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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
2fe5142f0167f855cae4321fe81f8bb69c4f6763 | 4727251e0cd73359b15b664c3170e5d754078599 | /archive/100-theorems-list/73_ascending_descending_sequences.lean | c51a69870e2ec6021e3215b6349e3d5f74ea75db | [
"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 | 8,116 | lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import tactic.basic
import data.fintype.basic
/-!
# Erdős–Szekeres theorem
This file proves Theorem 73 from the [100 Theorems List](https://www.cs.ru.nl/~freek/100/), a... |
0a79098f8bc52a4a4510d235066604ee95ee9ba0 | 957a80ea22c5abb4f4670b250d55534d9db99108 | /library/init/meta/exceptional.lean | 6f6b0859db3740fd2545421b623362be39bf7da3 | [
"Apache-2.0"
] | permissive | GaloisInc/lean | aa1e64d604051e602fcf4610061314b9a37ab8cd | f1ec117a24459b59c6ff9e56a1d09d9e9e60a6c0 | refs/heads/master | 1,592,202,909,807 | 1,504,624,387,000 | 1,504,624,387,000 | 75,319,626 | 2 | 1 | Apache-2.0 | 1,539,290,164,000 | 1,480,616,104,000 | C++ | UTF-8 | Lean | false | false | 1,802 | 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.category.monad init.meta.format init.util
/-
Remark: we use a function that produces a format object as the exception information.
Motiv... |
e6191f7274ff0a5d47131d198de5cde388c630d2 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/data/nat/gcd.lean | 9cedc4bc7a558890b6b5e529161c5242a269aa94 | [
"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 | 24,085 | 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
-/
import algebra.group_power.order
import algebra.big_operators.basic
/-!
# Definitions and properties of `gcd`, `lcm`, and `coprime`
-/
namespace n... |
ce5f629db9dd77dc5f678d257e0c660d0fe690af | 4727251e0cd73359b15b664c3170e5d754078599 | /src/data/sigma/lex.lean | 318941a4133797a3f3a671ba05e4485439496d3b | [
"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 | 6,829 | lean | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import data.sigma.basic
import order.rel_classes
/-!
# Lexicographic order on a sigma type
This defines the lexicographical order of two arbitrary relations on a sigma ... |
4fb4162e22dcc0b0d3eff9cf52e6a65c0892858b | 618003631150032a5676f229d13a079ac875ff77 | /src/order/complete_lattice.lean | 192cd624fd1b08d4d45f6bfa1d0d46938199cbec | [
"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 | 36,238 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Theory of complete lattices.
-/
import order.bounds
set_option old_structure_cmd true
open set
universes u v w w₂
variables {α : Type u} {β : Type v} {ι : Sort w} {ι₂... |
4672bb6c0e44901b4708c5c6dc32961653177e4c | 38bf3fd2bb651ab70511408fcf70e2029e2ba310 | /src/category_theory/monoidal/functor.lean | 80c249827f7c026f60581cc5891c19c8d3db426d | [
"Apache-2.0"
] | permissive | JaredCorduan/mathlib | 130392594844f15dad65a9308c242551bae6cd2e | d5de80376088954d592a59326c14404f538050a1 | refs/heads/master | 1,595,862,206,333 | 1,570,816,457,000 | 1,570,816,457,000 | 209,134,499 | 0 | 0 | Apache-2.0 | 1,568,746,811,000 | 1,568,746,811,000 | null | UTF-8 | Lean | false | false | 7,136 | lean | /-
Copyright (c) 2018 Michael Jendrusch. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Jendrusch, Scott Morrison
-/
import category_theory.monoidal.category
open category_theory
universes v₁ v₂ v₃ u₁ u₂ u₃
open category_theory.category
open category_theory.... |
f4b758856fe3a140d963af75e4a43bc6f8344dd7 | 947b78d97130d56365ae2ec264df196ce769371a | /src/Lean/KeyedDeclsAttribute.lean | f614d3cae0fcc90d39a8bebfb4c7b57630ff2c22 | [
"Apache-2.0"
] | permissive | shyamalschandra/lean4 | 27044812be8698f0c79147615b1d5090b9f4b037 | 6e7a883b21eaf62831e8111b251dc9b18f40e604 | refs/heads/master | 1,671,417,126,371 | 1,601,859,995,000 | 1,601,860,020,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,045 | 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.Attributes
import Lean.Compiler.InitAttr
import Lean.ToExpr
/-!
A builder for attributes that are applied to declarations of... |
3de25a9f8a6b6062cb1ab3472a115245ed698d97 | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /tests/compiler/closure_bug1.lean | 8673bfc11fd74767e2434335128e3ce708dbecb5 | [
"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 | 561 | 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 := ... |
490405c872eed2e9f441ef3996abe0b3aa4e4109 | df561f413cfe0a88b1056655515399c546ff32a5 | /3-function-world/l6.lean | 115201af08ad6a35324e85fdeb51b18ea4989b64 | [] | no_license | nicholaspun/natural-number-game-solutions | 31d5158415c6f582694680044c5c6469032c2a06 | 1e2aed86d2e76a3f4a275c6d99e795ad30cf6df0 | refs/heads/main | 1,675,123,625,012 | 1,607,633,548,000 | 1,607,633,548,000 | 318,933,860 | 3 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 143 | lean | example (P Q R : Type) : (P → (Q → R)) → ((P → Q) → (P → R)) :=
begin
intros f g p,
have h : Q -> R := f p,
apply h,
exact g p,
end |
2f7e8b2b0e231a31e37834d38cc2e20234932c12 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /scripts/yaml_check.lean | 9ea9b05b5dde73aa666c06d08efa89daea4f1219 | [
"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 | 1,799 | lean | import data.buffer.parser
import system.io
import tactic.core
import all
open native
section
variables {F : Type → Type} [alternative F]
def fails {α} (x : F α) : F bool := (x $> ff) <|> pure tt
end
open io io.fs tactic
meta instance coe_tactic_to_io {α} : has_coe (tactic α) (io α) :=
⟨run_tactic⟩
meta def list.... |
12c638ea8954cefd49d8dbd6e7dd6cde1b95ca2f | 0c1546a496eccfb56620165cad015f88d56190c5 | /library/init/logic.lean | efc26b4c9287cf577721e8e5ff6d804b43e6e945 | [
"Apache-2.0"
] | permissive | Solertis/lean | 491e0939957486f664498fbfb02546e042699958 | 84188c5aa1673fdf37a082b2de8562dddf53df3f | refs/heads/master | 1,610,174,257,606 | 1,486,263,620,000 | 1,486,263,620,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 37,481 | 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, Jeremy Avigad, Floris van Doorn
-/
prelude
import init.core
universe variables u v w
@[reducible] def id {α : Sort u} (a : α) : α := a
def flip {α : Sort u... |
dfc84f00113020d474ecbc84c8c4274f67942c43 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/measure_theory/function/strongly_measurable/basic.lean | efb7975a5578b7d3eaee92c5860b8d05c8381f82 | [
"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 | 87,479 | lean | /-
Copyright (c) 2021 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Sébastien Gouëzel
-/
import analysis.normed_space.bounded_linear_maps
import topology.metric_space.metrizable
import measure_theory.function.simple_func_dense
/-!
# Strong... |
ed4456d0054896ef5d5c5c68a6eda0cbe577adc7 | 9ad8d18fbe5f120c22b5e035bc240f711d2cbd7e | /src/data/int_lemmas.lean | 1fa802344fb03f5eeabb167b48fd4cec7d8555b0 | [] | no_license | agusakov/lean_lib | c0e9cc29fc7d2518004e224376adeb5e69b5cc1a | f88d162da2f990b87c4d34f5f46bbca2bbc5948e | refs/heads/master | 1,642,141,461,087 | 1,557,395,798,000 | 1,557,395,798,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,298 | lean | /-
Copyright (c) 2019 Neil Strickland. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Neil Strickland
Some basic lemmas about integers. I should check whether the
new coercion tactic makes them trivial.
-/
import data.fintype
lemma int.lt_succ_iff {n m : ℤ} : n <... |
8163f2094816d28f9a737598bf9adaaff5afe3b9 | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/computability/language.lean | 4830b1a3574bc075b9327b13839cd7f3f4778d53 | [
"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 | 9,074 | lean | /-
Copyright (c) 2020 Fox Thomson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fox Thomson
-/
import data.finset.basic
/-!
# Languages
This file contains the definition and operations on formal languages over an alphabet. Note strings
are implemented as lists over ... |
465413810f43928fd2df18917c6a9556c7b06cb4 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/tactic/omega/int/main_auto.lean | 9df090bbd3f5c5b2a3d8041c97e6298f7ffe0cc1 | [] | 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 | 748 | lean | /-
Copyright (c) 2019 Seul Baek. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Seul Baek
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.tactic.omega.prove_unsats
import Mathlib.tactic.omega.int.dnf
import Mathlib.PostPort
namespace Mathl... |
62cfb1409f9080c035ea7a13ac17ee3e33b2b36f | 968e2f50b755d3048175f176376eff7139e9df70 | /examples/prop_logic_lean_summary/unnamed_238.lean | c38702c1cc0c67a9a503a0da617c9d11f8adb80b | [] | no_license | gihanmarasingha/mth1001_sphinx | 190a003269ba5e54717b448302a27ca26e31d491 | 05126586cbf5786e521be1ea2ef5b4ba3c44e74a | refs/heads/master | 1,672,913,933,677 | 1,604,516,583,000 | 1,604,516,583,000 | 309,245,750 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 162 | lean | variables p q : Prop
-- BEGIN
example (h₁ : p → q) (h₂ : p) : q :=
h₁ h₂ -- h₁ h₂ is the result of implication elimination on h₁ and h₂.
-- END |
198b0b3e438f4b1e976892eb628fe4c5769500c7 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/group/conj_finite.lean | 44b67a8656686db8320ae9b96399bb5ba24123c7 | [
"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 | 1,128 | lean | /-
Copyright (c) 2022 Eric Rodriguez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Rodriguez
-/
import algebra.group.conj
import data.finite.basic
import data.fintype.units
/-!
# Conjugacy of elements of finite groups
-/
variables {α : Type*} [monoid α]
loca... |
7af1b9f9ec213f93f30ca6932ae7859697c85b76 | 13d50f9487a2afddb5e1ae1bbe68f7870f70e79a | /Import.lean | 0391626b260965ef0095a4e3543c49bded902b8a | [] | no_license | gebner/lean4-mathlib-import | 09a09d9cc30738bcc253e919ab3485e13b8f992d | 719c0558dfa9c4ec201aa40f4786d5f1c1e4bd1e | refs/heads/master | 1,649,553,984,859 | 1,584,121,837,000 | 1,584,121,837,000 | 238,557,672 | 4 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 8,645 | lean | import Import.OldRecursor
import Import.ExportParser
namespace Lean.Declaration
def names : Lean.Declaration → List Lean.Name
| axiomDecl v => [v.name]
| defnDecl v => [v.name]
| thmDecl v => [v.name]
| opaqueDecl v => [v.name]
| quotDecl => []
| mutualDefnDecl vs => vs.map (fun v => v.name)
| inductDecl _ _ is _ => ... |
4b8e554a2fec991dbf9105967c537fbbfcbb4d5f | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/topology/constructions.lean | bb369d2e07bb95a866e622eae89ecad8f01c0216 | [
"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 | 29,447 | 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
-/
import topology.maps
/-!
# Constructions of new topological spaces from old ones
This file constructs products, sums, subtypes and q... |
280fc818b995af4fe46e3a151e8c0f5018b66ba3 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/cute_binders.lean | ab6dad17ca1b21d2faf977f52808bc664ce1cb2f | [
"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 | 533 | lean | definition range (lower : nat) (upper : nat) : set nat :=
λ a, lower ≤ a ∧ a ≤ upper
local notation `[` L `, ` U `]` := range L U
variables s : set nat
variables p : nat → nat → Prop
-- #check a ∈ s
set_option pp.binder_types true
#check ∀ b c a ∈ s, a + b + c > 0
-- ∀ (b c a : ℕ), b ∈ s → c ∈ s → a ∈ s → a + b + c... |
f54d84f72bb00189ea47e0439ca7993c028f3f6c | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/group_theory/perm/option.lean | 504e4fe302ae62edfa21bc520b3db92456236c70 | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 3,700 | 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.perm.sign
import data.equiv.option
/-!
# Permutations of `option α`
-/
open equiv
lemma equiv_functor.map_equiv_option_injective {α β : Type*} :
fun... |
cefaf270bf522c3462e5264166d3387894d920b5 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /hott/algebra/priority.hlean | aa2ac4c5c8b93502bfee3df025801631f6b1a80c | [
"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 | 233 | hlean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
protected definition algebra.prio := num.sub std.priority.default 100
|
3dabc21d1d419066b7bdcd6ed89852fa6e63aa74 | 92c6b42948d74fe325c2d88530f1d36da388b2f7 | /src/common.lean | e0e36c64244f0cf4ba6522ff39c2bc64d48d10db | [
"MIT"
] | permissive | riaqn/smtlean | 8ad65055b6c1600cd03b9e345059a3b24419b6d5 | c11768cfb43cd634340b552f5039cba094701a87 | refs/heads/master | 1,584,569,627,940 | 1,535,314,713,000 | 1,535,314,713,000 | 135,333,334 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 705 | lean | import data.buffer
attribute [reducible]
def parse_error := string
class has_from_buffer (α : Type _) :=
(from_buffer {} : char_buffer → except parse_error α)
export has_from_buffer (from_buffer)
class has_from_string (α : Type _) :=
(from_string {} : string → except parse_error α)
export has_from_string (from_str... |
8a6e8d63d3336b3f42cf4c403530736fe7851884 | 592ee40978ac7604005a4e0d35bbc4b467389241 | /Library/generated/mathscheme-lean/AbelianGroup.lean | 716262acef8c8c0fc964077adb274b797e40ec56 | [] | 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 | 9,992 | 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 AbelianGroup
structure AbelianGroup (A : Type) : Type :=
(one : A)
(times : (A → (A → A)))
(lunit_one : (∀ {x : A} , (times one x) = x))
(runit_on... |
6a93170de7a37814c72ad99fea54f04dab45883c | 5df84495ec6c281df6d26411cc20aac5c941e745 | /src/formal_ml/semiring.lean | 90448d51e6dc01aab432dda9a827ae8e5c77b370 | [
"Apache-2.0"
] | permissive | eric-wieser/formal-ml | e278df5a8df78aa3947bc8376650419e1b2b0a14 | 630011d19fdd9539c8d6493a69fe70af5d193590 | refs/heads/master | 1,681,491,589,256 | 1,612,642,743,000 | 1,612,642,743,000 | 360,114,136 | 0 | 0 | Apache-2.0 | 1,618,998,189,000 | 1,618,998,188,000 | null | UTF-8 | Lean | false | false | 36,036 | lean | /-
Copyright 2020 Google LLC
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
di... |
34e10fc649d57c4bd8c712f66f0476390559f8e3 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/data/multiset/pi.lean | 13e166c86da7c6b28221dbe5a3a5e102082b8021 | [
"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 | 4,915 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import data.multiset.nodup
/-!
# The cartesian product of multisets
-/
namespace multiset
section pi
variables {α : Type*}
open function
/-- Given `δ : α → Type*`... |
42ddf7f88f12ec8a8a4e61649884ad4160aa8d3e | 35677d2df3f081738fa6b08138e03ee36bc33cad | /scripts/lint_mathlib.lean | a3cad959987e71e820fd644e1a5c64ea580212f0 | [
"Apache-2.0"
] | permissive | gebner/mathlib | eab0150cc4f79ec45d2016a8c21750244a2e7ff0 | cc6a6edc397c55118df62831e23bfbd6e6c6b4ab | refs/heads/master | 1,625,574,853,976 | 1,586,712,827,000 | 1,586,712,827,000 | 99,101,412 | 1 | 0 | Apache-2.0 | 1,586,716,389,000 | 1,501,667,958,000 | Lean | UTF-8 | Lean | false | false | 3,205 | lean | /-
Copyright (c) 2020 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Robert Y. Lewis, Gabriel Ebner
-/
import tactic.lint system.io -- these are required
import all -- then import everything, to parse the library for failing linters
/-!
# lint_math... |
0c0748c9b236a43f927687e69b48b171f2b4342b | 4727251e0cd73359b15b664c3170e5d754078599 | /src/combinatorics/simple_graph/subgraph.lean | c74b205190a7d43c13ac678f5bbb3b3224fee16d | [
"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 | 20,347 | lean | /-
Copyright (c) 2021 Hunter Monroe. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Hunter Monroe, Kyle Miller, Alena Gusakov
-/
import combinatorics.simple_graph.basic
/-!
# Subgraphs of a simple graph
A subgraph of a simple graph consists of subsets of the graph's ... |
41e91b1becfb0021534817308d853a778f892e0f | 1437b3495ef9020d5413178aa33c0a625f15f15f | /ring_theory/principal_ideal_domain.lean | 41b156d69a166bb418004eb09d8b885ae13f833d | [
"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 | 6,737 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Chris Hughes, Morenikeji Neri
-/
import algebra.euclidean_domain
import ring_theory.ideals ring_theory.noetherian ring_theory.unique_factorization_domain
variables {α : Type*}
open set... |
0346bd8eefe3a6d1964886b97dfbc3ae71ef6f15 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/deprecated/submonoid.lean | 7750164c2a044ce0655be54198105a92aa75110d | [
"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 | 16,121 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau, Johan Commelin, Mario Carneiro, Kevin Buzzard
-/
import group_theory.submonoid.basic
import algebra.big_operators.basic
import deprecated.group
/-!
# Unbund... |
8b6caf5b435295df447574e3e7e2e529ca42c65f | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/tactic/interactive_expr.lean | ac6b7f046bc11b100627f4499821899c70c5b962 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 17,542 | lean | /-
Copyright (c) 2020 E.W.Ayers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: E.W.Ayers
-/
/-!
# Widgets used for tactic state and term-mode goal display
The vscode extension supports the display of interactive widgets.
Default implementation of these widgets are i... |
ddde85f76b1381ef5dfc7833739dcb3f0647988d | 4727251e0cd73359b15b664c3170e5d754078599 | /src/probability/martingale.lean | 660fd65d7b7ee92cd16e918c58597a861c3b108a | [
"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 | 17,322 | lean | /-
Copyright (c) 2021 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Kexing Ying
-/
import probability.notation
import probability.stopping
/-!
# Martingales
A family of functions `f : ι → α → E` is a martingale with respect to a filtratio... |
a06299a8d3d499fdb3841ac19f7e19464cc2691e | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/quotient.lean | ff8b5d9cbd2705f897f570210d5858dc537d6e87 | [] | 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 | 5,736 | lean | /-
Copyright (c) 2020 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.category_theory.natural_isomorphism
import Mathlib.PostPort
universes v u l u_1 u_2
namespace Ma... |
83f1e094605a1e3d6a114813c08eebaf6e64c4ac | 4727251e0cd73359b15b664c3170e5d754078599 | /src/combinatorics/hall/finite.lean | e055708c15b7332555d5665ffe7c327be346c4e7 | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 10,867 | lean | /-
Copyright (c) 2021 Alena Gusakov, Bhavik Mehta, Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alena Gusakov, Bhavik Mehta, Kyle Miller
-/
import data.fintype.basic
import data.set.finite
/-!
# Hall's Marriage Theorem for finite index types
This modul... |
1290854d3009001a4853f0e5e2c010e7b4aedc48 | f3849be5d845a1cb97680f0bbbe03b85518312f0 | /library/tools/super/default.lean | d197740f2b4d8911d31db870b612a021dc5c5406 | [
"Apache-2.0"
] | permissive | bjoeris/lean | 0ed95125d762b17bfcb54dad1f9721f953f92eeb | 4e496b78d5e73545fa4f9a807155113d8e6b0561 | refs/heads/master | 1,611,251,218,281 | 1,495,337,658,000 | 1,495,337,658,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 178 | lean | /-
Copyright (c) 2016 Gabriel Ebner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner
-/
import tools.super.prover
|
181a6ef35e160cf6524734395a646c9c49cf3040 | 2a70b774d16dbdf5a533432ee0ebab6838df0948 | /_target/deps/mathlib/src/category_theory/monad/algebra.lean | e71cddb861b78e0d9726122c978aa8cbee18e145 | [
"Apache-2.0"
] | permissive | hjvromen/lewis | 40b035973df7c77ebf927afab7878c76d05ff758 | 105b675f73630f028ad5d890897a51b3c1146fb0 | refs/heads/master | 1,677,944,636,343 | 1,676,555,301,000 | 1,676,555,301,000 | 327,553,599 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,027 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Bhavik Mehta
-/
import category_theory.monad.basic
import category_theory.adjunction.basic
import category_theory.reflects_isomorphisms
/-!
# Eilenberg-Moore (co)algeb... |
72e9ea669f5314d64420abe4c5b61a619f40489b | c777c32c8e484e195053731103c5e52af26a25d1 | /src/algebra/order/smul.lean | b6cd7435b978bd1850dc520ac6b1188f36fb1064 | [
"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 | 12,508 | lean | /-
Copyright (c) 2020 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
import algebra.module.pi
import algebra.module.prod
import algebra.order.monoid.prod
import algebra.order.pi
import data.set.pointwise.smul
import tactic.positivity... |
fd3b31c24d015999362f35f64e9ee9f0370b9a4d | 5c7fe6c4a9d4079b5457ffa5f061797d42a1cd65 | /src/exercises/src_02_and_introduction.lean | cf5743d62c39b039d34dc9e6bc0dd32e4aa48dd5 | [] | no_license | gihanmarasingha/mth1001_tutorial | 8e0817feeb96e7c1bb3bac49b63e3c9a3a329061 | bb277eebd5013766e1418365b91416b406275130 | refs/heads/master | 1,675,008,746,310 | 1,607,993,443,000 | 1,607,993,443,000 | 321,511,270 | 3 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,878 | lean | variables p q r : Prop
namespace mth1001
section and_introduction
/-
In the previous section, we saw how to eliminate `∧`. That is, we saw how to take a premise
involving `∧` and derive a statement in which that occurrence of `∧` has been removed.
In this section, we do the opposite. We introduce `∧`.
-/
/-
The f... |
b9f2f14d467409e77513c8f115aa0d742c24efc9 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/limits/constructions/over/basic.lean | 9e71f7f3ed156a1c397e0d344422e1783b5646ef | [
"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 | 2,910 | lean | /-
Copyright (c) 2018 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Reid Barton, Bhavik Mehta
-/
import category_theory.limits.connected
import category_theory.limits.constructions.over.products
import category_theory.limits.constructio... |
3c36d452bf06bfc3d5c212e86e8c1a67188389d4 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/set/functor.lean | e39e448e1ddc5db5debaf2277423fc077a6980b4 | [
"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 | 1,766 | lean | /-
Copyright (c) 2016 Leonardo de Moura. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import data.set.lattice
/-!
# Functoriality of `set`
This file defines the functor structure of `set`.
-/
universes u
open function
namespace set
variables... |
7e51826470062e98fa93a73d0df052b81c4629b1 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/topology/sheaves/local_predicate.lean | dfc187bf943c073ad460985b6244661098d157bf | [
"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 | 16,365 | 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, Adam Topaz
-/
import topology.sheaves.sheaf_of_functions
import topology.sheaves.stalks
/-!
# Functions satisfying a local predicate form a sheaf.
At ... |
fd1ff33ec8207310723938f118c7abfc8644017d | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/ring_theory/integral_closure.lean | 06b750c9cd933e0eef1a0448c0ebef8e72c90b10 | [
"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 | 20,448 | 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 ring_theory.algebra_tower
import ring_theory.polynomial.scale_roots
/-!
# Integral closure of a subring.
If A is an R-algebra then `a : A` is integral over R if it is ... |
671ba24bd81d4eadf63ce52e43562c2035751ebc | ce6917c5bacabee346655160b74a307b4a5ab620 | /src/ch4/ex0207.lean | 931fa7f48549b337ec3dcbadd882fd4d5074244f | [] | 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 | 210 | lean | universe u
example (α : Type u) (a b : α) (p : α → Prop) (h1 : a = b) (h2 : p a) : p b :=
eq.subst h1 h2
example (α : Type u) (a b : α) (p : α → Prop) (h1 : a = b) (h2 : p a) : p b :=
h1 ▸ h2
|
603fc6661723b34f5508f9c6b730c9331c7f2261 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/group_with_zero/semiconj.lean | 224d3a3204145fce350d212720a4e8dbb40d52b0 | [
"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 | 1,942 | 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 algebra.group_with_zero.units.basic
import algebra.group.semiconj
/-!
# Lemmas about semiconjugate elements in a `group_with_zero`.
> THIS FILE IS SYNCHRONIZ... |
6c0d674207409e41c038825ce7c0d5fee4468a30 | 19a24126e4b7677703434d80717041622a5f1d61 | /logic_and_proof/first_order_logic_in_lean.lean | b0a1cc1caf39bbd9bb39eb55f8cfcc87932d10cf | [] | no_license | JoseBalado/lean-notes | f5ff8d4c99ba8c1f79d7894ba0f130fa4eb09695 | 0b579f83988cc844ac1ff0592d885061959a852e | refs/heads/master | 1,587,743,561,316 | 1,567,181,955,000 | 1,567,181,955,000 | 172,086,145 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 652 | lean | namespace one
variable U : Type
variable P : U → Prop
example (x : U) (h : P x) : ∃ x, P x :=
exists.intro x h
end one
namespace two
variable U : Type
variable P : U → Prop
variable Q : Prop
example (h1 : ∃ x, P x) (h2 : ∀ x, P x → Q) : Q :=
exists.elim h1
(assume (y : U) (h : P y),
have h3 : P y → Q, from h2 ... |
95c616bee3e48055aaa2069b1565af3cc66c6045 | cc060cf567f81c404a13ee79bf21f2e720fa6db0 | /lean/20170607-dependent-sorry.lean | fa8aee2106f4fd73b02de146da2f17dffdc0bb76 | [
"Apache-2.0"
] | permissive | semorrison/proof | cf0a8c6957153bdb206fd5d5a762a75958a82bca | 5ee398aa239a379a431190edbb6022b1a0aa2c70 | refs/heads/master | 1,610,414,502,842 | 1,518,696,851,000 | 1,518,696,851,000 | 78,375,937 | 2 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 720 | lean | -- structure F :=
-- (prop : 1 = 1)
-- def parameterized_type : F → Type := sorry
-- def parameterized_prop : Π (x : F), parameterized_type x → Prop := sorry
-- structure C :=
-- ( f : F )
-- ( p : parameterized_type f )
-- ( q : (parameterized_prop f) p )
-- def test : C := {
-- f := {
-- prop :=... |
13a3a26b21624f2f3831a9e730c65f188221b8fb | a047a4718edfa935d17231e9e6ecec8c7b701e05 | /src/group_theory/quotient_group.lean | 013d47f3ebb7efb481d5763e691deaa91af3554c | [
"Apache-2.0"
] | permissive | utensil-contrib/mathlib | bae0c9fafe5e2bdb516efc89d6f8c1502ecc9767 | b91909e77e219098a2f8cc031f89d595fe274bd2 | refs/heads/master | 1,668,048,976,965 | 1,592,442,701,000 | 1,592,442,701,000 | 273,197,855 | 0 | 0 | null | 1,592,472,812,000 | 1,592,472,811,000 | null | UTF-8 | Lean | false | false | 7,181 | lean | /-
Copyright (c) 2018 Kevin Buzzard and Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Patrick Massot.
This file is to a certain extent based on `quotient_module.lean` by Johannes Hölzl.
-/
import group_theory.coset
universes u v
names... |
a1ae2a2fab3f153147c15f210d4fea11d1f0e89d | f3a5af2927397cf346ec0e24312bfff077f00425 | /src/game/world5/level5.lean | 514c9b64e5a73a1e5fb4e10282f88a32a26fef42 | [
"Apache-2.0"
] | permissive | ImperialCollegeLondon/natural_number_game | 05c39e1586408cfb563d1a12e1085a90726ab655 | f29b6c2884299fc63fdfc81ae5d7daaa3219f9fd | refs/heads/master | 1,688,570,964,990 | 1,636,908,242,000 | 1,636,908,242,000 | 195,403,790 | 277 | 84 | Apache-2.0 | 1,694,547,955,000 | 1,562,328,792,000 | Lean | UTF-8 | Lean | false | false | 2,379 | lean | /-
# Function world.
## Level 5: `P → (Q → P)`.
In this level, our goal is to construct a function, like in level 2.
```
⊢ P → (Q → P)
```
So $P$ and $Q$ are sets, and our goal is to construct a function
which takes an element of $P$ and outputs a function from $Q$ to $P$.
We don't know anything at all about the s... |
7fad99d144dd7c62ce27987c3c4c0298fa6012e9 | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /tests/lean/run/coeSort2.lean | b7926e065a171e4d6b3eecbfda174fa601090faf | [
"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 | 263 | lean | universe u
structure Group :=
(carrier : Type u) (mul : carrier → carrier → carrier) (one : carrier)
instance GroupToType : CoeSort Group (Type u) :=
CoeSort.mk (fun g => g.carrier)
new_frontend
variable (g : Group.{1})
#check fun (a b : g) => g.mul a b
|
ea46531e3b8207a7056ded98c72ea91cbe3151e0 | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/ring_theory/jacobson_ideal.lean | ef50deddd4f86919c2c99e1c396e0cb2ccc22c14 | [
"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 | 14,407 | lean | /-
Copyright (c) 2020 Devon Tuma. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Devon Tuma
-/
import ring_theory.ideal.operations
import ring_theory.polynomial.basic
/-!
# Jacobson radical
The Jacobson radical of a ring `R` is defined to be the intersecti... |
12e1dceb2a767e6557b0834b091ee8a1bc75e0f9 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/control/functor.lean | c18cd665db28e36cb1ca425c4ce2229ed974d9ab | [
"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 | 8,772 | lean | /-
Copyright (c) 2017 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import tactic.lint
import control.basic
/-!
# Functors
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathlib4.
This... |
8dcca784c16dd81cb397a7522c0789115841b27a | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/group.lean | 3f370912e306a3c87bce8358f896349c2c8ce04c | [
"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 | 1,094 | lean | import logic
section
variable {A : Type}
variable f : A → A → A
variable one : A
variable inv : A → A
local infixl `*` := f
local postfix `^-1`:100 := inv
definition is_assoc := ∀ a b c, (a*b)*c = a*b*c
definition is_id := ∀ a, a*one = a
definition is_inv := ∀ a, a*a^-1 = one
end
inductive... |
b524cdbb706604c437ac96edcd359908e5fce3f9 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/model_theory/substructures.lean | bd98b13c40d2c8792fe193c0bd5ef55617bd474b | [
"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 | 29,689 | lean | /-
Copyright (c) 2021 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import order.closure
import model_theory.semantics
import model_theory.encoding
/-!
# First-Order Substructures
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any ch... |
1b5785795b4a9fb924bf82dc71cfe2945a748e8d | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /library/init/sigma_lex.lean | f57189ccee4145301bbff0084d575d17fe698235 | [
"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 | 5,770 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
prelude
import init.sigma init.meta init.combinator
universe variables u v
namespace sigma
section
variables {A : Type u} {B : A → Type v}
variable (Ra ... |
0ecd2f27311ae55f3b4a92696b51d090729e8dd7 | 995658a556256a6694fe5c98b91f7f6f6c11bb77 | /src/mathlib/impl.lean | 10ae90f7aa049c9f95e1af269a98e53bfebb0d08 | [
"MIT"
] | permissive | bhgomes/lean-riemann-hypothesis | d803047f27ea21f03414bbfb59395608ed0bc05f | c36b744a2dc4a7a50c7de770096bd9a051f42ab9 | refs/heads/master | 1,678,533,614,591 | 1,614,755,910,000 | 1,614,755,910,000 | 275,204,877 | 16 | 3 | null | null | null | null | UTF-8 | Lean | false | false | 10,196 | lean | /- ------------------------------------------------------------------------- -|
| @project: riemann_hypothesis |
| @file: mathlib/impl.lean |
| @authors: Brandon H. Gomes, Alex Kontorovich |
... |
6fbab71a9d232b6ecf42d081ec1f3fcc53d921b1 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/inst.lean | f8970fa05c8b436aa590063161824ce7211f232f | [
"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 | 496 | lean | import Lean.Expr
open Lean
def tst : IO Unit :=
do
let f := mkConst `f;
let x := mkBVar 0;
let y := mkBVar 1;
let t := mkApp (mkApp (mkApp f x) y) x;
let a := mkConst `a;
let b := mkApp f (mkConst `b);
let c := mkConst `c;
IO.println t;
IO.println (t.instantiate #[a, b]);
IO.println (t.instantiateRange 0 2 #[a, b]);
... |
6331815bf2c91b85e63e751ffe65bb9c2ee60fb0 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/deprecated/submonoid.lean | ef0921f7866d92727350bba2168beda9e52cc0a5 | [] | 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 | 17,405 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau, Johan Commelin, Mario Carneiro, Kevin Buzzard
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.group_theory.submonoid.basic
impo... |
4ab14c59203979c4611d21902069e127b166c303 | 2fbe653e4bc441efde5e5d250566e65538709888 | /src/tactic/core.lean | 09cdcb4eb561522489300f84a7fce5d6feb6052f | [
"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 | 57,458 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Simon Hudon, Scott Morrison, Keeley Hoek
-/
import data.dlist.basic category.basic meta.expr meta.rb_map data.bool tactic.library_note
tactic.derive_inhabited
namesp... |
2d66ae5f0afba9f6427a052652d00f32c563ebd4 | bb31430994044506fa42fd667e2d556327e18dfe | /src/data/nat/totient.lean | b3082bdf5a8950fe1c121f59b7dd4bad90b0252b | [
"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 | 15,309 | 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.char_p.two
import data.nat.factorization.basic
import data.nat.periodic
import data.zmod.basic
/-!
# Euler's totient function
This file defines [Euler's ... |
d9d95a02a51bf089a04ec03795087433e4dc9c6c | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/linear_algebra/lagrange.lean | 24416e95db4539a93e8f1304469f4daa7842948a | [
"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 | 24,207 | lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Wrenna Robson
-/
import algebra.big_operators.basic
import linear_algebra.vandermonde
import ring_theory.polynomial.basic
/-!
# Lagrange interpolation
## Main definitions
* In... |
0c9340172d628ebe5557f2c3231f55ce9fe1a22d | 5ae26df177f810c5006841e9c73dc56e01b978d7 | /src/algebra/punit_instances.lean | ab74fe62f48bb74b60a39ee361754e8416ff3d59 | [
"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 | 3,561 | lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
Instances on punit.
-/
import algebra.module algebra.group
universes u
open lattice
namespace punit
variables (x y : punit.{u+1}) (s : set punit.{u+1})
instance : comm_ring ... |
2dbe4ed167d9ec672b5804ab3bdf69889f0dc8f1 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/probability/independence.lean | 1b2268f2a888900042e0b8c0f6366e346bfbe32f | [
"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 | 52,353 | lean | /-
Copyright (c) 2021 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
import measure_theory.constructions.pi
/-!
# Independence of sets of sets and measure spaces (σ-algebras)
* A family of sets of sets `π : ι → set (set Ω)` is independen... |
26db43f79ab4b1309e514dfb5a8fadbb1c73e9a1 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/field_theory/normal.lean | 13261e704970dfbf5e42c31457fb775f741b7c0b | [
"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 | 15,457 | lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Thomas Browning, Patrick Lutz
-/
import field_theory.adjoin
import field_theory.tower
import group_theory.solvable
import ring_theory.power_basis
/-!
# Normal field extensions
... |
be60f30d84553e83f024d749711e573820a67429 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/complex/basic_auto.lean | 12f1fd810d6be66935621dc8e9d281cff0ce5a30 | [] | 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 | 21,633 | lean | /-
Copyright (c) 2017 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Mario Carneiro
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.real.sqrt
import Mathlib.PostPort
universes l u_1
namespace Mathlib
... |
57c888f31981e7c7d63ce52e71df91f843f487a1 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/compiler_bug1.lean | 98b36c979debaabcdeaa1c54fdd5b66fd4e908b4 | [
"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 | 226 | lean | inductive stmt : Type
| switch : list (nat × stmt) → stmt → stmt
| nop : stmt
meta def compile_cases_on_to_ir_expr : option stmt := do
do cs' ← return ([] : list (nat × stmt)),
return (stmt.switch cs' stmt.nop)
|
7421e7c36e68d8f42b4db90b78b4f7f57c247afb | 17eb1a9fda67ea006b0ea6e9f09e891681861bf9 | /iso-demo.lean | 9e9b6cecee2c9785ecaf41e6a537a546ff32c20e | [] | no_license | skaslev/zero-to-zipper | a9a402240a004da002aa9d4864ca910483e842b1 | d0615fc765d4a023df844fad5bb7f78a27bd01c2 | refs/heads/master | 1,597,028,473,080 | 1,571,393,101,000 | 1,571,393,101,000 | 214,240,337 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 335 | lean | structure iso (a b : Type) :=
(f : a → b) (g : b → a) (gf : Π x, g (f x) = x) (fg : Π x, f (g x) = x)
def inv {a b} : iso a b → iso b a
| ⟨f, g, gf, fg⟩ := ⟨_, _, _, _⟩
def comp {a b c} : iso a b → iso b c → iso a c
| ⟨f₁, g₁, g₁f₁, f₁g₁⟩ ⟨f₂, g₂, g₂f₂, f₂g₂⟩ := ⟨_, _, _, _⟩
|
eb9fdb43fddbcc19f4a604cb92b088e0ee9b3e6b | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/pkg/user_opt/lakefile.lean | 5657d60ed13f45fbef8ce1ed9957e57b4845d217 | [
"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 | 86 | lean | import Lake
open System Lake DSL
package user_opt
@[default_target] lean_lib UserOpt
|
3e92ac4fe0a7721b5cb51d3e6dd633961fac9d5e | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/ring_theory/polynomial/dickson.lean | 9bd08a2503d73eacfb102d7a1bc71b7117f76c3b | [
"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 | 10,539 | lean | /-
Copyright (c) 2021 Julian Kuelshammer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Kuelshammer
-/
import ring_theory.polynomial.chebyshev
import ring_theory.localization
import data.zmod.basic
import algebra.char_p.invertible
/-!
# Dickson polynomials
... |
bcb443e580d8d8ef773967c29726fabf6da651ac | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/ring_theory/valuation/integral.lean | 147393bd09a4cf9428ec616758e171240f5d9e9f | [
"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 | 2,211 | 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.integrally_closed
import ring_theory.valuation.integers
/-!
# Integral elements over the ring of integers of a valution
> THIS FILE IS SYNCHRONIZED WITH M... |
290c6c124bfe9005d9ed92d8e439d88f6ad7043b | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/measure_theory/measure/outer_measure.lean | deb94a1b926c9baad170a039d0faae49c8c439ed | [
"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 | 63,858 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import analysis.specific_limits
import measure_theory.pi_system
import data.fin.vec_notation
import topology.algebra.infinite_sum
/-!
# Outer Measure... |
e9ca952de74c4b79770ee8611e5bcd51956c8cd1 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/topology/algebra/module/basic.lean | 5691bf05bc9c32a04ca36a831416e62708a97338 | [
"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 | 83,273 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo, Yury Kudryashov, Frédéric Dupuis,
Heather Macbeth
-/
import topology.algebra.ring
import topology.algebra.mul_action
import topology... |
ce635361d83e30ab3cf99fa4042d6d4e931f1fb5 | efa51dd2edbbbbd6c34bd0ce436415eb405832e7 | /20160419_MIT/ex4.lean | 1093ed2d4f787db3a70c99bdc1c901a00082108f | [
"Apache-2.0"
] | permissive | leanprover/presentations | dd031a05bcb12c8855676c77e52ed84246bd889a | 3ce2d132d299409f1de269fa8e95afa1333d644e | refs/heads/master | 1,688,703,388,796 | 1,686,838,383,000 | 1,687,465,742,000 | 29,750,158 | 12 | 9 | Apache-2.0 | 1,540,211,670,000 | 1,422,042,683,000 | Lean | UTF-8 | Lean | false | false | 334 | lean | import data.nat theories.number_theory.primes
open nat subtype
eval is_true (∀ x, x < 5 → ∃ y, y < x ∧ y*y = x)
-- definition sub_dvd_of_not_prime {n : nat} : n ≥ 2 → ¬ prime n → {m : nat | m ∣ n ∧ m ≠ 1 ∧ m ≠ n} :=
eval elt_of (@sub_dvd_of_not_prime 10 dec_trivial dec_trivial)
check ex_dvd_of_not_prime
|
f07c24eb353b69c9f0e394fe9e61a966340f9f28 | c31182a012eec69da0a1f6c05f42b0f0717d212d | /src/for_mathlib/Profinite/product.lean | 517785dc4e4f98304799fc986264b2f0b60d6113 | [] | no_license | Ja1941/lean-liquid | fbec3ffc7fc67df1b5ca95b7ee225685ab9ffbdc | 8e80ed0cbdf5145d6814e833a674eaf05a1495c1 | refs/heads/master | 1,689,437,983,362 | 1,628,362,719,000 | 1,628,362,719,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,286 | lean | import category_theory.limits.shapes.binary_products
import topology.category.Profinite
namespace Profinite
universe u
variables (X Y : Profinite.{u})
open category_theory.limits
open category_theory
/-- An explicit cone for the product of two profinite sets. -/
@[simps]
def prod_cone : cone (pair X Y) :=
{ X := Pr... |
0fb697bc0fe5014b9c25b5adef4cc1ec0a8d6e79 | 0ddf2dd8409bcb923d11603846800bd9699616ea | /chapter3.lean | 25d8ac8e5d5904567067f69da5018e79e5188ff8 | [] | no_license | tounaishouta/Lean | 0cbaaa9340e7f8f884504ea170243e07a54f0566 | 1d75311f5506ca2bfd8b7ccec0b7d70c3319d555 | refs/heads/master | 1,610,229,383,935 | 1,459,950,226,000 | 1,459,950,226,000 | 50,836,185 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,431 | lean | print "\n Prop in Lean \n"
check Prop
check Type.{0} -- same as above
theorem HilbertS {P Q R : Prop}
: (P → Q → R) → (P → Q) → P → R
:=
assume g,
assume f,
assume x,
show R, from g x (f x)
check HilbertS
check fun (A : Type) (a b : A), a = b
constant A : Prop
theorem p1 : A → A → A :=
assume Ha1 : A,
assume Ha2... |
8ca5be7fb08f865b3f82af4231193530dc516171 | a7eef317ddec01b9fc6cfbb876fe7ac00f205ac7 | /src/algebra/module.lean | 9a710c5fbd0ca2798e1341a998016beddce55301 | [
"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 | 29,077 | lean | /-
Copyright (c) 2015 Nathaniel Thomas. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nathaniel Thomas, Jeremy Avigad, Johannes Hölzl, Mario Carneiro
-/
import group_theory.group_action
/-!
# Modules over a ring
In this file we define
* `semimodule R M` : an additi... |
72a4adc19036fce9f5b142b52aa01a821239f223 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/data/int/basic.lean | 5ad324e207851e96b8036f5422b493c7cfc79149 | [
"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 | 64,812 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
-/
import data.nat.pow
import order.min_max
import data.nat.cast
/-!
# Basic operations on the integers
This file contains:
* instances on `ℤ`. The stronger one is `int.... |
dbff9c8921095cac8d4bd72779c0f3fc91017ca8 | 9b9a16fa2cb737daee6b2785474678b6fa91d6d4 | /src/category_theory/products.lean | bbc51dc62e6e12c611aa61339d1d1fe5cd3c5bc5 | [
"Apache-2.0"
] | permissive | johoelzl/mathlib | 253f46daa30b644d011e8e119025b01ad69735c4 | 592e3c7a2dfbd5826919b4605559d35d4d75938f | refs/heads/master | 1,625,657,216,488 | 1,551,374,946,000 | 1,551,374,946,000 | 98,915,829 | 0 | 0 | Apache-2.0 | 1,522,917,267,000 | 1,501,524,499,000 | Lean | UTF-8 | Lean | false | false | 5,511 | lean | -- Copyright (c) 2017 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Stephen Morgan, Scott Morrison
import category_theory.functor_category
import category_theory.isomorphism
import tactic.interactive
namespace category_theory
universes v₁ v₂ v... |
77a48b3299ed628d217057ab3ee5fbcc5b695d0b | 2d34dfb0a1cc250584282618dc10ea03d3fa858e | /src/locally_constant/algebra.lean | 1f4874ff32f9696b5054711d77f86fb84d69d419 | [] | no_license | zeta1999/lean-liquid | 61e294ec5adae959d8ee1b65d015775484ff58c2 | 96bb0fa3afc3b451bcd1fb7d974348de2f290541 | refs/heads/master | 1,676,579,150,248 | 1,610,771,445,000 | 1,610,771,445,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,560 | lean | import locally_constant.basic
namespace locally_constant
variables {X Y : Type*} [topological_space X]
@[to_additive]
instance [has_one Y] : has_one (locally_constant X Y) :=
{ one := const X 1 }
@[simp, to_additive]
lemma one_apply [has_one Y] (x : X) : (1 : locally_constant X Y) x = 1 := rfl
@[to_additive]
insta... |
c36fee0450c1137653595cbda033c0c7a981f51d | ff5230333a701471f46c57e8c115a073ebaaa448 | /library/init/category/id.lean | a85afc6894c1326e5b78fcda4750aab9c52d940f | [
"Apache-2.0"
] | permissive | stanford-cs242/lean | f81721d2b5d00bc175f2e58c57b710d465e6c858 | 7bd861261f4a37326dcf8d7a17f1f1f330e4548c | refs/heads/master | 1,600,957,431,849 | 1,576,465,093,000 | 1,576,465,093,000 | 225,779,423 | 0 | 3 | Apache-2.0 | 1,575,433,936,000 | 1,575,433,935,000 | null | UTF-8 | Lean | false | false | 438 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Ullrich
The identity monad.
-/
prelude
import init.category.lift
universe u
@[inline] def id_bind {α β : Type u} (x : α) (f : α → id β) : id β := f x
@[inline] inst... |
d7c7aee50e60cac096a3de3527222cbe05a58016 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/init/data/nat/bitwise_auto.lean | d782a424b4204787584936db779922242794cccd | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,347 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.data.nat.lemmas
import Mathlib.Lean3Lib.init.meta.well_founded_tactics
universes u
namespace Mathlib
nam... |
061ea491363fc1c317a78e6aa85814409a77abe2 | 206422fb9edabf63def0ed2aa3f489150fb09ccb | /src/analysis/calculus/inverse.lean | d806c311315523c4cc639b5fd23b25bbd5a541cd | [
"Apache-2.0"
] | permissive | hamdysalah1/mathlib | b915f86b2503feeae268de369f1b16932321f097 | 95454452f6b3569bf967d35aab8d852b1ddf8017 | refs/heads/master | 1,677,154,116,545 | 1,611,797,994,000 | 1,611,797,994,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 25,938 | lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Heather Macbeth.
-/
import analysis.calculus.times_cont_diff
import topology.local_homeomorph
import topology.metric_space.contracting
/-!
# Inverse function theorem... |
902745ee3c2ec49a5622eee288f8ce962b11e348 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/lift_coe_off.lean | a14e48fddc7581b71e1a1c970e3672731be41bba | [
"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 | 403 | lean | open nat
inductive tree (A : Type) :=
leaf : A → tree A,
node : tree A → tree A → tree A
-- set_option elaborator.lift_coercions false
definition size {A : Type} (t : tree A) :nat:=
tree.rec (λ a, 1) (λ t₁ t₂ n₁ n₂, n₁ + n₂) t
--set_option elaborator.lift_coercions true
definition size2 {A : Type} (t : tree A) :na... |
2274390d07726e7b11d10539fc7515da39d22455 | e39f04f6ff425fe3b3f5e26a8998b817d1dba80f | /data/list/defs.lean | f14efa2f3f72526d6e806c4862c5b11f72919f59 | [
"Apache-2.0"
] | permissive | kristychoi/mathlib | c504b5e8f84e272ea1d8966693c42de7523bf0ec | 257fd84fe98927ff4a5ffe044f68c4e9d235cc75 | refs/heads/master | 1,586,520,722,896 | 1,544,030,145,000 | 1,544,031,933,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 15,068 | lean | import data.option logic.basic tactic.interactive
namespace list
open function nat
universes u v w x
variables {α : Type u} {β : Type v} {γ : Type w} {δ : Type x}
/-- Split a list at an index.
split_at 2 [a, b, c] = ([a, b], [c]) -/
def split_at : ℕ → list α → list α × list α
| 0 a := ([], a)
| ... |
bc392b93a2faf06a857393e3d9b42166737a7db1 | 367134ba5a65885e863bdc4507601606690974c1 | /src/algebra/lie/classical.lean | 6c70f3bdcfc58108809699497a90f8acb38cf2c9 | [
"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 | 13,446 | lean | /-
Copyright (c) 2020 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import algebra.invertible
import algebra.lie.skew_adjoint
import algebra.lie.abelian
/-!
# Classical Lie algebras
This file is the place to find definitions and basic pro... |
f9ca15d8bb9ddc4dddc2424a7acc74bfef1a6567 | 95dcf8dea2baf2b4b0a60d438f27c35ae3dd3990 | /src/category_theory/natural_isomorphism.lean | ae3b72b2337c26dd34b4099d2a94b89857ee1607 | [
"Apache-2.0"
] | permissive | uniformity1/mathlib | 829341bad9dfa6d6be9adaacb8086a8a492e85a4 | dd0e9bd8f2e5ec267f68e72336f6973311909105 | refs/heads/master | 1,588,592,015,670 | 1,554,219,842,000 | 1,554,219,842,000 | 179,110,702 | 0 | 0 | Apache-2.0 | 1,554,220,076,000 | 1,554,220,076,000 | null | UTF-8 | Lean | false | false | 5,516 | lean | -- Copyright (c) 2017 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Tim Baumann, Stephen Morgan, Scott Morrison
import category_theory.isomorphism
import category_theory.functor_category
open category_theory
namespace category_theory.nat_iso
... |
29ba2de2e3e604f63bb87dd27afd767d0714a995 | ed27983dd289b3bcad416f0b1927105d6ef19db8 | /src/inClassNotes/type_library/empty.lean | 2b51b3a5ab855f580d13b64629604ea8563f8a43 | [] | no_license | liuxin-James/complogic-s21 | 0d55b76dbe25024473d31d98b5b83655c365f811 | 13e03e0114626643b44015c654151fb651603486 | refs/heads/master | 1,681,109,264,463 | 1,618,848,261,000 | 1,618,848,261,000 | 337,599,491 | 0 | 0 | null | 1,613,141,619,000 | 1,612,925,555,000 | null | UTF-8 | Lean | false | false | 720 | lean | namespace hidden
/-
The empty data type has no
values/constructors at all.
This fact becomes interesting
and useful when one performs
a case analysis on values of
this type, as there are no
cases to consider.
-/
inductive empty : Type -- uninhabited
/-
Exercise: Show that you can
implement a function, e2n, that
take... |
059f8b7421c27224a7592e752120d3f1a3208b86 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/linear_algebra/free_algebra.lean | 4296cc3f500caddb95214a181599e388b6ddae84 | [
"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 | 1,066 | 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.basis
import algebra.free_algebra
import linear_algebra.finsupp_vector_space
/-!
# Linear algebra properties of `free_algebra R X`
This file provides... |
9fdb5d7319a31518334653f26988d2b27a71245c | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /tests/lean/run/revert1.lean | 707573a183d69b591c8e7bf1c748ccc2ffbd5491 | [
"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 | 292 | lean |
theorem tst1 (x y z : Nat) : y = z → x = x → x = y → x = z :=
by {
intros h1 h2 h3;
revert h2;
intro h2;
exact Eq.trans h3 h1
}
theorem tst2 (x y z : Nat) : y = z → x = x → x = y → x = z :=
by {
intros h1 h2 h3;
revert y;
intros y hb ha;
exact Eq.trans ha hb
}
|
a31ab03163652ed357dba39e6089a4a6270b2c81 | ce6917c5bacabee346655160b74a307b4a5ab620 | /src/ch5/ex0802.lean | 64368b474563db35b47e3b0297270081e4975e82 | [] | 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 | 191 | lean | example (p q r : Prop) (hp : p) : (p ∨ q ∨ r) ∧ (q ∨ p ∨ r) ∧ (q ∨ r ∨ p) :=
by { repeat { any_goals { split } }; repeat { { left, assumption } <|> right <|> assumption } }
|
2fc8c20bc2049f06c16071aacb93076bc3890b68 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/data/list/palindrome.lean | e38cc03ddc2d819d8c5f5df4beb25614d86950fe | [
"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 | 2,185 | lean | /-
Copyright (c) 2020 Google LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Wong
-/
import data.list.basic
/-!
# Palindromes
This module defines *palindromes*, lists which are equal to their reverse.
The main result is the `palindrome` inductive type, an... |
cb9eec299ba8bcdf1e7e585cd5d0301f4cd1825a | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/group_theory/perm/sign.lean | 3b9deff4ba19a4499c8118968154705c47a3ea80 | [
"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 | 31,098 | 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.fintype.basic
import data.finset.sort
import data.nat.parity
import group_theory.perm.support
import group_theory.order_of_element
import tactic.norm_swap
imp... |
d44892c7131b5db2c87a0e22067e0562db051189 | e0b0b1648286e442507eb62344760d5cd8d13f2d | /stage0/src/Lean/PrettyPrinter/Delaborator/Builtins.lean | 3354b85019ef5c07287f460e1a988036c8e5f02e | [
"Apache-2.0"
] | permissive | MULXCODE/lean4 | 743ed389e05e26e09c6a11d24607ad5a697db39b | 4675817a9e89824eca37192364cd47a4027c6437 | refs/heads/master | 1,682,231,879,857 | 1,620,423,501,000 | 1,620,423,501,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 24,420 | 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.PrettyPrinter.Delaborator.Basic
import Lean.Parser
namespace Lean.PrettyPrinter.Delaborator
open Lean.Meta
open Lean.Parser.Term
@[builtinDelab f... |
73f71dd5462455d711ba2d027083c57a04c3a269 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/reflects_isomorphisms_auto.lean | 23cb093cd698b53b4eacfd5f3bea92d974de37ce | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,433 | lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.category_theory.fully_faithful
import Mathlib.PostPort
universes v₁ v₂ u₁ u₂ l
namespace Mat... |
e7e25d92d9128374f21fdbbbe30625016d9d0a69 | a4673261e60b025e2c8c825dfa4ab9108246c32e | /src/Lean/Data/LOption.lean | b7a72ede920446f1108031ce5c4afcc89952c90a | [
"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 | 1,075 | 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
namespace Lean
inductive LOption (α : Type u) :=
| none : LOption α
| some : α → LOption α
| undef : LOption α
namespace LOption
vari... |
40dac21160299826f7d6a6a071cc9e0505672069 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/group_theory/specific_groups/dihedral.lean | 15cc944e65216f19d3691603e8e7b30e5fa9e964 | [
"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 | 5,852 | lean | /-
Copyright (c) 2020 Shing Tak Lam. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shing Tak Lam
-/
import data.fintype.card
import data.zmod.basic
import group_theory.exponent
import data.int.parity
/-!
# Dihedral Groups
We define the dihedral groups `dihedral_grou... |
0217183ed9f4e65c359afec4850d07f8aafc37e6 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/run/def9.lean | a05ac5068bce32ba8ee0aa65831b8a75c2a572a3 | [
"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 | 90 | lean |
lemma ex4 (A : Type) : ∀ (a b : A) (H : a = b), b = a
| .z z (eq.refl .z) := eq.refl z
|
0c77f51c683dd53e254b64865dd2bbc4f4e28b45 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/blast_cc_subsingleton_normalization_issue.lean | 32f5b69de0b3a2b3f14a4bf77e50ddf5c273ee43 | [
"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 | 529 | lean | import data.real
open real
namespace safe
definition pos (x : ℝ) := x > 0
constants (safe_log : Π (x : ℝ), pos x → ℝ)
lemma pos_add {x y : ℝ} : pos x → pos y → pos (x + y) := sorry
lemma pos_mul {x y : ℝ} : pos x → pos y → pos (x * y) := sorry
set_option blast.strategy "cc"
example (x y z w : ℝ)
(x_pos : pos x... |
25395f97c084097fc6e125faa18fbbaca3b5c51e | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /library/init/relation.lean | 1ff0e56e90a92870a1f050751120a93397acd2c5 | [
"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 | 1,729 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module init.relation
Authors: Leonardo de Moura
-/
prelude
import init.logic
-- TODO(Leo): remove duplication between this file and algebra/relation.lean
-- We need some of the followi... |
d41b68bf1d2984c8b9e5e39bce8df17fa7e66d79 | 92b50235facfbc08dfe7f334827d47281471333b | /library/data/nat/default.lean | ca7ef3aa9bbc261574f09545218acf5ba0474445 | [
"Apache-2.0"
] | permissive | htzh/lean | 24f6ed7510ab637379ec31af406d12584d31792c | d70c79f4e30aafecdfc4a60b5d3512199200ab6e | refs/heads/master | 1,607,677,731,270 | 1,437,089,952,000 | 1,437,089,952,000 | 37,078,816 | 0 | 0 | null | 1,433,780,956,000 | 1,433,780,955,000 | null | UTF-8 | Lean | false | false | 247 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad
-/
import .basic .order .sub .div .gcd .bquant .sqrt .pairing .power .choose .fact .parity
|
a07536e0807fedf3a87e7ee751bc36a7ce3aa054 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/open_tst.lean | a7336a73aaf6b802e99aab4f0a2e709fb930d291 | [
"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 | 582 | lean | section
check (1:nat) + 2
check add
end
section
variable a : nat
check a + a
check add a a
check a + 1
end
section
open - [class] nat
variable a : nat
check a + a
check add a a
check a + 1
definition foo1 : inhabited nat :=
_ -- Error inhabited instances was not loaded
end
section
open - ... |
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