blob_id stringlengths 40 40 | directory_id stringlengths 40 40 | path stringlengths 7 139 | content_id stringlengths 40 40 | detected_licenses listlengths 0 16 | license_type stringclasses 2
values | repo_name stringlengths 7 55 | snapshot_id stringlengths 40 40 | revision_id stringlengths 40 40 | branch_name stringclasses 6
values | visit_date int64 1,471B 1,694B | revision_date int64 1,378B 1,694B | committer_date int64 1,378B 1,694B | github_id float64 1.33M 604M ⌀ | star_events_count int64 0 43.5k | fork_events_count int64 0 1.5k | gha_license_id stringclasses 6
values | gha_event_created_at int64 1,402B 1,695B ⌀ | gha_created_at int64 1,359B 1,637B ⌀ | gha_language stringclasses 19
values | src_encoding stringclasses 2
values | language stringclasses 1
value | is_vendor bool 1
class | is_generated bool 1
class | length_bytes int64 3 6.4M | extension stringclasses 4
values | content stringlengths 3 6.12M |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
122bf84c288aff8ed0b107c2c1e6fe43a2f77446 | 5ae26df177f810c5006841e9c73dc56e01b978d7 | /src/topology/metric_space/completion.lean | 8b493174fb7ed4d7d71f8397a8e67502809a3987 | [
"Apache-2.0"
] | permissive | ChrisHughes24/mathlib | 98322577c460bc6b1fe5c21f42ce33ad1c3e5558 | a2a867e827c2a6702beb9efc2b9282bd801d5f9a | refs/heads/master | 1,583,848,251,477 | 1,565,164,247,000 | 1,565,164,247,000 | 129,409,993 | 0 | 1 | Apache-2.0 | 1,565,164,817,000 | 1,523,628,059,000 | Lean | UTF-8 | Lean | false | false | 8,572 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Sébastien Gouëzel
The completion of a metric space.
Completion of uniform spaces are already defined in `topology.uniform_space.completion`. We show
here that the uniform space com... |
cc4f41d5eef0442fac141aa9be18d7aa785bdee5 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/category_theory/full_subcategory.lean | b6c3038a5e08db9593145c9f42c2b7f2d748eef5 | [
"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 | 3,247 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Reid Barton
-/
import category_theory.fully_faithful
namespace category_theory
universes v u₁ u₂ -- declare the `v`'s first; see `category_theory.category` for an exp... |
5cc49bf3069ec2d02fc7c141e71e48ba7f0b188f | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Elab/Tactic/Conv/Congr.lean | 2fd218952e2d9c36a7acbb634fdb63a3edfb81c4 | [
"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 | 8,092 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Meta.Tactic.Simp.Main
import Lean.Meta.Tactic.Congr
import Lean.Elab.Tactic.Conv.Basic
namespace Lean.Elab.Tactic.Conv
open Meta
private def c... |
01b2abf954d09ad074ec0db447a6b54ec1a0cce8 | 36c7a18fd72e5b57229bd8ba36493daf536a19ce | /hott/algebra/ordered_group.hlean | 7d81fe1d04870e204bd993bda712c843838cea20 | [
"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 | 21,538 | hlean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
Partially ordered additive groups, modeled on Isabelle's library. We could refine the structures,
but we would have to declare more inheritance paths.
Ported from the sta... |
63fb8550d095b0c498c433313caeb9776682e2ea | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/data/set/basic.lean | 16c1cfe8eac6e17f0e05ac6c31970c8d9a6d12df | [
"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 | 117,723 | 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 logic.unique
import logic.relation
import order.boolean_algebra
/-!
# Basic properties of sets
Sets in Lean are homogeneous; all their eleme... |
bee1bc7e438cf180736586386cfef4817e4739bd | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/topology/order.lean | 4d4c61bb434e1e026f2324c40f04cf711af58f70 | [
"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 | 29,413 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import topology.tactic
/-!
# Ordering on topologies and (co)induced topologies
Topologies on a fixed type `α` are ordered, by reverse inclusion.
Tha... |
91110ed4f581939d54f956ce0989bb6973f482a5 | 791eaf247d44ef2d812f6b2fe1c021232e9ce686 | /src/bb_alg.lean | 92142193030cfb5ba1c6b7753d9c75b012c4c91f | [] | no_license | MarkosDe/bb_alg | 2f100b2e82bfa95a85863eedb33d9aea542bd5c2 | 11b12ab83de0da825857b4f9bb8304475be05877 | refs/heads/master | 1,587,996,505,019 | 1,558,014,699,000 | 1,558,014,699,000 | 174,397,884 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 11,653 | lean | import data.polynomial linear_algebra.multivariate_polynomial
import ring_theory.ideals data.nat.choose order.zorn
import algebra.module
open set
open ring
open polynomial
universes u
section
variables {σ : Type*} [decidable_linear_order σ]
-- '.sort' makes list
def multiset.lex (m1 m2 : multiset σ) : Prop :=
m1.sor... |
ca0a4e5f60bc74a9c7ca72ab2cec36d9fb71caae | 82b86ba2ae0d5aed0f01f49c46db5afec0eb2bd7 | /src/Lean/Parser/Extension.lean | 5ac78213036ea175c02917b9919c0b01ff346cae | [
"Apache-2.0"
] | permissive | banksonian/lean4 | 3a2e6b0f1eb63aa56ff95b8d07b2f851072d54dc | 78da6b3aa2840693eea354a41e89fc5b212a5011 | refs/heads/master | 1,673,703,624,165 | 1,605,123,551,000 | 1,605,123,551,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 25,754 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Sebastian Ullrich
-/
/-! Extensible parsing via attributes -/
import Lean.Parser.Basic
import Lean.Parser.StrInterpolation
import Lean.KeyedDeclsAttribute
... |
fb5da02fc6f1956505e2f6baa3edf536fa19a813 | 1f6fe2f89976b14a4567ab298c35792b21f2e50b | /univalent_subcategory.hlean | fca280a7e6a3386b2f8271dba786d0ba94d9d949 | [
"Apache-2.0"
] | permissive | jonas-frey/Spectral | e5c1c2f7bcac26aa55f7b1e041a81272a146198d | 72d521091525a4bc9a31cac859840efe9461cf66 | refs/heads/master | 1,610,235,743,345 | 1,505,417,795,000 | 1,505,417,795,000 | 102,653,342 | 0 | 0 | null | 1,504,728,483,000 | 1,504,728,483,000 | null | UTF-8 | Lean | false | false | 14,889 | hlean | import homotopy.sphere2 algebra.category.functor.attributes
open eq pointed sigma is_equiv equiv fiber algebra group is_trunc function prod prod.ops iso functor
namespace category
section univ_subcat
parameters {C : Precategory} {D : Category} (F : functor C D) (p : is_embedding F) (q : fully_faithful F)
varia... |
bd42093ed957c4e4f8635a99a50d9a7329d4c310 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Elab/MacroRules.lean | 8384c81fc0826657c49f8f87c8235bf4c96c320d | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 3,342 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Elab.Syntax
import Lean.Elab.AuxDef
namespace Lean.Elab.Command
open Lean.Syntax
open Lean.Parser.Term hiding macroArg
open Lean.Parser.Command... |
f1f9b2da65733d158d21646aafae905a94535744 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/data/pnat/basic.lean | a235d1e72c7309a89b4d71052f20d0db70699a49 | [
"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 | 14,158 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro, Neil Strickland
-/
import data.nat.basic
/-!
# The positive natural numbers
This file defines the type `ℕ+` or `pnat`, the subtype of natural numbers that are p... |
9a3499b0d34d20326d2ea8141b28a5b2ef5fdfa8 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/fin/vec_notation.lean | 29033f48f7911b5e0a095e1a5d6f7e9ccd24d6c9 | [
"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 | 15,355 | 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 data.fin.tuple.basic
import data.list.range
import group_theory.group_action.pi
import meta.univs
/-!
# Matrix and vector notation
> THIS FILE IS SYNCHRONIZED WITH... |
d6bac9da3cb4dc02ced21a833e0a2d86a6326fb8 | 4f643cce24b2d005aeeb5004c2316a8d6cc7f3b1 | /omin/def_choice/choice3.lean | d362b24726a77811522c76e25d71a5616e0e924e | [] | no_license | rwbarton/lean-omin | da209ed061d64db65a8f7f71f198064986f30eb9 | fd733c6d95ef6f4743aae97de5e15df79877c00e | refs/heads/master | 1,674,408,673,325 | 1,607,343,535,000 | 1,607,343,535,000 | 285,150,399 | 9 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,748 | lean | import algebra.module.ordered
import order.conditionally_complete_lattice
import o_minimal.sheaf.pfun
import o_minimal.sheaf.quantifiers
import .order
import ..oqm
-- import ..tame
-- Definable choice in 1 dimension.
section
-- TODO: for_mathlib order.bounds
-- also add mem_lower_bounds/is_least_def/etc.
lemma is_l... |
b69272c9169588aa7aaddc3400fd8625bdfbce37 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/probability/martingale/upcrossing.lean | 2bc98deb4de6a3d79054b73ba9296514a1e6129a | [
"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 | 41,393 | lean | /-
Copyright (c) 2022 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
import data.set.intervals.monotone
import probability.process.hitting_time
import probability.martingale.basic
/-!
# Doob's upcrossing estimate
Given a discrete real-val... |
ad2478664e676068fcb0eb196f694bef1b6c04f5 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/order/category/CompleteLat.lean | 1649a5cc2e6fc45620cd121670390481d2b89367 | [
"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 | 2,486 | lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import order.category.BddLat
import order.hom.complete_lattice
/-!
# The category of complete lattices
This file defines `CompleteLat`, the category of complete lattice... |
29a90efc26bf6007cf5d625cd98594d0e671ccbc | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/pprod_auto.lean | 1f75d13bf13c00c15e0cf814e76ab33dff37994f | [] | 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 | 503 | lean | /-
Copyright (c) 2020 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.PostPort
universes u_1 u_2
namespace Mathlib
/-!
# Extra facts about `pprod`
-/
@[simp] theo... |
74d2f4c62d43635369e9b2dbe559f8be86c7ffb8 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/linear_algebra/direct_sum/finsupp.lean | 2272e12a4104a9d68dc36724d698e791e0452e70 | [] | 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 | 3,659 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.linear_algebra.finsupp
import Mathlib.linear_algebra.direct_sum.tensor_product
import Mathli... |
d75c0fa0f872e54b11e56a4ec2cdb76465c76ddf | 390c7d44c0470f935f1ff06637607521791400da | /mk_inhabitant.lean | 2ab6b7eceaa0037f62cc0459977bc3350e1dd824 | [] | no_license | avigad/auto | 32baee2744dd3ae53f1cffd3f04523b953e5a9eb | 1aa4ebf60f900e8d61bb423105592a4010fa6ec5 | refs/heads/master | 1,594,791,920,875 | 1,475,608,824,000 | 1,475,608,824,000 | 67,415,120 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 551 | lean | open tactic
/- mk_inthabitant_using A t assumes A is an expression denoting a type. It creates
a goal with type A, applies t, and returns the expression that results. -/
meta_definition mk_inhabitant_using (A : expr) (t : tactic unit) : tactic expr :=
do m ← mk_meta_var A,
gs ← get_goals,
set_goals [m],
t,... |
d2152b09a3074f6cfedefdbbe4deff3888e6bd99 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/noncomp.lean | 62bef47d727fab2b405e26b9bf748f1cd83aa9dc | [
"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 | 137 | lean | open nat
axiom n : nat
definition f (x : nat) := -- Error this is not computable
x + n
noncomputable definition f (x : nat) := x + n
|
afbb6da3fca6b476ec7778202f8c5686445c9b72 | 2fb7334a212c3858db44039b5fa6cd57fd5d1443 | /experiments/equalizer_puzzle.lean | 234291aa71fd9cda2d1b7f518cffd338f899fc63 | [] | no_license | ImperialCollegeLondon/condensed-sets | 24514be041533b07fd62d337b1d6a5ce2b09c78c | e308291646396003dbed3896e5fbb40cb57c7050 | refs/heads/master | 1,628,397,992,041 | 1,601,549,576,000 | 1,601,549,576,000 | 224,198,323 | 3 | 1 | null | 1,601,549,578,000 | 1,574,774,780,000 | Lean | UTF-8 | Lean | false | false | 3,625 | lean | /-
# An equalizer lemma.
In category theory, if f and g are morphisms from X to Y, then
the equalizer of (f,g) is isomorphic to the equalizer of (g,f).
-/
import category_theory.limits.shapes.equalizers
import category_theory.discrete_category
open category_theory
open category_theory.limits
universes v u
variab... |
21fe440d5d259f5b678a9e996d610646aa2ac844 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/data/pfunctor/univariate/default.lean | 157e8d4adb6cd281abebdcb428cdb3b0e3cf4e9c | [
"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 | 72 | lean | import data.pfunctor.univariate.basic
import data.pfunctor.univariate.M
|
e52ec92d79016699228b8d149576c0cd9ac1f99f | e0f9ba56b7fedc16ef8697f6caeef5898b435143 | /src/topology/algebra/group.lean | 30cb0696cdd8b724958518913d9f8647e98294c3 | [
"Apache-2.0"
] | permissive | anrddh/mathlib | 6a374da53c7e3a35cb0298b0cd67824efef362b4 | a4266a01d2dcb10de19369307c986d038c7bb6a6 | refs/heads/master | 1,656,710,827,909 | 1,589,560,456,000 | 1,589,560,456,000 | 264,271,800 | 0 | 0 | Apache-2.0 | 1,589,568,062,000 | 1,589,568,061,000 | null | UTF-8 | Lean | false | false | 17,307 | 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, Patrick Massot
Theory of topological groups.
-/
import order.filter.pointwise
import group_theory.quotient_group
import topology.algebra.monoid
import... |
5d3b0366e786e9fe0ef553f2c11a6c4661c5a9f8 | 77c5b91fae1b966ddd1db969ba37b6f0e4901e88 | /src/data/pnat/interval.lean | 3505c0fe5fff13c4ed5fe6b3174754300ddb261a | [
"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 | 2,003 | 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.nat.interval
/-!
# Finite intervals of positive naturals
This file proves that `ℕ+` is a `locally_finite_order` and calculates the cardinality of its
interv... |
46d5d17d0b44c8dd8845e01713188507cefdcf44 | 2a70b774d16dbdf5a533432ee0ebab6838df0948 | /_target/deps/mathlib/src/measure_theory/outer_measure.lean | f74c7fa524c7f2ce159df240058bb5518117119d | [
"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 | 40,626 | 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 analysis.specific_limits
import measure_theory.measurable_space
import topology.algebra.infinite_sum
/-!
# Outer Measures
An outer measure is... |
123c335b98286c480af1e741d167fdf9b847ca02 | 968e2f50b755d3048175f176376eff7139e9df70 | /examples/prop_logic_lean_summary/unnamed_561.lean | a830f0dea58fbe9db965f048d8b00393680c203c | [] | no_license | gihanmarasingha/mth1001_sphinx | 190a003269ba5e54717b448302a27ca26e31d491 | 05126586cbf5786e521be1ea2ef5b4ba3c44e74a | refs/heads/master | 1,672,913,933,677 | 1,604,516,583,000 | 1,604,516,583,000 | 309,245,750 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 88 | lean | variables p : Prop
-- BEGIN
example (h₁ : ¬p) (h₂ : p) : false :=
h₁ h₂
-- END |
931f366ccddeb8404743f5631195d007ef7ea099 | 9b0cdc31ceef59f5fbd4e20acad77a7a59044088 | /src/exercises/03_forall_or.lean | 0a68d11c26dc72d8634465628db0468d05953029 | [
"Apache-2.0"
] | permissive | andrewparr/tutorials | 964ebb8b4eae2b658a946843f8f9fc5c69b79761 | 0fd6cefe7e62f0d4bfa12ebd115913f8ef4fbd62 | refs/heads/master | 1,687,573,595,883 | 1,626,653,659,000 | 1,626,653,659,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,146 | lean | import data.real.basic
import algebra.group.pi
set_option pp.beta true
/-
In this file, we'll learn about the ∀ quantifier, and the disjunction
operator ∨ (logical OR).
Let P be a predicate on a type X. This means for every mathematical
object x with type X, we get a mathematical statement P x.
In Lean, P x has ty... |
cd4b2791aadec8808bdbcc70f13d4c235b8f3b74 | efa51dd2edbbbbd6c34bd0ce436415eb405832e7 | /20161026_ICTAC_Tutorial/ex16.lean | a92633ce38e12570d42f6a1ccfc4e390f81f18cd | [
"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 | 449 | lean | def double (x : ℕ) : ℕ := x + x
print double
check double 3
eval double 3 -- 6
def square (x : ℕ) := x * x
print square
check square 3
eval square 3 -- 9
def do_twice (f : ℕ → ℕ) (x : ℕ) : ℕ := f (f x)
eval do_twice double 2 -- 8
/- These definitions are equivalent to -/
def double' : ℕ → ℕ := λ x, x + x
... |
734eaeefaca17d3c152165d296b69f33fa4e505a | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/order/cover.lean | b8b9b6e84213fc6dff64e61c8f3cb8a10804b809 | [
"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 | 16,172 | lean | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Violeta Hernández Palacios, Grayson Burton, Floris van Doorn
-/
import data.set.intervals.ord_connected
import order.antisymmetrization
/-!
# The covering relation
This f... |
57dd93bc5ce7b3d175b485a310501e0411eb4ec6 | 54d7e71c3616d331b2ec3845d31deb08f3ff1dea | /tests/lean/run/unification_hints.lean | bbf15fb89450d955c5484a77ff74cf07b65e42ff | [
"Apache-2.0"
] | permissive | pachugupta/lean | 6f3305c4292288311cc4ab4550060b17d49ffb1d | 0d02136a09ac4cf27b5c88361750e38e1f485a1a | refs/heads/master | 1,611,110,653,606 | 1,493,130,117,000 | 1,493,167,649,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 792 | lean | open list nat
namespace toy
constants (A : Type.{1}) (f h : A → A) (x y z : A)
attribute [irreducible]
noncomputable definition g (x y : A) : A := f z
@[unify]
noncomputable definition toy_hint (x y : A) : unification_hint :=
{ pattern := g x y ≟ f z,
constraints := [] }
open tactic
set_option trace.type_cont... |
e83261693609634c73db9fbf949bc6329bd3955e | f3849be5d845a1cb97680f0bbbe03b85518312f0 | /tests/lean/run/check_constants.lean | 6c679a8ead2728e47206118704a7d776ad532cde | [
"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 | 14,772 | lean | -- DO NOT EDIT, automatically generated file, generator scripts/gen_constants_cpp.py
import smt system.io
open tactic
meta def script_check_id (n : name) : tactic unit :=
do env ← get_env, (env^.get n >> return ()) <|> (guard $ env^.is_namespace n) <|> (attribute.get_instances n >> return ()) <|> fail ("identifier '" +... |
41d69664a34fc0212c39135d956e6c2a7c094b09 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/tactic/monotonicity/interactive.lean | c7ddbbbed9bb205282644cb1e5c994894d0e764e | [
"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 | 23,573 | lean | /-
Copyright (c) 2019 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import control.traversable.derive
import control.traversable.lemmas
import data.dlist
import tactic.monotonicity.basic
variables {a b c p : Prop}
namespace tactic.interac... |
fc109d3f03980f81e34cb3cc46463f2246c0d4a9 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/data/multiset/powerset.lean | 7c486c46bd5a550a9acdcea478f92dffbfbea3c9 | [
"Apache-2.0"
] | permissive | AntoineChambert-Loir/mathlib | 64aabb896129885f12296a799818061bc90da1ff | 07be904260ab6e36a5769680b6012f03a4727134 | refs/heads/master | 1,693,187,631,771 | 1,636,719,886,000 | 1,636,719,886,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,263 | 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 data.multiset.basic
/-!
# The powerset of a multiset
-/
namespace multiset
open list
variables {α : Type*}
/-! ### powerset -/
/-- A helper function for t... |
55f3273aa9824fb255a583fb01175f9b5e9c7624 | a7602958ab456501ff85db8cf5553f7bcab201d7 | /Assignment1/homework.lean | 098e344590fe306e8cda001754241650f34ee2b1 | [] | no_license | enlauren/math-logic | 081e2e737c8afb28dbb337968df95ead47321ba0 | 086b6935543d1841f1db92d0e49add1124054c37 | refs/heads/master | 1,594,506,621,950 | 1,558,634,976,000 | 1,558,634,976,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,201 | lean | -- Assignment 1
-- Dom Farolino, farolidm@mail.uc.edu
-- Math Logic
variables A B C: Prop
-- Exercise 1
section
example: ¬ (A ∧ B) → (A → ¬ B) :=
assume h1: ¬ (A ∧ B),
assume ha: A,
assume hb: B,
have hab: (A ∧ B), from and.intro ha hb,
show false, from h1 hab
end
-- Exercise 2
section
example: (A → C)... |
aba9a5e38efbd06898e159719f3db3bdae9ed347 | 8d65764a9e5f0923a67fc435eb1a5a1d02fd80e3 | /src/analysis/convex/integral.lean | 41844302c5bc14f02aa8c5b638a854606bd27a67 | [
"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 | 7,714 | 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
-/
import analysis.convex.basic
import measure_theory.integral.set_integral
/-!
# Jensen's inequality for integrals
In this file we prove four theorems:
* `co... |
55c7ee444deba97f3b2c13ce1594989af0c1d959 | 8c95816d6379a6864848d68ce735a5700c1cbbc3 | /src/smt2/default.lean | 7d6095b53880b6fa19f88e99c6b59717d153d790 | [
"Apache-2.0"
] | permissive | aqjune/smt2_interface | f00ed0a4317d7c9112deb0806c8e89e6512a901e | 598848a7a6fa47520fadcfe1b16891053a296084 | refs/heads/master | 1,631,518,664,718 | 1,524,489,340,000 | 1,524,489,340,000 | 115,204,811 | 0 | 0 | null | 1,514,043,428,000 | 1,514,043,427,000 | null | UTF-8 | Lean | false | false | 12,869 | lean | import system.io
import .solvers.z3
import .syntax
import .builder
import .tactic
import .attributes
import .lol
import init.data.option.basic
declare_trace smt2
open tactic
open smt2.builder
open native
meta structure smt2_state : Type :=
(ctxt : lol.context)
(type_map : rb_map expr lol.type)
meta def smt2_state.i... |
721b201cc591366fb4d80dbee1f290ab1165a151 | 969dbdfed67fda40a6f5a2b4f8c4a3c7dc01e0fb | /src/ring_theory/polynomial/basic.lean | cd39846b9169bcaece5436593b7023c7e0f22c70 | [
"Apache-2.0"
] | permissive | SAAluthwela/mathlib | 62044349d72dd63983a8500214736aa7779634d3 | 83a4b8b990907291421de54a78988c024dc8a552 | refs/heads/master | 1,679,433,873,417 | 1,615,998,031,000 | 1,615,998,031,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 38,898 | lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import algebra.char_p.basic
import data.mv_polynomial.comm_ring
import data.mv_polynomial.equiv
import data.polynomial.field_division
import ring_theory.principal_ideal_domain... |
e9acf3c04307eb31d56bea1b4881e16f66ee0486 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/category_theory/concrete_category/unbundled_hom.lean | ba9dab684813121c22cf2b7e1aed309f909d2718 | [
"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 | 2,191 | lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import category_theory.concrete_category.bundled_hom
/-!
# Category instances for structures that use unbundled homs
This file provides basic infrastructure to de... |
cb018535d39c33351fdcbc37fc3782765a407593 | c31182a012eec69da0a1f6c05f42b0f0717d212d | /src/prop819/strict_complex_iso.lean | 821616f14d2bfa37a7da4375a23db40543f1a87a | [] | 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 | 1,018 | lean | import for_mathlib.SemiNormedGroup
import algebra.homology.additive
namespace SemiNormedGroup
protected class strict_iso {A B : SemiNormedGroup} (f : A ≅ B) :=
(strict_hom' : ∀ a : A, ∥f.hom a∥₊ = ∥a∥₊)
@[simp]
lemma strict_iso_hom {A B : SemiNormedGroup} (f : A ≅ B) [strict_iso f] (a : A) :
∥f.hom a∥₊ = ∥a∥₊ := s... |
24141aa2b9b79acff0d8d4a61eb496b23d3b96be | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/data/nat/basic.lean | fa059febea6ee125b6cdb58da6979a9a5de46861 | [
"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 | 69,886 | lean | /-
Copyright (c) 2014 Floris van Doorn (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-/
import algebra.group.hom_instances
import algebra.order_functions
import algebra.... |
d96a99b73cae1f4cbf13af002444f06f350fbb59 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/data/subtype.lean | 51042c3eac46a9b39ed448b14681a7bbfbb46b98 | [
"Apache-2.0"
] | permissive | Lix0120/mathlib | 0020745240315ed0e517cbf32e738d8f9811dd80 | e14c37827456fc6707f31b4d1d16f1f3a3205e91 | refs/heads/master | 1,673,102,855,024 | 1,604,151,044,000 | 1,604,151,044,000 | 308,930,245 | 0 | 0 | Apache-2.0 | 1,604,164,710,000 | 1,604,163,547,000 | null | UTF-8 | Lean | false | false | 5,334 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl
-/
import tactic.lint
import tactic.ext
import tactic.simps
open function
namespace subtype
variables {α : Sort*} {β : Sort*} {γ : Sort*} {p : α → Prop} {q : α → Prop}
... |
3b7c306e1b159dc5cf0d88c2d19773bf7610e629 | 67190c9aacc0cac64fb4463d93e84c696a5be896 | /Classes/2019-10-03.lean | f888ff85e09e03a76957928ba85df7c1ec153aff | [] | no_license | lucasresck/Discrete-Mathematics | ffbaf55943e7ce2c7bc50cef7e3ef66a0212f738 | 0a08081c5f393e5765259d3f1253c3a6dd043dac | refs/heads/master | 1,596,627,857,734 | 1,573,411,500,000 | 1,573,411,500,000 | 212,489,764 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 944 | lean | constant U : Type
constant p : U → U → Prop
constants A B C : U → Prop
theorem ex1 : (∃ x, ∀ y, p x y) → (∀ y, ∃ x, p x y) :=
begin
intros h1,
intros a,
cases h1 with b h2,
existsi b,
have h3, from h2 a,
assumption
end
theorem ex2 (h1 : ∀ x, A x ∨ B x) (h2 : ∀ y, ¬ A y) :
∀ x, B x :=
beg... |
14dc2aed8679c7aba59cb73741116cc14fc8199c | ef6b7797dbbd7b1dfff69894d190a965b101c5ff | /src/euclid_props.lean | 6a75eeb44ccabf59d131cc3013c91d107eaf005b | [] | no_license | utensil-star/leanteach2020 | 43d57f1b23eded178e2049a0957b7ec38fd4e1a7 | 93326a5e5b0efeba30d9dc9ee85d52b1029cb24d | refs/heads/master | 1,666,413,811,198 | 1,592,598,394,000 | 1,592,598,394,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,056 | lean | import .euclid
import tactic
-- Redo the local notation
--------------------------
local infix ` ≃ `:55 := congruent -- typed as \ equiv
local infix `⬝`:56 := Segment.mk -- typed as \ cdot
-- Lemma needed for Proposition 1
lemma hypothesis1_about_circles_radius (s : Segment) :
let c₁ : Circle := ⟨s.p1, s.p2⟩ in... |
3589c36d72d0f82a0a72cd7a0170aa16e22d26b1 | 5c47d5f6f51310e594c57486e051666894b008a1 | /CategoryTheory/Limits.lean | 842143b53683d58171d635f8d39ba094e601bf6e | [
"Apache-2.0"
] | permissive | adrianmartir/category-theory-lean4 | 100ed364c07441b30d1483949152c39060563ccf | fa786c12114b7fad3f6c9e831d8ef2120a46bd05 | refs/heads/main | 1,687,620,544,571 | 1,626,958,787,000 | 1,626,958,787,000 | 372,252,151 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 937 | lean | import CategoryTheory.Category
namespace Category_theory
open CategoryTheory
open Category
variable (J : HomStruct) [Category J]
variable {C : HomStruct} [Category C]
def const (c: C.obj) : Functor J C := {
obj := (fun _ => c),
map := (fun _ => id' c),
map_id := rfl,
map_comp := by
intros
simp
}
de... |
15995d59a1d7d5f9a22c1d262edeb426f016cbe6 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/analysis/convex/extreme.lean | c27c474fdd252f961e5defe88019a059351ca96c | [
"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 | 8,842 | 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 linear_algebra.affine_space.independent
import algebra.big_operators.basic
import analysis.convex.topology
/-!
# Extreme sets
This fi... |
9d0c9b21ce876a5ae51af951ba9110507b420e34 | 367134ba5a65885e863bdc4507601606690974c1 | /src/measure_theory/group.lean | 5018e461c019d4ef672f1e1ce4a66e55a7e2a5ff | [
"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 | 8,303 | lean | /-
Copyright (c) 2020 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import measure_theory.integration
/-!
# Measures on Groups
We develop some properties of measures on (topological) groups
* We define properties on measures: l... |
1b80c98f3f1e024a7f89c8264da286490bdfe403 | 5719a16e23dfc08cdea7a5bf035b81690f307965 | /stage0/src/Init/Lean/Elab/Term.lean | 921896caab36c0dc02fcc0ffd8ca25acb126b0a3 | [
"Apache-2.0"
] | permissive | postmasters/lean4 | 488b03969a371e1507e1e8a4df9ebf63c7cbe7ac | f3976fc53a883ac7606fc59357d43f4b51016ca7 | refs/heads/master | 1,655,582,707,480 | 1,588,682,595,000 | 1,588,682,595,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 56,659 | 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.Util.Sorry
import Init.Lean.Structure
import Init.Lean.Meta.ExprDefEq
import Init.Lean.Meta.AppBuilder
import Init.Lean.Meta.SynthI... |
414e445acd6b4842663e8ff0b833f840188f774c | e00ea76a720126cf9f6d732ad6216b5b824d20a7 | /src/ring_theory/fractional_ideal.lean | 5dd1f9b393e2ceed2c62506dee47684ea900f82c | [
"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 | 14,200 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
Fractional ideals of an integral domain.
-/
import ring_theory.algebra_operations
import ring_theory.localization
/-!
# Fractional ideals
This file defines fractional ideal... |
d7c37b9729d6e2a86a923ba9c6de044a91663587 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/analysis/box_integral/partition/measure.lean | 886f829a265d60423193cb5c4fc547a743e1170d | [
"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 | 4,092 | 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.additive
import measure_theory.measure.lebesgue
/-!
# Box-additive functions defined by measures
In this file we prove a fe... |
f9d6aa3c29f1b0f91f595a2e5dd94a1c655145db | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /counterexamples/cyclotomic_105.lean | d600a7098a3d503712110b624bcd13d51066cc91 | [
"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 | 3,700 | lean | /-
Copyright (c) 2021 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca
-/
import ring_theory.polynomial.cyclotomic.basic
/-!
# Not all coefficients of cyclotomic polynomials are -1, 0, or 1
We show that not all coefficients of cyclotom... |
06b80cea8242180ed1ddd0e5bd4ade4b058d9185 | 9028d228ac200bbefe3a711342514dd4e4458bff | /src/measure_theory/set_integral.lean | 1ea1ca3a474305b3c830e4248c02f0897c5ab6f5 | [
"Apache-2.0"
] | permissive | mcncm/mathlib | 8d25099344d9d2bee62822cb9ed43aa3e09fa05e | fde3d78cadeec5ef827b16ae55664ef115e66f57 | refs/heads/master | 1,672,743,316,277 | 1,602,618,514,000 | 1,602,618,514,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 37,712 | lean | /-
Copyright (c) 2020 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Yury Kudryashov
-/
import measure_theory.bochner_integration
import analysis.normed_space.indicator_function
/-!
# Set integral
In this file we prove some properties of... |
ba100e34b74e9d63c4d601b16f4308aee6754b33 | 12dabd587ce2621d9a4eff9f16e354d02e206c8e | /world10/level08.lean | 5dfc5f034569bb3929472bca482ed5bbed702775 | [] | 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 | 127 | lean | lemma succ_le_succ (a b : mynat) (h : a ≤ b) : succ a ≤ succ b :=
begin
cases h with d hd,
use d,
rw hd,
rwa succ_add,
end
|
9d55ca17afd5643227ce23826d7a7a6b82e497d8 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/data/nat/multiplicity.lean | 4dd44ab1700a81a327e2b06a4bcbf65207c05fd1 | [
"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 | 11,874 | lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import algebra.big_operators.intervals
import data.nat.bitwise
import data.nat.log
import data.nat.parity
import ring_theory.int.basic
/-!
# Natural number multiplicity
... |
ec7b21bc65d4587caac9063eeadeca7be3841443 | 75db7e3219bba2fbf41bf5b905f34fcb3c6ca3f2 | /hott/choice.hlean | e03e1b5b7280c57b59cbefe7cf06282293f4d7c6 | [
"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 | 3,545 | hlean | import types.trunc types.bool
open eq bool equiv sigma sigma.ops trunc is_trunc pi
namespace choice
universe variable u
-- 3.8.1. The axiom of choice.
definition AC [reducible] := Π (X : Type.{u}) (A : X -> Type.{u}) (P : Π x, A x -> Type.{u}),
is_hset X -> (Π x, is_hset (A x)) -> (Π x a, is_hprop (P x a)) -... |
52aac2345ca2567b519667f860edfb2ac1ee8988 | b70031c8e2c5337b91d7e70f1e0c5f528f7b0e77 | /src/analysis/normed_space/inner_product.lean | 96b0b07c399aad194fcd5dd6a96680c958262b30 | [
"Apache-2.0"
] | permissive | molodiuc/mathlib | cae2ba3ef1601c1f42ca0b625c79b061b63fef5b | 98ebe5a6739fbe254f9ee9d401882d4388f91035 | refs/heads/master | 1,674,237,127,059 | 1,606,353,533,000 | 1,606,353,533,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 81,241 | lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Sébastien Gouëzel, Frédéric Dupuis
-/
import linear_algebra.bilinear_form
import linear_algebra.sesquilinear_form
import analysis.special_functions.pow
import topology.m... |
dd7b17550a34072e6aa1e29c29940d769a391b0b | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/order/complete_lattice.lean | 2988be0ae30981116be03985721029fb0a30077c | [
"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 | 45,798 | 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 order.bounds
/-!
# Theory of complete lattices
## Main definitions
* `Sup` and `Inf` are the supremum and the infimum of a set;
* `supr (f : ι → α)` and `in... |
cf06a138def93989bf033b4970534a07762c9acc | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/ring_theory/polynomial/scale_roots.lean | 5a4f6e7c6ab6a3e695670a340589331309b0fd2b | [
"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 | 5,338 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Devon Tuma
-/
import ring_theory.polynomial.basic
import ring_theory.non_zero_divisors
/-!
# Scaling the roots of a polynomial
This file defines `scale_roots p s` for a po... |
e489a21db572992fd991edb85ad17612e3f3ff0d | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/tooManyVarsAtInduction.lean | 0afd2467316488fdf8886f4e7ae362f71a740397 | [
"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 | 208 | lean | theorem ex1 (n : Nat) : 0 + n = n := by
induction n with
| succ x ih₁ ih₂ ih₃ => admit
| zero => rfl
theorem ex2 (n : Nat) : 0 + n = n := by
cases n with
| succ x ih => admit
| zero => rfl
|
d20831be14eb552f3491bbaddf25e6f7dcfefca5 | c61b91f85121053c627318ad8fcde30dfb8637d2 | /Chapter5/5-4.lean | 5845e8ba8a6998d841672dd349d04dfe73072fb2 | [] | no_license | robkorn/theorem-proving-in-lean-exercises | 9e2256360eaf6f8df6cdd8fd656e63dfb04c8cdb | 9c51da587105ee047a9db55d52709d881a39be7a | refs/heads/master | 1,585,403,341,988 | 1,540,142,619,000 | 1,540,142,619,000 | 148,431,678 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 966 | lean | example (n : ℕ) : n + 1 = nat.succ n :=
begin
show nat.succ n = nat.succ n,
reflexivity
end
example (p q : Prop) : p ∧ q → q ∧ p :=
begin
intro h,
cases h with hp hq,
split,
show q, from hq,
show p, from hp
end
example (p q r : Prop) : p ∧ (q ∨ r) → (p ∧ q) ∨ (p ∧ r) :=
begin
intro h,
cases h with h... |
bac5266d00444213905113fc7106781b6adcedbb | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/special_functions/log/monotone.lean | 8e248092cccd1dd17d834260ad251a3e299ee81f | [
"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 | 3,344 | lean | /-
Copyright (c) 2021 Bolton Bailey. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bolton Bailey
-/
import analysis.special_functions.pow.real
/-!
# Logarithm Tonality
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR t... |
3c2f3ab0f684ffcf64e8a1593220ac1d3246d56c | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/ordmap/ordset.lean | 5d1e42de124e593e60d078d88fd2c00bdcb2cdee | [
"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 | 64,264 | 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.ordmap.ordnode
import algebra.ordered_ring
import data.nat.dist
import tactic.linarith
/-!
# Verification of the `ordnode α` datatype
This file proves t... |
fcffc76c138e58dd2fbdbcc6ca07a8e30ec1f52b | d1a52c3f208fa42c41df8278c3d280f075eb020c | /src/Init/Data/Random.lean | 84de67063d07a8a956cacf4716634ce11c2242a3 | [
"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 | 4,118 | 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.System.IO
import Init.Data.Int
universe u
/-
Basic random number generator support based on the one
available on the Haskell library
-/... |
b8e2f248b7cdea77655e866941fb4feec9bb8138 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/ring_theory/witt_vector/witt_polynomial.lean | 5d20e8308e910c6c362fbe2f37050b09be7450e0 | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 10,755 | 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... |
0a0303718ece2542dfe5b6ae93e2ce683651e529 | e00ea76a720126cf9f6d732ad6216b5b824d20a7 | /src/algebra/lie_algebra.lean | bceab4a880110d662b767b29ef0eb18b1fae792f | [
"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 | 17,314 | lean | /-
Copyright (c) 2019 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import ring_theory.algebra data.matrix.basic linear_algebra.linear_action
/-!
# Lie algebras
This file defines Lie rings, and Lie algebras over a commutative ring. It sho... |
81a3bf0358865f008a21e75fa7e923b335308700 | bb31430994044506fa42fd667e2d556327e18dfe | /src/topology/metric_space/hausdorff_dimension.lean | 28dd8e7a54eeb39c84d3d1af5cafc1949f9443e7 | [
"Apache-2.0"
] | permissive | sgouezel/mathlib | 0cb4e5335a2ba189fa7af96d83a377f83270e503 | 00638177efd1b2534fc5269363ebf42a7871df9a | refs/heads/master | 1,674,527,483,042 | 1,673,665,568,000 | 1,673,665,568,000 | 119,598,202 | 0 | 0 | null | 1,517,348,647,000 | 1,517,348,646,000 | null | UTF-8 | Lean | false | false | 22,834 | 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 measure_theory.measure.hausdorff
/-!
# Hausdorff dimension
The Hausdorff dimension of a set `X` in an (extended) metric space is the unique number
`dimH s ... |
7f5ce3c2639e29b7001a4d31aaa2467a70036db2 | bb31430994044506fa42fd667e2d556327e18dfe | /src/data/multiset/sort.lean | 648d975765165e9448765c32afb2e744c427d921 | [
"Apache-2.0"
] | permissive | sgouezel/mathlib | 0cb4e5335a2ba189fa7af96d83a377f83270e503 | 00638177efd1b2534fc5269363ebf42a7871df9a | refs/heads/master | 1,674,527,483,042 | 1,673,665,568,000 | 1,673,665,568,000 | 119,598,202 | 0 | 0 | null | 1,517,348,647,000 | 1,517,348,646,000 | null | UTF-8 | Lean | false | false | 1,667 | 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.sort
import data.multiset.basic
/-!
# Construct a sorted list from a multiset.
-/
namespace multiset
open list
variables {α : Type*}
section sort
... |
a9c91c72525350bb7661e65b3055c13383e24b6e | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/664.lean | 39951d3fb390f5b608f7d306e7dd26365f4f21c0 | [
"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 | 131 | lean | class A (α : Type _) where a : α → Unit
instance : A Empty where a x := nomatch x
def test : A Empty where a x := nomatch x
|
d63c23483e7a480b30980431ceb04c36a75c1dfc | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /src/Lean/MonadEnv.lean | be1e8aabf0ac3459d9445d1ee56e0e349c351871 | [
"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 | 8,664 | 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
import Lean.Exception
import Lean.Declaration
import Lean.Log
import Lean.Util.FindExpr
import Lean.AuxRecursor
import Lean.Compiler... |
d4e2a473bee7644c2d7be7ff54766f3802fa3f30 | 798dd332c1ad790518589a09bc82459fb12e5156 | /category_theory/functor.lean | cce1c904952903b7ff7ac8229fe78c5bcc42e347 | [
"Apache-2.0"
] | permissive | tobiasgrosser/mathlib | b040b7eb42d5942206149371cf92c61404de3c31 | 120635628368ec261e031cefc6d30e0304088b03 | refs/heads/master | 1,644,803,442,937 | 1,536,663,752,000 | 1,536,663,907,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,495 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tim Baumann, Stephen Morgan, Scott Morrison
Defines a functor between categories.
(As it is a 'bundled' object rather than the `is_functorial` typeclass parametrised
by the underlyin... |
e5f5a47a34e79c74f9fe06aa78dc0dba695c74da | b87641ffb6358d6508ccbfa54e67c87070cb28d8 | /cat/curve_geometr.lean | 91eaea6b7ca61068f11b490714d9c197a2546393 | [] | no_license | Nolrai/LeanGiggle | a4b628745ae3f5a36ae79b673ee8543e18ed4899 | 8326b2a6685b60a3529ee0fe26bd86f5d849b071 | refs/heads/master | 1,545,396,766,168 | 1,538,238,458,000 | 1,538,238,458,000 | 105,524,473 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,279 | lean |
open function
structure distinct (size : ℕ) (α : Type) : Type :=
(f : fin size → α)
(injective : injective f)
namespace distinct
section
parameter {size : ℕ}
parameter {α : Type}
definition to_set (d : distinct size α) : set α :=
λ a : α, ∃ i, d.f i = a
instance distinct_has_coe : has_coe (distinct size... |
f049f612c331f93c5ff2fc52bc4e109fd768c1ea | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/decidelet.lean | 6d1a965287790a75a65c86cc363edb01495f437f | [
"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 | 56 | lean | theorem ex : let x := 1; x < 2 := by
intro x
decide
|
9a3c19045749480040fff481ce7c8682dd23434f | fcf3ffa92a3847189ca669cb18b34ef6b2ec2859 | /src/world7/level8.lean | fa8f452c9610f061be3d0305383806025a3eb558 | [
"Apache-2.0"
] | permissive | nomoid/lean-proofs | 4a80a97888699dee42b092b7b959b22d9aa0c066 | b9f03a24623d1a1d111d6c2bbf53c617e2596d6a | refs/heads/master | 1,674,955,317,080 | 1,607,475,706,000 | 1,607,475,706,000 | 314,104,281 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 413 | lean | lemma and_or_distrib_left (P Q R : Prop) : P ∧ (Q ∨ R) → (P ∧ Q) ∨ (P ∧ R) :=
begin
intro pqr,
cases pqr with p qr,
cases qr with q r,
{
left,
split,
{
exact p,
},
{
exact q,
},
},
{
right,
split,
{
... |
dca018939c7428992941c7e5616e469c24ddfee4 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/blast_ematch_cast3.lean | 18af9d273799c38bb83cae7257e177d472ee5c54 | [
"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 | 365 | lean | import data.nat
open nat
constant C : nat → Type₁
constant f : ∀ n, C n → C n
constant g : ∀ n, C n → C n → C n
lemma gffax [forward] (n : nat) (a b : C n) : (: g n a b :) = a :=
sorry
set_option blast.strategy "ematch"
set_option trace.blast.ematch true
example (n m : nat) (a c : C n) (b : C m) (e : m = n) : a == ... |
8a27d11df26614522a4e4d3b6be14327f712cce0 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/tactic/alias_auto.lean | 41e9b2873ffe8daca82bd30e37e4306cc4c79e1c | [] | 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 | 857 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.Lean3Lib.data.buffer.parser
import Mathlib.tactic.core
import Mathlib.PostPort
namespace M... |
463994bf120ae223ee1a80422e86569a094552e5 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/combinatorics/composition.lean | b67cfdf21c48d3d6d3130053481f92aa0dc33dfb | [
"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 | 36,463 | lean | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import data.fintype.card
import data.finset.sort
import algebra.big_operators.order
/-!
# Compositions
A composition of a natural number `n` is a decompositio... |
f144948cb9dd00a6aada72616727996f34d6b4c9 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebraic_geometry/EllipticCurve.lean | 5208e75178cf37e6eb2fcb77c31354e2fcf06047 | [
"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 | 10,972 | lean | /-
Copyright (c) 2021 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, David Kurniadi Angdinata
-/
import algebra.cubic_discriminant
import tactic.linear_combination
/-!
# The category of elliptic curves (over a field or a PID)
We give a ... |
c0e28902db4ddb0051fc7cbcbf648fad5253b71b | cc104245380aa3287223e0e350a8319e583aba37 | /src/h0reviewed.lean | 20112fb815f6e135c36ebd6183f06974238aa9fb | [] | no_license | anca797/group-cohomology | 7d10749d28430d30698e7ec0cc33adbac97fe5e7 | f896dfa5057bd70c6fbb09ee6fdc26a7ffab5e5d | refs/heads/master | 1,591,037,800,699 | 1,561,424,571,000 | 1,561,424,571,000 | 190,891,710 | 3 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,907 | lean | import algebra.module group_theory.subgroup
class group_module (G : Type*) [group G] (M : Type*) [add_comm_group M] extends has_scalar G M :=
(one_smul : ∀ m : M, (1 : G) • m = m)
(smul_smul : ∀ g h : G, ∀ m : M, g • (h • m) = (g * h) • m)
(smul_add : ∀ g : G, ∀ m n : M, g • (m + n) = g • m + g • n)
namespace group_m... |
608c4c5326b60aec083da958c8f0f747f747325a | 4034f8da6f54c838133a7ab6a8c0c61086c9c949 | /src/bundles.lean | e8beee6c51ae23420ff356da1dd0db24dba516dd | [] | no_license | mguaypaq/lean-topology | f9e6c69e2b85cca1377ee89d75c65bd384225170 | 57b15b3862d441095e254e65009856fa922758cc | refs/heads/main | 1,691,451,271,943 | 1,631,647,691,000 | 1,631,647,691,000 | 398,682,545 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 17,916 | lean | import tactic
import .topology
import .gluing
import .fiber_product
section fiber_bundle
/-
Bundles.
Goal: Show that trivializations pull back.
We distinguish between:
1. *trivial bundles* : these are bundles of the form
prod.fst : B × fiber → B
2. *trivializations of bundles* : given π : E → B, this is ... |
00b779129576ec56db86f2680e34b79d1bce99ee | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/list/nodup_equiv_fin.lean | 33e18caebd13e0d313814d2938e3e735f0c32297 | [
"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 | 2,381 | 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 data.list.sort
import data.fin
/-!
# Isomorphism between `fin (length l)` and `{x // x ∈ l}`
Given a list `l,
* if `l` has no duplicates, then `list.... |
5adeec578ed381147c285d5dbe33509de5179309 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/data/polynomial/monomial.lean | 8fab24988a903d219754a8cb573b35fa1c461b94 | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 2,538 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Scott Morrison, Jens Wagemaker
-/
import data.polynomial.basic
/-!
# Univariate monomials
Preparatory lemmas for degree_basic.
-/
noncomputable theory
n... |
28128fc18ce50cd91116c41834bd02be322b9c9e | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/focus.lean | 2032cfa07daa76f9d8c6a162292e84318de7776d | [
"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 | 338 | lean | open nat
example (n m : ℕ) : n + m = m + n :=
begin
induction m with m IHm,
focus { induction n with n IHn,
focus { reflexivity },
focus { exact congr_arg succ IHn }},
focus { apply eq.trans (congr_arg succ IHm),
clear IHm, induction n with n IHn,
focus { reflexivity },
focus { exact congr_arg... |
fe69a10e9bf3fc3e8a9008a9bebd7dbe80b0fb20 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/676.lean | d3e8b2c3fcd1e4ea68875bcbf25d30776dfe2b71 | [
"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 | 185 | lean | import data.nat
open nat
inductive foo : Prop :=
mk : ∀ {a : nat}, a > 0 → foo
example (b : nat) (h : b > 1) : foo :=
begin
fconstructor,
exact b,
exact lt_of_succ_lt h
end
|
beba37c3979d187c61e261e230fe01a1258b5b5f | d9ed0fce1c218297bcba93e046cb4e79c83c3af8 | /library/tools/super/splitting.lean | ccca05ada8f6976cac3afddeca77636a8192a39d | [
"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 | 2,716 | 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 .prover_state
open monad expr list tactic
namespace super
private meta def find_components : list expr → list (list (expr × ℕ)) → list (list (expr × ℕ))
| (e::... |
b8a87543d66abec648a2e28d99f030a894104f92 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/analysis/specific_limits.lean | e2a762dad8f655113d5e2b50a381fedcac150099 | [
"Apache-2.0"
] | permissive | stjordanis/mathlib | 51e286d19140e3788ef2c470bc7b953e4991f0c9 | 2568d41bca08f5d6bf39d915434c8447e21f42ee | refs/heads/master | 1,631,748,053,501 | 1,627,938,886,000 | 1,627,938,886,000 | 228,728,358 | 0 | 0 | Apache-2.0 | 1,576,630,588,000 | 1,576,630,587,000 | null | UTF-8 | Lean | false | false | 41,798 | 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.geom_sum
import analysis.asymptotics.asymptotics
import order.filter.archimedean
import order.iterate
import topology.instances.ennreal
/-!
# A collec... |
62d9b849b94f0d0c5aa988aa420281d300658594 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/group_theory/free_abelian_group.lean | 5718d236f50cffccdbec9ad5863ebe5c698e4113 | [
"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 | 19,479 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import algebra.group.pi
import group_theory.free_group
import group_theory.abelianization
import algebra.module.basic -- we use the ℤ-module structure on an add_comm_group in ... |
4b84a14914c1d19a741d2b18f3d327604038e142 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/topology/instances/ennreal.lean | ce2e438aba1692b16880965d5ddb32dcf778c5a7 | [
"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 | 67,407 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import topology.instances.nnreal
import topology.algebra.order.monotone_continuity
import analysis.normed.group.basic
/-!
# Extended non-negative reals
-/
noncomputa... |
49687db0be1981ef296f38d2167c8d89e20553c9 | 1dd482be3f611941db7801003235dc84147ec60a | /src/order/filter/basic.lean | 98941dee6d86976f10ce0a52b7a4b11a6676c450 | [
"Apache-2.0"
] | permissive | sanderdahmen/mathlib | 479039302bd66434bb5672c2a4cecf8d69981458 | 8f0eae75cd2d8b7a083cf935666fcce4565df076 | refs/heads/master | 1,587,491,322,775 | 1,549,672,060,000 | 1,549,672,060,000 | 169,748,224 | 0 | 0 | Apache-2.0 | 1,549,636,694,000 | 1,549,636,694,000 | null | UTF-8 | Lean | false | false | 93,964 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jeremy Avigad
Theory of filters on sets.
-/
import order.galois_connection order.zorn
import data.set.finite data.list data.pfun
import algebra.pi_instances
import cat... |
cf4cc218fec16f3744e46fc90e1d4204e90c4fbd | 94e33a31faa76775069b071adea97e86e218a8ee | /src/topology/sheaves/stalks.lean | 7199ba7708cd256cb6edc279b5867c2015682c8c | [
"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 | 24,393 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Justus Springer
-/
import topology.category.Top.open_nhds
import topology.sheaves.presheaf
import topology.sheaves.sheaf_condition.unique_gluing
import category_theory.... |
1eb44e35a1b6724d3b378f4e1087f7abf59ae5f3 | 968e2f50b755d3048175f176376eff7139e9df70 | /examples/prop_logic_theory/unnamed_650.lean | ae67021fc49836c58f911bcfd3caac02e2b7efc4 | [] | no_license | gihanmarasingha/mth1001_sphinx | 190a003269ba5e54717b448302a27ca26e31d491 | 05126586cbf5786e521be1ea2ef5b4ba3c44e74a | refs/heads/master | 1,672,913,933,677 | 1,604,516,583,000 | 1,604,516,583,000 | 309,245,750 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 203 | lean | variables p q r : Prop
-- BEGIN
example (h₁ : p ∧ q → r) (h₂ : p) (h₃ : q) : r :=
begin
apply h₁, -- By implication elimination on `h₁`, it suffices to prove `p ∧ q`.
sorry
end
-- END |
cecae6fd6a7a0bfa7666b3f624cd4dd97d6766c3 | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /tests/lean/newfrontend/t1.lean | 50ecb9dc2e47a9a89b0fa88c27caa60b84f1233c | [
"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 | 57 | lean | variable {α : Type}
def f (a : α) : α := a
#check f 1
|
265f9379c080ff2b125a39ea5f0a5ebfbf74fb11 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/linear_algebra/prod.lean | 887fba718abff34285ab2dc0c29c2ad10f5adf9c | [
"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 | 25,818 | 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.basic
import order.partial_sups
/-! ### Products of modules
This file defines con... |
8a572eeecc137e17064cfd2166cea89aa2b96f4b | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/algebra/category/Mon/adjunctions.lean | 8d81c9e599cfba4f9163a35036b7678ad527491b | [
"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 | 2,262 | lean | /-
Copyright (c) 2021 Julian Kuelshammer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Kuelshammer
-/
import algebra.category.Mon.basic
import algebra.category.Semigroup.basic
import algebra.group.with_one
import algebra.free_monoid
/-!
# Adjunctions regardin... |
479e82cdf4b9c951eddd21b7f9b1fc0cad75f03a | f47872278edfa65030d6cd0604480581b09ae4b5 | /src/ordered/dimality.lean | de8b6ad8504fc47e14e5a79d85db73fd940129e0 | [
"MIT"
] | permissive | ocornoc/geodude | c822c494d9ed5d6dd2efa434cbaa5e0e42c22691 | e63c87db67f1686c902e9bcd1863e74e1a29457f | refs/heads/master | 1,681,951,483,388 | 1,620,592,363,000 | 1,620,595,412,000 | 287,442,904 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,279 | lean | import .convex set_theory.cardinal order.well_founded set_theory.cardinal_ordinal
open_locale cardinal
section
universe u
parameters {α : Type u} [has_betweenness α]
@[reducible]
def generates (b : set α) (s : set α) (h : is_affine s) : Prop :=
affine_hull b = s
theorem generates.of_span {s : set α} (h : is_affine ... |
14f5b466d96e4d936d855ccfe6e26f682f5b6da4 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/category_theory/limits/shapes/constructions/binary_products.lean | db9d17bacbde0814ef634b60d8249d5c264f8fa2 | [
"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 | 1,638 | lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import category_theory.limits.shapes.terminal
import category_theory.limits.shapes.pullbacks
import category_theory.limits.shapes.binary_products
universes v u
/-!
# Co... |
875ef5b74733dff8ee048a938beb542bf399c194 | 9c1ad797ec8a5eddb37d34806c543602d9a6bf70 | /monoidal_categories/tensor_with_object.lean | 0ec31e69cf2d7faa588a5bfa972b232c44184347 | [] | no_license | timjb/lean-category-theory | 816eefc3a0582c22c05f4ee1c57ed04e57c0982f | 12916cce261d08bb8740bc85e0175b75fb2a60f4 | refs/heads/master | 1,611,078,926,765 | 1,492,080,000,000 | 1,492,080,000,000 | 88,348,246 | 0 | 0 | null | 1,492,262,499,000 | 1,492,262,498,000 | null | UTF-8 | Lean | false | false | 1,364 | 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 .monoidal_category
open tqft.categories
open tqft.categories.functor
open tqft.categories.products
open tqft.categories.natural_transformat... |
63985e5743f6b3da86feb3ec2a0c6f56ebbdc36e | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/number_theory/cyclotomic/basic.lean | 027d406fad74718e2c4a3e5bda02ac6c1b499c96 | [
"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 | 31,940 | lean | /-
Copyright (c) 2021 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca
-/
import ring_theory.polynomial.cyclotomic.basic
import number_theory.number_field.basic
import algebra.char_p.algebra
import field_theory.galois
/-!
# Cyclotomic e... |
62ef7bd40a209484c4dd4f0114d9f096fe2eb1c5 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebraic_topology/dold_kan/homotopies.lean | 5bc1fd2472a283946e834fa863e5bbb6a127bc8b | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 8,038 | lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import algebra.homology.homotopy
import algebraic_topology.dold_kan.notations
/-!
# Construction of homotopies for the Dold-Kan correspondence
TODO (@joelriou) continue add... |
903be65f059d602ff6ff75aa18e31af9d5d40f2a | 0d9b0a832bc57849732c5bd008a7a142f7e49656 | /src/XSokoban_90_l1_dl.lean | 48c3e84a8a59851c91780bd7d5344d04b34d3905 | [] | no_license | mirefek/sokoban.lean | bb9414af67894e4d8ce75f8c8d7031df02d371d0 | 451c92308afb4d3f8e566594b9751286f93b899b | refs/heads/master | 1,681,025,245,267 | 1,618,997,832,000 | 1,618,997,832,000 | 359,491,681 | 10 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 12,941 | lean | -- Deadlocks: var/XSokoban_90_l1/deadlocks
-- Levelset: data/Large Test Suite Sets/XSokoban_90.xsb
-- Level: 1
import .deadlocks
def XSokoban_90_l1 := sokolevel.from_string "
#####
# #
#$ #
### $##
# $ $ #
### # ## # ######
# # ## ##### ..#
# $... |
0f1323b2ac8f54724330f9f1f47906c184664eac | 54d7e71c3616d331b2ec3845d31deb08f3ff1dea | /tests/lean/elab1.lean | 1649dc47a627cef995aa1cacd47ecef6a5034a84 | [
"Apache-2.0"
] | permissive | pachugupta/lean | 6f3305c4292288311cc4ab4550060b17d49ffb1d | 0d02136a09ac4cf27b5c88361750e38e1f485a1a | refs/heads/master | 1,611,110,653,606 | 1,493,130,117,000 | 1,493,167,649,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 381 | lean | definition foo.subst := @eq.subst
definition boo.subst := @eq.subst
definition foo.add := @add
definition boo.add := @add
set_option pp.all true
open foo boo
#print raw subst -- subst is overloaded
#print raw add -- add is overloaded
#check @subst
#check @@subst
open eq
#check subst
constants a b : nat
consta... |
9dc58d896b9e39112a1dbcaa677cc3dce97d9505 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/playground/expander.lean | ee021238dda7b62f45e0eafdde78ea7c139589fd | [
"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 | 1,617 | lean | import init.lean.expander
open Lean
open Lean.Parser
open Lean.Expander
def prof {α : Type} (msg : String) (p : IO α) : IO α :=
let msg₁ := "Time for '" ++ msg ++ "':" in
let msg₂ := "Memory usage for '" ++ msg ++ "':" in
allocprof msg₂ (timeit msg₁ p)
def node : SyntaxNodeKind := ⟨`node⟩
def leaf : SyntaxNodeKind :... |
1cf8fc5ef72abaeb6c1e769007fbf03f5358224b | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/group_theory/schreier.lean | bf5b797a3e06ad389c95b9d4a8da84ad883c3fda | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 6,702 | 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 data.finset.pointwise
import group_theory.complement
import group_theory.finiteness
import group_theory.index
import tactic.group
/-!
# Schreier's Lemma
I... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.