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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
cc05872dd83ed1787ed60f5997d4de80a7b5b681 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/let_tac.lean | f92a4e43fa715ad8cd191f3a5158477af03ca9fb | [
"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 | 350 | lean | import data.nat
open algebra
example (a b : Prop) : a → b → a ∧ b :=
begin
intro Ha, intro Hb,
let Ha' := Ha,
let Hb' := Hb,
let aux := and.intro Ha Hb,
exact aux
end
open nat
example (a b : nat) : a > 0 → b > 0 → a + b + 0 > 0 :=
begin
intro agt0, intro bgt0,
let H := add_pos agt0 bgt0,
change a + b... |
ae9867306a63863c392d6ec319afe48550d67a4f | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/algebraic_geometry/locally_ringed_space.lean | 195edf9ccb7c7c7f3f691c79d0732b5ca796ccdb | [
"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 | 7,460 | lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import algebraic_geometry.ringed_space
import data.equiv.transfer_instance
/-!
# The category of locally ringed spaces
We define (bundled) locally ringed spaces (a... |
d375fd97f7d6cc485a5091270ddb80201c55c43c | cbb1957fc3e28e502582c54cbce826d666350eda | /fabstract/Bauer_A_InjBaireNat/realizability.lean | 2f96d4b777dfa53e6dbab15ab0ced9ad44799835 | [
"CC-BY-4.0"
] | permissive | andrejbauer/formalabstracts | 9040b172da080406448ad1b0260d550122dcad74 | a3b84fd90901ccf4b63eb9f95d4286a8775864d0 | refs/heads/master | 1,609,476,417,918 | 1,501,541,742,000 | 1,501,541,760,000 | 97,241,872 | 1 | 0 | null | 1,500,042,191,000 | 1,500,042,191,000 | null | UTF-8 | Lean | false | false | 673 | lean | -- the folklore does not yet contain anything about realizability toposes,
-- so we include partial formalization here. Eventually this should be
-- moved to folklore.
import meta_data
.toposes
run_cmd tactic.skip -- temporary fix
-- TODO (@andrejbauer): give real descriptions and dois
-- missing definition o... |
7e81fc20254b1fb78c50cc557347a3398a3e5a8a | cf39355caa609c0f33405126beee2739aa3cb77e | /library/init/meta/type_context.lean | 88914133e4242318eed63fdd3d2c51ede3949bcb | [
"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 | 7,313 | lean | prelude
import init.control.monad init.meta.local_context init.meta.tactic init.meta.fun_info
namespace tactic.unsafe
/-- A monad that exposes the functionality of the C++ class `type_context_old`.
The idea is that the methods to `type_context` are more powerful but _unsafe_ in the
sense that you can create terms that ... |
8fc1ac472f1b88b406090011ffc4ee7e89f4095e | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/group_theory/eckmann_hilton.lean | a234bb987e938d410a0a532078cefdaa9a41f231 | [
"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 | 4,384 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Kenny Lau, Robert Y. Lewis
-/
import algebra.group.basic
/-!
# Eckmann-Hilton argument
The Eckmann-Hilton argument says that if a type carries two monoid structures that d... |
044b6cc7a4c4ccf8c6b2f357153d5587985d1a1c | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/order/sub/defs.lean | 56595998a36733a9de77f55d8982b054aa1a65d3 | [
"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 | 13,333 | 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.covariant_and_contravariant
import algebra.group.basic
import algebra.order.monoid.lemmas
import order.lattice
/-!
# Ordered Subtraction
> THIS F... |
959ec55f2684a1e5a571becae52a53f9a0cf984c | 4727251e0cd73359b15b664c3170e5d754078599 | /src/topology/algebra/group_completion.lean | 56870cdb4804471542d301978d667fe450e917d6 | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 7,995 | 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 algebra.hom.group_instances
import topology.algebra.uniform_group
import topology.uniform_space.completion
/-!
# Completion of topological gro... |
72aab1c1ccb3fc502f026d8857502ba8fbb07053 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/topology/sheaves/limits.lean | 52412f0608a87ff5f17f975a8167158b4f176501 | [
"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 | 1,887 | 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 topology.sheaves.sheaf_condition.sites
import category_theory.sites.limits
import category_theory.adjunction
import category_theory.limits.functor_category
/-... |
f56eabee191f2eecb1c50da51840b29e77e4a115 | f20db13587f4dd28a4b1fbd31953afd491691fa0 | /tests/lean/run/simp_norm.lean | 7cc5d4e212c7de009862590c7f4aa31c852653fb | [
"Apache-2.0"
] | permissive | AHartNtkn/lean | 9a971edfc6857c63edcbf96bea6841b9a84cf916 | 0d83a74b26541421fc1aa33044c35b03759710ed | refs/heads/master | 1,620,592,591,236 | 1,516,749,881,000 | 1,516,749,881,000 | 118,697,288 | 1 | 0 | null | 1,516,759,470,000 | 1,516,759,470,000 | null | UTF-8 | Lean | false | false | 381 | lean | universes u v
axiom map_bind_lemma : ∀ {α β : Type u} {m : Type u → Type v} [monad m] (f : α → β) (x : m α), f <$> x = x >>= pure ∘ f
attribute [norm] function.comp map_bind_lemma
example : nat.succ <$> [1, 2] = [2, 3] :=
begin
simp with norm,
guard_target [1, 2] >>= (λ x, pure (nat.succ x)) = [2, 3],
simp [has... |
dd47ddeadd0832207b8846daf0d408c7289601eb | 9a0b1b3a653ea926b03d1495fef64da1d14b3174 | /tidy/lib/interaction_monad.lean | 33be1f9b7cd859c9288becd0571740f191d35feb | [
"Apache-2.0"
] | permissive | khoek/mathlib-tidy | 8623b27b4e04e7d598164e7eaf248610d58f768b | 866afa6ab597c47f1b72e8fe2b82b97fff5b980f | refs/heads/master | 1,585,598,975,772 | 1,538,659,544,000 | 1,538,659,544,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 683 | lean | universes u v
variable {state : Type}
variables {α : Type u} {β : Type v}
local notation `m` := interaction_monad state
meta def interaction_monad_orelse_intercept_safe {α : Type u} (t₁ : m α) (t₂ : option (unit → format) → option pos → m α) (fallback : α) : m α :=
let t₃ : m α := do return fallback in
λ s, interactio... |
4f158ea839359dcfc0fbc3791d18ca1c4ca36adf | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/linear_algebra/tensor_algebra/grading.lean | e51bdd02f6441d4b735539ba76a7a07f0c2986c8 | [
"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 | 2,338 | 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 linear_algebra.tensor_algebra.basic
import ring_theory.graded_algebra.basic
/-!
# Results about the grading structure of the tensor algebra
The main result is `ten... |
8906520e108449c9a238aed1173c94f510563b2d | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/group_theory/free_product.lean | 5d600dd93e9f59d68798b2ad6f8f5099642d724f | [
"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 | 6,383 | lean | /-
Copyright (c) 2021 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn
-/
import algebra.free_monoid
import group_theory.congruence
/-!
# The free product of groups or monoids
Given an `ι`-indexed family `M` of monoids, we define their free product... |
8f02fd447bfba49bbeb308d8ca7025d422601e74 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/number_theory/legendre_symbol/jacobi_symbol.lean | fda88a30d30cfa7a09a7b7ca8587156a496c3323 | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 17,554 | lean | /-
Copyright (c) 2022 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
import number_theory.legendre_symbol.quadratic_reciprocity
/-!
# The Jacobi Symbol
We define the Jacobi symbol and prove its main properties.
## Main definitions
We... |
cb790351c88f113cea648622c15e6a932a8f6994 | 4950bf76e5ae40ba9f8491647d0b6f228ddce173 | /src/group_theory/subgroup.lean | d0308acf00ec9e9dde966bafa80c9199e06a4f00 | [
"Apache-2.0"
] | permissive | ntzwq/mathlib | ca50b21079b0a7c6781c34b62199a396dd00cee2 | 36eec1a98f22df82eaccd354a758ef8576af2a7f | refs/heads/master | 1,675,193,391,478 | 1,607,822,996,000 | 1,607,822,996,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 48,380 | lean | /-
Copyright (c) 2020 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
import group_theory.submonoid
import algebra.group.conj
/-!
# Subgroups
This file defines multiplicative and additive subgroups as an extension of submonoids, in a bundle... |
9411a654f198d27ea75aa8f1611e011ebdbf170c | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/category/Module/filtered_colimits.lean | 01cb3e6a786ef8a83c561c6d87ea1ebf644eab47 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 7,375 | lean | /-
Copyright (c) 2021 Justus Springer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Justus Springer
-/
import algebra.category.Group.filtered_colimits
import algebra.category.Module.basic
/-!
# The forgetful functor from `R`-modules preserves filtered colimits.
> T... |
b1ba3ca009b7a06768d201d1a85ff2c1f57c78b4 | aa5a655c05e5359a70646b7154e7cac59f0b4132 | /tests/lean/StxQuot.lean | 71c6c9837b7102272e27b991e04614dd6e5c5a8d | [
"Apache-2.0"
] | permissive | lambdaxymox/lean4 | ae943c960a42247e06eff25c35338268d07454cb | 278d47c77270664ef29715faab467feac8a0f446 | refs/heads/master | 1,677,891,867,340 | 1,612,500,005,000 | 1,612,500,005,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,930 | lean | import Lean
open Lean
open Lean.Elab
def run {α} [ToString α] : Unhygienic α → String := toString ∘ Unhygienic.run
#eval run `(Nat.one)
#eval run `($Syntax.missing)
namespace Lean.Syntax
#eval run `($missing)
#eval run `($(missing))
#eval run `($(id Syntax.missing) + 1)
#eval run $ let id := Syntax.missing; `($id + ... |
2e57a5305c4ce8d8690532ce707aea878f8ada31 | bdb33f8b7ea65f7705fc342a178508e2722eb851 | /analysis/ennreal.lean | 57766823c627d5dad14337cbc1cf6f97f2f2d106 | [
"Apache-2.0"
] | permissive | rwbarton/mathlib | 939ae09bf8d6eb1331fc2f7e067d39567e10e33d | c13c5ea701bb1eec057e0a242d9f480a079105e9 | refs/heads/master | 1,584,015,335,862 | 1,524,142,167,000 | 1,524,142,167,000 | 130,614,171 | 0 | 0 | Apache-2.0 | 1,548,902,667,000 | 1,524,437,371,000 | Lean | UTF-8 | Lean | false | false | 43,749 | 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 order.bounds algebra.ordered_group analysis.real analysis.topology.infinite_sum
noncomputable theory
open classical set lattice fil... |
57eb9e4216362d0624a6245e6e36630853b50c6f | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/algebra/star/pi.lean | 3f4a1e23184bdb64085f8135e7a066553d78c10d | [
"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 | 2,127 | 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.star.basic
import algebra.ring.pi
import algebra.module.pi
/-!
# `star` on pi types
We put a `has_star` structure on pi types that operates elementwise, su... |
76cde18823f8a971a69208e00a17868e05e4fba1 | ba202b5df889db60057325d9f940c616e8cb44f3 | /src/brouwer.lean | c97f8fb99ffa7783a8551200c7787943741448ad | [] | no_license | damiatorres/brouwerfixedpoint | 0a4ec331de6f9992685e5fc71eb2d3418ff1b2bc | 45411c64f3cbf14c4821342c9dd7153825e0a9bf | refs/heads/main | 1,685,778,289,255 | 1,623,877,752,000 | 1,623,877,752,000 | 377,779,620 | 0 | 0 | null | 1,623,923,011,000 | 1,623,923,011,000 | null | UTF-8 | Lean | false | false | 527 | lean | import data.real.basic
import data.list
import barycentric_subdivision
import combinatorics.simplicial_complex.basic
import combinatorics.simplicial_complex.finite
import combinatorics.simplicial_complex.sperner
variables {m n : ℕ}
local notation `E` := fin m → ℝ
open affine
open set
-- The proposition that a given... |
d701608603823d68564b6d46f03eedec995f3c1f | c777c32c8e484e195053731103c5e52af26a25d1 | /src/linear_algebra/bilinear_form.lean | 8befd53e09164d8b93b0cfe38950f5fe454aed74 | [
"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 | 54,740 | lean | /-
Copyright (c) 2018 Andreas Swerdlow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andreas Swerdlow, Kexing Ying
-/
import linear_algebra.dual
import linear_algebra.free_module.finite.matrix
/-!
# Bilinear form
This file defines a bilinear form over a module. Ba... |
5da8eafc9c3c669a2e9106e7673553e6e55538de | d1a52c3f208fa42c41df8278c3d280f075eb020c | /src/Lean/Meta/FunInfo.lean | c77d86bad65d6ff2d8510ac00480d2b139450354 | [
"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 | 3,067 | 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.Meta.Basic
import Lean.Meta.InferType
namespace Lean.Meta
@[inline] private def checkFunInfoCache (fn : Expr) (maxArgs? : Option Nat) (k : Met... |
d2c6a17d562420f4e9b7e20de1f01da9278cd13d | b7f22e51856f4989b970961f794f1c435f9b8f78 | /hott/homotopy/cofiber.hlean | 68d857e27641289b157450a3fab15b9905be1a2c | [
"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 | 3,674 | hlean | /-
Copyright (c) 2016 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer
The Cofiber Type
-/
import hit.pointed_pushout function .susp types.unit
open eq pushout unit pointed is_trunc is_equiv susp unit
definition cofiber {A B : Type} ... |
8ead927db303cc16436fa4d4a7dacfafc9e86459 | 592ee40978ac7604005a4e0d35bbc4b467389241 | /Library/generated/mathscheme-lean/RightBinaryInverse.lean | 6a2d0beb35f54ef81a26ccd1e765ade69103b378 | [] | 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 | 9,168 | 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 RightBinaryInverse
structure RightBinaryInverse (A : Type) : Type :=
(linv : (A → (A → A)))
(rinv : (A → (A → A)))
(rightInverse : (∀ {x y : A} , (linv x... |
abe768fdb08e89888e9250d89dd6e9ad72556f54 | 205f0fc16279a69ea36e9fd158e3a97b06834ce2 | /EXAMS/Exam2-Review-key.lean | aaabd68f17ce92dc48c6ad80f2572c58efc6cd23 | [] | no_license | kevinsullivan/cs-dm-lean | b21d3ca1a9b2a0751ba13fcb4e7b258010a5d124 | a06a94e98be77170ca1df486c8189338b16cf6c6 | refs/heads/master | 1,585,948,743,595 | 1,544,339,346,000 | 1,544,339,346,000 | 155,570,767 | 1 | 3 | null | 1,541,540,372,000 | 1,540,995,993,000 | Lean | UTF-8 | Lean | false | false | 12,145 | lean | /-
You need to understand the following
elements of automated predicate logic
for Exam 2
Suppose P and Q are arbitrary propositions
(i.e., P Q : Prop) and T and V are arbitrary
types (i.e., T V : Type).
Know the following forms, how to prove them,
how to use proofs of them, and how to do these
things in Lean.
... |
fe8c10e7cace19b09e1dafa7ddf59dc691cb2975 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /archive/100-theorems-list/37_solution_of_cubic.lean | 8c96a063bd3e3f6fffb6dc2c13b9b46a90c8d8ad | [
"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 | 7,451 | lean | /-
Copyright (c) 2022 Jeoff Lee. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeoff Lee
-/
import tactic.basic
import ring_theory.roots_of_unity
import ring_theory.polynomial.cyclotomic.basic
/-!
# The Solution of a Cubic
This file proves Theorem 37 from the [100 T... |
4ea46697ab0795e47a3e0bdade190199f2e14c74 | 30b012bb72d640ec30c8fdd4c45fdfa67beb012c | /analysis/measure_theory/measure_space.lean | 4edbcbc08e4a6171ed7601f28940500a9c1b8878 | [
"Apache-2.0"
] | permissive | kckennylau/mathlib | 21fb810b701b10d6606d9002a4004f7672262e83 | 47b3477e20ffb5a06588dd3abb01fe0fe3205646 | refs/heads/master | 1,634,976,409,281 | 1,542,042,832,000 | 1,542,319,733,000 | 109,560,458 | 0 | 0 | Apache-2.0 | 1,542,369,208,000 | 1,509,867,494,000 | Lean | UTF-8 | Lean | false | false | 28,225 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
Measure spaces -- measures
Measures are restricted to a measurable space (associated by the type class `measurable_space`).
This allows us to prove equ... |
c5ab221befe460abc53818aef5dd3752fd2e6f5f | 626e312b5c1cb2d88fca108f5933076012633192 | /src/data/finset/basic.lean | 1f8a5239871a169b1c2c0290c3ff4bfb224c9982 | [
"Apache-2.0"
] | permissive | Bioye97/mathlib | 9db2f9ee54418d29dd06996279ba9dc874fd6beb | 782a20a27ee83b523f801ff34efb1a9557085019 | refs/heads/master | 1,690,305,956,488 | 1,631,067,774,000 | 1,631,067,774,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 128,447 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad, Minchao Wu, Mario Carneiro
-/
import data.multiset.finset_ops
import tactic.apply
import tactic.monotonicity
import tactic.nth_rewrite
/-!
# F... |
6dde4f8c05742c0c031fb20f34e8cb8b8667b4de | a7eef317ddec01b9fc6cfbb876fe7ac00f205ac7 | /src/data/set/finite.lean | 8a3cf59f9f42de3c2b5b5127226391315e9f4424 | [
"Apache-2.0"
] | permissive | kmill/mathlib | ea5a007b67ae4e9e18dd50d31d8aa60f650425ee | 1a419a9fea7b959317eddd556e1bb9639f4dcc05 | refs/heads/master | 1,668,578,197,719 | 1,593,629,163,000 | 1,593,629,163,000 | 276,482,939 | 0 | 0 | null | 1,593,637,960,000 | 1,593,637,959,000 | null | UTF-8 | Lean | false | false | 24,344 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import data.fintype.basic
import algebra.big_operators
/-!
# Finite sets
This file defines predicates `finite : set α → Prop` and `infinite : set α ... |
708fb7e31888011cee1ad9b2cdbdd9f6a95f45a3 | 2c096fdfecf64e46ea7bc6ce5521f142b5926864 | /src/Lean/Elab/Deriving/FromToJson.lean | 0e6bc16f63613c9a00e8519be1c5b5ab89e41b3a | [
"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 | 9,509 | lean | /-
Copyright (c) 2020 Sebastian Ullrich. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Ullrich, Dany Fabian
-/
import Lean.Meta.Transform
import Lean.Elab.Deriving.Basic
import Lean.Elab.Deriving.Util
import Lean.Data.Json.FromToJson
namespace Lean.Elab.Der... |
edf5a6d00ed21743f31dc252d4ef0c4a38af91da | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/order/cover.lean | 4c44601db170e285baf188206e89c75620ed1c6b | [
"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 | 3,751 | 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
-/
import data.set.intervals.ord_connected
/-!
# The covering relation
This file defines the covering relation in an order. `b`... |
ac44fda3173b876751953cf856f4a2842eec084a | 1437b3495ef9020d5413178aa33c0a625f15f15f | /analysis/metric_space.lean | 9af6e400ae5ff1110408787d375f4eac5582b2f5 | [
"Apache-2.0"
] | permissive | jean002/mathlib | c66bbb2d9fdc9c03ae07f869acac7ddbfce67a30 | dc6c38a765799c99c4d9c8d5207d9e6c9e0e2cfd | refs/heads/master | 1,587,027,806,375 | 1,547,306,358,000 | 1,547,306,358,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 55,003 | lean | /-
Copyright (c) 2015, 2017 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Metric spaces.
Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
Many definitions and theorems expected on metric spaces are already introduced o... |
7ec12c3e33a4b7a2956f8eaefcfafb0cc996b67b | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/group_theory/group_action.lean | 10f73ee53f83bcf64726b98e62528903b4f280eb | [
"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 | 6,718 | 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 data.set.finite group_theory.coset
universes u v w
variables {α : Type u} {β : Type v} {γ : Type w}
/-- Typeclass for types with a scalar multiplication operatio... |
b26782d4e0e1de53f23cbdd450b9499a7248310b | 59cb0b250f036506a327b29abf0b51ff1efbb0c9 | /src/syndrome_decoding.lean | 3e70373c0290b577f2740792e45e7e809d14682b | [] | no_license | GeorgeTillisch/coding_theory_lean | ea26861a3d5d8ca897ca50b056d9cae53104bc27 | 920e14b433080854d4248714c93a09ce4e391522 | refs/heads/main | 1,681,707,926,918 | 1,619,008,763,000 | 1,619,008,763,000 | 343,145,352 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,991 | lean | import tactic
import binary
import hamming
/-!
# Syndrome Decoding for the Hamming(7,4) code.
This file contains a formalization of the Hamming(7,4) code.
In particular, we formalize encoding, decoding, and error correction procedures.
We use a structure `BECC` (Binary Error Correcting Code) to guide this formalizati... |
fedf0aa67b14376e53eee6a4cdbae88989622516 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/geometry/manifold/diffeomorph.lean | 0e4a19a412fa27b2e5d0d3bcfd7b9b8147f22cd9 | [
"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 | 19,777 | lean | /-
Copyright © 2020 Nicolò Cavalleri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolò Cavalleri, Yury Kudryashov
-/
import geometry.manifold.times_cont_mdiff_map
/-!
# Diffeomorphisms
This file implements diffeomorphisms.
## Definitions
* `diffeomorph I I' M ... |
88fd68feb52bef6a0eb04ad89be0aefe5a67db74 | ad0c7d243dc1bd563419e2767ed42fb323d7beea | /data/nat/prime.lean | a1564a95f507fff31183cf73d97865f83c17e1b8 | [
"Apache-2.0"
] | permissive | sebzim4500/mathlib | e0b5a63b1655f910dee30badf09bd7e191d3cf30 | 6997cafbd3a7325af5cb318561768c316ceb7757 | refs/heads/master | 1,585,549,958,618 | 1,538,221,723,000 | 1,538,221,723,000 | 150,869,076 | 0 | 0 | Apache-2.0 | 1,538,229,323,000 | 1,538,229,323,000 | null | UTF-8 | Lean | false | false | 15,855 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad, Mario Carneiro
Prime numbers.
-/
import data.nat.sqrt data.nat.gcd data.list.basic data.list.perm
open bool subtype
namespace nat
open decida... |
c3de97a7ab7764d85c54ac4333373110e2598f1f | 6dc0c8ce7a76229dd81e73ed4474f15f88a9e294 | /stage0/src/Lean/Meta/Tactic/Clear.lean | fcb972baf8c953886de910275e1401bd425207df | [
"Apache-2.0"
] | permissive | williamdemeo/lean4 | 72161c58fe65c3ad955d6a3050bb7d37c04c0d54 | 6d00fcf1d6d873e195f9220c668ef9c58e9c4a35 | refs/heads/master | 1,678,305,356,877 | 1,614,708,995,000 | 1,614,708,995,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,465 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Meta.Tactic.Util
namespace Lean.Meta
def clear (mvarId : MVarId) (fvarId : FVarId) : MetaM MVarId :=
withMVarContext mvarId do
checkNotA... |
164ae739c9be0f93c821044e5dda57216947c7f0 | 19cc34575500ee2e3d4586c15544632aa07a8e66 | /src/data/finset/basic.lean | b5430638be53b97951fa7c3627fd7604406bbd3e | [
"Apache-2.0"
] | permissive | LibertasSpZ/mathlib | b9fcd46625eb940611adb5e719a4b554138dade6 | 33f7870a49d7cc06d2f3036e22543e6ec5046e68 | refs/heads/master | 1,672,066,539,347 | 1,602,429,158,000 | 1,602,429,158,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 93,420 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad, Minchao Wu, Mario Carneiro
-/
import data.multiset.finset_ops
import tactic.monotonicity
import tactic.apply
/-!
# Finite sets
mathlib has se... |
ae174e0dc6d13afac391b2bef1099354520373ad | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/scopedMacros.lean | ec002a70de1e5d4dbde62d8a3da7bd65cc3843b6 | [
"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 | 954 | lean | namespace Foo
scoped macro "foo!" x:term:max : term => `($x + 1)
#check foo! 10
theorem ex1 : foo! 10 = 11 := rfl
end Foo
#check foo! 10 -- Error
open Foo
#check foo! 10 -- works
theorem ex2 : foo! 10 = 11 := rfl
scoped macro "bla!" x:term:max : term => `($x * 2) -- Error scoped macros must be used inside name... |
2a43b593ade5f6e1bcc24f5a6ed0efe2e77b395d | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/set_theory/ordinal/principal.lean | ce63acccbfca86a22d17e5ba9cb58df11d663cc0 | [
"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 | 16,098 | lean | /-
Copyright (c) 2022 Violeta Hernández Palacios. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Violeta Hernández Palacios
-/
import set_theory.ordinal.fixed_point
/-!
### Principal ordinals
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file requ... |
8ca76bc0f53b4d5818507841ebddbd7df86e25f1 | 6e44fda625e48340c6ffc7b1109a9e3b208e5384 | /src/topology/examples.lean | ed6b1c5475dc2b36a0d521b7f31e53ad8b76eb57 | [] | no_license | JasonKYi/learn_mspaces | 9f998a265b907af6be6a54061637fcf1f6d1ee9d | 54083e81da420d2d362a7024a8c86bea8529fe66 | refs/heads/master | 1,619,008,842,896 | 1,609,897,382,000 | 1,609,897,382,000 | 249,780,600 | 5 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,726 | lean | import topology.theorems
import data.set.finite
open definitions set
variables {X : Type*}
namespace examples
-- The cofinite topology
def example_topology : topological_space X :=
{ is_open := λ U, U ∈ {∅} ∪ {U' : set X | finite U'ᶜ},
is_open_univ :=
by right; rw mem_set_of_eq; convert finite_empty; exact ... |
f878f8b1f10607f36cb5f3ecf2dd655dc9c11a03 | 4fa118f6209450d4e8d058790e2967337811b2b5 | /src/for_mathlib/nonarchimedean/is_subgroups_basis.lean | 35cd96356acf5472d54a93e00bf41dafa8e70f10 | [
"Apache-2.0"
] | permissive | leanprover-community/lean-perfectoid-spaces | 16ab697a220ed3669bf76311daa8c466382207f7 | 95a6520ce578b30a80b4c36e36ab2d559a842690 | refs/heads/master | 1,639,557,829,139 | 1,638,797,866,000 | 1,638,797,866,000 | 135,769,296 | 96 | 10 | Apache-2.0 | 1,638,797,866,000 | 1,527,892,754,000 | Lean | UTF-8 | Lean | false | false | 6,510 | lean | import for_mathlib.nonarchimedean.basic
import for_mathlib.topological_rings
open set filter function lattice add_group_with_zero_nhd
--local attribute [instance] pointwise_mul pointwise_add
local attribute [instance] set.pointwise_mul_semiring
local attribute [instance] set.smul_set_action
local notation `𝓝` x: 70... |
4afbecc182e61c29ee8720e33d7744631d2f2b4e | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/smartUnfoldingMatch.lean | 11c5d74770daba4e6b922a4ddc29974a4135a02b | [
"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 | 266 | lean | import Lean
open Lean Meta Elab Term in
elab "whnf%" t:term : term <= expectedType => do
let r ← whnf (← elabTerm t expectedType)
trace[Meta.debug] "r: {r}"
return r
opaque x : Option Nat := some 42
set_option trace.Meta.debug true
#eval whnf% x.getD 0
|
ebfde529e9db441814af3227d2ec053c15c1fab8 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/linear_algebra/projection.lean | db341846f0b42b5e2022de7fa62aace850d67c5a | [
"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 | 13,099 | lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import linear_algebra.quotient
import linear_algebra.prod
/-!
# Projection to a subspace
In this file we define
* `linear_proj_of_is_compl (p q : submodule R E) (... |
7c832a74295df8db142724333b1170416dc9748a | 61ccc57f9d72048e493dd6969b56ebd7f0a8f9e8 | /src/algebra/ring.lean | 443c4d616014840bb07fd2a867c123780f91bf64 | [
"Apache-2.0"
] | permissive | jtristan/mathlib | 375b3c8682975df28f79f53efcb7c88840118467 | 8fa8f175271320d675277a672f59ec53abd62f10 | refs/heads/master | 1,651,072,765,551 | 1,588,255,641,000 | 1,588,255,641,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 29,085 | 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, Floris van Doorn, Amelia Livingston
-/
import algebra.group.with_one
import deprecated.group
import tactic.norm_cast
/-!
# Properties and homomorphism... |
d234e2dc7d7f056d234342259c50033bd7001f4d | 87a08a8e9b222ec02f3327dca4ae24590c1b3de9 | /src/category/fold.lean | 311bd09e6d8af5abf682a0295f0100371406da20 | [
"Apache-2.0"
] | permissive | naussicaa/mathlib | 86d05223517a39e80920549a8052f9cf0e0b77b8 | 1ef2c2df20cf45c21675d855436228c7ae02d47a | refs/heads/master | 1,592,104,950,080 | 1,562,073,069,000 | 1,562,073,069,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,595 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Sean Leather
List folds generalized to `traversable`. Informally, we can think of
`foldl` as a special case of `traverse` where we do not care about the
reconstructed data s... |
0a0dea8331adf391a3e96b7c160b03bf425a56f4 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/analysis/normed_space/extr.lean | b458f8d5dc8aaab4139be8ed0799923d511d7b2a | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 4,001 | lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import analysis.normed_space.ray
import topology.local_extr
/-!
# (Local) maximums in a normed space
In this file we prove the following lemma, see `is_max_filter... |
2a773e9df71b7a320fc98f850e9d9f543358bf40 | 649957717d58c43b5d8d200da34bf374293fe739 | /src/topology/Top/limits.lean | bdffd05d47e39f3bba47444dbfdf6eac7c0c1184 | [
"Apache-2.0"
] | permissive | Vtec234/mathlib | b50c7b21edea438df7497e5ed6a45f61527f0370 | fb1848bbbfce46152f58e219dc0712f3289d2b20 | refs/heads/master | 1,592,463,095,113 | 1,562,737,749,000 | 1,562,737,749,000 | 196,202,858 | 0 | 0 | Apache-2.0 | 1,562,762,338,000 | 1,562,762,337,000 | null | UTF-8 | Lean | false | false | 2,723 | lean | -- Copyright (c) 2017 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Patrick Massot, Scott Morrison, Mario Carneiro
import topology.Top.basic
import category_theory.limits.types
import category_theory.limits.preserves
open topological_space
open... |
4a552b8e13c74986d33845d9968cb2bba3150984 | 5ae26df177f810c5006841e9c73dc56e01b978d7 | /src/group_theory/free_group.lean | fab4a18a4056383456cae59485c17bea389294bb | [
"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 | 30,839 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
Free groups as a quotient over the reduction relation `a * x * x⁻¹ * b = a * b`.
First we introduce the one step reduction relation
`free_group.red.step`: w * x * x⁻¹ * v ~... |
54d68dfe9fc6b9f2d3de56c718f712086d1adff8 | 08bd4ba4ca87dba1f09d2c96a26f5d65da81f4b4 | /src/Lean/Elab/Command.lean | cb3e9471bd33c0e8e286df4d6cee3a31025e8e94 | [
"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 | 20,776 | 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.Elab.Binders
import Lean.Elab.SyntheticMVars
namespace Lean.Elab.Command
structure Scope where
header : String
opts : Opti... |
95dc58a6d20451d4d969dd5eab04b1a8c4729f81 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/data/qpf/multivariate/constructions/cofix.lean | 773ad67d19afb20225e6b9dc30532dda0a994dfa | [
"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 | 19,012 | lean | /-
Copyright (c) 2018 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Simon Hudon
-/
import control.functor.multivariate
import data.pfunctor.multivariate.basic
import data.pfunctor.multivariate.M
import data.qpf.multivariate.basic
/-!
# ... |
512c145a0fbc19996a3855760354f82df963e4ab | 4950bf76e5ae40ba9f8491647d0b6f228ddce173 | /src/data/equiv/ring_aut.lean | 28d60af30fc23f8715cb5d21fadf89d4dda085c3 | [
"Apache-2.0"
] | permissive | ntzwq/mathlib | ca50b21079b0a7c6781c34b62199a396dd00cee2 | 36eec1a98f22df82eaccd354a758ef8576af2a7f | refs/heads/master | 1,675,193,391,478 | 1,607,822,996,000 | 1,607,822,996,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,980 | 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 data.equiv.ring
import data.equiv.mul_add_aut
/-!
# Ring automorphisms
This file defines the automorphism group structure on ... |
4c5ad3c494862f568ce12ebd757f63e9c49f43dc | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/geometry/manifold/smooth_manifold_with_corners.lean | e149284da479dd3d06e37c106addf1443cf9f6f0 | [] | 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 | 41,408 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.analysis.calculus.times_cont_diff
import Mathlib.geometry.manifold.charted_space
impo... |
9964dba0798b872c492cbf7ce6a26e2d14733ee8 | ae1e94c332e17c7dc7051ce976d5a9eebe7ab8a5 | /src/Init/Data/Int/Basic.lean | b021e13016b03db16ddcd3e16875e3d56b6e018e | [
"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 | 4,419 | 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
The integers, with addition, multiplication, and subtraction.
-/
prelude
import Init.Coe
import Init.Data.Nat.Div
import Init.Data.List.Basic
open Nat
... |
be4a4e3c4a60fccbccdeb03ddfb9e42be5d4766a | d65db56b17d72b62013ed1f438f74457ad25b140 | /src/induction.lean | 13a2e7bc41f9832ce8259ee360cc11a3ab52991c | [] | no_license | swgillespie/proofs | cfa65722fdb4bb7d7910a0856d0cbea8e8b9a3f9 | 168ef7ef33d372ae0ed6ee4ca336137a52b89f8f | refs/heads/master | 1,585,700,692,028 | 1,540,162,775,000 | 1,540,162,775,000 | 152,695,805 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,366 | lean | /-
- Exercises and theorems using induction.
-/
open function
section example_6
inductive aexpr : Type
| const : ℕ → aexpr
| var : ℕ → aexpr
| plus : aexpr → aexpr → aexpr
| times : aexpr → aexpr → aexpr
open aexpr
def sample_aexpr : aexpr :=
plus (times (var 0) (const 7)) (times (const 2) (var 1)... |
01b59bf0c327641f78c2bda6dfcbdc9c99b9d13e | df7bb3acd9623e489e95e85d0bc55590ab0bc393 | /lean/love04_functional_programming_exercise_solution.lean | 685b7d542bb4241d7f3f4b3f5394a3f712fb74da | [] | no_license | MaschavanderMarel/logical_verification_2020 | a41c210b9237c56cb35f6cd399e3ac2fe42e775d | 7d562ef174cc6578ca6013f74db336480470b708 | refs/heads/master | 1,692,144,223,196 | 1,634,661,675,000 | 1,634,661,675,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,232 | lean | import .love03_forward_proofs_demo
/- # LoVe Exercise 4: Functional Programming -/
set_option pp.beta true
set_option pp.generalized_field_notation false
namespace LoVe
/- ## Question 1: Reverse of a List
We define a new accumulator-based version of `reverse`. The first argument,
`as`, serves as the accumulator... |
34e14b19967c5eee0ef6a041ebc9f445f2340991 | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/topology/algebra/nonarchimedean/basic.lean | 118fc5918e6526d9b8e4fd7e82a13fe85462488c | [
"Apache-2.0"
] | permissive | hikari0108/mathlib | b7ea2b7350497ab1a0b87a09d093ecc025a50dfa | a9e7d333b0cfd45f13a20f7b96b7d52e19fa2901 | refs/heads/master | 1,690,483,608,260 | 1,631,541,580,000 | 1,631,541,580,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,845 | lean | /-
Copyright (c) 2021 Ashwin Iyengar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Johan Commelin, Ashwin Iyengar, Patrick Massot
-/
import topology.algebra.ring
import topology.algebra.open_subgroup
import data.set.basic
import group_theory.subgroup
... |
fc4a0aa10d09fcd95f5ad2efb47a607181aa667f | 94e33a31faa76775069b071adea97e86e218a8ee | /src/algebra/algebra/unitization.lean | fb95c376eb44f87750c545d7d5d3a201d8f1895b | [
"Apache-2.0"
] | permissive | urkud/mathlib | eab80095e1b9f1513bfb7f25b4fa82fa4fd02989 | 6379d39e6b5b279df9715f8011369a301b634e41 | refs/heads/master | 1,658,425,342,662 | 1,658,078,703,000 | 1,658,078,703,000 | 186,910,338 | 0 | 0 | Apache-2.0 | 1,568,512,083,000 | 1,557,958,709,000 | Lean | UTF-8 | Lean | false | false | 21,741 | lean | /-
Copyright (c) 2022 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import algebra.algebra.basic
import linear_algebra.prod
import algebra.hom.non_unital_alg
/-!
# Unitization of a non-unital algebra
Given a non-unital `R`-algebra `A... |
57f7e03a7a1b48548a2904a54618df8cb98f88cc | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/data/finset/gcd.lean | a222874861b44d21c77642c533e59650ce09234a | [
"Apache-2.0"
] | permissive | abentkamp/mathlib | d9a75d291ec09f4637b0f30cc3880ffb07549ee5 | 5360e476391508e092b5a1e5210bd0ed22dc0755 | refs/heads/master | 1,682,382,954,948 | 1,622,106,077,000 | 1,622,106,077,000 | 149,285,665 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,009 | lean | /-
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import data.finset.fold
import data.multiset.gcd
/-!
# GCD and LCM operations on finsets
## Main definitions
- `finset.gcd` - the greatest common denominator of a ... |
23aa92cff27ee4d3647d958cf5b8cf7c49048621 | 4bcaca5dc83d49803f72b7b5920b75b6e7d9de2d | /stage0/src/Init/WF.lean | 3bda551f86b21efec33211052ba0c4cf0f0aff83 | [
"Apache-2.0"
] | permissive | subfish-zhou/leanprover-zh_CN.github.io | 30b9fba9bd790720bd95764e61ae796697d2f603 | 8b2985d4a3d458ceda9361ac454c28168d920d3f | refs/heads/master | 1,689,709,967,820 | 1,632,503,056,000 | 1,632,503,056,000 | 409,962,097 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,539 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
prelude
import Init.SizeOf
import Init.Data.Nat.Basic
universe u v
set_option codegen false
inductive Acc {α : Sort u} (r : α → α → Prop) : α → Prop where... |
47e63a282bf51fb51c76ab846fd6e8e5401b29e4 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/ring_theory/mv_polynomial/tower.lean | 9877c4389812bed9c9f3bafed2c246f3b62ab87c | [
"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 | 2,458 | lean | /-
Copyright (c) 2022 Yuyang Zhao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuyang Zhao
-/
import algebra.algebra.tower
import data.mv_polynomial.basic
/-!
# Algebra towers for multivariate polynomial
This file proves some basic results about the algebra tower... |
43c4aa1fb8a73624dffab90a45c77ab060dc73b7 | 07c6143268cfb72beccd1cc35735d424ebcb187b | /src/category_theory/adjunction/limits.lean | e1fb85036cef2394d825d114834383861038b846 | [
"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 | 8,597 | lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Johan Commelin
-/
import category_theory.adjunction.basic
import category_theory.limits.preserves
import category_theory.limits.creates
open opposite
namespace category_the... |
5d6be74ecc4efa14eef435c4da2ebc4e92081cfc | 626e312b5c1cb2d88fca108f5933076012633192 | /src/algebra/category/Module/subobject.lean | 6496a4b6498459fb80cb4dc257765deeb804f0b9 | [
"Apache-2.0"
] | permissive | Bioye97/mathlib | 9db2f9ee54418d29dd06996279ba9dc874fd6beb | 782a20a27ee83b523f801ff34efb1a9557085019 | refs/heads/master | 1,690,305,956,488 | 1,631,067,774,000 | 1,631,067,774,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,253 | lean | /-
Copyright (c) 2021 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import algebra.category.Module.epi_mono
import category_theory.subobject.well_powered
/-!
# Subobjects in the category of `R`-modules
We construct an explicit order i... |
14928af252254f8ef053e78af8dce2e9f9ef359a | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/complex/isometry.lean | 44eaf6f25e9c0ed9970dec1f51d278418056bf47 | [
"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 | 6,834 | lean | /-
Copyright (c) 2021 François Sunatori. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: François Sunatori
-/
import analysis.complex.circle
import linear_algebra.determinant
import linear_algebra.matrix.general_linear_group
/-!
# Isometries of the Complex Plane
> THI... |
0ad6a0966b547e4cb505451ec0efd30c332da353 | 6e9cd8d58e550c481a3b45806bd34a3514c6b3e0 | /src/algebra/archimedean.lean | 1c332c2b96004aa0c344625be82fc57fa0bb561b | [
"Apache-2.0"
] | permissive | sflicht/mathlib | 220fd16e463928110e7b0a50bbed7b731979407f | 1b2048d7195314a7e34e06770948ee00f0ac3545 | refs/heads/master | 1,665,934,056,043 | 1,591,373,803,000 | 1,591,373,803,000 | 269,815,267 | 0 | 0 | Apache-2.0 | 1,591,402,068,000 | 1,591,402,067,000 | null | UTF-8 | Lean | false | false | 10,112 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
Archimedean groups and fields.
-/
import algebra.field_power
import data.rat
variables {α : Type*}
class archimedean (α) [ordered_add_comm_monoid α] : Prop :=
(arch :... |
03bcc281cfe79c33299e7589c07b32e1d511c0d9 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/computability/halting.lean | d53b1ea727d88834b22a3f94b9877025819d6efe | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 15,257 | 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 computability.partrec_code
/-!
# Computability theory and the halting problem
A universal partial recursive function, Rice's theorem, and the halting problem... |
0a874e85cb1b577eeb7c1ab93fdf427e69f3305c | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/set/intervals/proj_Icc.lean | d1658095ae3b2ad9fa34354967205d2cc4304db0 | [] | 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 | 5,843 | 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, Patrick Massot
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.set.intervals.basic
import Mathlib.PostPort
universes u_1 u_2... |
93461ffdaae2252c662793738c495b6c48fee0a7 | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /stage0/src/Lean/Elab.lean | a77fadd5dfb73fcf25697cad8fbf22e7add23dc9 | [
"Apache-2.0"
] | permissive | walterhu1015/lean4 | b2c71b688975177402758924eaa513475ed6ce72 | 2214d81e84646a905d0b20b032c89caf89c737ad | refs/heads/master | 1,671,342,096,906 | 1,599,695,985,000 | 1,599,695,985,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 770 | 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.Elab.Import
import Lean.Elab.Exception
import Lean.Elab.StrategyAttrs
import Lean.Elab.Command
import Lean.Elab.Term
import Lean.Elab.App
import... |
01ace82dea9048d6df2ead686a179004674fcc63 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/run/def10.lean | 86ff74ffff95be9b99fa4d4d171f4d367949a04c | [
"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 | 450 | lean | open nat
inductive bv : nat → Type
| nil : bv 0
| cons : ∀ (n) (hd : bool) (tl : bv n), bv (succ n)
open bv bool
definition h : ∀ {n}, bv (succ (succ n)) → bool
| .(succ m) (cons (succ (succ m)) b v) := b
| .0 (cons (succ nat.zero) b v) := bnot b
example (m : nat) (b : bool) (v : bv (succ (succ m))) : @h (s... |
0d2b2f07793a440c0a37156b2c0e2a29d3526944 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/algebraic_geometry/sheafed_space.lean | 3f42c317cab80b2912ce41de1f329f923a82fbb0 | [
"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 | 6,020 | 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 algebraic_geometry.presheafed_space.has_colimits
import topology.sheaves.functors
/-!
# Sheafed spaces
Introduces the category of topological spaces equipped... |
11c514244964166df1b374e6deab7cbb4a52e717 | 22e97a5d648fc451e25a06c668dc03ac7ed7bc25 | /src/linear_algebra/basis.lean | 81c6162d2fe3d0cbca0ba4085e0a054a160ac271 | [
"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 | 53,148 | 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, Alexander Bentkamp
-/
import linear_algebra.finsupp
import linear_algebra.projection
import order.zorn
import data.fintype.card
/-!
# Linear independe... |
bf85191818788b56d3307a16706b5bb50c0c9ce0 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/exact_error_pos.lean | d25d321c694952a74a17db9bcc17639edde3a325 | [
"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 | 166 | lean | constant f : nat → nat → nat
def ex1 : nat :=
begin
exact 10 +
(f 1 (f 0 tt))
end
def ex₂ : nat :=
begin
apply 10 +
(f 1 (f 0 tt))
end
|
ec368edb67d83e952d7b88e0ebbb529d818eb5c5 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/combinatorics/configuration.lean | d87b2a2ebb7c3c22c54407baaa4f2fc4c0db4d51 | [
"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 | 23,689 | lean | /-
Copyright (c) 2021 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import algebra.big_operators.order
import combinatorics.hall.basic
import data.fintype.card
import set_theory.cardinal.finite
/-!
# Configurations of Points and li... |
a9413858cc7e427f858276cb86cb41552737bbe7 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/order/field/inj_surj.lean | 01a1d0f929096fe5d6a42a79ba085b93d171e377 | [
"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 | 3,087 | lean | /-
Copyright (c) 2014 Robert Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Lewis, Leonardo de Moura, Mario Carneiro, Floris van Doorn
-/
import algebra.order.field.defs
import algebra.field.basic
import algebra.order.ring.inj_surj
/-!
# Pulling back lin... |
08ef9abe7fb7d4a92e32903ac8e300c731ee200a | 94e33a31faa76775069b071adea97e86e218a8ee | /src/category_theory/limits/shapes/multiequalizer.lean | 7292893ebb255d366bb2bb02b86adecdec33b600 | [
"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 | 26,580 | 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.limits.shapes.products
import category_theory.limits.shapes.equalizers
import category_theory.limits.cone_category
import category_theory.adjunction
/... |
768184a9d650a15ffbf324ffd71f3ce0275e0e5c | 969dbdfed67fda40a6f5a2b4f8c4a3c7dc01e0fb | /src/algebraic_topology/simplex_category.lean | 0cffbb754a4cbd1f9b5f73e049987181600597e8 | [
"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 | 10,854 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Scott Morrison
-/
import order.category.NonemptyFinLinOrd
import category_theory.skeletal
import data.finset.sort
import tactic.linarith
/-! # The simplex category
W... |
d3600afaf4fd8b2f649a9a259bb2113056fc2171 | ce6917c5bacabee346655160b74a307b4a5ab620 | /src/ch5/ex0415.lean | d20e1278529085081c9590fe7b76791df9e283ab | [] | no_license | Ailrun/Theorem_Proving_in_Lean | ae6a23f3c54d62d401314d6a771e8ff8b4132db2 | 2eb1b5caf93c6a5a555c79e9097cf2ba5a66cf68 | refs/heads/master | 1,609,838,270,467 | 1,586,846,743,000 | 1,586,846,743,000 | 240,967,761 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 300 | lean | example (p q : Prop) : p ∧ q ↔ q ∧ p :=
begin
apply iff.intro,
{ intro h,
have hp : p := h.left,
have hq : q := h.right,
show q ∧ p,
exact ⟨hq, hp⟩ },
intro h,
have hp : p := h.right,
have hq : q := h.left,
show p ∧ q,
exact ⟨hp, hq⟩
end
|
15cdf73d11512713174f1c38bbc1c35f2bb9f0db | 8d65764a9e5f0923a67fc435eb1a5a1d02fd80e3 | /src/group_theory/sylow.lean | f6fee760fefd2fcab601f977be3668ff5f3c1809 | [
"Apache-2.0"
] | permissive | troyjlee/mathlib | e18d4b8026e32062ab9e89bc3b003a5d1cfec3f5 | 45e7eb8447555247246e3fe91c87066506c14875 | refs/heads/master | 1,689,248,035,046 | 1,629,470,528,000 | 1,629,470,528,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,901 | 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
import group_theory.quotient_group
import group_theory.order_of_element
import data.zmod.basic
import data.fintype.card
import data.list.... |
915e66b7a1dffdb3336cd6c9e60c09fedbaf7c28 | 969dbdfed67fda40a6f5a2b4f8c4a3c7dc01e0fb | /src/ring_theory/subsemiring.lean | 2ed674ff87d379a8f85618751ee4e7c53be2ba4e | [
"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 | 27,148 | lean | /-
Copyright (c) 2020 Yury Kudryashov All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import algebra.ring.prod
import group_theory.submonoid
import data.equiv.ring
/-!
# Bundled subsemirings
We define bundled subsemirings and some standard construc... |
7a093a06f14700efd0ae7b60633613f82b9f39ee | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/967.lean | a225f0aff384233993c6a25bd3ada919b1ed6823 | [
"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 | 153 | lean | variables (A : Type)
definition f (A : Type) (a : A) := a
inductive bla (A : Type)
| mk : A → bla
structure foo (A : Type) (f : A → A) :=
(a : A)
|
36a2f8193db78c10b8fa0d4613d5e4d71a039f05 | e0f9ba56b7fedc16ef8697f6caeef5898b435143 | /src/data/monoid_algebra.lean | 3262f4d89057511a6e722b15bff993beaac60bcb | [
"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 | 23,773 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yury G. Kudryashov, Scott Morrison
-/
import data.finsupp ring_theory.algebra
/-!
# Monoid algebras
When the domain of a `finsupp` has a multiplicative or additive st... |
6817116c46bfdbe91e521fc626152b40d0c19c38 | 43390109ab88557e6090f3245c47479c123ee500 | /src/category_theory/Problems/1_3.lean | 94fee3f95ed5230d377c6aaa081e59658e6a0a81 | [
"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 | 949 | lean | import categories.category
import categories.isomorphism
import categories.tactics
import categories.functor
import categories.Ndefs
open categories categories.isomorphism categories.functor categories.idempotent tactic
--delaration of universes and variables
universes u v u₁ v₁
variables (C : Type u₁) [𝒞 : category.... |
f96536ae3248bf830abc0422db7e7827b26f0ca8 | ae1e94c332e17c7dc7051ce976d5a9eebe7ab8a5 | /stage0/src/Std/Data/PersistentArray.lean | 2e3f40de76f74cac165f527cb2572523ba554c03 | [
"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 | 13,734 | 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
-/
universes u v w
namespace Std
inductive PersistentArrayNode (α : Type u) where
| node (cs : Array (PersistentArrayNode α)) : PersistentArrayNode α
| l... |
81481423b52e41c16a66bdc4835d33a145ce1eec | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/order/to_interval_mod.lean | 30cba2c693fb98b45b6bd3f440761f25b706a610 | [
"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 | 40,612 | lean | /-
Copyright (c) 2022 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import algebra.modeq
import algebra.module.basic
import algebra.order.archimedean
import algebra.periodic
import data.int.succ_pred
import group_theory.quotient_group
imp... |
2717a57f2735fd5c571d71bb66f4e130c928ab92 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/irCompilerBug.lean | 24385860e716922a5d1a31dcc4ca78d97a2b0ba1 | [
"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 | 801 | lean | --
structure Payload :=
(key : Nat)
(val : Nat)
@[noinline] def get? (p : Payload) (k : Nat) : Option Nat :=
if p.key == k then pure p.val else failure
inductive T
| a (i : Nat)
| b (i : Nat)
| c (i : Nat)
| d (i : Nat)
@[noinline] def foo (p : Payload) : Option T :=
(do
let i ← get? p 1;
pure (T.a i))
<|> (d... |
74dc4d18db03010e1fce7d15dff8669124c4e5be | 36c7a18fd72e5b57229bd8ba36493daf536a19ce | /tests/lean/run/blast_cc14.lean | 31829c590eb1a4b36d105cdd6456e3b575a60c71 | [
"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 | 206 | lean | constant R : nat → nat → Prop
axiom R_trans : ∀ a b c, R a b → R b c → R a c
attribute R_trans [trans]
set_option blast.subst false
example (a b c : nat) : a = b → R a b → R a a :=
by blast
|
6bee9da8bd441d51f18e44c6b63674e0c1d19114 | 390c7d44c0470f935f1ff06637607521791400da | /test2.lean | 7c885b24d4fb4c7ee22ac1284ecd8d1454a4698b | [] | 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 | 12,895 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Nathaniel Thomas
More examples to test the tableau provers, stolen shamelessly by Jeremy from Nathaniel's "tauto".
Notes: Most things using "safe" (a classical ... |
474c247dc8ade327211b45df6aec2b8ed0a142a9 | 4fa161becb8ce7378a709f5992a594764699e268 | /src/algebra/group/semiconj.lean | 99f3592dadda7b1dbbf4479ef9653c900b1ad84b | [
"Apache-2.0"
] | permissive | laughinggas/mathlib | e4aa4565ae34e46e834434284cb26bd9d67bc373 | 86dcd5cda7a5017c8b3c8876c89a510a19d49aad | refs/heads/master | 1,669,496,232,688 | 1,592,831,995,000 | 1,592,831,995,000 | 274,155,979 | 0 | 0 | Apache-2.0 | 1,592,835,190,000 | 1,592,835,189,000 | null | UTF-8 | Lean | false | false | 5,623 | lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
Some proofs and docs came from `algebra/commute` (c) Neil Strickland
-/
import algebra.group.units
import tactic.rewrite
/-!
# Semiconjugate elements of a semigroup
... |
aa0f8195c022d176b5867284d2887c2ca6cfc0d2 | f20db13587f4dd28a4b1fbd31953afd491691fa0 | /library/init/meta/congr_tactic.lean | 49dfe671bf7dfbb4b124a0b078318cfe218d1deb | [
"Apache-2.0"
] | permissive | AHartNtkn/lean | 9a971edfc6857c63edcbf96bea6841b9a84cf916 | 0d83a74b26541421fc1aa33044c35b03759710ed | refs/heads/master | 1,620,592,591,236 | 1,516,749,881,000 | 1,516,749,881,000 | 118,697,288 | 1 | 0 | null | 1,516,759,470,000 | 1,516,759,470,000 | null | UTF-8 | Lean | false | false | 1,894 | lean | /-
Copyright (c) 2017 Daniel Selsam. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Daniel Selsam
-/
prelude
import init.meta.tactic init.meta.congr_lemma init.meta.relation_tactics init.function
namespace tactic
meta def apply_congr_core (clemma : congr_lemma) : tact... |
437ba816f42dbdcd3451a33ffc56ecfb8db3aa5c | da23b545e1653cafd4ab88b3a42b9115a0b1355f | /test/force.lean | a0b64e8356baf2454cd02ebf4470381d2537b49e | [] | no_license | minchaowu/lean-tidy | 137f5058896e0e81dae84bf8d02b74101d21677a | 2d4c52d66cf07c59f8746e405ba861b4fa0e3835 | refs/heads/master | 1,585,283,406,120 | 1,535,094,033,000 | 1,535,094,033,000 | 145,945,792 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 129 | lean | import tidy.force
-- open tactic
example : ∀ x : ℕ, 1 = 1 :=
begin
intros,
success_if_fail { force `[intros] },
refl
end |
ebb979102b1481e9f5d625d5cea9514c24545cb0 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/ring_theory/polynomial/basic.lean | 42324d24dab15f01a3be0f1823df880419beb52d | [
"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 | 49,103 | 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 ring_theory.polynomial.content
import ring_theory.unique_factorization_d... |
4f451cc10fdade3798270c7cfb98f118b1170482 | 367134ba5a65885e863bdc4507601606690974c1 | /src/algebra/char_p/pi.lean | 61bbe3ee9cfa5795e3c47dad3d6765511b93294e | [
"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 | 859 | 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.char_p.basic
import algebra.ring.pi
/-!
# Characteristic of semirings of functions
-/
universes u v
namespace char_p
instance pi (ι : Type u) [hi : nonempty... |
a20ae116ce79a607ec142d7cbbd5d8417ba4d76e | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /src/Init/Data/List.lean | 9af534e50928a5f5c0efcb9242917c3cc4ead96c | [
"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 | 293 | 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.Data.List.Basic
import Init.Data.List.BasicAux
import Init.Data.List.Instances
import Init.Data.List.Control
|
696999554ab93866871594af7be1d4c3554e4f58 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/rat/defs.lean | e0b4580e5eccaff010a9dfdb805b1d8e25b8a45e | [
"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 | 23,021 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import data.rat.init
import data.int.cast.defs
import data.int.dvd.basic
import algebra.ring.regular
import data.nat.gcd.basic
import data.pnat.defs
... |
20c6fcdd8d001ea121c3f7b2acaafdce0705d823 | 22e97a5d648fc451e25a06c668dc03ac7ed7bc25 | /src/analysis/analytic/basic.lean | df89f9b2b3df159991ccaf43220da73bcb651eb2 | [
"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 | 38,053 | 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 analysis.calculus.times_cont_diff
import tactic.omega
import analysis.special_functions.pow
/-!
# Analytic functions
A function is analytic in one dime... |
d4273003e94cdcc7b671ab27e9552e4ce8414a06 | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /src/Lean/PrettyPrinter/Parenthesizer.lean | dc6d5df08d43f1bee68707ce0df1d655d17bf1c6 | [
"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 | 29,632 | lean | /-
Copyright (c) 2020 Sebastian Ullrich. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Ullrich
-/
/-!
The parenthesizer inserts parentheses into a `Syntax` object where syntactically necessary, usually as an intermediary
step between the delaborator and the... |
c86bcfa39b13f456d05540b9285f4d3ba7bc342c | a523fc1740c8cb84cd0fa0f4b52a760da4e32a5c | /src/missing_mathlib/ring_theory/polynomial/basic.lean | 475229ef9e767da72ac935a09a7a1867b0c422a5 | [] | no_license | abentkamp/spectral | a1aff51e85d30b296a81d256ced1d382345d3396 | 751645679ef1cb6266316349de9e492eff85484c | refs/heads/master | 1,669,994,798,064 | 1,597,591,646,000 | 1,597,591,646,000 | 287,544,072 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,690 | lean | import ring_theory.polynomial.basic
import ring_theory.principal_ideal_domain
import data.polynomial.field_division
import missing_mathlib.data.multiset
import missing_mathlib.data.polynomial
import missing_mathlib.data.list.basic
noncomputable theory
local attribute [instance, priority 100] classical.prop_decidable
... |
ad37c4cd13d3ce8583f8967dd08f02696815c192 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/module/torsion.lean | fae52a8083c44f96994533ce1443e9998d858c61 | [
"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 | 27,568 | lean | /-
Copyright (c) 2022 Pierre-Alexandre Bazin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Pierre-Alexandre Bazin
-/
import algebra.direct_sum.module
import algebra.module.big_operators
import linear_algebra.isomorphisms
import group_theory.torsion
import ring_theory... |
351b58ab733210edb66fde923e6824f82dc23732 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/group_theory/group_action/big_operators.lean | af25d91dc1244b1338740dfd0ed7873f1874952f | [
"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 | 1,716 | lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import algebra.big_operators.basic
import data.finset.basic
import data.multiset.basic
import group_theory.group_action.defs
/-!
# Lemmas about group actions on bi... |
fd3ad6f628a25c3812024baf7c4e6495d911e918 | bb31430994044506fa42fd667e2d556327e18dfe | /src/combinatorics/double_counting.lean | 3c042ba9a7ed4a3bf2647957bd6ed910d44ce56b | [
"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 | 5,041 | 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 algebra.big_operators.order
/-!
# Double countings
This file gathers a few double counting arguments.
## Bipartite graphs
In a bipartite graph (considered as a... |
cea70a018f85b9d18d865d10449dac5a60c66102 | ea4aee6b11f86433e69bb5e50d0259e056d0ae61 | /src/tidy/transport.lean | 7dfd3ddbeb110664e072d8f5ea799fe29605461b | [] | no_license | timjb/lean-tidy | e18feff0b7f0aad08c614fb4d34aaf527bf21e20 | e767e259bf76c69edfd4ab8af1b76e6f1ed67f48 | refs/heads/master | 1,624,861,693,182 | 1,504,411,006,000 | 1,504,411,006,000 | 103,740,824 | 0 | 0 | null | 1,505,553,968,000 | 1,505,553,968,000 | null | UTF-8 | Lean | false | false | 282 | lean | -- Copyright (c) 2017 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Scott Morrison
definition {u v} transport {A : Type u} { P : A → Type v} {x y : A} (u : P x) (p : x = y) : P y :=
by induction p; exact u |
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