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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
b6607597bb9970cd6e3fef63181d496233f431b1 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/data/seq/wseq.lean | 9d375e3e4b6a39a52560d5e592f9251210490f98 | [
"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 | 55,303 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import data.seq.seq
import data.dlist
open function
universes u v w
/-
coinductive wseq (α : Type u) : Type u
| nil : wseq α
| cons : α → wseq α → wseq α
| t... |
2da2336e020dc5e6568e50cd550bf7092b421770 | 9b9a16fa2cb737daee6b2785474678b6fa91d6d4 | /src/topology/algebra/quotient.lean | c60edc9ff7a9550a76145c93494abe1b83d5681c | [
"Apache-2.0"
] | permissive | johoelzl/mathlib | 253f46daa30b644d011e8e119025b01ad69735c4 | 592e3c7a2dfbd5826919b4605559d35d4d75938f | refs/heads/master | 1,625,657,216,488 | 1,551,374,946,000 | 1,551,374,946,000 | 98,915,829 | 0 | 0 | Apache-2.0 | 1,522,917,267,000 | 1,501,524,499,000 | Lean | UTF-8 | Lean | false | false | 8,280 | lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl
Topological structures on quotient rings and groups.
-/
import topology.uniform_space.completion
import group_theory.quotient_group
@[simp] lemma {u} e... |
f9731ba467a37af215a5ec1e99e389ca8ec83ea2 | 7f15a2b0775be8a2fcb4936c6b0f127f683c4666 | /library/init/meta/tactic.lean | 4cc3291318212a8b2e24d45ced563b94dc8dc2eb | [
"Apache-2.0"
] | permissive | mwillsey/lean | 0b90b5016a3158490d7c9cf8b836e8fe7bb3df81 | 8621be63353b299b0da9106f4e7c8ca5e271941d | refs/heads/master | 1,630,587,469,685 | 1,514,924,859,000 | 1,514,925,180,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 50,842 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.function init.data.option.basic init.util
import init.category.combinators init.category.monad init.category.alternative init.category.m... |
3162b3155e1f5e5b47e48e3771cae940c68ddfc6 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/measure_theory/constructions/pi.lean | 33632d0bbee4374af6b200a3874fb4c3fefe6df3 | [
"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 | 28,297 | lean | /-
Copyright (c) 2020 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import measure_theory.constructions.prod
/-!
# Product measures
In this file we define and prove properties about finite products of measures
(and at some point... |
42f0abc6a286b4b931b3f85bacc1ee12d3c92285 | 2fbe653e4bc441efde5e5d250566e65538709888 | /src/algebra/module.lean | 83baeed93867b561901c1b357e0d068d018d3365 | [
"Apache-2.0"
] | permissive | aceg00/mathlib | 5e15e79a8af87ff7eb8c17e2629c442ef24e746b | 8786ea6d6d46d6969ac9a869eb818bf100802882 | refs/heads/master | 1,649,202,698,930 | 1,580,924,783,000 | 1,580,924,783,000 | 149,197,272 | 0 | 0 | Apache-2.0 | 1,537,224,208,000 | 1,537,224,207,000 | null | UTF-8 | Lean | false | false | 18,192 | lean | /-
Copyright (c) 2015 Nathaniel Thomas. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nathaniel Thomas, Jeremy Avigad, Johannes Hölzl, Mario Carneiro
Modules over a ring.
## Implementation notes
Throughout the `linear_map` section implicit `{}` brackets are often ... |
cda3c3152e041b0317eb282ff5da145986890369 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/topology/continuous_function/bounded.lean | 0b0cf93d3dbb6b5b00eb0fbf57ee06ab870fd094 | [
"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 | 42,479 | lean | /-
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Mario Carneiro, Yury Kudryashov, Heather Macbeth
-/
import analysis.normed_space.operator_norm
import topology.continuous_function.algebra
/-!
# Bounded continuo... |
a46981a6f0918f5a6bb7e3523dd618bf60d25aab | 137c667471a40116a7afd7261f030b30180468c2 | /src/algebra/invertible.lean | 4cc9950dc3c5231e84f458ccb8f61430c771251e | [
"Apache-2.0"
] | permissive | bragadeesh153/mathlib | 46bf814cfb1eecb34b5d1549b9117dc60f657792 | b577bb2cd1f96eb47031878256856020b76f73cd | refs/heads/master | 1,687,435,188,334 | 1,626,384,207,000 | 1,626,384,207,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,076 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import algebra.group.units
import algebra.ring.basic
/-!
# Invertible elements
This file defines a typeclass `invertible a` for elements `a` with a two-sided
multiplicat... |
6070728461e2274e3c13fcd0eee81ef22fcb92ff | 1d265c7dd8cb3d0e1d645a19fd6157a2084c3921 | /src/chapter_exercises/chap3_exercises.lean | 647098bdcdbb045501512a6a6af24c8694a7770e | [
"MIT"
] | permissive | hanzhi713/lean-proofs | de432372f220d302be09b5ca4227f8986567e4fd | 4d8356a878645b9ba7cb036f87737f3f1e68ede5 | refs/heads/master | 1,585,580,245,658 | 1,553,646,623,000 | 1,553,646,623,000 | 151,342,188 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 11,137 | lean | variables p q r s : Prop
-- commutativity of ∧ and ∨
example : p ∧ q ↔ q ∧ p :=
begin
apply iff.intro,
assume pq,
show q ∧ p, from and.intro pq.2 pq.1,
assume qp,
show p ∧ q, from and.intro qp.2 qp.1
end
example : p ∨ q ↔ q ∨ p :=
begin
apply iff.intro,
assume pq,
... |
8b60fd59a6becb72fcb3880452462a9341b290b4 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/category_theory/functor.lean | b7e0fa13610d0e3386fdf8bc223706f2ef733aff | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 3,696 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tim Baumann, Stephen Morgan, Scott Morrison
Defines a functor between categories.
(As it is a 'bundled' object rather than the `is_functorial` typeclass parametrised
by the underlyin... |
4f30f470ad7437e0172fc33e92792a0e8cc2060c | cf39355caa609c0f33405126beee2739aa3cb77e | /library/init/data/set.lean | 34a13a4b056de1b710991e62be3422bc9f287bca | [
"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 | 1,132 | 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.interactive
import init.control.lawful
universes u v
/-- A set of elements of type `α`; implemented as a predicate `α → Prop`. -/... |
ec2ffb3f8a26eb2531221625e8f12da3222897d9 | 26ac254ecb57ffcb886ff709cf018390161a9225 | /src/category_theory/groupoid.lean | c003975c04a95ced169de074755cba71d541614a | [
"Apache-2.0"
] | permissive | eric-wieser/mathlib | 42842584f584359bbe1fc8b88b3ff937c8acd72d | d0df6b81cd0920ad569158c06a3fd5abb9e63301 | refs/heads/master | 1,669,546,404,255 | 1,595,254,668,000 | 1,595,254,668,000 | 281,173,504 | 0 | 0 | Apache-2.0 | 1,595,263,582,000 | 1,595,263,581,000 | null | UTF-8 | Lean | false | false | 2,202 | lean | /-
Copyright (c) 2018 Reid Barton All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Scott Morrison, David Wärn
-/
import category_theory.category
import category_theory.epi_mono
namespace category_theory
universes v v₂ u u₂ -- declare the `v`'s first; see `... |
8361f9f23c36ef55cc53c5ff6da2cd3c28f48236 | 38bf3fd2bb651ab70511408fcf70e2029e2ba310 | /src/category_theory/comma.lean | a924907f8bd00efb4105d69167d38bb4641ab919 | [
"Apache-2.0"
] | permissive | JaredCorduan/mathlib | 130392594844f15dad65a9308c242551bae6cd2e | d5de80376088954d592a59326c14404f538050a1 | refs/heads/master | 1,595,862,206,333 | 1,570,816,457,000 | 1,570,816,457,000 | 209,134,499 | 0 | 0 | Apache-2.0 | 1,568,746,811,000 | 1,568,746,811,000 | null | UTF-8 | Lean | false | false | 11,331 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Johan Commelin
-/
import category_theory.isomorphism
import category_theory.punit
namespace category_theory
universes v₁ v₂ v₃ u₁ u₂ u₃ -- declare the `v`'s first; se... |
6e2fcaa958950e3a37caae0b95079addd52e86d8 | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /src/Lean/Elab/Attributes.lean | aaf8b61cb3335240cbea97c25e9511695c13e9a8 | [
"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 | 2,049 | 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.Parser.Basic
import Lean.Attributes
import Lean.MonadEnv
namespace Lean
namespace Elab
structure Attribute :=
(name : Name)... |
a1f484dc9d3727575dab9f89fa22338d1dbf33e8 | 5d166a16ae129621cb54ca9dde86c275d7d2b483 | /library/init/native/result.lean | 5bedf464d8435b718d87995a0d4eb784e364293d | [
"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 | 2,411 | lean | /-
Copyright (c) 2016 Jared Roesch. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jared Roesch
-/
prelude
import init.meta.interactive
namespace native
inductive result (E : Type) (R : Type) : Type
| err {} : E → result
| ok {} : R → result
def unwrap_or {E T : Ty... |
e87342782fb147ce9d9bb9ac27027479dcebf678 | 4f643cce24b2d005aeeb5004c2316a8d6cc7f3b1 | /src/o_minimal/definable.lean | e69524deeaa26478bc99a6571499b08dea61ab1b | [] | no_license | rwbarton/lean-omin | da209ed061d64db65a8f7f71f198064986f30eb9 | fd733c6d95ef6f4743aae97de5e15df79877c00e | refs/heads/master | 1,674,408,673,325 | 1,607,343,535,000 | 1,607,343,535,000 | 285,150,399 | 9 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 16,451 | lean | import category_theory.category
import o_minimal.structure
import o_minimal.coordinates
universe u
namespace o_minimal
open set
-- Carrier for the (o-minimal) structure.
variables {R : Type u}
-- A structure on `R`.
variables (S : struc R)
/--
A type with coordinates valued in R is *definable* with respect to a g... |
3c368faf98b2d131e0121f787ea88ec7e117482b | f3a5af2927397cf346ec0e24312bfff077f00425 | /src/game/world6/level1.lean | 9ff64e24578a8df02d896cf58b7670e9211f0c45 | [
"Apache-2.0"
] | permissive | ImperialCollegeLondon/natural_number_game | 05c39e1586408cfb563d1a12e1085a90726ab655 | f29b6c2884299fc63fdfc81ae5d7daaa3219f9fd | refs/heads/master | 1,688,570,964,990 | 1,636,908,242,000 | 1,636,908,242,000 | 195,403,790 | 277 | 84 | Apache-2.0 | 1,694,547,955,000 | 1,562,328,792,000 | Lean | UTF-8 | Lean | false | false | 3,043 | lean | /-
# Proposition world.
A Proposition is a true/false statement, like `2 + 2 = 4` or `2 + 2 = 5`.
Just like we can have concrete sets in Lean like `mynat`, and abstract
sets called things like `X`, we can also have concrete propositions like
`2 + 2 = 5` and abstract propositions called things like `P`.
Mathematic... |
8dcf5d562711eb6a5b5696cfae47ae0869109e42 | 4f643cce24b2d005aeeb5004c2316a8d6cc7f3b1 | /src/for_mathlib/finite.lean | cc938b425291f7c99017a59d3cced895eae02ad1 | [] | no_license | rwbarton/lean-omin | da209ed061d64db65a8f7f71f198064986f30eb9 | fd733c6d95ef6f4743aae97de5e15df79877c00e | refs/heads/master | 1,674,408,673,325 | 1,607,343,535,000 | 1,607,343,535,000 | 285,150,399 | 9 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,351 | lean | import data.set.finite
import logic.function.iterate
variables {α : Type*} {β : Type*}
@[simp]
lemma finset.not_nonempty (s : finset α) :
¬s.nonempty ↔ s = ∅ :=
begin
classical,
rw [finset.nonempty_iff_ne_empty, not_not],
end
namespace set
lemma finite_of_finite_image_fibers {s : set α} {f : α → β}
(himg : ... |
25f326d987dbea599490c3b4b2c259966d0182e8 | 18425d4bab0b5e4677ef791d0065e16639493248 | /data/fintype.lean | ae8823f1fd43368c484fd27259a51e33b4a87813 | [
"MIT"
] | permissive | tizmd/lean-finitary | 5feb94a2474b55c0f23e4b61b9ac42403bf222f7 | 8958fdb3fa3d9fcc304e116fd339448875025e95 | refs/heads/master | 1,611,397,193,043 | 1,497,517,825,000 | 1,497,517,825,000 | 93,048,842 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,768 | lean | import finitary data.fin.misc
universe u
class fintype (α : Type u) :=
(size : ℕ)
(finitary : finitary α size)
namespace fintype
variables {α : Type u}[fintype α]
@[reducible]
def enum : α → fin (size α) := (finitary α).map
@[reducible]
def index : fin (size α) → α := (finitary α).bijection.inv
def elems : lis... |
97a20335ae63332bae69b11bc1021a746386d3bd | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/deprecated/subgroup.lean | e6eddcd5c7c44cdb8f747137e8c291cefed2b245 | [] | 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 | 24,573 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mitchell Rowett, Scott Morrison, Johan Commelin, Mario Carneiro,
Michael Howes
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.group_the... |
45daafd319042e1aeef59b2b1dc52f718a05c56f | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /stage0/src/Lean/Modifiers.lean | 66d926c28f92fd02c26b22c2a86d428b7c8cef14 | [
"Apache-2.0"
] | permissive | collares/lean4 | 861a9269c4592bce49b71059e232ff0bfe4594cc | 52a4f535d853a2c7c7eea5fee8a4fa04c682c1ee | refs/heads/master | 1,691,419,031,324 | 1,618,678,138,000 | 1,618,678,138,000 | 358,989,750 | 0 | 0 | Apache-2.0 | 1,618,696,333,000 | 1,618,696,333,000 | null | UTF-8 | Lean | false | false | 2,491 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Environment
namespace Lean
builtin_initialize protectedExt : TagDeclarationExtension ← mkTagDeclarationExtension `protected
@[export lean_add... |
7a1de0545a5638bdefc2287cd3d7d2ad69c9b8bd | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/tactic/default.lean | 394413d005f4c70b3df0ee6fc87232767eb02401 | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,326 | lean | /-
This file imports many useful tactics ("the kitchen sink").
You can use `import tactic` at the beginning of your file to get everything.
(Although you may want to strip things down when you're polishing.)
Because this file imports some complicated tactics, it has many transitive dependencies
(which of course may n... |
a73383bf1a8493497807b97c80fc1e6e7d305c35 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/topology/local_extr.lean | cbab9367d8934648ed9e43a6854300af4404c653 | [
"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 | 14,833 | lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import order.filter.extr topology.continuous_on
/-! # Local extrema of functions on topological spaces
## Main definitions
This file defines special versions of... |
c1d61b99b299058b579c23c63064275a79949257 | 64874bd1010548c7f5a6e3e8902efa63baaff785 | /library/data/prod.lean | c1e5e5a7cb15fc16f8d9c73190043d137fc1021c | [
"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 | 4,900 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.prod
Author: Leonardo de Moura, Jeremy Avigad
-/
import logic.eq
open inhabited decidable eq.ops
namespace prod
variables {A B : Type} {a₁ a₂ : A} {b₁ b₂ : B} {u : A × ... |
c24e063035891a66d64edfe47f3699ce0dd556b3 | ae1e94c332e17c7dc7051ce976d5a9eebe7ab8a5 | /stage0/src/Lean/Compiler/IR.lean | e9412fed3b81f5177ea45ef94e41f760bb0d2123 | [
"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 | 2,693 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Compiler.IR.Basic
import Lean.Compiler.IR.Format
import Lean.Compiler.IR.CompilerM
import Lean.Compiler.IR.PushProj
import Lean.Compiler.IR.Elim... |
9ae3b72a1fb3d86cbf272f66e391f8d54fdedbee | 4727251e0cd73359b15b664c3170e5d754078599 | /src/order/category/Preorder.lean | b28dd988e00b257e72cde0ab7d6285252c0edb9d | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 2,577 | lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import category_theory.concrete_category.bundled_hom
import algebra.punit_instances
import order.hom.basic
import category_theory.category.Cat
import category_theory.... |
3ac46ebe7e9207e5ddb9a124b272118b77e840a5 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/topology/support.lean | 35b0b9e55261e6d7f583d5682b14d70f4fea7a9a | [
"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 | 12,035 | lean | /-
Copyright (c) 2022 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Patrick Massot
-/
import topology.separation
/-!
# The topological support of a function
In this file we define the topological support of a function `f`, `tsupp... |
6710f359e00d48dce00c8691c1cf4414a131a2c7 | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/geometry/manifold/mfderiv.lean | 4bc9632fe1624f3c418d9c5291a51a1b2ddc3f5a | [
"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 | 65,745 | 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 geometry.manifold.basic_smooth_bundle
/-!
# The derivative of functions between smooth manifolds
Let `M` and `M'` be two smooth manifolds with corners ... |
288b29a1bd720f2e5997b23992564f9027d8925a | b70031c8e2c5337b91d7e70f1e0c5f528f7b0e77 | /src/linear_algebra/tensor_product.lean | f47ad291d0a071d39a0913478a493bc2177153d1 | [
"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 | 28,956 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Mario Carneiro
-/
import group_theory.congruence
import linear_algebra.basic
/-!
# Tensor product of semimodules over commutative semirings.
This file constructs the tensor pr... |
e44d627040a2646596e33c5f0934e76fb9f1c656 | 367134ba5a65885e863bdc4507601606690974c1 | /src/tactic/omega/nat/form.lean | 2c9899c5bdb2dbe4f4de20e7c64397d7e2f897fe | [
"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 | 5,766 | lean | /-
Copyright (c) 2019 Seul Baek. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Seul Baek
-/
/-
Linear natural number arithmetic preformulas in pre-normalized preform.
-/
import tactic.omega.nat.preterm
namespace omega
namespace nat
/-- Intermediate shadow syntax f... |
76de8ee49c523d8058005ed5afaa173ed1724334 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/category_theory/limits/opposites.lean | 8c0e25b9d42b078c9e75dda19176c7553a404e12 | [
"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 | 21,869 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Floris van Doorn
-/
import category_theory.limits.shapes.finite_products
import category_theory.discrete_category
import tactic.equiv_rw
/-!
# Limits in `C` give colim... |
9f05a8a819699cd1b023214199cb04b65e4a6821 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/group_theory/free_group.lean | 18153bb9dd8727523ec480462156f74b447d8bf6 | [
"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 | 32,883 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import data.fintype.basic
import group_theory.subgroup.basic
/-!
# Free groups
This file defines free groups over a type. Furthermore, it is shown that the free group constru... |
9243667591d6b7fb47bddaaa4137affc6fc12c37 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/linear_algebra/matrix/to_lin.lean | 72c3054c71bf5f49a30984a9eae2f2457c1da702 | [
"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 | 28,661 | 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 data.matrix.block
import linear_algebra.matrix.finite_dimensional
import linear_algebra.std_basis
import ring_theory.... |
40594fc53fcb0246b0e8fb4a42c3609f6cdf7485 | 367134ba5a65885e863bdc4507601606690974c1 | /src/category_theory/abelian/exact.lean | 47df0b5e3ea1b312fa2f08d9825d8dbeb999ae6b | [
"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 | 4,387 | 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... |
de108f392eb40b098e40e162f3bef8735c9b0299 | 367134ba5a65885e863bdc4507601606690974c1 | /src/algebra/opposites.lean | 2ed464573724bbbee6dd71277e05ef7c14d347e5 | [
"Apache-2.0"
] | permissive | kodyvajjha/mathlib | 9bead00e90f68269a313f45f5561766cfd8d5cad | b98af5dd79e13a38d84438b850a2e8858ec21284 | refs/heads/master | 1,624,350,366,310 | 1,615,563,062,000 | 1,615,563,062,000 | 162,666,963 | 0 | 0 | Apache-2.0 | 1,545,367,651,000 | 1,545,367,651,000 | null | UTF-8 | Lean | false | false | 10,750 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import data.opposite
import algebra.field
import algebra.group.commute
import group_theory.group_action.defs
import data.equiv.mul_add
/-!
# Algebraic operations on `αᵒᵖ`
Thi... |
47e09537539d2dc16176a77230e08527475c17ec | 957a80ea22c5abb4f4670b250d55534d9db99108 | /tests/lean/run/comp_val2.lean | 322f8efea1e11ae0cecdb32b5ace13637974f576 | [
"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 | 477 | lean | open tactic
example : 'a' ≠ 'b' := by comp_val
example : '0' ≠ 'a' := by comp_val
example : "hello worlg" ≠ "hhello world" := by comp_val
example : "hello world" ≠ "hhello world" := by comp_val
example : "abc" ≠ "cde" := by comp_val
example : "abc" ≠ "" := by comp_val
example : "" ≠ "cde" := by comp_val
example : @f... |
3d9c32ba4405b0522dbd5f2e1472ae219f75b9ce | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/jason1.lean | a4b58feb6cfaa37ad3a54bd0680df1dc64b1c2e2 | [
"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 | 215 | lean | structure Name where
name : Unit
inductive Foo (Name : Type) where
| foo (x : Name)
def bar : Foo Name → Type
| Foo.foo (Name.mk n) => Nat
def bar' : Foo Name → Type
| Foo.foo (_root_.Name.mk n) => Nat
|
71a3976d95216b5a4f629eca564afee8e73b5139 | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/topology/stone_cech.lean | ef0343a9885f86d621aa2e20952b047e3a96620a | [
"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 | 11,323 | lean | /-
Copyright (c) 2018 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton
-/
import topology.bases
import topology.dense_embedding
/-! # Stone-Čech compactification
Construction of the Stone-Čech compactification using ultrafilters.
Parts of the ... |
abf1c0eefecb9e284e5cd62a90720e618fd220cb | c777c32c8e484e195053731103c5e52af26a25d1 | /src/ring_theory/tensor_product.lean | 203263beb8cd15729db4ba326b54cbad4bf0bd7c | [
"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 | 37,410 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Johan Commelin
-/
import linear_algebra.finite_dimensional
import ring_theory.adjoin.basic
import linear_algebra.direct_sum.finsupp
/-!
# The tensor product of R-alge... |
0075e4b78c8b273c0bb3dabb6207263d5bc874db | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/box_integral/basic.lean | a02b18afc77bdf520763efc17291387c3531c8a9 | [
"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 | 43,394 | lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import analysis.box_integral.partition.filter
import analysis.box_integral.partition.measure
import topology.uniform_space.compact
/-!
# Integrals of Riemann, Hens... |
ed033a6621b5116fa4f0424b5b6f24e7fdd94227 | dc253be9829b840f15d96d986e0c13520b085033 | /algebra/submodule.hlean | a325b3541fb58d8a86a0745d6636148f0cc548c2 | [
"Apache-2.0"
] | permissive | cmu-phil/Spectral | 4ce68e5c1ef2a812ffda5260e9f09f41b85ae0ea | 3b078f5f1de251637decf04bd3fc8aa01930a6b3 | refs/heads/master | 1,685,119,195,535 | 1,684,169,772,000 | 1,684,169,772,000 | 46,450,197 | 42 | 13 | null | 1,505,516,767,000 | 1,447,883,921,000 | Lean | UTF-8 | Lean | false | false | 26,188 | hlean | /- submodules and quotient modules -/
-- Authors: Floris van Doorn, Jeremy Avigad
import .left_module .quotient_group .module_chain_complex
open algebra eq group sigma sigma.ops is_trunc function trunc equiv is_equiv property
universe variable u
namespace left_module
/- submodules -/
variables {R : Ring} {M M₁ M₁' M₂... |
9a0708c337b290b2b307449d739e4a60ffafd110 | 8b9f17008684d796c8022dab552e42f0cb6fb347 | /hott/init/relation.hlean | e68f545cbc1deee56732a7c6080ea2db86f6b5d8 | [
"Apache-2.0"
] | permissive | chubbymaggie/lean | 0d06ae25f9dd396306fb02190e89422ea94afd7b | d2c7b5c31928c98f545b16420d37842c43b4ae9a | refs/heads/master | 1,611,313,622,901 | 1,430,266,839,000 | 1,430,267,083,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,466 | hlean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: init.relation
Authors: Leonardo de Moura
-/
prelude
import init.logic
-- TODO(Leo): remove duplication between this file and algebra/relation.lean
-- We need some of the follo... |
f5afc0c8fa8eb7ec253f3a5880b385e5bf4dc341 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/order/liminf_limsup.lean | 5b3381d8bc7139845818d628723ca0254e17f5cc | [] | 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 | 28,927 | lean | /-
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Johannes Hölzl
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.order.filter.partial
import Mathlib.order.filter.at_top_bot
import Ma... |
f841b3dbfdc61e4b7247ec15122cc730c67ab322 | ebb7367fa8ab324601b5abf705720fd4cc0e8598 | /homotopy/cohomology.hlean | a0ea06071a1130632f84b7b510991fc0b42e17db | [
"Apache-2.0"
] | permissive | radams78/Spectral | 3e34916d9bbd0939ee6a629e36744827ff27bfc2 | c8145341046cfa2b4960ef3cc5a1117d12c43f63 | refs/heads/master | 1,610,421,583,830 | 1,481,232,014,000 | 1,481,232,014,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,673 | hlean | /-
Copyright (c) 2016 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
Reduced cohomology
-/
import algebra.arrow_group .spectrum homotopy.EM
open eq spectrum int trunc pointed EM group algebra circle sphere nat EM.ops
definition EM... |
b09acaeae05802b5714de3a99edad7fd340229c9 | f4bff2062c030df03d65e8b69c88f79b63a359d8 | /src/game/functions/composition_injective.lean | be2c9f1f07ebd32f9928bc40a71ba7ef032a89fd | [
"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 | 526 | lean | import data.real.basic
open function
/-
# Chapter 6 : Functions
## Level 5
A classical result in composition of functions.
Now going the other way around.
-/
/- Lemma
If composition of $f$ and $g$ is injective, then $f$ is injective.
-/
theorem composition_injective
(X Y Z : set ℝ) (f : X → Y) (g : Y → Z) : in... |
eb183067058fcf83fcf8254db358037bd0db8676 | 46ee5dc7248ccc9ee615639c0c003c05f58975cd | /src/completeness.lean | ae6e710d5ef282e842aab02345f02229fadced23 | [
"Apache-2.0"
] | permissive | m4lvin/tablean | e61d593b4dde6512245192c577edeb36c48f63c0 | 836202612fc2bfacb5545696412e7d27f7704141 | refs/heads/main | 1,685,613,112,076 | 1,676,755,678,000 | 1,676,755,678,000 | 454,064,275 | 8 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 8,597 | lean | -- COMPLETENESS
import syntax
import tableau
import soundness
-- import modelgraphs
open has_sat
-- Each local rule preserves truth "upwards"
lemma localRuleTruth {W : Type} {M : kripkeModel W} {w : W} {X : finset formula} {B : finset (finset formula)} :
localRule X B → (∃ Y ∈ B, (M,w) ⊨ Y) → (M,w) ⊨ X :=
begin
... |
02c3264e2a1c9a18714e8d5db3172e48cffde2d1 | 01ae0d022f2e2fefdaaa898938c1ac1fbce3b3ab | /categories/walking.lean | 2467ecab66bafd5bd536226c3ba6ba6240af885f | [] | no_license | PatrickMassot/lean-category-theory | 0f56a83464396a253c28a42dece16c93baf8ad74 | ef239978e91f2e1c3b8e88b6e9c64c155dc56c99 | refs/heads/master | 1,629,739,187,316 | 1,512,422,659,000 | 1,512,422,659,000 | 113,098,786 | 0 | 0 | null | 1,512,424,022,000 | 1,512,424,022,000 | null | UTF-8 | Lean | false | false | 3,342 | 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
import .discrete_category
import .path_category
import .util.finite
open categories
open categories.graphs
open categories.functor
open categorie... |
d160621ccf64a67c81824b2bf04e3039b5a2b608 | 54c9ed381c63410c9b6af3b0a1722c41152f037f | /Lib4/PostPort/Coe.lean | 7f9aa5a71e563f4d8907ef5fb8f51c7fddb70fbc | [
"Apache-2.0"
] | permissive | dselsam/binport | 0233f1aa961a77c4fc96f0dccc780d958c5efc6c | aef374df0e169e2c3f1dc911de240c076315805c | refs/heads/master | 1,687,453,448,108 | 1,627,483,296,000 | 1,627,483,296,000 | 333,825,622 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 868 | lean | import Lean3Lib.init.coe
universe u v
variable {α : Sort u} {β : Sort v}
noncomputable instance hasCoe [inst : Mathlib.has_coe α β] : Coe α β := {
coe := @Mathlib.has_coe.coe _ _ inst
}
-- TODO: why does mathlib declare these instances directly?
-- topology/algebra/open_subgroup.lean:42:instance has_coe_set : has_... |
a1b040a0d97ba9c9ccec008aac53fc11ea80491b | 64874bd1010548c7f5a6e3e8902efa63baaff785 | /tests/lean/slow/path_groupoids.lean | f71fb7d850c61da2a869f3472b87ad7991e94fe4 | [
"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 | 24,012 | lean | -- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Author: Jeremy Avigad
-- Ported from Coq HoTT
definition id {A : Type} (a : A) := a
definition compose {A : Type} {B : Type} {C : Type} (g : B → C) (f : A → B) := λ x, g (f x)
infi... |
03ab609644dfcd6a953b5dcfaf71281a772faa39 | ee8cdbabf07f77e7be63a449b8483ce308d37218 | /lean/src/valid/mathd-algebra-101.lean | e4a8f31b8c9a42a2849640e093ff78e97e37222a | [
"MIT",
"Apache-2.0"
] | permissive | zeta1999/miniF2F | 6d66c75d1c18152e224d07d5eed57624f731d4b7 | c1ba9629559c5273c92ec226894baa0c1ce27861 | refs/heads/main | 1,681,897,460,642 | 1,620,646,361,000 | 1,620,646,361,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 265 | lean | /-
Copyright (c) 2021 OpenAI. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kunhao Zheng
-/
import data.real.basic
example (x : ℝ) (h₀ : x ^ 2 - 5 * x - 4 ≤ 10 ) : x ≥ -2 ∧ x ≤ 7 :=
begin
sorry
end
|
0bcd8ab2a19b7e8db8f3047108c9dc04ec7877e7 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/group_theory/perm/list.lean | 9b931cda52ffdc5c581b0e16f9f96cbf8ddd0044 | [
"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 | 17,171 | lean | /-
Copyright (c) 2021 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
import data.list.rotate
import group_theory.perm.support
/-!
# Permutations from a list
A list `l : list α` can be interpreted as a `equiv.perm α` where each ele... |
1e920b738eb743082a2227da2985a11f0df220a1 | 947b78d97130d56365ae2ec264df196ce769371a | /tests/compiler/float.lean | 94edec44c0d6e1a3c6bb765612b8322c12c30b7a | [
"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 | 967 | lean | def tst1 : IO Unit := do
IO.println (1 : Float);
IO.println ((1 : Float) + 2);
IO.println ((2 : Float) - 3);
IO.println ((3 : Float) * 2);
IO.println ((3 : Float) / 2);
IO.println (decide ((3 : Float) < 2));
IO.println (decide ((3 : Float) < 4));
IO.println ((3 : Float) == 2);
IO.println ((2 : Float) == 2);
IO.println ... |
c7ded692a159bce84129a9622e47593df2857d61 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/number_theory/function_field.lean | bccb243f2de047ede088498f79568c79a8aa0634 | [
"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 | 10,592 | lean | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Ashvni Narayanan
-/
import field_theory.ratfunc
import ring_theory.algebraic
import ring_theory.dedekind_domain.integral_closure
import ring_theory.integrally_closed
import t... |
e3fefadb589b23e49c799621ca8787738683bc28 | e38d5e91d30731bef617cc9b6de7f79c34cdce9a | /src/examples/adjacency.lean | 029ccedfe351b5824d8ffc2aec1856794a0aa588 | [
"Apache-2.0"
] | permissive | bbentzen/cubicalean | 55e979c303fbf55a81ac46b1000c944b2498be7a | 3b94cd2aefdfc2163c263bd3fc6f2086fef814b5 | refs/heads/master | 1,588,314,875,258 | 1,554,412,699,000 | 1,554,412,699,000 | 177,333,390 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,425 | lean | /-
Copyright (c) 2019 Bruno Bentzen. All rights reserved.
Released under the Apache License 2.0 (see "License");
Author: Bruno Bentzen
-/
import ..core.interval
open interval
variables (A : I → I → Type) (a : Π j i, A j i)
-- adjacency conditions are immediate
example : a i0 i0 = (λ i, a i i0) i0 := ... |
7fadb35776f97cdbb491eb65af4b05459cf9e6fd | 12dabd587ce2621d9a4eff9f16e354d02e206c8e | /world10/level06.lean | 2c171a231d43e74b59bd716d22ed4fe51f002342 | [] | 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 | 283 | lean | theorem le_antisymm (a b : mynat) (hab : a ≤ b) (hba : b ≤ a) : a = b :=
begin
cases hab with c hc,
cases hba with d hd,
rw hc at hd,
rw add_assoc at hd,
symmetry at hd,
have h1 := eq_zero_of_add_right_eq_self hd,
have h2 := add_right_eq_zero h1,
rw hc,
rw h2,
rwa add_zero,
end
|
e82dda9ff67c08c1457c761fe56400148be81104 | ae1e94c332e17c7dc7051ce976d5a9eebe7ab8a5 | /src/Lean/Meta/Tactic/Injection.lean | 5d4cf04e5a947a22883b4b408a4b79b24319c22c | [
"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 | 3,613 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Meta.AppBuilder
import Lean.Meta.Tactic.Clear
import Lean.Meta.Tactic.Assert
import Lean.Meta.Tactic.Intro
namespace Lean.Meta
inductive Injec... |
c1f891e5b78c32cad16518b7e7e1e3f1fd438711 | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/category/traversable/equiv.lean | 1058c0332350e198973eb803655c6448e7c846c6 | [
"Apache-2.0"
] | permissive | fpvandoorn/mathlib | b21ab4068db079cbb8590b58fda9cc4bc1f35df4 | b3433a51ea8bc07c4159c1073838fc0ee9b8f227 | refs/heads/master | 1,624,791,089,608 | 1,556,715,231,000 | 1,556,715,231,000 | 165,722,980 | 5 | 0 | Apache-2.0 | 1,552,657,455,000 | 1,547,494,646,000 | Lean | UTF-8 | Lean | false | false | 4,789 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
Transferring `traversable` instances using isomorphisms.
-/
import data.equiv.basic category.traversable.lemmas
universes u
namespace equiv
section functor
parameters {t t... |
cd7b761d01ca2d7e77fc0026288ed69da916a656 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/init/data/sum/instances_auto.lean | 0c9123ae768bca34005cc179056259ccf4935996 | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,030 | 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
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.meta.mk_dec_eq_instance
universes u v
namespace Mathlib
protected instance sum.decidable_eq {α : Typ... |
70965ebd25086049a81aaf90617de544e736d692 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/analysis/normed/group/SemiNormedGroup/completion.lean | a6d79cf48c9140ba8400c1a9a3851aa6755b612c | [
"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 | 4,479 | lean | /-
Copyright (c) 2021 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca, Johan Commelin
-/
import analysis.normed.group.SemiNormedGroup
import category_theory.preadditive.additive_functor
import analysis.normed.group.hom_completion
/-!
# ... |
3ed8d6ea7b8362f720f61fb2426e7da9e162e8fb | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/algebra/module/pi.lean | 1eaf724c9c0eb04d26072c56ba606570699bcb77 | [
"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 | 9,679 | 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
/-!
# Pi instances for module and multiplicative actions
This file defines ... |
526c44c5f59d4a6855c82d04804cc8220f972291 | 4bcaca5dc83d49803f72b7b5920b75b6e7d9de2d | /tests/lean/run/633.lean | d293d660df80ecba63f2a192a64b3c8c8b4aadd3 | [
"Apache-2.0"
] | permissive | subfish-zhou/leanprover-zh_CN.github.io | 30b9fba9bd790720bd95764e61ae796697d2f603 | 8b2985d4a3d458ceda9361ac454c28168d920d3f | refs/heads/master | 1,689,709,967,820 | 1,632,503,056,000 | 1,632,503,056,000 | 409,962,097 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,380 | lean | abbrev semantics (α:Type) := StateM (List Nat) α
inductive expression : Nat → Type
| const : (n : Nat) → expression n
def uext {w:Nat} (x: expression w) (o:Nat) : expression w := expression.const w
def eval {n : Nat} (v:expression n) : semantics (expression n) := pure (expression.const n)
def set_overflow {w : Nat} (... |
326d2d3e98f7a52b36b880e7c4c8f7ee0dba28f9 | 0845ae2ca02071debcfd4ac24be871236c01784f | /library/init/lean/compiler/ir/borrow.lean | 1b7f2da77295388edc5d7c4a3d0fbdb6306adefd | [
"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 | 10,846 | 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.compiler.exportattr
import init.lean.compiler.ir.compilerm
import init.lean.compiler.ir.normids
namespace Lean
namespace IR
namesp... |
88afb19989f029f543e59319e90239f9d0e87e10 | a5271082abc327bbe26fc4acdaa885da9582cefa | /src/exp.lean | 759d7f0208a6d371ede90351a131b436e6cb2aaa | [
"Apache-2.0"
] | permissive | avigad/embed | 9ee7d104609eeded173ca1e6e7a1925897b1652a | 0e3612028d4039d29d06239ef03bc50576ca0f8b | refs/heads/master | 1,584,548,951,613 | 1,527,883,346,000 | 1,527,883,346,000 | 134,967,973 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,052 | lean | import .list .misc
variable {α : Type }
@[derive has_reflect]
inductive exp (α : Type) : Type
| bvr : nat → exp
| fvr : nat → exp
| cst : α → exp
| lam : exp → exp
| app : exp → exp → exp
notation `#` n := exp.bvr _ n
notation `&` n := exp.fvr _ n
def seq (α : Type) : Type := (list (exp α)) × (list (exp α))... |
1c496cc0c8f68dfc62401bd9da0a7bedcbc840d2 | 5a5e1bb8063d7934afac91f30aa17c715821040b | /lean3SOS/src/lib/eigenvalues.lean | d7d51c258cab15473b04e579fcbaae30c061caae | [] | no_license | ramonfmir/leanSOS | 1883392d73710db5c6e291a2abd03a6c5b44a42b | 14b50713dc887f6d408b7b2bce1f8af5bb619958 | refs/heads/main | 1,683,348,826,105 | 1,622,056,982,000 | 1,622,056,982,000 | 341,232,766 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,831 | lean | import lib.psd float.basic
variables {n m : nat}
def delta (A : matrix (fin n) (fin n) float) (R : matrix (fin m) (fin n) float)
: matrix (fin n) (fin n) float :=
A - (matrix.mul R.transpose R)
open matrix module.End
-- prove that RtR is symmetric.
lemma RTR_symmetric
(R : matrix (fin m) (fin n) float)
: symme... |
c88936b06934be0fb843ed2a81c791589d78f2e3 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/group_theory/group_action/basic.lean | 88f649e9ab8ff641977a7a43160eb32319ae3cba | [
"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 | 25,673 | 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.hom.group_action
import group_theory.group_action.defs
import group_theory.group_action.group
import group_theory.quotient_group
import data.setoid.basic
i... |
445d6e9947517d05ea8a7919d0a1e77767f21ca2 | 02005f45e00c7ecf2c8ca5db60251bd1e9c860b5 | /src/ring_theory/witt_vector/truncated.lean | 53e63f99a751630321750f5bef081dab9cef3940 | [
"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 | 14,222 | lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Robert Y. Lewis
-/
import ring_theory.witt_vector.init_tail
import tactic.equiv_rw
/-!
# Truncated Witt vectors
The ring of truncated Witt vectors (of length `n`) i... |
588a341595ca99667bf66afac77506f74a557924 | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/data/list/min_max.lean | 24582c1a89f5a52bb51a8e6340f85ebffd8e4839 | [
"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 | 11,132 | lean | /-
Copyright (c) 2019 Minchao Wu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Minchao Wu, Chris Hughes
-/
import data.list.basic
/-!
# Minimum and maximum of lists
## Main definitions
The main definitions are `argmax`, `argmin`, `minimum` and `maximum` for lists.
... |
d5ce9982646a79fe1b302e3234ec8d3111d2eda6 | d436468d80b739ba7e06843c4d0d2070e43448e5 | /src/measure_theory/measure_space.lean | c74ed79ee70759303dffe563496666797b042f0f | [
"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 | 35,559 | 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
Measure spaces -- measures
Measures are restricted to a measurable space (associated by the type class `measurable_space`).
This allows us to prove equ... |
873de540922ee4680f323cbabca113695cd70c24 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/pack_unpack3.lean | 1d7e15e8d21b402655b3240efe53c965cda0991e | [
"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 | 1,002 | lean | inductive {u} vec (A : Type u) : nat -> Type u
| vnil : vec 0
| vcons : Pi (n : nat), A -> vec n -> vec (n+1)
inductive {u} tree (A : Type u) : Type u
| leaf : A -> tree
| node : Pi (n : nat), vec (list (list tree)) n -> tree
-- set_option trace.eqn_compiler true
constant {u} P {A : Type u} : tree A → Type
constant ... |
b0de00b0b259b4c258e0f35736c1d2b297e1bc14 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/data/set/lattice.lean | a29d0eb26cd68881c3b719f88da9e2c273ef1544 | [
"Apache-2.0"
] | permissive | ramonfmir/mathlib | c5dc8b33155473fab97c38bd3aa6723dc289beaa | 14c52e990c17f5a00c0cc9e09847af16fabbed25 | refs/heads/master | 1,661,979,343,526 | 1,660,830,384,000 | 1,660,830,384,000 | 182,072,989 | 0 | 0 | null | 1,555,585,876,000 | 1,555,585,876,000 | null | UTF-8 | Lean | false | false | 72,994 | 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
-/
import data.nat.basic
import order.complete_boolean_algebra
import order.directed
import order.galois_connection
/-!... |
ec16476b85f55461ce01ebd176f757c88209ff16 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/control/functor.lean | 66020bb9dfa54c639920f4d0fec0ad1c1ea15a83 | [
"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 | 8,658 | lean | /-
Copyright (c) 2017 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import tactic.ext
import tactic.lint
/-!
# Functors
This module provides additional lemmas, definitions, and instances for `functor`s.
## Main definitions
* `const α` i... |
9de7841cd48fab802930558165df7085bb0781e3 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/tacUnsolvedGoalsErrors.lean | 54644d28f69ce430181becbc6a1f3ff1614b3b16 | [
"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 | 684 | lean | theorem ex1 (p q r : Prop) (h1 : p ∨ q) (h2 : p → q) : q :=
have : q := by -- Error here
skip
by skip -- Error here
skip
theorem ex2 (p q r : Prop) (h1 : p ∨ q) (h2 : p → q) : q :=
have : q := by {
skip
} -- Error here
by skip -- Error here
skip
theorem ex3 (p q r : Prop) (h1 : p ∨ q) (h2 ... |
e8814ea48d9150dc2fc6a62cf9cfa374529ac56f | 78630e908e9624a892e24ebdd21260720d29cf55 | /src/logic_first_order/fol_01.lean | 659dee5e6437b97b4c9f6c5197111066b9050cee | [
"CC0-1.0"
] | permissive | tomasz-lisowski/lean-logic-examples | 84e612466776be0a16c23a0439ff8ef6114ddbe1 | 2b2ccd467b49c3989bf6c92ec0358a8d6ee68c5d | refs/heads/master | 1,683,334,199,431 | 1,621,938,305,000 | 1,621,938,305,000 | 365,041,573 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 217 | lean | namespace fol_01
variable A : Type
variable R : A → A → Prop
theorem fol_01 : (∀ x y, R x y) → (∀ x, R x x) :=
assume h1: (∀ x y, R x y),
show ∀ x, R x x, from
(assume hx: A,
h1 hx hx)
end fol_01 |
14ffda229211a4003b702ee255fcb69c8eafe5a1 | aa2345b30d710f7e75f13157a35845ee6d48c017 | /category_theory/yoneda.lean | 7ae8613fdd0f8388c0653557da719c05cda47276 | [
"Apache-2.0"
] | permissive | CohenCyril/mathlib | 5241b20a3fd0ac0133e48e618a5fb7761ca7dcbe | a12d5a192f5923016752f638d19fc1a51610f163 | refs/heads/master | 1,586,031,957,957 | 1,541,432,824,000 | 1,541,432,824,000 | 156,246,337 | 0 | 0 | Apache-2.0 | 1,541,434,514,000 | 1,541,434,513,000 | null | UTF-8 | Lean | false | false | 5,077 | lean | -- Copyright (c) 2017 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Scott Morrison
/- The Yoneda embedding, as a functor `yoneda : C ⥤ ((Cᵒᵖ) ⥤ (Type v₁))`,
along with instances that it is `full` and `faithful`.
Also the Yoneda lemma, ... |
6ccbfb32518268ed36430942328e5ac5a29ef046 | 3dc4623269159d02a444fe898d33e8c7e7e9461b | /.github/workflows/geo/src/to_mathlib.lean | 2de050d688fa34db12753389c42f222fe2e4780b | [] | no_license | Or7ando/lean | cc003e6c41048eae7c34aa6bada51c9e9add9e66 | d41169cf4e416a0d42092fb6bdc14131cee9dd15 | refs/heads/master | 1,650,600,589,722 | 1,587,262,906,000 | 1,587,262,906,000 | 255,387,160 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 928 | lean | /-
Copyright (c) 2020 Wojciech Nawrocki. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wojciech Nawrocki
-/
import category_theory.epi_mono
import category_theory.limits.shapes.binary_products
/-! # Stuff that should be in mathlib -/
namespace category_theory
unive... |
ce5dbf9195f3318d8aaf7b1926edf9ef42323aca | d1a52c3f208fa42c41df8278c3d280f075eb020c | /stage0/src/Lean/Meta/Tactic/Induction.lean | 42a42567ba725d6ace032e1cbb689f9e3d6f002a | [
"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 | 11,804 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Meta.RecursorInfo
import Lean.Meta.SynthInstance
import Lean.Meta.Tactic.Util
import Lean.Meta.Tactic.Revert
import Lean.Meta.Tactic.Intro
impor... |
36442d7de1acbc10aababdc910b4f17f403c3184 | a7eef317ddec01b9fc6cfbb876fe7ac00f205ac7 | /src/category_theory/limits/shapes/equalizers.lean | b02a851686ea5b47e9fa90a0fe843d3d30e14570 | [
"Apache-2.0"
] | permissive | kmill/mathlib | ea5a007b67ae4e9e18dd50d31d8aa60f650425ee | 1a419a9fea7b959317eddd556e1bb9639f4dcc05 | refs/heads/master | 1,668,578,197,719 | 1,593,629,163,000 | 1,593,629,163,000 | 276,482,939 | 0 | 0 | null | 1,593,637,960,000 | 1,593,637,959,000 | null | UTF-8 | Lean | false | false | 28,315 | lean | /-
Copyright (c) 2018 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.epi_mono
import category_theory.limits.shapes.finite_limits
/-!
# Equalizers and coequalizers
This file defines (co)equalizers... |
ee8fbee3925df9953cfc47f4ba2695ee69001eb3 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/finset/basic.lean | 9bb6c39eb6a061f508201c0134971c82def05105 | [
"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 | 115,232 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad, Minchao Wu, Mario Carneiro
-/
import data.multiset.finset_ops
import tactic.apply
import tactic.nth_rewrite
import tactic.monotonicity
/-!
# F... |
ee6aa7645be11f5bf7d800b616b03ad875f41c50 | 88fb7558b0636ec6b181f2a548ac11ad3919f8a5 | /library/init/meta/inductive_compiler.lean | dd305914f1eefd5d86e4f0891e1ffeec14fc7045 | [
"Apache-2.0"
] | permissive | moritayasuaki/lean | 9f666c323cb6fa1f31ac597d777914aed41e3b7a | ae96ebf6ee953088c235ff7ae0e8c95066ba8001 | refs/heads/master | 1,611,135,440,814 | 1,493,852,869,000 | 1,493,852,869,000 | 90,269,903 | 0 | 0 | null | 1,493,906,291,000 | 1,493,906,291,000 | null | UTF-8 | Lean | false | false | 4,392 | lean | /-
Copyright (c) 2017 Daniel Selsam. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Daniel Selsam
-/
prelude
import init.meta.tactic init.meta.simp_tactic init.meta.rewrite_tactic init.meta.converter init.function
namespace inductive_compiler
namespace tactic
open tac... |
ad7e45b4f3460f64f9cb68791ab726bf88d8da49 | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/control/uliftable.lean | 926cb00dd25d5df1ae5961f3aae7ee62d59c231e | [
"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 | 5,579 | lean | /-
Copyright (c) 2020 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author(s): Simon Hudon
-/
import control.monad.basic
import control.monad.cont
import control.monad.writer
import data.equiv.basic
import tactic.interactive
/-!
# Universe lifting for type famili... |
9b0b73696c6f68433dabd2b36b0ab3178faa1aa1 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/category_theory/connected_components.lean | ba3c0b93c162f27b9cca985668e0fa017ff15809 | [
"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 | 5,839 | 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.list.chain
import category_theory.punit
import category_theory.is_connected
import category_theory.sigma.basic
import category_theory.full_subcategory
/-!
# ... |
d077f55448c10bbb85f85cd5e37d0490e5677db8 | 206422fb9edabf63def0ed2aa3f489150fb09ccb | /src/set_theory/ordinal.lean | 279be2b0791a7a2e1cc4f96f314501e3ba54590c | [
"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 | 56,627 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
-/
import set_theory.cardinal
/-!
# Ordinals
Ordinals are defined as equivalences of well-ordered sets under order isomorphism. They are endowed
with a total order, whe... |
6885b37c4c90d30f2474bd5090ce16f7337ff15c | 592ee40978ac7604005a4e0d35bbc4b467389241 | /Library/generated/mathscheme-lean/InvolutiveFixes.lean | 64810bc17a02897ad652d209cb41d73ad74b984b | [] | no_license | ysharoda/Deriving-Definitions | 3e149e6641fae440badd35ac110a0bd705a49ad2 | dfecb27572022de3d4aa702cae8db19957523a59 | refs/heads/master | 1,679,127,857,700 | 1,615,939,007,000 | 1,615,939,007,000 | 229,785,731 | 4 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,527 | lean | import init.data.nat.basic
import init.data.fin.basic
import data.vector
import .Prelude
open Staged
open nat
open fin
open vector
section InvolutiveFixes
structure InvolutiveFixes (A : Type) : Type :=
(one : A)
(prim : (A → A))
(fixes_prim_one : (prim one) = one)
open InvolutiveFixes
... |
a33ff318746e108ef9e9aeb4c6d4b4145f4d8e8d | 5ee26964f602030578ef0159d46145dd2e357ba5 | /src/Huber_pair.lean | 722f98fee08fd6e6b057f8ef0cef0452c2a6c372 | [
"Apache-2.0"
] | permissive | fpvandoorn/lean-perfectoid-spaces | 569b4006fdfe491ca8b58dd817bb56138ada761f | 06cec51438b168837fc6e9268945735037fd1db6 | refs/heads/master | 1,590,154,571,918 | 1,557,685,392,000 | 1,557,685,392,000 | 186,363,547 | 0 | 0 | Apache-2.0 | 1,557,730,933,000 | 1,557,730,933,000 | null | UTF-8 | Lean | false | false | 1,348 | lean | import power_bounded Huber_ring.basic data.polynomial
universes u v
--notation
local postfix `ᵒ` : 66 := power_bounded_subring
open power_bounded
section integral
variables {R : Type u} [comm_ring R] [decidable_eq R]
instance subtype.val.is_ring_hom (S : set R) [is_subring S] : is_ring_hom (@subtype.val _ S) :=
by... |
d4c0bbe5d948ebcda46a98e913956079c95b103a | 08bd4ba4ca87dba1f09d2c96a26f5d65da81f4b4 | /src/Lean/Meta/AppBuilder.lean | ee59df2fcea22244314b3fe5e44a6813d0ade2a0 | [
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"Apache-2.0",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | gebner/lean4 | d51c4922640a52a6f7426536ea669ef18a1d9af5 | 8cd9ce06843c9d42d6d6dc43d3e81e3b49dfc20f | refs/heads/master | 1,685,732,780,391 | 1,672,962,627,000 | 1,673,459,398,000 | 373,307,283 | 0 | 0 | Apache-2.0 | 1,691,316,730,000 | 1,622,669,271,000 | Lean | UTF-8 | Lean | false | false | 23,673 | 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.Structure
import Lean.Util.Recognizers
import Lean.Meta.SynthInstance
import Lean.Meta.Check
import Lean.Meta.DecLevel
namespace Lean.Meta
/--... |
9bd7d799da1ab6572d59c9a4f581df3a78ee602f | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/data/list/zip.lean | 40f8860c19f43374fc0b75e4f97b7c443d1faedc | [
"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 | 5,465 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Kenny Lau
-/
import data.list.basic
universes u v w z
variables {α : Type u} {β : Type v} {γ : Type w} {δ : Type z}
open nat
namespace list
/- zip & unzip -/
@[si... |
7fd5969c3b721875b33f9e91bcbf642f65244e50 | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /13_More_Tactics.org.13.lean | a16414a7163cb7ed3b48f8525b125d8abafb6f96 | [] | no_license | cjmazey/lean-tutorial | ba559a49f82aa6c5848b9bf17b7389bf7f4ba645 | 381f61c9fcac56d01d959ae0fa6e376f2c4e3b34 | refs/heads/master | 1,610,286,098,832 | 1,447,124,923,000 | 1,447,124,923,000 | 43,082,433 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 434 | lean | import standard
import data.set
open set function eq.ops
variables {X Y Z : Type}
lemma image_compose (f : Y → X) (g : X → Y) (a : set X) : (f ∘ g) '[a] = f '[g '[a]] :=
set.ext (take z,
iff.intro
(assume Hz,
obtain x Hx₁ Hx₂, from Hz,
by repeat (apply mem_image | assumption | reflexivity))
(assume Hz,
obtain y [x Hz... |
5b9e1395236ae86463a401b5e37f62ca7c2d789b | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/set_theory/schroeder_bernstein.lean | 573b3041c96c02396be46be9dc0d7afc3c744fa9 | [
"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 | 5,041 | 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
The Schröder-Bernstein theorem, and well ordering of cardinals.
-/
import order.fixed_points data.set.lattice logic.function logic.embedding order.zorn
... |
ff842bcc6f4b496e3a1612cedd3148498314470f | 43390109ab88557e6090f3245c47479c123ee500 | /src/Topology/Material/homotopy.lean | e052e7725dd1ea2041f52a10b10b64bb460e4b62 | [
"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 | 11,891 | lean | /-
Copyright (c) 2018 Luca Gerolla. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Luca Gerolla, Kevin Buzzard
Definition of homotopy, properties and equivalence relation.
-/
import analysis.topology.continuity
import analysis.topology.topological_space
import analysi... |
9e89037a7162329e717676936a7b07eb66d35c8c | b00eb947a9c4141624aa8919e94ce6dcd249ed70 | /stage0/src/Lean/PrettyPrinter/Delaborator/Basic.lean | fb3643675927f6b510d7627089814c692974bf6e | [
"Apache-2.0"
] | permissive | gebner/lean4-old | a4129a041af2d4d12afb3a8d4deedabde727719b | ee51cdfaf63ee313c914d83264f91f414a0e3b6e | refs/heads/master | 1,683,628,606,745 | 1,622,651,300,000 | 1,622,654,405,000 | 142,608,821 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 17,034 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Ullrich
-/
/-!
The delaborator is the first stage of the pretty printer, and the inverse of the
elaborator: it turns fully elaborated `Expr` core terms back into surf... |
6252da25d354dd8a97a25b29ba35c05f4d33d146 | 9ad8d18fbe5f120c22b5e035bc240f711d2cbd7e | /src/undergraduate/MAS114/Semester 1/Q05.lean | fb811f705656d3f877fef7302d095a27c357b516 | [] | no_license | agusakov/lean_lib | c0e9cc29fc7d2518004e224376adeb5e69b5cc1a | f88d162da2f990b87c4d34f5f46bbca2bbc5948e | refs/heads/master | 1,642,141,461,087 | 1,557,395,798,000 | 1,557,395,798,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,848 | lean | import data.fintype
namespace MAS114
namespace exercises_1
namespace Q05
def A : finset ℕ := [0,1,2].to_finset
def B : finset ℕ := [0,1,2,3].to_finset
def C : finset ℤ := [-2,-1,0,1,2].to_finset
def D : finset ℤ := [-3,-2,-1,0,1,2,3].to_finset
lemma int.lt_succ_iff {n m : ℤ} : n < m + 1 ↔ n ≤ m :=
⟨int.le_of_lt_a... |
01d7dd07c0fd069ed254e91daa12ed484d7742ff | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /hott/types/W.hlean | 51d1f6e67ed49f74caca493e47f9d7a3ef1dc64b | [
"Apache-2.0"
] | permissive | davidmueller13/lean | 65a3ed141b4088cd0a268e4de80eb6778b21a0e9 | c626e2e3c6f3771e07c32e82ee5b9e030de5b050 | refs/heads/master | 1,611,278,313,401 | 1,444,021,177,000 | 1,444,021,177,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,680 | hlean | /-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Floris van Doorn
Theorems about W-types (well-founded trees)
-/
import .sigma .pi
open eq equiv is_equiv sigma sigma.ops
inductive Wtype.{l k} {A : Type.{l}} (B : A → Type.{k}) : T... |
30f2921efea0d13e46a3ca9ab46ac15d99538c47 | ae1e94c332e17c7dc7051ce976d5a9eebe7ab8a5 | /src/Lean/PrettyPrinter/Delaborator/Basic.lean | 6587c17080ffad6e26c7ab1288c3f28a1ac87b26 | [
"Apache-2.0"
] | permissive | dupuisf/lean4 | d082d13b01243e1de29ae680eefb476961221eef | 6a39c65bd28eb0e28c3870188f348c8914502718 | refs/heads/master | 1,676,948,755,391 | 1,610,665,114,000 | 1,610,665,114,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 11,639 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Ullrich
-/
/-!
The delaborator is the first stage of the pretty printer, and the inverse of the
elaborator: it turns fully elaborated `Expr` core terms back into surf... |
45e9e2671e3f2ad08f4e66000f87a3a2eaea3542 | 3dc4623269159d02a444fe898d33e8c7e7e9461b | /.github/workflows/geo/src/beck.lean | 056623f32e5f783ec7cb24a06918551ed0078e79 | [] | no_license | Or7ando/lean | cc003e6c41048eae7c34aa6bada51c9e9add9e66 | d41169cf4e416a0d42092fb6bdc14131cee9dd15 | refs/heads/master | 1,650,600,589,722 | 1,587,262,906,000 | 1,587,262,906,000 | 255,387,160 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,017 | lean | import data.fintype
import category_theory.limits.limits
import category_theory.monad.limits
import category_theory.monad
import category_theory.limits.shapes.equalizers
import tactic
import category_theory.monad.adjunction
universes u v u₂ v₂ v₁ u₁
namespace category_theory
open limits
section reflexive_pair
def ref... |
45e330193cd05861d1b72e44c487d6efdd4adb24 | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/topology/continuous_on.lean | 217e3a6e9efa9cbdae859b5ba7b27f9cdad730bd | [
"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 | 33,923 | lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import topology.constructions
/-!
# Neighborhoods and continuity relative to a subset
This file defines relative versions
* `nhds_within` of `nhds`
* `co... |
2b73b772553cc37cc4f1ed80f82cd3098dd311d7 | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/logic/embedding.lean | 2abfaf94bd77a0bdd159627c50a9b79df77717d6 | [
"Apache-2.0"
] | permissive | agjftucker/mathlib | d634cd0d5256b6325e3c55bb7fb2403548371707 | 87fe50de17b00af533f72a102d0adefe4a2285e8 | refs/heads/master | 1,625,378,131,941 | 1,599,166,526,000 | 1,599,166,526,000 | 160,748,509 | 0 | 0 | Apache-2.0 | 1,544,141,789,000 | 1,544,141,789,000 | null | UTF-8 | Lean | false | false | 10,248 | 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 data.equiv.basic
import data.sigma.basic
/-!
# Injective functions
-/
universes u v w x
namespace function
/-- `α ↪ β` is a bundled injecti... |
ad2c8ab50b40e960b53032f8bcdb67b5451c142b | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/815b.lean | 33a2ea0cfe50d81286610f3fd61a58f4b1bcda7d | [
"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 | 942 | lean | def is_smooth {α β} (f : α → β) : Prop := sorry
class IsSmooth {α β} (f : α → β) : Prop where
(proof : is_smooth f)
instance identity : IsSmooth fun a : α => a := sorry
instance const (b : β) : IsSmooth fun a : α => b := sorry
instance swap (f : α → β → γ) [∀ a, IsSmooth (f a)] : IsSmooth (λ b a => f a b) := sorry
... |
3110f26c185d8eb9ba017b535a22bf1b3fa61145 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/analysis/normed_space/banach.lean | 2b6429edd4b0f3f7ec0b02161f24dbfdef221ebd | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 18,382 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import topology.metric_space.baire
import analysis.normed_space.operator_norm
import analysis.normed_space.affine_isometry
/-!
# Banach open mapping theorem
T... |
9d455ab0ad8caed846aaabcd43cb6effbf3ce389 | 6fca17f8d5025f89be1b2d9d15c9e0c4b4900cbf | /src/game/world9/level2.lean | 226377e58743a33971ac5e29f6e34ce13031b9b0 | [
"Apache-2.0"
] | permissive | arolihas/natural_number_game | 4f0c93feefec93b8824b2b96adff8b702b8b43ce | 8e4f7b4b42888a3b77429f90cce16292bd288138 | refs/heads/master | 1,621,872,426,808 | 1,586,270,467,000 | 1,586,270,467,000 | 253,648,466 | 0 | 0 | null | 1,586,219,694,000 | 1,586,219,694,000 | null | UTF-8 | Lean | false | false | 398 | lean | import game.world9.level1 -- hide
namespace mynat -- hide
/-
# Advanced Multiplication World
## Level 2: `eq_zero_or_eq_zero_of_mul_eq_zero`
A variant on the previous level.
-/
/- Theorem
If $ab = 0$, then at least one of $a$ or $b$ is equal to zero.
-/
theorem eq_zero_or_eq_zero_of_mul_eq_zero (a b : mynat) (h : a... |
d5836f59633ce8fd20514887d8265b7270c96953 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/order/category/NonemptyFinLinOrd.lean | d281dff7e3125faf1571f5ecad6a6b58560b232a | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 3,413 | lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import data.fintype.order
import order.category.LinearOrder
/-!
# Nonempty finite linear orders
This defines `NonemptyFinLinOrd`, the category of nonempty finite li... |
a8149d99a3ef42c1cf41a1e2cecdbf515d9df2c9 | 93b17e1ec33b7fd9fb0d8f958cdc9f2214b131a2 | /src/sep/option.lean | e6c9dc533c0e7f6383225b73d6c4c3ec3a70a0bd | [] | no_license | intoverflow/timesink | 93f8535cd504bc128ba1b57ce1eda4efc74e5136 | c25be4a2edb866ad0a9a87ee79e209afad6ab303 | refs/heads/master | 1,620,033,920,087 | 1,524,995,105,000 | 1,524,995,105,000 | 120,576,102 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,917 | lean | import .basic
namespace Sep
universes ℓ
namespace Option
inductive join {A : Type.{ℓ}} (j : A → A → A → Prop)
: option A → option A → option A → Prop
| base : ∀ {x₁ x₂ x₃} (Jx : j x₁ x₂ x₃)
, join (option.some x₁) (option.some x₂) (option.some x₃)
| none_r : ∀ {x}, join none x x
| none_l : ∀ {x}, join x n... |
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