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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
76f0fde12767ef4cf7db9c90e6f0313ec201541d | a45212b1526d532e6e83c44ddca6a05795113ddc | /test/monotonicity.lean | 4d017db90a70f72a845bf46bb076763017f0a451 | [
"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 | 8,090 | lean |
import tactic.monotonicity tactic.norm_num
import algebra.ordered_ring
import data.list.basic
open list tactic tactic.interactive
example
(h : 3 + 6 ≤ 4 + 5)
: 1 + 3 + 2 + 6 ≤ 4 + 2 + 1 + 5 :=
begin
ac_mono,
end
example
(h : 3 ≤ (4 : ℤ))
(h' : 5 ≤ (6 : ℤ))
: (1 + 3 + 2) - 6 ≤ (4 + 2 + 1 : ℤ) - 5 :=
by ac_... |
5d7ea16c6db2aac28d3ea25fa73356ad271e54b3 | cf39355caa609c0f33405126beee2739aa3cb77e | /library/init/meta/converter/interactive.lean | 007db38ad7312ab6e9aa1e807360d65090a1e2c7 | [
"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 | 6,929 | 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
Converter monad for building simplifiers.
-/
prelude
import init.meta.interactive
import init.meta.converter.conv
namespace conv
meta def save_info (p : pos)... |
073218770986c6875f08605450640831c51a0583 | 4a092885406df4e441e9bb9065d9405dacb94cd8 | /src/for_mathlib/uniform_space/separation.lean | 4b7ef639421349e6ede1ac8d710c0621d2b228a5 | [
"Apache-2.0"
] | permissive | semorrison/lean-perfectoid-spaces | 78c1572cedbfae9c3e460d8aaf91de38616904d8 | bb4311dff45791170bcb1b6a983e2591bee88a19 | refs/heads/master | 1,588,841,765,494 | 1,554,805,620,000 | 1,554,805,620,000 | 180,353,546 | 0 | 1 | null | 1,554,809,880,000 | 1,554,809,880,000 | null | UTF-8 | Lean | false | false | 9,998 | lean | import topology.uniform_space.separation
import for_mathlib.function
import for_mathlib.quotient
import for_mathlib.topology
import for_mathlib.uniform_space.basic
noncomputable theory
local attribute [instance, priority 0] classical.prop_decidable
open filter
universes u v w
section
variables {α : Type u} {β : Ty... |
c6d108e14b5495fad90adb777c9762f006fabd23 | 957a80ea22c5abb4f4670b250d55534d9db99108 | /library/init/category/combinators.lean | e45afc8d46e084505801b1bbcccf12cb251f9bbf | [
"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 | 3,834 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura
Monad combinators, as in Haskell's Control.Monad.
-/
prelude
import init.category.monad init.category.alternative init.data.list.basic
universe... |
b08bf650037d86cf697268fe642418d4d171da2a | 54f4ad05b219d444b709f56c2f619dd87d14ec29 | /my_project/src/love03_forward_proofs_exercise_sheet.lean | c8d6320b3f371189d5cb77921cf3ccf559298b7f | [] | no_license | yizhou7/learning-lean | 8efcf838c7276e235a81bd291f467fa43ce56e0a | 91fb366c624df6e56e19555b2e482ce767cd8224 | refs/heads/master | 1,675,649,087,737 | 1,609,022,281,000 | 1,609,022,281,000 | 272,072,779 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,557 | lean | import .lovelib
/-! # LoVe Exercise 3: Forward Proofs -/
set_option pp.beta true
namespace LoVe
/-! ## Question 1: Connectives and Quantifiers
1.1. Supply structured proofs of the following lemmas. -/
lemma I (a : Prop) :
a → a :=
assume ha : a,
show a, from
ha
lemma K (a b : Prop) :
a → b → b :=
assume... |
2f40bfa082973d57fe4527701411afc2bb940896 | efa51dd2edbbbbd6c34bd0ce436415eb405832e7 | /20161026_ICTAC_Tutorial/ex33.lean | 712526082c17c272346c31234e8b905335eb1d39 | [
"Apache-2.0"
] | permissive | leanprover/presentations | dd031a05bcb12c8855676c77e52ed84246bd889a | 3ce2d132d299409f1de269fa8e95afa1333d644e | refs/heads/master | 1,688,703,388,796 | 1,686,838,383,000 | 1,687,465,742,000 | 29,750,158 | 12 | 9 | Apache-2.0 | 1,540,211,670,000 | 1,422,042,683,000 | Lean | UTF-8 | Lean | false | false | 849 | lean | /- Conjunction -/
/- Introduction -/
variables p q : Prop
example (hp : p) (hq : q) : p ∧ q := and.intro hp hq
check assume (hp : p) (hq : q), and.intro hp hq
/- Elimination -/
example (h : p ∧ q) : p := and.elim_left h
example (h : p ∧ q) : q := and.elim_right h
example (h : p ∧ q) : p := and.left h
example (h :... |
bd5927fbe237967f01ac997cb57a303b250a0b1c | 271e26e338b0c14544a889c31c30b39c989f2e0f | /stage0/src/Init/Lean/Meta/Exception.lean | bc739fe88b8f382e16a19d9f29907104fef55ff8 | [
"Apache-2.0"
] | permissive | dgorokho/lean4 | 805f99b0b60c545b64ac34ab8237a8504f89d7d4 | e949a052bad59b1c7b54a82d24d516a656487d8a | refs/heads/master | 1,607,061,363,851 | 1,578,006,086,000 | 1,578,006,086,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,244 | 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.Environment
import Init.Lean.MetavarContext
import Init.Lean.Util.Message
namespace Lean
namespace Meta
abbrev ExceptionContext :... |
cc26cf0b327dc25458461b76a2053f0a4dc42ea0 | f1b175e38ffc5cc1c7c5551a72d0dbaf70786f83 | /data/int/basic.lean | 6a12602b85961b10e574096c4c7550ae3d765bba | [
"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 | 45,429 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
The integers, with addition, multiplication, and subtraction.
-/
import data.nat.basic algebra.char_zero algebra.order_functions
open nat
namespace int
instance : inhab... |
d48d295140d9888ea7a42bc41e9d456abe64dbd7 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/algebra/category/Group/limits.lean | b73b23bc4bc3c2d78d1335d51e0d4dcf053c93dc | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 9,745 | 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 algebra.category.Mon.limits
import algebra.category.Group.preadditive
import category_theory.over
import category_theory.limits.concrete_category
import catego... |
09452ca294562f90dae816af5aa31faa4e4cda53 | a537b538f2bea3181e24409d8a52590603d1ddd9 | /test/rewrite_search_logic.lean | 61f76acf819cbc48aca391f58c9d4dec896304f2 | [] | no_license | rwbarton/lean-tidy | 6134813ded72b275d19d4d32514dba80c21708e3 | fe1125d32adb60decda7a77d0f679614ba9f6fbb | refs/heads/master | 1,585,549,718,705 | 1,538,120,619,000 | 1,538,120,624,000 | 150,864,330 | 0 | 0 | null | 1,538,225,790,000 | 1,538,225,790,000 | null | UTF-8 | Lean | false | false | 8,305 | lean | import logic.basic
import tidy.tidy
import tidy.rewrite_search.discovery
open tidy.rewrite_search.tracer
open tidy.rewrite_search.metric
local attribute [instance] classical.prop_decidable
@[suggest] private def use_logic := `logic
example {A B C : Prop} : ((B → C) → (¬(A → C) ∧ ¬(A ∨ B))) = (B ∧ ¬C) :=
calc
... |
9be918c29ba6885ef2eb04e01ef15352a9b97680 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/341.lean | b81d2d20797bd3772d6c6615559be3d8d055246d | [
"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 | 4,787 | lean | section
variable (G : Type 1) (T : Type 1) (Tm : Type 1)
(EG : G → G → Type) (ET : T → T → Type) (ETm : Tm → Tm → Type)
(getCtx : T → G) (getTy : Tm → T)
inductive CtxSyntaxLayer where
| emp : CtxSyntaxLayer
| snoc : (Γ : G) → (t : T) → EG Γ (getCtx t) → CtxSyntaxLayer
end
section
va... |
b2dce189a4ff45302989836e1db8033e2b6e791c | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/measure_theory/measure/measure_space.lean | 74128d22e0b4f8b9b88ca18c3b5e662cb69a0a02 | [
"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 | 159,820 | 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 measure_theory.measure.null_measurable
import measure_theory.measurable_space
/-!
# Measure spaces
The definition of a measure and a measure ... |
d9f382846990b49807876c2458654bc6a6f24255 | 5412d79aa1dc0b521605c38bef9f0d4557b5a29d | /stage0/src/Lean/Environment.lean | a5b0c4e099e8e14f6087d152d78cc769106c9e89 | [
"Apache-2.0"
] | permissive | smunix/lean4 | a450ec0927dc1c74816a1bf2818bf8600c9fc9bf | 3407202436c141e3243eafbecb4b8720599b970a | refs/heads/master | 1,676,334,875,188 | 1,610,128,510,000 | 1,610,128,521,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 28,489 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Std.Data.HashMap
import Lean.Data.SMap
import Lean.Declaration
import Lean.LocalContext
import Lean.Util.Path
import Lean.Util.FindExpr
import Lean.U... |
a95d6378e0abaf7786b7d1156f92585c21a96435 | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/algebra/big_operators/basic.lean | 7116d4b10886f3e63b36fda3de40d15946451abe | [
"Apache-2.0"
] | permissive | ayush1801/mathlib | 78949b9f789f488148142221606bf15c02b960d2 | ce164e28f262acbb3de6281b3b03660a9f744e3c | refs/heads/master | 1,692,886,907,941 | 1,635,270,866,000 | 1,635,270,866,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 63,576 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import algebra.group.pi
import data.equiv.mul_add
import data.finset.fold
import data.fintype.basic
/-!
# Big operators
In this file we define products and sums in... |
b5b4417a91c99a388301142b07120afd91fc62e3 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/data/finset/pairwise.lean | 3e10441a7f9bc0caabf80ef5c29c81bdd144b030 | [
"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 | 2,009 | lean | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import data.finset.lattice
/-!
# Relations holding pairwise on finite sets
In this file we prove a few results about the interaction of `set.pairwise_disjoint` and `fin... |
1a97380fee291c6ef11259ae43273af5a11d2335 | 88892181780ff536a81e794003fe058062f06758 | /src/xena_challenge/challenge06.lean | bd6c1450cfeee1028ca5824b83375a81c135aff6 | [] | no_license | AtnNn/lean-sandbox | fe2c44280444e8bb8146ab8ac391c82b480c0a2e | 8c68afbdc09213173aef1be195da7a9a86060a97 | refs/heads/master | 1,623,004,395,876 | 1,579,969,507,000 | 1,579,969,507,000 | 146,666,368 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 543 | lean | import data.set.basic
import lib.attempt
open set
def equivalence_class {X : Type} (R : X → X → Prop) (x : X) := {y : X | R x y}
theorem challenge06 (X : Type) (R : X → X → Prop) (hR : equivalence R) (x : X) : equivalence_class R x ≠ ∅ :=
attempt begin
intro h,
replace h := congr_fun h x,
have r := hR.1 x,
r... |
cfa32c6054ef794da67ba3721ecc36aee98e6791 | 4fa161becb8ce7378a709f5992a594764699e268 | /src/algebra/group/defs.lean | 7661e5c55259a4e64f8b0edb97c1a3c3e76879a2 | [
"Apache-2.0"
] | permissive | laughinggas/mathlib | e4aa4565ae34e46e834434284cb26bd9d67bc373 | 86dcd5cda7a5017c8b3c8876c89a510a19d49aad | refs/heads/master | 1,669,496,232,688 | 1,592,831,995,000 | 1,592,831,995,000 | 274,155,979 | 0 | 0 | Apache-2.0 | 1,592,835,190,000 | 1,592,835,189,000 | null | UTF-8 | Lean | false | false | 10,986 | 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, Simon Hudon, Mario Carneiro
-/
import algebra.group.to_additive
import tactic.protected
/-!
# Typeclasses for (semi)groups and monoid
In this file we... |
36cfa44034dc5ddd48576e687f369eaec6d37ef8 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/measure_theory/measure/portmanteau.lean | debe09934a0d4b718be74baa5bf686b04af66051 | [
"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 | 24,740 | lean | /-
Copyright (c) 2021 Kalle Kytölä. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kalle Kytölä
-/
import measure_theory.measure.probability_measure
import measure_theory.measure.lebesgue
/-!
# Characterizations of weak convergence of finite measures and probability m... |
93ba05dadb4824fd10a18de51d90d94acb321bc4 | 02005f45e00c7ecf2c8ca5db60251bd1e9c860b5 | /src/data/indicator_function.lean | e427408351c6621242d73397f14da4aca489864d | [
"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 | 15,498 | lean | /-
Copyright (c) 2020 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou
-/
import algebra.group.pi
import group_theory.group_action
import data.support
import data.finset.lattice
/-!
# Indicator function
`indicator (s : set α) (f : α → β) (a... |
f80f1d2f6648218be0d28d404366d47f2d2edcd5 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/tactic/lean_core_docs_auto.lean | 9638111f47995bec0a8b6459f916e4c5ffcf774e | [] | 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 | 8,537 | lean | /-
Copyright (c) 2020 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Bryan Gin-ge Chen, Robert Y. Lewis, Scott Morrison
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.tactic.doc_commands
import Mathlib.PostPo... |
93bbec086b032bb64fa78819b365574a29f94a34 | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /tests/lean/run/matchArrayLit.lean | 38b1b5fc303bc14443ce68974ebafb51953cd6f2 | [
"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 | 2,476 | lean | universes u v
theorem eqLitOfSize0 {α : Type u} (a : Array α) (hsz : a.size = 0) : a = #[] :=
a.toArrayLitEq 0 hsz
theorem eqLitOfSize1 {α : Type u} (a : Array α) (hsz : a.size = 1) : a = #[a.getLit 0 hsz (ofDecideEqTrue rfl)] :=
a.toArrayLitEq 1 hsz
theorem eqLitOfSize2 {α : Type u} (a : Array α) (hsz : a.size = 2)... |
c8f9048c3a082cf2fbe07e4c87c32e9b4ad7b3e9 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/normed_space/affine_isometry.lean | 5e6869ea196f4bc59c702379304ae0a28ed49423 | [
"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 | 24,810 | lean | /-
Copyright (c) 2021 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
import analysis.normed_space.linear_isometry
import analysis.normed.group.add_torsor
import analysis.normed_space.basic
import linear_algebra.affine_space.restrict
... |
0f237a7d25eac50441728dff12a1aa521e88ff8c | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/tactic/ring_exp_auto.lean | 166d2c1a5af616b80b78239323dadcded23a064c | [] | 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 | 29,425 | lean | /-
Copyright (c) 2019 Tim Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Tim Baanen.
Solve equations in commutative (semi)rings with exponents.
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.tactic.norm_num
import Mathlib.control.... |
db5a39fca28d9d0fd360ebe3137a2a5bab8dc468 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/order/upper_lower/hom.lean | 99096745ac062d1becff8e8dfe37bb000f659238 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 2,018 | lean | /-
Copyright (c) 2022 Yaël Dillies, Sara Rousta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import order.upper_lower.basic
import order.hom.complete_lattice
/-!
# `upper_set.Ici` etc as `sup`/`Sup`/`inf`/`Inf`-homomorphisms
> THIS FILE IS SYNCHRON... |
a18f29117f1a2fb86a2c9207870256356d1659c4 | 510e96af568b060ed5858226ad954c258549f143 | /data/set/basic.lean | b06cbe69c2e9407628db01261d9612b537218744 | [] | no_license | Shamrock-Frost/library_dev | cb6d1739237d81e17720118f72ba0a6db8a5906b | 0245c71e4931d3aceeacf0aea776454f6ee03c9c | refs/heads/master | 1,609,481,034,595 | 1,500,165,215,000 | 1,500,165,347,000 | 97,350,162 | 0 | 0 | null | 1,500,164,969,000 | 1,500,164,969,000 | null | UTF-8 | Lean | false | false | 32,454 | 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
-- QUESTION: can make the first argument in ∀ x ∈ a, ... implicit?
-/
import logic.basic data.set -- from the library in the main repo
... |
1d77142d7880c5ef112da3fa16a38c7232256097 | c6da0300d417abe3464e750ab51a63502b93acfa | /src/struct_tact/debugging.lean | 2513837ab74bd8e628864ba5c5b37d3ebf1b8125 | [
"Apache-2.0"
] | permissive | uwplse/struct_tact | 55bc1d260fac498cff83a4d71461041f8ed74bd6 | 22188ea2e97705d1185f75dde24e6bab88054ab0 | refs/heads/master | 1,630,670,592,496 | 1,515,453,299,000 | 1,515,453,299,000 | 104,603,771 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 132 | lean | open tactic
meta def trace_goals : tactic unit :=
do gs ← get_goals,
ts ← monad.mapm infer_type gs,
trace (to_string ts)
|
dce11f7e3f5b785db99af1a0594be1dbe8763d5c | c777c32c8e484e195053731103c5e52af26a25d1 | /src/analysis/special_functions/exp_deriv.lean | ff0b7ade2a6419c9888c8c1080d3834268e3b26f | [
"Apache-2.0"
] | permissive | kbuzzard/mathlib | 2ff9e85dfe2a46f4b291927f983afec17e946eb8 | 58537299e922f9c77df76cb613910914a479c1f7 | refs/heads/master | 1,685,313,702,744 | 1,683,974,212,000 | 1,683,974,212,000 | 128,185,277 | 1 | 0 | null | 1,522,920,600,000 | 1,522,920,600,000 | null | UTF-8 | Lean | false | false | 10,119 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne
-/
import analysis.calculus.inverse
import analysis.complex.real_deriv
/-!
# Complex and real exponential
In this file we p... |
7977558291bf9e5edd54673c2592f2fd92eb2882 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /tests/lean/run/602.lean | 2a564734a30a26fb8d4bec11edc0371fe0e2644d | [
"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 | 1,197 | lean | class Semiring (α : Type) where add : α → α → α
class Ring (α : Type) where add : α → α → α
class AddCommMonoid (α : Type) where
class AddCommGroup (α : Type) where
class Module (α β : Type) [Semiring α] [AddCommMonoid β] where
class NormedField (α : Type) where
add : α → α → α
add_comm : ∀ (x y : α), @Add.add ... |
38dfc654081378126f97120668309881e57b3aa6 | 87a08a8e9b222ec02f3327dca4ae24590c1b3de9 | /src/topology/instances/nnreal.lean | 52711c6e36469663191c5bde764b4b73b0dfd51f | [
"Apache-2.0"
] | permissive | naussicaa/mathlib | 86d05223517a39e80920549a8052f9cf0e0b77b8 | 1ef2c2df20cf45c21675d855436228c7ae02d47a | refs/heads/master | 1,592,104,950,080 | 1,562,073,069,000 | 1,562,073,069,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,501 | lean | /-
Copyright (c) 2018 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
Nonnegative real numbers.
-/
import data.real.nnreal topology.instances.real topology.algebra.infinite_sum
noncomputable theory
open set topological_space metric
names... |
53bf6499df21da3dbc83380f31b85453fef6723f | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/data/real/nnreal.lean | d3db89b38a3f17286718a38dc2ea28c5fcd5613b | [
"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 | 30,461 | 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.big_operators.ring
import data.real.basic
import algebra.indicator_function
import algebra.algebra.basic
import algebra.order.nonneg
/-!
# Nonnegative... |
65a305249d556077b429b842eac81cacab9f391b | 4727251e0cd73359b15b664c3170e5d754078599 | /src/ring_theory/witt_vector/mul_coeff.lean | 4decf41963be371310dcde5251313d37381495ba | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 13,214 | lean | /-
Copyright (c) 2022 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Heather Macbeth
-/
import ring_theory.witt_vector.truncated
import data.mv_polynomial.supported
/-!
# Leading terms of Witt vector multiplication
The goal of this ... |
0ff51eb35bf14ce2a36497a486ddf61a8748100e | 761d983a78bc025071bac14a3facced881cf5e53 | /new_affine/affine_coordinate_space.lean | 988b8dc8c5997b5b78e366c1cc149db8d231e9ec | [] | no_license | rohanrajnair/affine_lib | bcf22ff892cf74ccb36a95bc9b7fff8e0adb2d0d | 83076864245ac547b9d615bc6a23804b1b4a8f70 | refs/heads/master | 1,673,320,928,343 | 1,603,036,653,000 | 1,603,036,653,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,264 | lean | import .list_as_k_tuple linear_algebra.affine_space.basic
import .affine_with_frame
universes u v w
variables (X : Type u) (k : Type v) (V : Type w) (n : ℕ) (id : ℕ)
[inhabited k] [ring k] [add_comm_group V] [module k V] [affine_space V X]
open list
open vecl
/-- type class for affine vectors. This models n-dimension... |
5c6f4121667c6a845eb8760eb8baf9735c64962b | 618003631150032a5676f229d13a079ac875ff77 | /src/control/bitraversable/instances.lean | 9f8197aa4f5d6f10ac2b418ef5491a1790f401f3 | [
"Apache-2.0"
] | permissive | awainverse/mathlib | 939b68c8486df66cfda64d327ad3d9165248c777 | ea76bd8f3ca0a8bf0a166a06a475b10663dec44a | refs/heads/master | 1,659,592,962,036 | 1,590,987,592,000 | 1,590,987,592,000 | 268,436,019 | 1 | 0 | Apache-2.0 | 1,590,990,500,000 | 1,590,990,500,000 | null | UTF-8 | Lean | false | false | 4,363 | lean | /-
Copyright (c) 2019 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author(s): Simon Hudon
-/
import control.bitraversable.lemmas
import control.traversable.lemmas
/-!
# bitraversable instances
## Instances
* prod
* sum
* const
* flip
* bicompl
* bicompr
... |
a0ac96f390952038cbe4e05395c6d4ef9a5256db | 0d7f5899c0475f9e105a439896d9377f80c0d7c3 | /src/.old/for_mathlib.lean | 22c20b19450d2b4cf584060b07e512951dbc46ca | [] | no_license | adamtopaz/UnivAlg | 127038f320e68cdf3efcd0c084c9af02fdb8da3d | 2458d47a6e4fd0525e3a25b07cb7dd518ac173ef | refs/heads/master | 1,670,320,985,286 | 1,597,350,882,000 | 1,597,350,882,000 | 280,585,500 | 4 | 0 | null | 1,597,350,883,000 | 1,595,048,527,000 | Lean | UTF-8 | Lean | false | false | 5,415 | lean | import tactic
import data.vector
import data.nat.basic
--import category_theory.types
--------------------- Vector Stuff ----------------------
namespace vector
variables {A : Type*} {B : Type*} {C : Type*}
def of : A → vector A 1 := λ a, ⟨[a],rfl⟩
def of₂ : A → A → vector A 2 := λ a b, ⟨[a,b],rfl⟩
def of₃ : A → A → ... |
3be600c197c03bc740f272722d9f5481920bb615 | e9dbaaae490bc072444e3021634bf73664003760 | /src/Geo/Analytic.lean | f4ee841ede8fb0830d3713162a4f00068d90c092 | [
"Apache-2.0"
] | permissive | liaofei1128/geometry | 566d8bfe095ce0c0113d36df90635306c60e975b | 3dd128e4eec8008764bb94e18b932f9ffd66e6b3 | refs/heads/master | 1,678,996,510,399 | 1,581,454,543,000 | 1,583,337,839,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,307 | lean | import Geo.Background.Real
import Geo.Background.List
import Geo.Background.Vec
import Geo.Background.Set
import Geo.Background.Tuple
/-
Currently, we do not require NDGs in the constructions.
We will experiment with requiring them only for the theorems about the constructions,
and perhaps auto-generating them from th... |
478684d514118ef44f3a87b567f67886a88fa59e | 05b503addd423dd68145d68b8cde5cd595d74365 | /src/topology/algebra/ordered.lean | e1047dc33cd9957a77f55b43696f9af5ccc1da84 | [
"Apache-2.0"
] | permissive | aestriplex/mathlib | 77513ff2b176d74a3bec114f33b519069788811d | e2fa8b2b1b732d7c25119229e3cdfba8370cb00f | refs/heads/master | 1,621,969,960,692 | 1,586,279,279,000 | 1,586,279,279,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 78,887 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Yury Kudryashov
-/
import tactic.tfae
import order.liminf_limsup
import data.set.intervals
import topology.algebra.group
import topology.constructions
... |
9694829cb214781dbb3fd2223d4a246b71e5e59f | da23b545e1653cafd4ab88b3a42b9115a0b1355f | /src/tidy/timing.lean | eeae85e531ac1cf8b5b9f9cbe3999f1c9265e505 | [] | no_license | minchaowu/lean-tidy | 137f5058896e0e81dae84bf8d02b74101d21677a | 2d4c52d66cf07c59f8746e405ba861b4fa0e3835 | refs/heads/master | 1,585,283,406,120 | 1,535,094,033,000 | 1,535,094,033,000 | 145,945,792 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,980 | lean |
import system.io
open tactic
universe variables u
/-- This function has a native implementation that returns the system time in microseconds since the epoch. -/
-- see patch below for adding this to Lean
-- it currently suffers from overflow issues, which aren't a problem for profiling.
meta def systemtime : ℕ :=
0... |
e5f1d38f090ee11056e21da747576fbfbd7ebd2d | b00eb947a9c4141624aa8919e94ce6dcd249ed70 | /src/Leanpkg.lean | 74559d0344c768be1231e64bdd2b280c04491706 | [
"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 | 8,861 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner, Sebastian Ullrich
-/
import Leanpkg.Resolve
import Leanpkg.Git
import Leanpkg.Build
open System
namespace Leanpkg
def readManifest : IO Manifest := do
let m ... |
bba49487752dc00fe7b60a9d99ca2b131aa81084 | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/algebra/homology/exact.lean | afe608390ef10cbc8bd9a88d72adf94fd110bc97 | [
"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 | 2,335 | 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 algebra.homology.image_to_kernel_map
/-!
# Exact sequences
In a category with zero morphisms, images, and equalizers we say that `f : A ⟶ B` and `g : B ⟶ C`
ar... |
7976d1e328713d46ee08991da9a05f1b6575beae | 137c667471a40116a7afd7261f030b30180468c2 | /src/measure_theory/measurable_space_def.lean | 06c4a776a138b5d689d92bb106fbfed65aedf616 | [
"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 | 17,090 | 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.set.disjointed
import data.set.countable
import algebra.indicator_function
import data.equiv.encodable.lattice
import data.tprod
import or... |
ee092f54612d56b453a2c092ce58135b8fe9e4dd | 36c7a18fd72e5b57229bd8ba36493daf536a19ce | /hott/algebra/ring.hlean | 353a217192a73b9bbcc69ce589c03b3ba3b93454 | [
"Apache-2.0"
] | permissive | YHVHvx/lean | 732bf0fb7a298cd7fe0f15d82f8e248c11db49e9 | 038369533e0136dd395dc252084d3c1853accbf2 | refs/heads/master | 1,610,701,080,210 | 1,449,128,595,000 | 1,449,128,595,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 13,278 | hlean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura
Structures with multiplicative and additive components, including semirings, rings, and fields.
The development is modeled after Isabelle's library.
Po... |
ae06d90218738a548aa60c0f173f2563d10a60e3 | 626e312b5c1cb2d88fca108f5933076012633192 | /src/data/real/sqrt.lean | e86da1e80a80dec80c8a895f4d0e2ed76812eae7 | [
"Apache-2.0"
] | permissive | Bioye97/mathlib | 9db2f9ee54418d29dd06996279ba9dc874fd6beb | 782a20a27ee83b523f801ff34efb1a9557085019 | refs/heads/master | 1,690,305,956,488 | 1,631,067,774,000 | 1,631,067,774,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,493 | lean | /-
Copyright (c) 2020 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Floris van Doorn, Yury Kudryashov
-/
import topology.instances.nnreal
/-!
# Square root of a real number
In this file we define
* `nnreal.sqrt` to be the square root... |
6593c3a3c8bb626e38428d5d7f361c7e1c475156 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/sec_param_pp.lean | e671ce5b47c1a7a15ae0d9837a2d8a504c534be8 | [
"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 | 275 | lean | section
parameters {A : Type} (a : A)
variable f : A → A → A
definition id2 : A := a
check id2
definition pr (b : A) : A := f a b
check pr f id2
set_option pp.universes true
check pr f id2
definition pr2 (B : Type) (b : B) : A := a
check pr2 num 10
end
|
b090d0388742aa802f848200051b9fc96d488679 | 05b503addd423dd68145d68b8cde5cd595d74365 | /src/set_theory/pgame.lean | f65c5aa0fe28cf472e417c1eac59d912900daedd | [
"Apache-2.0"
] | permissive | aestriplex/mathlib | 77513ff2b176d74a3bec114f33b519069788811d | e2fa8b2b1b732d7c25119229e3cdfba8370cb00f | refs/heads/master | 1,621,969,960,692 | 1,586,279,279,000 | 1,586,279,279,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 38,641 | lean | /-
Copyright (c) 2019 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Mario Carneiro, Isabel Longbottom, Scott Morrison
-/
import data.equiv.basic logic.embedding
import data.nat.cast
/-!
# Combinatorial (pre-)games.
The basic theory of co... |
3c7127e33a2cc5d4019dd2de4503bf629722daa5 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/negFloat.lean | 608a1ccbc6b9e2b9738e922ae661b76aa37dd35a | [
"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 | 83 | lean | #check 42
#check -42
#check -42.0
#eval -42.0
#eval Neg.neg 42.0
#eval 1.0 * -42.0
|
2d09c1a492be25e9e33166e6a70c49d386fc81f4 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/ring_theory/trace.lean | d7f15da50986e535cda4adf6915658f26897f5ef | [
"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 | 16,128 | 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 linear_algebra.bilinear_form
import linear_algebra.matrix.charpoly.coeff
import linear_algebra.determinant
import linear_algebra.vandermonde
import linear_algebra.t... |
4fc7fc804f82ea8b94c7e8b410496fc459a5a50b | c777c32c8e484e195053731103c5e52af26a25d1 | /src/linear_algebra/prod.lean | 2b190f6abffca20728a103e1d715fa808f567cb5 | [
"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 | 31,522 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov, Eric Wieser
-/
import linear_algebra.span
import order.partial_sups
import algebra.algebra.prod
/-! ### Products of mod... |
a5ab49644963ff36455d93a2b24f8259639fa5ea | 02005f45e00c7ecf2c8ca5db60251bd1e9c860b5 | /src/topology/path_connected.lean | c336a980ba933787c3fde3186bfab2d8f86e1e73 | [
"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 | 34,364 | lean | /-
Copyright (c) 2020 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import topology.instances.real
import topology.algebra.ordered.proj_Icc
/-!
# Path connectedness
## Main definitions
In the file the unit interval `[0, 1]` in `ℝ` ... |
8f32cab399513edb20c89eba57fb2dc062bda32f | 8d65764a9e5f0923a67fc435eb1a5a1d02fd80e3 | /src/data/matrix/kronecker.lean | dd35062da7e293bd3414f599e62e3607843c82ed | [
"Apache-2.0"
] | permissive | troyjlee/mathlib | e18d4b8026e32062ab9e89bc3b003a5d1cfec3f5 | 45e7eb8447555247246e3fe91c87066506c14875 | refs/heads/master | 1,689,248,035,046 | 1,629,470,528,000 | 1,629,470,528,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,691 | lean | /-
Copyright (c) 2021 Filippo A. E. Nuccio. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Filippo A. E. Nuccio, Eric Wieser
-/
import data.matrix.basic
import linear_algebra.tensor_product
import ring_theory.tensor_product
/-!
# Kronecker product of matrices
This d... |
f53056f5fa4bca9d55580366dc604ba0adcd9d12 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/linear_algebra/isomorphisms.lean | a362f4542c7afbae9716fd155ee008724f4f9cdf | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 6,394 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov
-/
import linear_algebra.quotient
/-!
# Isomorphism theorems for modules.
* The Noether's first, second, and third isom... |
10c12eaacdbb360855307b0f12b3348d9dde6d10 | 592ee40978ac7604005a4e0d35bbc4b467389241 | /Library/generated/mathscheme-lean/RegularSemigroup.lean | 0b51a379de45a1047f881c0e51c3770efba378a8 | [] | 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 | 8,313 | 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 RegularSemigroup
structure RegularSemigroup (A : Type) : Type :=
(op : (A → (A → A)))
(associative_op : (∀ {x y z : A} , (op (op x y) z) = (op x (op y z))))
... |
3b48a7ff42c842ef7dd4aa582dd39cf3d2753c49 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebraic_topology/fundamental_groupoid/basic.lean | 9c3fea201bd586b0da386cd479d173608899bb8a | [
"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 | 12,789 | lean | /-
Copyright (c) 2021 Shing Tak Lam. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shing Tak Lam
-/
import category_theory.category.Groupoid
import category_theory.groupoid
import topology.category.Top.basic
import topology.homotopy.path
/-!
# Fundamental groupoid of... |
f929871f2bf961d288fca774913947b161942f39 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/apply_elim.lean | 96269eb14d2cc04b21d7cc5db9b235e6f4df15e9 | [
"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 | 252 | lean | open nat
def nat.ind_on {p : nat → Prop} (n : nat) (h₁ : p 0) (h₂ : ∀ n, p n → p (succ n)) : p n :=
nat.rec_on n h₁ h₂
example : ∀ a b : nat, a + b = b + a :=
begin
intro a,
apply nat.ind_on a,
trace_state,
repeat {admit}
end
|
b56c7425cde103d8e06c3a046029571fff3f0241 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/geometry/manifold/smooth_manifold_with_corners.lean | ac630c7d734a6841678ba0145405d93fe1398b5f | [
"Apache-2.0"
] | permissive | rmitta/mathlib | 8d90aee30b4db2b013e01f62c33f297d7e64a43d | 883d974b608845bad30ae19e27e33c285200bf84 | refs/heads/master | 1,585,776,832,544 | 1,576,874,096,000 | 1,576,874,096,000 | 153,663,165 | 0 | 2 | Apache-2.0 | 1,544,806,490,000 | 1,539,884,365,000 | Lean | UTF-8 | Lean | false | false | 19,124 | 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 analysis.calculus.times_cont_diff geometry.manifold.manifold
/-!
# Smooth manifolds (possibly with boundary or corners)
A smooth manifold is a manifol... |
8d908c02b9bee3684f25d8fb9a8cf79a991ec744 | 0ce335c3cee4b6a212935fdfd1a5270985454648 | /src/data/finset.lean | 8f3ac693b231aecc56afc664b34925de7864ad67 | [
"Apache-2.0"
] | permissive | yashen32768/mathlib | 191f6113ccd0ef74091c3f5951ae84c0aa85516f | f54463254784b400da2e33dfa58f94775e3de845 | refs/heads/master | 1,598,060,530,541 | 1,571,523,082,000 | 1,571,523,082,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 89,468 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura, Jeremy Avigad, Minchao Wu, Mario Carneiro
Finite sets.
-/
import logic.embedding algebra.order_functions
data.multiset data.sigma.basic data.set.lattice
op... |
0bc1c2419ae21b506f829cd19fa7621b71d79919 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/special_functions/trigonometric/series.lean | a3ece09d3d75ab22248d712e414f6f47089afc6d | [
"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 | 4,686 | lean | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import analysis.special_functions.exponential
/-!
# Trigonometric functions as sums of infinite series
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this fil... |
f7d1f195434bb3d68281e872c2c134bec5d28e6c | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/group_theory/subgroup.lean | d43a1a27ba8df00e05f5df0842c5b4019235e008 | [
"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 | 94,732 | lean | /-
Copyright (c) 2020 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
import group_theory.submonoid
import group_theory.submonoid.center
import algebra.group.conj
import algebra.pointwise
import order.atoms
/-!
# Subgroups
This file defines... |
02bef5df03244c8004aab19f526ede8ffa7f52f9 | ae1e94c332e17c7dc7051ce976d5a9eebe7ab8a5 | /stage0/src/Lean/Util/Path.lean | ec273e533b0cbc52718bbfca67f3ac0b5b025868 | [
"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 | 3,465 | 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
Management of the Lean search path (`LEAN_PATH`), which is a list of
paths containing package roots: an import `A.B.C` resolves to
`path/A/... |
67d8b195ef6b2ea748ebcbc79a1d46bf6c539763 | 75db7e3219bba2fbf41bf5b905f34fcb3c6ca3f2 | /hott/algebra/category/constructions/functor.hlean | debbfe89fd66d6b7e9bf2728d6be3b1eaf659910 | [
"Apache-2.0"
] | permissive | jroesch/lean | 30ef0860fa905d35b9ad6f76de1a4f65c9af6871 | 3de4ec1a6ce9a960feb2a48eeea8b53246fa34f2 | refs/heads/master | 1,586,090,835,348 | 1,455,142,203,000 | 1,455,142,277,000 | 51,536,958 | 1 | 0 | null | 1,455,215,811,000 | 1,455,215,811,000 | null | UTF-8 | Lean | false | false | 16,113 | 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, Jakob von Raumer
Functor precategory and category
-/
import ..nat_trans ..category .opposite
open eq category is_trunc nat_trans iso is_equiv category.hom
names... |
155e2698ac04ba67ef101e3b4a14dfdc044b7e64 | e61a235b8468b03aee0120bf26ec615c045005d2 | /stage0/src/Init/Lean.lean | aa64318cbd7f0c13a1b8c2c6448c90bbe6c11da9 | [
"Apache-2.0"
] | permissive | SCKelemen/lean4 | 140dc63a80539f7c61c8e43e1c174d8500ec3230 | e10507e6615ddbef73d67b0b6c7f1e4cecdd82bc | refs/heads/master | 1,660,973,595,917 | 1,590,278,033,000 | 1,590,278,033,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 733 | 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
import Init.Lean.Environment
import Init.Lean.Modifiers
import Init.Lean.ProjFns
import Init.Lean.Runtime
import Init.Lean... |
d675b478a96eac784175de3ba0edb26eb68816d1 | 9a0b1b3a653ea926b03d1495fef64da1d14b3174 | /tidy/rewrite_all_wrappers.lean | ca843031f1db9ad506f37c2a869a275ba1d2cb96 | [
"Apache-2.0"
] | permissive | khoek/mathlib-tidy | 8623b27b4e04e7d598164e7eaf248610d58f768b | 866afa6ab597c47f1b72e8fe2b82b97fff5b980f | refs/heads/master | 1,585,598,975,772 | 1,538,659,544,000 | 1,538,659,544,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,059 | lean | import .rewrite_all
open tactic
open lean.parser
open interactive
-- TODO We currently don't use `list.erase_duplicates`. Is it necessary?!
-- return a list of (e', prf, n, k) where
-- e' is a new expression,
-- prf : e = e',
-- n is the index of the rule r used from rs, and
-- k is the index of (e', prf) in... |
ee26a89a07ec44f9af39f1d50799bc4d0ae500e5 | 64874bd1010548c7f5a6e3e8902efa63baaff785 | /library/data/nat/basic.lean | 6b95cab2469ce01dfdec6e48baa3536e54438785 | [
"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 | 9,354 | lean | /-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.nat.basic
Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad
Basic operations on the natural numbers.
-/
import logic.connectives data.num algebra.binary
open binary e... |
d44e69dd9f89a627398b694c35c8594be3b37ea0 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/linear_algebra/matrix/polynomial.lean | 4045bbe16a2cb21ef69829a2b9d8f2ff30857bfe | [
"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 | 4,157 | 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 algebra.polynomial.big_operators
import data.polynomial.degree.lemmas
import linear_algebra.matrix.determinant
/-!
# Matrices of polynomials and polynomials... |
77199c1955ab4890991d0e28f4b1b8b3950455e5 | e7de183433d907275be4926240a8c8ddb5915131 | /recipes/literate_lean3.lean | c098e9987fb0761f77aec9fd2dac296cc24818bd | [
"MIT"
] | permissive | cpitclaudel/alectryon | 70b01086e9b4aee4f18017621578004903ce74d3 | 11e8cdc8395d66858baa7371b6cf8e827ca38f4a | refs/heads/master | 1,683,666,125,135 | 1,683,473,634,000 | 1,683,473,844,000 | 260,735,576 | 206 | 29 | MIT | 1,655,000,579,000 | 1,588,439,321,000 | HTML | UTF-8 | Lean | false | false | 2,151 | lean | /-!
==================================================
Literate programming with Alectryon (Lean3 input)
==================================================
Alectryon supports literate programs and documents (combinations of code and prose) written in Lean3 and reStructuredText. Here is an example written in Lean3. ... |
98453c347dd2b37839994104b1887e763b5fb0e5 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/tactic/monotonicity/lemmas.lean | 44b47397ef8eb09477375ef0a92ba03cfdcb1e0e | [
"Apache-2.0"
] | permissive | rmitta/mathlib | 8d90aee30b4db2b013e01f62c33f297d7e64a43d | 883d974b608845bad30ae19e27e33c285200bf84 | refs/heads/master | 1,585,776,832,544 | 1,576,874,096,000 | 1,576,874,096,000 | 153,663,165 | 0 | 2 | Apache-2.0 | 1,544,806,490,000 | 1,539,884,365,000 | Lean | UTF-8 | Lean | false | false | 1,771 | lean | /-
Copyright (c) 2019 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Simon Hudon
-/
import tactic.monotonicity.basic
variables {α : Type*}
@[mono]
lemma mul_mono_nonneg {x y z : α} [ordered_semiring α]
(h' : 0 ≤ z)
(h : x ≤ y)
: x * z ≤ y * z :=
by ap... |
85cba011916b4c160b8d36c4ebafe3a14a2310ce | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/data/fintype/fin.lean | 7e44c50adab13218d8649a94e427ed1436a039a5 | [
"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 | 1,441 | lean | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import data.fin.basic
import data.fintype.basic
/-!
# The structure of `fintype (fin n)`
This file contains some basic results about the `fintype` instance for `fin`,
espe... |
6fd14eeae8c76d0c2841d6508bc4fa2598c7d0eb | 8cae4802a568c5efee3f39770b464eda3c64abc7 | /src/exercise-3.7.lean | af3138f4d4eff277173fed3a925de26714d8c88f | [] | no_license | jagadishb09/lean | c8c2884c09dd85b6d1d01037c4d113b0f9e5314b | c37d0e0a4e27e78d52bc44ddd7b9851f29b91e0d | refs/heads/master | 1,685,788,126,674 | 1,623,973,211,000 | 1,623,973,211,000 | 375,844,657 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,779 | lean | --Exercise 3.7.1
-- Author : Jagadish Bapanapally
variables p q r : Prop
-- commutativity of ∧ and ∨
example : p ∨ q ↔ q ∨ p :=
iff.intro
(assume h : p ∨ q,
or.elim h (λ hp, or.inr hp) (λ hq, or.inl hq))
(assume h : q ∨ p,
or.elim h (λ hp, or.inr hp) (λ hq, or.inl hq))
example : p ∨ q ↔ q ∨ p :=
iff.intro
(ass... |
a1ce8aa47e95767a523f06d032c42be198307be9 | b73bd2854495d87ad5ce4f247cfcd6faa7e71c7e | /src/game/world1/level2.lean | 5b230238b4685399051895b4706d99603e42be55 | [] | no_license | agusakov/category-theory-game | 20db0b26270e0c95a3d5605498570273d72f731d | 652dd7e90ae706643b2a597e2c938403653e167d | refs/heads/master | 1,669,201,216,310 | 1,595,740,057,000 | 1,595,740,057,000 | 280,895,295 | 12 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,548 | lean | import category_theory.category.default
universes v u -- The order in this declaration matters: v often needs to be explicitly specified while u often can be omitted
namespace category_theory
variables (C : Type u) [category.{v} C]
/-
# Category world
## Level 2: Definition of category
A category `C` consists of... |
36d894426dfdb0589ffd449a894237a4a8e4687b | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/ring_theory/algebraic.lean | e8adc60a7b5833fa390cf8e2619ccb6970909bed | [
"Apache-2.0"
] | permissive | dupuisf/mathlib | 62de4ec6544bf3b79086afd27b6529acfaf2c1bb | 8582b06b0a5d06c33ee07d0bdf7c646cae22cf36 | refs/heads/master | 1,669,494,854,016 | 1,595,692,409,000 | 1,595,692,409,000 | 272,046,630 | 0 | 0 | Apache-2.0 | 1,592,066,143,000 | 1,592,066,142,000 | null | UTF-8 | Lean | false | false | 4,713 | lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import linear_algebra.finite_dimensional
import ring_theory.integral_closure
import data.polynomial.field_division
import data.polynomial.integral_normalization
/-!... |
fbf46a300889e925dfaf7d07710ec26b37a67a96 | 0c9c1ff8e5013c525bf1d72338b62db639374733 | /library/init/data/sum/basic.lean | d62e04656a7d1855c4748d46feb22982cbf33e84 | [
"Apache-2.0"
] | permissive | semorrison/lean | 1f2bb450c3400098666ff6e43aa29b8e1e3cdc3a | 85dcb385d5219f2fca8c73b2ebca270fe81337e0 | refs/heads/master | 1,638,526,143,586 | 1,634,825,588,000 | 1,634,825,588,000 | 258,650,844 | 0 | 0 | Apache-2.0 | 1,587,772,955,000 | 1,587,772,954,000 | null | UTF-8 | Lean | false | false | 525 | 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, Jeremy Avigad
The sum type, aka disjoint union.
-/
prelude
import init.logic
infixr ` ⊕ `:30 := sum
universes u v
variables {α : Type u} {β : Type v}
ins... |
1fe0f70f3a0538839a67aba2903e2a788c3e3ad1 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/ring_theory/roots_of_unity.lean | bc08c65e07527c4f0211d41fea75ca5c584fcf46 | [
"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 | 40,603 | 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.nat.parity
import data.polynomial.ring_division
import group_theory.specific_groups.cyclic
import ring_theory.integral_domain
import number_theory.diviso... |
41f79bdd027a7eb0b163d6ff9a6f47bc09f1ad44 | 4727251e0cd73359b15b664c3170e5d754078599 | /archive/imo/imo1994_q1.lean | 07c78f44c9bb99aa9e75859f8f64d81d337437b7 | [
"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 | 4,112 | lean | /-
Copyright (c) 2021 Antoine Labelle. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Labelle
-/
import algebra.big_operators.basic
import algebra.big_operators.order
import data.fintype.card
import data.finset.sort
import data.fin.interval
import tactic.linari... |
c6b560b810469533d9dfe8e7a232c7ff6a3bced1 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/contra3.lean | 393817e791fbdf215ac2497c6b4570c5343174bd | [
"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 | 349 | lean | open tactic nat
example (a b c : Prop) : a → b → ¬ a → c :=
by do intros, contradiction
example (a b c : Prop) : a → false → b → c :=
by do intros, contradiction
example (a b : nat) : succ a = 0 → b = 0 :=
by do intro `H, contradiction
example (a b : nat) : succ a = succ b → succ a = 0 → b = 0 :=
by do intros, cont... |
bb5ae1a6b8b088fbbab9094c78e13f4976df6363 | 4bcaca5dc83d49803f72b7b5920b75b6e7d9de2d | /tests/lean/run/meta7.lean | 6d3b32993cafe606bd5c15da80ab34917e02a647 | [
"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 | 5,449 | lean | import Lean.Meta
open Lean
open Lean.Meta
partial def fact : Nat → Nat
| 0 => 1
| n+1 => (n+1)*fact n
set_option trace.Meta.debug true
set_option trace.Meta.check false
def print (msg : MessageData) : MetaM Unit := do
trace[Meta.debug] msg
def checkM (x : MetaM Bool) : MetaM Unit :=
unless (← x) do throwError "c... |
6e7afe83e1d419cba969cd9ac85b8fd53aefe03e | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/analysis/convex/measure.lean | 3a82f562c9094d450c2fbf257000644e999ce73d | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 4,363 | lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import analysis.convex.topology
import analysis.normed_space.add_torsor_bases
import measure_theory.measure.haar_lebesgue
/-!
# Convex sets are null-measurable
Le... |
2a932fc7e792da41b46304e02d331310dd007798 | 3446e92e64a5de7ed1f2109cfb024f83cd904c34 | /src/game/world2/level12.lean | 2c182734a1088345e4112f52f1449a4710fb02e8 | [] | no_license | kckennylau/natural_number_game | 019f4a5f419c9681e65234ecd124c564f9a0a246 | ad8c0adaa725975be8a9f978c8494a39311029be | refs/heads/master | 1,598,784,137,722 | 1,571,905,156,000 | 1,571,905,156,000 | 218,354,686 | 0 | 0 | null | 1,572,373,319,000 | 1,572,373,318,000 | null | UTF-8 | Lean | false | false | 977 | lean | import mynat.definition -- hide
import mynat.add -- hide
import game.world2.level11 -- hide
namespace mynat -- hide
/-
# World 2 -- Addition World
## Level 12 -- `eq_zero_of_add_right_eq_self`
You have : the usual stuff.
* `succ_inj : ∀ a b : mynat, succ(a) = succ(b) → a = b`
will be useful for this one.
You... |
9768ade22e0d2c37d33854c653f1bbe033baa22b | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/ring_theory/witt_vector/frobenius.lean | 757e03c45f4e5e5e009a90f856e7efe778658bce | [
"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 | 13,396 | 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.nat.multiplicity
import ring_theory.witt_vector.basic
import ring_theory.witt_vector.is_poly
/-!
## The Frobenius operator
If `R` has characteristic `... |
ff3ea11bb83b3e5427dd0e120e6a5a75863c0f5a | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/category_theory/sites/pretopology.lean | 3b213a29975490150c07c304e3452683aa343518 | [
"Apache-2.0"
] | permissive | AntoineChambert-Loir/mathlib | 64aabb896129885f12296a799818061bc90da1ff | 07be904260ab6e36a5769680b6012f03a4727134 | refs/heads/master | 1,693,187,631,771 | 1,636,719,886,000 | 1,636,719,886,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,201 | 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.sites.grothendieck
/-!
# Grothendieck pretopologies
Definition and lemmas about Grothendieck pretopologies.
A Grothendieck pretopology for a cat... |
093df5cf29eaaeb3241df31f18a0da08f1b30fa1 | a4673261e60b025e2c8c825dfa4ab9108246c32e | /tests/compiler/rbmap_library.lean | 2a2f86e748cfaf869ded5207caae9885475532c4 | [
"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 | 2,334 | lean | #lang lean4
import Std
open Std
def check (b : Bool) : IO Unit := do
unless b do IO.println "ERROR"
def sz {α β : Type} {lt : α → α → Bool} (m : RBMap α β lt) : Nat :=
m.fold (fun sz _ _ => sz+1) 0
def depth {α β : Type} {lt : α → α → Bool} (m : RBMap α β lt) : Nat :=
m.depth Nat.max
def tst1 : IO Unit :=
do let Ma... |
2c04d5fff14f7634a90d04475f866af516aa9198 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/data/finsupp/to_dfinsupp.lean | 8825cff0c0c7248e9948adaa45c42e5d8dd7a99b | [
"Apache-2.0"
] | permissive | abentkamp/mathlib | d9a75d291ec09f4637b0f30cc3880ffb07549ee5 | 5360e476391508e092b5a1e5210bd0ed22dc0755 | refs/heads/master | 1,682,382,954,948 | 1,622,106,077,000 | 1,622,106,077,000 | 149,285,665 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,198 | lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import data.dfinsupp
import data.finsupp.basic
import algebra.module.linear_map
/-!
# Conversion between `finsupp` and homogenous `dfinsupp`
This module provides conversi... |
51b004a245294a213ab8799ad9a71adeffac72ef | e61a235b8468b03aee0120bf26ec615c045005d2 | /stage0/src/Init/Coe.lean | 4d65730d9e08ea1bb61b07c5461e6dde869777d7 | [
"Apache-2.0"
] | permissive | SCKelemen/lean4 | 140dc63a80539f7c61c8e43e1c174d8500ec3230 | e10507e6615ddbef73d67b0b6c7f1e4cecdd82bc | refs/heads/master | 1,660,973,595,917 | 1,590,278,033,000 | 1,590,278,033,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,354 | 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
-/
prelude
import Init.HasCoe -- import legacy HasCoe
import Init.Core
universes u v w w'
class Coe (α : Sort u) (β : Sort v) :=
(coe : α → β)
/-- Auxiliary... |
85aa27d77ef7225925923b2a82252436e5d90d14 | c31182a012eec69da0a1f6c05f42b0f0717d212d | /src/for_mathlib/free_abelian_group.lean | 3ef4299a2afb8d63f91b026c7a4ab60981e0e534 | [] | no_license | Ja1941/lean-liquid | fbec3ffc7fc67df1b5ca95b7ee225685ab9ffbdc | 8e80ed0cbdf5145d6814e833a674eaf05a1495c1 | refs/heads/master | 1,689,437,983,362 | 1,628,362,719,000 | 1,628,362,719,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,221 | lean | import group_theory.free_abelian_group_finsupp
import data.finsupp.basic
/-!
In this file we define the equivalence between `free_abelian_group X`
and `X →₀ ℤ` (the type of finitely supported function `X → ℤ`).
Both types come with useful machinery, and the purpose of this file
is to transport some of the machinery fr... |
edebe107a98ca2343426bbcf6986a9a35072b598 | acc85b4be2c618b11fc7cb3005521ae6858a8d07 | /data/set/enumerate.lean | dec556ec07bcc16958fa6438fec44d80e61b74cf | [
"Apache-2.0"
] | permissive | linpingchuan/mathlib | d49990b236574df2a45d9919ba43c923f693d341 | 5ad8020f67eb13896a41cc7691d072c9331b1f76 | refs/heads/master | 1,626,019,377,808 | 1,508,048,784,000 | 1,508,048,784,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,784 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl
Enumerate elements of a set with a select function.
-/
import data.encodable data.set.finite data.set.lattice data.set.prod logic.function
noncomputable theory
open fu... |
d6972c84ccfcd939e5ceafb0e17781bf3deb3334 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/analysis/box_integral/partition/filter.lean | 8954ff270d1861a3540bfd99a8a3131b7197544e | [
"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 | 28,290 | 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.subbox_induction
import analysis.box_integral.partition.split
/-!
# Filters used in box-based integrals
First we define a s... |
f6de77fc613e746a7b6ae4b5354d0e287a1563f6 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/topology/algebra/uniform_group.lean | 645bbd699ff49c6b07a901bb1d4b96dfd043d5ca | [
"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 | 31,140 | lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl
-/
import topology.uniform_space.uniform_convergence
import topology.uniform_space.uniform_embedding
import topology.uniform_space.complete_separated
imp... |
6af510cbd22033e3f22db86520cbb39e222d9d39 | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /tests/lean/run/typeclass_coerce.lean | 5ba1bff87882ed040a6ff8dd7954c75ab60c9d90 | [
"Apache-2.0"
] | permissive | mhuisi/lean4 | 28d35a4febc2e251c7f05492e13f3b05d6f9b7af | dda44bc47f3e5d024508060dac2bcb59fd12e4c0 | refs/heads/master | 1,621,225,489,283 | 1,585,142,689,000 | 1,585,142,689,000 | 250,590,438 | 0 | 2 | Apache-2.0 | 1,602,443,220,000 | 1,585,327,814,000 | C | UTF-8 | Lean | false | false | 3,795 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Daniel Selsam, Leonardo de Moura
Declare new, simpler coercion class without the special support for transitivity.
Test that new tabled typeclass resolution deals with loops an... |
45a54ebbb5de38b19b0c90910710e5b21def2483 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/topology/bases.lean | a810eb0fc81e60f529b351392c32ffd13a79854b | [
"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 | 18,419 | 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
Bases of topologies. Countability axioms.
-/
import topology.constructions data.set.countable
open set filter classical
open_locale topological_space
... |
a8021962b623ea3dd6842b0fda7e9b6adceb8a37 | 43390109ab88557e6090f3245c47479c123ee500 | /src/Topology/Material/path.lean | b79e3f86e217bc762b97143b723d2a1d773319a7 | [
"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 | 13,695 | lean | /-
Copyright (c) 2018 Luca Gerolla. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Luca Gerolla, Mario Carneiro, Kevin Buzzard
Definition of path, loop and basic properties.
-/
import analysis.topology.continuity
import analysis.topology.topological_space
import analy... |
15d099b0e44fab3f050b1a45bea84c4930a8bb4c | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/634d.lean | cbc2d7b0d0d5dfda00b704e095abce114324f372 | [
"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 | 420 | lean | section
universe l
definition A {n : ℕ} (t : Type l) := t
check A
check _root_.A.{1}
set_option pp.universes true
check A
check _root_.A.{1}
end
section
universe l
parameters {B : Type.{l}}
definition P {n : ℕ} (b : B) := b
check P
check @_root_.P.{1} nat
set_option pp.universes true
check ... |
f5c18d93048c5dc8001c76953338e34633e70ebe | 12dabd587ce2621d9a4eff9f16e354d02e206c8e | /world04/level04.lean | 1d102fa40ea15ae6c5eb3399d2785a8d39153662 | [] | 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 | 124 | lean | lemma one_pow (m : mynat) : (1 : mynat) ^ m = 1 :=
begin
induction m with h hd,
rwa pow_zero,
rw pow_succ,
rw hd,
refl,
end
|
5f37f255e1026ca014872939b65e099f8d4c3aa3 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/analysis/normed_space/continuous_linear_map.lean | 693adffcd123ef2772889eaaff9ab6737134240a | [
"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 | 11,545 | lean | /-
Copyright (c) 2019 Jan-David Salchow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo
-/
import analysis.normed_space.basic
/-! # Constructions of continuous linear maps between (semi-)normed spaces
> THIS FILE IS SYNCH... |
df5dbd6ef900fa9effd7b744746128f5d6b4cae4 | 9c2e8d73b5c5932ceb1333265f17febc6a2f0a39 | /src/apps/examples.lean | 39291c04eb2bb3382879e04b1497543e8b780fba | [
"MIT"
] | permissive | minchaowu/ModalTab | 2150392108dfdcaffc620ff280a8b55fe13c187f | 9bb0bf17faf0554d907ef7bdd639648742889178 | refs/heads/master | 1,626,266,863,244 | 1,592,056,874,000 | 1,592,056,874,000 | 153,314,364 | 12 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 388 | lean | -- import .topo_translation ..K.jump
-- open nnf
-- def boom : nnf := dia (and (var 1) (neg 1))
-- -- #eval is_sat [boom]
-- -- #check tableau [boom]
-- def topo_fact_of (φ : nnf) : psum (∀ (α) (tm : topo_model α) s, ¬ topo_force tm s φ) unit :=
-- match tableau [φ] with
-- | node.closed _ h _ := psum.inl $ not_to... |
e3651ad1406d4f8e2f3ff1ccb2a17164cf6380ef | d9ed0fce1c218297bcba93e046cb4e79c83c3af8 | /library/tools/super/clause_ops.lean | d4f59722d026f5804fae985d43f4d91fd4c1025c | [
"Apache-2.0"
] | permissive | leodemoura/lean_clone | 005c63aa892a6492f2d4741ee3c2cb07a6be9d7f | cc077554b584d39bab55c360bc12a6fe7957afe6 | refs/heads/master | 1,610,506,475,484 | 1,482,348,354,000 | 1,482,348,543,000 | 77,091,586 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,560 | lean | /-
Copyright (c) 2016 Gabriel Ebner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner
-/
import .clause data.monad.transformers
open monad tactic expr
namespace super
meta def on_left_at {m} [monad m] (c : clause) (i : ℕ)
[has_monad_li... |
a52685738eac62a86015c922691564e544eeaaa8 | 30b012bb72d640ec30c8fdd4c45fdfa67beb012c | /data/fin.lean | d99e700da986639244ba2adab344a4a33c8921e2 | [
"Apache-2.0"
] | permissive | kckennylau/mathlib | 21fb810b701b10d6606d9002a4004f7672262e83 | 47b3477e20ffb5a06588dd3abb01fe0fe3205646 | refs/heads/master | 1,634,976,409,281 | 1,542,042,832,000 | 1,542,319,733,000 | 109,560,458 | 0 | 0 | Apache-2.0 | 1,542,369,208,000 | 1,509,867,494,000 | Lean | UTF-8 | Lean | false | false | 7,097 | lean | /-
Copyright (c) 2017 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Robert Y. Lewis
More about finite numbers.
-/
import data.nat.basic
open fin nat
/-- `fin 0` is empty -/
def fin_zero_elim {C : Sort*} : fin 0 → C :=
λ x, false.elim $ nat.not_lt_ze... |
7bf050f3c0295c4d3d03dab27c228fa8253ee4c2 | d436468d80b739ba7e06843c4d0d2070e43448e5 | /src/logic/basic.lean | 33ec838420cedd81bbeb88fb7f6848b4139c372a | [
"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 | 30,033 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura
-/
/-!
Theorems that require decidability hypotheses are in the namespace "decidable".
Classical versions are in the namespace "classical".
Note: in t... |
92cfabf179769dc8d65c3b0b271bf8a4a9eda604 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /tests/leanpkg/cyclic/Cyclic/A.lean | 31d5d96dcc615c0f58e496b325126334679486fe | [
"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 | 18 | lean | import Cyclic.A.B
|
6d142cd675c18e4a738491c5115de360be7d433e | 947b78d97130d56365ae2ec264df196ce769371a | /src/Lean/Util/Recognizers.lean | 694ca71301c3beb9315b0c8e0a8746ee7a9f0148 | [
"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 | 3,063 | 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.Environment
namespace Lean
namespace Expr
@[inline] def app1? (e : Expr) (fName : Name) : Option Expr :=
if e.isAppOfArity fName 1 then
some... |
48e0e3b2264ccb99cc27a294916899febc7afa42 | 5018a4b64e607056eac7db06751a3243a32d000a | /hott/types/prod.hlean | 38d33bed38d67c5d94c24bc9fc8ac33f064f48fc | [
"Apache-2.0"
] | permissive | spiceghello/lean2 | 6dea968cdbd80c32f435c0756df8e80125066e8f | ba5368c4ae229ea0e67c20f0207bbf6d28c5cb77 | refs/heads/master | 1,610,512,976,042 | 1,495,219,479,000 | 1,495,428,965,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,690 | hlean | /-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Jakob von Raumer
Ported from Coq HoTT
Theorems about products
-/
open eq equiv is_equiv is_trunc prod prod.ops unit
variables {A A' B B' C D : Type} {P Q : A → T... |
7a99b17c0637e2607ab1764e53a8280e4f5196cf | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/order/category/NonemptyFinLinOrd.lean | 73bddd81f550eaf062db732a3eb7347a9d1dca59 | [
"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 | 7,314 | 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 data.set.finite
import order.category.FinPartOrd
import order.category.LinOrd
import category_theory.limits.shapes.images
import cate... |
f11fb9888b4e0c00a73e2f12ff7208c0acaafe4b | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/linear_algebra/sesquilinear_form.lean | e889d05091b0ab74ed9b010dbae448cb1dd4886a | [
"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 | 9,643 | lean | /-
Copyright (c) 2018 Andreas Swerdlow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Andreas Swerdlow
-/
import algebra.module.basic
import ring_theory.ring_invo
/-!
# Sesquilinear form
This file defines a sesquilinear form over a module. The definition requires a r... |
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