure_theory.measurable_space
import measure_theory.pi_system
import topology.algebra.infinite_sum
/-!
# Out... |
b339a50c89c5ebb1ca2e09a7d7ab88e38c9260f5 | f1b175e38ffc5cc1c7c5551a72d0dbaf70786f83 | /ring_theory/associated.lean | b3c6a760654b595e8813ba751d5cf00d8c78c46f | [
"Apache-2.0"
] | permissive | mjendrusch/mathlib | df3ae884dd5ce38c7edf452bcbfd3baf4e3a6214 | 5c209edb7eb616a26f64efe3500f2b1ba95b8d55 | refs/heads/master | 1,585,663,284,800 | 1,539,062,055,000 | 1,539,062,055,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 16,680 | lean | /-
Copyright (c) 2018 Johannes HΓΆlzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes HΓΆlzl, Jens Wagemaker
Associated and irreducible elements.
-/
import order.galois_connection algebra.group data.equiv.basic data.multiset data.int.gcd
variables {Ξ± : Type*} ... |
c1e60e2f5bc6c864809ba1aa8dfc7fe098a76c6f | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/topology/algebra/order/liminf_limsup.lean | c16bae4dda7256a1c059f1554eb6c37d318bb89a | [
"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 | 20,708 | lean | /-
Copyright (c) 2017 Johannes HΓΆlzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes HΓΆlzl, Mario Carneiro, Yury Kudryashov
-/
import algebra.big_operators.intervals
import algebra.big_operators.order
import algebra.indicator_function
import order.liminf_limsu... |
a3c348f0f8a64db5fed886e58642ca1b2a2c8516 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/model_theory/finitely_generated.lean | 1ce88447d7115a751f9f1dcdf6596f1f74811091 | [
"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 | 9,379 | lean | /-
Copyright (c) 2022 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import model_theory.substructures
/-!
# Finitely Generated First-Order Structures
This file defines what it means for a first-order (sub)structure to be finitely or ... |
60608cd8a2f3b686c4934ff7e735471a784ae089 | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/category_theory/adjunction/reflective.lean | ce0622537d1adf3b0a1eb4a4a1d14f091d7b97b8 | [
"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 | 4,313 | lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import category_theory.limits.preserves.shapes.binary_products
import category_theory.limits.preserves.shapes.terminal
import category_theory.adjunction.fully_faithful
/... |
0fb1eb47e9339a3ca1daaec602bd15cf5282792d | 1a61aba1b67cddccce19532a9596efe44be4285f | /hott/types/bool.hlean | 941672e5595fd89e99e01e26f5793d4651389bbe | [
"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 | 1,311 | 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
Theorems about the booleans
-/
open is_equiv eq equiv function is_trunc option unit
namespace bool
definition ff_ne_tt : ff = tt β empty
| [none]
definiti... |
41d69c835b4855e4788ef12ffa69d06f89e40e79 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /test/group.lean | 8c36d0e2e4d0c989b87cf8a5314df9de85433ef4 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 1,706 | lean | import tactic.group
variables {G : Type} [group G]
example (a b c d : G) : c *(a*b)*(bβ»ΒΉ*aβ»ΒΉ)*c = c*c :=
by group
example (a b c d : G) : (b*cβ»ΒΉ)*c *(a*b)*(bβ»ΒΉ*aβ»ΒΉ)*c = b*c :=
by group
example (a b c d : G) : cβ»ΒΉ*(b*cβ»ΒΉ)*c *(a*b)*(bβ»ΒΉ*aβ»ΒΉ*bβ»ΒΉ)*c = 1 :=
by group
-- The following is known as the Hall-Witt identity,
... |
2ff0ce3c7ebfff06e781f7f1234fd523d49b1288 | 12dabd587ce2621d9a4eff9f16e354d02e206c8e | /world10/level02.lean | 4195f44965f036f5dc063cab26a0c782da4de43b | [] | no_license | abdelq/natural-number-game | a1b5b8f1d52625a7addcefc97c966d3f06a48263 | bbddadc6d2e78ece2e9acd40fa7702ecc2db75c2 | refs/heads/master | 1,668,606,478,691 | 1,594,175,058,000 | 1,594,175,058,000 | 278,673,209 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 92 | lean | lemma le_refl (x : mynat) : x β€ x :=
begin
rw le_iff_exists_add,
use 0,
rwa add_zero,
end
|
a2cc52b7001415b5681bd7bf5b3bf8e04f0e7665 | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/measure_theory/decomposition/lebesgue.lean | 958004437b4e96547c83bfbf3dd9c28895198828 | [
"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 | 35,456 | 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.jordan
/-!
# Lebesgue decomposition
This file proves the Lebesgue decomposition theorem. The Lebesgue decomposition theorem states tha... |
00e797c17df0874f0cf4daa769c07e257c55849e | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/group_theory/sylow.lean | ed32ed6fb76719955e8be4008d96ac4f1e020b3c | [
"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 | 14,053 | 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 group_theory.group_action
import group_theory.quotient_group
import group_theory.order_of_element
import data.zmod.basic
import data.fintype.card
import data.list.... |
2f3750e2f19e12d5954a6291a490d65ea4ef4684 | b70031c8e2c5337b91d7e70f1e0c5f528f7b0e77 | /src/analysis/normed_space/multilinear.lean | fb8c71d84254705c3ff0021b1e43489a1811ca3a | [
"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 | 58,206 | lean | /-
Copyright (c) 2020 SΓ©bastien GouΓ«zel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: SΓ©bastien GouΓ«zel
-/
import analysis.normed_space.operator_norm
import topology.algebra.multilinear
/-!
# Operator norm on the space of continuous multilinear maps
When `f` is a c... |
4555550e8cefccb0e58e6aea46659f23d2fe1e66 | 54d7e71c3616d331b2ec3845d31deb08f3ff1dea | /library/init/relator.lean | 019dc3525ad7ee0785785cfca6b84bb31feee893 | [
"Apache-2.0"
] | permissive | pachugupta/lean | 6f3305c4292288311cc4ab4550060b17d49ffb1d | 0d02136a09ac4cf27b5c88361750e38e1f485a1a | refs/heads/master | 1,611,110,653,606 | 1,493,130,117,000 | 1,493,167,649,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,155 | lean | /-
Copyright (c) 2017 Johannes HΓΆlzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes HΓΆlzl
Relator for functions, pairs, sums, and lists.
-/
prelude
import init.core init.data.basic
namespace relator
universe variables uβ uβ vβ vβ
reserve infixr ` β `:40
... |
45992bd82c4a8bb68d79ae66bbe0378ea9074944 | fecda8e6b848337561d6467a1e30cf23176d6ad0 | /src/ring_theory/multiplicity.lean | 55a527f8573527878fab0ddd57595131bc59299b | [
"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 | 17,863 | lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Chris Hughes
-/
import algebra.associated
import data.int.gcd
import algebra.big_operators.basic
import data.nat.enat
import tactic
variables {Ξ± : Type*}
open nat r... |
6307a677c0d260546295f262be9ff06f0836bdca | efce24474b28579aba3272fdb77177dc2b11d7aa | /src/homotopy_theory/formal/cofibrations/cylinder.lean | 1bfab49e5f1eb728fc2856c11211a350b7f22d0e | [
"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 | 15,505 | lean | import category_theory.pasting_pushouts
import homotopy_theory.formal.cylinder.definitions
import .cofibration_category
universes v u
open category_theory
open category_theory.category
local notation f ` β `:80 g:80 := g β« f
namespace homotopy_theory.cofibrations
open homotopy_theory.cylinder (endpoint)
open homotop... |
3a6050b91601be5e5dff2b70f4b5aa10a571e175 | 46125763b4dbf50619e8846a1371029346f4c3db | /src/algebra/category/CommRing/colimits.lean | 65ac2e2b5f24ba2becb03714adbebb6dd4243d59 | [
"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 | 11,843 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import algebra.category.CommRing.basic
import category_theory.limits.limits
/-!
# The category of commutative rings has all colimits.
This file uses a "pre-automate... |
012bbd0a46cfc5ee232863a567b51208d6b93189 | f5f7e6fae601a5fe3cac7cc3ed353ed781d62419 | /src/category_theory/instances/CommRing/basic.lean | caed3e56dd9a3a782e7b1bd0c62b422efb57a224 | [
"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 | 3,143 | lean | /- Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Johannes HΓΆlzl
Introduce CommRing -- the category of commutative rings.
-/
import category_theory.instances.monoids
import category_theory.fully_faithful
import algeb... |
345692a0317065a566189076ef4a39b8a084d6ba | e00ea76a720126cf9f6d732ad6216b5b824d20a7 | /src/group_theory/congruence.lean | 58e1f8878ed110b68d4109804c6267a32f1b8b66 | [
"Apache-2.0"
] | permissive | vaibhavkarve/mathlib | a574aaf68c0a431a47fa82ce0637f0f769826bfe | 17f8340912468f49bdc30acdb9a9fa02eeb0473a | refs/heads/master | 1,621,263,802,637 | 1,585,399,588,000 | 1,585,399,588,000 | 250,833,447 | 0 | 0 | Apache-2.0 | 1,585,410,341,000 | 1,585,410,341,000 | null | UTF-8 | Lean | false | false | 43,481 | lean | /-
Copyright (c) 2019 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
import group_theory.submonoid
import data.setoid
import algebra.pi_instances
/-!
# Congruence relations
This file defines congruence relations: equivalence r... |
42036e66a62238287952026dc09291d92dfb47de | 7b66d83f3b69dae0a3dfb684d7ebe5e9e3f3c913 | /src/solutions/wednesday/afternoon/topological_spaces.lean | 1fe3c9e518077fcfb2a37bb2707a3f6e4753b565 | [] | permissive | dpochekutov/lftcm2020 | 58a09e10f0e638075b97884d3c2612eb90296adb | cdfbf1ac089f21058e523db73f2476c9c98ed16a | refs/heads/master | 1,669,226,265,076 | 1,594,629,725,000 | 1,594,629,725,000 | 279,213,346 | 1 | 0 | MIT | 1,594,622,757,000 | 1,594,615,843,000 | null | UTF-8 | Lean | false | false | 8,042 | lean | import tactic
import data.set.finite
/-
# (Re)-Building topological spaces in Lean
Mathlib has a large library of results on topological spaces, including various construcions,
separation axioms, Tychonoff's theorem, sheaves, Stone-Δech compactification, Heine-Cantor, to name
but a few.
See https://leanprover-communi... |
713a1d93ea05859360acc61e4224882f28dd5414 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/data/int/gcd.lean | b729e3d99a083a1b9bcb56ea257f4281ded62760 | [
"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 | 24,448 | lean | /-
Copyright (c) 2018 Guy Leroy. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sangwoo Jo (aka Jason), Guy Leroy, Johannes HΓΆlzl, Mario Carneiro
-/
import data.nat.prime
/-!
# Extended GCD and divisibility over β€
## Main definitions
* Given `x y : β`, `xgcd x y` com... |
20f49dfe125f699e883f266da83c50c4ba9dd818 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/topology/sheaves/sheaf_condition/opens_le_cover.lean | ed758a26eae2c980a346f6252a4c18d951b57dbf | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,419 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.topology.sheaves.presheaf
import Mathlib.category_theory.limits.cofinal
import Mathlib.topo... |
ee47d1cf2b8ac55f1d21618e663e10a6342081ef | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/linear_algebra/invariant_basis_number.lean | 2051aecab4c283d0ca09bcc1241b1c4b9a0e1e2c | [
"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 | 5,650 | 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 linear_algebra.finite_dimensional
import ring_theory.ideal.basic
/-!
# Invariant basis number property
We say that a ring `R` satisfies the invariant basis num... |
ed4055bcc360d5dd8b18408ad932eb624fee93ec | 95dcf8dea2baf2b4b0a60d438f27c35ae3dd3990 | /src/field_theory/subfield.lean | 8755f1c15fefa43af56da2093298214f6bbbb30c | [
"Apache-2.0"
] | permissive | uniformity1/mathlib | 829341bad9dfa6d6be9adaacb8086a8a492e85a4 | dd0e9bd8f2e5ec267f68e72336f6973311909105 | refs/heads/master | 1,588,592,015,670 | 1,554,219,842,000 | 1,554,219,842,000 | 179,110,702 | 0 | 0 | Apache-2.0 | 1,554,220,076,000 | 1,554,220,076,000 | null | UTF-8 | Lean | false | false | 2,417 | lean | /-
Copyright (c) 2018 Andreas Swerdlow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andreas Swerdlow
-/
import ring_theory.subring
variables {F : Type*} [field F] (S : set F)
class is_subfield extends is_subring S : Prop :=
(inv_mem : β {x : F}, x β 0 β x β S β x... |
80ccb0b8115677bef58a8dfcf40ed989a81d0760 | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /tests/lean/eraseSimp.lean | f52d35f84f2d5854a1c9fc3d59e4842d6d3b5d7b | [
"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 | 645 | lean | theorem foo (n : Nat) : n + n = 2*n := by
rw [Nat.mul_comm, Nat.mul_succ, Nat.mul_succ, Nat.mul_zero, Nat.zero_add]
attribute [-simp] foo -- Error
theorem ex1 {a b : Nat} (hβ : a = b) : 0 + a = b := by
simp
assumption
section
attribute [-simp] Nat.zero_add
theorem ex2 {a b : Nat} (hβ : a = b) : 0 + a = b := ... |
124a3ab8e2d54932f05796288aacf981b75fa23a | 947b78d97130d56365ae2ec264df196ce769371a | /src/Init/WF.lean | 60d6689fc4167d637abcb2edff6149f2dbe3d396 | [
"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 | 13,434 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
prelude
import Init.Data.Nat.Basic
universes u v
set_option codegen false
inductive Acc {Ξ± : Sort u} (r : Ξ± β Ξ± β Prop) : Ξ± β Prop
| intro (x : Ξ±) (h : β ... |
f04005f50c6839613d0b44f82de3181954c78b32 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/rw_at_failure.lean | 14e4d5cf75e4075e0ad835701d794f20878b3e5c | [
"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 | 161 | lean | import data.nat
open nat algebra
example (a b : nat) : a = b β 0 + a = 0 + b :=
begin
rewrite zero_add at {2} -- Should fail since nothing is rewritten
end
|
f66564bdaca740721c782801005ae3a8df08e667 | 8cb37a089cdb4af3af9d8bf1002b417e407a8e9e | /library/data/rbtree/min_max.lean | a9232886a9b62d5362fcf6057767d33281ad7b63 | [
"Apache-2.0"
] | permissive | kbuzzard/lean | ae3c3db4bb462d750dbf7419b28bafb3ec983ef7 | ed1788fd674bb8991acffc8fca585ec746711928 | refs/heads/master | 1,620,983,366,617 | 1,618,937,600,000 | 1,618,937,600,000 | 359,886,396 | 1 | 0 | Apache-2.0 | 1,618,936,987,000 | 1,618,936,987,000 | null | UTF-8 | Lean | false | false | 3,710 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import data.rbtree.basic
universe u
namespace rbnode
variables {Ξ± : Type u} {lt : Ξ± β Ξ± β Prop}
lemma mem_of_min_eq (lt : Ξ± β Ξ± β Prop) [is_irrefl Ξ± lt] {... |
280c1d586a47056a91fac9e20f39f2fd26eb1f66 | 649957717d58c43b5d8d200da34bf374293fe739 | /src/algebra/direct_limit.lean | cf8c2d47ece6ebca87a99c97c887c38ab83a7c9c | [
"Apache-2.0"
] | permissive | Vtec234/mathlib | b50c7b21edea438df7497e5ed6a45f61527f0370 | fb1848bbbfce46152f58e219dc0712f3289d2b20 | refs/heads/master | 1,592,463,095,113 | 1,562,737,749,000 | 1,562,737,749,000 | 196,202,858 | 0 | 0 | Apache-2.0 | 1,562,762,338,000 | 1,562,762,337,000 | null | UTF-8 | Lean | false | false | 25,110 | lean | /-
Copyright (c) 2019 Kenny Lau, Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Chris Hughes
Direct limit of modules, abelian groups, rings, and fields.
See Atiyah-Macdonald PP.32-33, Matsumura PP.269-270
Generalizes the notion of "union", o... |
0ba4a0c1b65e694cb3cd0eb4adfdba24fecd767d | 32da3d0f92cab08875472ef6cacc1931c2b3eafa | /src/measure_theory/simple_func_dense.lean | 7fe2def69820b18b3b18a28665d7398ce16f970d | [
"Apache-2.0"
] | permissive | karthiknadig/mathlib | b6073c3748860bfc9a3e55da86afcddba62dc913 | 33a86cfff12d7f200d0010cd03b95e9b69a6c1a5 | refs/heads/master | 1,676,389,371,851 | 1,610,061,127,000 | 1,610,061,127,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,622 | lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Yury Kudryashov
-/
import measure_theory.l1_space
/-!
# Density of simple functions
Show that each Borel measurable function can be approximated,
both pointwise and in ... |
443ee3bebedc0ce844b2ced040e6b565bb2c800f | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/topology/algebra/continuous_affine_map.lean | 9671798ddb28624f856c6a02233fefadbdf5bed7 | [
"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 | 5,043 | 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 linear_algebra.affine_space.affine_map
import topology.continuous_function.basic
/-!
# Continuous affine maps.
This file defines a type of bundled continuous affin... |
12cd43fe3814617867899ec510ed46657d7bfc57 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/algebra/ring/prod.lean | a258cf0830e4d96628ac41654795535f9e692500 | [
"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 | 6,646 | lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes HΓΆlzl, Chris Hughes, Mario Carneiro, Yury Kudryashov
-/
import algebra.group.prod
import algebra.ring.basic
import data.equiv.ring
/-!
# Semiring, ring etc structures on `R ... |
cff3e0e39e5ea30aa490f3f691d00018de589bbf | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/list/sigma.lean | a8cd0ad82d71533c689b9b6132dc2efc72e94d23 | [
"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 | 24,699 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Sean Leather
Functions on lists of sigma types.
-/
import data.list.perm
import data.list.range
import data.sigma
universes u v
namespace list
variables {Ξ± : Type u}... |
705b5cebac6d7e04f94253010d199239c38c06b4 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/is_nil.lean | 7459b9693aec16b11c9a429821b92396818f64e0 | [
"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 | 669 | lean | import logic
open tactic
inductive list (A : Type) : Type :=
| nil {} : list A
| cons : A β list A β list A
namespace list end list open list
open eq
definition is_nil {A : Type} (l : list A) : Prop
:= list.rec true (fun h t r, false) l
theorem is_nil_nil (A : Type) : is_nil (@nil A)
:= of_eq_true (refl true)
the... |
d2133435cbf923e6fcf9c964ec948ed278ca6f47 | 0003047346476c031128723dfd16fe273c6bc605 | /src/analysis/normed_space/deriv.lean | 67d64aac0e2b117df106c590c02e549cdb6dbe8c | [
"Apache-2.0"
] | permissive | ChandanKSingh/mathlib | d2bf4724ccc670bf24915c12c475748281d3fb73 | d60d1616958787ccb9842dc943534f90ea0bab64 | refs/heads/master | 1,588,238,823,679 | 1,552,867,469,000 | 1,552,867,469,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 13,853 | lean | /-
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad
The FrΓ©chet derivative.
Let `E` and `F` be normed spaces, and `f : E β F`. Then
`has_fderiv_at_within f f' x s`
says that the function `f' : E β F` is a bounded linea... |
101c5234676fe5ba89144e8cfd440e6cd442a0e1 | 9db059bff49b1090a86ec0050ac6c577eb16ac67 | /src/meetings/numbers.lean | 1ec3832ad1ffb71f4bf45655e508c3e8ebb9407e | [] | no_license | fpvandoorn/Harvard-tutoring | d64cd75c4c529009ee562c30e9cb245fe237e760 | a8846c08e32cdc7b91a7e28adfa5d9b2810088b0 | refs/heads/master | 1,680,870,428,641 | 1,617,022,194,000 | 1,617,022,194,000 | 330,297,467 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,944 | lean | import tactic.omega
import data.real.basic
import data.real.sqrt
import data.nat.prime
import data.nat.factorial
/- Dealing with numbers:
β natural numbers
β€ integers
β rational numbers
β real numbers
β complex numbers
Tactics:
norm_num, linarith, ring, norm_cast, field_simp, omega
Also... |
bb4b0cb19ddb40d9e0e5ecd2fe6372683446090c | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/geometry/manifold/times_cont_mdiff_map.lean | cb7988ed528c1466c564250c50623f6392f4e06c | [] | 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 | 10,227 | lean | /-
Copyright Β© 2020 NicolΓ² Cavalleri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: NicolΓ² Cavalleri.
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.geometry.manifold.times_cont_mdiff
import Mathlib.topology.continuous_map
import Mathlib.... |
3331d5ef0218e2f1005c689037d0b387810d127f | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/parity.lean | 61410fc5820ece17f3ab08ceea005cd356651486 | [
"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 | 12,191 | lean | /-
Copyright (c) 2022 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
import algebra.group_power.lemmas
/-! # Squares, even and odd elements
This file proves some general facts about squares, even and odd elements of semirings.
In the... |
2dfeb60f6b0b3031b5cb3c6a5803ac41fdee4624 | cfef816283af58a9ea4678b69595e86562fd4c6a | /src/scone/deq.lean | 29749e0292853c05bf97c3b41a6a2a7d44bc2ee8 | [] | no_license | rwbarton/scone | 6fc5bee6766c170d2edeefaf608ee32d665c7c77 | 6f3d35f7a3bed772475ff7954875b9ee7554aae3 | refs/heads/master | 1,672,462,177,915 | 1,603,245,162,000 | 1,603,245,162,000 | 305,762,158 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 836 | lean | import tactic.basic
/-
dependent equality / dependent path / "pathover" from HoTT/cubical type theory
-/
inductive deq {Ξ± : Sort*} {C : Ξ± β Sort*} :
Ξ {a a' : Ξ±} (e : a = a') (x : C a) (x' : C a'), Prop
| refl {a : Ξ±} (x : C a) : deq (eq.refl a) x x
attribute [refl] deq.refl
notation x ` =[`:50 e:50 `] `:50 x':50... |
e9a3b9970ffaaa454d0ad2ccc6c5554be1bc0062 | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /src/builtin/list.lean | a950aeeb770ef4578c53b25d7d17744219143ddb | [
"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 | 8,349 | lean | -- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Author: Leonardo de Moura
import num subtype optional macros tactic
using num
using subtype
namespace list
definition none {A : (Type U)} : optional A
:= optional::@none A
defini... |
314c52c29d33e6bdfc101b3905a71382d590c0d5 | d436468d80b739ba7e06843c4d0d2070e43448e5 | /src/category_theory/monoidal/category.lean | 1c35baae6cd833aca6d20972b70e67618855932f | [
"Apache-2.0"
] | permissive | roro47/mathlib | 761fdc002aef92f77818f3fef06bf6ec6fc1a28e | 80aa7d52537571a2ca62a3fdf71c9533a09422cf | refs/heads/master | 1,599,656,410,625 | 1,573,649,488,000 | 1,573,649,488,000 | 221,452,951 | 0 | 0 | Apache-2.0 | 1,573,647,693,000 | 1,573,647,692,000 | null | UTF-8 | Lean | false | false | 16,139 | lean | /-
Copyright (c) 2018 Michael Jendrusch. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Jendrusch, Scott Morrison
-/
import category_theory.products.basic
import category_theory.natural_isomorphism
import tactic.basic
import tactic.slice
open category_theory
... |
7c58fa13fc4703b1c53b6e501cefba37e4545c54 | 4964756ed24f92f51f71d6928cd37e5ddf7bbbf9 | /mm0-lean/mm0/basic.lean | e5a22ae9e3fd65d319c4acd28768543833d085b6 | [] | no_license | graydon/mm0 | 5009336a3c324207c55372dfae3fa9ae2ad482bf | f8b03d92c86d2446575a5dc33f94044d7045df07 | refs/heads/master | 1,593,406,774,913 | 1,564,787,132,000 | 1,564,787,132,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,861 | lean | import data.buffer category.basic tactic.core
def name.to_simple : name β string
| (name.mk_string s _) := s
| _ := ""
meta def lean.parser.tk' (n : name) : lean.parser unit :=
do x β lean.parser.ident, tactic.trace (x, n), guard (x = n)
meta def user_attribute.get_param' {Ξ± Ξ² : Type} [reflected Ξ²] (attr : user_attr... |
d0dbe5aae8cb978a9fe3ea3ff9afc6d1a76d275a | 130c49f47783503e462c16b2eff31933442be6ff | /src/Lean/PrettyPrinter/Delaborator/Basic.lean | fdb32397fc744e69699c13bc263c90317cf7b692 | [
"Apache-2.0"
] | permissive | Hazel-Brown/lean4 | 8aa5860e282435ffc30dcdfccd34006c59d1d39c | 79e6732fc6bbf5af831b76f310f9c488d44e7a16 | refs/heads/master | 1,689,218,208,951 | 1,629,736,869,000 | 1,629,736,896,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,892 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Ullrich
-/
import Lean.KeyedDeclsAttribute
import Lean.ProjFns
import Lean.Syntax
import Lean.Meta.Match
import Lean.Elab.Term
import Lean.PrettyPrinter.Delaborator.Op... |
d884d6d70d787f9ed81722cb1c0d1262446f4f7a | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/topology/uniform_space/absolute_value.lean | e18019eb9fed72f1fb6766b78b5aca9d1785030d | [
"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 | 2,942 | lean | /-
Copyright (c) 2019 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import data.real.cau_seq
import topology.uniform_space.basic
/-!
# Uniform structure induced by an absolute value
We build a uniform space structure on a commutativ... |
9c76b1a5c7ea5502cdebc250f9bea75d2bfe0ba8 | ec62863c729b7eedee77b86d974f2c529fa79d25 | /22/a.lean | 04d4a3aa1d64ad8195fe1c9f0e3576a1eccc4539 | [] | no_license | rwbarton/advent-of-lean-4 | 2ac9b17ba708f66051e3d8cd694b0249bc433b65 | 417c7e2718253ba7148c0279fcb251b6fc291477 | refs/heads/main | 1,675,917,092,057 | 1,609,864,581,000 | 1,609,864,581,000 | 317,700,289 | 24 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 670 | lean | def parseInput (input : String) : List Nat Γ List Nat:=
match input.trim.splitOn "\n\n" with
| [p1, p2] => (((p1.splitOn "\n").drop 1).map String.toNat!, ((p2.splitOn "\n").drop 1).map String.toNat!)
| _ => panic! "invalid parse"
def score (deck : List Nat) : Nat :=
let N := deck.length
deck.enum.foldl (Ξ» sum β¨i, valβ©... |
87ef2671b1901dc72a64c4dd2596ec043535502a | 86f6f4f8d827a196a32bfc646234b73328aeb306 | /examples/basics/unnamed_992.lean | 07274415503ed292bd78363b2ec323d3278deb98 | [] | 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 | 138 | lean | import data.real.basic
variables a b c : β
#check (le_refl : β a : β, a β€ a)
#check (le_trans : a β€ b β b β€ c β a β€ c) |
fbd103bdfbd14ad90369b9abb2610ec3036e59b8 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/namespace_bug.lean | 0ddb03c0fce2bd07bc0aa244869381412bcac30c | [
"Apache-2.0"
] | permissive | soonhokong/lean-osx | 4a954262c780e404c1369d6c06516161d07fcb40 | 3670278342d2f4faa49d95b46d86642d7875b47c | refs/heads/master | 1,611,410,334,552 | 1,474,425,686,000 | 1,474,425,686,000 | 12,043,103 | 5 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 68 | lean | namespace playground
namespace nat
check 2+3
end nat
end playground
|
5a59650e32ca7a3892c2ac615c59a173ef2213ab | 94637389e03c919023691dcd05bd4411b1034aa5 | /src/inClassNotes/typeclasses/structures/field_inheritance.lean | 4b206b7d94292bfa874cdbf96364e2ae3829b0e3 | [] | 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 | 670 | lean | /-
How to inherit field values from parent objects.
-/
@[class]
structure A (Ξ± : Type) := (n m : nat)
instance a : A nat := β¨ 1, 4 β© -- anonymous constructor
instance a' : A nat := { m := 4, n := 1 } -- alternative notation for objects
#reduce a
#reduce a'
class B (Ξ± : Type) := (h : nat) (k : nat)
ins... |
05f87f1d57f477d29bc9c4cce1c61ba37948f279 | c5b07d17b3c9fb19e4b302465d237fd1d988c14f | /src/functors/analytic.lean | e55747983a4c11c0c9d525253ac0ef9a6f87dc8b | [
"MIT"
] | permissive | skaslev/papers | acaec61602b28c33d6115e53913b2002136aa29b | f15b379f3c43bbd0a37ac7bb75f4278f7e901389 | refs/heads/master | 1,665,505,770,318 | 1,660,378,602,000 | 1,660,378,602,000 | 14,101,547 | 0 | 1 | MIT | 1,595,414,522,000 | 1,383,542,702,000 | Lean | UTF-8 | Lean | false | false | 2,140 | lean | import data.fseq
import data.iso
import functors.polynomial
-- Analytic functor
-- This is definition 1.2 from [3] but the relation r doesn't depend
-- on the index i, only on its size s(i)
-- [3] https://www.ms.u-tokyo.ac.jp/~ryu/papers/taa.ps
-- af(r,I,s,x) = Ξ£ i:I, x^s(i) / r(s(i))
def af (r : Ξ n A, rel (fseq n A)... |
47ac327553d63d96b3fd7e59f0b7e38b972ee14e | 6b7c9c6393bac7cb1c64582a1c62597e24f5bb80 | /src/tactic/gptf/utils/util.lean | 97b936e2ee6e975522c2dfc20974437107803a8f | [
"Apache-2.0"
] | permissive | alreadydone/lean-gptf | 56a7d9cbd9400af72fb143d60c8774b8cfbc09cb | b4ab1eb2da0178f3dcdc49771d9fed6b50e35d98 | refs/heads/master | 1,679,371,993,063 | 1,614,479,778,000 | 1,614,479,778,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 16,526 | lean | /-
Copyright (c) 2021 Jesse Michael Han. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author(s): Jesse Michael Han, Ed Ayers
Utils for `gptf`.
-/
import system.io
import tactic
import tactic.gptf.utils.derive_has_to_format
section string
namespace string
def replace_char... |
edc985ef1e40bd788da4f77ac6b2e76fdc069bc9 | 02005f45e00c7ecf2c8ca5db60251bd1e9c860b5 | /src/algebra/lie/quotient.lean | 92593b439cf2414e353f50535a30e4dbc2f54b94 | [
"Apache-2.0"
] | permissive | anthony2698/mathlib | 03cd69fe5c280b0916f6df2d07c614c8e1efe890 | 407615e05814e98b24b2ff322b14e8e3eb5e5d67 | refs/heads/master | 1,678,792,774,873 | 1,614,371,563,000 | 1,614,371,563,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,037 | 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.submodule
import algebra.lie.of_associative
/-!
# Quotients of Lie algebras and Lie modules
Given a Lie submodule of a Lie module, the quotient carries... |
b0a1eaf4e93a1d4077b53ad3f057debd8f338bb6 | 8b9f17008684d796c8022dab552e42f0cb6fb347 | /library/data/set/default.lean | 600339d2386ef5be24660b8f2006637a3ffc3583 | [
"Apache-2.0"
] | permissive | chubbymaggie/lean | 0d06ae25f9dd396306fb02190e89422ea94afd7b | d2c7b5c31928c98f545b16420d37842c43b4ae9a | refs/heads/master | 1,611,313,622,901 | 1,430,266,839,000 | 1,430,267,083,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 206 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.set.default
Author: Jeremy Avigad
-/
import .basic .function .map
|
83fa5d3be371e1d8d360c1d10d87fe516edb8d88 | 564ebb83138d490783aa8aaa0a0e0e86f29a884f | /PrimeLean4/solution_1/PrimeLean4.lean | 16f7331e21ac1b7b5f6570c3259f082dffdc0a19 | [] | no_license | Lucretia/Primes | 156e9b25e65359c63258ce579ccdb3447fbee794 | c55cd2f184b2af58871881605f1f58344b45d0cf | refs/heads/add-optimised-ada | 1,689,446,644,352 | 1,630,767,440,000 | 1,630,767,440,000 | 384,164,908 | 1 | 1 | null | 1,632,662,711,000 | 1,625,757,095,000 | TeX | UTF-8 | Lean | false | false | 3,184 | lean | import Init
/- From lean4 tests -/
structure Loop where
@[inline]
partial def Loop.forIn {Ξ² : Type u} {m : Type u β Type v} [Monad m] (loop : Loop) (init : Ξ²) (f : Unit β Ξ² β m (ForInStep Ξ²)) : m Ξ² :=
let rec @[specialize] loop (b : Ξ²) : m Ξ² := do
match β f () b with
| ForInStep.done b => pure b
| F... |
9ac9dc05acf0b69d5ba6c9bccca816b9c13802c1 | a721fe7446524f18ba361625fc01033d9c8b7a78 | /src/principia/sequence.lean | 117e2ac29d7a8a44ccd81d5b666748f0dff8a976 | [] | no_license | Sterrs/leaning | 8fd80d1f0a6117a220bb2e57ece639b9a63deadc | 3901cc953694b33adda86cb88ca30ba99594db31 | refs/heads/master | 1,627,023,822,744 | 1,616,515,221,000 | 1,616,515,221,000 | 245,512,190 | 2 | 0 | null | 1,616,429,050,000 | 1,583,527,118,000 | Lean | UTF-8 | Lean | false | false | 3,550 | lean | import .mynat.lt
namespace hidden
def sequence (Ξ± : Type) := mynat β Ξ±
namespace sequence
variable {Ξ± : Type}
def is_increasing (k_n: mynat β mynat): Prop :=
β m n: mynat, m < n β k_n m < k_n n
def subsequence
(a: sequence Ξ±) (k_n: mynat β mynat)
(h_incr: is_increasing k_n): sequence Ξ± :=
a β k_n
theorem subsequ... |
79db6d095b1fe6c22d4dea6b343997821f59de5e | 46125763b4dbf50619e8846a1371029346f4c3db | /src/category_theory/limits/shapes/kernels.lean | 39055966f63ec1b1c02ed80f53718995ddf8c099 | [
"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 | 8,820 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Markus Himmel
-/
import category_theory.limits.shapes.zero
import category_theory.limits.shapes.equalizers
/-!
# Kernels and cokernels
In a category with zero morphis... |
0e98601b7f683cdabe6795e154300718618f33e7 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/order/lattice_auto.lean | 718df1fd00fae40b8c093f048ef18fa41f727f6b | [] | 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 | 22,423 | lean | /-
Copyright (c) 2017 Johannes HΓΆlzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes HΓΆlzl
Defines the inf/sup (semi)-lattice with optionally top/bot type class hierarchy.
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.order.rel... |
c06e286aa866f7aaf35181ac1579b6276239c30b | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/bad_inaccessible.lean | 0450738da89199dda9ff60062451c1ca6bb520e9 | [
"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 | 583 | lean | -- These definitions can be processed by the new equation compiler without producing errors.
universe variables u
definition f1 : nat β nat β nat
| a .(a) := a
definition f2 : β (a b c : nat), a = c β c = a
| a b .(b) rfl := rfl
inductive vec (A : Type u) : nat β Type (max 1 u)
| nil {} : vec 0
| cons : Ξ {n}, A β v... |
cc95a2a70c126169bb3ff758a0446c59e190d7e0 | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /src/Lean/Elab/Declaration.lean | 8fd1036e251f3824a78042bb1ce051d1ca2e0288 | [
"Apache-2.0"
] | permissive | WojciechKarpiel/lean4 | 7f89706b8e3c1f942b83a2c91a3a00b05da0e65b | f6e1314fa08293dea66a329e05b6c196a0189163 | refs/heads/master | 1,686,633,402,214 | 1,625,821,189,000 | 1,625,821,258,000 | 384,640,886 | 0 | 0 | Apache-2.0 | 1,625,903,617,000 | 1,625,903,026,000 | null | UTF-8 | Lean | false | false | 12,348 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Sebastian Ullrich
-/
import Lean.Util.CollectLevelParams
import Lean.Elab.DeclUtil
import Lean.Elab.DefView
import Lean.Elab.Inductive
import Lean.Elab.Struct... |
08ddfc90847257a0792179c336a14b8a2f8c62a5 | 3aad12fe82645d2d3173fbedc2e5c2ba945a4d75 | /src/tactic/to_int.lean | ff72dce760864527dbf4d7de60bae3549a791394 | [] | no_license | seanpm2001/LeanProver-Community_MathLIB-Nursery | 4f88d539cb18d73a94af983092896b851e6640b5 | 0479b31fa5b4d39f41e89b8584c9f5bf5271e8ec | refs/heads/master | 1,688,730,786,645 | 1,572,070,026,000 | 1,572,070,026,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,954 | lean | import data.int.basic
namespace tactic.interactive
open tactic
lemma translate_nat (P : β€ β Sort*) (h : β i : β€, i β₯ 0 β P i) :
β i : β, P i :=
assume i,
h i (int.coe_nat_nonneg i)
run_cmd mk_simp_attr `to_int
@[to_int]
lemma coe_nat_inj {m n : β} : m = n β (βm : β€) = βn := by rw int.coe_nat_inj'
@[to_int]
lemm... |
5fc7330500ed072a68cdf3ac566d63e6413fb5ee | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /library/data/nat/fact.lean | b3b91b713f43e3d78b7f39c89a0e030ad96ce588 | [
"Apache-2.0"
] | permissive | soonhokong/lean-osx | 4a954262c780e404c1369d6c06516161d07fcb40 | 3670278342d2f4faa49d95b46d86642d7875b47c | refs/heads/master | 1,611,410,334,552 | 1,474,425,686,000 | 1,474,425,686,000 | 12,043,103 | 5 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 1,459 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
Factorial
-/
import data.nat.div
namespace nat
definition fact : nat β nat
| 0 := 1
| (succ n) := (succ n) * fact n
lemma fact_zero : fact 0 = 1 :=
r... |
a52f771c701c41d6b8fbe373a3cd838a814d9aed | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/field_theory/fixed.lean | 7ccd8bad700892eed87f53aa9e00d567229c8a55 | [
"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 | 14,513 | 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.polynomial.group_ring_action
import field_theory.normal
import field_theory.separable
import field_theory.tower
import ring_theory.polynomial
/-!
# Fixed field... |
750651ef92937c3d04e79c85fb427d47828440c8 | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /stage0/src/Lean/Parser/Command.lean | b961814d06becae43effec214d029ce79fd969ab | [
"Apache-2.0"
] | permissive | walterhu1015/lean4 | b2c71b688975177402758924eaa513475ed6ce72 | 2214d81e84646a905d0b20b032c89caf89c737ad | refs/heads/master | 1,671,342,096,906 | 1,599,695,985,000 | 1,599,695,985,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,895 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Sebastian Ullrich
-/
import Lean.Parser.Term
namespace Lean
namespace Parser
@[init] def regBuiltinCommandParserAttr : IO Unit :=
registerBuiltinParserAttri... |
17bbe625ecd5f265afd196560fbb92c2fd925430 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/hom/freiman.lean | 08a9903902c697fee0e05dd0c2894f0bf5a3ba76 | [
"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 | 17,629 | lean | /-
Copyright (c) 2022 YaΓ«l Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: YaΓ«l Dillies
-/
import algebra.big_operators.multiset.basic
import data.fun_like.basic
/-!
# Freiman homomorphisms
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file... |
62cd5033fdf79543db27a24ff5f0457f64943821 | a339bc2ac96174381fb610f4b2e1ba42df2be819 | /hott/algebra/bundled.hlean | e05ff916cfb88eda7907e541f906ca14869e812f | [
"Apache-2.0"
] | permissive | kalfsvag/lean2 | 25b2dccc07a98e5aa20f9a11229831f9d3edf2e7 | 4d4a0c7c53a9922c5f630f6f8ebdccf7ddef2cc7 | refs/heads/master | 1,610,513,122,164 | 1,483,135,198,000 | 1,483,135,198,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,606 | hlean | /-
Copyright (c) 2015 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
Bundled structures
-/
import algebra.group homotopy.interval
open algebra pointed is_trunc
namespace algebra
structure Semigroup :=
(carrier : Type) (struct : semigroup ... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.