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e7efb468de19fca40888837a0380752e61a033b1 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/number_theory/bertrand.lean | b9dbb2af60d55c4cc15d6d2191b65ed4bebd6ed3 | [
"Apache-2.0"
] | permissive | kbuzzard/mathlib | 2ff9e85dfe2a46f4b291927f983afec17e946eb8 | 58537299e922f9c77df76cb613910914a479c1f7 | refs/heads/master | 1,685,313,702,744 | 1,683,974,212,000 | 1,683,974,212,000 | 128,185,277 | 1 | 0 | null | 1,522,920,600,000 | 1,522,920,600,000 | null | UTF-8 | Lean | false | false | 11,296 | lean | /-
Copyright (c) 2020 Patrick Stevens. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Stevens, Bolton Bailey
-/
import data.nat.choose.factorization
import data.nat.prime_norm_num
import number_theory.primorial
import analysis.convex.specific_functions
/-!
# B... |
f1e6187f53ee341ee7bcd64d3de8f5ef8c8babd2 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/algebra/polynomial/big_operators_auto.lean | 98f442ed2c703a868b3724b514b75ca03e01c63e | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,228 | lean | /-
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson, Jalex Stark.
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.polynomial.monic
import Mathlib.tactic.linarith.default
import Mathlib.P... |
758abdfb006497b6d723fc941c782546b59aba70 | 2c096fdfecf64e46ea7bc6ce5521f142b5926864 | /src/Lean/KeyedDeclsAttribute.lean | 21dfbd8d2c485194b1e698ab7facc0734652040c | [
"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 | 7,379 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Sebastian Ullrich
-/
import Lean.Compiler.InitAttr
import Lean.ScopedEnvExtension
import Lean.Compiler.IR.CompilerM
/-!
A builder for attributes that are app... |
4088e22fe35a308b6b2fbf3e727c303c8eb110af | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/category_theory/graded_object.lean | a9e96c5dedd075a318cb26b836618606d65c22c3 | [
"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 | 6,842 | 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.group.basic
import category_theory.pi.basic
import category_theory.shift
/-!
# The category of graded objects
For any type `β`, a `β`-graded object o... |
9857036729d04751f5a1dcddaca1647f6f007a38 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/order/lattice.lean | 14128e9768f957356e654e1ed6a08c2194a18444 | [
"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 | 46,671 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import order.monotone.basic
import tactic.simps
import tactic.pi_instances
/-!
# (Semi-)lattices
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this fi... |
8c61b02a6305c859765f6a7b67cca0adca4ae384 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/data/nat/part_enat.lean | a808fd603f7b4e42dc7cf3c8b055f2f84e42ebe7 | [
"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 | 21,095 | 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 algebra.hom.equiv
import data.part
import data.nat.enat
import tactic.norm_num
/-!
# Natural numbers with infinity
The natural numbers and an extra `top` element... |
192ba813e19b147667991aaa8ac7d1bba6a84288 | 1abd1ed12aa68b375cdef28959f39531c6e95b84 | /src/ring_theory/fractional_ideal.lean | db0d7dba611666cec42b7c551a6efae720e04e59 | [
"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 | 50,262 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Filippo A. E. Nuccio
-/
import ring_theory.localization
import ring_theory.noetherian
import ring_theory.principal_ideal_domain
import tactic.field_simp
/-!
# Fractional ide... |
3cb5c5d8855d9f3da16ba2b85c7dda0a2fbd014e | bd12a817ba941113eb7fdb7ddf0979d9ed9386a0 | /src/order/filter/filter_product.lean | 6fee246a4a2e26b73e5742360fa3de9a7a0fc4dd | [
"Apache-2.0"
] | permissive | flypitch/mathlib | 563d9c3356c2885eb6cefaa704d8d86b89b74b15 | 70cd00bc20ad304f2ac0886b2291b44261787607 | refs/heads/master | 1,590,167,818,658 | 1,557,762,121,000 | 1,557,762,121,000 | 186,450,076 | 0 | 0 | Apache-2.0 | 1,557,762,289,000 | 1,557,762,288,000 | null | UTF-8 | Lean | false | false | 20,329 | lean | /-
Copyright (c) 2019 Abhimanyu Pallavi Sudhir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Abhimanyu Pallavi Sudhir
"Filterproducts" (ultraproducts on general filters), ultraproducts.
-/
import order.filter.basic
universes u v
variables {α : Type u} (β : Type v) ... |
2d982089b5ff10622e9cd08655698f92cd31e949 | 37da0369b6c03e380e057bf680d81e6c9fdf9219 | /hott/hit/prop_trunc.hlean | 717e9a5f7292cbdb8a360515e144589c1fc6bf6f | [
"Apache-2.0"
] | permissive | kodyvajjha/lean2 | 72b120d95c3a1d77f54433fa90c9810e14a931a4 | 227fcad22ab2bc27bb7471be7911075d101ba3f9 | refs/heads/master | 1,627,157,512,295 | 1,501,855,676,000 | 1,504,809,427,000 | 109,317,326 | 0 | 0 | null | 1,509,839,253,000 | 1,509,655,713,000 | C++ | UTF-8 | Lean | false | false | 15,280 | hlean | import types.trunc hit.colimit homotopy.connectedness
open eq is_trunc unit quotient seq_colim pi nat equiv sum algebra is_conn function
/-
In this file we define the propositional truncation, which, given (X : Type)
has constructors
* tr : X → trunc X
* is_prop_trunc : is_prop (trunc X)
and wi... |
bd52288cf0afcbccae95cc64e4318e28df6ef668 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/number_theory/modular_forms/slash_actions.lean | 0f73ab5dd46f62f3d40421290c97009a997425f7 | [
"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 | 5,136 | lean | /-
Copyright (c) 2022 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
import analysis.complex.upper_half_plane.basic
import linear_algebra.general_linear_group
import linear_algebra.special_linear_group
/-!
# Slash actions
This file d... |
fd8843d23146e30b67ba1caa8696787497d0b49d | a53d207bb311090dc4b68b72150140e042bd1631 | /src/hw1.lean | c174d37d7cba840f484563b82da441104ce6a27f | [] | no_license | krismanaya/learnLean | f09ae1ed8bfd025bf17430dc2e679d128c65f49c | 784123bb6598cba00ddee7193230a5b79ea7f86a | refs/heads/master | 1,598,118,915,447 | 1,571,881,083,000 | 1,571,881,083,000 | 216,452,203 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,648 | lean | theorem easy (P Q: Prop) (HP : P) (HPQ: P → Q) : Q :=
begin
apply HPQ, -- now i just have to prove p -> Q
exact HP -- i know HP of P
end
theorem prove_P_implies_Q (P Q : Prop)(HQ: Q): P → Q :=
begin
intro HP, -- assume HP of P
exact HQ,
end
theorem P_implies_P (P: Pro... |
dd178294d6d26fea176fce2cadac65f6073f3199 | 2fbe653e4bc441efde5e5d250566e65538709888 | /src/topology/subset_properties.lean | e64357308dd596ffe33c50abd6704e889020aa59 | [
"Apache-2.0"
] | permissive | aceg00/mathlib | 5e15e79a8af87ff7eb8c17e2629c442ef24e746b | 8786ea6d6d46d6969ac9a869eb818bf100802882 | refs/heads/master | 1,649,202,698,930 | 1,580,924,783,000 | 1,580,924,783,000 | 149,197,272 | 0 | 0 | Apache-2.0 | 1,537,224,208,000 | 1,537,224,207,000 | null | UTF-8 | Lean | false | false | 35,026 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Yury Kudryashov
-/
import topology.continuous_on
/-!
# Properties of subsets of topological spaces
## Main definitions
`compact`, `is_clopen`, `is_i... |
11efa87c7610dd927d7be875d54b347f5d53bd39 | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/finset/nat_antidiagonal.lean | 91b9dbafa986cc12629bc3ed6e178e361f8e1b12 | [
"Apache-2.0"
] | permissive | kodyvajjha/mathlib | 9bead00e90f68269a313f45f5561766cfd8d5cad | b98af5dd79e13a38d84438b850a2e8858ec21284 | refs/heads/master | 1,624,350,366,310 | 1,615,563,062,000 | 1,615,563,062,000 | 162,666,963 | 0 | 0 | Apache-2.0 | 1,545,367,651,000 | 1,545,367,651,000 | null | UTF-8 | Lean | false | false | 2,313 | lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import data.finset.basic
import data.multiset.nat_antidiagonal
/-!
# The "antidiagonal" {(0,n), (1,n-1), ..., (n,0)} as a finset.
-/
namespace finset
namespace nat... |
5ad46383a71e57c920f014d4fab8d10ca0df0306 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/algebra/direct_sum/internal.lean | d7ba46b643318681099ffe37dfb566c10c6f8bb3 | [
"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 | 9,889 | lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Kevin Buzzard, Jujian Zhang
-/
import algebra.algebra.operations
import algebra.algebra.subalgebra.basic
import algebra.direct_sum.algebra
/-!
# Internally graded rings and... |
e0248cee8fcd374971978799bf955deb29636b0b | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /tests/lean/run/946.lean | 5d89516eb4a579f5e70d6967ee275d5d7c9952f2 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | EdAyers/lean4 | 57ac632d6b0789cb91fab2170e8c9e40441221bd | 37ba0df5841bde51dbc2329da81ac23d4f6a4de4 | refs/heads/master | 1,676,463,245,298 | 1,660,619,433,000 | 1,660,619,433,000 | 183,433,437 | 1 | 0 | Apache-2.0 | 1,657,612,672,000 | 1,556,196,574,000 | Lean | UTF-8 | Lean | false | false | 2,547 | 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... |
f1de601afbd3ae6f399da51f6ef1ae8b3b782b69 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /library/data/countable.lean | c635b67b1cacdd1e2b26fc369c507bd49dd478d7 | [
"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 | 275 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
Define countable types
-/
open function
definition countable (A : Type) : Prop := ∃ f : A → nat, injective f
|
d1c3a9e492bdb4f7f5fa49723875d66e1b3aa768 | ebf7140a9ea507409ff4c994124fa36e79b4ae35 | /src/exercises_sources/thursday/category_theory/exercise3.lean | 08297f8c84a78ee817bfb94d8048f1133269577f | [] | no_license | fundou/lftcm2020 | 3e88d58a92755ea5dd49f19c36239c35286ecf5e | 99d11bf3bcd71ffeaef0250caa08ecc46e69b55b | refs/heads/master | 1,685,610,799,304 | 1,624,070,416,000 | 1,624,070,416,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 694 | lean | import category_theory.equivalence
open category_theory
variables {C : Type*} [category C]
variables {D : Type*} [category D]
lemma equiv_reflects_mono {X Y : C} (f : X ⟶ Y) (e : C ≌ D)
(hef : mono (e.functor.map f)) : mono f :=
-- Hint: when `e : C ≌ D`, `e.functor.map_injective` says
-- `∀ f g, e.functor.map f... |
025ff69e5df0b16382df8a15261782018d0884af | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/big_operators/basic.lean | c81e48ab7fcc90e741bb46e26a5dfc1d8fe39aa1 | [
"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 | 79,118 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import algebra.big_operators.multiset.lemmas
import algebra.group.pi
import algebra.group_power.lemmas
import algebra.hom.equiv.basic
import algebra.ring.opposite
im... |
b6248664280e4928c716664450289819d37ad34d | ba4794a0deca1d2aaa68914cd285d77880907b5c | /src/game/world7/level9.lean | 017284d97b4484c70b13a42b86f57525f9fa39f1 | [
"Apache-2.0"
] | permissive | ChrisHughes24/natural_number_game | c7c00aa1f6a95004286fd456ed13cf6e113159ce | 9d09925424da9f6275e6cfe427c8bcf12bb0944f | refs/heads/master | 1,600,715,773,528 | 1,573,910,462,000 | 1,573,910,462,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,026 | lean | import game.world6.level8 -- hide
import tactic.tauto -- useful high-powered tactic
local attribute [instance, priority 10] classical.prop_decidable -- we are mathematicians
/-
# Advanced proposition world.
You already know enough to embark on advanced addition world. But here are just a couple
more things.
## Level... |
02669ef38f190f8343c21968afae3a7f8c1f3264 | a4673261e60b025e2c8c825dfa4ab9108246c32e | /tests/lean/precissues.lean | 1dead871ae262ca343db528719507b2e1c70db6f | [
"Apache-2.0"
] | permissive | jcommelin/lean4 | c02dec0cc32c4bccab009285475f265f17d73228 | 2909313475588cc20ac0436e55548a4502050d0a | refs/heads/master | 1,674,129,550,893 | 1,606,415,348,000 | 1,606,415,348,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 691 | lean |
#check id fun x => x -- should work
#check 0
def f (x : Nat) (g : Nat → Nat) := g x
#check f 1 fun x => x -- should fail
#check 0
#check f 1 (fun x => x)
#check id have True from ⟨⟩; this -- should fail
#check id let x := 10; x
#check 1
#check id (have True from ⟨⟩; this)
#check 0 = have Nat from 1; this
#c... |
5ea6da0a1118ed15930d84fe67167fc3abb932a2 | 9dd3f3912f7321eb58ee9aa8f21778ad6221f87c | /library/init/meta/smt/rsimp.lean | dfedee78240e2ce8faa074231f430cdda3870ce8 | [
"Apache-2.0"
] | permissive | bre7k30/lean | de893411bcfa7b3c5572e61b9e1c52951b310aa4 | 5a924699d076dab1bd5af23a8f910b433e598d7a | refs/heads/master | 1,610,900,145,817 | 1,488,006,845,000 | 1,488,006,845,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,586 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.meta.smt.smt_tactic init.meta.fun_info init.meta.rb_map
open tactic
private meta def add_lemma (m : transparency) (h : name) (hs : hin... |
231c2c5fbbc1b46ff3d8c51656b98a8de463a6e3 | 6dc0c8ce7a76229dd81e73ed4474f15f88a9e294 | /stage0/src/Lean/Elab/Binders.lean | 0da728b456820df0fa57400e1bf087e869afea88 | [
"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 | 24,788 | 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.Term
import Lean.Parser.Term
namespace Lean.Elab.Term
open Meta
open Lean.Parser.Term
/--
Given syntax of the forms
a) (`:` term)?
... |
27b06547979b0d918db0975efeb2b7522b4a98de | 74caf7451c921a8d5ab9c6e2b828c9d0a35aae95 | /library/init/data/nat/lemmas.lean | 8acec0d7fe7bd9c39f705a56e3d776ab56e23cc1 | [
"Apache-2.0"
] | permissive | sakas--/lean | f37b6fad4fd4206f2891b89f0f8135f57921fc3f | 570d9052820be1d6442a5cc58ece37397f8a9e4c | refs/heads/master | 1,586,127,145,194 | 1,480,960,018,000 | 1,480,960,635,000 | 40,137,176 | 0 | 0 | null | 1,438,621,351,000 | 1,438,621,351,000 | null | UTF-8 | Lean | false | false | 19,113 | 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.nat.basic init.meta init.algebra
namespace nat
protected lemma zero_add : ∀ n : ℕ, 0 + n = n
| 0 := rfl
| (n+1) := congr_arg ... |
60778c0195fca0d51c5ead0733b4aeac9804030c | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/951.lean | b107b0c87db5f065d46243334abf5d94dcd979fc | [
"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 | 494 | lean | inductive ThingA where
| mkA
deriving Ord
instance : LE ThingA where
le a b := (compare a b).isLE
instance (t₁ t₂ : ThingA) : Decidable (t₁ <= t₂) := inferInstance
-- TODO: we may want to suppress the name of nested instances
#check instDecidableLeThingAInstLEThingA
inductive ThingB where
| mkB
deriving Ord
instanc... |
3d1360ad430e5924c9108a58ce32e0d0478c71fb | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/algebra/lie/submodule.lean | 3a99d0b13dad931628e5d6437b1b5a37935408d8 | [
"Apache-2.0"
] | permissive | ilitzroth/mathlib | ea647e67f1fdfd19a0f7bdc5504e8acec6180011 | 5254ef14e3465f6504306132fe3ba9cec9ffff16 | refs/heads/master | 1,680,086,661,182 | 1,617,715,647,000 | 1,617,715,647,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 28,725 | lean | /-
Copyright (c) 2021 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import algebra.lie.subalgebra
import ring_theory.noetherian
/-!
# Lie submodules of a Lie algebra
In this file we define Lie submodules and Lie ideals, we construct the l... |
8663036768a519e7748b11325489a19b68a2f66e | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/pnat/prime.lean | 6427d339b8c0a4da703933063a007b1249958929 | [
"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 | 7,561 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Neil Strickland
-/
import data.nat.prime
import data.pnat.basic
/-!
# Primality and GCD on pnat
This file extends the theory of `ℕ+` with `gcd`, `lcm` and `pri... |
3043e12b8c8cd6e9f2f4d730758af3cdc223fd16 | 649957717d58c43b5d8d200da34bf374293fe739 | /src/data/list/sort.lean | 45714ec1b7e254c7347f94971fd22005c0a31427 | [
"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 | 10,338 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad
Insertion sort and merge sort.
-/
import data.list.perm
open list.perm
namespace list
section sorted
universe variable uu
variables {α : Type uu} {r : α → α → Prop}
/--... |
277c730bd6d5fe11ec986bd656add001f63b6dd9 | 367134ba5a65885e863bdc4507601606690974c1 | /src/ring_theory/polynomial/content.lean | c33c684fdbf36bb43e7d6fc5d91df733f7103a96 | [
"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 | 16,782 | lean | /-
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Aaron Anderson
-/
import data.finset.gcd
import data.polynomial
import data.polynomial.erase_lead
import data.polynomial.cancel_leads
/-!
# GCD structures on polynomials
Definitions a... |
6296c3beabcd8512d19b733467db4ce747ac63a2 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/number_theory/legendre_symbol/quadratic_reciprocity.lean | 93215318f6248694db8989e837c8d11c1730040d | [
"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 | 14,395 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Michael Stoll
-/
import number_theory.legendre_symbol.quadratic_char
/-!
# Legendre symbol and quadratic reciprocity.
This file contains results about quadratic residues ... |
64907c27ffad2d54a398c5d2feecefbceb5c3dbe | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/convolution.lean | 199a713352ea1c31de2081c95ba5591bf8869f2b | [
"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 | 83,952 | lean | /-
Copyright (c) 2022 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import analysis.calculus.bump_function_inner
import analysis.calculus.parametric_integral
import measure_theory.constructions.prod.integral
import measure_theory.... |
1a557be5877a4e4f0720982f0da46c6bc685647a | a156d865507798f08f46a2f6ca204d9727f4734d | /src/group_theory/sporadic_group.lean | a5d3ea492a651d5dd8ad090f87f2e2330a03bdad | [] | no_license | jesse-michael-han/formalabstracts | 4e2fc8c107a3388823ffbd1671dd1e54108ea394 | 63a949de7989f17c791c40e580c3011516af57e0 | refs/heads/master | 1,625,470,495,408 | 1,551,315,841,000 | 1,551,316,547,000 | 136,272,424 | 0 | 0 | null | 1,528,259,798,000 | 1,528,259,798,000 | null | UTF-8 | Lean | false | false | 14,718 | lean | import .basic .monster .presentation .suzuki .higman_sims .mclaughlin .conway_groups .mathieu_group
import tactic.fattribute
import tactic.metadata
noncomputable theory
open monster suzuki higman_sims mclaughlin conway_groups mathieu_group is_monoid_action coxeter_vertices
open category_theory (mk_ob)
local infix ` ≅ `... |
6b33532f4c07116a8345cea675759fcbbdaa67cb | 02005f45e00c7ecf2c8ca5db60251bd1e9c860b5 | /src/algebra/big_operators/order.lean | 01f2f2fd9e13c6891fce163ee388c4ddaded2f08 | [
"Apache-2.0"
] | permissive | anthony2698/mathlib | 03cd69fe5c280b0916f6df2d07c614c8e1efe890 | 407615e05814e98b24b2ff322b14e8e3eb5e5d67 | refs/heads/master | 1,678,792,774,873 | 1,614,371,563,000 | 1,614,371,563,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,907 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import algebra.big_operators.basic
/-!
# Results about big operators with values in an ordered algebraic structure.
Mostly monotonicity results for the `∑` operati... |
dec1474fd5f4b07fb555a0c79243a0afe287b614 | 432d948a4d3d242fdfb44b81c9e1b1baacd58617 | /src/algebra/lie/matrix.lean | a8a0433eb84df4b7b9842862042d2c43f9ed110c | [
"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 | 3,419 | lean | /-
Copyright (c) 2021 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import algebra.lie.of_associative
import linear_algebra.matrix
/-!
# Lie algebras of matrices
An important class of Lie algebras are those arising from the associative al... |
53b6c263acd0e86491eccafcc6fe86dd6e064e5c | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/ring_theory/polynomial/bernstein.lean | 6a6aecf3fc47ab5ace65d68f41e0edef811bbe5f | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 16,773 | 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 data.polynomial.derivative
import data.nat.choose.sum
import ring_theory.polynomial.pochhammer
import data.polynomial.algebra_map
import linear_algebra.linear_... |
bd9b9b22d8a6c5f4596fec9871aec876ce4d596c | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /src/Lean/Server.lean | a27ad465c51b049aee310cbb4b30f97f2d1e3b6d | [
"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 | 372 | lean | /-
Copyright (c) 2020 Marc Huisinga. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Marc Huisinga, Wojciech Nawrocki
-/
import Lean.Server.Utils
import Lean.Server.AsyncList
import Lean.Server.Snapshots
import Lean.Server.FileSource
import Lean.Server.Watchdog
import ... |
41c1c0be69cdd8ce42e23d4604dfef5136c3baa3 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /archive/imo/imo2019_q1.lean | b19fd9475f693747f98e42cd49363330726efeea | [
"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 | 1,898 | lean | /-
Copyright (c) 2020 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard
-/
import tactic.linarith
/-!
# IMO 2019 Q1
Determine all functions `f : ℤ → ℤ` such that, for all integers `a` and `b`,
`f(2a) + 2f(b) = f(f(a+b))`.
The desired theore... |
c5fb8e5e7948318bd79f84ebca487df0bcf374fc | 4f643cce24b2d005aeeb5004c2316a8d6cc7f3b1 | /src/for_mathlib/closure.lean | db15d6824f51529487309e30912b014f433ff2f2 | [] | no_license | rwbarton/lean-omin | da209ed061d64db65a8f7f71f198064986f30eb9 | fd733c6d95ef6f4743aae97de5e15df79877c00e | refs/heads/master | 1,674,408,673,325 | 1,607,343,535,000 | 1,607,343,535,000 | 285,150,399 | 9 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,605 | lean | import data.finset
import data.fintype.basic
/-
Closure under finite unions or intersections.
TODO: Generalize the whole thing to sub-(meet/join)-semilattices?
-/
open set
section finite_unions
variables {α : Type*} (B : set (set α))
/-- The property of a family of sets being closed under finite unions. -/
struct... |
d7ab44fd25876489af71c4a5d5cfce1d47ebdbde | 54ce0561cebde424526f41d45f490ed56be2bd0c | /scratch/scratchPad.lean | 84bc227080a15c1bfc0d11eacf81406c740b4e73 | [] | no_license | melembroucarlitos/Tao_Analysis-LEAN | cf7b3298d317891a09e4bf21cfe7c7ffcb57b9a9 | 3f4fc7e090d96b6cef64896492fba4bef124794b | refs/heads/master | 1,692,952,385,694 | 1,636,287,522,000 | 1,636,287,522,000 | 400,630,166 | 3 | 0 | null | 1,635,910,807,000 | 1,630,096,823,000 | Lean | UTF-8 | Lean | false | false | 4,029 | lean | namespace hidden
-- myNatural Numbers
-- 2.1.1
inductive myNat : Type
| zero : myNat
| succ : myNat → myNat
-- Can these be proven?? Or must they be axioms??
-- Axiom 2.1 (0 is a myNatural number)
-- Axiom 2.2 (If n is a myNatural number, n++ is also a myNatural number)
-- Axiom 2.3 (For all n, n++ != 0)
-- Axio... |
7d7d99da2b462dbf4427056223ac859a0dc3cb4f | fcf3ffa92a3847189ca669cb18b34ef6b2ec2859 | /src/world2/level2.lean | 1e039cc13a4ef88681828502b36244a62d8163f6 | [
"Apache-2.0"
] | permissive | nomoid/lean-proofs | 4a80a97888699dee42b092b7b959b22d9aa0c066 | b9f03a24623d1a1d111d6c2bbf53c617e2596d6a | refs/heads/master | 1,674,955,317,080 | 1,607,475,706,000 | 1,607,475,706,000 | 314,104,281 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 378 | lean | import mynat.definition
import mynat.add
import world2.level1
namespace mynat
lemma add_assoc (a b c : mynat) : (a + b) + c = a + (b + c) :=
begin [nat_num_game]
induction c with d hd,
{
rw add_zero,
rw add_zero,
refl,
},
{
rw add_succ,
rw add_succ,
rw a... |
cf0d9a359ae1f895f8be8c09c24f8993d47d917d | 437dc96105f48409c3981d46fb48e57c9ac3a3e4 | /src/algebra/associated.lean | 7ead0d36da346405dafe514e01ccc36b7a137708 | [
"Apache-2.0"
] | permissive | dan-c-k/mathlib | 08efec79bd7481ee6da9cc44c24a653bff4fbe0d | 96efc220f6225bc7a5ed8349900391a33a38cc56 | refs/heads/master | 1,658,082,847,093 | 1,589,013,201,000 | 1,589,013,201,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 25,122 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jens Wagemaker
-/
import data.multiset
/-!
# Associated, prime, and irreducible elements.
-/
variables {α : Type*} {β : Type*} {γ : Type*} {δ : Type*}
@[simp] theore... |
dda5556c5373a2220d654e023445fe94c300ff00 | 367134ba5a65885e863bdc4507601606690974c1 | /src/geometry/euclidean/monge_point.lean | ab03206176420c3042b31eca6f37558691a0b12a | [
"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 | 38,569 | lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Joseph Myers.
-/
import geometry.euclidean.circumcenter
noncomputable theory
open_locale big_operators
open_locale classical
open_locale real
open_locale real_inner_product_space
/-!
# ... |
db7331e0272e259e8ae60ce01cc3d3d4641c41dc | 4727251e0cd73359b15b664c3170e5d754078599 | /src/field_theory/finite/polynomial.lean | ab9d717b709f43b8e498c41e81a050199f284b41 | [
"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 | 7,980 | 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 linear_algebra.finite_dimensional
import linear_algebra.basic
import ring_theory.mv_polynomial.basic
import data.mv_polynomial.expand
import field_theory.fini... |
a421b386bc8b3b5df08d6289ae7b35deae73e2e3 | c1a29ca460720df88ab68dc42d9a1a02e029d505 | /examples/logic/unnamed_491.lean | 4aafb6ef4e1e3382fd2dc6c038fd6c792a2dafeb | [] | no_license | agusakov/mathematics_in_lean | acb5b3d659e4522ae4b4836ea550527f03f6546c | 2539562e4d91c858c73dbecb5b282ce1a7d38b6d | refs/heads/master | 1,665,963,365,241 | 1,592,080,022,000 | 1,592,080,022,000 | 272,078,062 | 0 | 0 | null | 1,592,078,772,000 | 1,592,078,772,000 | null | UTF-8 | Lean | false | false | 237 | lean | import data.real.basic
-- BEGIN
open function
example (c : ℝ) : injective (λ x, x + c) :=
begin
intros x₁ x₂ h',
apply eq_of_add_eq_add_right h',
end
example {c : ℝ} (h : c ≠ 0) : injective (λ x, c * x) :=
sorry
-- END |
03dc1d3033586906f980c1ca48f2235cf5c67ea3 | f618aea02cb4104ad34ecf3b9713065cc0d06103 | /src/data/set/intervals.lean | 22a4369eaec438285b4be7b746b49c616324dd23 | [
"Apache-2.0"
] | permissive | joehendrix/mathlib | 84b6603f6be88a7e4d62f5b1b0cbb523bb82b9a5 | c15eab34ad754f9ecd738525cb8b5a870e834ddc | refs/heads/master | 1,589,606,591,630 | 1,555,946,393,000 | 1,555,946,393,000 | 182,813,854 | 0 | 0 | null | 1,555,946,309,000 | 1,555,946,308,000 | null | UTF-8 | Lean | false | false | 11,892 | 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
Intervals
Naming conventions:
`i`: infinite
`o`: open
`c`: closed
Each interval has the name `I` + letter for left side + letter... |
3a6558b183f9970c738c80964ed3e7ae1c87f98f | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/ring_theory/adjoin/tower.lean | eb67e7e843c1ff523c9b06a3b48c3beab156b48e | [
"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 | 6,910 | 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 ring_theory.adjoin.fg
/-!
# Adjoining elements and being finitely generated in an algebra tower
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file r... |
a1fc9eb2120c78ec0dfe7f7eb9e0337ffd59c03c | 0ec6b5eb2131429a4464b8e6c6f09897abba3de1 | /src/torus.lean | ad5a2ef93d359e89715309a5bf9c3329ee74943d | [] | no_license | kckennylau/local-langlands-abelian | ba1b86e9d956778cd28ac900ffec02b0f0ba172a | ee22666898357dab800a0432214a22c519ed26a9 | refs/heads/master | 1,584,671,060,846 | 1,545,151,246,000 | 1,545,151,246,000 | 137,111,892 | 8 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,533 | lean | import algebra.pi_instances analysis.complex
import .algebra_tensor .monoid_ring .field_extensions
universes u v w
instance subtype.comm_group {α : Type u} [comm_group α] (s : set α) [is_subgroup s] : comm_group s :=
by subtype_instance
noncomputable theory
local attribute [instance] classical.prop_decidabl... |
64c807f71d960f068ef2d28b26caab25d4dd4b82 | 0e175f34f8dca5ea099671777e8d7446d7d74227 | /library/init/default.lean | d7cfeb690f6f23c91a2eae2907c0648f9108256a | [
"Apache-2.0"
] | permissive | utensil-contrib/lean | b31266738071c654d96dac8b35d9ccffc8172fda | a28b9c8f78d982a4e82b1e4f7ce7988d87183ae8 | refs/heads/master | 1,670,045,564,075 | 1,597,397,599,000 | 1,597,397,599,000 | 287,528,503 | 0 | 0 | Apache-2.0 | 1,597,408,338,000 | 1,597,408,337,000 | null | UTF-8 | Lean | false | false | 589 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.core init.logic init.control init.data.basic init.version
import init.propext init.cc_lemmas init.funext init.control.combinators init.f... |
989815b7214acc23210029d6502be3cfff8e06d3 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/system/random/basic.lean | 3e7ffc4c4093d77f193655d7d18f101b03487732 | [
"Apache-2.0"
] | permissive | AntoineChambert-Loir/mathlib | 64aabb896129885f12296a799818061bc90da1ff | 07be904260ab6e36a5769680b6012f03a4727134 | refs/heads/master | 1,693,187,631,771 | 1,636,719,886,000 | 1,636,719,886,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,940 | lean | /-
Copyright (c) 2020 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import algebra.group_power
import control.uliftable
import control.monad.basic
import data.bitvec.basic
import data.fin.basic
import data.list.basic
import data.set.inter... |
cc58e985962927843f456355d516f1cd1f0c17ef | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /src/Lean/Elab/Quotation/Util.lean | 341bbbd8657d8cf9b6fbada3d15f4c13431ae7a1 | [
"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 | 1,211 | lean | /-
Copyright (c) 2020 Sebastian Ullrich. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Ullrich
-/
import Lean.Elab.Term
namespace Lean.Elab.Term.Quotation
open Lean.Syntax
partial def getAntiquotationIds (stx : Syntax) : TermElabM (Array Syntax) := do
le... |
0619999e68153e0b5d1b47033a48bbeed1262c23 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/pempty.lean | 003d021913812bb985d88b80b6860d0d0cd3d78f | [
"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 | 1,682 | lean | /-
Copyright (c) 2018 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.discrete_category
/-!
# The empty category
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corr... |
f9e7a6cec9b6182e7baa183610e4577c7581053d | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/revapp.lean | c88e0d89b40c048f32d93b182b8bd11426fbb16a | [
"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 | 759 | lean | import Int.
definition revapp {A : (Type U)} {B : A -> (Type U)} (a : A) (f : forall (x : A), B x) : (B a) := f a.
infixl 100 |> : revapp
check 10 |> (fun x, x + 1)
|> (fun x, x + 2)
|> (fun x, 2 * x)
|> (fun x, 3 - x)
|> (fun x, x + 2)
definition revcomp {A B C: (Type U)} (f : A -... |
4af65002bdcfd6056c4001474b547ef85f15aca9 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/eraseInsts.lean | f53ecb9c413c06e18d7f4cf327fcfad274a62562 | [
"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 | 230 | lean | structure Foo where
a : Nat
instance fooAdd : Add Foo where
add x y := ⟨x.a + y.a⟩
def f1 (a b : Foo) := a + b
section
attribute [-instance] fooAdd
def f2 (a b : Foo) := a + b -- Error
end
def f3 (a b : Foo) := a + b
|
31654ef196a83310860561c8cbcb39438be91155 | 80162757f50b09d3cad5564907e4c9b00742e045 | /set.lean | cb591d8ab4fc04814e9e1b72fcbbe37e3ec83512 | [] | no_license | EdAyers/edlib | cc30d0a54fed347a85b6df6045f68e6b48bc71a3 | 78b8c5d91f023f939c102837d748868e2f3ed27d | refs/heads/master | 1,586,459,758,216 | 1,571,322,179,000 | 1,571,322,179,000 | 160,538,917 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,888 | lean | namespace set
universes u v
variables {α : Type u} {ι : Type v}
variables {A B C D X Y : set α}
variables {a b c : α}
theorem ext (h : ∀ a, a ∈ A ↔ a ∈ B) : A = B :=
funext (λ a, propext (h a))
lemma pair₁ : a ∈ ({a,b} : set α) := begin apply or.inr, apply or.inl, refl end
lemma pair₂ : b ∈ ({a,b} : set α) := begi... |
fb674a02d28c3f2aa80b7e2e4f5c2454302e4dc2 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/ring_theory/witt_vector/verschiebung.lean | b688b8271410b90b4cf0b281c05a86dbfd19a313 | [
"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 | 5,947 | 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 ring_theory.witt_vector.basic
import ring_theory.witt_vector.is_poly
/-!
## The Verschiebung operator
## References
* [Hazewinkel, *Witt Vectors*][Haze09]... |
496555d9ec525a2006ff7361ea45baf712c03a6b | 3aad12fe82645d2d3173fbedc2e5c2ba945a4d75 | /src/category/nursery.lean | 7eeedf5cf3f6cd2a5f8f515cf7f234bf0aa8bda0 | [] | no_license | seanpm2001/LeanProver-Community_MathLIB-Nursery | 4f88d539cb18d73a94af983092896b851e6640b5 | 0479b31fa5b4d39f41e89b8584c9f5bf5271e8ec | refs/heads/master | 1,688,730,786,645 | 1,572,070,026,000 | 1,572,070,026,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,827 | lean |
import tactic
import category.functor
import category.applicative
universes u v
namespace monad
@[simp]
lemma bind_pure_star {m} [monad m] [is_lawful_monad m] (x : m punit) :
x >>= (λ (_x : punit), pure punit.star : punit → m punit) = x :=
by { transitivity,
{ apply congr_arg, ext z, cases z, refl },
{ ... |
715b667407a90b0bc7bb9295eec25bb72f27d02a | d0f9af2b0ace5ce352570d61b09019c8ef4a3b96 | /notes/2020.01.23-objects.identifiers.lean | a394d82573285b4047e309a5c9eb079bff301039 | [] | no_license | jngo13/Discrete-Mathematics | 8671540ef2da7c75915d32332dd20c02f001474e | bf674a866e61f60e6e6d128df85fa73819091787 | refs/heads/master | 1,675,615,657,924 | 1,609,142,011,000 | 1,609,142,011,000 | 267,190,341 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,221 | lean | def b := tt -- "":="" binds
def s := "hello"
def n := 5
#eval tt
#eval b
#eval s
#eval n
/-
mutable store. storing values in
memory that can be "overwritten"
-/
/-
imperative vs functional
command vs expression
mutable vs immutable
variable vs identifier
-/
/-
Types
Every term has exactly one type
A type defines ... |
d0f19b2e016bf1afeb946aa1782b87354ca4dad9 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/interactive/amb.lean | 0a1bba1843b2db61a581c45f4c89af1dba10613c | [
"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 | 288 | lean | namespace Foo
def f (n : Nat) : Bool :=
n == 0
end Foo
namespace Boo
def f (n : String) : String :=
n ++ n
end Boo
open Foo
open Boo
def g := fun x => (f x : Bool)
--^ textDocument/hover
def h := fun x => (f x : String)
--^ textDocument/hover
|
ca1420bf6225269c86581d69739825db169a0fe1 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/measure_theory/function/jacobian.lean | 5c801a92066b23866128531a371e2fe59289e64d | [
"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 | 68,565 | lean | /-
Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import measure_theory.covering.besicovitch_vector_space
import measure_theory.measure.haar_lebesgue
import analysis.normed_space.pointwise
import measure_theory... |
c79086969dc53128ef42b2de87cc303da63bbdaa | 592ee40978ac7604005a4e0d35bbc4b467389241 | /Library/generated/mathscheme-lean/BoundedMeetLattice.lean | 37536ac9e489c711a3d6aac9e69c26f1b3557459 | [] | 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 | 11,901 | 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 BoundedMeetLattice
structure BoundedMeetLattice (A : Type) : Type :=
(times : (A → (A → A)))
(associative_times : (∀ {x y z : A} , (times (times x y) z) = (time... |
473db96344eacbe36f840054698c2cfe45696ad4 | 78269ad0b3c342b20786f60690708b6e328132b0 | /src/library_dev/data/int/div.lean | fe126c720149c34ff3d6a61d959b8a80828f44a5 | [] | no_license | dselsam/library_dev | e74f46010fee9c7b66eaa704654cad0fcd2eefca | 1b4e34e7fb067ea5211714d6d3ecef5132fc8218 | refs/heads/master | 1,610,372,841,675 | 1,497,014,421,000 | 1,497,014,421,000 | 86,526,137 | 0 | 0 | null | 1,490,752,133,000 | 1,490,752,132,000 | null | UTF-8 | Lean | false | false | 845 | lean | import ...algebra.ring
namespace int
lemma coe_nat_dvd_coe_nat_of_dvd {m n : ℕ} (h : m ∣ n) : (↑m : ℤ) ∣ ↑n :=
dvd.elim h $ λk e, dvd.intro k $ by rw [e, int.coe_nat_mul]
lemma dvd_of_coe_nat_dvd_coe_nat {m n : ℕ} (h : (↑m : ℤ) ∣ ↑n) : m ∣ n :=
dvd.elim h $ λa ae,
m.eq_zero_or_pos.elim
(λm0, by rw[m0, int.coe_na... |
5bbb2ed59f7f217f71667c19caee44e35496723b | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/data/list/basic.lean | ed79051ef83c4d5aead6509de049638692230074 | [
"Apache-2.0"
] | permissive | fpvandoorn/mathlib | b21ab4068db079cbb8590b58fda9cc4bc1f35df4 | b3433a51ea8bc07c4159c1073838fc0ee9b8f227 | refs/heads/master | 1,624,791,089,608 | 1,556,715,231,000 | 1,556,715,231,000 | 165,722,980 | 5 | 0 | Apache-2.0 | 1,552,657,455,000 | 1,547,494,646,000 | Lean | UTF-8 | Lean | false | false | 206,095 | lean | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
Basic properties of lists.
-/
import
tactic.interactive tactic.mk_iff_of_inductive_prop
logi... |
76e3f1ad4386d15816d5af0741f7a4b26b73cc37 | 93b17e1ec33b7fd9fb0d8f958cdc9f2214b131a2 | /src/sep/ordalg.lean | e778d295749d0e27b231226888380b4b58006400 | [] | no_license | intoverflow/timesink | 93f8535cd504bc128ba1b57ce1eda4efc74e5136 | c25be4a2edb866ad0a9a87ee79e209afad6ab303 | refs/heads/master | 1,620,033,920,087 | 1,524,995,105,000 | 1,524,995,105,000 | 120,576,102 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 18,201 | lean | /- Ordered separation algebras
-
-/
import .rel
import ..cat.basic
namespace Sep
universes ℓ₁ ℓ₂ ℓ₃ ℓ₄
structure OrdAlg : Type.{ℓ₁ + 1}
:= (alg : Alg.{ℓ₁})
(ord : Rel alg alg)
(refl : ord.Refl)
(trans : ord.Trans)
-- (closed : ord.Closed)
def OrdAlg.ord_ord (A : OrdAlg.{ℓ₁})
: A.ord ∘ A.ord = A.... |
67ae6990efac3a15e98b9fb51366e8cba12bb99f | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /tmp/new-frontend/parser/syntax.lean | 7d3018842490244f19f71508f3a0a8b5b3b6dd54 | [
"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 | 8,406 | lean | /-
Copyright (c) 2018 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Sebastian Ullrich
-/
prelude
import init.lean.name init.lean.parser.parsec
namespace Lean
namespace Parser
--TODO(Sebastian): move
structure Substring :=
(start : String.OldIte... |
9910860c04dc7a70490bbf7a31aaa56fa168429e | 1446f520c1db37e157b631385707cc28a17a595e | /tests/compiler/closure_bug3.lean | 95b79d0e65d7d4ea0b36eeea848e155155c81404 | [
"Apache-2.0"
] | permissive | bdbabiak/lean4 | cab06b8a2606d99a168dd279efdd404edb4e825a | 3f4d0d78b2ce3ef541cb643bbe21496bd6b057ac | refs/heads/master | 1,615,045,275,530 | 1,583,793,696,000 | 1,583,793,696,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 548 | lean | def f (x : Nat) : Nat × (Nat → String) :=
let x1 := x + 1;
let x2 := x + 2;
let x3 := x + 3;
let x4 := x + 4;
let x5 := x + 5;
let x6 := x + 6;
let x7 := x + 7;
let x8 := x + 8;
let x9 := x + 9;
let x10 := x + 10;
let x11 := x + 11;
let x12 := x + 12;
let x13 := x + 13;
let x14 := x + 14;
let x15 := x + 15;
let x16 := ... |
eb1a24d3339dba3a980a6a814b7ca76e77a63808 | 618003631150032a5676f229d13a079ac875ff77 | /src/number_theory/primorial.lean | 71b183cac49527820010ba5fe87b68f2df398b76 | [
"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 | 7,307 | lean | /-
Copyright (c) 2020 Patrick Stevens. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Stevens
-/
import tactic
import data.nat.parity
import data.nat.choose
/-!
# Primorial
This file defines the primorial function (the product of primes less than or equal to ... |
f528c61e5c3826f444cc595c5e4713049d2634b8 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/data/set/intervals/unordered_interval.lean | 24c2c018fa20c50604b5f524f1417f737daceee2 | [
"Apache-2.0"
] | permissive | AntoineChambert-Loir/mathlib | 64aabb896129885f12296a799818061bc90da1ff | 07be904260ab6e36a5769680b6012f03a4727134 | refs/heads/master | 1,693,187,631,771 | 1,636,719,886,000 | 1,636,719,886,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,065 | lean | /-
Copyright (c) 2020 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou
-/
import order.bounds
import data.set.intervals.image_preimage
/-!
# Intervals without endpoints ordering
In any decidable linear order `α`, we define the set of elemen... |
7b774dcbdffbd947b6bc62e218d84df488dcc2cd | f02b05b665ad2d2cd970e93758a98d57f310a822 | /test/struct.lean | e98a27c3afa5ac5fd28f224fd044ed0a1636a1b8 | [] | no_license | khoek/leancache | b0ed5d2a9a2e87f58d4ad27343d957a9cd49ce5f | 5c8329f7b647b8d82966ab180c4473b20d1f249c | refs/heads/master | 1,585,344,140,717 | 1,549,094,327,000 | 1,549,094,327,000 | 147,138,187 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 279 | lean | import tactic.linarith
import tactic.tcache
set_option trace.cache true
structure prerat :=
(n : ℤ)
(m : ℕ)
(h₁ : m ≠ 0)
(h₂ : m ≥ 0)
def mk_prerat : prerat :=
{
n := 3,
m := 2,
h₁ := by c begin
trivial
end,
h₂ := by c begin
linarith
end
}
|
be3c8d4d54f9ca96082045b45597db9284bf372b | bdb33f8b7ea65f7705fc342a178508e2722eb851 | /data/prod.lean | b0bd950686ed34c73925f09eb837a49e632f0f6e | [
"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 | 2,035 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Extends theory on products
-/
universes u v
variables {α : Type u} {β : Type v}
@[simp] theorem prod.forall {p : α × β → Prop} : (∀ x, p x) ↔ (∀ a b, p (a, b)) :=
⟨as... |
2a28114a703325dab71f953f4f9f411d53d0b8a5 | f57749ca63d6416f807b770f67559503fdb21001 | /hott/algebra/hott.hlean | 430ebcb9bc02fbea14fee050e711408be7ab7493 | [
"Apache-2.0"
] | permissive | aliassaf/lean | bd54e85bed07b1ff6f01396551867b2677cbc6ac | f9b069b6a50756588b309b3d716c447004203152 | refs/heads/master | 1,610,982,152,948 | 1,438,916,029,000 | 1,438,916,029,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,114 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Floris van Doorn
Theorems about algebra specific to HoTT
-/
import .group arity types.pi types.hprop_trunc
open equiv eq equiv.ops is_trunc
namespace algebra
open Group has_mul ... |
f35b6b5dc7a69f688ef14cd41606229a6034d74a | e0f9ba56b7fedc16ef8697f6caeef5898b435143 | /src/control/traversable/basic.lean | d947de909ae519e4c4d452133e7a9608017d2e89 | [
"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 | 5,765 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Simon Hudon
-/
import control.applicative
/-!
# Traversable type class
Type classes for traversing collections. The concepts and laws are taken from
<http://hackage.haskell.org/package/b... |
bd9b230d8a9e99f22b73aa4deae8bcb0fbfe8464 | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /src/Lean/Elab/Command.lean | 4921aada245e5257603798998ce94615c2ad04a2 | [
"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 | 23,992 | 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.Alias
import Lean.Elab.Log
import Lean.Elab.ResolveName
import Lean.Elab.Term
import Lean.Elab.Binders
import Lean.Elab.SyntheticMVars
impo... |
f5e5f2641f81b1d4373bd80b1bb6fe3360f261cd | 49d1ff3d0fc0688d81e4b505d423e6215881caa6 | /src/theorems/no-cloning.lean | 57c53b3ce4f624184f936334672b15e8f9011faa | [] | no_license | jvlmdr/lean-quantum | 813e9453eade9f4ce64c8b473f9f75571df549c4 | 160cabcbd22bf24819b72930f56578e23b109a27 | refs/heads/master | 1,680,342,797,940 | 1,615,047,803,000 | 1,615,049,187,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 13,880 | lean | import quantum_lemmas
open Matrix
local notation `|0^(` n `)⟩` := ket_zeros n
------------------------------------------------------------------------------
-- no-cloning theorem (with 1 input qubit and 1 ancilla qubit)
section no_cloning_1
-- Note: lean can't detect contradiction from `/√2 = 1/2`. Convert it to r... |
08a4fd2cebd0551c97ca4c92184a66ee19ec90c2 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/analysis/box_integral/divergence_theorem.lean | 3b1d6577ad7582b0a1425f74832a2ec240ecb440 | [
"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 | 16,372 | lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import analysis.box_integral.basic
import analysis.box_integral.partition.additive
import analysis.calculus.fderiv
/-!
# Divergence integral for Henstock-Kurzweil ... |
06bc58aa55148694a51450206bc840ae269951c8 | cf39355caa609c0f33405126beee2739aa3cb77e | /library/init/meta/interaction_monad.lean | dd33f1c3cf6f646261bf215dfe87787a30c58e39 | [
"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 | 4,439 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Sebastian Ullrich
-/
prelude
import init.function init.data.option.basic init.util
import init.control.combinators init.control.monad init.control.alternative... |
164f7b4585d4226b288a844aef6460c330b13e47 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/check.lean | 05ecc7e3002a441d36ab1a37fc1feb242e04bd62 | [
"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 | 56 | lean | --
check and.intro
check or.elim
check eq
check eq.rec
|
3f64c9d6a354b14764512611b861f32c1a730b2f | 0b3933727d99a2f351f5dbe6e24716bb786a6649 | /src/sesh/matrix.lean | 7620b0849f0fa31e1b7c0e76c6cde26f1b9cf566 | [] | no_license | Vtec234/lean-sesh | 1e770858215279f65aba92b4782b483ab4f09353 | d11d7bb0599406e27d3a4d26242aec13d639ecf7 | refs/heads/master | 1,587,497,515,696 | 1,558,362,223,000 | 1,558,362,223,000 | 169,809,439 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,923 | lean | /- Introduces matrices and horrifying linear algebra. -/
import sesh.context
open context
open debrujin_idx
/- For every variable (given by a debrujin idx), a matrix gives the context
required by that variable. This is used when simultaneously substituting
a bunch of terms for variables - the context required... |
c7c2dea2820e764f57474c85cee914b382290eaf | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/dsimp_partial_app.lean | 467c4204c9375ce7ee11468a91483b559bd5db54 | [
"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 | 240 | lean | open tactic
example (a : list nat) : a = [1, 2] → a.map nat.succ = [2, 3] :=
begin
intros,
guard_target list.map nat.succ a = [2, 3],
subst a,
dsimp [list.map],
guard_target [nat.succ 1, nat.succ 2] = [2, 3],
reflexivity
end
|
304f5e0377354f4d7c53869cc3a4f3aaefc93971 | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /src/Std/Control/Nondet.lean | eb1d3881fbf4f2b91c5bc638115db5df914ada2f | [
"Apache-2.0"
] | permissive | WojciechKarpiel/lean4 | 7f89706b8e3c1f942b83a2c91a3a00b05da0e65b | f6e1314fa08293dea66a329e05b6c196a0189163 | refs/heads/master | 1,686,633,402,214 | 1,625,821,189,000 | 1,625,821,258,000 | 384,640,886 | 0 | 0 | Apache-2.0 | 1,625,903,617,000 | 1,625,903,026,000 | null | UTF-8 | Lean | false | false | 5,260 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
/-
NondetT monad transformer.
It is uses `unsafe` features to workaround the positivity constraints
in the definition of `Alts`.
-/
namespace Std
namespace... |
8dabfec0ca11cf5cb2ed01f4f9d86fdca93eb104 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/linear_algebra/multilinear.lean | 09b3d3e8b70265d2d64794b9bc7da2c1ef0a4841 | [
"Apache-2.0"
] | permissive | gebner/mathlib | eab0150cc4f79ec45d2016a8c21750244a2e7ff0 | cc6a6edc397c55118df62831e23bfbd6e6c6b4ab | refs/heads/master | 1,625,574,853,976 | 1,586,712,827,000 | 1,586,712,827,000 | 99,101,412 | 1 | 0 | Apache-2.0 | 1,586,716,389,000 | 1,501,667,958,000 | Lean | UTF-8 | Lean | false | false | 32,993 | 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 linear_algebra.basic tactic.omega data.fintype.card
/-!
# Multilinear maps
We define multilinear maps as maps from `Π(i : ι), M₁ i` to `M₂` which are ... |
a9078076a6901a763795c6f4e65554076019842f | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/group_theory/subgroup/actions.lean | 53a3f2a0e46f06a4f83e604f050a2e361cfa97e6 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 2,481 | 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 group_theory.subgroup.basic
/-!
# Actions by `subgroup`s
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathl... |
6c49f9718f07d27084cb073920c29782beb53f5a | 7cdf3413c097e5d36492d12cdd07030eb991d394 | /src/game/world3/level2.lean | 0b329cf607816d4ecd1eaf6b21b1f1aab3e3fcb5 | [] | no_license | alreadydone/natural_number_game | 3135b9385a9f43e74cfbf79513fc37e69b99e0b3 | 1a39e693df4f4e871eb449890d3c7715a25c2ec9 | refs/heads/master | 1,599,387,390,105 | 1,573,200,587,000 | 1,573,200,691,000 | 220,397,084 | 0 | 0 | null | 1,573,192,734,000 | 1,573,192,733,000 | null | UTF-8 | Lean | false | false | 804 | lean | import game.world3.level1 -- hide
import mynat.mul -- hide
namespace mynat -- hide
/-
# Multiplication World
## Level 2: `mul_one`
Currently our tools for multiplication are the
following:
* `mul_zero (m : mynat) : m * 0 = 0`
* `zero_mul (m : mynat) : 0 * m = 0`
* `mul_succ (a b : mynat) : a * succ b = a * b + a`... |
ba2bc7e5ea9e768e45ac8f05e26948385ce959f4 | aa5a655c05e5359a70646b7154e7cac59f0b4132 | /src/Lean/Parser/Tactic.lean | 3650ca41b74e7ac386b0e0b4c6d06f9c784b6b2c | [
"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 | 883 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Sebastian Ullrich
-/
import Lean.Parser.Term
namespace Lean
namespace Parser
namespace Tactic
builtin_initialize
registerParserAlias! "tacticSeq" tacti... |
43c150024ae31a1a9659c7fa320947aa6d0d4efb | 853df553b1d6ca524e3f0a79aedd32dde5d27ec3 | /test/library_search/basic.lean | 3ddb53f355f9bda8c065102477071b381ff496de | [
"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 | 6,676 | 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 tactic.suggest
import data.nat.basic
/- Turn off trace messages so they don't pollute the test build: -/
set_option trace.silence_library_search true
/- For d... |
875bddd2947077d91204fb5fa0b83a2e9d76428e | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/algebra/pointwise.lean | 2db254360f7c26ad4639b9bd1781b526e9af8ec2 | [
"Apache-2.0"
] | permissive | lacker/mathlib | f2439c743c4f8eb413ec589430c82d0f73b2d539 | ddf7563ac69d42cfa4a1bfe41db1fed521bd795f | refs/heads/master | 1,671,948,326,773 | 1,601,479,268,000 | 1,601,479,268,000 | 298,686,743 | 0 | 0 | Apache-2.0 | 1,601,070,794,000 | 1,601,070,794,000 | null | UTF-8 | Lean | false | false | 15,116 | lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Floris van Doorn
-/
import algebra.module.basic
import data.set.finite
/-!
# Pointwise addition, multiplication, and scalar multiplication of sets.
This file defines ... |
d87397a2769b5e3760ad8de0c80d355cfd84dfc9 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/analysis/special_functions/compare_exp.lean | 9df5efde21bea7de4f76e2955fae030eb0f5f87e | [
"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 | 9,148 | 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.special_functions.pow
import analysis.asymptotics.asymptotic_equivalent
import analysis.asymptotics.specific_asymptotics
/-!
# Growth estimates on ... |
fdc57a824105fafcca3594d0e4630e6309cb4109 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/analysis/normed_space/mazur_ulam.lean | ff8c8ce673de29d7f41eee5b8971cee81dc6744b | [
"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 | 6,863 | 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 topology.instances.real_vector_space
import analysis.normed_space.affine_isometry
/-!
# Mazur-Ulam Theorem
Mazur-Ulam theorem states that an isometric bije... |
3a7dc027403a8a5eab5c6902b36e4f9ab122877b | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/data/nat/parity.lean | 5fbd5a8ebf050bf0132926a5fe0e023556cdd0c1 | [
"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 | 4,551 | lean | /-
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
The `even` and `odd` predicates on the natural numbers.
-/
import data.nat.modeq
namespace nat
@[simp] theorem mod_two_ne_one {n : ℕ} : ¬ n % 2 = 1 ↔ n % 2 = 0 :=
by ca... |
f0786a53df86c26e767934c12fc1915cc686c597 | b2e508d02500f1512e1618150413e6be69d9db10 | /src/category_theory/concrete_category.lean | 0d57c7ddcda9b3d5c34d0a9179021f980b1731c2 | [
"Apache-2.0"
] | permissive | callum-sutton/mathlib | c3788f90216e9cd43eeffcb9f8c9f959b3b01771 | afd623825a3ac6bfbcc675a9b023edad3f069e89 | refs/heads/master | 1,591,371,888,053 | 1,560,990,690,000 | 1,560,990,690,000 | 192,476,045 | 0 | 0 | Apache-2.0 | 1,568,941,843,000 | 1,560,837,965,000 | Lean | UTF-8 | Lean | false | false | 3,456 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Johannes Hölzl, Reid Barton, Sean Leather
Bundled type and structure.
-/
import category_theory.functor
import category_theory.types
universes u v
namespace category... |
b965e78041161e9249e67d31478a7244db29bb6a | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/algebra/group/pi.lean | d1685c1e915634fa335a6fde4296584134e3501f | [
"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 | 17,220 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Patrick Massot
-/
import algebra.hom.group_instances
import data.pi.algebra
import data.set.function
import data.set.pairwise
import tactic.pi_instances
/-!
# Pi instances f... |
222fda2d393d9c0c77f160034c5ad4f1b947cc8a | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/topology/metric_space/gromov_hausdorff_realized.lean | c5f09a4aaed7da21b48d7ff65939ec2c74b74dac | [
"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 | 27,322 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import topology.metric_space.gluing
import topology.metric_space.hausdorff_distance
import topology.continuous_function.bounded
/-!
# The Gromov-Hausdorff dist... |
f2699fd307063839aa1ac8fac2f15fa3714ab5ca | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Compiler/AtMostOnce.lean | 10457749f70325fde443c1b45e97173a6325ad67 | [
"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 | 1,543 | 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.Environment
namespace Lean.Compiler
namespace atMostOnce
structure AtMostOnceData where
found : Bool
result : Bool
def Visitor := AtMost... |
ca80660b393de49a4fe3c2b29938de4ae0a3f559 | 9dd3f3912f7321eb58ee9aa8f21778ad6221f87c | /tests/lean/pp_zero_bug.lean | fe3889b46fb93a34b740c30ba92124f15e4fc678 | [
"Apache-2.0"
] | permissive | bre7k30/lean | de893411bcfa7b3c5572e61b9e1c52951b310aa4 | 5a924699d076dab1bd5af23a8f910b433e598d7a | refs/heads/master | 1,610,900,145,817 | 1,488,006,845,000 | 1,488,006,845,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 28 | lean | check @zero
check @zero nat
|
e8a46a1b2cc0624ec18dd00cac299b06eef7c0a2 | 874a8d2247ab9a4516052498f80da2e32d0e3a48 | /take_three.lean | c8ddcdbd1306562dcabc300534d83b7bc03024ac | [] | no_license | AlexKontorovich/Spring2020Math492 | 378b36c643ee029f5ab91c1677889baa591f5e85 | 659108c5d864ff5c75b9b3b13b847aa5cff4348a | refs/heads/master | 1,610,780,595,457 | 1,588,174,859,000 | 1,588,174,859,000 | 243,017,788 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 983 | lean | import analysis.normed_space.basic
import topology.instances.ennreal
import analysis.normed_space.basic
import topology.instances.ennreal
import algebra.archimedean algebra.geom_sum
import data.nat.choose data.complex.basic
import tactic.linarith
import analysis.calculus.deriv
import data.complex.exponential
... |
f1e67d52117863086e13683d2ecd04b6e36fc012 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/algebra/direct_sum/module.lean | 3a6f7865f52c4bdbb590710f23a3eca79918abcd | [
"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 | 14,873 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import algebra.direct_sum.basic
import linear_algebra.dfinsupp
/-!
# Direct sum of modules
The first part of the file provides constructors for direct sums of modules. It pro... |
06346815d6065c8f8f26aa6c484e730a6dbc8c84 | bb31430994044506fa42fd667e2d556327e18dfe | /src/topology/locally_constant/algebra.lean | 3f1eda30bc7b0f75aaf14fd8d7b1fa52a6004071 | [
"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 | 9,485 | lean | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import algebra.algebra.pi
import topology.locally_constant.basic
/-!
# Algebraic structure on locally constant functions
This file puts algebraic structure (`add_gr... |
eb18b7a4da478533fa7c271a5677788ffcc00a76 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/fun_info1.lean | 1ff9c492f3014d49cfd69f1c0d6dc17e936d933d | [
"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 | 554 | lean | open tactic
set_option pp.binder_types true
definition foo (A : Type) : A → A :=
sorry
example (a : nat) (H : foo unit () = ()) : true :=
by do
(lhs, rhs) ← get_local `H >>= infer_type >>= match_eq ,
get_spec_subsingleton_info lhs >>= trace,
trace "-----------",
trace "ite information:",
c ← mk_const `ite, ... |
433f44588fb91605ac5fe5a13e4cde0490757434 | 46125763b4dbf50619e8846a1371029346f4c3db | /src/topology/instances/real.lean | 94e1856af96d404c26f202ff483debc8ad97eacb | [
"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 | 14,900 | 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... |
85305498dfaa399e5a175bf6fed6666506d77337 | 076f5040b63237c6dd928c6401329ed5adcb0e44 | /instructor-notes/2019.09.05_spec-vs-impl-fib/fib.lean | 476874646642bf7c0b302777c5f28d26b25d225a | [] | no_license | kevinsullivan/uva-cs-dm-f19 | 0f123689cf6cb078f263950b18382a7086bf30be | 09a950752884bd7ade4be33e9e89a2c4b1927167 | refs/heads/master | 1,594,771,841,541 | 1,575,853,850,000 | 1,575,853,850,000 | 205,433,890 | 4 | 9 | null | 1,571,592,121,000 | 1,567,188,539,000 | Lean | UTF-8 | Lean | false | false | 237 | lean | /-
An executable specification
of the standard Fibonacci function. Takes one
natural number, n, as an argument, and
returns the n'th Fibonacci number (fib n).
-/
def fib: nat → nat
| 0 := 0
| 1 := 1
| (n' + 2) := fib n' + fib (n'+1)
|
74aece60b4aac5c3411b90cff17fe5a469391d07 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/data/vector/basic.lean | 006431584bc1bd2eccc004ff3a4615511a85a594 | [
"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 | 20,377 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import data.vector
import data.list.nodup
import data.list.of_fn
import control.applicative
/-!
# Additional theorems and definitions about the `vector` type
This fi... |
d9082372020727bed9eeb1b7cccc193fd1c1478c | 0d107d7abd6ae235d586830f8e09b1b30e7eef0b | /src/math_limit_2/Preloaded.lean | 2d1cf2bc2ed29ee3b8137e322a9609796775b94c | [] | no_license | ukikagi/codewars-lean | 6b9a83ebbb159e7eebf8551b745a1c4d450e747f | 1912f2a4e25e917abfce70d65c0469cfac19dc93 | refs/heads/master | 1,672,948,190,244 | 1,603,361,004,000 | 1,603,795,841,000 | 303,746,208 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 582 | lean | import data.real.basic
open classical
attribute [instance] prop_decidable
/-
Rigorous definition of a limit
For a sequence x_n, we say that \lim_{n \to \infty} x_n = l if
∀ ε > 0, ∃ N, n ≥ N → |x_n - l| < ε
-/
def lim_to_inf (x : ℕ → ℝ) (l : ℝ) :=
∀ ε > 0, ∃ N, ∀ n ≥ N, abs (x n - l) < ε
-- Suppose |x_n - ... |
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