blob_id stringlengths 40 40 | directory_id stringlengths 40 40 | path stringlengths 7 139 | content_id stringlengths 40 40 | detected_licenses listlengths 0 16 | license_type stringclasses 2
values | repo_name stringlengths 7 55 | snapshot_id stringlengths 40 40 | revision_id stringlengths 40 40 | branch_name stringclasses 6
values | visit_date int64 1,471B 1,694B | revision_date int64 1,378B 1,694B | committer_date int64 1,378B 1,694B | github_id float64 1.33M 604M ⌀ | star_events_count int64 0 43.5k | fork_events_count int64 0 1.5k | gha_license_id stringclasses 6
values | gha_event_created_at int64 1,402B 1,695B ⌀ | gha_created_at int64 1,359B 1,637B ⌀ | gha_language stringclasses 19
values | src_encoding stringclasses 2
values | language stringclasses 1
value | is_vendor bool 1
class | is_generated bool 1
class | length_bytes int64 3 6.4M | extension stringclasses 4
values | content stringlengths 3 6.12M |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
33bdaa2972651c531b2071e108d770e8ad328393 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/t13.lean | cef8024b67b5acd19aa5fcac33203dbc2dac1600 | [
"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 | 327 | lean | prelude constant A : Type.{1}
constant f : A → A → A
constant g : A → A → A
precedence `+` : 65
infixl + := f
infixl + := g
constant a : A
constant b : A
print raw a+b -- + is overloaded
check fun (h : A → A → A)
(infixl + := h), -- Like local declarations, local notation "shadows" global one.
a+b
|
e1d086be1777cbea86b66e37c9766d087fe0def0 | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/ring_theory/adjoin_root.lean | 83445af23e45ad3ccf6e2360371617cfffc2ccf3 | [
"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 | 3,691 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Chris Hughes
Adjoining roots of polynomials
-/
import data.polynomial ring_theory.principal_ideal_domain
universes u v w
variables {α : Type u} {β : Type v} {γ : Ty... |
f0cdf48916a94106c2efc4fc0da228f0b4998d63 | 38bf3fd2bb651ab70511408fcf70e2029e2ba310 | /src/category_theory/groupoid.lean | 23fd1e92bdde7aecedfb4cddffe78165c28f1f39 | [
"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 | 1,034 | lean | /-
Copyright (c) 2018 Reid Barton All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton
-/
import category_theory.category
import category_theory.isomorphism
namespace category_theory
universes v u -- declare the `v`'s first; see `category_theory.category` for ... |
6243aa796b92dfd2dc30f1b17418a4b24ab856dc | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Data/SSet.lean | 578340f86402462562d3a02c867fb09298b73ca9 | [
"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 | 1,379 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Data.SMap
namespace Lean
/-- Staged set. It is just a simple wrapper on top of Staged maps. -/
def SSet (α : Type u) [BEq α] [Hashable α] := S... |
725950a956f5d7c420363a2f4c7c88c0787851d2 | 5719a16e23dfc08cdea7a5bf035b81690f307965 | /stage0/src/Init/Data/Array/Basic.lean | 875106bbdc49935e96cf3fd5d2b95dcb2c0e091d | [
"Apache-2.0"
] | permissive | postmasters/lean4 | 488b03969a371e1507e1e8a4df9ebf63c7cbe7ac | f3976fc53a883ac7606fc59357d43f4b51016ca7 | refs/heads/master | 1,655,582,707,480 | 1,588,682,595,000 | 1,588,682,595,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 24,820 | lean | /-
Copyright (c) 2018 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
import Init.Data.Fin.Basic
import Init.Data.UInt
import Init.Data.Repr
import Init.Data.ToString
import Init.Control.Id
i... |
2707ebccf7f0b9ae1c5468e56fefb5903dcc6ddb | d1a52c3f208fa42c41df8278c3d280f075eb020c | /tests/lean/run/270.lean | 6d6b122b6d67cad36f978981bd50549d0cfe25c3 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | cipher1024/lean4 | 6e1f98bb58e7a92b28f5364eb38a14c8d0aae393 | 69114d3b50806264ef35b57394391c3e738a9822 | refs/heads/master | 1,642,227,983,603 | 1,642,011,696,000 | 1,642,011,696,000 | 228,607,691 | 0 | 0 | Apache-2.0 | 1,576,584,269,000 | 1,576,584,268,000 | null | UTF-8 | Lean | false | false | 1,083 | lean | class CommAddSemigroup (α : Type u) extends Add α where
addComm : {a b : α} → a + b = b + a
addAssoc : {a b c : α} → a + b + c = a + (b + c)
open CommAddSemigroup
theorem addComm3 [CommAddSemigroup α] {a b c : α} : a + b + c = a + c + b := by {
have h : b + c = c + b := addComm;
have h' := congrArg (a... |
1834d5e85c8740fe1c118a07c3fd9c1fe8bcaedc | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /03_Propositions_and_Proofs.org.22.lean | da22fad0928e1b41d20c90199a96657752b04ea1 | [] | no_license | cjmazey/lean-tutorial | ba559a49f82aa6c5848b9bf17b7389bf7f4ba645 | 381f61c9fcac56d01d959ae0fa6e376f2c4e3b34 | refs/heads/master | 1,610,286,098,832 | 1,447,124,923,000 | 1,447,124,923,000 | 43,082,433 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 225 | lean | /- page 40 -/
import standard
variables p q r: Prop
-- BEGIN
example (H : p ∨ q) : q ∨ p :=
or.elim H
(assume Hp : p,
show q ∨ p, from or.intro_right q Hp)
(assume Hq : q,
show q ∨ p, from or.intro_left p Hq)
-- END
|
fc29a24fd0c3b8068cd718cedbc11a619cdebd49 | 8d65764a9e5f0923a67fc435eb1a5a1d02fd80e3 | /src/algebra/ordered_ring.lean | b61bae03643de571aa7339a53df69f81d346a229 | [
"Apache-2.0"
] | permissive | troyjlee/mathlib | e18d4b8026e32062ab9e89bc3b003a5d1cfec3f5 | 45e7eb8447555247246e3fe91c87066506c14875 | refs/heads/master | 1,689,248,035,046 | 1,629,470,528,000 | 1,629,470,528,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 65,617 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro
-/
import algebra.ordered_group
import algebra.invertible
import data.set.intervals.basic
set_option old_structure_cmd true
universe u... |
606fb8687b71cbfeb760b567668448a8acd0bc88 | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /src/Init/Control/Applicative.lean | 2de9cd3cdff8df095e8579427a01c224962bf026 | [
"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 | 1,366 | 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, Sebastian Ullrich
-/
prelude
import Init.Control.Functor
open Function
universes u v
class HasPure (f : Type u → Type v) :=
(pure {} {α : Type u} : α → f α)
... |
0edf1cffa9f13e2970387ef622e3faa72efce9ef | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/tactic/zify_auto.lean | 698bbc46ce8ad5c80eea526b0342df983717859e | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,060 | lean | /-
Copyright (c) 2020 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.tactic.norm_cast
import Mathlib.data.int.cast
import Mathlib.PostPort
namespace Mathlib
... |
2b53d8f100f7bd879fc5b083d9c0cf5ea42fb99c | fe25de614feb5587799621c41487aaee0d083b08 | /src/Init/Data/Array/Basic.lean | d1f5f73a3d97036d5980b8ced6e1601598903e5f | [
"Apache-2.0"
] | permissive | pollend/lean4 | e8469c2f5fb8779b773618c3267883cf21fb9fac | c913886938c4b3b83238a3f99673c6c5a9cec270 | refs/heads/master | 1,687,973,251,481 | 1,628,039,739,000 | 1,628,039,739,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 27,617 | lean | /-
Copyright (c) 2018 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
import Init.Data.Fin.Basic
import Init.Data.UInt
import Init.Data.Repr
import Init.Data.ToString.Basic
import Init.Util
u... |
637e060a4cdd2be7889a4fcd8053745cc1404bbe | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/algebra/smul_with_zero.lean | 6e7dc416dd4993bf4eeb793ae0ff16ea6770fbbc | [
"Apache-2.0"
] | permissive | abentkamp/mathlib | d9a75d291ec09f4637b0f30cc3880ffb07549ee5 | 5360e476391508e092b5a1e5210bd0ed22dc0755 | refs/heads/master | 1,682,382,954,948 | 1,622,106,077,000 | 1,622,106,077,000 | 149,285,665 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,251 | lean | /-
Copyright (c) 2021 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
import group_theory.group_action.defs
import algebra.group_power.basic
/-!
# Introduce `smul_with_zero`
In analogy with the usual monoid action on a Type `M`, we intr... |
dd246ed8b460d46eee667217f455c28934a9aead | 87fd6b43d22688237c02b87c30d2a524f53bab24 | /src/game/sets/sqrtOfTwo.lean | 5a65e871c9572b49759280cd6b01c3a521b95ead | [
"Apache-2.0"
] | permissive | grthomson/real-number-game | 66142fedf0987db90f66daed52f9c8b42b70f909 | 8ddc15fdddc241c246653f7bb341df36e4e880a8 | refs/heads/master | 1,668,059,330,605 | 1,592,873,454,000 | 1,592,873,454,000 | 262,025,764 | 0 | 0 | null | 1,588,849,107,000 | 1,588,849,106,000 | null | UTF-8 | Lean | false | false | 3,895 | lean | import data.nat.prime
open nat
theorem sqrt_two_irrational_V1 {a b : ℕ} (co : gcd a b = 1) : a^2 ≠ 2 * b^2 :=
assume h : a^2 = 2 * b^2,
have 2 ∣ a^2,
by simp [h],
have ha : 2 ∣ a,
from prime.dvd_of_dvd_pow prime_two this,
-- usually after exists.elim the rest of the proof should be inside
-- parantheses
exists... |
b900dc735393a5cf55a8864037bf8ec78b5ad49f | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/algebra/field_power.lean | bb35ad0880d844bd5f370942e8b7cd6ab5622bb6 | [
"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 | 8,735 | lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis
-/
import algebra.group_with_zero.power
import tactic.linarith
import data.equiv.ring
/-!
# Integer power operation on fields and division rings
This file collects b... |
5b4e959c149be6357e933dc51e74ce1c74868460 | 8e6cad62ec62c6c348e5faaa3c3f2079012bdd69 | /src/topology/instances/real.lean | 17b963588a19e227a0b70bea3f21d3eb86eea478 | [
"Apache-2.0"
] | permissive | benjamindavidson/mathlib | 8cc81c865aa8e7cf4462245f58d35ae9a56b150d | fad44b9f670670d87c8e25ff9cdf63af87ad731e | refs/heads/master | 1,679,545,578,362 | 1,615,343,014,000 | 1,615,343,014,000 | 312,926,983 | 0 | 0 | Apache-2.0 | 1,615,360,301,000 | 1,605,399,418,000 | Lean | UTF-8 | Lean | false | false | 16,892 | 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
-/
import topology.metric_space.basic
import topology.algebra.uniform_group
import topology.algebra.ring
import topology.algebra.continuous_functions
imp... |
db5c99292b7b9c65f68721369617b42d2e6e8be7 | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /tests/lean/run/elab_cmd.lean | c835a715370cab4dc00910b2ba1cc876b697fbbf | [
"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 | 652 | lean | import Lean
open Lean.Elab.Term
open Lean.Elab.Command
elab "∃'" b:term "," P:term : term => do
let ex ← `(Exists (fun $b => $P));
elabTerm ex none
elab "#check2" b:term : command => do
let cmd ← `(#check $b #check $b);
elabCommand cmd
#check ∃' x, x > 0
#check ∃' (x : UInt32), x > 0
#check2 10
elab "try... |
73a91713cf6be41c3deba387719e1fc3c3c6d778 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/ring_theory/finiteness.lean | 98242602f66305c1502562c1ca51d8861a9b0a35 | [
"Apache-2.0"
] | permissive | abentkamp/mathlib | d9a75d291ec09f4637b0f30cc3880ffb07549ee5 | 5360e476391508e092b5a1e5210bd0ed22dc0755 | refs/heads/master | 1,682,382,954,948 | 1,622,106,077,000 | 1,622,106,077,000 | 149,285,665 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 33,018 | 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.noetherian
import ring_theory.ideal.operations
import ring_theory.algebra_tower
import group_theory.finiteness
/-!
# Finiteness conditions in com... |
06a9bbe9cdf66220a47844414d5545e0976a98e0 | 1a61aba1b67cddccce19532a9596efe44be4285f | /tests/lean/hott/614.hlean | bd35214793bae6eacf7b911596574efc78bc1462 | [
"Apache-2.0"
] | permissive | eigengrau/lean | 07986a0f2548688c13ba36231f6cdbee82abf4c6 | f8a773be1112015e2d232661ce616d23f12874d0 | refs/heads/master | 1,610,939,198,566 | 1,441,352,386,000 | 1,441,352,494,000 | 41,903,576 | 0 | 0 | null | 1,441,352,210,000 | 1,441,352,210,000 | null | UTF-8 | Lean | false | false | 588 | hlean | import hit.circle
open circle eq int pi
attribute circle.rec [recursor]
protected definition my_decode {x : circle} (c : circle.code x) : base = x :=
begin
induction x,
{ revert c, exact power loop },
{ apply arrow_pathover_left, intro b, apply concato_eq, apply pathover_eq_r,
rewrite [power_con,transport_... |
6ad0abb78d657a6a9f3df88d2a7cee88304d0562 | aa3f8992ef7806974bc1ffd468baa0c79f4d6643 | /tests/lean/run/proj.lean | 724bdc01e851ad4e271462ce7df39b6be1493f4d | [
"Apache-2.0"
] | permissive | codyroux/lean | 7f8dff750722c5382bdd0a9a9275dc4bb2c58dd3 | 0cca265db19f7296531e339192e9b9bae4a31f8b | refs/heads/master | 1,610,909,964,159 | 1,407,084,399,000 | 1,416,857,075,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 341 | lean | import logic
inductive sigma {A : Type} (B : A → Type) :=
mk : Π (a : A), B a → sigma B
#projections sigma :: proj1 proj2
check sigma.proj1
check sigma.proj2
variables {A : Type} {B : A → Type}
variables (a : A) (b : B a)
theorem tst1 : sigma.proj1 (sigma.mk a b) = a :=
rfl
theorem tst2 : sigma.proj2 (sigma.mk a ... |
fe1e47ff5180c64c363ab780f7dc49814ee72df4 | 367134ba5a65885e863bdc4507601606690974c1 | /src/probability_theory/integration.lean | ecdb312b921ffb8bffa3df02bc71d7ed3353ce62 | [
"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 | 5,750 | lean | /-
Copyright (c) 2021 Martin Zinkevich. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Martin Zinkevich
-/
import measure_theory.integration
import probability_theory.independence
/-!
# Integration in Probability Theory
Integration results for independent random vari... |
560b85de160befc201ad745fc1c9ff1a170ab325 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/normed_space/add_torsor_bases.lean | 5e162d8f02c820269a316023e0706e0779060608 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 7,168 | 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 analysis.normed_space.finite_dimension
import analysis.calculus.affine_map
import analysis.convex.combination
import linear_algebra.affine_space.finite_dimensional
... |
5b81d0f24ba46b24134bfb0f537a3381500d3531 | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /tests/lean/calcErrors.lean | c83e2edc9eb34744d6d3f0e92328669e96eb4a65 | [
"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 | 1,566 | lean | theorem ex1 (a b c : Nat) (h₁ : a = b) (h₂ : b = c) : a + b = 0 + c + b :=
calc a + b = b + b := by rw [h₁]
_ = 0 + c + b := rfl
theorem ex2 (a b c : Nat) (h₁ : a = b) (h₂ : b = c) : a + b = 0 + c + b :=
calc a + b = b + b := by rw [h₁]
0 + c + b = 0 + c + b := rfl
theorem ex3 ... |
1c07a78c9dda155704f41f29891a690f284f32be | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/algebra/homology/additive.lean | 3eb6121fe66855fcdd594290903ec71a140aa0e7 | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 8,810 | lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import algebra.homology.homology
import algebra.homology.single
import category_theory.preadditive.additive_functor
/-!
# Homology is an additive functor
When `V` i... |
50305d9ca023b7ea223f011e4725ff3d1e2068a2 | 96e44fc78cabfc9d646dc37d0e756189b6b79181 | /library/init/meta/tactic.lean | d4803e27b54bcdd9f99b39fb6a5f011c65923364 | [
"Apache-2.0"
] | permissive | TwoFX/lean | 23c73c10a340f5a381f6abf27a27f53f1fb7e2e3 | 7e3f336714055869690b7309b6bb651fbc67e76e | refs/heads/master | 1,612,504,908,183 | 1,594,641,622,000 | 1,594,641,622,000 | 243,750,847 | 0 | 0 | Apache-2.0 | 1,582,890,661,000 | 1,582,890,661,000 | null | UTF-8 | Lean | false | false | 72,322 | 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.function init.data.option.basic init.util
import init.control.combinators init.control.monad init.control.alternative init.control.monad... |
f8f858a233214742bb95ba81edc63a3a221f40b7 | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/ring_theory/perfection.lean | 1555bfd49b631d7f06ad2da26d6836ad6b064853 | [
"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 | 24,280 | lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import algebra.char_p
import algebra.ring.pi
import analysis.special_functions.pow
import field_theory.perfect_closure
import ring_theory.localization
import ring_theory.subri... |
b9612fc2b04dfd2c45fdad6f73ea6935528c5ee4 | b70031c8e2c5337b91d7e70f1e0c5f528f7b0e77 | /src/analysis/special_functions/exp_log.lean | 2ea61436da3b327da5fb57994ad0a8ee9fb0845e | [
"Apache-2.0"
] | permissive | molodiuc/mathlib | cae2ba3ef1601c1f42ca0b625c79b061b63fef5b | 98ebe5a6739fbe254f9ee9d401882d4388f91035 | refs/heads/master | 1,674,237,127,059 | 1,606,353,533,000 | 1,606,353,533,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 28,774 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne
-/
import data.complex.exponential
import analysis.complex.basic
import analysis.calculus.mean_value
import measure_theory.bo... |
e918f7dbbc7dc4ab6a5068d0550d34ea3ebedfef | 94e33a31faa76775069b071adea97e86e218a8ee | /src/analysis/special_functions/bernstein.lean | 9965481e753404db10801a8701ae1b3f7f35d5db | [
"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 | 12,949 | lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import algebra.order.field
import ring_theory.polynomial.bernstein
import topology.continuous_function.polynomial
/-!
# Bernstein approximations and Weierstrass' the... |
ae154ddbbac95a2da8379b4b238c27f00cedb70a | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/data/bitvec/basic.lean | 2b7cc5a1f1cfb2332edd78762727bd010a8c6906 | [
"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 | 3,679 | 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 data.bitvec.core
import data.fin
import tactic.norm_num
import tactic.monotonicity
namespace bitvec
instance (n : ℕ) : preorder (bitvec n) :=
preorder.lift bitvec.... |
5699b395840f7bcaad00475c5aeeabd86a802790 | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/group_theory/sylow.lean | 249864b8cddcfa8bd5a784227d1c26bf92311442 | [
"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 | 11,385 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import group_theory.group_action group_theory.quotient_group
import group_theory.order_of_element data.zmod.basic
open equiv fintype finset mul_action function
open equi... |
970f5779fa0f4c5c3581c33331a449f1e6d6d989 | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /06_Inductive_Types.org.44.lean | d565171c28ab01036fd95afe39953afce20464ca | [] | no_license | cjmazey/lean-tutorial | ba559a49f82aa6c5848b9bf17b7389bf7f4ba645 | 381f61c9fcac56d01d959ae0fa6e376f2c4e3b34 | refs/heads/master | 1,610,286,098,832 | 1,447,124,923,000 | 1,447,124,923,000 | 43,082,433 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 243 | lean | /- page 92 -/
import standard
namespace hide
inductive eq {A : Type} (a : A) : A → Prop :=
refl : eq a a
-- BEGIN
theorem subst {A : Type} {a b : A} {P : A → Prop}
(H₁ : eq a b) (H₂ : P a) : P b :=
eq.rec H₂ H₁
-- END
end hide
|
9f73db18641603941b430194a1a5ed70cd3f77d8 | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /tests/lean/986.lean | 3f88415f8622a2009bf2a10a8c3721ac21abd932 | [
"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 | 133 | lean | attribute [simp] Array.insertionSort.swapLoop
#check @Array.insertionSort.swapLoop._eq_1
#check @Array.insertionSort.swapLoop._eq_2
|
b30f4fe5d428f41b249944dbdf56baf4d25780ba | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /tests/lean/unzip_error.lean | 25fb95ce239b81d2b90ffd7a726aebb2f4216ad9 | [
"Apache-2.0"
] | permissive | davidmueller13/lean | 65a3ed141b4088cd0a268e4de80eb6778b21a0e9 | c626e2e3c6f3771e07c32e82ee5b9e030de5b050 | refs/heads/master | 1,611,278,313,401 | 1,444,021,177,000 | 1,444,021,177,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 364 | lean | import data.examples.vector
open nat vector prod
variables {A B : Type}
definition unzip : Π {n : nat}, vector (A × B) n → vector A n × vector B n
| unzip nil := (nil, nil)
| unzip ((a, b) :: v) :=
match unzip v with
(va, vb) := (a :: va, b :: vb)
end
example : unzip ((1, 20) :: (2, 30) :: nil) = (... |
f5015aaff2daff6f1085d103fc3ab1253841b108 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /stage0/src/Lean/PrettyPrinter/Delaborator/Builtins.lean | 7d5fcda18b5406021d11495a0224426b96aaf974 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | cipher1024/lean4 | 6e1f98bb58e7a92b28f5364eb38a14c8d0aae393 | 69114d3b50806264ef35b57394391c3e738a9822 | refs/heads/master | 1,642,227,983,603 | 1,642,011,696,000 | 1,642,011,696,000 | 228,607,691 | 0 | 0 | Apache-2.0 | 1,576,584,269,000 | 1,576,584,268,000 | null | UTF-8 | Lean | false | false | 31,987 | 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.PrettyPrinter.Delaborator.SubExpr
import Lean.PrettyPrinter.Delaborator.TopDownAnalyze
import Lean.Pars... |
e1b6c3975fcfb116ab432987c53113bd9985250d | c777c32c8e484e195053731103c5e52af26a25d1 | /counterexamples/linear_order_with_pos_mul_pos_eq_zero.lean | 6e08c5f9f847f451787435f5987042be48c19607 | [
"Apache-2.0"
] | permissive | kbuzzard/mathlib | 2ff9e85dfe2a46f4b291927f983afec17e946eb8 | 58537299e922f9c77df76cb613910914a479c1f7 | refs/heads/master | 1,685,313,702,744 | 1,683,974,212,000 | 1,683,974,212,000 | 128,185,277 | 1 | 0 | null | 1,522,920,600,000 | 1,522,920,600,000 | null | UTF-8 | Lean | false | false | 2,190 | lean | /-
Copyright (c) 2021 Johan Commelin.
All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Damiano Testa, Kevin Buzzard
-/
import algebra.order.monoid.defs
import algebra.order.monoid.with_zero.defs
/-!
An example of a `linear_ordered_comm_monoid_with_zero` ... |
cbb1699ea004d10086a3951e78e605eec5da6a77 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /counterexamples/linear_order_with_pos_mul_pos_eq_zero.lean | 8484b0d9cf9172ffb3611f5dc0daca8a8b2fe9ac | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 2,136 | lean | /-
Copyright (c) 2021 Johan Commelin.
All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Damiano Testa, Kevin Buzzard
-/
import algebra.order.monoid
/-!
An example of a `linear_ordered_comm_monoid_with_zero` in which the product of two positive
elements va... |
9d40f45f80273b5e726a5f77f50cff948b9417d3 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/ring_theory/eisenstein_criterion.lean | 9dcce2f4139fe98a522dccba21746f271deacbd8 | [
"Apache-2.0"
] | permissive | Lix0120/mathlib | 0020745240315ed0e517cbf32e738d8f9811dd80 | e14c37827456fc6707f31b4d1d16f1f3a3205e91 | refs/heads/master | 1,673,102,855,024 | 1,604,151,044,000 | 1,604,151,044,000 | 308,930,245 | 0 | 0 | Apache-2.0 | 1,604,164,710,000 | 1,604,163,547,000 | null | UTF-8 | Lean | false | false | 5,397 | lean | /-
Copyright (c) 2020 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import ring_theory.ideal.operations
import data.polynomial.ring_division
import tactic.apply_fun
import ring_theory.prime
/-!
# Eisenstein's criterion
A proof of a sligh... |
8960748776ab7c0f649ddce21bef6ef2bbb49bbc | 4fa118f6209450d4e8d058790e2967337811b2b5 | /src/sheaves/f_map.lean | 488dfc5fa39d1a5608056993029a97bcd1aa3c34 | [
"Apache-2.0"
] | permissive | leanprover-community/lean-perfectoid-spaces | 16ab697a220ed3669bf76311daa8c466382207f7 | 95a6520ce578b30a80b4c36e36ab2d559a842690 | refs/heads/master | 1,639,557,829,139 | 1,638,797,866,000 | 1,638,797,866,000 | 135,769,296 | 96 | 10 | Apache-2.0 | 1,638,797,866,000 | 1,527,892,754,000 | Lean | UTF-8 | Lean | false | false | 10,099 | lean | import for_mathlib.open_embeddings
import sheaves.sheaf_of_topological_rings
import sheaves.stalk_of_rings
universe variable u
open topological_space
variables {X : Type u} {Y : Type u} {Z : Type u}
variables [topological_space X] [topological_space Y] [topological_space Z]
namespace presheaf_of_rings
variables {F... |
594c219cb039bdeb202e45741287c48a5a11d625 | e39f04f6ff425fe3b3f5e26a8998b817d1dba80f | /category_theory/limits/functor_category.lean | d077e795c172673fc3bfd7aaff0260e509e880dc | [
"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 | 4,788 | lean | -- Copyright (c) 2018 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Scott Morrison
import category_theory.products
import category_theory.limits.preserves
open category_theory category_theory.category
namespace category_theory.limits
universe... |
64110e384ba30dc38ff9d651a1e3d922dc4cab67 | 2d34dfb0a1cc250584282618dc10ea03d3fa858e | /src/for_mathlib/add_monoid_hom.lean | 44bcce7198410d803aceef30b26d0f3fcbfeec1e | [] | 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 | 815 | lean | import algebra.group.hom
import algebra.big_operators
open_locale big_operators
namespace add_monoid_hom
variables {M₁ M₂ : Type*}
section
variables [add_monoid M₁] [add_comm_monoid M₂]
@[simp] lemma sum_apply {ι : Type*} (s : finset ι) (f : ι → (M₁ →+ M₂)) (m : M₁) :
(∑ i in s, f i) m = ∑ i in s, (f i m) :=
beg... |
0705441c73e04dbc341c7758a02438917853dabd | 5883d9218e6f144e20eee6ca1dab8529fa1a97c0 | /src/aeq/id.lean | 1ebcdbdadd3ac37af5cd244f29c2092c25a90d0f | [] | no_license | spl/alpha-conversion-is-easy | 0d035bc570e52a6345d4890e4d0c9e3f9b8126c1 | ed937fe85d8495daffd9412a5524c77b9fcda094 | refs/heads/master | 1,607,649,280,020 | 1,517,380,240,000 | 1,517,380,240,000 | 52,174,747 | 4 | 0 | null | 1,456,052,226,000 | 1,456,001,163,000 | Lean | UTF-8 | Lean | false | false | 1,853 | lean | /-
This file contains declarations related to `aeq` identity or reflexivity.
-/
import .equiv
namespace acie -----------------------------------------------------------------
namespace aeq ------------------------------------------------------------------
variables {V : Type} [decidable_eq V] -- Type of variable n... |
776c32829432509c8de622912bd3a436d6178183 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/struct1.lean | f6cc3037f4e9b21fd7485df6dc19822abaef0959 | [
"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 | 983 | lean | --
structure A (α : Type) :=
(x : α)
structure B (α : Type) :=
(x : α)
structure S : Nat := -- error expected Type
(x : Nat)
structure S extends Nat → Nat := -- error expected structure
(x : Nat)
set_option structureDiamondWarning true in
structure S' extends A Nat, A Bool := -- error field toA already declared
(x ... |
8bc69d36aa0c03cc0f2c217cbe71138cb9540584 | 08bd4ba4ca87dba1f09d2c96a26f5d65da81f4b4 | /src/Lean/Elab/InfoTree/Main.lean | bad0d0a48ffc22c6cc5a5a9802ef3d2f38225802 | [
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"Apache-2.0",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | gebner/lean4 | d51c4922640a52a6f7426536ea669ef18a1d9af5 | 8cd9ce06843c9d42d6d6dc43d3e81e3b49dfc20f | refs/heads/master | 1,685,732,780,391 | 1,672,962,627,000 | 1,673,459,398,000 | 373,307,283 | 0 | 0 | Apache-2.0 | 1,691,316,730,000 | 1,622,669,271,000 | Lean | UTF-8 | Lean | false | false | 15,844 | lean | /-
Copyright (c) 2020 Wojciech Nawrocki. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wojciech Nawrocki, Leonardo de Moura, Sebastian Ullrich
-/
import Lean.Meta.PPGoal
namespace Lean.Elab.ContextInfo
variable [Monad m] [MonadEnv m] [MonadMCtx m] [MonadOptions m] ... |
b6b5ce4e410ab6f0f7330b2c752b81127ff1a530 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/category_theory/limits/yoneda.lean | 65dd54a9e3b4489fb63e383b005e7413ea5afa87 | [
"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 | 5,498 | lean | /-
Copyright (c) 2020 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.limits.functor_category
import tactic.assert_exists
/-!
# Limit properties relating to the (co)yoneda embedding.
We calculate t... |
e06b994e6443a23c0b0285da4ec2228534dbb0a9 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/ring_theory/witt_vector/witt_polynomial.lean | 5d2ba835a6a6d59559841072a8bf7806b977fcce | [
"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 | 10,592 | lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Robert Y. Lewis
-/
import algebra.invertible
import data.mv_polynomial.variables
import data.mv_polynomial.comm_ring
import data.mv_polynomial.expand
import data.zmod.... |
af5382d5d1a811d12d81d13ab724da544716c90c | 6df8d5ae3acf20ad0d7f0247d2cee1957ef96df1 | /ExamPractice/quiz1.lean | 91bc5d613617fefe6ef9fd562ee2b9114869deb2 | [] | no_license | derekjohnsonva/CS2102 | 8ed45daa6658e6121bac0f6691eac6147d08246d | b3f507d4be824a2511838a1054d04fc9aef3304c | refs/heads/master | 1,648,529,162,527 | 1,578,851,859,000 | 1,578,851,859,000 | 233,433,207 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 416 | lean | -- Derek Johnson
def s1 := "Hello, "
def s2 := "Nifty!"
def s3 := s1 ++ s2
theorem t1 : (s1 ++ s2) = s3 := eq.refl s3
theorem t2 : 4^2 = 16 := eq.refl 16
theorem t3 : (s1 ++ s2) = s3 ∧ (5^2 = 25) := and.intro
(eq.refl s3)
(eq.refl 25)
theorem t4 :
∀ (P Q R : Prop), (P ∧ Q) ∧ (Q ∧ R) → (P ∧ R) :=
λ... |
b44ef53d9b436b4d95e3b8bd69e1ac09fb2fb662 | be30445afb85fcb2041b437059d21f9a84dff894 | /move_to_main.hlean | aa2a6d005a7e456e5948e66475cc8466b9fda79a | [
"Apache-2.0"
] | permissive | EgbertRijke/GraphModel | 784efde97299c4f3cb1760369e8a260e02caafd5 | 2a473880764093dd151554a913292ed465e80e62 | refs/heads/master | 1,609,477,731,119 | 1,476,299,056,000 | 1,476,299,056,000 | 58,213,801 | 6 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,026 | hlean | import types
open eq
inductive pathover2 {A B : Type} (C : A → B → Type) :
Π {a a' : A} (p : a=a') {b b' : B} (q : b=b') (x : C a b) (y : C a' b'), Type :=
| idpo2 : Π {a : A} {b : B} (x : C a b), pathover2 C (idpath a) (idpath b) x x
definition tr_eq_of_homotopy {A : Type} {B : A → Type} (x y : A) (C : B x → B ... |
0727642dc573820eb3fb5392873ccc8a91f02880 | 947b78d97130d56365ae2ec264df196ce769371a | /tests/lean/macroscopes.lean | 37ea91c864792a62c771c9492aec8079da25e9df | [
"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 | 1,136 | lean | new_frontend
open Lean
def check (b : Bool) : IO Unit :=
«unless» b $ throw $ IO.userError "check failed"
def test1 : IO Unit := do
let x := `x;
let x := addMacroScope `main x 1;
IO.println $ x;
let v := extractMacroScopes x;
let x := { v with name := `y }.review;
IO.println $ x;
let v := extractMacroScopes x;
let x :... |
8c9159d58439e7f5d4e57a5a2a82923b1683ead7 | aa5a655c05e5359a70646b7154e7cac59f0b4132 | /tests/lean/mvar3.lean | 77033e4d434e3f7b7b3f66261ecafb76e5a4a9d2 | [
"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 | 2,853 | lean | import Lean.MetavarContext
open Lean
def mkLambdaTest (mctx : MetavarContext) (ngen : NameGenerator) (lctx : LocalContext) (xs : Array Expr) (e : Expr)
: Except MetavarContext.MkBinding.Exception (MetavarContext × NameGenerator × Expr) :=
match MetavarContext.mkLambda xs e lctx { mctx := mctx, ngen := ngen } with... |
d619eaab696dad63010ca0eec5347cea7d9026b0 | 29cc89d6158dd3b90acbdbcab4d2c7eb9a7dbf0f | /Exercises week 5/22_homework_sheet.lean | 3d2c22b3762be204a671061e5245afcfe7af2c1d | [] | no_license | KjellZijlemaker/Logical_Verification_VU | ced0ba95316a30e3c94ba8eebd58ea004fa6f53b | 4578b93bf1615466996157bb333c84122b201d99 | refs/heads/master | 1,585,966,086,108 | 1,549,187,704,000 | 1,549,187,704,000 | 155,690,284 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,177 | lean | /- Homework 2.2: Functional Programming — Trees -/
/- Question 1: Huffman's algorithm -/
/- Recall the following definition from the lecture. -/
inductive tree (α : Type)
| leaf : ℕ → α → tree
| inner : ℕ → tree → tree → tree
export tree (leaf inner)
/- To make our lives easy, we will fix a type α of symbols equip... |
13f88bc647f83a337126b9419ae6d85c28f316a4 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/algebra/homology/exact_auto.lean | f92b32fd408632ec89c527c66a05276edcc10fcf | [] | 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 | 5,713 | lean | /-
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebra.homology.image_to_kernel_map
import Mathlib.PostPort
universes v u l
namespace Mat... |
11842e33b48acf54d70f35af8dda59e61f1b04bf | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/qpf/multivariate/constructions/prj_auto.lean | 8bb64c4813618f90404fb24cda7d6c00814a743b | [] | 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 | 1,816 | lean | /-
Copyright (c) 2020 Simon Hudon All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Simon Hudon
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.control.functor.multivariate
import Mathlib.data.qpf.multivariate.basic
import Mathlib.PostPort
un... |
c18e0fdd790908046d2306cfcc95399e9da780ba | 7490bf5d40d31857a58062614642bb5a41c36154 | /dm_box.lean | a634a587ec8d3ac90c090c9582f81afedcd54236 | [] | no_license | reesegrayallen/Lean-Discrete-Mathematics | 9f1d6fe1c814cc9264ce868a67adcf5a82566e22 | 00c875284613ea12e0a729f519738aab8599456b | refs/heads/main | 1,674,181,372,629 | 1,606,801,004,000 | 1,606,801,004,000 | 317,387,970 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 513 | lean | /-
HOMEWORK 3
Reese Allen (rga2uz)
CS2102 - Sullivan
-/
-- defining new polymorphic abstract data type
inductive dm_box (α : Type) : Type
| mk : (α : Type) → dm_box
-- function defintions using lambda expressions, c-style (') and by cases ('')
def unbox {α : Type} : (dm_box α) → α :=
λ (b : dm_box α),
match b... |
845f4afdd8c2f03b49c75dd076f709d5a42a8a9d | 6b02ce66658141f3e0aa3dfa88cd30bbbb24d17b | /src/Lean/Elab/SetOption.lean | 60c0880b2dfe3ad414d7fdae98756673c654fe5f | [
"Apache-2.0"
] | permissive | pbrinkmeier/lean4 | d31991fd64095e64490cb7157bcc6803f9c48af4 | 32fd82efc2eaf1232299e930ec16624b370eac39 | refs/heads/master | 1,681,364,001,662 | 1,618,425,427,000 | 1,618,425,427,000 | 358,314,562 | 0 | 0 | Apache-2.0 | 1,618,504,558,000 | 1,618,501,999,000 | null | UTF-8 | Lean | false | false | 1,338 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Elab.Log
import Lean.Elab.InfoTree
namespace Lean.Elab
variable [Monad m] [MonadOptions m] [MonadExceptOf Exception m] [MonadRef m]
variable [A... |
ad84b28b025c0edc780cfb20df420ff18c3789d4 | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/ring_theory/discrete_valuation_ring.lean | c8433e754c71085c5377d2bc6f623a25e0c12bb2 | [
"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 | 13,139 | 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 ring_theory.principal_ideal_domain
import order.conditionally_complete_lattice
import ring_theory.multiplicity
import ring_theory.valuation.basic
/-!
# Discret... |
92a9c556ebfd8532cb9cfe1918132ebaf73df455 | bb31430994044506fa42fd667e2d556327e18dfe | /src/data/finset/card.lean | 8a6f1f2e0e381e91ff227e813bcac0d1967c5b78 | [
"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 | 24,538 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad
-/
import data.finset.image
import tactic.by_contra
/-!
# Cardinality of a finite set
This defines the cardinality of a `finset` and provides ... |
55ba3bdee59e06e80f74773457e47120e90539d4 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/set/intervals/iso_Ioo.lean | 1ce9692e865e7818d13a7ddf5ed2ccb57e68c221 | [
"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 | 1,693 | lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import order.monotone.odd
import tactic.field_simp
/-!
# Order isomorphism between a linear ordered field and `(-1, 1)`
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.... |
46a8949b35cde5affb6a7892e0f958505f62266a | cf39355caa609c0f33405126beee2739aa3cb77e | /library/init/meta/name.lean | 46d5d6a052866ba36934b3138398b205fc65f117 | [
"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 | 4,104 | 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.ordering.basic init.coe init.data.to_string
/-- Reflect a C++ name object. The VM replaces it with the C++ implementation. -/
indu... |
cf313373a9872fe3334a3620ab9b4e75c5ead83f | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/protected.lean | 66aa2130683e70b691f721902fa72108c4fe8ec0 | [
"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 | 1,022 | lean |
namespace Foo
protected def x := 10
end Foo
open Foo
#check x -- error unknown identifier `x`
#check Foo.x
namespace Bla.Foo
protected def y := 20
def z := 30
end Bla.Foo
open Bla
#check Foo.y
open Bla.Foo
#check y -- error unknown identifier `y`
#check z
protected def x := 0 -- Error
protected partial def F... |
480cb0cfd39bcc5db323099e687c2eb48db2529f | 4727251e0cd73359b15b664c3170e5d754078599 | /src/model_theory/direct_limit.lean | b228a91cfa896ee54d3d341268f0f4d198178fb7 | [
"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 | 14,744 | lean | /-
Copyright (c) 2022 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import data.fintype.order
import algebra.direct_limit
import model_theory.quotients
import model_theory.finitely_generated
/-!
# Direct Limits of First-Order Structu... |
a61f73c1437c8d5b32e593983cbaab6add4bf354 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/category_theory/products/bifunctor.lean | 805e65ffc4b02e7faab316bd8e6cbb17bcaa7166 | [
"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 | 1,819 | 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.products.basic
open category_theory
namespace category_theory.bifunctor
universes v₁ v₂ v₃ u₁ u₂ u₃
variables {C : Type u₁} ... |
f097ed3e78336ef622262611686f478f48b0ec82 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/order/filter/small_sets.lean | 96269fff4611391672d1b47368052c063cac9b6a | [
"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 | 5,257 | lean | /-
Copyright (c) 2022 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Floris van Doorn, Yury Kudryashov
-/
import order.filter.lift
import order.filter.at_top_bot
/-!
# The filter of small sets
This file defines the filter of small sets... |
3d1df3ef69d78c2db35db786aa3a4e0fd5f9edc8 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/analysis/complex/polynomial.lean | 7a7bd7cbe7eaa1a04a253e397000bc2003495490 | [
"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 | 5,622 | lean | /-
Copyright (c) 2019 Chris Hughes All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import analysis.special_functions.pow
import field_theory.algebraic_closure
import topology.algebra.polynomial
/-!
# The fundamental theorem of algebra
This file proves ... |
218c930ab8b3348fb0c34de1926a293b0f88e55b | 4727251e0cd73359b15b664c3170e5d754078599 | /archive/examples/prop_encodable.lean | 64da2837b4f0bad5499490f2f3bb90a74516be79 | [
"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 | 2,982 | lean | /-
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
-/
import data.W.basic
/-!
# W types
The file `data/W.lean` shows that if `α` is an an encodable fintype and for every `a : α`,
`β a` is encodable, then `W β` is encoda... |
4023e20deba7d981dd1c1d61bc49ad778b710bd9 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/intNegSucc.lean | d9e9089290b572d762f5fb10c9af7cd1903e0878 | [
"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 | 570 | lean | def Int64Min : Int := -1*(Int.ofNat ((UInt64.size / 2)))
#eval Int.negSucc 9223372036854775807
#reduce Int.negSucc 9223372036854775807
#print "---"
#eval - Int.negSucc 9223372036854775807
#reduce - Int.negSucc 9223372036854775807
#print "---"
#eval Int.negSucc 9223372036854775807 == 0
#reduce Int.negSucc 9223372... |
886d1a7e190098ea0f07330934ccbddbd9b4d211 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/algebra/big_operators/pi.lean | 7ad8db101e32df8e28f6e07aaf03a6361ffbb8ad | [
"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 | 3,658 | 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.ring.pi
import algebra.big_operators.basic
import data.fintype.basic
import algebra.group.prod
/-!
# Big operators for Pi Types
This file co... |
d847ea1902ad7dfd4b716564805810bdce7328a1 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/algebra/module/ordered_auto.lean | 6b623ac69e89f7036513e423949e764af51d7262 | [] | 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 | 8,901 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebra.module.pi
import Mathlib.algebra.ordered_pi
import Mathlib.algebra.module.prod
im... |
35b773d1b6a15596cb53acfd489c0d07b63422c3 | 9cba98daa30c0804090f963f9024147a50292fa0 | /old/src/classical_geometry_test.lean | aee05ab64abc460025f1daaa13ce3259141b8135 | [] | no_license | kevinsullivan/phys | dcb192f7b3033797541b980f0b4a7e75d84cea1a | ebc2df3779d3605ff7a9b47eeda25c2a551e011f | refs/heads/master | 1,637,490,575,500 | 1,629,899,064,000 | 1,629,899,064,000 | 168,012,884 | 0 | 3 | null | 1,629,644,436,000 | 1,548,699,832,000 | Lean | UTF-8 | Lean | false | false | 107 | lean | import .classical_geometry
noncomputable def aGeom1DSpace : classicalGeometry := classicalGeometry.mk 0 1
|
364e80023a08e810b0e604e3a84b35ffe3338697 | 6094e25ea0b7699e642463b48e51b2ead6ddc23f | /tests/lean/unifier_bug.lean | af6f1136d45464c3e191ae5842e211a32ea3ba06 | [
"Apache-2.0"
] | permissive | gbaz/lean | a7835c4e3006fbbb079e8f8ffe18aacc45adebfb | a501c308be3acaa50a2c0610ce2e0d71becf8032 | refs/heads/master | 1,611,198,791,433 | 1,451,339,111,000 | 1,451,339,111,000 | 48,713,797 | 0 | 0 | null | 1,451,338,939,000 | 1,451,338,939,000 | null | UTF-8 | Lean | false | false | 200 | lean | import logic
theorem test {A B : Type} {a : A} {b : B} (H : a == b) :
eq.rec_on (heq.type_eq H) a = b
:=
-- Remark the error message should not occur in the token theorem
heq.rec_on H rfl
|
3edfe055151f41ed906a9d0bb75cc30c242605ab | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/topology/continuous_function/algebra.lean | 1fdde95a636b9637b3011350f3ac31de229bd547 | [
"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 | 33,360 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Nicolò Cavalleri
-/
import topology.algebra.module.basic
import topology.continuous_function.ordered
import topology.algebra.uniform_group
import topology.uniform_space... |
92ec93dde275324a165910c86ba9b9fcdab4631c | 49bd2218ae088932d847f9030c8dbff1c5607bb7 | /src/analysis/normed_space/basic.lean | 50f9c4f81c6ec4e69be23253d7a838ca7f15e2fc | [
"Apache-2.0"
] | permissive | FredericLeRoux/mathlib | e8f696421dd3e4edc8c7edb3369421c8463d7bac | 3645bf8fb426757e0a20af110d1fdded281d286e | refs/heads/master | 1,607,062,870,732 | 1,578,513,186,000 | 1,578,513,186,000 | 231,653,181 | 0 | 0 | Apache-2.0 | 1,578,080,327,000 | 1,578,080,326,000 | null | UTF-8 | Lean | false | false | 34,264 | lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Normed spaces.
Authors: Patrick Massot, Johannes Hölzl
-/
import algebra.pi_instances
import linear_algebra.basic
import topology.instances.nnreal topology.instances.complex
import topology.a... |
741a51d972ff7ddff7a8cd1fc93cf897d105addf | 26ac254ecb57ffcb886ff709cf018390161a9225 | /src/algebra/ordered_group.lean | 48dd292eef73cd08a49d238a0722bcd2d2a3056a | [
"Apache-2.0"
] | permissive | eric-wieser/mathlib | 42842584f584359bbe1fc8b88b3ff937c8acd72d | d0df6b81cd0920ad569158c06a3fd5abb9e63301 | refs/heads/master | 1,669,546,404,255 | 1,595,254,668,000 | 1,595,254,668,000 | 281,173,504 | 0 | 0 | Apache-2.0 | 1,595,263,582,000 | 1,595,263,581,000 | null | UTF-8 | Lean | false | false | 65,167 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro, Johannes Hölzl
-/
import algebra.group.with_one
import algebra.group.type_tags
import order.bounded_lattice
set_option old_structure_c... |
e19322cc4f7f3b691a9d9c239ae84166e9eab8f3 | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/data/quot.lean | dd78d5304721a1e54564d507fe0f7dc0a1983719 | [
"Apache-2.0"
] | permissive | dupuisf/mathlib | 62de4ec6544bf3b79086afd27b6529acfaf2c1bb | 8582b06b0a5d06c33ee07d0bdf7c646cae22cf36 | refs/heads/master | 1,669,494,854,016 | 1,595,692,409,000 | 1,595,692,409,000 | 272,046,630 | 0 | 0 | Apache-2.0 | 1,592,066,143,000 | 1,592,066,142,000 | null | UTF-8 | Lean | false | false | 16,449 | 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 logic.relator
/-!
# Quotients -- extends the core library
-/
variables {α : Sort*} {β : Sort*}
namespace setoid
lemma ext {α : Sort*} :
∀{s t : setoid α}... |
9903f405866ec36e15d902bf4811dcc18e9c04eb | b70031c8e2c5337b91d7e70f1e0c5f528f7b0e77 | /src/analysis/normed_space/basic.lean | 657bfe6632fc6d32bdb41e93b732c7a03ab22291 | [
"Apache-2.0"
] | permissive | molodiuc/mathlib | cae2ba3ef1601c1f42ca0b625c79b061b63fef5b | 98ebe5a6739fbe254f9ee9d401882d4388f91035 | refs/heads/master | 1,674,237,127,059 | 1,606,353,533,000 | 1,606,353,533,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 54,189 | lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl
-/
import topology.instances.nnreal
import topology.instances.complex
import topology.algebra.module
import topology.metric_space.antilipschitz
/-!
# No... |
f111f7dae6ed71d9641f16b8d79e5c4dde836ac6 | 7b02c598aa57070b4cf4fbfe2416d0479220187f | /homotopy/3x3.hlean | 646421b034b2fab9f5d3e894744d7f03e35195f9 | [
"Apache-2.0"
] | permissive | jdchristensen/Spectral | 50d4f0ddaea1484d215ef74be951da6549de221d | 6ded2b94d7ae07c4098d96a68f80a9cd3d433eb8 | refs/heads/master | 1,611,555,010,649 | 1,496,724,191,000 | 1,496,724,191,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,018 | hlean | -- WIP
import ..move_to_lib
open function eq
namespace pushout
section
-- structure span2 : Type :=
-- {A₀₀ A₀₂ A₀₄ A₂₀ A₂₂ A₂₄ A₄₀ A₄₂ A₄₄ : Type}
-- {f₀₁ : A₀₂ → A₀₀} {f₂₁ : A₂₂ → A₂₀} {f₄₁ : A₄₂ → A₄₀}
-- {f₀₃ : A₀₂ → A₀₄} {f₂₃ : A₂₂ → A₂₄} {f₄₃ : A₄₂ → A₄₄}
-- {f₁₀ : A₂₀ → A₀₀} {f₁₂ : A₂₂ → A... |
1e5281e1543a3a5635ceb820b263cdbdafaeabff | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/category_theory/limits/shapes/zero.lean | 931afaf6827a87d315f2475ab4a63fe58e58cc99 | [
"Apache-2.0"
] | permissive | agjftucker/mathlib | d634cd0d5256b6325e3c55bb7fb2403548371707 | 87fe50de17b00af533f72a102d0adefe4a2285e8 | refs/heads/master | 1,625,378,131,941 | 1,599,166,526,000 | 1,599,166,526,000 | 160,748,509 | 0 | 0 | Apache-2.0 | 1,544,141,789,000 | 1,544,141,789,000 | null | UTF-8 | Lean | false | false | 15,031 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.limits.shapes.terminal
import category_theory.limits.shapes.binary_products
import category_theory.limits.shapes.products
import category_theor... |
88b630cc199edb09c101994185701844225b0e7c | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/setoid/basic.lean | a52a98afd17ac6be01039ec9d397016fbb119670 | [
"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 | 16,337 | lean | /-
Copyright (c) 2019 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston, Bryan Gin-ge Chen
-/
import order.galois_connection
/-!
# Equivalence relations
This file defines the complete lattice of equivalence relations on a type, resul... |
05999bf236e687e8e71a7bfc556174e5c0b8d8b1 | d757fb8bb0d538df3510904d3c09a0da191d06b9 | /sf_weekdays.lean | b8b31b1be398396dd7d63cb558fa03740ef2e21d | [] | no_license | happy-bracket/lean_playground | 188f64c2a431dec5617c75e33c7a75e475b9c23d | 137b76966001091c445f6f472d27bbe5a8cf5d49 | refs/heads/master | 1,600,889,668,807 | 1,575,375,570,000 | 1,575,375,570,000 | 225,569,694 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 400 | lean | inductive day : Type
| monday
| tuesday
| wednesday
| thursday
| friday
| saturday
| sunday
def next_weekday : day -> day
| day.monday := day.tuesday
| day.tuesday := day.wednesday
| day.wednesday := day.thursday
| day.thursday := day.friday
| day.friday := day.saturday
| day.saturday := day.sunday
| day.sunday := day... |
dd4b6099c8fd5280bd48c51d42dcdb66f213d147 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/topology/algebra/order/compact.lean | c7e46e18e122e81b85903b4be221930c8701fd2e | [
"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 | 19,243 | lean | /-
Copyright (c) 2021 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Yury Kudryashov
-/
import topology.algebra.order.intermediate_value
import topology.local_extr
/-!
# Compactness of a closed interval
> THIS FILE IS SYNCHRONIZED WITH... |
ddcbdeac7e1b5d60a0f17dd53eb487805f5c3cfa | 222111140d2023e142b07e9cd5119ac2829b36f5 | /src/row_equivalence_fields.lean | fc4e8bd7cf310d163ed001c4b1a58383bc16ea05 | [] | no_license | jjcrawford/lean-gaussian-elimination | 740dfdf2de89dc99c088c53e5221d9dfad3c0b92 | c473d33c07fa6f141d17d9dc42ad07956c33dd03 | refs/heads/master | 1,585,793,867,436 | 1,540,443,865,000 | 1,540,443,865,000 | 153,901,939 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,430 | lean | import ring_theory.matrix
import row_equivalence
import .finset_sum
universes u
variables {m n : ℕ}
variable {α : Type u}
variable [division_ring α]
variable [decidable_eq α]
def elementary.inv : (elementary α m) → (elementary α m) :=
begin
intros e,
cases e with i₁ s hs i₁ i₂ i₁ s i₂ h_ne,
... |
c5f740012c5195ee1f6956a25b5299d454b88aa3 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/algebra/lie/skew_adjoint.lean | 16e91f11ac0ca83d2f38125a8fb9758865ec137e | [
"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 | 7,181 | 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.lie.matrix
import linear_algebra.bilinear_form
/-!
# Lie algebras of skew-adjoint endomorphisms of a bilinear form
When a module carries a bilinear form, t... |
2b6d03b03a8ddf8adac02e639f735dadb38cc2bd | 4727251e0cd73359b15b664c3170e5d754078599 | /src/algebra/direct_sum/basic.lean | 7ffa3730b81b880188294d790849002fc3409fa4 | [
"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 | 12,061 | 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 data.dfinsupp.basic
import group_theory.submonoid.operations
import group_theory.subgroup.basic
/-!
# Direct sum
This file defines the direct sum of abelian groups, ind... |
a1e03cb2067a8d8664beee652ab9bdf2670dfd7c | e0f9ba56b7fedc16ef8697f6caeef5898b435143 | /src/data/fintype/basic.lean | a5ae272ef743e52e53ce0e56f62ffa36334e0c75 | [
"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 | 40,502 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
Finite types.
-/
import data.finset
import data.array.lemmas
universes u v
variables {α : Type*} {β : Type*} {γ : Type*}
/-- `fintype α` means that `α` is finite, i.e.... |
817df3dd2ab6215e27d71e056833230bd7988642 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/limits/limits_auto.lean | 2c830b3b1e93ab34ffbb7488c3bddddd05224de6 | [] | 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 | 92,745 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Mario Carneiro, Scott Morrison, Floris van Doorn
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.category_theory.adjunction.basic
import Math... |
792363af4478f89612b35c196adfa938fbd8d309 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/data/bitvec/basic.lean | 354ec842d1a930fdbac31837ccc39c94d50bcccb | [
"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 | 3,652 | 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 data.bitvec.core
import data.fin.basic
import tactic.norm_num
import tactic.monotonicity
namespace bitvec
instance (n : ℕ) : preorder (bitvec n) :=
preorder.lift b... |
2fafb771744de8dfab48ad789df0fddd2d1c0bac | 86f6f4f8d827a196a32bfc646234b73328aeb306 | /examples/logic/unnamed_36.lean | 0debe9d82e9f5771e407e9217e7f575ab0928442 | [] | no_license | jamescheuk91/mathematics_in_lean | 09f1f87d2b0dce53464ff0cbe592c568ff59cf5e | 4452499264e2975bca2f42565c0925506ba5dda3 | refs/heads/master | 1,679,716,410,967 | 1,613,957,947,000 | 1,613,957,947,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 137 | lean | import data.real.basic
-- BEGIN
#check ∀ x y ε : ℝ,
0 < ε → ε ≤ 1 → abs x < ε → abs y < ε → abs (x * y) < ε
-- END |
b3d3c77c95accba7fe4f5c7624295dcd39db8069 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/order/filter/cofinite.lean | 5d48989dd924b2c83eac4b26f63c373a985a4c70 | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,069 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jeremy Avigad, Yury Kudryashov
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.order.filter.at_top_bot
import Mathlib.PostPort
universes ... |
435e1d3182a42d6ee670d2184df8dedc3d657edf | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/run/opaque_hint_bug.lean | 3c60c133e89e4c594ac53a80d4a3cae8ff7d2d26 | [
"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 | 236 | lean | inductive List (T : Type) : Type
| nil {} : List
| cons : T → List → List
section
variable {T : Type}
definition concat (s t : List T) : List T
:= List.rec t (fun x l u, List.cons x u) s
attribute concat [reducible]
end
|
2fd7b28441059586f955f44c2b64d11cafde9aca | b794ca1df49bc5a3bd3fd5552eed3bc4f63b8b93 | /src/mywork/practice_1.lean | 42045c8f59f0e44062770a378143e9f5e07ad6db | [] | no_license | akraisinger/cs2120f21 | 8235ac98375e04ffcec504cff5cab7833ee69e54 | 4ef83d7151bb6a284028092aa4f1d509c0eb8237 | refs/heads/main | 1,691,714,771,612 | 1,632,889,465,000 | 1,632,889,465,000 | 399,946,508 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,204 | lean | /-
EQUALITY (due before class WED! (9/15/2021))
-/
/- #1
Suppose that x, y, z, and w are arbitrary objects of some type,
T; and suppose further that we know (have proofs of the facts)
that x = y, y = z, and w = z. Give a very, very short English
proof of the conjecture that z = w. You can use not only the
axioms... |
0876925fb3bce8aba28a07d905b8280389405e6c | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/data/mv_polynomial/comm_ring.lean | 1133761292e2b80a1304ae20ff18e68610fcf0b8 | [
"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 | 5,008 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
-/
import data.mv_polynomial.variables
/-!
# Multivariate polynomials over a ring
Many results about polynomials hold when the coeffic... |
e38562cca0f1bff2728e5f8d34a081a76e4c59a3 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/algebraic_geometry/limits.lean | 21a2b67b861308832ea10473751697b1fc746a7a | [
"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 | 4,637 | lean | /-
Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import algebraic_geometry.pullbacks
import algebraic_geometry.AffineScheme
import category_theory.limits.constructions.finite_products_of_binary_products
import category_th... |
56dad3a3ead3ced901ed20044ba580cecac6d5db | 6fca17f8d5025f89be1b2d9d15c9e0c4b4900cbf | /src/game/world7/level7.lean | fda5f1338c260c49a6600ce5ed5ddc02b1ed5759 | [
"Apache-2.0"
] | permissive | arolihas/natural_number_game | 4f0c93feefec93b8824b2b96adff8b702b8b43ce | 8e4f7b4b42888a3b77429f90cce16292bd288138 | refs/heads/master | 1,621,872,426,808 | 1,586,270,467,000 | 1,586,270,467,000 | 253,648,466 | 0 | 0 | null | 1,586,219,694,000 | 1,586,219,694,000 | null | UTF-8 | Lean | false | false | 768 | lean | import game.world7.level6 -- hide
/-
# Advanced proposition world.
## Level 7: `or_symm`
Proving that $(P\lor Q)\implies(Q\lor P)$ involves an element of danger.
`intro h,` is the obvious start. But now,
even though the goal is an `∨` statement, both `left` and `right` put
you in a situation with an impossible goal... |
f40d45bda9c68383d342013915ba173faa14c8ea | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/data/set/disjointed.lean | c03ae4e53216f89caeecf810dacc5643ff3428cc | [
"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 | 3,426 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Disjointed sets
-/
import data.set.lattice data.nat.basic tactic.wlog
open set classical lattice
local attribute [instance] prop_decidable
universes u v w x
variables ... |
5bbfcd0b0edd02260d062190300aeed1e2d1c13d | 33340b3a23ca62ef3c8a7f6a2d4e14c07c6d3354 | /lia/remove_neg.lean | c89530dbb3cc55bad38d5512d5e2e575d62551b3 | [] | no_license | lclem/cooper | 79554e72ced343c64fed24b2d892d24bf9447dfe | 812afc6b158821f2e7dac9c91d3b6123c7a19faf | refs/heads/master | 1,607,554,257,488 | 1,578,694,133,000 | 1,578,694,133,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,579 | lean | import .wf
open list
def remove_neg : atom → atom
| (atom.le i ks) := atom.le (1 - i) (map_neg ks)
| (atom.dvd d i ks) := atom.ndvd d i ks
| (atom.ndvd d i ks) := atom.dvd d i ks
meta def neg_prsv_normal_aux :=
`[unfold remove_neg at hb,
rewrite (eq_of_mem_singleton hb), trivial]
lemma wf_remove_neg : ∀ {a... |
977542362009c204fd17de3a069387e009b9bb2b | 618003631150032a5676f229d13a079ac875ff77 | /src/algebra/ring.lean | 4a7a27b85ba786c5d9a0f920d86d8cca359938a0 | [
"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 | 37,105 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Amelia Livingston
-/
import algebra.group.hom
import algebra.group.units
import tactic.norm_cast
import tactic.split_ifs
/-!
# Prope... |
e653ea57fa8ffc89bcdd99a07b453ed666034834 | 6dbfa3fb323bb2e2c3917c61d46053dd0de739cd | /src/lemmas2.lean | 0a2b97786a6e09857a798c20398d76242638681a | [] | no_license | amichaelsen/Lean-Chinese-Remainder-Theorem | b054fc32e0f5383eb83ec7155932c50d92de1038 | 9efb4b97da30e5aedb6af3c95d5132ac300f2902 | refs/heads/master | 1,680,787,277,127 | 1,619,155,524,000 | 1,619,155,524,000 | 275,883,966 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,747 | lean | import data.nat.basic
import data.nat.modeq
import data.nat.gcd
import data.zmod.basic
import tactic
import algebra.euclidean_domain
import data.int.basic
import data.equiv.ring
noncomputable theory
open nat nat.modeq zmod euclidean_domain
namespace lemmas2
/- LEMMAS FOR CHINESE REMAINDER THEOREM WITH 2 CONGRUENCE R... |
ac1631a2baa48dfc06006b6ae70852bd544b812a | a4673261e60b025e2c8c825dfa4ab9108246c32e | /stage0/src/Lean/Meta/DiscrTree.lean | 4c9e6b7aced4d5e3799a72b769e69ea8555a4397 | [
"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 | 14,746 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Meta.Basic
import Lean.Meta.FunInfo
import Lean.Meta.InferType
namespace Lean.Meta.DiscrTree
/-
(Imperfect) discrimination trees.
We use a... |
f112a3ec95bde0d47df97b5a708c2ae7aed028f5 | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /stage0/src/Lean/Server/FileWorker/Utils.lean | 8b8b33f2def7c541c8a5a6e29ee57fa60ca74306 | [
"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 | 1,557 | lean | /-
Copyright (c) 2020 Wojciech Nawrocki. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wojciech Nawrocki, Marc Huisinga
-/
import Lean.Server.Utils
import Lean.Server.Snapshots
import Lean.Server.AsyncList
namespace Lean.Server.FileWorker
open Snapshots
open IO
pri... |
11afc48a1a01b61c551fcd7f332f85f8a0cfd7a9 | a7eef317ddec01b9fc6cfbb876fe7ac00f205ac7 | /src/linear_algebra/dimension.lean | 7596f469e8fa96c39476204db73bb8dc008231f2 | [
"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 | 18,076 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro, Johannes Hölzl, Sander Dahmen
-/
import linear_algebra.basis
import set_theory.ordinal
/-!
# Dimension of modules and vector spaces
## Main definitions
* The dimension... |
e658978c956aec04033d20e70f95cc185b8a4f38 | 7cdf3413c097e5d36492d12cdd07030eb991d394 | /src/game/world5/level4.lean | 5bde5af8d86916ca431a87e98830bee44a3f7416 | [] | 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 | 1,809 | lean | /- Tactic : apply
If you have a function `h : P → Q` and your goal is `⊢ Q`
then `apply h` changes the goal to `⊢ P`. The logic is
simple: if you are trying to create a term of type `Q`,
but `h` is a function which turns terms of type `P` into
terms of type `Q`, then it will suffice to construct a
term of type `P`. A m... |
4133c5fedc2644a287cbdcc81960f8162542a4ba | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/783.lean | 3d19b694944b64299d8176988ee0014c0cc89c64 | [
"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 | 125 | lean | structure MyStruct where
{α : Type u}
{β : Type v}
a : α
b : β
#check { a := 10, b := true : MyStruct }
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.