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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
f4d5bf1b4d3482739ad658d446a78fb5ee8cc406 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/probability/moments.lean | bbbdc72197fdff2524d6c977c0b94c6e54ef0733 | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 15,587 | lean | /-
Copyright (c) 2022 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
import probability.variance
/-!
# Moments and moment generating function
## Main definitions
* `probability_theory.moment X p μ`: `p`th moment of a real random variab... |
f6b4afb47d286167705c1abc46904cc047830b4c | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/topology/instances/ennreal.lean | 921ad489aaf3e62d523d4acbf189535e0993ca78 | [
"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 | 56,389 | 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 topology.instances.nnreal
import topology.algebra.ordered.liminf_limsup
import topology.metric_space.lipschitz
/-!
# Extended non-negative reals
-/
noncomputa... |
60306bf2519eceeb56fa1f6dd6434159a127c535 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/abstract_notation.lean | 07515d45c8be4f381f3a042cf1255f7e43222818 | [
"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 | 178 | lean | import data.nat
open nat
notation `$`:max := abstract by blast end
definition foo (a b : nat) : a + b = b + a ∧ a = 0 + a :=
and.intro $ $
check foo_1
check foo_2
print foo
|
511cfbbf2722258a8f843e68b788a415c7acba79 | 99b5e6372af1f404777312358869f95be7de84a3 | /src/hott/algebra/ring.lean | 71daaf83c345961d337dc87690f6bcc736efc717 | [
"Apache-2.0"
] | permissive | forked-from-1kasper/hott3 | 8fa064ab5e8c9d6752a783d74ab226ddc5b5232a | 2db24de7a361a7793b0eae4ca5c3fd4d4a0fc691 | refs/heads/master | 1,584,867,131,028 | 1,530,766,841,000 | 1,530,766,841,000 | 139,797,034 | 0 | 0 | Apache-2.0 | 1,530,766,961,000 | 1,530,766,961,000 | null | UTF-8 | Lean | false | false | 20,931 | 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
Structures with multiplicative and additive components, including semirings, rings, and fields.
The development is modeled after Isabelle's library.
-/... |
92aa3e2b6f1ad9b6433c98ca34f5e2c580fe9de2 | 46125763b4dbf50619e8846a1371029346f4c3db | /src/ring_theory/ideal_operations.lean | eb478cb10d9f867c8bb34b5cd7b29c289a9ac78f | [
"Apache-2.0"
] | permissive | thjread/mathlib | a9d97612cedc2c3101060737233df15abcdb9eb1 | 7cffe2520a5518bba19227a107078d83fa725ddc | refs/heads/master | 1,615,637,696,376 | 1,583,953,063,000 | 1,583,953,063,000 | 246,680,271 | 0 | 0 | Apache-2.0 | 1,583,960,875,000 | 1,583,960,875,000 | null | UTF-8 | Lean | false | false | 26,863 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
More operations on modules and ideals.
-/
import ring_theory.ideals data.nat.choose order.zorn
import linear_algebra.tensor_product
import data.equiv.algebra
import ring_theory.... |
cd2dab5681d5288420ceb31ebc82a23be03843fd | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/topology/category/Top/open_nhds.lean | c75a34011a24a74108c5c46b87885b6f9086d1a3 | [] | 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 | 4,638 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.topology.category.Top.opens
import Mathlib.category_theory.filtered
import Mathlib.PostPort... |
6407ac97bb62a007db760079e1d01e5f84b6bb48 | 07c76fbd96ea1786cc6392fa834be62643cea420 | /hott/algebra/category/groupoid.hlean | 837869c75c8476c48b0835e4c5f232106a1cafc9 | [
"Apache-2.0"
] | permissive | fpvandoorn/lean2 | 5a430a153b570bf70dc8526d06f18fc000a60ad9 | 0889cf65b7b3cebfb8831b8731d89c2453dd1e9f | refs/heads/master | 1,592,036,508,364 | 1,545,093,958,000 | 1,545,093,958,000 | 75,436,854 | 0 | 0 | null | 1,480,718,780,000 | 1,480,718,780,000 | null | UTF-8 | Lean | false | false | 2,841 | hlean | /-
Copyright (c) 2014 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer, Floris van Doorn
Ported from Coq HoTT
-/
import .iso algebra.bundled
open eq is_trunc iso category algebra nat unit
namespace category
structure groupoid [cl... |
ff4b6562d323e8693b6b4c937857f73e3d5d8249 | 1a61aba1b67cddccce19532a9596efe44be4285f | /library/algebra/group_power.lean | e8c5f196989bfba5ea69bd2019779f273950567a | [
"Apache-2.0"
] | permissive | eigengrau/lean | 07986a0f2548688c13ba36231f6cdbee82abf4c6 | f8a773be1112015e2d232661ce616d23f12874d0 | refs/heads/master | 1,610,939,198,566 | 1,441,352,386,000 | 1,441,352,494,000 | 41,903,576 | 0 | 0 | null | 1,441,352,210,000 | 1,441,352,210,000 | null | UTF-8 | Lean | false | false | 8,041 | lean | /-
Copyright (c) 2015 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad
The power operation on monoids and groups. We separate this from group, because it depends on
nat, which in turn depends on other parts of algebra.
We have "pow a n" for ... |
40b69f22613cc039e5bfa36ea30f9c4bd95bd9c9 | 2a70b774d16dbdf5a533432ee0ebab6838df0948 | /_target/deps/mathlib/src/analysis/p_series.lean | e55321c6f9ed2d2999424e4841652e96f1a4e645 | [
"Apache-2.0"
] | permissive | hjvromen/lewis | 40b035973df7c77ebf927afab7878c76d05ff758 | 105b675f73630f028ad5d890897a51b3c1146fb0 | refs/heads/master | 1,677,944,636,343 | 1,676,555,301,000 | 1,676,555,301,000 | 327,553,599 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,263 | lean | /-
Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Yury G. Kudryashov
-/
import analysis.special_functions.pow
/-!
# Convergence of `p`-series
In this file we prove that the series `∑' k in ℕ, 1 / k ^ p` converges if and only if `... |
3b3d4ac756b4ae1e882d4aa7ac1a38dc6cb3edd0 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/measure_theory/integral/circle_transform.lean | 4ba4ce3582103d532efef4f11ba604b2cc428fe3 | [
"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 | 7,969 | lean | /-
Copyright (c) 2022 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
import data.complex.basic
import measure_theory.integral.circle_integral
/-!
# Circle integral transform
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to ... |
94140bb49d6e5ac8587b09d3ccc0002b37600f10 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/group_theory/transfer.lean | 1202268a0a7b74c4a53fda376b42def644191cba | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 10,635 | lean | /-
Copyright (c) 2022 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import group_theory.complement
import group_theory.sylow
/-!
# The Transfer Homomorphism
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file re... |
2877196dfcd7936bc781f256d0d433b6804d0fde | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /stage0/src/Init/Core.lean | 55fb9ddbe6ec20649858a07d1592336a34162663 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | EdAyers/lean4 | 57ac632d6b0789cb91fab2170e8c9e40441221bd | 37ba0df5841bde51dbc2329da81ac23d4f6a4de4 | refs/heads/master | 1,676,463,245,298 | 1,660,619,433,000 | 1,660,619,433,000 | 183,433,437 | 1 | 0 | Apache-2.0 | 1,657,612,672,000 | 1,556,196,574,000 | Lean | UTF-8 | Lean | false | false | 38,992 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
notation, basic datatypes and type classes
-/
prelude
import Init.Prelude
import Init.SizeOf
universe u v w
def inline {α : Sort u} (a : α) : α := a
@[inli... |
d85ab07a8101f41ce2b16880d04148db303c8ba8 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/run/fun.lean | 5f019237377d377644f4070b573e5b8b8b462eae | [
"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 | 314 | lean | open function bool
constant f : num → bool
constant g : num → num
check f ∘ g ∘ g
check (id : num → num)
constant h : num → bool → num
check swap h
check swap h ff num.zero
check (swap h ff num.zero : num)
constant f1 : num → num → bool
constant f2 : bool → num
check (f1 on f2) ff tt
|
fe45a18eb3362118b7dd8f368e3d152ba524a014 | e030b0259b777fedcdf73dd966f3f1556d392178 | /library/tools/super/superposition.lean | 6782649cb2ee79579c7187ec4e34a8942acd6619 | [
"Apache-2.0"
] | permissive | fgdorais/lean | 17b46a095b70b21fa0790ce74876658dc5faca06 | c3b7c54d7cca7aaa25328f0a5660b6b75fe26055 | refs/heads/master | 1,611,523,590,686 | 1,484,412,902,000 | 1,484,412,902,000 | 38,489,734 | 0 | 0 | null | 1,435,923,380,000 | 1,435,923,379,000 | null | UTF-8 | Lean | false | false | 4,946 | 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 .prover_state .utils
open tactic monad expr
namespace super
def position := list ℕ
meta def get_rwr_positions : expr → list position
| (app a b) := [[... |
2baebe23ed5d05014b872ad6911953c7da5ac646 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/order/field/inj_surj.lean | dcdde29d91008db6315911d552bba96c220a2d82 | [
"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 | 2,976 | lean | /-
Copyright (c) 2014 Robert Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Lewis, Leonardo de Moura, Mario Carneiro, Floris van Doorn
-/
import algebra.order.field.defs
import algebra.field.basic
import algebra.order.ring.inj_surj
/-!
# Pulling back lin... |
ac2d961220c8e883cc7aa5490b183e834d6ccfd5 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/501.lean | c2e68857b3d5a7702d4b464b60b2af1608bd621b | [
"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 | 575 | lean | structure S where
x : Bool
y : Nat
def S.Z (s : S) : Type :=
if s.x then Nat else Int
def S.z : (s : S) → s.Z
| s@{ x := true, .. } => s.y
| s@{ x := false, .. } => Int.ofNat s.y
def S.a : (s : S) → s.Z
| s => s.z
def S.b : (s : S) → s.Z
| s@h:{ x := true, .. } => h ▸ s.z
| s => s.z
#check @S.b.mat... |
afed8c903cc2ecf085d4a6bb500f5426981f84c3 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/vars_anywhere.lean | 6c80908a8343c79db1d7a71e62b723e3dab1aadb | [
"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 | 110 | lean | variable {A : Type}
check @id
inductive list :=
| nil : list
| cons : A → list → list
check @list.cons
|
4091a8edf2237247776c59643c3f233262568d94 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/analysis/special_functions/sqrt.lean | 7cf611587351fef69f74942346f8307a404955ab | [
"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 | 6,432 | lean | /-
Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import data.real.sqrt
import analysis.calculus.inverse
/-!
# Smoothness of `real.sqrt`
In this file we prove that `real.sqrt` is infinitely smooth at all po... |
883a8a13a6894cc46d8b0d1490f0733d43121eb0 | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /08_Building_Theories_and_Proofs.org.32.lean | f02e43a4f5c42c7764c381d3239ccb5514290aea | [] | 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 | 77 | lean | import standard
import data.nat
section
open [notations] nat
/- ... -/
end
|
3009bcef37284791eeb32af58127b8f2ed679bb2 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/number_theory/pell.lean | afcb6b13660a4792da47c7ac8bf0bcb4cffc2dd8 | [
"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 | 37,771 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import data.nat.modeq
import number_theory.zsqrtd.basic
/-!
# Pell's equation and Matiyasevic's theorem
This file solves Pell's equation, i.e. integer solutions to... |
befc93b9942065f3b46b1a555529d602c2918229 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/algebra/algebra/tower.lean | d2de541f23ddd1145e48d67434c7720f85e5461d | [] | 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 | 11,983 | lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebra.algebra.subalgebra
import Mathlib.PostPort
universes u v₁ w v u₁ u_1 u_2 u_3
namespace Mat... |
ef8067e64b6cab54f558e5031cec0bd14c85d77d | 78630e908e9624a892e24ebdd21260720d29cf55 | /src/logic_first_order/fol_12.lean | aacaa6361c4a9da25d5341b86b57f71387ebd888 | [
"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 | 407 | lean | namespace fol_12
variable A : Type
variable P : A → Prop
variable R : A → A → Prop
theorem fol_12 : (∀ y, P y → (∀ x, R x y)) → (∃ y, P y) → (∃ z, ∀ x, R x z) :=
assume h1: ∀ y, P y → (∀ x, R x y),
assume h2: ∃ y, P y,
exists.elim h2
(assume t (h3: P t),
have h4: P t → (∀ x, R x t), from h1 t,
have h5: ∀ x, R... |
120aa649142e90570ab870ff82408ae723b42e79 | 592ee40978ac7604005a4e0d35bbc4b467389241 | /Library/generated/mathscheme-lean/CancellativeSemigroup.lean | 45c9d2d68e0926b50378d7a025f569f88ed8d27a | [] | 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 | 6,874 | 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 CancellativeSemigroup
structure CancellativeSemigroup (A : Type) : Type :=
(op : (A → (A → A)))
(associative_op : (∀ {x y z : A} , (op (op x y) z) = (op x (op y... |
a371cd9decff211202ad4720a6c5c2fcc98d5102 | aa3f8992ef7806974bc1ffd468baa0c79f4d6643 | /library/algebra/function.lean | 6bfdf402d9fb1504523608770596dc65e11379eb | [
"Apache-2.0"
] | permissive | codyroux/lean | 7f8dff750722c5382bdd0a9a9275dc4bb2c58dd3 | 0cca265db19f7296531e339192e9b9bae4a31f8b | refs/heads/master | 1,610,909,964,159 | 1,407,084,399,000 | 1,416,857,075,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,405 | lean | -- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Author: Leonardo de Moura
namespace function
variables {A : Type} {B : Type} {C : Type} {D : Type} {E : Type}
definition compose [reducible] (f : B → C) (g : A → B) : A → C :=
λx... |
89e9bb1a5dd7e0b20926910fd39ae1e05cded318 | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /tests/lean/run/group2.lean | a609eeb8a22a6e418a4a38fe87c357af7d836ada | [
"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 | 1,696 | lean | import logic
section
variable {A : Type}
variable f : A → A → A
variable one : A
variable inv : A → A
local infixl `*` := f
local postfix `^-1`:100 := inv
definition is_assoc := ∀ a b c, (a*b)*c = a*b*c
definition is_id := ∀ a, a*one = a
definition is_inv := ∀ a, a*a^-1 = one
end
inducti... |
551cd6725e793a9f48e80d0b869c81394b57b862 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/1808.lean | 7d949d36338ad8c519c933ea0cb85c81c4dcc58e | [
"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 | 307 | lean | class Preorder (α : Type u) extends LT α :=
(le : α → α → Prop)
(lt_iff_le_not_le : ∀ a b : α, lt a b ↔ (le a b ∧ ¬ le b a) := by intros; rfl)
theorem Preorder.toLE_injective (A B : Preorder α) (h : A.le = B.le) (h2 : A.toLT = B.toLT) : A = B := by
cases A; cases B; cases h
congr
|
c6dd93764114a06dd99188b57584bf1b37018830 | c31182a012eec69da0a1f6c05f42b0f0717d212d | /src/thm95/double_complex.lean | 29d57eb0234173b0f970782c73d7882ac926c08f | [] | 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 | 8,939 | lean | import algebra.homology.functor
import for_mathlib.simplicial.complex
import polyhedral_lattice.Hom
import pseudo_normed_group.system_of_complexes
import system_of_complexes.rescale
import normed_spectral
import thm95.modify_complex
/-!
# The double complex that is the protagonist in the proof of Theorem 9.5
-/
no... |
0905bf3b6b0d5c742e5d429e3c6c4c80ca582005 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/category_theory/limits/shapes/terminal.lean | 3c8cd3fa89c1dcbd09e682a3391e2b185dacddfd | [
"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 | 27,209 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Bhavik Mehta
-/
import category_theory.pempty
import category_theory.limits.has_limits
import category_theory.epi_mono
import category_theory.category.preorder
/-!
# I... |
064a3cc4fcc9684fdd580eccd0f40f0143db85eb | 7c4610454cf55b49f0c3cdaeb6b856eb3249cb2d | /src/relatively_prime.lean | c658c009b8e902f623e88650af58e973d78fc135 | [] | no_license | 101damnations/fg_over_pid | 097be43e11c3680a3fd4b6de2265de393cf4d4ef | a1a587c455a54a802f6ff61b07bb033701e451a7 | refs/heads/master | 1,669,708,904,636 | 1,597,259,770,000 | 1,597,259,770,000 | 287,097,363 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 11,169 | lean |
import ring_theory.principal_ideal_domain set_lemmas linear_algebra.basic torsion
open unique_factorization_domain multiset associates
variables {R : Type*} [integral_domain R] [is_principal_ideal_ring R] [decidable_eq R]
[decidable_eq (associates R)] (r : R)
open_locale classical
local infix ` ~ᵤ ` : 50 :... |
0d669bc67f649e051bb6f3091a2f3653e538ebcf | e00ea76a720126cf9f6d732ad6216b5b824d20a7 | /src/analysis/calculus/mean_value.lean | 11ae358f739caa66584f56215c37b05bda91b2ba | [
"Apache-2.0"
] | permissive | vaibhavkarve/mathlib | a574aaf68c0a431a47fa82ce0637f0f769826bfe | 17f8340912468f49bdc30acdb9a9fa02eeb0473a | refs/heads/master | 1,621,263,802,637 | 1,585,399,588,000 | 1,585,399,588,000 | 250,833,447 | 0 | 0 | Apache-2.0 | 1,585,410,341,000 | 1,585,410,341,000 | null | UTF-8 | Lean | false | false | 38,685 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Yury Kudryashov
-/
import analysis.calculus.local_extr
import analysis.convex.topology
/-!
# The mean value inequality and equalities
In this file we prove the... |
420037dd61f6c9b59ad98a6129cc4d4df2fa0678 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/combinatorics/set_family/compression/uv.lean | 4c1dd364e0b6de9640d9a3b1979d3f3a7a1d0bd8 | [
"Apache-2.0"
] | permissive | urkud/mathlib | eab80095e1b9f1513bfb7f25b4fa82fa4fd02989 | 6379d39e6b5b279df9715f8011369a301b634e41 | refs/heads/master | 1,658,425,342,662 | 1,658,078,703,000 | 1,658,078,703,000 | 186,910,338 | 0 | 0 | Apache-2.0 | 1,568,512,083,000 | 1,557,958,709,000 | Lean | UTF-8 | Lean | false | false | 8,873 | lean | /-
Copyright (c) 2021 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
import data.finset.card
/-!
# UV-compressions
This file defines UV-compression. It is an operation on a set family that reduces its shadow.
UV-compressin... |
e0eaa94220b9af2152a573be636b5e99ec44c684 | acc85b4be2c618b11fc7cb3005521ae6858a8d07 | /analysis/of_nat.lean | 1c91f839c02f09f36cf198d91b949e6cd2c8584a | [
"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 | 3,935 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Morphism from `nat` into a semiring with 1.
TODO: move to `data.nat` and split into the different parts for `int`, `rat`, and `real`.
-/
import data.rat analysis.real
... |
e1d62411b2d67681ab27cd55686a8e8d70897cbf | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/linear_algebra/matrix/basis.lean | dd1d97858ab9c56aa20d2590bcb2746c20ea2d90 | [
"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 | 9,883 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
-/
import linear_algebra.matrix.nonsingular_inverse
import linear_algebra.matrix.reindex
import linear_algebra.matrix.to_lin
/... |
ebd63dd575f0f3a93d3080397cf581964dbd16a0 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/analysis/normed/group/hom_completion.lean | 2e3227117b81f5ccf27e0af185947e4f59335d9c | [
"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 | 11,156 | lean | /-
Copyright (c) 2021 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import analysis.normed.group.hom
import analysis.normed.group.completion
/-!
# Completion of normed group homs
Given two (semi) normed groups `G` and `H` and a norm... |
ee33976fdd324d279cb9f3872a5a28efa83eaa7d | 3bdd27ffdff3ffa22d4bb010eba695afcc96bc4a | /src/combinatorics/simplicial_complex/convex_independence.lean | 745f0e4a0e9e266a1637c189c492c561c1821a35 | [] | no_license | mmasdeu/brouwerfixedpoint | 684d712c982c6a8b258b4e2c6b2eab923f2f1289 | 548270f79ecf12d7e20a256806ccb9fcf57b87e2 | refs/heads/main | 1,690,539,793,996 | 1,631,801,831,000 | 1,631,801,831,000 | 368,139,809 | 4 | 3 | null | 1,624,453,250,000 | 1,621,246,034,000 | Lean | UTF-8 | Lean | false | false | 4,260 | lean | /-
Copyright (c) 2021 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
import analysis.convex.basic
import combinatorics.simplicial_complex.to_move.default
import data.finset.sort
import data.matrix.notation
impor... |
ca5f005824ff40486694e656862dd3097ff53c0f | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/topology/metric_space/cau_seq_filter_auto.lean | d889d23a8a47d60e58efaffcc8533257777a72bc | [] | 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 | 2,435 | lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Sébastien Gouëzel
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.analysis.normed_space.basic
import Mathlib.PostPort
universes v u
n... |
a4246a4f483ddc25907acde9d7034ec02f251d56 | d7189ea2ef694124821b033e533f18905b5e87ef | /galois/vector/init_last.lean | 519bc4df8a304c7bb35af6c58b3532209d6646d4 | [
"Apache-2.0"
] | permissive | digama0/lean-protocol-support | eaa7e6f8b8e0d5bbfff1f7f52bfb79a3b11b0f59 | cabfa3abedbdd6fdca6e2da6fbbf91a13ed48dda | refs/heads/master | 1,625,421,450,627 | 1,506,035,462,000 | 1,506,035,462,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,029 | lean | /- This defines init and last on vectors. -/
import ..list.init
import .simplify_eq
universe variables u
namespace vector
variable {α : Type u}
variable {n : ℕ}
local infix `++`:65 := vector.append
-- Generate proof list non-null from proof length is sucessor some number
private
lemma eq_succ_implies_non_nil {l : ... |
e9ae5126b8213c711e9adb9555827d3214bc3af3 | 026eca3e4f104406f03192524c0ebed8b40e468b | /library/init/data/int/basic.lean | 40d2bb9b53b95762f364a34acc5a583d5d5a9d7a | [
"Apache-2.0"
] | permissive | jpablo/lean | 99bebe8f1c3e3df37e19fc4af27d4261efa40bc6 | bec8f0688552bc64f9c08fe0459f3fb20f93cb33 | refs/heads/master | 1,679,677,848,004 | 1,615,913,211,000 | 1,615,913,211,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 23,225 | 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.
-/
prelude
import init.data.nat.lemmas init.data.nat.gcd
open nat
/- the type, coercions, and notation -/
... |
d030d4ce5c579923c95b670e49a133bcaf3d7e9f | f083c4ed5d443659f3ed9b43b1ca5bb037ddeb58 | /analysis/nnreal.lean | a83308b31355d5b70c9ce72a4ab1d817d58993bf | [
"Apache-2.0"
] | permissive | semorrison/mathlib | 1be6f11086e0d24180fec4b9696d3ec58b439d10 | 20b4143976dad48e664c4847b75a85237dca0a89 | refs/heads/master | 1,583,799,212,170 | 1,535,634,130,000 | 1,535,730,505,000 | 129,076,205 | 0 | 0 | Apache-2.0 | 1,551,697,998,000 | 1,523,442,265,000 | Lean | UTF-8 | Lean | false | false | 3,915 | 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 analysis.real analysis.topology.infinite_sum
noncomputable theory
open set topological_space
namespace nnreal
loca... |
800f93eefba20024ce9020a071927bafd3a7dcee | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/t6.lean | 12e3537794c9bfe1ef596f18ce3e80ec5e61aa85 | [
"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 | 342 | lean | prelude definition Prop : Type.{1} := Type.{0}
section
variable {A : Type} -- Mark A as implicit parameter
variable R : A → A → Prop
definition id (a : A) : A := a
definition refl : Prop := forall (a : A), R a a
definition symm : Prop := forall (a b : A), R a b -> R b a
end
check id.{2}
check refl.{... |
4b0ed56d629ef739f20d514e39447ec881f8cc19 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/sum/basic.lean | bec135e6da38c446745e2c9edf50eeff82689295 | [
"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 | 19,080 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Yury G. Kudryashov
-/
import logic.function.basic
import tactic.basic
/-!
# Disjoint union of types
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this f... |
42d3ac8bf5fa4cc92744f2df08ff5eeac9f2413b | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/init/data/nat/default_auto.lean | dc59b8f4982a180967df5db0f2fd3f5e915d329c | [] | 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 | 395 | 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.data.nat.basic
import Mathlib.Lean3Lib.init.data.nat.div
import Mathlib.Lean3Lib.init.data.nat.lemmas
im... |
44de2e947e44f3ea9811d3908d9f0a06ced0df1e | 958488bc7f3c2044206e0358e56d7690b6ae696c | /lean/while/ReducePar.lean | 08c90d6a49c3ec6aa7884dfd0252e0300c4f79ba | [] | no_license | possientis/Prog | a08eec1c1b121c2fd6c70a8ae89e2fbef952adb4 | d4b3debc37610a88e0dac3ac5914903604fd1d1f | refs/heads/master | 1,692,263,717,723 | 1,691,757,179,000 | 1,691,757,179,000 | 40,361,602 | 3 | 0 | null | 1,679,896,438,000 | 1,438,953,859,000 | Coq | UTF-8 | Lean | false | false | 485 | lean | import Stmt
import Reduce
open list
open Stmt
inductive ReducePar : list Stmt → Env → list Stmt → Env → Prop
| Step : ∀ (e₁ e₂:Stmt) (s₁ s₂:Env) (es : list Stmt),
Reduce e₁ s₁ e₂ s₂ → ReducePar (e₁ :: es) s₁ (e₂ :: es) s₂
| Cons : ∀ (es₁ es₂:list Stmt) (s₁ s₂:Env) (e:Stmt),
ReducePar es₁ s₁ es₂ s₂ → ReducePar... |
ed9b17117ccc6a7fd3d984041a3295ee9890333f | ad0c7d243dc1bd563419e2767ed42fb323d7beea | /data/real/irrational.lean | 526f44fd4ad43820f9f697e68eb582ff677443bd | [
"Apache-2.0"
] | permissive | sebzim4500/mathlib | e0b5a63b1655f910dee30badf09bd7e191d3cf30 | 6997cafbd3a7325af5cb318561768c316ceb7757 | refs/heads/master | 1,585,549,958,618 | 1,538,221,723,000 | 1,538,221,723,000 | 150,869,076 | 0 | 0 | Apache-2.0 | 1,538,229,323,000 | 1,538,229,323,000 | null | UTF-8 | Lean | false | false | 1,121 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
Irrationality of real numbers.
-/
import data.real.basic data.nat.prime
open real rat
def irrational (x : ℝ) := ¬ ∃ q : ℚ, x = q
theorem sqrt_two_irrational : irrati... |
df01dfe74862259efc11555b81a9285df10d764c | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/order/zorn.lean | 50fab3552e4aed6cef0470e1696200af835ac168 | [
"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 | 16,761 | 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 data.set.lattice
/-!
# Chains and Zorn's lemmas
This file defines chains for an arbitrary relation and proves several formulations of Zorn's Lemma,
along wit... |
6037803a168167298473bbac2fd1e66adc5486fc | 97f752b44fd85ec3f635078a2dd125ddae7a82b6 | /library/theories/group_theory/finsubg.lean | 51d1d74c3fafc6498b8f5e8b5cd9862da491c89f | [
"Apache-2.0"
] | permissive | tectronics/lean | ab977ba6be0fcd46047ddbb3c8e16e7c26710701 | f38af35e0616f89c6e9d7e3eb1d48e47ee666efe | refs/heads/master | 1,532,358,526,384 | 1,456,276,623,000 | 1,456,276,623,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 20,494 | lean | /-
Copyright (c) 2015 Haitao Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author : Haitao Zhang
-/
-- develop the concept of finite subgroups based on finsets so that the properties
-- can be used directly without translating from the set based theory first
import d... |
5dd8072343f1ddf465638acc15aa74c6996f005e | 83c8119e3298c0bfc53fc195c41a6afb63d01513 | /library/init/meta/simp_tactic.lean | a032b31a1dc7c90647d0d0fee79be5962817aebd | [
"Apache-2.0"
] | permissive | anfelor/lean | 584b91c4e87a6d95f7630c2a93fb082a87319ed0 | 31cfc2b6bf7d674f3d0f73848b842c9c9869c9f1 | refs/heads/master | 1,610,067,141,310 | 1,585,992,232,000 | 1,585,992,232,000 | 251,683,543 | 0 | 0 | Apache-2.0 | 1,585,676,570,000 | 1,585,676,569,000 | null | UTF-8 | Lean | false | false | 26,850 | 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.tactic init.meta.attribute init.meta.constructor_tactic
import init.meta.relation_tactics init.meta.occurrences
import init.data.op... |
ce02fdce603f42a6281a383a2d848031c0cf771f | 957a80ea22c5abb4f4670b250d55534d9db99108 | /tests/lean/run/cc_ac4.lean | d90f380bf3502dd76a02b91b43b11e23fe5ab2f0 | [
"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 | 503 | lean | --import data.set.basic
open tactic
constant union_is_assoc {α} : is_associative (set α) (∪)
constant union_is_comm {α} : is_commutative (set α) (∪)
attribute [instance] union_is_assoc union_is_comm
section
universe variable u
variables {α : Type u}
example (a b c d₁ d₂ e₁ e₂ : set α) (f : set α → set α → set ... |
d64c435eeaef3e5e3217c14d1f6f48d469df3082 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/set_theory/game/domineering.lean | bf6c59e05a9c550355ef9a0bb9891a7daeca6da5 | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 7,964 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import set_theory.game.state
/-!
# Domineering as a combinatorial game.
We define the game of Domineering, played on a chessboard of arbitrary shape
(possibly even ... |
233c8e35a1211bca6bd3d4f2940aad0ce2d1565b | 1e561612e7479c100cd9302e3fe08cbd2914aa25 | /mathlib4_experiments/Tactic/Exfalso.lean | bd1cdfdbae4c49469533fc2d03875f9563ccecee | [
"Apache-2.0"
] | permissive | kbuzzard/mathlib4_experiments | 8de8ed7193f70748a7529e05d831203a7c64eedb | 87cb879b4d602c8ecfd9283b7c0b06015abdbab1 | refs/heads/master | 1,687,971,389,316 | 1,620,336,942,000 | 1,620,336,942,000 | 353,994,588 | 7 | 4 | Apache-2.0 | 1,622,410,748,000 | 1,617,361,732,000 | Lean | UTF-8 | Lean | false | false | 189 | lean | /-
## `exfalso`
-/
syntax "exfalso" : tactic
macro_rules
| `(tactic| exfalso) => `(tactic| apply False.elim)
/-
example : False -> p := by
intro h;
exfalso;
skip;
exact h;
-/ |
c8b45d10afb586020b73645badfd0e2a6f8c3449 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/combinatorics/colex.lean | 0441534ef83ca50b7d22db1b3674d8b4871e2ef5 | [
"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 | 15,018 | lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Alena Gusakov
-/
import data.fintype.basic
import algebra.geom_sum
/-!
# Colex
We define the colex ordering for finite sets, and give a couple of important
lemmas and pro... |
95b2a8ebbf555097cb0af5923f72681dc871fb17 | 5a6ff5f8d173cbfe51967eb4c96837e3a791fe3d | /mm0-lean/mm0/set/basic.lean | 936cd9183efa6246368ed826d026e5f3d141dcce | [
"CC0-1.0"
] | permissive | digama0/mm0 | 491ac09146708aa1bb775007bf3dbe339ffc0096 | 98496badaf6464e56ed7b4204e7d54b85667cb01 | refs/heads/master | 1,692,321,030,902 | 1,686,254,458,000 | 1,686,254,458,000 | 172,456,790 | 273 | 38 | CC0-1.0 | 1,689,939,563,000 | 1,551,080,059,000 | Rust | UTF-8 | Lean | false | false | 124,962 | lean | /-#
This file is not autogenerated, but it is meant as a prelude for the
autogenerated set.mm import. To use this file, you should run mm0-hs on set.mm
to generate the MM0 files out.mm0 and out.mmu, and then feed these back into
mm0-hs to generate files setN.lean in this directory.
* The `-a .basic` says that all axio... |
622894bedb3a7f950ba2a91a9368ea6b20a19524 | af6139dd14451ab8f69cf181cf3a20f22bd699be | /library/init/meta/decl_cmds.lean | 7869970a52407dfcf4061024a59435791632e25f | [
"Apache-2.0"
] | permissive | gitter-badger/lean-1 | 1cca01252d3113faa45681b6a00e1b5e3a0f6203 | 5c7ade4ee4f1cdf5028eabc5db949479d6737c85 | refs/heads/master | 1,611,425,383,521 | 1,487,871,140,000 | 1,487,871,140,000 | 82,995,612 | 0 | 0 | null | 1,487,905,618,000 | 1,487,905,618,000 | null | UTF-8 | Lean | false | false | 2,066 | 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.tactic init.meta.rb_map
open tactic
private meta def apply_replacement (replacements : name_map name) (e : expr) : expr :=
e^.repl... |
3464318e8c458de663c2fd230786d133128458f0 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/1956.lean | f62b235542272ec9f693e07ce57de00d4f3ff2bc | [
"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 | 38 | lean | example : 1000 * 1000 = 123456 :=
rfl
|
0f76c8009f350cc08ec574b6269dc5c2e61e90a7 | 77c5b91fae1b966ddd1db969ba37b6f0e4901e88 | /src/order/closure.lean | 7feb1e920037778f87a4b079fa64ab1dd7de10cc | [
"Apache-2.0"
] | permissive | dexmagic/mathlib | ff48eefc56e2412429b31d4fddd41a976eb287ce | 7a5d15a955a92a90e1d398b2281916b9c41270b2 | refs/heads/master | 1,693,481,322,046 | 1,633,360,193,000 | 1,633,360,193,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 17,255 | lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Yaël Dillies
-/
import data.set_like.basic
import order.preorder_hom
import order.galois_connection
import tactic.monotonicity
/-!
# Closure operators between preorders
W... |
8dc7e3198a120069cb16c588fd51cfa2aa26acc9 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/tactic/generalizes.lean | 691c7926346fe566248fa926203210df31b3eb07 | [
"Apache-2.0"
] | permissive | AntoineChambert-Loir/mathlib | 64aabb896129885f12296a799818061bc90da1ff | 07be904260ab6e36a5769680b6012f03a4727134 | refs/heads/master | 1,693,187,631,771 | 1,636,719,886,000 | 1,636,719,886,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,901 | lean | /-
Copyright (c) 2020 Jannis Limperg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jannis Limperg
-/
import tactic.core
/-!
# The `generalizes` tactic
This module defines the `tactic.generalizes'` tactic and its interactive version
`tactic.interactive.generalizes`... |
f6eac3d4015fc699b6d67365f258eb4f681ca3d8 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/homology/differential_object.lean | 03f8f3839d349fd516f07b61624e00007620fc18 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 5,077 | lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import algebra.homology.homological_complex
import category_theory.differential_object
/-!
# Homological complexes are differential graded objects.
> THIS FILE IS S... |
7493f92835bfc9221fac3807bb85fe4dbf452abd | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/topology/sheaves/sheaf_condition/sites.lean | 911d141b211caffaf36867bcac6326fe8ffc883e | [
"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 | 20,078 | lean | /-
Copyright (c) 2021 Justus Springer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Justus Springer
-/
import category_theory.sites.sheaf
import category_theory.sites.spaces
import topology.sheaves.sheaf
/-!
# The sheaf condition in terms of sites.
The theory of ... |
9648253fb33b76d5dea72c6f78e0a02f166e6346 | 6b2a480f27775cba4f3ae191b1c1387a29de586e | /group_rep1/irreductible.lean | 307ec99fdaff75b9a946c295494cd4812a4f409a | [] | no_license | Or7ando/group_representation | a681de2e19d1930a1e1be573d6735a2f0b8356cb | 9b576984f17764ebf26c8caa2a542d248f1b50d2 | refs/heads/master | 1,662,413,107,324 | 1,590,302,389,000 | 1,590,302,389,000 | 258,130,829 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 4,411 | lean | import tactic
import .sub_module
import tactic.push_neg
import .morphism
import .homothetic
import .kernel
open Kernel range morphism homothetic
open stability
universe variables u v w w'
lemma Fact {R : Type v}[ring R]{M1 : Type w}[add_comm_group M1] [module R M1]
(p1 : submodule R M1) (hyp : p1 = ⊤ ∨ p1 = ⊥ )(z :... |
3188e0072d27bf4c69309d6550cddd3dd813b994 | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /hott/algebra/category/colimits.hlean | b6a33f1d8a9b8cd2a4f90eeb387a84b9dc1d8ee0 | [
"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 | 12,522 | 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
Colimits in a category
-/
import .limits .constructions.opposite
open is_trunc functor nat_trans eq
-- we define colimits to be the dual of a limit
namespace ca... |
3c44e3e6dd42bd08100a579df01089d10e946a75 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/ring_theory/witt_vector/witt_polynomial.lean | e8127c9c519b8d868dd2c9469773f20d36790d24 | [
"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 | 10,804 | 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 algebra.char_p.invertible
import data.fintype.card
import data.mv_polynomial.variables
import data.mv_polynomial.comm_ring
import data.mv_pol... |
3d8ca280533332a1c7661c3aa4c58639243104a2 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/field_theory/minpoly.lean | 815e312a7717da6a81673cae4140b6871153f040 | [
"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 | 18,026 | lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johan Commelin
-/
import data.polynomial.field_division
import ring_theory.integral_closure
import ring_theory.polynomial.gauss_lemma
/-!
# Minimal polynomials
This file ... |
e891cbd13141bdcf1ce4a36b68eee93fc885ae9e | 432d948a4d3d242fdfb44b81c9e1b1baacd58617 | /src/set_theory/schroeder_bernstein.lean | 8015ca5aee560b4cb24ff762ea8d41a1f7dec1ef | [
"Apache-2.0"
] | permissive | JLimperg/aesop3 | 306cc6570c556568897ed2e508c8869667252e8a | a4a116f650cc7403428e72bd2e2c4cda300fe03f | refs/heads/master | 1,682,884,916,368 | 1,620,320,033,000 | 1,620,320,033,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,052 | 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
import order.zorn
open set classical
open_locale classical... |
d3b468374a4b6cc5163d8378078c82b160519255 | 22e97a5d648fc451e25a06c668dc03ac7ed7bc25 | /src/linear_algebra/bilinear_form.lean | dda43292d42a7e0045ca7466ac25ad62952c2eff | [
"Apache-2.0"
] | permissive | keeferrowan/mathlib | f2818da875dbc7780830d09bd4c526b0764a4e50 | aad2dfc40e8e6a7e258287a7c1580318e865817e | refs/heads/master | 1,661,736,426,952 | 1,590,438,032,000 | 1,590,438,032,000 | 266,892,663 | 0 | 0 | Apache-2.0 | 1,590,445,835,000 | 1,590,445,835,000 | null | UTF-8 | Lean | false | false | 15,959 | 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 linear_algebra.matrix
import linear_algebra.tensor_product
/-!
# Bilinear form
This file defines a bilinear form over a module. Basic ideas
such as ortho... |
7d6fe97543b7c7a90ad81efba8df665471e055a6 | 3dc4623269159d02a444fe898d33e8c7e7e9461b | /.github/workflows/project_1_a_decrire/foncteur/Idempotent_group/Idempotent_group.lean | a315299c6366533c9d4974a562ab804edf2cdaa4 | [] | 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 | 4,896 | lean | import algebra.category.CommRing.basic
import algebra.ring
import tactic
import category_theory.functor_category -- this transitively imports
import algebra.category.CommRing.basic
import algebra.ring
import category_theory.types
universes v u
/--
## This is the groupe AGL_1(R) : x ↦ ax + b invertible i.e with a inve... |
2e1d335fa2d8b08ca57679a3731a0d82f6701ef1 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/class3.lean | 1daa55a1ed1e60d7d365cdc0b89beeb0898774e7 | [
"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 | 238 | lean | import logic data.prod
open prod inhabited
section
variable {A : Type}
variable {B : Type}
variable Ha : inhabited A
variable Hb : inhabited B
include Ha Hb
theorem tst : inhabited (Prop × A × B)
end
reveal tst
print tst
|
9082ebfe38dbccb3297b2121acd4383ca0d871e6 | a8ca99e8fae20e1383a6a786312b9f44f7dfdb42 | /coq/step_01.lean | 4e90a85c6de0c8355ff3af927f65f4ebce600042 | [
"MIT"
] | permissive | nolmeunion/learn | b715a4e9560101275c9c418d191cc198c905d189 | 482f4b8a5de81375e5663ea0b065d25f2f7da4b6 | refs/heads/master | 1,671,751,332,943 | 1,601,261,285,000 | 1,601,261,285,000 | 287,418,011 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 199 | lean | -- BEGIN
theorem and_commutative (p q : Prop) : p ∧ q → q ∧ p :=
assume hpq : p ∧ q,
have hp : p, from and.left hpq,
have hq : q, from and.right hpq,
show q ∧ p, from and.intro hq hp
-- END |
7af71ef9ee5cdca55fc6e575bdfda022b6a44921 | 01ae0d022f2e2fefdaaa898938c1ac1fbce3b3ab | /categories/products/switch.lean | 962004171f5404a9d1c874b9e6b88761e063b6b9 | [] | 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 | 893 | 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 ..products
import ..natural_isomorphism
open categories
open categories.functor
open categories.natural_transformation
namespace categorie... |
552fd58d5742e261b048e2868a307db6407ae2c5 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/list/infix.lean | 89bb5ba243d146177ee69dadc820b7dc3ab70f12 | [
"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 | 21,933 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import data.list.basic
/-!
# Prefixes, subfixes, infixes
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathlib... |
e721423f0230be14bce6d50421d39484b9641203 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/order/filter/germ.lean | c12241e63ed32d698d48679c047760370897a2e7 | [] | 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 | 25,598 | lean | /-
Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov, Abhimanyu Pallavi Sudhir
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.order.filter.basic
import Mathlib.algebra.module.pi
impor... |
780c932fa832949317e47697d64c7797307c2ef4 | f3849be5d845a1cb97680f0bbbe03b85518312f0 | /tests/lean/fail/run_command.lean | 17a3b3c35875096c65ffdf0ce66811958c3647c5 | [
"Apache-2.0"
] | permissive | bjoeris/lean | 0ed95125d762b17bfcb54dad1f9721f953f92eeb | 4e496b78d5e73545fa4f9a807155113d8e6b0561 | refs/heads/master | 1,611,251,218,281 | 1,495,337,658,000 | 1,495,337,658,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 32 | lean | run_command tactic.fail "Error"
|
e4cd50c01cb11f8ed62b83b1475f1aa7b58071fa | f3a5af2927397cf346ec0e24312bfff077f00425 | /src/game/world3/level3.lean | 348823f21ab1cf750f480ac0b7100f43597271b2 | [
"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 | 814 | lean | import game.world3.level2 -- hide
import mynat.mul -- hide
namespace mynat -- hide
/-
# Multiplication World
## Level 3: `one_mul`
These proofs from addition world might be useful here:
* `one_eq_succ_zero : 1 = succ(0)`
* `succ_eq_add_one a : succ(a) = a + 1`
We just proved `mul_one`, now let's prove `one_mul`.... |
0f8bfb6b0d700195352fc5ba3a337f447877ffcd | 94e33a31faa76775069b071adea97e86e218a8ee | /src/geometry/manifold/charted_space.lean | 0379cfba3af20ec63f3081583991136845558c7e | [
"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 | 48,418 | 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.local_homeomorph
/-!
# Charted spaces
A smooth manifold is a topological space `M` locally modelled on a euclidean space (or a euclidean
half-... |
6f8e0f44edb7fe9ce2eb7194ed98fe6fc7ba834b | 8eeb99d0fdf8125f5d39a0ce8631653f588ee817 | /src/algebra/pointwise.lean | 9ba9673a888c02fdee137c8db5e0d496cc14251f | [
"Apache-2.0"
] | permissive | jesse-michael-han/mathlib | a15c58378846011b003669354cbab7062b893cfe | fa6312e4dc971985e6b7708d99a5bc3062485c89 | refs/heads/master | 1,625,200,760,912 | 1,602,081,753,000 | 1,602,081,753,000 | 181,787,230 | 0 | 0 | null | 1,555,460,682,000 | 1,555,460,682,000 | null | UTF-8 | Lean | false | false | 15,368 | lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Floris van Doorn
-/
import algebra.module.basic
import data.set.finite
/-!
# Pointwise addition, multiplication, and scalar multiplication of sets.
This file defines ... |
07578392b1bacc88d9a848b9092d5b62af9f4210 | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /11_Tactic-Style_Proofs.org.41.lean | 1d73858104b798fab0129e0bceec67e9a95f70e9 | [] | 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 | 206 | lean | import standard
import data.nat
open nat
-- BEGIN
variables (a b : nat)
example (H₁ : a + 0 = 0) (H₂ : b + 0 = 0) : a + b = 0 :=
begin
rewrite add_zero at (H₁, H₂),
rewrite [H₁, H₂]
end
-- END
|
fec2f2722fd632de0d6520b9b3672fb1cec3b042 | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/data/equiv/basic.lean | f2d228cb70a7bcbee3fbdb9a90a864c3dfa58cd7 | [
"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 | 70,741 | 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, Mario Carneiro
In the standard library we cannot assume the univalence axiom.
We say two types are equivalent if they are isomorphic.
Two equivalent types h... |
4cfa90fea4c9f907166dc42a121f7e07345876c5 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/tactic/replacer.lean | 4d8517311131776827f38b0f47406537b573c8a2 | [] | 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 | 1,411 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.tactic.core
import Mathlib.PostPort
namespace Mathlib
/-!
# `def_replacer`
A mechanism fo... |
6116a114439144d44d9d1af83067dc83eaf2d6e5 | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /src/Lean/MetavarContext.lean | 8e6401f9c6bbaff54334a0cc8a3a4d9a879e0700 | [
"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 | 48,960 | 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.Util.MonadCache
import Lean.LocalContext
namespace Lean
/-
The metavariable context stores metavariable declarations and their
assignments. It... |
887f065240b0af6e557fc403cc77f1dac9e13a20 | b561a44b48979a98df50ade0789a21c79ee31288 | /src/Lean/Parser/Command.lean | 8dbcc7c93f3b6267b54557299f9bea585847b812 | [
"Apache-2.0"
] | permissive | 3401ijk/lean4 | 97659c475ebd33a034fed515cb83a85f75ccfb06 | a5b1b8de4f4b038ff752b9e607b721f15a9a4351 | refs/heads/master | 1,693,933,007,651 | 1,636,424,845,000 | 1,636,424,845,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 11,301 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Sebastian Ullrich
-/
import Lean.Parser.Term
import Lean.Parser.Do
namespace Lean
namespace Parser
/--
Syntax quotation for terms and (lists of) commands.... |
d19747ff0f884278d2051a6f4fda3853792c3947 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/data/set/image.lean | fba4f00b8d959dd2a61ef078e2d6d51f2c10fcf5 | [
"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 | 50,201 | 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
-/
import data.set.basic
/-!
# Images and preimages of sets
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a correspond... |
3d4e30353dd572b740925dfee25e7b7ae5b7896b | 5749d8999a76f3a8fddceca1f6941981e33aaa96 | /src/topology/subset_properties.lean | ec1a3c9ee041626bbc3b25abf5eb9abbb605e0cf | [
"Apache-2.0"
] | permissive | jdsalchow/mathlib | 13ab43ef0d0515a17e550b16d09bd14b76125276 | 497e692b946d93906900bb33a51fd243e7649406 | refs/heads/master | 1,585,819,143,348 | 1,580,072,892,000 | 1,580,072,892,000 | 154,287,128 | 0 | 0 | Apache-2.0 | 1,540,281,610,000 | 1,540,281,609,000 | null | UTF-8 | Lean | false | false | 35,156 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Yury Kudryashov
-/
import topology.continuous_on
/-!
# Properties of subsets of topological spaces
## Main definitions
`compact`, `is_clopen`, `is_i... |
0955ba7989d5100f69788c7cf1d7fc818d9aa34a | a6ea0e5de8b451a584e78d2a3a22466083fd8069 | /src/submission/practice_1.lean | c9c06d319551e54befbe74ab069b9d7784e3ceef | [] | no_license | simonejefferson03/cs2120f21 | cabf9bb8fd636cba947d3a33383a24a9efa51e1e | ee0edf0c5e6f66f28eafbc6787681065800eb7e5 | refs/heads/main | 1,692,061,780,990 | 1,631,910,003,000 | 1,631,910,003,000 | 399,946,493 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,485 | lean | /-
EQUALITY
-/
/- #1
Suppose that x, y, z, and w are arbitrary objects of some type,
T; and suppose further that we know (have proofs of the facts)
that x = y, y = z, and w = z. Give a very, very short English
proof of the conjecture that z = w. You can use not only the
axioms of equality, but either of the theo... |
546a2bf4cf672bc65bfdc8cc860c8f0198850392 | e151e9053bfd6d71740066474fc500a087837323 | /src/hott/hit/pushout.lean | 4d61686ba75dbd202656169a73d95594afc56625 | [
"Apache-2.0"
] | permissive | daniel-carranza/hott3 | 15bac2d90589dbb952ef15e74b2837722491963d | 913811e8a1371d3a5751d7d32ff9dec8aa6815d9 | refs/heads/master | 1,610,091,349,670 | 1,596,222,336,000 | 1,596,222,336,000 | 241,957,822 | 0 | 0 | Apache-2.0 | 1,582,222,839,000 | 1,582,222,838,000 | null | UTF-8 | Lean | false | false | 12,059 | lean | /-
Copyright (c) 2015-16 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Ulrik Buchholtz, Jakob von Raumer
Declaration and properties of the pushout
-/
import .quotient ..types.arrow_2
universes u v w
hott_theory
namespace hott
ope... |
628eadcf4a953ad4a4af04f07665c0f6941bed8d | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/gcd_monoid/integrally_closed.lean | ac3990150f937489a40932a646ae4e4f075f18c4 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 1,806 | lean | /-
Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import algebra.gcd_monoid.basic
import ring_theory.integrally_closed
import ring_theory.polynomial.eisenstein.basic
/-!
# GCD domains are integrally closed
> THIS FILE I... |
5ae4208ad518b96b2b918eb1690c900358e91a1b | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/topology/uniform_space/compare_reals.lean | ded30248ad255aefe35fdad659ae984dd6a28fe9 | [
"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 | 4,655 | lean | /-
Copyright (c) 2019 Patrick MAssot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import topology.uniform_space.absolute_value
import topology.instances.real
import topology.instances.rat
import topology.uniform_space.completion
/-!
# Comparison o... |
1883c2e0f9bfbb6548233803b9d4618af7a02177 | 037dba89703a79cd4a4aec5e959818147f97635d | /src/2021/functions/sheet1.lean | d3c9aa9dec6ef6c3a61a3897fa3ba99f9e9471bd | [] | no_license | ImperialCollegeLondon/M40001_lean | 3a6a09298da395ab51bc220a535035d45bbe919b | 62a76fa92654c855af2b2fc2bef8e60acd16ccec | refs/heads/master | 1,666,750,403,259 | 1,665,771,117,000 | 1,665,771,117,000 | 209,141,835 | 115 | 12 | null | 1,640,270,596,000 | 1,568,749,174,000 | Lean | UTF-8 | Lean | false | false | 5,833 | lean | /-
Copyright (c) 2021 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author : Kevin Buzzard
-/
import tactic -- imports all the Lean tactics
/-!
# Functions in Lean, example sheet 1 : injectivity and surjectivity
In this sheet we'll learn how to manipulate th... |
463df830f74cd23fd2f72d5e4b63eecd9c9d352e | 94e33a31faa76775069b071adea97e86e218a8ee | /src/category_theory/monoidal/free/coherence.lean | 2d28aae09bc78bcb084c2b5d4581a05f2c67a301 | [
"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 | 12,094 | lean | /-
Copyright (c) 2021 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import category_theory.monoidal.free.basic
import category_theory.groupoid
import category_theory.discrete_category
/-!
# The monoidal coherence theorem
In this file,... |
0ea52ae8fee03ca51d17fdeb5cb4e5a8f82eb931 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/meta4.lean | ea2eb872b6d45e71a5e602bfd831eb67bde9dbd5 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 1,358 | lean | import Lean.Meta
open Lean
open Lean.Meta
def print (msg : MessageData) : MetaM Unit := do
trace[Meta.debug] msg
def checkM (x : MetaM Bool) : MetaM Unit :=
unless (← x) do throwError "check failed"
axiom Ax : forall (α β : Type), α → β → DecidableEq β
set_option trace.Meta.debug true
def tst1 : MetaM Unit := do
... |
53d701e302cdad863b61b5e968be10c6d8b6992a | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/algebra/ordered_ring.lean | 9250ab320085c52452de947ecfb5a11c473b91a9 | [
"Apache-2.0"
] | permissive | ilitzroth/mathlib | ea647e67f1fdfd19a0f7bdc5504e8acec6180011 | 5254ef14e3465f6504306132fe3ba9cec9ffff16 | refs/heads/master | 1,680,086,661,182 | 1,617,715,647,000 | 1,617,715,647,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 51,147 | 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, Mario Carneiro
-/
import algebra.ordered_group
import algebra.invertible
import data.set.intervals.basic
set_option old_structure_cmd true
universe u... |
ecdb8ad812b4fa9d3f1b80a943c4709ee8091021 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/algebra/group/type_tags.lean | 7fe91067dcb80544d4a9fb21b502076272c6e2ac | [
"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 | 12,205 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import algebra.group.hom
import data.equiv.basic
/-!
# Type tags that turn additive structures into multiplicative, and vice versa
We define two type tags:
* `addit... |
6be4347a351ea8db8ad5c71b6ee49c91e75e839d | a76f677b87d42a9470ba3a0a78cfddd3063118e6 | /src/exercise.lean | 28f6351688ee2f040e60d5a2d735ea710eb83d84 | [] | no_license | Ja1941/hilberts-axioms | 50219c732ad5fa167408432e8c8baae259777a40 | 5b653a92e448b77da41c9893066b641bc4e6b316 | refs/heads/master | 1,693,238,884,856 | 1,635,702,120,000 | 1,635,702,120,000 | 385,546,384 | 9 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 2,693 | lean | /-Some geometry exercises I did during high school
I will be gradually adding more of them here -/
import congruence.Elements
open incidence_geometry incidence_order_geometry hilbert_plane
variables [C : hilbert_plane]
include C
example {a b c d e f : pts} (habc : noncol a b c) (hd : midpt d (b-ₛc)) (haed : betw... |
cd2804c810256810c3849180baf317164a36a516 | df561f413cfe0a88b1056655515399c546ff32a5 | /3-function-world/l3.lean | da1496ac60efcd08134c916326d18b957c0be331 | [] | no_license | nicholaspun/natural-number-game-solutions | 31d5158415c6f582694680044c5c6469032c2a06 | 1e2aed86d2e76a3f4a275c6d99e795ad30cf6df0 | refs/heads/main | 1,675,123,625,012 | 1,607,633,548,000 | 1,607,633,548,000 | 318,933,860 | 3 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 191 | lean | example (P Q R S T U: Type)
(p : P)
(h : P → Q)
(i : Q → R)
(j : Q → T)
(k : S → T)
(l : T → U)
: U :=
begin
have q : Q := h(p),
have t : T := j(q),
have u : U := l(t),
exact u,
end |
b1faa0c786317f88973b1f91fc65512564298e42 | 5f83eb0c32f15aeed5993a3ad5ededb6f31fe7aa | /lean/src/jit.lean | 187dcffa821c68feadcb1abedffa38757d57ad10 | [] | no_license | uw-unsat/jitterbug | 45b54979b156c0f5330012313052f8594abd6f14 | 78d1e75ad506498b585fbac66985ff9d9d05952d | refs/heads/master | 1,689,066,921,433 | 1,687,061,448,000 | 1,688,415,161,000 | 244,440,882 | 46 | 5 | null | null | null | null | UTF-8 | Lean | false | false | 27,466 | lean |
import tactic.tauto
/-!
This file contains the metatheory of JIT correctness.
The main theorem is interpreter_equivalence, proved based on the following two sets of axioms.
Two axioms are assumed to be correct (e.g., ensured by the Linux kernel):
* ctx_correctness: the JIT computes a correct JIT context for the so... |
a83aa452a59412936989082ffb98ac5f96f0f73e | 618003631150032a5676f229d13a079ac875ff77 | /src/data/hash_map.lean | 11a252b8e634813a226942860a8603bbb6df6402 | [
"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 | 27,897 | 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, Mario Carneiro
-/
import data.pnat.basic
import data.array.lemmas
import algebra.group
import data.sigma.basic
universes u v w
/-- `bucket_array α β` is the... |
1c6a3dc42605b6ff77317882c1517f489cc6489a | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /tests/lean/mvar1.lean | 56aa57c5e40047efd4c7815368158029803430bf | [
"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 | 3,089 | lean | import Init.Lean.MetavarContext
open Lean
def check (b : Bool) : IO Unit :=
unless b (throw $ IO.userError "error")
def f := mkConst `f []
def g := mkConst `g []
def a := mkConst `a []
def b := mkConst `b []
def c := mkConst `c []
def b0 := mkBVar 0
def b1 := mkBVar 1
def b2 := mkBVar 2
def u := mkLevelParam `u
de... |
354135f2ef818bc775556f1e5b7e7a77862aac77 | 5756a081670ba9c1d1d3fca7bd47cb4e31beae66 | /Mathport/Util/System.lean | 8ca9d5709c25d377d56870217edd53486508241c | [
"Apache-2.0"
] | permissive | leanprover-community/mathport | 2c9bdc8292168febf59799efdc5451dbf0450d4a | 13051f68064f7638970d39a8fecaede68ffbf9e1 | refs/heads/master | 1,693,841,364,079 | 1,693,813,111,000 | 1,693,813,111,000 | 379,357,010 | 27 | 10 | Apache-2.0 | 1,691,309,132,000 | 1,624,384,521,000 | Lean | UTF-8 | Lean | false | false | 402 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Daniel Selsam
-/
open System (FilePath)
def createDirectoriesIfNotExists (path : FilePath) : IO Unit := do
match System.FilePath.parent path with
| some d => discard <| IO.... |
403f053f6930290f7e21c861372233ce5ef17130 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/tactic/transfer.lean | d337bc0906ac2a1af110193c97ebee66bf5a122e | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 7,486 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl (CMU)
-/
prelude
import init.meta.tactic
import init.meta.match_tactic
import init.meta.mk_dec_eq_instance
import init.data.list.instances
import logic.relator
open tac... |
14ec2d466238ed3141d90e3b694a4b30a5134a80 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/category_theory/monad/basic.lean | cc9ac77b2929baddc54fbbbc98bf13cdd2d78261 | [
"Apache-2.0"
] | permissive | urkud/mathlib | eab80095e1b9f1513bfb7f25b4fa82fa4fd02989 | 6379d39e6b5b279df9715f8011369a301b634e41 | refs/heads/master | 1,658,425,342,662 | 1,658,078,703,000 | 1,658,078,703,000 | 186,910,338 | 0 | 0 | Apache-2.0 | 1,568,512,083,000 | 1,557,958,709,000 | Lean | UTF-8 | Lean | false | false | 10,879 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Bhavik Mehta, Adam Topaz
-/
import category_theory.functor.category
import category_theory.functor.fully_faithful
import category_theory.functor.reflects_isomorphisms
... |
40eec0a78cebd612b303194f1e1e4546ea3bbbe1 | 4aca55eba10c989f0d58647d3c2f371e7da44355 | /src/examples.lean | a8134edb251571f85b06925735e2c6450aea1d18 | [] | no_license | eric-wieser/l534zhan-my_project | f9fc75fb5454405e1a2fa9b56cf96c355f6f2336 | febc91e76b7b00fe2517f258ca04d27b7f35fcf3 | refs/heads/master | 1,689,218,910,420 | 1,630,439,440,000 | 1,630,439,440,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,519 | lean | import tactic.gptf
import data.matrix.basic
import data.complex.basic
import field_theory.finite.basic
section sec1
lemma irrelevant (P : Prop) (pf1 pf2 : P) : pf1 = pf2 := by simp
universe u
variable a : Type u
#check a -- prints `a : Type u`
#check unit
#check punit --universe polymorphic version H i₁ i₂ α β γ ... |
6732a9cc0cf9e4d61733f2c0b5861076bc173e93 | 367134ba5a65885e863bdc4507601606690974c1 | /src/linear_algebra/affine_space/midpoint.lean | c2cfd6b5b1a814deb9d6fb506276b0309fce97b4 | [
"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 | 7,615 | lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Yury Kudryashov
-/
import algebra.invertible
import linear_algebra.affine_space.affine_equiv
/-!
# Midpoint of a segment
## Main definitions
* `midpoint R x y`: midpoint of the segm... |
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