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2b80f7024436386b61dfb776a84a44ff46f33270 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/string_imp2.lean | 6a41f7eceaecfb322c36755a48aacb9a8be68460 | [
"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 | 2,722 | lean | def f (s : string) : string :=
s ++ " " ++ s
def g (s : string) : string :=
s.push ' ' ++ s.push '-'
def h (s : string) : string :=
let it₁ := s.mk_iterator in
let it₂ := it₁.next in
it₁.next_to_string ++ "-" ++ it₂.next_to_string
def r (s : string) : string :=
let it₁ := s.mk_iterator.to_end in
let it₂ := it₁.prev ... |
a89beb8bfd962121007ff34a5f2a337bc37ade9d | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/linear_algebra/std_basis.lean | 8faf05b3608cd72ec2eea4be2ab35db6a500e59c | [
"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 | 10,387 | 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 linear_algebra.basis
import linear_algebra.pi
import data.matrix.basis
/-!
# The standard basis
This file defines the standard basis `std_basis R φ i b j`, w... |
90eeee0a25d008cb9dd8cc06570b9c3b8815ff79 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/category_theory/limits/lattice.lean | f6c4ddf0591068bb0823233d5f8e77066c1b6a4a | [
"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 | 8,725 | 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 order.complete_lattice
import data.fintype.lattice
import category_theory.limits.shapes.pullbacks
import category_theory.category.preorder
imp... |
43ecc9f12540f5e48eb82a2b6b79e56cf66f887a | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /03_Propositions_and_Proofs.org.4.lean | fd53a2b0a6de835b3b21f8f8098032ce92a9e945 | [] | 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 | 232 | lean | /- page 33 -/
import standard
namespace hide
constant implies : Prop → Prop → Prop
constant Proof : Prop → Type
-- BEGIN
constant implies_intro (p q : Prop) : (Proof p → Proof q) → Proof (implies p q).
-- END
end hide
|
661782887a03e66083b0d2fdeb03421946d21369 | 367134ba5a65885e863bdc4507601606690974c1 | /src/ring_theory/jacobson_ideal.lean | ae36f6d5071065cacb89c0314cf954ce258513be | [
"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 | 14,422 | lean | /-
Copyright (c) 2020 Devon Tuma. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Devon Tuma
-/
import ring_theory.ideal.operations
import ring_theory.polynomial.basic
/-!
# Jacobson radical
The Jacobson radical of a ring `R` is defined to be the intersecti... |
d1638e21d3c45799e0009048afae85caac3dd0e9 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/algebraic_geometry/presheafed_space.lean | 9285971acbb683ad87c66048a566ebf200129651 | [
"Apache-2.0"
] | permissive | rmitta/mathlib | 8d90aee30b4db2b013e01f62c33f297d7e64a43d | 883d974b608845bad30ae19e27e33c285200bf84 | refs/heads/master | 1,585,776,832,544 | 1,576,874,096,000 | 1,576,874,096,000 | 153,663,165 | 0 | 2 | Apache-2.0 | 1,544,806,490,000 | 1,539,884,365,000 | Lean | UTF-8 | Lean | false | false | 7,600 | 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 topology.sheaves.presheaf
/-!
# Presheafed spaces
Introduces the category of topological spaces equipped with a presheaf (taking values in an
arbitrary targe... |
1655570a97bedf0aedcb02859cf8ffa139c13620 | e00ea76a720126cf9f6d732ad6216b5b824d20a7 | /src/data/monoid_algebra.lean | 567f888f69a5c9c472dc3aa288b6ad9278879acc | [
"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 | 10,416 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Scott Morrison
-/
import data.finsupp
/-!
# Monoid algebras
When the domain of a `finsupp` has a multiplicative or additive structure, we can define
a convolution pro... |
9f3a26eba974389f86a6c29a5d3cce5a9281836f | 618003631150032a5676f229d13a079ac875ff77 | /src/tactic/abel.lean | 95ceadf93e28c5fce49c57b03a98741327691aab | [
"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 | 13,107 | 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 tactic.norm_num
/-!
# The `abel` tactic
Evaluate expressions in the language of additive, commutative monoids and groups.
-/
namespace tactic
namespace ab... |
ca5fff31b7aa986e440d214294826dc6d5cbb1a8 | dac4e6671410f506c880986cbb2212dd7f5b3dfd | /folklore/metric.lean | 70fd8d73f8a6acfa3b8fa44fae62c22e35081c98 | [
"CC-BY-4.0"
] | permissive | thalesant/formalabstracts-2018 | e6ddfe8b3ce5c6f055ddcccf345bf55c41f850c1 | d206dfa32a6b4a84aacc3a5500a144757e6d3454 | refs/heads/master | 1,642,678,879,231 | 1,561,648,713,000 | 1,561,648,713,000 | 97,608,420 | 1 | 0 | null | 1,564,063,995,000 | 1,500,388,250,000 | Lean | UTF-8 | Lean | false | false | 9,780 | lean | /-
Metric Spaces.
The starting point was the HOL Light library, but many changes
and additions have been made.
-/
import order.filter data.set meta_data data.list data.vector
topology.topological_space topology.real
.complex -- .measure_theory
noncomputable theory
namespace metric
open set filte... |
45c60e41082b4e17191bf8381787f613837613de | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/data/equiv/mul_add_aut.lean | f8b87b8442fd2b44fb2cfbe621e579adbe35224d | [
"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 | 7,304 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Callum Sutton, Yury Kudryashov
-/
import group_theory.perm.basic
/-!
# Multiplicative and additive group automorphisms
This file defines the automorphism group struct... |
612d63612192170b02b08ec7f2028064962e9473 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/pp_unit.lean | 5468cb6c8df49fddf53c7ef1e4ce4c5a75c17519 | [
"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 | 60 | lean | #check unit.star
#check ()
set_option pp.all true
#check ()
|
427b2b2175c94a157c41163a79ed76fb906d5e2f | 7b02c598aa57070b4cf4fbfe2416d0479220187f | /pointed.hlean | 8f1ea827f21b8604db17fe455a49a6a67eea687f | [
"Apache-2.0"
] | permissive | jdchristensen/Spectral | 50d4f0ddaea1484d215ef74be951da6549de221d | 6ded2b94d7ae07c4098d96a68f80a9cd3d433eb8 | refs/heads/master | 1,611,555,010,649 | 1,496,724,191,000 | 1,496,724,191,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,483 | hlean | /- equalities between pointed homotopies and other facts about pointed types/functions/homotopies -/
-- Author: Floris van Doorn
import types.pointed2
open pointed eq equiv function is_equiv unit is_trunc trunc nat algebra sigma group
namespace pointed
-- /- the pointed type of (unpointed) dependent maps -/
--... |
23d3190d8b8a253c423f7b4ec46dd61d7b9ebcfd | c777c32c8e484e195053731103c5e52af26a25d1 | /src/algebra/star/basic.lean | 9b18517de2d79dccd3890a0bccb70c1d9554312f | [
"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 | 20,205 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import algebra.ring.aut
import algebra.ring.comp_typeclasses
import data.rat.cast
import group_theory.group_action.opposite
import data.set_like.basic
/-!
# Star mon... |
8cea8163ab11febaf6e3f395b74d798e1741663d | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/limits/comma.lean | f687492af07778cbdf0fd27a1b2ca51d617cd6a8 | [
"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 | 10,365 | lean | /-
Copyright (c) 2021 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import category_theory.arrow
import category_theory.limits.constructions.epi_mono
import category_theory.limits.creates
import category_theory.limits.unit
import category... |
1885386734686766348a9869a3106fc34f4c6b60 | 1abd1ed12aa68b375cdef28959f39531c6e95b84 | /src/order/liminf_limsup.lean | 882711e2a1fbd2d10cb66069bda7755768aecc34 | [
"Apache-2.0"
] | permissive | jumpy4/mathlib | d3829e75173012833e9f15ac16e481e17596de0f | af36f1a35f279f0e5b3c2a77647c6bf2cfd51a13 | refs/heads/master | 1,693,508,842,818 | 1,636,203,271,000 | 1,636,203,271,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 24,819 | lean | /-
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Johannes Hölzl, Rémy Degenne
-/
import order.filter.partial
import order.filter.at_top_bot
/-!
# liminfs and limsups of functions and filters
Defines the Liminf... |
4d1849185c094797c7be3d55d60408dcc9d0491c | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/monad_univ_lift.lean | b88516a82a7b3d49755c2dd39bacfed4d545e0d0 | [
"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 | 464 | lean | universe variables u v
def M : Type u → Type v :=
sorry
instance : monad M :=
sorry
def act1 : M unit :=
return ()
def act2 : M (Σ (A : Type), A) :=
return ⟨nat, 0⟩
def {t s} up {A : Type s} (a : M A) : M (ulift.{t} A) :=
sorry
def {t s} down {A : Type s} (a : M (ulift.{t} A)) : M A :=
sorry
prefix (name := up)... |
493b6ccac6d2555525857be35f5619cadc353332 | c777c32c8e484e195053731103c5e52af26a25d1 | /counterexamples/homogeneous_prime_not_prime.lean | 8692774542313b1fd1fb6a9f1b99f1c184bfa7db | [
"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 | 5,651 | lean | /-
Copyright (c) 2022 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Eric Wieser, Jujian Zhang
-/
import ring_theory.graded_algebra.homogeneous_ideal
import data.zmod.basic
import tactic.derive_fintype
/-!
# A homogeneous prime that is ho... |
6372bcdc696b58456b953ec4dc5d900fbd94320e | c3f2fcd060adfa2ca29f924839d2d925e8f2c685 | /tests/lean/run/t11.lean | 80e4051815cbca3f3d44b5a2d29900e1387b36a3 | [
"Apache-2.0"
] | permissive | respu/lean | 6582d19a2f2838a28ecd2b3c6f81c32d07b5341d | 8c76419c60b63d0d9f7bc04ebb0b99812d0ec654 | refs/heads/master | 1,610,882,451,231 | 1,427,747,084,000 | 1,427,747,429,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 266 | lean | constant A : Type.{1}
constants a b c : A
constant f : A → A → A
check f a b
context
parameters A B : Type
parameters {C D : Type}
parameters [e d : A]
check A
check B
definition g (a : A) (b : B) (c : C) : A := e
end
check g.{2 1}
constants x y : A
|
73f86510f084b80158294ab0a2942f339633af90 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/matrix/invertible.lean | b7ab93f0e6d2fec99375f6ef484296a3838e4f4e | [
"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 | 4,097 | lean | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import algebra.invertible
import data.matrix.basic
/-! # Extra lemmas about invertible matrices
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file requ... |
63520bc340c6ecb64e729babd82d20e0d62f9020 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/category_theory/sites/compatible_plus.lean | bb82c2ad7f30856644ec7d581d084a6ac40c3990 | [
"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 | 8,738 | lean | /-
Copyright (c) 2021 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz
-/
import category_theory.sites.sheafification
import category_theory.sites.whiskering
/-!
In this file, we prove that the plus functor is compatible with functors which
prese... |
16a6d1d3e8d9129b25046637c1c08788c5b760fb | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /src/Std/Data/HashSet.lean | 108b42576bd352c71f4f4516a21c92417f348e5b | [
"Apache-2.0"
] | permissive | collares/lean4 | 861a9269c4592bce49b71059e232ff0bfe4594cc | 52a4f535d853a2c7c7eea5fee8a4fa04c682c1ee | refs/heads/master | 1,691,419,031,324 | 1,618,678,138,000 | 1,618,678,138,000 | 358,989,750 | 0 | 0 | Apache-2.0 | 1,618,696,333,000 | 1,618,696,333,000 | null | UTF-8 | Lean | false | false | 6,063 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
namespace Std
universes u v w
def HashSetBucket (α : Type u) :=
{ b : Array (List α) // b.size > 0 }
def HashSetBucket.update {α : Type u} (data : HashSe... |
06631f1c4ab4678a657f94d351824d0feaf64530 | 2a70b774d16dbdf5a533432ee0ebab6838df0948 | /src/modal-logic.lean | 843bb81488bfeb0052c11c7a33e7f61ffbd62309 | [] | no_license | 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 | 8,221 | lean | /-
Copyright (c) 2023 Huub Vromen. All rights reserved.
Author: Huub Vromen
-/
import data.finset.basic
-- # Modal propositional logic
/- First, we define some not previously defined properties of relations that we will use later on -/
variable {α : Type}
def euclidean (r: α → α → Prop) : Prop := ∀a b c, r a b... |
ab072f40c70edac8c5af335fe8e15b918ca87def | 592ee40978ac7604005a4e0d35bbc4b467389241 | /Library/generated/mathscheme-lean/PrimAdditiveGroup.lean | 4c39ad390a3ff39d940eb07137f2a1c3a36ef19d | [] | 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 | 10,768 | 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 PrimAdditiveGroup
structure PrimAdditiveGroup (A : Type) : Type :=
(zero_ : A)
(times_ : (A → (A → A)))
(lunit_zero_ : (∀ {x : A} , (times_ zero_ x) = x)... |
2d3db8c68b497632e656761d51300c0145e50abe | 80746c6dba6a866de5431094bf9f8f841b043d77 | /src/topology/instances/ennreal.lean | 89ed85c1bf23eb4721c21a96e1dd61c7e6f82169 | [
"Apache-2.0"
] | permissive | leanprover-fork/mathlib-backup | 8b5c95c535b148fca858f7e8db75a76252e32987 | 0eb9db6a1a8a605f0cf9e33873d0450f9f0ae9b0 | refs/heads/master | 1,585,156,056,139 | 1,548,864,430,000 | 1,548,864,438,000 | 143,964,213 | 0 | 0 | Apache-2.0 | 1,550,795,966,000 | 1,533,705,322,000 | Lean | UTF-8 | Lean | false | false | 27,210 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl
Extended non-negative reals
-/
import topology.instances.nnreal data.real.ennreal
noncomputable theory
open classical set lattice filter metric
local attribute [instance... |
c48fd22ee3f01dfee31b26ed262364a28dd45b1f | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/algebra/continued_fractions/computation/basic_auto.lean | 0813f309f2021224d3d81e685346d68a0769a7ed | [] | 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 | 7,608 | lean | /-
Copyright (c) 2020 Kevin Kappelmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebra.continued_fractions.basic
import Mathlib.algebra.ordered_field
import Mathlib.a... |
f52c02ce64606ddf832e5cc006b5faea6871a66e | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/analysis/normed/group/infinite_sum.lean | 29cb794586107e11e14a6cb7e18ca3c3b3cb3cf9 | [
"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 | 8,522 | lean | /-
Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Heather Macbeth, Johannes Hölzl, Yury Kudryashov
-/
import analysis.normed.group.basic
import topology.instances.nnreal
/-!
# Infinite sums in (semi)normed group... |
98dae7a3151c2ddd23165b878fa11796424e30f2 | 82b86ba2ae0d5aed0f01f49c46db5afec0eb2bd7 | /stage0/src/Lean/Elab/PreDefinition/Basic.lean | 77de270d4b561342f3f1b72bd16af2be0f75e754 | [
"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 | 6,578 | 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.Util.SCC
import Lean.Meta.AbstractNestedProofs
import Lean.Elab.Term
import Lean.Elab.DefView
import Lean.Elab.PreDefinition.MkInhabitant
names... |
cdbc4f3238c6368a7e207f0595f559705f4a1c94 | ae1e94c332e17c7dc7051ce976d5a9eebe7ab8a5 | /src/Lean/Meta/AppBuilder.lean | 8513ddfe9a76e6e01d336322a204a548e8113d85 | [
"Apache-2.0"
] | permissive | dupuisf/lean4 | d082d13b01243e1de29ae680eefb476961221eef | 6a39c65bd28eb0e28c3870188f348c8914502718 | refs/heads/master | 1,676,948,755,391 | 1,610,665,114,000 | 1,610,665,114,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 16,911 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Structure
import Lean.Util.Recognizers
import Lean.Meta.SynthInstance
import Lean.Meta.Check
namespace Lean.Meta
/-- Return `id e` -/
def mkId... |
910a2906be9b4030e62c18a5d0f5cea08309cb9b | 3dc4623269159d02a444fe898d33e8c7e7e9461b | /.github/workflows/project_1_a_decrire/lean-scheme-submission/src/spectrum_of_a_ring/structure_sheaf_condition.lean | 6ce384bf05f23bcd16abd72969fe393d807d558c | [] | 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 | 13,763 | lean | /-
If (fᵢ) = R, the sequene R → Π R[1/fᵢ] → Π R[1/fᵢfⱼ] is exact.
https://stacks.math.columbia.edu/tag/00EJ
TODO : Factor out all the finset sum lemmas and clean up the main proof.
-/
import ring_theory.localization
import algebra.pi_instances
import linear_algebra.finsupp
import to_mathlib.localization.locali... |
7bdc3f48c11017d7dd868c6b9b3e06339a8d36b6 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/set_theory/pgame.lean | 7a09573125ce414fafdf62a84be22f96006fecd3 | [
"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 | 43,065 | lean | /-
Copyright (c) 2019 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Mario Carneiro, Isabel Longbottom, Scott Morrison
-/
import data.fin.basic
import data.nat.cast
import logic.embedding
/-!
# Combinatorial (pre-)games.
The basic theory ... |
123e3ee0ca5deedad622f4f42b7bc8110b111156 | 31f556cdeb9239ffc2fad8f905e33987ff4feab9 | /stage0/src/Lean/Compiler/LCNF/AlphaEqv.lean | 01c477528661da9e2c7ae1bc5b31c5b876c43331 | [
"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 | tobiasgrosser/lean4 | ce0fd9cca0feba1100656679bf41f0bffdbabb71 | ebdbdc10436a4d9d6b66acf78aae7a23f5bd073f | refs/heads/master | 1,673,103,412,948 | 1,664,930,501,000 | 1,664,930,501,000 | 186,870,185 | 0 | 0 | Apache-2.0 | 1,665,129,237,000 | 1,557,939,901,000 | Lean | UTF-8 | Lean | false | false | 4,009 | lean | /-
Copyright (c) 2022 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Compiler.LCNF.Basic
namespace Lean.Compiler.LCNF
/-!
Alpha equivalence for LCNF Code
-/
namespace AlphaEqv
abbrev EqvM := ReaderM (FVarIdMap... |
bd7a9b6f4b0f942fc4d2a83342d31ad18f514f05 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/int/cast/defs.lean | 2579953147c047a1f3ce5652e2b8acacf3243c80 | [
"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 | 2,452 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Gabriel Ebner
-/
import data.nat.cast.defs
/-!
# Cast of integers
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> https://github.com/leanprover-community/mathlib4/pull/6... |
905141ea210a17949bbb93157af2447a55d6b9e6 | 3bd26f8e9c7eeb6ae77ac4ba709b5b3c65b8d7cf | /ack_is_not_prim_rec.lean | 9f79ab9debf7f8e749ae4102a8f9b09ae52778ee | [] | no_license | koba-e964/lean-work | afac5677efef6905fce29cac44f36f309c3bcd62 | 6ab0506b9bd4e5a2e1ba6312d4ac6bdaf6ae1594 | refs/heads/master | 1,659,773,150,740 | 1,659,289,453,000 | 1,659,289,453,000 | 100,273,655 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 11,863 | lean | import .ack .prim_rec
def sum_of_fin: forall {n}, (fin n -> nat) -> nat
| 0 _ := 0
| (n' + 1) ls := sum_of_fin (fun i, ls (fin.succ i)) + ls 0
lemma sum_of_fin_ge_arg : forall n, forall tuple: fin n -> nat, forall i: fin n,
sum_of_fin tuple >= tuple i :=
fun n tuple i,
begin
induction n with n' ih_1,
show sum... |
f5179da93de66e51a53d40e066aa7a0224783d21 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/measure_theory/function/convergence_in_measure.lean | 823d8e060d4c400c1fbb2d10e664afc33fe18b5c | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 17,071 | lean | /-
Copyright (c) 2022 Rémy Degenne, Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Kexing Ying
-/
import analysis.special_functions.pow.real
import measure_theory.function.egorov
import measure_theory.function.lp_space
/-!
# Convergence in m... |
1f5dfed9f8d3cc2f0ce134fb56a7f49b86a33e98 | e8159fb1a58abf09f7d75106ba3aa6c1c504c038 | /theorem-proving-in-lean/2.10.4 matrix.lean | d3bd5cb4956758080d08fc1ccde6c538f6767d08 | [] | no_license | ndcroos/lean-snippets | cbf53e777a72964b6875a8c98bdd7eb02e74e246 | b66736347cd80a4143e43397f359dbdf9cbcd491 | refs/heads/master | 1,584,160,922,314 | 1,525,542,053,000 | 1,525,542,053,000 | 131,447,243 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 692 | lean | /-
Similarly, declare a constant matrix so that matrix α m n could represent the type of m by n matrices.
Declare some constants to represent functions on this type, such as matrix addition and multiplication, and (using vec) multiplication of a matrix by a vector. Once again, declare some variables and check some exp... |
a780f75532f1a1bf7cd1da9961c8cd620c78dd20 | 77c5b91fae1b966ddd1db969ba37b6f0e4901e88 | /src/data/matrix/notation.lean | 859e6f8cea99a594ce90a7ad25a169d483993b8c | [
"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 | 18,754 | 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.fintype.card
import data.matrix.basic
import tactic.fin_cases
/-!
# Matrix and vector notation
This file defines notation for vectors and matrices. Given `a ... |
fc650ce62e0de6da21bfce4c6e4e4b3b3fb0689e | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/group_theory/group_action/basic.lean | dcd0d478b0309dfa8e2d3c64fd026a9822a8b6b1 | [
"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 | 23,071 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import group_theory.group_action.defs
import group_theory.group_action.group
import group_theory.quotient_group
import data.setoid.basic
import data.fintype.card
/-!
# B... |
c4b0f4431e63b85331282570cc11319b27d50262 | 682dc1c167e5900ba3168b89700ae1cf501cfa29 | /src/del/semantics/semanticsDEL.lean | edc84dc0f39809819c081ee450779eac37da7708 | [] | no_license | paulaneeley/modal | 834558c87f55cdd6d8a29bb46c12f4d1de3239bc | ee5d149d4ecb337005b850bddf4453e56a5daf04 | refs/heads/master | 1,675,911,819,093 | 1,609,785,144,000 | 1,609,785,144,000 | 270,388,715 | 13 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 7,348 | lean | /-
Copyright (c) 2021 Paula Neeley. All rights reserved.
Author: Paula Neeley
Following the textbook "Dynamic Epistemic Logic" by
Hans van Ditmarsch, Wiebe van der Hoek, and Barteld Kooi
-/
import del.languageDEL del.syntax.syntaxDEL data.set.basic
import del.semantics.translationfunction
local attribute [instance] ... |
f58604a845b9cffe660f5e3fe01c2769393a0650 | 46125763b4dbf50619e8846a1371029346f4c3db | /src/tactic/lint.lean | f9011b2bf5c58480a9740628409abf3362741908 | [
"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 | 44,842 | lean | /-
Copyright (c) 2019 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Robert Y. Lewis
-/
import tactic.core
/-!
# lint command
This file defines the following user commands to spot common mistakes in the code.
* `#lint`: check all dec... |
579ffdda77dde9566b10cf8bc2210cbd12a65818 | da3a76c514d38801bae19e8a9e496dc31f8e5866 | /library/init/meta/contradiction_tactic.lean | 2df0102393030fd7cc72ff7d723e8d49c9d52163 | [
"Apache-2.0"
] | permissive | cipher1024/lean | 270c1ac5781e6aee12f5c8d720d267563a164beb | f5cbdff8932dd30c6dd8eec68f3059393b4f8b3a | refs/heads/master | 1,611,223,459,029 | 1,487,566,573,000 | 1,487,566,573,000 | 83,356,543 | 0 | 0 | null | 1,488,229,336,000 | 1,488,229,336,000 | null | UTF-8 | Lean | false | false | 2,625 | 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.function
namespace tactic
open expr tactic decidable environment
private meta def contra_p_not_p : list expr → list ... |
6d61817892e1a3772c233b6787189c3656ec583c | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/category_theory/full_subcategory.lean | be4212e392249bcdb93662c16603914d6d10c6bf | [
"Apache-2.0"
] | permissive | agjftucker/mathlib | d634cd0d5256b6325e3c55bb7fb2403548371707 | 87fe50de17b00af533f72a102d0adefe4a2285e8 | refs/heads/master | 1,625,378,131,941 | 1,599,166,526,000 | 1,599,166,526,000 | 160,748,509 | 0 | 0 | Apache-2.0 | 1,544,141,789,000 | 1,544,141,789,000 | null | UTF-8 | Lean | false | false | 3,814 | 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.groupoid
namespace category_theory
universes v u₁ u₂ -- declare the `v`'s first; see `category_theory.category` for an explanati... |
36690d84249099d72c8543b8755909ad770721c1 | cb3da1b91380e7462b579b426a278072c688954a | /src/wspace.lean | 47b7d63724129fd20ecad1189e300e5376e3161c | [] | no_license | hcheval/tikhonov-mann | 35c93e46a8287f6479a848a9d4f02013e0bc2035 | 6ab7fcefe9e1156c20bd5d1998a7deabd1eeb018 | refs/heads/master | 1,689,232,126,344 | 1,630,182,255,000 | 1,630,182,255,000 | 399,859,996 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,861 | lean | import data.real.basic
import topology.metric_space.basic
import tactic
class has_wmap (α : Type*) :=
(wmap : ℝ → α → α → α)
export has_wmap (wmap)
instance : has_wmap ℝ :=
⟨λ a x y, (1 - a) * x + a * y⟩
class whyperbolic_space (X : Type*) extends has_wmap X, metric_space X :=
(dist_conv : ∀ {a : ℝ} (x y z : X), 0 ... |
2f82d36ff38abea43fa74f59299354b0fac3c80c | 22e97a5d648fc451e25a06c668dc03ac7ed7bc25 | /src/ring_theory/algebra.lean | 7c32612dbe534366e18b5f4c1c8ffab6d748ba27 | [
"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 | 28,940 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Yury Kudryashov
-/
import data.matrix.basic
import linear_algebra.tensor_product
import algebra.commute
import data.equiv.ring
/-!
# Algebra over Commutative Semiring (under cat... |
5551a7050732ba5498fac18f68bc5bd088837af5 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/order/nonneg/floor.lean | ad01bc8b5c5ffd5f02cd0ab74529b26692aaa499 | [
"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 | 1,864 | lean | /-
Copyright (c) 2021 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import algebra.order.nonneg.ring
import algebra.order.archimedean
/-!
# Nonnegative elements are archimedean
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any ch... |
30a910c5e8d5a0ab0391dc25b9faa1d7e8e00add | 9ad8d18fbe5f120c22b5e035bc240f711d2cbd7e | /src/homotopy/subdiv.lean | a27b709b552fcbf0ff61b83cf4429ea5ef5624c1 | [] | no_license | agusakov/lean_lib | c0e9cc29fc7d2518004e224376adeb5e69b5cc1a | f88d162da2f990b87c4d34f5f46bbca2bbc5948e | refs/heads/master | 1,642,141,461,087 | 1,557,395,798,000 | 1,557,395,798,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,563 | lean | /-
Copyright (c) 2019 Neil Strickland. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Neil Strickland
Given a poset `P`, we define `subdiv P` to be the poset of
finite nonempty chains `s ⊆ P`. Any such `s` has a largest
element, and the map `max : (subdiv P) → P` i... |
5e61ac25fbdbc8912d9ac1afeede4abb20d5c104 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/analysis/special_functions/polynomials.lean | b9c190472cf71beb5e7a628e1a49f81351edc486 | [
"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 | 9,821 | lean | /-
Copyright (c) 2020 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker, Devon Tuma
-/
import analysis.asymptotics.asymptotic_equivalent
import analysis.asymptotics.specific_asymptotics
import data.polynomial.ring_division
/-!
# Limits ... |
fc82e406864283e6266673f11e28cde8742dc1be | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/order/succ_pred/interval_succ.lean | 82d875a0264c866d3689d4a8eec2705a10f70a41 | [
"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 | 6,838 | lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import order.succ_pred.basic
import data.set.lattice
/-!
# Intervals `Ixx (f x) (f (order.succ x))`
In this file we prove
* `monotone.bUnion_Ico_Ioc_map_succ`: i... |
f5f9626df5a261320a6ae742b2bfa405072d1956 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/pp_notation_rbp_bug.lean | e27796a4a6b44dc4f11eb62555ce1439d3284f3d | [
"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 | 59 | lean | def foo := (λ a : ℕ, a) = (λ a, a) ↔ true
#print foo
|
37a9ee5a22e5d9afafd75d89d4e97636112cbde7 | d4df7c538bbc0b06771d7b7a6f46fbadebb8c5eb | /src/comonad_transformers/comonad_trans.lean | 8a5bc85002cfcfcdf59812db78286e01bcd92fe0 | [] | no_license | breakerzirconia/LeanTransformers | 11bb924b59ac589d0c6b39586d27cccc8f9e939c | 3c52441b8990bab7d8cf1817df6e04f657a14e1c | refs/heads/main | 1,682,610,526,027 | 1,620,477,129,000 | 1,620,477,129,000 | 365,507,838 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 166 | lean | import comonad_transformers.comonad
class comonad_trans (t : (Type → Type) → Type → Type) :=
(lower {w : Type → Type} [comonad w] {a : Type} : t w a → w a) |
748fc1d5eebfc91fbf1a2648288872939a30d26a | 07c6143268cfb72beccd1cc35735d424ebcb187b | /src/algebra/category/Group/colimits.lean | 4106292bdc6f1459b1057de3dbae4cda15a3e903 | [
"Apache-2.0"
] | permissive | khoek/mathlib | bc49a842910af13a3c372748310e86467d1dc766 | aa55f8b50354b3e11ba64792dcb06cccb2d8ee28 | refs/heads/master | 1,588,232,063,837 | 1,587,304,803,000 | 1,587,304,803,000 | 176,688,517 | 0 | 0 | Apache-2.0 | 1,553,070,585,000 | 1,553,070,585,000 | null | UTF-8 | Lean | false | false | 8,868 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import algebra.category.Group.basic
import category_theory.limits.limits
import category_theory.limits.concrete_category
/-!
# The category of additive commutative g... |
e4316e3bdfff644fcec42ddd980f222516476f06 | 592f865bb4e2e537ae3552cb83c32fb99c8d4c68 | /src/Lemma3.lean | 6bfc21b2e240a83ee081bc40befe8b936078520f | [] | no_license | BassemSafieldeen/Entropy_and_reversible_catalysis | 250dbb9446690ab89d89a6a512c8f888e09e8596 | 5dd6ee062f61e26bbcf254477e3e24aa3fc489af | refs/heads/master | 1,678,747,213,156 | 1,615,540,586,000 | 1,615,540,586,000 | 322,216,014 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 923 | lean | import algebra.big_operators
import to_mathlib_maybe.Hilbert_space
import to_mathlib_maybe.pTrace
import to_qShannon_theory_maybe.entropy
import to_qShannon_theory_maybe.state
import to_qShannon_theory_maybe.channel
open_locale big_operators
variables
{ι : Type} [fintype ι] [decidable_eq ι]
{ℋ : Type} [complex_hilb... |
7c403f576e598cd940cc415e91b484c2612a44a3 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/category_theory/limits/essentially_small.lean | 28d3a6488773f1f75a22eb0b890d1ebf7fe33c77 | [
"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 | 1,536 | lean | /-
Copyright (c) 2022 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import category_theory.limits.shapes.products
import category_theory.essentially_small
/-!
# Limits over essentially small indexing categories
If `C` has limits of si... |
7ef7fda001bd1cb23c7f575b38fdd874393f3630 | 037dba89703a79cd4a4aec5e959818147f97635d | /src/2020/problem_sheets/Part_II/sheet1_q3_solutions.lean | c10ae265cc25d98c01077dd6913dd724b534e8e3 | [] | 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 | 2,469 | lean | import tactic
variables (x y : ℕ)
open nat
theorem Q1a : x + y = y + x :=
begin
induction y with d hd,
{ rw [add_zero, zero_add]},
{ rw [add_succ, succ_add, hd]}
end
theorem Q1b : x + y = x → y = 0 :=
begin
intro h,
induction x with d hd,
{ convert h, rw zero_add},
{ apply hd,
rw succ_add at h,
... |
f2c0bb0ed4569a201ee878535235385660495e97 | 592ee40978ac7604005a4e0d35bbc4b467389241 | /Library/generated/mathscheme-lean/Absorption.lean | ebb0503d66bc078f0536a5cf416a25b0ce791d2f | [] | no_license | ysharoda/Deriving-Definitions | 3e149e6641fae440badd35ac110a0bd705a49ad2 | dfecb27572022de3d4aa702cae8db19957523a59 | refs/heads/master | 1,679,127,857,700 | 1,615,939,007,000 | 1,615,939,007,000 | 229,785,731 | 4 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,782 | 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 Absorption
structure Absorption (A : Type) : Type :=
(times : (A → (A → A)))
(plus : (A → (A → A)))
(leftAbsorp_times_plus : (∀ {x y : A} , (times x (plu... |
cd9cd9d3632a4d3765042d8f33971d039f82d606 | 08bd4ba4ca87dba1f09d2c96a26f5d65da81f4b4 | /src/Lean/Elab/Syntax.lean | 165c8e46631d542bf2c780060a0942737144d3f1 | [
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"Apache-2.0",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | gebner/lean4 | d51c4922640a52a6f7426536ea669ef18a1d9af5 | 8cd9ce06843c9d42d6d6dc43d3e81e3b49dfc20f | refs/heads/master | 1,685,732,780,391 | 1,672,962,627,000 | 1,673,459,398,000 | 373,307,283 | 0 | 0 | Apache-2.0 | 1,691,316,730,000 | 1,622,669,271,000 | Lean | UTF-8 | Lean | false | false | 18,704 | 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.Elab.Command
import Lean.Parser.Syntax
import Lean.Elab.Util
namespace Lean.Elab.Term
/--
Expand `optional «precedence»` where
«precedence» :=... |
4f04a2072f4d12b83fa87b9a0900b206cb87b359 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/group_theory/exponent.lean | 7e4325b97d79eaa7c66dc347d74d5fdc498f2a5d | [
"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 | 11,263 | 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 group_theory.order_of_element
import algebra.punit_instances
import algebra.gcd_monoid.finset
import tactic.by_contra
import number_theory.padics.padic... |
62a0f653c01176f6d60e136fe3759976dc705215 | ae1e94c332e17c7dc7051ce976d5a9eebe7ab8a5 | /src/Lean/Elab/InfoTree.lean | 11a2ae9c9b14f40ce20c11d0c37ff9707a360dca | [
"Apache-2.0"
] | permissive | dupuisf/lean4 | d082d13b01243e1de29ae680eefb476961221eef | 6a39c65bd28eb0e28c3870188f348c8914502718 | refs/heads/master | 1,676,948,755,391 | 1,610,665,114,000 | 1,610,665,114,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,593 | lean | /-
Copyright (c) 2020 Wojciech Nawrocki. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wojciech Nawrocki, Leonardo de Moura
-/
import Lean.Data.Position
import Lean.Expr
import Lean.Message
import Lean.Data.Json
import Lean.Meta.Basic
import Lean.Meta.PPGoal
namespa... |
bed61ddd5f254dc05f71df5b613bdd1335da4ca8 | 206422fb9edabf63def0ed2aa3f489150fb09ccb | /src/data/equiv/basic.lean | b2725f3abc48ff39460ed147f9000ee5a8537601 | [
"Apache-2.0"
] | permissive | hamdysalah1/mathlib | b915f86b2503feeae268de369f1b16932321f097 | 95454452f6b3569bf967d35aab8d852b1ddf8017 | refs/heads/master | 1,677,154,116,545 | 1,611,797,994,000 | 1,611,797,994,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 88,101 | 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
-/
import data.set.function
/-!
# Equivalence between types
In this file we define two types:
* `equiv α β` a.k.a. `α ≃ β`: a bijective map ... |
1e0b7a51b72bd28e35caf157ed7ec1c867318e5c | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/algebra/monoid_algebra/to_direct_sum.lean | e92b268e4f355750521637e59152b55a0a2156ec | [
"Apache-2.0"
] | permissive | AntoineChambert-Loir/mathlib | 64aabb896129885f12296a799818061bc90da1ff | 07be904260ab6e36a5769680b6012f03a4727134 | refs/heads/master | 1,693,187,631,771 | 1,636,719,886,000 | 1,636,719,886,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,850 | lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import algebra.direct_sum.algebra
import algebra.monoid_algebra.basic
import data.finsupp.to_dfinsupp
/-!
# Conversion between `add_monoid_algebra` and homogenous `direct_... |
c440c390ce09dce0df0590b88dfe699cf7979892 | c3f2fcd060adfa2ca29f924839d2d925e8f2c685 | /tests/lean/run/n4.lean | 3ed24fafa54cb615453a0050d0b19c654648fe46 | [
"Apache-2.0"
] | permissive | respu/lean | 6582d19a2f2838a28ecd2b3c6f81c32d07b5341d | 8c76419c60b63d0d9f7bc04ebb0b99812d0ec654 | refs/heads/master | 1,610,882,451,231 | 1,427,747,084,000 | 1,427,747,429,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 422 | lean | prelude
definition Prop : Type.{1} := Type.{0}
context
variable N : Type.{1}
variables a b c : N
variable and : Prop → Prop → Prop
infixr `∧`:35 := and
variable le : N → N → Prop
variable lt : N → N → Prop
precedence `≤`:50
precedence `<`:50
infixl ≤ := le
infixl < := lt
check a ≤ b
definition T... |
dbb8d80e598946404417c03622ddf6e921733b9a | 1f6fe2f89976b14a4567ab298c35792b21f2e50b | /colim.hlean | 31030e337df4f15090c67b17dc822f13c5fec363 | [
"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 | 22,571 | hlean | -- authors: Floris van Doorn, Egbert Rijke, Stefano Piceghello
import hit.colimit types.fin homotopy.chain_complex types.pointed2
open seq_colim pointed algebra eq is_trunc nat is_equiv equiv sigma sigma.ops chain_complex
namespace seq_colim
definition pseq_colim [constructor] {X : ℕ → Type*} (f : Πn, X n →* X (n+... |
34ddf385c7108aebe0db3665f882145e8a9b788c | 6dbfa3fb323bb2e2c3917c61d46053dd0de739cd | /src/CRT2.lean | 19ebc95bc5cb24435331d23c8b6192e493cf347e | [] | no_license | amichaelsen/Lean-Chinese-Remainder-Theorem | b054fc32e0f5383eb83ec7155932c50d92de1038 | 9efb4b97da30e5aedb6af3c95d5132ac300f2902 | refs/heads/master | 1,680,787,277,127 | 1,619,155,524,000 | 1,619,155,524,000 | 275,883,966 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,469 | lean | import data.nat.basic
import data.nat.modeq
import data.nat.gcd
import data.zmod.basic
import tactic
import algebra.euclidean_domain
import data.int.basic
import data.equiv.ring
import lemmas2
noncomputable theory
open nat nat.modeq zmod euclidean_domain lemmas2
namespace CRT2
/- CHINESE REMAINDER THEOREM WITH 2 CONG... |
d119b3aa4cfb1de39e7a304ecc3fd40dd8e02299 | 2c096fdfecf64e46ea7bc6ce5521f142b5926864 | /tests/pkg/misc/Misc/Foo.lean | 077786d034b2df4890a355a493c49a013650f514 | [
"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 | Kha/lean4 | 1005785d2c8797ae266a303968848e5f6ce2fe87 | b99e11346948023cd6c29d248cd8f3e3fb3474cf | refs/heads/master | 1,693,355,498,027 | 1,669,080,461,000 | 1,669,113,138,000 | 184,748,176 | 0 | 0 | Apache-2.0 | 1,665,995,520,000 | 1,556,884,930,000 | Lean | UTF-8 | Lean | false | false | 137 | lean | import Lean
open Lean Meta
#eval id (α := MetaM Unit) do
modifyEnv fun env => env.addExtraName `auxDecl1
return ()
def foo := 42
|
705cdd07548a0d978543ee14f61ba388792aee84 | 98beff2e97d91a54bdcee52f922c4e1866a6c9b9 | /src/internal_category.lean | f6480c35fac35875193dde16fac2d2d3fbfb0bda | [] | no_license | b-mehta/topos | c3fc43fb04ba16bae1965ce5c26c6461172e5bc6 | c9032b11789e36038bc841a1e2b486972421b983 | refs/heads/master | 1,629,609,492,867 | 1,609,907,263,000 | 1,609,907,263,000 | 240,943,034 | 43 | 3 | null | 1,598,210,062,000 | 1,581,877,668,000 | Lean | UTF-8 | Lean | false | false | 19,344 | lean | import category_theory.limits.shapes.pullbacks
import category_theory.limits.limits
import category_theory.types
import category_theory.limits.types
import category_theory.monad.algebra
import category_theory.category.Cat
import tactic.equiv_rw
import category.pullbacks
import data.sigma
namespace category_theory
ope... |
4342df5105604233abf6d9017cd20aa3a933cd1c | 37a833c924892ee3ecb911484775a6d6ebb8984d | /src/category_theory/universal/constructions/colimits_from.lean | cb76290f3d8fd489c43520d8b44b69f1e20740f9 | [] | no_license | silky/lean-category-theory | 28126e80564a1f99e9c322d86b3f7d750da0afa1 | 0f029a2364975f56ac727d31d867a18c95c22fd8 | refs/heads/master | 1,589,555,811,646 | 1,554,673,665,000 | 1,554,673,665,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 921 | lean | -- -- Copyright (c) 2018 Scott Morrison. All rights reserved.
-- -- Released under Apache 2.0 license as described in the file LICENSE.
-- -- Authors: Scott Morrison
-- import category_theory.universal.constructions.limits_from
-- import category_theory.universal.opposites
-- open category_theory
-- open category_the... |
2dab02a4d76e3167604266640031ecde64c7d3e0 | c76cc4eaee3c806716844e49b5175747d1aa170a | /src/problems_sheet_four.lean | 2b680ac2ccb417705aaf38a91093cf14aa8b8d9b | [] | no_license | ImperialCollegeLondon/M40002 | 0fb55848adbb0d8bc4a65ca5d7ed6edd18764c28 | a499db70323bd5ccae954c680ec9afbf15ffacca | refs/heads/master | 1,674,878,059,748 | 1,607,624,828,000 | 1,607,624,828,000 | 309,696,750 | 3 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,799 | lean | import tactic
import data.real.basic
import data.pnat.basic
import measure_theory.interval_integral
local notation `|` x `|` := abs x
def is_limit (a : ℕ+ → ℝ) (l : ℝ) : Prop :=
∀ ε > 0, ∃ N, ∀ n ≥ N, | a n - l | < ε
def is_convergent (a : ℕ+ → ℝ) : Prop :=
∃ l : ℝ, is_limit a l
/-
1. Consider the following proper... |
0e997064c13abc64c356195e40a3180488484653 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/finLit.lean | a32ce1c0bb80d4a8298b671e66d91ac02ad2c6a3 | [
"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 | 310 | lean | def f : Fin 2 → Nat
| 0 => 5
| 1 => 45
example : f 0 = 5 := rfl
example : f 1 = 45 := rfl
def g : Fin 11 → Nat
| 0 => 5
| 1 => 10
| 2 => 15
| 3 => 2
| 4 => 48
| 5 => 0
| 6 => 87
| 7 => 64
| 8 => 32
| 9 => 64
| 10 => 21
def h : Fin 15 → Nat
| 0 => 5
| 1 => 45
| _ => 50
|
afa13fc90e5acc3aa4f72b69c971d15dafb39fa0 | 7541ac8517945d0f903ff5397e13e2ccd7c10573 | /src/category_theory/functor_categories/isomorphisms.lean | d398672d26761996382b631d3b0c859983a2ea60 | [] | no_license | ramonfmir/lean-category-theory | 29b6bad9f62c2cdf7517a3135e5a12b340b4ed90 | be516bcbc2dc21b99df2bcb8dde0d1e8de79c9ad | refs/heads/master | 1,586,110,684,637 | 1,541,927,184,000 | 1,541,927,184,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,141 | 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 category_theory.isomorphism
import category_theory.tactics.obviously
open category_theory
namespace category_theory.functor
universes u₁... |
62f655a73c6e1983d1fa65696fb0e873577aa4c2 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/field_theory/splitting_field.lean | 074c61a81080df2faa48f8b9848539d7a6321894 | [
"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 | 35,661 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
Definition of splitting fields, and definition of homomorphism into any field that splits
-/
import ring_theory.adjoin_root
import ring_theory.algebra_tower
import ring_the... |
1a9c9fd109368f71103bc6fc407b5fbfdd0685fa | 94e33a31faa76775069b071adea97e86e218a8ee | /src/category_theory/eq_to_hom.lean | 65f70dda347ecbafe0ef7e7169ae6416956e7c63 | [
"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 | 8,018 | lean | /-
Copyright (c) 2018 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Scott Morrison
-/
import category_theory.opposites
/-!
# Morphisms from equations between objects.
When working categorically, sometimes one encounters an equation `h : X =... |
51cd7f4b86953fd748bd2a57231bc87519ec05c6 | 38bf3fd2bb651ab70511408fcf70e2029e2ba310 | /src/topology/instances/real.lean | d522867cfb327e2d7d0ec6a11a4689fca4d54d64 | [
"Apache-2.0"
] | permissive | JaredCorduan/mathlib | 130392594844f15dad65a9308c242551bae6cd2e | d5de80376088954d592a59326c14404f538050a1 | refs/heads/master | 1,595,862,206,333 | 1,570,816,457,000 | 1,570,816,457,000 | 209,134,499 | 0 | 0 | Apache-2.0 | 1,568,746,811,000 | 1,568,746,811,000 | null | UTF-8 | Lean | false | false | 18,731 | 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 real numbers ℝ.
They are constructed as the topological completion of ℚ. With the following steps:
(1) prove that ℚ forms a uniform space.
(2) subt... |
daa2a45037bf0cf73c20c5414654d7508cb70ffc | 432d948a4d3d242fdfb44b81c9e1b1baacd58617 | /src/ring_theory/algebra_tower.lean | ea9ffca62b6d1264bcd82ab2682c1f34f28771c3 | [
"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 | 12,630 | lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import algebra.algebra.tower
import algebra.invertible
import linear_algebra.basis
import ring_theory.adjoin.basic
import ring_theory.polynomial.tower
/-!
# Towers of algebra... |
afc9c59856b469edb1dacee6774ed9ad259a46cc | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/int/sqrt_auto.lean | e507636a1864720ced42e21f55931ae21a4ec76e | [] | 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 | 868 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.nat.sqrt
import Mathlib.PostPort
namespace Mathlib
namespace int
/-- `sqrt n` is the square ... |
7d43ed64ab9a1c8766ab5638d154ad74bd5e0dce | 77c5b91fae1b966ddd1db969ba37b6f0e4901e88 | /src/data/set/intervals/basic.lean | 0bc287d456f11e076691d173d047babc2e082b5f | [
"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 | 54,147 | 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, Yury Kudryashov, Rémy Degenne
-/
import algebra.order.group
import data.set.basic
import order.rel_iso
/-!
# Intervals
In any preorder... |
aad0369af5dcece84202d8f6ccbb2b9bc994dbec | 853df553b1d6ca524e3f0a79aedd32dde5d27ec3 | /src/data/complex/basic.lean | 326144eafd06ff3cff452cef2cb7e46420e7cffe | [
"Apache-2.0"
] | permissive | DanielFabian/mathlib | efc3a50b5dde303c59eeb6353ef4c35a345d7112 | f520d07eba0c852e96fe26da71d85bf6d40fcc2a | refs/heads/master | 1,668,739,922,971 | 1,595,201,756,000 | 1,595,201,756,000 | 279,469,476 | 0 | 0 | null | 1,594,696,604,000 | 1,594,696,604,000 | null | UTF-8 | Lean | false | false | 19,817 | lean | /-
Copyright (c) 2017 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Mario Carneiro
-/
import data.real.basic
/-!
# The complex numbers
The complex numbers are modelled as ℝ^2 in the obvious way.
-/
/-! ### Definition and basic arithmme... |
f0ce067edeb407be3533cd994bcef21cd8f6a984 | 43390109ab88557e6090f3245c47479c123ee500 | /src/Topology/Problem_Sheets/FINSETS_ps_2_ex_4b(incomplete).lean | 7ce9c07a4ef729318eca1e481d2d62497536183a | [
"Apache-2.0"
] | permissive | Ja1941/xena-UROP-2018 | 41f0956519f94d56b8bf6834a8d39473f4923200 | b111fb87f343cf79eca3b886f99ee15c1dd9884b | refs/heads/master | 1,662,355,955,139 | 1,590,577,325,000 | 1,590,577,325,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,874 | lean | import analysis.topology.continuity
import analysis.topology.topological_space
import analysis.topology.infinite_sum
import analysis.topology.topological_structures
import analysis.topology.uniform_space
universe u
open set filter lattice classical
#print definition set
#check empty
def empty_topology : topologic... |
1b63e77ac3c5ebb2ca89ce8d1bb88582487f4c77 | 07c6143268cfb72beccd1cc35735d424ebcb187b | /src/logic/basic.lean | 576cf8f45cc8a9fb671b0290e1985da9686d4287 | [
"Apache-2.0"
] | permissive | khoek/mathlib | bc49a842910af13a3c372748310e86467d1dc766 | aa55f8b50354b3e11ba64792dcb06cccb2d8ee28 | refs/heads/master | 1,588,232,063,837 | 1,587,304,803,000 | 1,587,304,803,000 | 176,688,517 | 0 | 0 | Apache-2.0 | 1,553,070,585,000 | 1,553,070,585,000 | null | UTF-8 | Lean | false | false | 35,835 | 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
-/
import tactic.doc_commands
/-!
# Basic logic properties
This file is one of the earliest imports in mathlib.
## Implementation notes
Theorems th... |
8bf792e7ab6bcbe1f5033c0a34b1b3f35b49949c | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/analysis/normed/field/basic.lean | 9c66d6aa5ea051fd03e322242e5c6a0c4adf3051 | [
"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 | 38,912 | lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl
-/
import analysis.normed.group.infinite_sum
import topology.algebra.module.basic
import topology.instances.ennreal
import topology.instances.rat
/-!
# ... |
a323bf4917a11b20fe3eeaa0115ad07894a03c07 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/946.lean | e47a678ac4a7d22cfc4a936614d7e111289ee5c8 | [
"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 | 2,544 | lean | inductive DataType
| TInt
| TFloat
| TString
open DataType
inductive DataEntry
| EInt (i : Int)
| EFloat (f : Float)
| EString (s : String)
| NULL
def NULL := DataEntry.NULL
instance : Coe Int DataEntry where
coe := DataEntry.EInt
instance : Coe Float DataEntry where
coe := DataEntry.EFloat
inst... |
0c9b5e072ca15424702d9a435043a61b0e900ea7 | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/algebra/homology/image_to_kernel_map.lean | a8730cf81075612cd23f178ea008c1b8d5e6ae3c | [
"Apache-2.0"
] | permissive | dupuisf/mathlib | 62de4ec6544bf3b79086afd27b6529acfaf2c1bb | 8582b06b0a5d06c33ee07d0bdf7c646cae22cf36 | refs/heads/master | 1,669,494,854,016 | 1,595,692,409,000 | 1,595,692,409,000 | 272,046,630 | 0 | 0 | Apache-2.0 | 1,592,066,143,000 | 1,592,066,142,000 | null | UTF-8 | Lean | false | false | 2,567 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.limits.shapes.images
import category_theory.limits.shapes.kernels
/-!
# The morphism from `image f` to `kernel g` when `f ≫ g = 0`
We define ... |
54b522cf058afabdc25587346e6a97c8aa1c29af | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/data/dlist/instances.lean | 2d43fdc18efd638d6ae24de3adee8ef21a399746 | [
"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 | 863 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
Traversable instance for dlists.
-/
import data.dlist
import control.traversable.equiv
import control.traversable.instances
namespace dlist
variables (α : Type*)
open func... |
32bf51907844b70377397c3b29024acb8ac6f4ce | f68ef9a599ec5575db7b285d4960e63c5d464ccc | /Exercises/firtst_examples.lean | ab0db7a3fa3be694b645cd22ed7dd0f50124636b | [] | no_license | lucasmoschen/discrete-mathematics | a38d5970cc571b0b9d202bf6a43efeb8ed6f66e3 | 0f1945cc5eb094814c926cd6ae4a8b4c5c579a1e | refs/heads/master | 1,677,111,757,003 | 1,611,500,097,000 | 1,611,500,097,000 | 205,903,359 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 663 | lean | variables A B C: Prop
section
variable h1: A → B
variable h2: B → C
example: A → C :=
assume h: A,
show C, from h2 (h1 h)
end
section
example: (A → (B → C)) → (A ∧ B → C) :=
assume h1: (A → (B → C)),
assume h2: A ∧ B,
show C, from h1 (and.left h2) (and.right h2)
end
section
... |
d437961bc8f9a547feb36aae179787d5777e6fc1 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/monad/adjunction_auto.lean | 2abecc2b47b94a83c766650dffc00324b746afb1 | [] | 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 | 5,529 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.category_theory.monad.algebra
import Mathlib.category_theory.adjunction.defau... |
98297a70d8b1af7b8a1ec2fb75c7fa44fe78d513 | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /examples/lean/hurkens.lean | 0e68876a279e01ddfe1b3f0a786db49933d55219 | [
"Apache-2.0"
] | permissive | codyroux/lean0.1 | 1ce92751d664aacff0529e139083304a7bbc8a71 | 0dc6fb974aa85ed6f305a2f4b10a53a44ee5f0ef | refs/heads/master | 1,610,830,535,062 | 1,402,150,480,000 | 1,402,150,480,000 | 19,588,851 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,161 | lean | -- Hurkens' paradox in lean
import macros
import tactic
definition app {A B : Type} (f : A → B) (x : A) : B := (f x).
infix 1 $ : app.
variable large : Bool.
variable False : Bool.
variable inj : ∀ A : Bool, large.
variable proj : large → Bool.
axiom proj_ax : ∀ A : Bool, proj (inj A) = A.
definition V := ∀ A ... |
1ec525abcf06aa19c188f0b133bd631206965141 | 35b83be3126daae10419b573c55e1fed009d3ae8 | /_target/deps/mathlib/analysis/topology/continuity.lean | 875e1ca1646eeae288336686f695c742c499720a | [] | no_license | AHassan1024/Lean_Playground | ccb25b72029d199c0d23d002db2d32a9f2689ebc | a00b004c3a2eb9e3e863c361aa2b115260472414 | refs/heads/master | 1,586,221,905,125 | 1,544,951,310,000 | 1,544,951,310,000 | 157,934,290 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 68,988 | 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
Continuous functions.
Parts of the formalization is based on the books:
N. Bourbaki: General Topology
I. M. James: Topologies and U... |
0e31d2ad25a621c3906fec8359114972f0d72e4a | 5e3548e65f2c037cb94cd5524c90c623fbd6d46a | /src_icannos_totilas/aops/1997-USAMO-Problem_5.lean | cd3c243534d864ffce586b234064cd09444c06a8 | [] | no_license | ahayat16/lean_exos | d4f08c30adb601a06511a71b5ffb4d22d12ef77f | 682f2552d5b04a8c8eb9e4ab15f875a91b03845c | refs/heads/main | 1,693,101,073,585 | 1,636,479,336,000 | 1,636,479,336,000 | 415,000,441 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 195 | lean | import data.real.basic
import data.real.nnreal
theorem USAMO_problem_5_1997 (a b c : nnreal) :
1 / (a^3 + b^3 +a*b*c) + 1 / (b^3 + c^3 +a*b*c) + 1 /(a^3 + c^3 + a*b*c) ≤ 1 /(a*b*c) := sorry
|
a63d56dfa712b0ed02e4e51bd1fee47734015d73 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/data/padics/padic_norm.lean | 3508ff6d75aab43527ebe9691d4041986d97b73b | [
"Apache-2.0"
] | permissive | rmitta/mathlib | 8d90aee30b4db2b013e01f62c33f297d7e64a43d | 883d974b608845bad30ae19e27e33c285200bf84 | refs/heads/master | 1,585,776,832,544 | 1,576,874,096,000 | 1,576,874,096,000 | 153,663,165 | 0 | 2 | Apache-2.0 | 1,544,806,490,000 | 1,539,884,365,000 | Lean | UTF-8 | Lean | false | false | 17,017 | 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
-/
import data.rat algebra.gcd_domain algebra.field_power
import ring_theory.multiplicity tactic.ring
import data.real.cau_seq
import tactic.norm_cast
/-!
# p-adic n... |
28d6f275ad61b871f6c9a8de847a8f38e35c4f62 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/run/pack_unpack1.lean | 01ab87037087ca68db2ddfe0d7a2c5c2277fce96 | [
"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 | 2,268 | lean |
inductive tree_core (A : Type*) : bool → Type*
| leaf' : A → tree_core ff
| node' : tree_core tt → tree_core ff
| nil' {} : tree_core tt
| cons' : tree_core ff → tree_core tt → tree_core tt
attribute [reducible]
definition tree (A : Type*) := tree_core A ff
attribute [reducible]
definition tree_list (A : T... |
f5551f4293a7234770a02cf993ada7b22713b04f | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/derivingBEq.lean | 1a0417f649b93db28b7a886dfc24698e8c6a767b | [
"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 | 1,373 | lean | inductive Foo
| mk1 | mk2 | mk3
deriving BEq
namespace Foo
theorem ex1 : (mk1 == mk2) = false :=
rfl
theorem ex2 : (mk1 == mk1) = true :=
rfl
theorem ex3 : (mk2 == mk2) = true :=
rfl
theorem ex4 : (mk3 == mk3) = true :=
rfl
theorem ex5 : (mk2 == mk3) = false :=
rfl
end Foo
inductive Vec (α : Type u) : N... |
fd13dddd5b5260418ebf50f2215c56a0e0ced490 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/category_theory/functor/reflects_isomorphisms.lean | f017a78d626930c3e6ddc7b0c3c6b96b5dbc305a | [
"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 | 2,355 | 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.balanced
import category_theory.functor.epi_mono
import category_theory.functor.fully_faithful
/-!
# Functors which reflect isomorphisms
A functo... |
c42da08592347421d2b068dd8323ddee3337c0ee | 3c453925e3aae41b20e0567130c33a61fb1c5854 | /src/exercises/chapter_1/section_B.lean | fe52571657df7e358f986a3b3221319ef588df27 | [] | no_license | agusakov/vector_spaces | f7e272e9403a87a72b49d92ce759e4ebe9e4d55c | b23954c19b357a689e2a73e07fcf6c9e4a74713a | refs/heads/master | 1,670,493,487,137 | 1,596,908,778,000 | 1,596,908,778,000 | 283,599,211 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,495 | lean | import vec_space
universes u v w
namespace vector_space
-- 1.) Prove that -(-v) = v for every v ∈ V
lemma neg_neg' (F : Type u) (α : Type v) [field F] [add_comm_group α] [vector_space F α] :
∀ v : α, - (- v) = v :=
begin
intro v,
apply @add_right_cancel _ _ _ (-v),
rw add_neg_self,
rw neg_add_se... |
d6ee40fa3b6f0b7a6b26463c38904b88bb7928e9 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/number_theory/bernoulli_polynomials.lean | 82df7a3f2e5bdd9d190860d49b6ce4b20a3a42ea | [
"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 | 10,083 | lean | /-
Copyright (c) 2021 Ashvni Narayanan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ashvni Narayanan, David Loeffler
-/
import data.polynomial.algebra_map
import data.polynomial.derivative
import data.nat.choose.cast
import number_theory.bernoulli
/-!
# Bernoulli p... |
7e4640054177cb105a8b567b03e0ecba93acc6f6 | 853df553b1d6ca524e3f0a79aedd32dde5d27ec3 | /src/topology/metric_space/gromov_hausdorff_realized.lean | 47c518cc9fc5689b9518d57fcc957c7d4aab5dfe | [
"Apache-2.0"
] | permissive | DanielFabian/mathlib | efc3a50b5dde303c59eeb6353ef4c35a345d7112 | f520d07eba0c852e96fe26da71d85bf6d40fcc2a | refs/heads/master | 1,668,739,922,971 | 1,595,201,756,000 | 1,595,201,756,000 | 279,469,476 | 0 | 0 | null | 1,594,696,604,000 | 1,594,696,604,000 | null | UTF-8 | Lean | false | false | 26,284 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Sébastien Gouëzel
Construction of a good coupling between nonempty compact metric spaces, minimizing
their Hausdorff distance. This construction is instrumental to study the Gromov-... |
4cd7ea0c6e630a70c3160876f9f420910150ecc2 | 041929c569a4eeeafb4efdddab8a644f6df383c5 | /src/mazes/gcd_maze/level.lean | 723d2d7bfe9867d2da9b30d751ba94b850943ed0 | [] | no_license | kbuzzard/xena-maze-game | 30ffbe956762dd6603e74efd823d375649e037c3 | 098454dd6acc4c06beccf52b6547bf4cd99cc581 | refs/heads/master | 1,670,840,300,174 | 1,598,554,198,000 | 1,598,554,198,000 | 290,856,036 | 4 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 958 | lean | -- import the definition of the example maze
import mazes.gcd_maze.definition
import data.int.gcd
/-!
# Non-euclidean maze.
You are in a maze of integers, all distinct.
You can go north, south east or west.
north adds 8 to your integer, south subtracts 8
east adds 3 to your integer, west subtrascts 3
When you're... |
1d86892562f46e0f8499c2905062d232d9a25798 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/category_theory/monad/limits.lean | 6e6f4f2ebfe9f601222d16decd94f359d03ab391 | [
"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 | 14,919 | 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.monad.adjunction
import category_theory.adjunction.limits
import category_theory.limits.preserves.shapes.terminal
namespace cate... |
190013cc908d7dd4ce92a53ef0fa7dc4583aedaf | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/linear_algebra/char_poly/basic.lean | a2d2fe443273535ec943e44daed242831f046ae6 | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 3,816 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import tactic.apply_fun
import ring_theory.matrix_algebra
import ring_theory.polynomial_algebra
import linear_algebra.matrix.nonsingular_inverse
import tactic.squeeze... |
85610a07c6f601890450e932bed7f096ab1c3dda | b7f22e51856f4989b970961f794f1c435f9b8f78 | /hott/homotopy/quaternionic_hopf.hlean | f4b235e59fb1bb56b7b5f4a14138a0dd6430ad0c | [
"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 | 4,259 | hlean | /-
Copyright (c) 2016 Ulrik Buchholtz and Egbert Rijke. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ulrik Buchholtz, Egbert Rijke
The H-space structure on S³ and the quaternionic Hopf fibration
(using the imaginaroid structure on S⁰).
-/
import .complex_hopf .ima... |
8a1382652bb9133cedbd5b96ac3a87b1ef8a395b | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/nat/totient.lean | dd1001f69203f67ac908e7d7751005215a9aba09 | [] | 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 | 983 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebra.big_operators.basic
import Mathlib.PostPort
namespace Mathlib
namespace nat
/-- Eul... |
53e695632c53a9c79b59930ad0057e2149b73a9d | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/ring_theory/derivation.lean | 3f249a07dd6f61264dc2d56c45ed75b8600b707a | [
"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 | 30,849 | lean | /-
Copyright © 2020 Nicolò Cavalleri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolò Cavalleri, Andrew Yang
-/
import ring_theory.adjoin.basic
import algebra.lie.of_associative
import ring_theory.tensor_product
import ring_theory.ideal.cotangent
/-!
# Derivati... |
51a58680cbdb323818a32e68ba7a23baa2b5f5cc | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/mv_polynomial/monad.lean | a1b138f35320f2234b047bcd58615a0bfbd41393 | [
"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 | 13,142 | lean | /-
Copyright (c) 2020 Johan Commelin, Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Robert Y. Lewis
-/
import data.mv_polynomial.rename
/-!
# Monad operations on `mv_polynomial`
This file defines two monadic operations on `mv_polyn... |
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