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32fc677dd6d931e1cfe91869bfc1640c1c4414b3 | 6b2a480f27775cba4f3ae191b1c1387a29de586e | /group_rep_2/orthoganality_of_character/orthoganality_2.lean | 22988922286ae51504bf99dc03ae6eec8161f33f | [] | no_license | Or7ando/group_representation | a681de2e19d1930a1e1be573d6735a2f0b8356cb | 9b576984f17764ebf26c8caa2a542d248f1b50d2 | refs/heads/master | 1,662,413,107,324 | 1,590,302,389,000 | 1,590,302,389,000 | 258,130,829 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 3,232 | lean | import orthoganality_of_character.orthogonality
noncomputable theory
set_option pp.generalized_field_notation false
open_locale big_operators
universes u v w w'
open car_pol
open Schur₂ morphism.from_irreductible equiv_morphism shur₁_comm_ring stability
open Reynold
open matrix linear_map character
namespace deco... |
fa7fbbf970b43d9fc2b52ccc3339a85edc61251d | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/topology/category/Top/open_nhds.lean | aa2289508e1156e7f05d2336b91cd16ff6112290 | [
"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 | 3,463 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import topology.category.Top.opens
import category_theory.filtered
open category_theory
open topological_space
open opposite
universe u
variables {X Y : Top.{u}} (... |
287e9a504f168f5f399da843916998fc262f7afa | 206422fb9edabf63def0ed2aa3f489150fb09ccb | /src/ring_theory/subring.lean | 92d230a4eb71a18c7866e4a43daba2c813070672 | [
"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 | 31,032 | lean | /-
Copyright (c) 2020 Ashvni Narayanan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors : Ashvni Narayanan
-/
import deprecated.subring
import group_theory.subgroup
import ring_theory.subsemiring
/-!
# Subrings
Let `R` be a ring. This file defines the "bundled" subrin... |
0cba0141b8cdb81028b8b6d771ac504005539723 | 952248371e69ccae722eb20bfe6815d8641554a8 | /src/control.lean | 1c0f24a2e5778e03fb7bef3829560ed19359936e | [] | no_license | robertylewis/lean_polya | 5fd079031bf7114449d58d68ccd8c3bed9bcbc97 | 1da14d60a55ad6cd8af8017b1b64990fccb66ab7 | refs/heads/master | 1,647,212,226,179 | 1,558,108,354,000 | 1,558,108,354,000 | 89,933,264 | 1 | 2 | null | 1,560,964,118,000 | 1,493,650,551,000 | Lean | UTF-8 | Lean | false | false | 4,289 | lean | import .blackboard .proof_reconstruction .additive .multiplicative data.hash_map .normalizer
open polya tactic
meta structure module_op (α : Type) :=
(a : α)
(op : α → polya_state α)
meta def module_op.update {α} : module_op α → polya_state (module_op α)
| ⟨a, op⟩ := do a' ← op a, return ⟨a', op⟩
meta ... |
6f63a72897fd01bfd4fd01997039ff494b0b4b16 | 6b10c15e653d49d146378acda9f3692e9b5b1950 | /examples/basic_skills/fourtytwo.lean | 3f9fdb2eb3c79b1ef5dcae6398e7985dad0f549b | [] | no_license | gebner/mathematics_in_lean | 3cf7f18767208ea6c3307ec3a67c7ac266d8514d | 6d1462bba46d66a9b948fc1aef2714fd265cde0b | refs/heads/master | 1,655,301,945,565 | 1,588,697,505,000 | 1,588,697,505,000 | 261,523,603 | 0 | 0 | null | 1,588,695,611,000 | 1,588,695,610,000 | null | UTF-8 | Lean | false | false | 138 | lean | import data.real.basic
example (a b c : ℝ) : (a * b) * c = b * (a * c) :=
begin
rw mul_comm a b,
rw mul_assoc b a c
end |
b174f0c865763fd9cecfaa760bcd86933f9a673e | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/1279.lean | fe3930e4f5b6b0b7dcc2745ad00401b4ac0de34c | [
"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 | 560 | lean | structure Category : Type 2 :=
(Obj : Type)
(Hom : Obj → Obj → Type)
(compose : Π ⦃A B C : Obj⦄, Hom A B → Hom B C → Hom A C)
open Category
structure Functor (source target : Category) : Type :=
(onObjects : Obj source → Obj target)
(onMorphisms : Π ⦃A B : Obj source⦄, Hom source A B → Hom target (onO... |
2d59124c7525477245f505df8926f39be2ac86be | dd24e6c3b8dc14dc504f8a906fc04c51e4312e6b | /src/mywork/homework/review 9/13.lean | d8e0d7ed58cb0b9fcffd9bee8c297ccf0d10b3a6 | [] | no_license | njeyasingh/CS-2120 | dd781a90dd0645b74e61cee1813483fb7cb4a111 | b3356f665a246f295b3f1e6d61901bfca331810d | refs/heads/main | 1,693,294,711,274 | 1,635,188,659,000 | 1,635,188,659,000 | 399,945,420 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 758 | lean | /-
How do I write a conditional:
- axioms( P Q : Prop) - arbitrary propositions shorthands for expressive identifiers
Elimination rule:
Rules for and and US implies
4. halve in le
-/
axioms (P Q : Prop)
def if_P_is_true_so_is_Q: Prop := P
axiom p : P
-- assume P is true
-- assume we have a proof of P (p)... |
560291598ad5481c1c220bef5e113d15b26c7385 | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/mod1.lean | 69e69fc5e72fcaba97566d7d22aa65b5e60eb69b | [
"Apache-2.0"
] | permissive | codyroux/lean0.1 | 1ce92751d664aacff0529e139083304a7bbc8a71 | 0dc6fb974aa85ed6f305a2f4b10a53a44ee5f0ef | refs/heads/master | 1,610,830,535,062 | 1,402,150,480,000 | 1,402,150,480,000 | 19,588,851 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 200 | lean | import specialfn
import specialfn
(*
local env = environment() -- create new environment
parse_lean_cmds([[
import specialfn
import specialfn
check sin
]], env)
*)
check sin |
2017f64fedbdb95fa2bb06db636935316b7aaa6e | 85485c410781936e7dd6aba0ba77b8a82f76c1d6 | /src/cluster_algebra.lean | 30f4a6a68d477b260c984d3690f321a51712a0a7 | [] | no_license | yuma-mizuno/lean-cluster-algebra | 5b33657b3cf27c24cab292d4ac62d6e1e5e715b9 | 4a4fb128566305eda2b82aea068157cb43afdf18 | refs/heads/master | 1,689,542,026,900 | 1,630,963,668,000 | 1,630,964,456,000 | 392,828,775 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,345 | lean | import category_theory.category.Quiv
import category_theory.over
import algebra.category.CommRing
import mutation
/-!
# Cluster algebras
This file defines the upper cluster algebra and the cluter algebras associated with a seed.
Let `N` be a ℤ-module equipped with a skew-symmetric form. A finite multiset
on `N` is c... |
e0d7ad51318c6ed337982ab250f7ec42e048aa3e | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /test/inhabit.lean | 34df4f216717220d100c25b5137cf2dee8e97f7f | [
"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 | 388 | lean | import tactic.interactive
lemma a {α} [nonempty α] : ∃ a : α, a = a :=
by inhabit α; use default; refl
noncomputable def b {α} [nonempty α] : α :=
by inhabit α; apply default
lemma c {α} [nonempty α] : ∀ n : ℕ, ∃ b : α, n = n :=
by inhabit α; intro; use default; refl
noncomputable def d {α} [nonempty α] : ∀ n : ℕ, ... |
08168c5ece897c108aa4175798b24d80e6cab313 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/415.lean | d3110a1870ff89bd82e8ca208dcc2397f4dfaa8f | [
"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 | 758 | lean | structure Point where
x : Nat
y : Nat
def f (x : Nat) : Point :=
let y := x + 1
{ x, y }
theorem ex1 : f x = { x, y := x + 1 } :=
rfl
def g (p : Point) : Nat :=
p.x + p.y
def Set (α : Type u) : Type u :=
α → Prop
def Set.empty : Set α :=
fun a => False
def Set.insert (s : Set α) (a : α) : Set α :=... |
c13d4afe26f1a3c9abdffa57d4b7a09ef24ad4ae | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/int/interval.lean | 4b0c1c7b8464192ca791b744132491d74cb9cc42 | [
"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 | 7,452 | 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 algebra.char_zero.lemmas
import order.locally_finite
import data.finset.locally_finite
/-!
# Finite intervals of integers
> THIS FILE IS SYNCHRONIZED WITH MATHLI... |
96dd486a30528bfa50f7b5bac41c8885535c9e4d | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/group_theory/perm/subgroup.lean | 781aaeb300935a1cd4fda2cc148e3f2abb2b06d5 | [] | 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 | 1,508 | lean | /-
Copyright (c) 2020 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.group_theory.perm.basic
import Mathlib.data.fintype.basic
import Mathlib.group_theory.subgroup
im... |
cfcb40f5624edd2a5195b1563039d208a9297f64 | 271e26e338b0c14544a889c31c30b39c989f2e0f | /stage0/src/Init/Control/State.lean | 29f04092b5cf05b1237920d555da89ad30eaf5da | [
"Apache-2.0"
] | permissive | dgorokho/lean4 | 805f99b0b60c545b64ac34ab8237a8504f89d7d4 | e949a052bad59b1c7b54a82d24d516a656487d8a | refs/heads/master | 1,607,061,363,851 | 1,578,006,086,000 | 1,578,006,086,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,318 | 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
The State monad transformer.
-/
prelude
import Init.Control.Alternative
import Init.Control.Lift
import Init.Control.Id
import Init.Control... |
d417b0fa72f9b7c688ec7d2f8a33d3f57694b9d8 | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/data/multiset/fold.lean | 2d85014ff9aca3ee3a246739b5fd82b543613dcf | [
"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 | 3,797 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import data.multiset.erase_dup
/-!
# The fold operation for a commutative associative operation over a multiset.
-/
namespace multiset
variables {α β : Type*}
/-! ... |
f78d73a2e47305ebab4d0eacb42accd39a584b81 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/struct_value.lean | 2e93bfc51efb1bcccf89016e1bb82758359026cd | [
"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 | 711 | lean | #check { prod . fst := 10, snd := 20 }
#check ({ fst := 10, snd := 20 } : nat × nat)
definition p : nat × nat :=
{ snd := 20, fst := 10 }
#print p
meta def attr : user_attribute :=
{ name := `foo, descr := "hello world" }
#print attr
definition p2 :=
{ p with fst := 20 }
#print p2
structure point :=
(x : nat) (... |
52fc6f48814d5738d23262cc8039827e7f60dcfe | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/category_theory/grothendieck.lean | e472d592b97fdd35e02313b54fa7c8b725dcabbf | [
"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 | 5,460 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.category.Cat
import category_theory.elements
/-!
# The Grothendieck construction
Given a functor `F : C ⥤ Cat`, the objects of `grothendieck ... |
a56852017366f7b7aab2d887168977bbb0e10a52 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/algebra/order/group.lean | 081f861d78bae041d7f7c9a38d17b3c2807414f0 | [
"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 | 49,358 | 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.abs
import algebra.order.sub
/-!
# Ordered groups
This file develops the basics of ordered groups.
... |
6ef730c78a6d938c3fff0c9c231a60c71ba0e717 | ea11767c9c6a467c4b7710ec6f371c95cfc023fd | /src/monoidal_categories/examples/monoid_as_category.lean | 1048f4f992e32705dabaae558282bff2f8f22994 | [] | no_license | RitaAhmadi/lean-monoidal-categories | 68a23f513e902038e44681336b87f659bbc281e0 | 81f43e1e0d623a96695aa8938951d7422d6d7ba6 | refs/heads/master | 1,651,458,686,519 | 1,529,824,613,000 | 1,529,824,613,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,982 | 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 ..monoidal_category
open categories
open categories.monoidal_category
namespace categories.examples
universe u
local attribute [ematch]... |
15e600f55ef5fe58578b08aaaa89e6d92777631b | d5bef83c55d40cb88f9a01b755c882a93348a847 | /tests/lean/run/simp_univ_poly.lean | 8f6c018bfc126c339c4c65836be55e0ab267684f | [
"Apache-2.0"
] | permissive | urkud/lean | 587d78216e1f0c7f651566e9e92cf8ade285d58d | 3526539070ea6268df5dd373deeb3ac8b9621952 | refs/heads/master | 1,660,171,634,921 | 1,657,873,466,000 | 1,657,873,466,000 | 249,789,456 | 0 | 0 | Apache-2.0 | 1,585,075,263,000 | 1,585,075,263,000 | null | UTF-8 | Lean | false | false | 793 | lean | namespace test
universes u v
def equinumerous (α : Type u) (β : Type v) :=
∃ f : α → β, function.bijective f
local infix ` ≈ `:50 := equinumerous
@[refl] lemma refl {α} : α ≈ α := sorry
@[trans] lemma trans {α β γ} :
α ≈ β → β ≈ γ → α ≈ γ := sorry
@[congr] lemma equinumerous.congr_eqn {α α' β β'} :
α ≈ α' →... |
65c718401f62629059d6dde01dcac5c24f352b5f | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/structure_result_universe.lean | daeed723d1d4328b406561a98cf58f40eb720db3 | [
"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 | 297 | lean | structure foo1 (A : Type) : Type :=
(elt : A)
structure {u} foo2 (A : Type u) : Type (u+1) :=
(val : A)
structure {u} foo3 (A : Type u) : Type (max u 1) :=
(val : A)
universe variable u
structure foo4 (A : Type u) : Type (max u 1) :=
(val : A)
#check foo1
#check foo2
#check foo3
#check foo4
|
977c4e44395537216ef0bf29eaa7357215eea299 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Parser/Command.lean | 4ff7107243f2912d33ac1eb1b9541b3662f9c5f3 | [
"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 | 15,630 | 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, Sebastian Ullrich
-/
import Lean.Parser.Term
import Lean.Parser.Do
namespace Lean
namespace Parser
/-- Syntax quotation for terms. -/
@[builtin_term_parser]... |
cdb52aacc4e7ce9b1a794011f3f66c01899253d5 | a338c3e75cecad4fb8d091bfe505f7399febfd2b | /src/measure_theory/prod.lean | 9a535ab4ccec053ffe607dbeb68721836a4eea95 | [
"Apache-2.0"
] | permissive | bacaimano/mathlib | 88eb7911a9054874fba2a2b74ccd0627c90188af | f2edc5a3529d95699b43514d6feb7eb11608723f | refs/heads/master | 1,686,410,075,833 | 1,625,497,070,000 | 1,625,497,070,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 46,959 | lean | /-
Copyright (c) 2020 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import measure_theory.giry_monad
import measure_theory.set_integral
/-!
# The product measure
In this file we define and prove properties about the binary produ... |
99f2bf2c4a3a7db0feb52f282ac916df8c9617fb | 8930e38ac0fae2e5e55c28d0577a8e44e2639a6d | /data/set/lattice.lean | c98feea561e7d36fab79f09637ae4856ec016cb0 | [
"Apache-2.0"
] | permissive | SG4316/mathlib | 3d64035d02a97f8556ad9ff249a81a0a51a3321a | a7846022507b531a8ab53b8af8a91953fceafd3a | refs/heads/master | 1,584,869,960,527 | 1,530,718,645,000 | 1,530,724,110,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 21,332 | 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, Johannes Hölzl, Mario Carneiro
-- QUESTION: can make the first argument in ∀ x ∈ a, ... implicit?
-/
import logic.basic data.set.basic data.equiv.basic... |
156596a62496c8c562703da25281b821bec35725 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/analysis/normed_space/enorm.lean | a6c4b9d4bf089802a2ec663d0d8539724d6741c9 | [
"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 | 7,695 | lean | /-
Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import analysis.normed_space.basic
/-!
# Extended norm
In this file we define a structure `enorm 𝕜 V` representing an extended norm (i.e., a norm that can
... |
4b414a1c9a63936a859293d481da832911e64955 | d7189ea2ef694124821b033e533f18905b5e87ef | /galois/list/take_drop_lemmas.lean | c9a4e73373ad68253d9e3c653fd83ae240c115a3 | [
"Apache-2.0"
] | permissive | digama0/lean-protocol-support | eaa7e6f8b8e0d5bbfff1f7f52bfb79a3b11b0f59 | cabfa3abedbdd6fdca6e2da6fbbf91a13ed48dda | refs/heads/master | 1,625,421,450,627 | 1,506,035,462,000 | 1,506,035,462,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,413 | lean | /- This file contains lemmas for take and drop -/
import galois.nat.simplify_eq
import galois.nat.simplify_le
import data.list.basic
universe variable u
namespace list
variable {α : Type u}
/- take theorems -/
@[simp]
theorem take_succ_cons (n : ℕ) (x : α) (xs : list α) : take (nat.succ n) (x :: xs) = x :: take n x... |
dfb89f979bb947e7fcf3253ecb7a7e3ec08443e3 | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/measure_theory/constructions/pi.lean | edef9021f3bcca5ca802aa113abf58b6b7a6bd64 | [
"Apache-2.0"
] | permissive | ayush1801/mathlib | 78949b9f789f488148142221606bf15c02b960d2 | ce164e28f262acbb3de6281b3b03660a9f744e3c | refs/heads/master | 1,692,886,907,941 | 1,635,270,866,000 | 1,635,270,866,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 33,402 | lean | /-
Copyright (c) 2020 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import measure_theory.constructions.prod
/-!
# Product measures
In this file we define and prove properties about finite products of measures
(and at some point... |
42e465cefc3ffd2f93dd4e2210808241fa7052c4 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/filtered.lean | f5a59fff5254159c7c2c9b52a24feb7d00d3c0f5 | [
"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 | 28,410 | lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Scott Morrison
-/
import category_theory.fin_category
import category_theory.limits.cones
import category_theory.adjunction.basic
import category_theory.category.preorder
imp... |
ffa37f9935faf8d46178a0e6b85806da0649049f | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /src/Lean/Server/AsyncList.lean | 22539ec77dd45007883b975c0814020aa2ae4517 | [
"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 | 4,946 | lean | /-
Copyright (c) 2020 Wojciech Nawrocki. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wojciech Nawrocki
-/
import Init.System.IO
namespace IO
universes u v
/-- An async IO list is like a lazy list but instead of being *unevaluated* `Thunk`s,
lazy tails are `Task`... |
c7d3452630539b1a6d69d0c238177613462aead5 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/topology/uniform_space/basic.lean | dc7e96694c5021c2f89dbbce2d875e5af8fa9be2 | [
"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 | 70,169 | 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 order.filter.lift
import topology.separation
/-!
# Uniform spaces
Uniform spaces are a generalization of metric spaces and top... |
afbe7c0e531f2210c6f42273e1ef79d939b3cc43 | 246309748072bf9f8da313401699689ebbecd94d | /src/ring_theory/algebra.lean | 11308d3c3711143488dfdadb9c1f9333ae7aa94f | [
"Apache-2.0"
] | permissive | YJMD/mathlib | b703a641e5f32a996f7842f7c0043bab2b462ee2 | 7310eab9fa8c1b1229dca42682f1fa6bfb7dbbf9 | refs/heads/master | 1,670,714,479,314 | 1,599,035,445,000 | 1,599,035,445,000 | 292,279,930 | 0 | 0 | null | 1,599,050,561,000 | 1,599,050,560,000 | null | UTF-8 | Lean | false | false | 54,534 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Yury Kudryashov
-/
import data.matrix.basic
import linear_algebra.tensor_product
import ring_theory.subsemiring
import deprecated.subring
/-!
# Algebra over Commutative Semiring... |
98339995bc3f1c368e3fd4981a5c3387b856e2d2 | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/rat/cast.lean | fccd0ee1530e8bc3b9ef2d6b2df5b2bfd3ab17dc | [
"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 | 11,860 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import data.rat.order
import data.int.char_zero
/-!
# Casts for Rational Numbers
## Summary
We define the canonical injection from ℚ into an arbitr... |
69c523b90f5f744504c5c22f375aa3dbf2b47d63 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/algebra/order/module.lean | 191c1b490e5e4ca7b1a4e5d48627134bc98204c9 | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 8,041 | lean | /-
Copyright (c) 2020 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis, Yaël Dillies
-/
import algebra.order.smul
/-!
# Ordered module
In this file we provide lemmas about `ordered_smul` that hold once a module structure is present.
##... |
ff04dc32d2d992840e959d69c96978a551e5464c | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/renaming.lean | 4534517ed6f7e4a60641ae587501bad226124043 | [
"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 | 853 | lean | -- Renaming for intrinsically typed lambda calculus
inductive Ty
| base
| arr (a b : Ty)
def Cxt := List Ty
inductive Var : (g : Cxt) → (a : Ty) → Type
| vz {g a} : Var (a :: g) a
| vs {g a b} : Var g a → Var (b :: g) a
inductive Term : Cxt → Ty → Type
| var {g a} : Var g a → Term g a
| app {g a b} ... |
d2272890ed92906b10b62b97a98c82761033ea78 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/fun_like/embedding.lean | fa5f28da6027aa68bda3467f50c7ce9508858c3a | [
"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 | 5,729 | lean | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import data.fun_like.basic
/-!
# Typeclass for a type `F` with an injective map to `A ↪ B`
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require ... |
03648f77b128c75b8cd28baccc89b794b64de73d | f083c4ed5d443659f3ed9b43b1ca5bb037ddeb58 | /order/conditionally_complete_lattice.lean | 3ba5549deb8f8130fdd697efc8a62079f931e6c4 | [
"Apache-2.0"
] | permissive | semorrison/mathlib | 1be6f11086e0d24180fec4b9696d3ec58b439d10 | 20b4143976dad48e664c4847b75a85237dca0a89 | refs/heads/master | 1,583,799,212,170 | 1,535,634,130,000 | 1,535,730,505,000 | 129,076,205 | 0 | 0 | Apache-2.0 | 1,551,697,998,000 | 1,523,442,265,000 | Lean | UTF-8 | Lean | false | false | 27,962 | lean | /-
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
Adapted from the corresponding theory for complete lattices.
Theory of conditionally complete lattices.
A conditionally complete lattice is a lattice in which ev... |
1e8de8a3cf528fe953d9d628bfe4cb12c7f29e87 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/algebra/lie/non_unital_non_assoc_algebra.lean | 8ccd3e24c341764495b8827d5f2bb5ce28b7ffbf | [
"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 | 2,830 | lean | /-
Copyright (c) 2021 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import algebra.hom.non_unital_alg
import algebra.lie.basic
/-!
# Lie algebras as non-unital, non-associative algebras
The definition of Lie algebras uses the `has_bracket... |
dbfc9d4f95525f335942eb83b35235e42d8fdf8a | 0845ae2ca02071debcfd4ac24be871236c01784f | /library/init/control/option.lean | f2456ef807529bf83235cb2ae443c50167f8a18d | [
"Apache-2.0"
] | permissive | GaloisInc/lean4 | 74c267eb0e900bfaa23df8de86039483ecbd60b7 | 228ddd5fdcd98dd4e9c009f425284e86917938aa | refs/heads/master | 1,643,131,356,301 | 1,562,715,572,000 | 1,562,715,572,000 | 192,390,898 | 0 | 0 | null | 1,560,792,750,000 | 1,560,792,749,000 | null | UTF-8 | Lean | false | false | 2,215 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Sebastian Ullrich
-/
prelude
import init.control.alternative init.control.lift init.control.except
universes u v
def OptionT (m : Type u → Type v) (α : Type... |
29580371dddafff89b1ae3b3b5377e34eb55dda2 | 0845ae2ca02071debcfd4ac24be871236c01784f | /library/init/lean/smap.lean | 7699f16d1efcb8cddbd2efea59d7da2676e94fca | [
"Apache-2.0"
] | permissive | GaloisInc/lean4 | 74c267eb0e900bfaa23df8de86039483ecbd60b7 | 228ddd5fdcd98dd4e9c009f425284e86917938aa | refs/heads/master | 1,643,131,356,301 | 1,562,715,572,000 | 1,562,715,572,000 | 192,390,898 | 0 | 0 | null | 1,560,792,750,000 | 1,560,792,749,000 | null | UTF-8 | Lean | false | false | 2,934 | 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
-/
prelude
import init.data.hashmap init.data.rbmap
universes u v w w'
namespace Lean
/- Staged map for implementing the Environment. The idea is to store
... |
9dfb94ea84522f3082d3e71035099614e2d68964 | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /stage0/src/Lean/Meta/Match/MatcherInfo.lean | 87f78e6092bc61e8f15a2760ef8e063462ebf0e3 | [
"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 | 5,937 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Meta.Basic
namespace Lean.Meta
namespace Match
structure DiscrInfo where
/-- `some h` if the discriminant is annotated with `h:` -/
hName?... |
673341a0699eaf80a66aa24ea290eb5d8568df7b | 2385ce0e3b60d8dbea33dd439902a2070cca7a24 | /tests/lean/apply_elim.lean | f431d3af8fd079bab5715426e4658c2a3db5a22d | [
"Apache-2.0"
] | permissive | TehMillhouse/lean | 68d6fdd2fb11a6c65bc28dec308d70f04dad38b4 | 6bbf2fbd8912617e5a973575bab8c383c9c268a1 | refs/heads/master | 1,620,830,893,339 | 1,515,592,479,000 | 1,515,592,997,000 | 116,964,828 | 0 | 0 | null | 1,515,592,734,000 | 1,515,592,734,000 | null | UTF-8 | Lean | false | false | 252 | lean | open nat
def nat.ind_on {p : nat → Prop} (n : nat) (h₁ : p 0) (h₂ : ∀ n, p n → p (succ n)) : p n :=
nat.rec_on n h₁ h₂
example : ∀ a b : nat, a + b = b + a :=
begin
intro a,
apply nat.ind_on a,
trace_state,
repeat {sorry}
end
|
7ea15b73a5d5cafe7b76469e1f1b54c532dcd353 | a7eef317ddec01b9fc6cfbb876fe7ac00f205ac7 | /src/ring_theory/algebraic.lean | 871bc6d4073a18618c975bbcd7dcf80b390b8f40 | [
"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 | 4,774 | lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import linear_algebra.finite_dimensional
import ring_theory.integral_closure
/-!
# Algebraic elements and algebraic extensions
An element of an R-algebra is algebr... |
93430228d4a2ccc76d6ef215d1e518094a94183d | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/set_theory/zfc.lean | b927947809a74ef50cc9275251ff33e151845425 | [
"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 | 30,809 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
A model of ZFC in Lean.
-/
import data.set.basic
universes u v
/-- The type of `n`-ary functions `α → α → ... → α`. -/
def arity (α : Type u) : nat → Type u
| 0 :... |
045be6bd51a7c1bee8d461acd7403c660f3bcfd1 | dc253be9829b840f15d96d986e0c13520b085033 | /cohomology/projective_space.hlean | 1d7b020381913b1052b4ac1948b38a3e454f0ca0 | [
"Apache-2.0"
] | permissive | cmu-phil/Spectral | 4ce68e5c1ef2a812ffda5260e9f09f41b85ae0ea | 3b078f5f1de251637decf04bd3fc8aa01930a6b3 | refs/heads/master | 1,685,119,195,535 | 1,684,169,772,000 | 1,684,169,772,000 | 46,450,197 | 42 | 13 | null | 1,505,516,767,000 | 1,447,883,921,000 | Lean | UTF-8 | Lean | false | false | 5,731 | hlean | /- A computation of the cohomology groups of K(ℤ,2) using the Serre spectral sequence
Author: Floris van Doorn-/
import .serre
open eq spectrum EM EM.ops int pointed cohomology left_module algebra group fiber is_equiv equiv
prod is_trunc function exact_couple
namespace temp
definition uH0_circle : uH^0[circ... |
34cc6b6decd1e010aa69a51bdacd7c5251959208 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/induction_tac1.lean | 9420d96c1e0a6b6fa570c03f7af7644f82b4e167 | [
"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 | 691 | lean | open tactic
example (p q : Prop) : p ∨ q → q ∨ p :=
by do
H ← intro `H,
induction_core semireducible H `or.rec [`Hp, `Hq],
trace_state,
constructor_idx 2, assumption,
constructor_idx 1, assumption
print "-----"
open nat
example (n : ℕ) : n = 0 ∨ n = succ (pred n) :=
by do
n ← get_local `n,
induction_co... |
4a1925bd6fda710776385cce0882d12281969de2 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/category_theory/opposites.lean | b24883da7675c5a84cebbb78f903686ac8882f32 | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 14,713 | 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.types
import category_theory.equivalence
universes v₁ v₂ u₁ u₂ -- morphism levels before object levels. See note [category_the... |
c5ca82e88a2c8506615b9955d20a8eddf401f0a8 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/compiler/foreign/Main/S.lean | 5bd1d4348298a3bdedcbdb5d69cfe56cb65aa091 | [
"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 | 595 | lean | opaque SPointed : NonemptyType
def S : Type := SPointed.type
instance : Nonempty S := SPointed.property
@[extern "lean_mk_S"] opaque mkS (x y : UInt32) (s : @& String) : S
@[extern "lean_S_add_x_y"] opaque S.addXY (s : @& S) : UInt32
@[extern "lean_S_string"] opaque S.string (s : @& S) : String
-- The following 3 exte... |
ffdeea53261e4e5111912062fd45b4101b8de1f9 | ea5678cc400c34ff95b661fa26d15024e27ea8cd | /algebraic_closure_experiment.lean | f9639eb64bfe7f89f5c29416d98baa310e79a7f1 | [] | no_license | ChrisHughes24/leanstuff | dca0b5349c3ed893e8792ffbd98cbcadaff20411 | 9efa85f72efaccd1d540385952a6acc18fce8687 | refs/heads/master | 1,654,883,241,759 | 1,652,873,885,000 | 1,652,873,885,000 | 134,599,537 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,560 | lean | import data.mv_polynomial ring_theory.ideal_operations ring_theory.adjoin_root
import ring_theory.integral_closure
namespace adjoin_root
variables {α : Type*} [comm_ring α] {f : polynomial α}
open polynomial ideal
lemma coe_injective_of_degree_pos_of_monic (hf : 0 < degree f) (hm : monic f) :
function.injective (co... |
f6309a95535b348d255abdf5ef92494cce36d776 | e967488e2008f07b0aa7b6b18d4398d02c7460e2 | /src/defs.lean | 452c41e6b5041bdc92482bd37f835a38ca3793d4 | [] | no_license | thyrgle/real-number-game | 5c53eefaa815051f3d70ca5782e41d2adb76fd6e | a420eecef62209b729c910c2170d1dd27b74bc9f | refs/heads/master | 1,606,405,407,612 | 1,574,956,743,000 | 1,574,956,743,000 | 229,126,103 | 0 | 0 | null | 1,576,784,273,000 | 1,576,784,272,000 | null | UTF-8 | Lean | false | false | 1,800 | lean | import data.real.basic
import data.set.intervals
import tactic.norm_num
-- nonempty is a class but let's have it working on set ℝ
namespace real_number_game
-- hide (need to choose this or P)
class nonemptyT (S : set ℝ) : Type :=
(x : ℝ)
(thm : x ∈ S)
-- hide (need to choose this or T)
class nonemptyP (S : set ℝ) :... |
8153f76156dabe6ad4057d48fce27392550c1b37 | e0f9ba56b7fedc16ef8697f6caeef5898b435143 | /src/geometry/manifold/real_instances.lean | 7e82b16143e40b1ae8aa64e85b57fcdd9636f49e | [
"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 | 14,167 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import geometry.manifold.smooth_manifold_with_corners
import linear_algebra.finite_dimensional
/-!
# Constructing examples of manifolds over ℝ
We introduce th... |
f9fe63b0db5713ccecba78e400c0b1bcd1b9fbd0 | 6dc0c8ce7a76229dd81e73ed4474f15f88a9e294 | /stage0/src/Lean/Elab/Command.lean | fb7158241cd29b605407c6d0b70b173616a60eb0 | [
"Apache-2.0"
] | permissive | williamdemeo/lean4 | 72161c58fe65c3ad955d6a3050bb7d37c04c0d54 | 6d00fcf1d6d873e195f9220c668ef9c58e9c4a35 | refs/heads/master | 1,678,305,356,877 | 1,614,708,995,000 | 1,614,708,995,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 28,526 | 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.Parser.Command
import Lean.ResolveName
import Lean.Meta.Reduce
import Lean.Elab.Log
import Lean.Elab.Term
import Lean.Elab.Binders
import Lean.E... |
40427f9db187212185b01f228d027211e1ca4c45 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/order/filter/archimedean.lean | a9d9291068ed0f43d9fe0940ee4c0a20f98935b7 | [
"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 | 5,477 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yury Kudryashov
-/
import order.filter.at_top_bot
import algebra.archimedean
/-!
# `at_top` filter and archimedean (semi)rings/fields
In this file we prove that for a... |
b6192ee9cfe14884d49b8557f2cd4bdfdffc2b03 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/category_theory/bicategory/coherence_tactic.lean | f999bdc5e4b95f745f8fd7ea6c9e923c8e5ec818 | [
"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 | 10,036 | lean | /-
Copyright (c) 2022 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno
-/
import category_theory.bicategory.coherence
/-!
# A `coherence` tactic for bicategories, and `⊗≫` (composition up to associators)
We provide a `coherence` tactic,
which p... |
658d568e66c25935de55b6372fb28233ecdf6f68 | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/simp11.lean | fef2b0e9b659fefdf59acf18134d5aae3d11ff36 | [
"Apache-2.0"
] | permissive | codyroux/lean0.1 | 1ce92751d664aacff0529e139083304a7bbc8a71 | 0dc6fb974aa85ed6f305a2f4b10a53a44ee5f0ef | refs/heads/master | 1,610,830,535,062 | 1,402,150,480,000 | 1,402,150,480,000 | 19,588,851 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 580 | lean | variables a b c d e f : Nat
rewrite_set simple
add_rewrite Nat::add_assoc Nat::add_comm Nat::add_left_comm Nat::distributer Nat::distributel : simple
(*
local opts = options({"simplifier", "max_steps"}, 100)
local t = parse_lean("f + (c + f + d) + (e * (a + c) + (d + a))")
local t2, pr = simplify(t, "simple", op... |
9011fbf23a16ba062fed494b3e845215d015e8e6 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/finset/functor.lean | 32dd58644474c6e4a7b7a5d7a70289a5c97c2f96 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 6,213 | lean | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Scott Morrison
-/
import data.finset.lattice
import data.finset.n_ary
import data.multiset.functor
/-!
# Functoriality of `finset`
> THIS FILE IS SYNCHRONIZED WITH MATHLI... |
ed651d4e93e792e1ea9fe3f5c1a131212d7d2a78 | d29d82a0af640c937e499f6be79fc552eae0aa13 | /src/ring_theory/polynomial/cyclotomic.lean | cac2791ff8acfb005e922ccb2f375ad4abf49fbf | [
"Apache-2.0"
] | permissive | AbdulMajeedkhurasani/mathlib | 835f8a5c5cf3075b250b3737172043ab4fa1edf6 | 79bc7323b164aebd000524ebafd198eb0e17f956 | refs/heads/master | 1,688,003,895,660 | 1,627,788,521,000 | 1,627,788,521,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 30,782 | lean | /-
Copyright (c) 2020 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca
-/
import field_theory.splitting_field
import ring_theory.roots_of_unity
import algebra.polynomial.big_operators
import number_theory.arithmetic_function
import data.... |
d7a0ac3e45d953b0ba4c9d08a647d31b3dbb2bb3 | 30b012bb72d640ec30c8fdd4c45fdfa67beb012c | /linear_algebra/basis.lean | 5df6b723e5bb11a878688a0bd38cf69a01a41e5d | [
"Apache-2.0"
] | permissive | kckennylau/mathlib | 21fb810b701b10d6606d9002a4004f7672262e83 | 47b3477e20ffb5a06588dd3abb01fe0fe3205646 | refs/heads/master | 1,634,976,409,281 | 1,542,042,832,000 | 1,542,319,733,000 | 109,560,458 | 0 | 0 | Apache-2.0 | 1,542,369,208,000 | 1,509,867,494,000 | Lean | UTF-8 | Lean | false | false | 23,641 | 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
Linear independence and basis sets in a module or vector space.
This file is inspired by Isabelle/HOL's linear algebra, and hence indirectly by HOL Lig... |
57af627402200474465c24b41c681e30003434d0 | 4f643cce24b2d005aeeb5004c2316a8d6cc7f3b1 | /omin/oqm.lean | a6ef20eb9a8d40580a00e980fe4b841deec3471f | [] | no_license | rwbarton/lean-omin | da209ed061d64db65a8f7f71f198064986f30eb9 | fd733c6d95ef6f4743aae97de5e15df79877c00e | refs/heads/master | 1,674,408,673,325 | 1,607,343,535,000 | 1,607,343,535,000 | 285,150,399 | 9 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 350 | lean | import algebra.module
import o_minimal.o_minimal
import o_minimal.algebra
open o_minimal
set_option old_structure_cmd true
class OQM (R : Type*) extends DUNLO R, ordered_add_comm_group R :=
[qmod : vector_space ℚ R]
attribute [instance] OQM.qmod
class o_minimal_add {R : Type*} [OQM R] (S : struc R) extends o_minim... |
f81efe5de5c7d5559f8bd95c7f5c0678b4e4e0a2 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/combinatorics/simple_graph/subgraph.lean | 4895851c4e9fdd5d6c6489c321c542b590a34a16 | [
"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 | 33,466 | 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 ... |
473ac5d17fe79baed0cb29f4e686911188c9b59f | f57749ca63d6416f807b770f67559503fdb21001 | /hott/types/sigma.hlean | e871109bd896ca2839c6950887b1f7753ca0d804 | [
"Apache-2.0"
] | permissive | aliassaf/lean | bd54e85bed07b1ff6f01396551867b2677cbc6ac | f9b069b6a50756588b309b3d716c447004203152 | refs/heads/master | 1,610,982,152,948 | 1,438,916,029,000 | 1,438,916,029,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 15,487 | hlean | /-
Copyright (c) 2014-15 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Floris van Doorn
Partially ported from Coq HoTT
Theorems about sigma-types (dependent sums)
-/
import types.prod
open eq sigma sigma.ops equiv is_equiv function
namespace sigma... |
d7c9ff03e395dea0e659cce47b38242bce34c77a | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/group_ring_action/subobjects.lean | 6857d2e8969a0354e53561d3d538aedd28e2f131 | [
"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 | 1,049 | lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import algebra.group_ring_action.basic
import group_theory.subgroup.basic
/-!
# Instances of `mul_semiring_action` for subobjects
These are defined in this file as `semir... |
8b151ae665685a709a9cc2c0fd0c395c56320fee | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/linear_algebra/matrix/trace.lean | 9b642f3f2c175ad809f800e5297d7469798d5e9d | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 4,471 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
-/
import data.matrix.basic
/-!
# Trace of a matrix
This file defines the trace of a matrix, the map sending a matrix to the ... |
c6876ce22165df0908db6f85521ca3fdf92a80c0 | 822db2da46120ba6835fb6b1567bd86d074d7b80 | /lean3/wp.lean | b9ad2dac8e87c0fe2b9d19610766a2a3be1b6745 | [] | no_license | atomb/prover-comparison-wp | 38151051c672a58aafa618a66cc277865da3a770 | 04e2795638914aaabe62d04e7a608a03c87aeec5 | refs/heads/master | 1,623,228,155,066 | 1,618,696,673,000 | 1,618,696,673,000 | 132,378,282 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,322 | lean | import init.logic
namespace expr
inductive Var : Type
| vn : nat -> Var
inductive Value : Type
| const : nat -> Value
inductive Store : Type
| empty : Store
| extend : Var -> Value -> Store -> Store
def Expr := Store -> Value
end expr
namespace assertion
open expr
open expr.Store
def Assertion := Store... |
e441a14b7779812f0fcb9f69924b487a20bd92f3 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/combinatorics/simple_graph/basic.lean | 6c1d56bed8893a4c0782b99b86c6aa12ae2e7e8e | [
"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 | 37,210 | lean | /-
Copyright (c) 2020 Aaron Anderson, Jalex Stark, Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson, Jalex Stark, Kyle Miller, Alena Gusakov, Hunter Monroe
-/
import data.rel
import data.set.finite
import data.sym.sym2
/-!
# Simple graphs
Th... |
c870c44d539ccad12ce186b1bfa7fe484330dac9 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/measure_theory/lebesgue_measure.lean | 376ee04e614ddac786239c946b3db444d3f508f7 | [
"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 | 22,444 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yury Kudryashov
-/
import measure_theory.pi
/-!
# Lebesgue measure on the real line and on `ℝⁿ`
-/
noncomputable theory
open classical set filter
open ennreal (of_rea... |
eb23ac73fb7e6cd4305a5ed43a54829a5d992072 | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/qpf/multivariate/constructions/quot.lean | ba03fee89a9b0ed60b115adcfeeaed4a2a9a06dc | [
"Apache-2.0"
] | permissive | kodyvajjha/mathlib | 9bead00e90f68269a313f45f5561766cfd8d5cad | b98af5dd79e13a38d84438b850a2e8858ec21284 | refs/heads/master | 1,624,350,366,310 | 1,615,563,062,000 | 1,615,563,062,000 | 162,666,963 | 0 | 0 | Apache-2.0 | 1,545,367,651,000 | 1,545,367,651,000 | null | UTF-8 | Lean | false | false | 2,293 | lean | /-
Copyright (c) 2018 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad, Simon Hudon
-/
import data.qpf.multivariate.basic
/-!
# The quotient of QPF is itself a QPF
The quotients are here defined using a surjective function and
its right inv... |
a70492a296979bcaa69fdf7113b352b173c15c84 | 86f6f4f8d827a196a32bfc646234b73328aeb306 | /examples/logic/unnamed_761.lean | 4238722f4be4840fbe48de8471119bb229936ee3 | [] | 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 | 837 | lean | import data.real.basic
def fn_ub (f : ℝ → ℝ) (a : ℝ) : Prop := ∀ x, f x ≤ a
def fn_lb (f : ℝ → ℝ) (a : ℝ) : Prop := ∀ x, a ≤ f x
def fn_has_ub (f : ℝ → ℝ) := ∃ a, fn_ub f a
def fn_has_lb (f : ℝ → ℝ) := ∃ a, fn_lb f a
variables {f g : ℝ → ℝ}
theorem fn_ub_add {f g : ℝ → ℝ} {a b : ℝ}
(hfa : fn_ub f a) (hgb : fn_u... |
2e387052dfefe652e35940782dbf72e87781f2ab | 7565ffb53cc64430691ce89265da0f944ee43051 | /hott/algebra/homotopy_group.hlean | e5abcf3e3a8df17bf181e4404beec88b44f18ab6 | [
"Apache-2.0"
] | permissive | EgbertRijke/lean2 | cacddba3d150f8b38688e044960a208bf851f90e | 519dcee739fbca5a4ab77d66db7652097b4604cd | refs/heads/master | 1,606,936,954,854 | 1,498,836,083,000 | 1,498,910,882,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 12,137 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
homotopy groups of a pointed space
-/
import .trunc_group types.trunc .group_theory types.nat.hott
open nat eq pointed trunc is_trunc algebra group function equiv... |
3eaa2d6ebb88da0edae45f07520f5b651e828fdc | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/arrow.lean | e3ad0c1e6e28b4ca9989d17b9f5a402c3818c8c4 | [] | 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 | 7,856 | 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.category_theory.comma
import Mathlib.PostPort
universes v u l u₁ u₂ v₁ v₂
namespace Mathli... |
52f1132f94e10305fb0f1957917caaa686d946b1 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/set_theory/fincard.lean | 1f1197978aaa66ad4aca55499bce00b3871e717e | [
"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 | 1,303 | 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 set_theory.cardinal
/-!
# Finite Cardinality Functions
## Main Definitions
* `nat.card α` is the cardinality of `α` as a natural number.
If `α` is infinit... |
4a01ad0a2bf088f9ba48d472f842381a0142c61e | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/760.lean | c3dab686c1f53443945fa1e1c02b4d5a7037ba84 | [
"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 | 71 | lean | inductive MultiTrue : Prop where
| k1 : MultiTrue
| k2 : MultiTrue
|
9a6aefe4ce6eb35b8e28be9f48573be0c8fb22c3 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/tactic/nth_rewrite/default.lean | 5b9ccae8cc3ac5fb500c3fb187fcceb3b3a6888d | [
"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 | 5,116 | lean | /-
Copyright (c) 2018 Keeley Hoek. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Keeley Hoek, Scott Morrison
-/
import tactic.nth_rewrite.congr
/-!
# Advanced rewriting tactics
This file provides three interactive tactics
that give the user more con... |
b99345827c716d5553975bdf1612689a9251c729 | 097294e9b80f0d9893ac160b9c7219aa135b51b9 | /instructor/higher_order_funcs/higher_order_examples.lean | ce87eb31107d92cdd6d154af5410698b3b8eb9aa | [] | no_license | AbigailCastro17/CS2102-Discrete-Math | cf296251be9418ce90206f5e66bde9163e21abf9 | d741e4d2d6a9b2e0c8380e51706218b8f608cee4 | refs/heads/main | 1,682,891,087,358 | 1,621,401,341,000 | 1,621,401,341,000 | 368,749,959 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,768 | lean |
import .higher_order
/-
Iterated function application
-/
#eval apply_n nat.succ 2 5
#eval (apply_n (λ n : ℕ, n^2) 2) 5
def square_2 := apply_n (λ n : ℕ, n^2) 2
#eval square_2 5
/-
Map function over list
-/
#eval map_list nat.succ [1,2,3,4,5]
#eval map_list (λ (n : ℕ), n^2) [1,2,3,4,5]
#eval map_list string.length... |
2bdc0beee0b6f633c494b026982201e4162d8a38 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/limits/shapes/kernel_pair.lean | 14eb7de4806dcb94f5546295b6655c4526278956 | [] | 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 | 6,987 | 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.limits.shapes.equalizers
import Mathlib.category_theory.limits.shapes.pullbacks... |
2f5af5eaba22bdbe90487f2629453ba9ef9ebffe | 618003631150032a5676f229d13a079ac875ff77 | /test/mk_iff_of_inductive.lean | b0a3e8f589a21fef7c30f56b20c92c64a0a6a9f3 | [
"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 | 737 | lean | import tactic.mk_iff_of_inductive_prop
import data.list
import data.list.perm
import data.multiset
mk_iff_of_inductive_prop list.chain test.chain_iff
mk_iff_of_inductive_prop false test.false_iff
mk_iff_of_inductive_prop true test.true_iff
mk_iff_of_inductive_prop nonempty test.non_empty_iff
mk_iff_of_indu... |
2394596582733995ef0964bd1b56b29374312599 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/algebra/order/smul.lean | f7f874104681fcdf494f9382a8b2fe34bd0a6648 | [
"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 | 8,382 | 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 group_theory.group_action.group
import algebra.smul_with_zero
/-!
# Ordered scalar product
In this file we define
* `ordered_smul R M` : an ordered addit... |
3d80c3a80b4450153e1d16d8dbabcc96c496169c | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/finset/intervals_auto.lean | a9684aaed1f58b24cb667e0b15972f3f3b1bc521 | [] | 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 | 6,686 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.finset.basic
import Mathlib.data.multiset.intervals
import Mathlib.PostPort
namespace... |
b5c838eede5c56587bc7b2b90307fa241331b826 | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /tests/lean/reserve_bugs.lean | 0bd5016356461c95152f84427e137e014ccb133f | [
"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 | 455 | lean | import logic
constant f : num → num
constant g : num → num → num
constant h : num → num → num
reserve infixl `+`:65
reserve infixr `&`:70
reserve infixl `-`:65
reserve prefix `-`:100
infixl `+` := g
infixl `-` := h
prefix `-` := f
infixr `&` := h
set_option pp.notation false
check -1 + 2
check 1 & 2 & 3 & 4
check... |
25e7ed2d11c93a1e5730575d80b3920bd460d5a8 | a4673261e60b025e2c8c825dfa4ab9108246c32e | /stage0/src/Lean/Data/Format.lean | cbdfda77de471002840361706420fc60d8b5f7d5 | [
"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 | 10,648 | lean | /-
Copyright (c) 2018 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
import Lean.Data.Options
universes u v
namespace Lean
namespace Format
inductive FlattenBehavior :=
| allOrNone
| fill
namespace FlattenBehavior
insta... |
763493aec120ee5fe70699f8a09522743ec429ea | 799b5de27cebaa6eaa49ff982110d59bbd6c6693 | /mechanized/metafunctions.lean | 9de194daa3ad295fba32c57c4eab396350d3e5e6 | [
"MIT"
] | permissive | philnguyen/soft-contract | 263efdbc9ca2f35234b03f0d99233a66accda78b | 13e7d99e061509f0a45605508dd1a27a51f4648e | refs/heads/master | 1,625,975,131,435 | 1,617,775,585,000 | 1,617,775,704,000 | 17,326,137 | 33 | 7 | MIT | 1,613,722,535,000 | 1,393,714,126,000 | Racket | UTF-8 | Lean | false | false | 1,484 | lean | import data.set definitions
def set_del {τ: Type} (x: τ) (xs: set τ) := set.diff xs (set.insert x ∅)
attribute [reducible] set_del
-- Collect free variables in expression
noncomputable def fv: e → set x
| (e.n _) := ∅
| e.s := ∅
| (e.lam x e) := set_del x (fv e)
| (e.x x) := set.insert x ∅... |
910223c55408399604462adf19e55cff21199978 | 9dd3f3912f7321eb58ee9aa8f21778ad6221f87c | /library/init/data/nat/default.lean | ac93e59093027a3f1914d8431acec724857c79b8 | [
"Apache-2.0"
] | permissive | bre7k30/lean | de893411bcfa7b3c5572e61b9e1c52951b310aa4 | 5a924699d076dab1bd5af23a8f910b433e598d7a | refs/heads/master | 1,610,900,145,817 | 1,488,006,845,000 | 1,488,006,845,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 238 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.data.nat.basic init.data.nat.div init.data.nat.lemmas
|
95e242d73e6cb4d853e99817cf35de1db5568f0b | 7a76361040c55ae1eba5856c1a637593117a6556 | /src/exercises/love01_definitions_and_statements_exercise_solution.lean | a3196b8caf0d13cf74e1149f07c5146a26254486 | [] | no_license | rgreenblatt/fpv2021 | c2cbe7b664b648cef7d240a654d6bdf97a559272 | c65d72e48c8fa827d2040ed6ea86c2be62db36fa | refs/heads/main | 1,692,245,693,819 | 1,633,364,621,000 | 1,633,364,621,000 | 407,231,487 | 0 | 0 | null | 1,631,808,608,000 | 1,631,808,608,000 | null | UTF-8 | Lean | false | false | 6,451 | lean | import ..lectures.love01_definitions_and_statements_demo
/-! # LoVe Exercise 1: Definitions and Statements
Replace the placeholders (e.g., `:= sorry`) with your solutions. -/
set_option pp.beta true
set_option pp.generalized_field_notation false
namespace LoVe
/-! ## Question 1: Truncated Subtraction
1.1. Defi... |
147bd1da7684a3d31e8c60a33e74a2964196af35 | c3f2fcd060adfa2ca29f924839d2d925e8f2c685 | /library/init/sigma.lean | 419d53e1c3884e244d5a2ef3d543e128e23f9c67 | [
"Apache-2.0"
] | permissive | respu/lean | 6582d19a2f2838a28ecd2b3c6f81c32d07b5341d | 8c76419c60b63d0d9f7bc04ebb0b99812d0ec654 | refs/heads/master | 1,610,882,451,231 | 1,427,747,084,000 | 1,427,747,429,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,600 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: init.sigma
Author: Leonardo de Moura, Jeremy Avigad, Floris van Doorn
-/
prelude
import init.datatypes init.num init.wf init.logic init.tactic
definition dpair := @sigma.mk
not... |
74f19154c9f112b3efda7466bab001a6a7280e27 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/data/nat/succ_pred.lean | 0dede1290e77db5a48092e7088fe7e2615132b11 | [
"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 | 1,591 | 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 order.succ_pred
/-!
# Successors and predecessors of naturals
In this file, we show that `ℕ` is both an archimedean `succ_order` and an archimedean `pred_order`.... |
b5542b9df83e7d9320c82e179c5c7e92b774ddb3 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/sym2.lean | 563851f08f911c35283589e0a218e434afc337f5 | [] | 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 | 10,804 | lean | /-
Copyright (c) 2020 Kyle Miller All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Kyle Miller.
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.tactic.linarith.default
import Mathlib.data.sym
import Mathlib.PostPort
universes u u_1 u_2 u_3
... |
2f85e9ace29fb145ffa4210a730f8d25057cdf87 | 206422fb9edabf63def0ed2aa3f489150fb09ccb | /src/field_theory/galois.lean | 56f7c07f08265f77eebab60315e5fb7e55fe5137 | [
"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 | 18,327 | lean | /-
Copyright (c) 2020 Thomas Browning and Patrick Lutz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning and Patrick Lutz
-/
import field_theory.normal
import field_theory.primitive_element
import field_theory.fixed
import ring_theory.power_basis
/-!
# ... |
bced34762f25655189afa8cbd7bb348633346181 | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /tests/bench/rbmap_checkpoint2.lean | 2ae95a5f2be5bdfe1621271dd772f87a47e9f600 | [
"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 | 3,346 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.coe init.data.option.basic init.system.io
universes u v w w'
inductive color
| Red | Black
inductive Tree
| Leaf {} ... |
4bd283cd374dada32647cde47b99e22353351b6b | 618003631150032a5676f229d13a079ac875ff77 | /src/data/list/sort.lean | 77ce3baeb702af6355e1f4a340a22d3a12271019 | [
"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 | 11,316 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad
Insertion sort and merge sort.
-/
import data.list.perm
open list.perm
namespace list
section sorted
universe variable uu
variables {α : Type uu} {r : α → α → Prop}
/--... |
49ce7c363f9de7e9aebcad76e4377a287ccb85a9 | fcf3ffa92a3847189ca669cb18b34ef6b2ec2859 | /src/world8/level11.lean | b21d2d675a133ca22b2238bb46061232b1314367 | [
"Apache-2.0"
] | permissive | nomoid/lean-proofs | 4a80a97888699dee42b092b7b959b22d9aa0c066 | b9f03a24623d1a1d111d6c2bbf53c617e2596d6a | refs/heads/master | 1,674,955,317,080 | 1,607,475,706,000 | 1,607,475,706,000 | 314,104,281 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 360 | lean | import mynat.definition
import mynat.add
import world8.level6
import world8.level9
namespace mynat
theorem add_right_eq_zero (a b : mynat) (h : a + b = 0) : a = 0 :=
begin [nat_num_game]
cases a with d,
{
refl,
},
{
exfalso,
rw succ_add at h,
apply succ_ne_zero (d + b),... |
2aa66e591a17a5ca668b363b8c6afdfc4ad0012e | 592ee40978ac7604005a4e0d35bbc4b467389241 | /Library/generated/mathscheme-lean/ShelfSig.lean | 9a1626c9b4a239e29762b7e4c4baa7be0a2ca4a9 | [] | no_license | ysharoda/Deriving-Definitions | 3e149e6641fae440badd35ac110a0bd705a49ad2 | dfecb27572022de3d4aa702cae8db19957523a59 | refs/heads/master | 1,679,127,857,700 | 1,615,939,007,000 | 1,615,939,007,000 | 229,785,731 | 4 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,198 | 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 ShelfSig
structure ShelfSig (A : Type) : Type :=
(linv : (A → (A → A)))
(rinv : (A → (A → A)))
open ShelfSig
structure Sig (AS : Type) : Type :=
... |
1d69d4e162abda6c91752b1897e2c833e0b894c7 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/algebra/category/BoolRing.lean | 87b85254a8bf94e1b108a9b10155243842bedb39 | [
"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 | 1,935 | lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import algebra.category.Ring.basic
import algebra.ring.boolean_ring
import order.category.BoolAlg
/-!
# The category of Boolean rings
This file defines `BoolRing`, the ... |
19348e060f76edf8ec10011b1bdf39181f42736e | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/topology/uniform_space/basic.lean | f7793013a46e0228dea77765f550d14e3672c590 | [
"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 | 47,016 | 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
Theory of uniform spaces.
Uniform spaces are a generalization of metric spaces and topological groups. Many concepts directly
generaliz... |
ab85b0d51f7ff15b09123a24bbb200601375cf69 | 4950bf76e5ae40ba9f8491647d0b6f228ddce173 | /src/ring_theory/power_series.lean | f29f3f81df0c08688814453109bfa8021b7042da | [
"Apache-2.0"
] | permissive | ntzwq/mathlib | ca50b21079b0a7c6781c34b62199a396dd00cee2 | 36eec1a98f22df82eaccd354a758ef8576af2a7f | refs/heads/master | 1,675,193,391,478 | 1,607,822,996,000 | 1,607,822,996,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 59,057 | lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Kenny Lau
-/
import data.mv_polynomial
import ring_theory.ideal.operations
import ring_theory.multiplicity
import tactic.linarith
/-!
# Formal power series
This file ... |
f855f15906f0600409c0876c3c2963e8cd7c7160 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/421.lean | 43df298d415602909f2ff1c43534ce9dd0e5b82b | [
"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 | 178 | lean | inductive Con : Type
| nil : Con
| foo : Con
inductive Conw : Con → Prop
| nilw : Conw Con.nil
example (x : Conw Con.nil) : x = Conw.nilw := by
cases x
trace_state
rfl
|
2601cd37a64fed049c55ceabeb3aeea077cec707 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/data/opposite.lean | c87d1fad7c813ccedfe5e9fbe6c59a73dddeaa1b | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 4,731 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Reid Barton, Simon Hudon, Kenny Lau
-/
import data.equiv.basic
/-!
# Opposites
In this file we define a type synonym `opposite α := α`, denoted by `αᵒᵖ` and two synon... |
d60940e433b18d0ed5113f1c871e4e99a2b35230 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/order/chain.lean | 45a8e7f8e9fc39f16032be82194e18c66143a657 | [
"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 | 12,033 | 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 data.set.pairwise
import data.set_like.basic
/-!
# Chains and flags
This file defines chains for an arbitrary relation and flags for an order and proves Haus... |
64b9404d3fe99e0cd4934eb8690e9e399d6621a3 | 75db7e3219bba2fbf41bf5b905f34fcb3c6ca3f2 | /hott/init/ua.hlean | fba2c1dd5551cf8687a052cf94fda1a4e7b091b5 | [
"Apache-2.0"
] | permissive | jroesch/lean | 30ef0860fa905d35b9ad6f76de1a4f65c9af6871 | 3de4ec1a6ce9a960feb2a48eeea8b53246fa34f2 | refs/heads/master | 1,586,090,835,348 | 1,455,142,203,000 | 1,455,142,277,000 | 51,536,958 | 1 | 0 | null | 1,455,215,811,000 | 1,455,215,811,000 | null | UTF-8 | Lean | false | false | 2,979 | hlean | /-
Copyright (c) 2014 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer, Floris van Doorn
Ported from Coq HoTT
-/
prelude
import .equiv
open eq equiv is_equiv equiv.ops
--Ensure that the types compared are in the same universe
section... |
405eb6fff1bb78583c865b68d4f9eed03bb913ba | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/num/basic.lean | 7e091c13a33d8af96d8e153d6ad577cf448f7148 | [] | 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 | 8,532 | 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, Mario Carneiro
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.PostPort
universes l u_1
namespace Mathlib
/-!
# Binary repre... |
acc80ea617dc3f1e4de045a679c76c26c122a4a0 | 367134ba5a65885e863bdc4507601606690974c1 | /src/computability/encoding.lean | b63ac53fadb82ce6aaf0386ee9ec3fb96211ae2b | [
"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 | 6,116 | lean | /-
Copyright (c) 2020 Pim Spelier, Daan van Gent. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Pim Spelier, Daan van Gent.
-/
import data.fintype.basic
import data.num.lemmas
import tactic.derive_fintype
/-!
# Encodings
This file contains the definition of a (fini... |
0fc7870c2ca2505f7d9e28eede2d2c29c6df8588 | 8b9f17008684d796c8022dab552e42f0cb6fb347 | /hott/algebra/precategory/yoneda.hlean | 071c39631d3afab8d8a6fba16de29c0e8ceaf064 | [
"Apache-2.0"
] | permissive | chubbymaggie/lean | 0d06ae25f9dd396306fb02190e89422ea94afd7b | d2c7b5c31928c98f545b16420d37842c43b4ae9a | refs/heads/master | 1,611,313,622,901 | 1,430,266,839,000 | 1,430,267,083,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,098 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.precategory.yoneda
Authors: Floris van Doorn
-/
--note: modify definition in category.set
import algebra.category.constructions .iso
open category eq category.ops functor p... |
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