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values | content stringlengths 3 6.12M |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
3f6c6b65839afd17319375179009da717d69c4a2 | 8f67b34bba98f894155dedf263bc8d61c31e89cd | /2ltt/fibrant.lean | 0b2d36e7ffb528adb39e42d53206fedf45a8b175 | [] | no_license | 5HT/two-level | 3b1523db242cba819681b862fbc8f490d9571a66 | 370f5a91311db3b463b10a31891370721e2476e2 | refs/heads/master | 1,648,254,367,420 | 1,576,269,550,000 | 1,576,269,550,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 11,475 | lean | import data.equiv .facts
open eq
-- we use the isomorphism definition from the standard library
notation X `≃` Y := equiv X Y
constant is_fibrant' : Type → Prop
structure is_fibrant [class] (X : Type) := mk ::
fib_internal : is_fibrant' X
constant equiv_is_fibrant {X Y : Type}(e : X ≃ Y)[fib : is_fibrant X] : is_... |
dc77dda3a7e5c5b98c2155bcef52abd414af28d6 | 12dabd587ce2621d9a4eff9f16e354d02e206c8e | /world10/level12.lean | f48acdf72c7ad9ebef4d36cab2669f59042cdae9 | [] | no_license | abdelq/natural-number-game | a1b5b8f1d52625a7addcefc97c966d3f06a48263 | bbddadc6d2e78ece2e9acd40fa7702ecc2db75c2 | refs/heads/master | 1,668,606,478,691 | 1,594,175,058,000 | 1,594,175,058,000 | 278,673,209 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 164 | lean | theorem le_of_succ_le_succ (a b : mynat) : succ a ≤ succ b → a ≤ b :=
begin
intro h,
cases h with d hd,
use d,
apply succ_inj,
rw ← succ_add,
exact hd,
end
|
4823ec06084a020438b883d75ab05373bfa05dc6 | 1abd1ed12aa68b375cdef28959f39531c6e95b84 | /src/ring_theory/polynomial/content.lean | 7b0fb45508cae06e03579ea2bdef9ccea576aaa7 | [
"Apache-2.0"
] | permissive | jumpy4/mathlib | d3829e75173012833e9f15ac16e481e17596de0f | af36f1a35f279f0e5b3c2a77647c6bf2cfd51a13 | refs/heads/master | 1,693,508,842,818 | 1,636,203,271,000 | 1,636,203,271,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 17,139 | lean | /-
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import algebra.gcd_monoid.finset
import data.polynomial.field_division
import data.polynomial.erase_lead
import data.polynomial.cancel_leads
/-!
# GCD structures on ... |
af561401c361f19af06490d914fafd2eacb2344d | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/tactic/norm_num.lean | f3fddb3fc7046eafbc4e76174f339bda31fd8b51 | [
"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 | 63,666 | lean | /-
Copyright (c) 2017 Simon Hudon All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Mario Carneiro
-/
import data.rat.cast
import data.rat.meta_defs
/-!
# `norm_num`
Evaluating arithmetic expressions including `*`, `+`, `-`, `^`, `≤`.
-/
universes u v w
n... |
850aa42d27d42d112481f32ae19ec92968bdcf2a | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/real/cau_seq_completion.lean | f2aa9825397dd426ea20201aef10b5065a9b1328 | [] | 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 | 12,056 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Robert Y. Lewis
Generalizes the Cauchy completion of (ℚ, abs) to the completion of a
commutative ring with absolute value.
-/
import Mathlib.PrePort
import Mathlib.Lea... |
1ab06ab0a90240ae2d2e43218ad256eef2651f1e | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Compiler/LCNF/LCtx.lean | ba50bf037d5d0f2b5585573b8b04c0303cb295f7 | [
"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 | 2,673 | lean | /-
Copyright (c) 2022 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.LocalContext
import Lean.Compiler.LCNF.Basic
namespace Lean.Compiler.LCNF
/--
LCNF local context.
-/
structure LCtx where
params : HashMap... |
59f5bbc9c871e9142ea0a9f5308611ae6258219d | a9fe717b93ccfa4b2e64faeb24f96dfefb390240 | /nat/sub_elim.lean | 8460aab3e1a06d336c3ea57dc37c0dad26bebac5 | [] | no_license | skbaek/omega | ab1f4a6daadfc8c855f14c39d9459ab841527141 | 715e384ed14e8eb177a326700066e7c98269e078 | refs/heads/master | 1,588,000,876,352 | 1,552,645,917,000 | 1,552,645,917,000 | 174,442,914 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,693 | lean | import .form ..list
namespace nat
def update (m n) (v : nat → nat) : nat → nat
| x := if x = m then n else v x
lemma update_eq (m n v) : update m n v m = n :=
begin simp only [update, if_pos rfl] end
lemma update_eq_of_ne {m n v k} :
m ≠ k → update m n v k = v k :=
begin
intro h1, simp only [update],
rw if_... |
00b82720536844b240dfafb8727b0b41454ebad1 | 01ae0d022f2e2fefdaaa898938c1ac1fbce3b3ab | /categories/adjunctions/hom_adjunction.lean | fb8e2a9a4d7e16c3119ce820d5ea1977d36ea35d | [] | no_license | PatrickMassot/lean-category-theory | 0f56a83464396a253c28a42dece16c93baf8ad74 | ef239978e91f2e1c3b8e88b6e9c64c155dc56c99 | refs/heads/master | 1,629,739,187,316 | 1,512,422,659,000 | 1,512,422,659,000 | 113,098,786 | 0 | 0 | null | 1,512,424,022,000 | 1,512,424,022,000 | null | UTF-8 | Lean | false | false | 1,413 | lean | -- Copyright (c) 2017 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Scott Morrison
import ..natural_isomorphism
import ..opposites
import ..products
import ..isomorphism
import ..types
open categories
open categories.functor
open categories.nat... |
2cb4e72c4a2cd3d03a87fc79e8ff37379bb1fc4e | a46270e2f76a375564f3b3e9c1bf7b635edc1f2c | /5.8.1-4.6.1.lean | 7f617e772ccd7580c7f7c6400c083ae5353323bb | [
"CC0-1.0"
] | permissive | wudcscheme/lean-exercise | 88ea2506714eac343de2a294d1132ee8ee6d3a20 | 5b23b9be3d361fff5e981d5be3a0a1175504b9f6 | refs/heads/master | 1,678,958,930,293 | 1,583,197,205,000 | 1,583,197,205,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 611 | lean | variables (α : Type) (p q : α → Prop)
example : (∀ x, p x ∧ q x) ↔ (∀ x, p x) ∧ (∀ x, q x) := begin
apply iff.intro, {
intro h,
constructor, {
intro x, exact (h x).1
}, {
intro x, exact (h x).2
}
}, {
intro h, intro x,
constructor, exact (h.1 x), exact (h.2 x)
}
end
example : (∀ x,... |
1dd30716d55b3aa7a1996e081db6a47a473057ce | 82b86ba2ae0d5aed0f01f49c46db5afec0eb2bd7 | /src/Init/Data/String/Basic.lean | c60d02de9234d8549733d071cb0c3aea3d36b458 | [
"Apache-2.0"
] | permissive | banksonian/lean4 | 3a2e6b0f1eb63aa56ff95b8d07b2f851072d54dc | 78da6b3aa2840693eea354a41e89fc5b212a5011 | refs/heads/master | 1,673,703,624,165 | 1,605,123,551,000 | 1,605,123,551,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 15,678 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
prelude
import Init.Data.List.Basic
import Init.Data.Char.Basic
import Init.Data.Option.Basic
universes u
/-- A byte position in a `String`. Internally, `St... |
3c0159adb012ae3797ae6d0748baa0046b767653 | 437dc96105f48409c3981d46fb48e57c9ac3a3e4 | /src/data/array/lemmas.lean | 94c46329f6a15301c879ca71340287648a9ccd0c | [
"Apache-2.0"
] | permissive | dan-c-k/mathlib | 08efec79bd7481ee6da9cc44c24a653bff4fbe0d | 96efc220f6225bc7a5ed8349900391a33a38cc56 | refs/heads/master | 1,658,082,847,093 | 1,589,013,201,000 | 1,589,013,201,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,874 | 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, Mario Carneiro
-/
import control.traversable.equiv
import data.vector2
universes u v w
namespace d_array
variables {n : ℕ} {α : fin n → Type u}
instance [∀... |
623f01f4461dfe300f4acef89f0af53a7e607f88 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/run/fib_wrec.lean | c0e0eca5e0f067079d06399012c78107d81e1c88 | [
"Apache-2.0"
] | permissive | soonhokong/lean-osx | 4a954262c780e404c1369d6c06516161d07fcb40 | 3670278342d2f4faa49d95b46d86642d7875b47c | refs/heads/master | 1,611,410,334,552 | 1,474,425,686,000 | 1,474,425,686,000 | 12,043,103 | 5 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 1,142 | lean | open nat
definition fib.F (n : nat) : (Π (m : nat), m < n → nat) → nat :=
nat.cases_on n
(λ (f : Π (m : nat), m < 0 → nat), succ 0)
(λ (n₁ : nat), nat.cases_on n₁
(λ (f : Π (m : nat), m < (succ 0) → nat), succ 0)
(λ (n₂ : nat) (f : Π (m : nat), m < (succ (succ n₂)) → nat),
have l₁ : succ n₂ < succ (... |
f8c7fd503128e97eda33a7edccf05a02422fe35b | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/structSorryBug.lean | c2c53213c40a6a94483d7f1a3d40f58ddc4a5c99 | [
"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 | 129 | lean | set_option relaxedAutoImplicit false
instance has_arr : HasArr Preorder := { Arr := Function }
def foo : Nat := { first := 10 }
|
a22e87a679406a4bcdfa0fed4af2c5d326068d27 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/auto_param_in_structures.lean | affc3c0d46c723689412e389d673ac6dd9e2bf19 | [
"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 | 461 | lean | namespace test
open tactic
meta def my_tac : tactic unit := abstract (intros >> `[simp])
local attribute [simp] nat.add_assoc nat.mul_assoc
structure monoid (α : Type) :=
(op : α → α → α)
(assoc : ∀ a b c, op (op a b) c = op a (op b c) . my_tac)
def m1 : monoid nat :=
monoid.mk (+)
def m2 : monoid nat :=
monoid.... |
6bf9b9c328123cd3ccd94cd6a1ad28987a08016e | 618003631150032a5676f229d13a079ac875ff77 | /test/choose.lean | aa516ab3f631611fccac212750e29f783bdf1381 | [
"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 | 852 | lean | import tactic.interactive
/- choice -/
example (h : ∀n m : ℕ, ∃i j, m = n + i ∨ m + j = n) : true :=
begin
choose i j h using h,
guard_hyp i := ℕ → ℕ → ℕ,
guard_hyp j := ℕ → ℕ → ℕ,
guard_hyp h := ∀ (n m : ℕ), m = n + i n m ∨ m + j n m = n,
trivial
end
example (h : ∀n m : ℕ, ∃i, ∀n:ℕ, ∃j, m = n + i ∨ m + j =... |
406cdbe44d13e0e22766bf4a3e93ebe609c7cf4b | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/ring_theory/etale.lean | 93367714fc187f4049d2ad9af4de403ab8556086 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 23,057 | 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 ring_theory.quotient_nilpotent
import ring_theory.kaehler
/-!
# Formally étale morphisms
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file req... |
5b9b1fa08e819c0a223d20b88b11c94ba6b55613 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/data/int/succ_pred.lean | 1e8cf596bda2114d9167740d47f3132c00658720 | [
"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 | 2,097 | lean | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import data.int.basic
import data.nat.succ_pred
/-!
# Successors and predecessors of integers
In this file, we show that `ℤ` is both an archimedean `succ_order` and an ... |
3b48a66c2cb33ad7397ab1efbb3cf0cfe16bbf5f | ea5678cc400c34ff95b661fa26d15024e27ea8cd | /non_tactic.lean | 45efbbc9e9d3639ab809e38983d412fd944074ee | [] | 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 | 2,979 | lean | import data.nat.prime data.finset
open nat
def island_rules : ℕ → ℕ → ℕ → Prop
| 0 b B := (B = b ∨ B = b - 1) ∧ B > 0
| (d + 1) b B := island_rules d b B ∧
((∀ C, island_rules d b C → C = b) ↔ ∀ C, island_rules d B C → C = B)
def island_rules2 : ℕ → ℕ → finset ℕ
| 0 b := ({b - 1, b} : finset ℕ).filter (> 0... |
9da50e4396349a2fe3ead526314bbb41478a8057 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/init/data/sum/basic.lean | 85bc0ae1b73bc9eda355680d03348b95d0aec05d | [] | 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 | 657 | 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, Jeremy Avigad
The sum type, aka disjoint union.
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.logic
universes u v
namespace Mathlib
infixr:30 ... |
def3d22fec00055330104f8728bf0cf9feb4fb3c | 90109f8736c31bdbe0cf5318c1c226250ff3bbff | /lean/effects.lean | 721976dba8a147115266b9131e3c83c38745c2ed | [] | no_license | akella/groupoid.space | c64db5a98a04cd73ae1259eeb6bc14dd1676e28c | 18ba185b80e2114c13faf983dbe0edb335a63587 | refs/heads/master | 1,584,768,713,904 | 1,529,586,461,000 | 1,529,586,461,000 | 138,165,171 | 1 | 0 | null | 1,529,582,805,000 | 1,529,582,804,000 | null | UTF-8 | Lean | false | false | 667 | lean |
import data.nat data.bool data.prod data.list data.sum data.stream
data.unit data.uprod data.tuple data.option
namespace effects open nat bool prod sum list classical option stream
record eff (x: Type) := (carrier : x)
record io (x: Type) extends eff x :=... |
df6f80edeb1c95ac74e0467555542e20a9b5e278 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/number_theory/legendre_symbol/quadratic_char/gauss_sum.lean | ef6cb184b7bcd1c49f6b98858909639c043d9ae7 | [
"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 | 6,328 | lean | /-
Copyright (c) 2022 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
import number_theory.legendre_symbol.quadratic_char.basic
import number_theory.legendre_symbol.gauss_sum
/-!
# Quadratic characters of finite fields
> THIS FILE IS SY... |
9cb23e771f53d54974f3b56ecbad3ff0f8cd1d66 | 205f0fc16279a69ea36e9fd158e3a97b06834ce2 | /src/01_Equality/05_automation.lean | a2c593fb48cb1c6ba95e4dcc61a9fd521381a7cb | [] | no_license | kevinsullivan/cs-dm-lean | b21d3ca1a9b2a0751ba13fcb4e7b258010a5d124 | a06a94e98be77170ca1df486c8189338b16cf6c6 | refs/heads/master | 1,585,948,743,595 | 1,544,339,346,000 | 1,544,339,346,000 | 155,570,767 | 1 | 3 | null | 1,541,540,372,000 | 1,540,995,993,000 | Lean | UTF-8 | Lean | false | false | 2,645 | lean | /-
In Lean and related proof assistants, such
as Coq, you can obtain proofs not only by
applying inference rules, such as eq.refl,
directly, but also by using programs, called
tactics, that automate some of the details
of finding and applying inference rules or
sequences of such rules.
As an example, we look at the "r... |
0b7017702bb12fa5cd9b39737c913a0a9beb0837 | 1abd1ed12aa68b375cdef28959f39531c6e95b84 | /src/algebra/big_operators/order.lean | 885031ecd46df676515d14d3ebe3b641586147ec | [
"Apache-2.0"
] | permissive | jumpy4/mathlib | d3829e75173012833e9f15ac16e481e17596de0f | af36f1a35f279f0e5b3c2a77647c6bf2cfd51a13 | refs/heads/master | 1,693,508,842,818 | 1,636,203,271,000 | 1,636,203,271,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 22,517 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import algebra.order.absolute_value
import algebra.big_operators.basic
/-!
# Results about big operators with values in an ordered algebraic structure.
Mostly mono... |
21de9e35f5f852f6e12ccaabf3222eb7f9dd7795 | 1a61aba1b67cddccce19532a9596efe44be4285f | /hott/algebra/group.hlean | 4c1b44bab45f6e088b2a880b63f18021f8586170 | [
"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 | 19,092 | hlean | /-
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
Various multiplicative and additive structures.
Ported from the standard library
-/
import algebra.binary
open eq is_trunc binary -- note: ⁻¹ will b... |
441dd40b1ad37c4acf0761e1b7850f149d53a258 | 85d23ae5fcdcd77981feb67549852ff901e8a583 | /cset.lean | 510485aec128b7dcd666fe0b7b16fdcdd8a2dbf2 | [] | no_license | javra/cubes | 5b480abcf1a869335a82b4fb5357ec4d16ab56bc | 734bdf71b9086b0ba9ef7dba3ede0c71f10872cc | refs/heads/master | 1,611,513,591,851 | 1,489,495,303,000 | 1,489,495,303,000 | 84,469,571 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,575 | lean | /- CUBICAL SETS -/
import .cubes
import .fi
import .cubes_fin
universes u v
open cmonad
/- Cubical Sets -/
structure cset {base : Type u} {fam : base → Type v} :=
(obj : base → Type)
(mor : Π {m n} (f : cmor (fam m) (fam n)), obj m → obj n)
(id : Π {m} u, mor (@dim (fam m)) u = u)
(co... |
3e7c437951ea8885abe5f3757d825f77dd8de04e | 3d2a7f1582fe5bae4d0bdc2fe86e997521239a65 | /spatial-reasoning/spatial-reasoning-problem-01.lean | fe77140b3d194bca21b9a4cd26f1bb8525ecfa20 | [] | no_license | own-pt/common-sense-lean | e4fa643ae010459de3d1bf673be7cbc7062563c9 | f672210aecb4172f5bae265e43e6867397e13b1c | refs/heads/master | 1,622,065,660,261 | 1,589,487,533,000 | 1,589,487,533,000 | 254,167,782 | 3 | 2 | null | 1,589,487,535,000 | 1,586,370,214,000 | Lean | UTF-8 | Lean | false | false | 738 | lean | /- Spatial Reasoning Problem 01 -/
/- It can be found at: SpatialQs.txt -/
/- (1) A is on the right of B. C is on the left of B. Hence, A is on the right of C -/
constant U : Type
constants A B C : U
constants Left Right : U
constant orientation : U → U → U → Prop
axiom a1 : orientation A B Right
axiom a2 : orienta... |
1651e66b8facae1ba9f6b9d74a8339e9a3686836 | ef47cc39429c8f578004338bf040c9c309b26766 | /src/for_mathlib/algebra/category/Group/kernels.lean | 0737c2d13ebf54b21a0a7e2ae8a5b9792184722c | [] | no_license | farmanb/lftcm2020 | 29f1c646437a8f8b00ee2e07c8b663ca04bfa16f | 1948bfaf58e3b340b39cd9b8366aa4f13e5ffa7d | refs/heads/master | 1,669,697,152,764 | 1,595,275,412,000 | 1,595,275,412,000 | 285,654,242 | 0 | 0 | null | 1,596,742,086,000 | 1,596,742,085,000 | null | UTF-8 | Lean | false | false | 4,557 | lean | import algebra.category.Group.limits
import algebra.category.Group.images
import category_theory.limits.shapes.kernels
import group_theory.quotient_group
import category_theory.over
open category_theory
open category_theory.limits
universes u
section
variables {C : Type (u+1)} [large_category C] [concrete_category C... |
cc30fc9ea11c41800c0834eabbc436cd3a1678f4 | 38bf3fd2bb651ab70511408fcf70e2029e2ba310 | /src/data/polynomial.lean | 97c8d194160fad8549af4d425621c4a75feeb155 | [
"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 | 100,153 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Jens Wagemaker
Theory of univariate polynomials, represented as `ℕ →₀ α`, where α is a commutative semiring.
-/
import data.finsupp algebra.gcd_domain ring... |
657eb535d806c926c28012b717255f0150c71a14 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/Ord.lean | 6a1918887f3c875bfec1120faec19f6f409b7cd9 | [
"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 | 789 | lean |
inductive SimpleInd
| A
| B
deriving Ord
mutual
inductive Foo
| A : Int → (3 = 3) → String → Foo
| B : Bar → Foo
deriving Ord
inductive Bar
| C
| D : Foo → Bar
deriving Ord
end
inductive ManyConstructors | A | B | C | D | E | F | G | H | I | J | K | L
| M | N | O | P | Q | R | S | T | U | V | W | X |... |
223c484913fd296dda30f9535d65d07c8838e81c | 02005f45e00c7ecf2c8ca5db60251bd1e9c860b5 | /src/topology/metric_space/gromov_hausdorff_realized.lean | ac96ec50e766fdbcbd3da743cf52bdf68c6b7edd | [
"Apache-2.0"
] | permissive | anthony2698/mathlib | 03cd69fe5c280b0916f6df2d07c614c8e1efe890 | 407615e05814e98b24b2ff322b14e8e3eb5e5d67 | refs/heads/master | 1,678,792,774,873 | 1,614,371,563,000 | 1,614,371,563,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 26,194 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Sébastien Gouëzel
Construction of a good coupling between nonempty compact metric spaces, minimizing
their Hausdorff distance. This construction is instrumental to study the Gromov-... |
a46d68609f630581448f9816e7175fc5c3ab1f29 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/logic/lemmas.lean | 8464431f686cfe821cc5bf3f88991881b82ae646 | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 2,406 | 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 tactic.protected
import tactic.split_ifs
import logic.basic
/-!
# More basic logic properties
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> https://github.com/lea... |
029a5699ac8082b29cafbaef254e6fc96c0e209b | 4727251e0cd73359b15b664c3170e5d754078599 | /src/linear_algebra/determinant.lean | 2ff658c34c9d52f544d46672fe966b533dc1ee12 | [
"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 | 22,637 | 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 linear_algebra.multilinear.basis
import linear_algebra.matrix.reindex
import ring_theory.algebra_tower
import tactic.... |
618293cb47671cfdcfb676a74820b2457b894f95 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/data/sym/sym2.lean | f6c68e55179a3393673bd3855eff24e6ab49c544 | [
"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 | 20,079 | lean | /-
Copyright (c) 2020 Kyle Miller All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
import data.sym.basic
import tactic.linarith
/-!
# The symmetric square
This file defines the symmetric square, which is `α × α` modulo
swapping. This is also known as th... |
0dc88a05f8e2611c61b2970eee2d7e5b613fcb4a | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/data/polynomial/ring_division.lean | 964e01ccc20afeb13360219ce1454482d5969fc0 | [
"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 | 15,885 | lean |
/-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Scott Morrison, Jens Wagemaker
-/
import data.polynomial.basic
import data.polynomial.div
import data.polynomial.algebra_map
/-!
# Theory of univariate p... |
f2f5815e69dd13584453df6a181ba122d3f27d59 | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/data/zsqrtd/gaussian_int.lean | 6ea476818aca1ba3da4e5552ac31a7fd470ebc53 | [
"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 | 7,095 | lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Chris Hughes
The gaussian integers ℤ[i].
-/
import data.zsqrtd.basic data.complex.basic algebra.euclidean_domain
open zsqrtd complex
@[reducible] def gaussian_int : Type := zsqrtd (-1)... |
f57829ab3ef9f45217b2c0f039a7ac91e0a6e08f | 12dabd587ce2621d9a4eff9f16e354d02e206c8e | /world05/level09.lean | 868ae65e0b1779767c00d2a57478944c7c7825e2 | [] | no_license | abdelq/natural-number-game | a1b5b8f1d52625a7addcefc97c966d3f06a48263 | bbddadc6d2e78ece2e9acd40fa7702ecc2db75c2 | refs/heads/master | 1,668,606,478,691 | 1,594,175,058,000 | 1,594,175,058,000 | 278,673,209 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 386 | lean | example (A B C D E F G H I J K L : Type)
(f1 : A → B) (f2 : B → E) (f3 : E → D) (f4 : D → A) (f5 : E → F)
(f6 : F → C) (f7 : B → C) (f8 : F → G) (f9 : G → J) (f10 : I → J)
(f11 : J → I) (f12 : I → H) (f13 : E → H) (f14 : H → K) (f15 : I → L)
: A → L :=
begin
intro a,
apply f15,
apply f11,
apply f9,
apply f8,
apply f5,... |
af09d72edb7e55dd7546720fdcf909c6ade7ff32 | 1abd1ed12aa68b375cdef28959f39531c6e95b84 | /src/measure_theory/constructions/pi.lean | 7cb435d0e8f9d210ca64b4121fb88119681e6574 | [
"Apache-2.0"
] | permissive | jumpy4/mathlib | d3829e75173012833e9f15ac16e481e17596de0f | af36f1a35f279f0e5b3c2a77647c6bf2cfd51a13 | refs/heads/master | 1,693,508,842,818 | 1,636,203,271,000 | 1,636,203,271,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 33,407 | 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... |
44f83a193f91fadc51a6dcfa3b86765558a4e8a3 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/category_theory/monad/types.lean | 962cb2e07c726488a9fbc45e8297a7cbb4a01b5f | [
"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 | 2,058 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Bhavik Mehta
-/
import category_theory.monad.basic
import category_theory.monad.kleisli
import category_theory.category.Kleisli
import category_theory.types
/-!
# Con... |
ac0960d912d27709f6bad6963a72665cecfbfae3 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/data/rbmap/default.lean | d9041033f8727a7eaa256b3b1e9e60479d636adb | [
"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 | 15,092 | 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
-/
import data.rbtree
import data.rbmap.basic
universes u v
namespace rbmap
variables {α : Type u} {β : Type v} {lt : α → α → Prop}
/- Auxiliary instances -... |
6c263d4510bbaa0a51a67774623cc4ece949200b | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/data/vector2.lean | 9f6804866f549bd428ba62c740f88a8a41d2b3ed | [
"Apache-2.0"
] | permissive | rmitta/mathlib | 8d90aee30b4db2b013e01f62c33f297d7e64a43d | 883d974b608845bad30ae19e27e33c285200bf84 | refs/heads/master | 1,585,776,832,544 | 1,576,874,096,000 | 1,576,874,096,000 | 153,663,165 | 0 | 2 | Apache-2.0 | 1,544,806,490,000 | 1,539,884,365,000 | Lean | UTF-8 | Lean | false | false | 10,293 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
Additional theorems about the `vector` type.
-/
import data.vector data.list.basic category.traversable.basic data.set.basic tactic.tauto
universes u
variables {n : ℕ}... |
60e655a86f6c0c69aef00f4bc7eb61c90b50bfc8 | 798dd332c1ad790518589a09bc82459fb12e5156 | /linear_algebra/prod_module.lean | fbda107b9b8a2a87df9a5d14bb30c7676f26f555 | [
"Apache-2.0"
] | permissive | tobiasgrosser/mathlib | b040b7eb42d5942206149371cf92c61404de3c31 | 120635628368ec261e031cefc6d30e0304088b03 | refs/heads/master | 1,644,803,442,937 | 1,536,663,752,000 | 1,536,663,907,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 11,828 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl
Semigroup, monoid, group and module structures on product spaces.
-/
import data.prod linear_algebra.basic
open set function
universes u v w x
variables {α : Type u} {... |
c7dddf601f0290339633700ea9d0d2a72aa63b34 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/data/list/basic.lean | 1d2e00858677ae5792740a0a0662553c665df19f | [
"Apache-2.0"
] | permissive | ramonfmir/mathlib | c5dc8b33155473fab97c38bd3aa6723dc289beaa | 14c52e990c17f5a00c0cc9e09847af16fabbed25 | refs/heads/master | 1,661,979,343,526 | 1,660,830,384,000 | 1,660,830,384,000 | 182,072,989 | 0 | 0 | null | 1,555,585,876,000 | 1,555,585,876,000 | null | UTF-8 | Lean | false | false | 158,418 | lean | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
-/
import data.nat.basic
/-!
# Basic properties of lists
-/
open function nat (hiding one_pos)
... |
9f65a9b6b0a7d6bc1236d72a0e69fa1dbf0be57a | ba4794a0deca1d2aaa68914cd285d77880907b5c | /src/game/world2/level3.lean | dc0731ce3b1a33d72619f67e15dc631f68ce25dd | [
"Apache-2.0"
] | permissive | ChrisHughes24/natural_number_game | c7c00aa1f6a95004286fd456ed13cf6e113159ce | 9d09925424da9f6275e6cfe427c8bcf12bb0944f | refs/heads/master | 1,600,715,773,528 | 1,573,910,462,000 | 1,573,910,462,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,388 | lean | import mynat.definition -- hide
import mynat.add -- hide
import game.world2.level2 -- hide
namespace mynat -- hide
/-
# Addition World
## Level 3: `succ_add`
Oh no! On the way to `add_comm`, a wild `succ_add` appears. `succ_add`
is the proof that `succ(a) + b = succ(a + b)` for `a` and `b` in your
natural number ty... |
2bc4bb11e7f4834141aa0a44b22c7fa21ecdcc55 | 853df553b1d6ca524e3f0a79aedd32dde5d27ec3 | /src/category_theory/limits/limits.lean | b159889422a2051e1992725c92ed4926a52410bc | [
"Apache-2.0"
] | permissive | DanielFabian/mathlib | efc3a50b5dde303c59eeb6353ef4c35a345d7112 | f520d07eba0c852e96fe26da71d85bf6d40fcc2a | refs/heads/master | 1,668,739,922,971 | 1,595,201,756,000 | 1,595,201,756,000 | 279,469,476 | 0 | 0 | null | 1,594,696,604,000 | 1,594,696,604,000 | null | UTF-8 | Lean | false | false | 51,354 | 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 category_theory.limits.cones
import category_theory.adjunction.basic
import category_theory.reflect_isomorphisms... |
e0ed9ff492383ac31fdf4ab31d56fe5a647a8952 | 2b2a05a7af89c79da194505bf88205a6c4e05d68 | /src/game/world_02_addition.lean | 6dfa6bdb97140f262208362506ebe12f70458798 | [] | no_license | lacrosse/natural_number_game | 6401a11a8c965da3903ae6695f84586edf6fac85 | 400179cde1d3fcc9744901dabff98813ba2b544f | refs/heads/master | 1,677,566,006,582 | 1,612,576,917,000 | 1,612,576,917,000 | 335,655,947 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 964 | lean | import game.world_01_tutorial
namespace mynat
lemma zero_add (n : mynat) : 0 + n = n := begin[nat_num_game]
induction n,
rwa add_zero,
rwa [add_succ, n_ih],
end
lemma add_assoc (a b c : mynat) : (a + b) + c = a + (b + c) := begin[nat_num_game]
induction c,
rwa [add_zero, add_zero],
rwa [add_succ, add_succ... |
184f4c65a9cae8e9fbf42a2c58e487897aa053ef | 6e44fda625e48340c6ffc7b1109a9e3b208e5384 | /src/metric_spaces/definitions.lean | 45d2740d03167c48c7816b9636c42e43006882c0 | [] | no_license | JasonKYi/learn_mspaces | 9f998a265b907af6be6a54061637fcf1f6d1ee9d | 54083e81da420d2d362a7024a8c86bea8529fe66 | refs/heads/master | 1,619,008,842,896 | 1,609,897,382,000 | 1,609,897,382,000 | 249,780,600 | 5 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,260 | lean | import topology.metric_space.basic
variables {X : Type*} [metric_space X]
variables {Y : Type*} [metric_space Y]
namespace definitions
open set
/- Definition of continuity on metric spaces -/
def is_continuous_at (f : X → Y) (a : X) :=
∀ ε > 0, ∃ δ > 0, ∀ x : X, dist x a < δ → dist (f x) (f a) < ε
def is_continu... |
191613a74070c75dc12eb793fec7782320de2a05 | a45212b1526d532e6e83c44ddca6a05795113ddc | /test/tactics.lean | 94962f21414dd16e8b494a2c7165995b28ffb27a | [
"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 | 19,059 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Scott Morrison
-/
import tactic data.set.lattice data.prod data.vector
tactic.rewrite data.stream.basic
tactic.tfae tactic.converter.interactive
tactic.r... |
927b18b8650009c9f84223ffa6a272ec0dd3565e | 30b012bb72d640ec30c8fdd4c45fdfa67beb012c | /tactic/ext.lean | a7b3d68daccabf42a670ab66a5456db68fcb834c | [
"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 | 6,744 | lean |
import tactic.basic core data.sum tactic.rcases
universes u₁ u₂
open interactive interactive.types
open lean.parser nat tactic
meta def get_ext_subject : expr → tactic name
| (expr.pi n bi d b) :=
do v ← mk_local' n bi d,
b' ← whnf $ b.instantiate_var v,
get_ext_subject b'
| (expr.app _ e) :=
do t ← i... |
32403e0f8997a9aafbfd3a93e55352951876d3bb | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/measure_theory/integral/lebesgue.lean | fc8753ab54958b8632a4d7df956c2c06599d38df | [
"Apache-2.0"
] | permissive | waynemunro/mathlib | e3fd4ff49f4cb43d4a8ded59d17be407bc5ee552 | 065a70810b5480d584033f7bbf8e0409480c2118 | refs/heads/master | 1,693,417,182,397 | 1,634,644,781,000 | 1,634,644,781,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 109,066 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johannes Hölzl
-/
import measure_theory.measure.measure_space
import measure_theory.constructions.borel_space
import algebra.indicator_function
import algebra.support
... |
e5765ef04ffaa21f969cf0ca8f5af7623d3a5eb1 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/ring_theory/witt_vector/frobenius_fraction_field.lean | b8df1f484e2a91be49ed6d5188bd1e8ddeabd5d5 | [
"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 | 11,147 | lean | /-
Copyright (c) 2022 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Heather Macbeth
-/
import field_theory.is_alg_closed.basic
import ring_theory.witt_vector.discrete_valuation_ring
/-!
# Solving equations about the Frobenius map on... |
17857b0c9eedbe238d5becac2a0c3604a2c1b866 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/600c.lean | 8c92f202b9b88fa8f7539fc3543be030f27a9f54 | [
"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 | 99 | lean | /- /- -/ -/
/- - /--/-/
/-/-/--/-/-/
/- -/
/- -----------/
/- --/
/- ---/
/-
-/
----/
#print "ok"
|
feaca4d04b88ffc76369b6fe220be8873bc379fc | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/topology/metric_space/emetric_space.lean | 15f1883ba55c47bc407c16eb9b75d79b332854ad | [
"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 | 53,351 | lean | /-
Copyright (c) 2015, 2017 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
-/
import data.real.ennreal
import data.finset.intervals
import topology.uniform_space.uniform_em... |
cc2afdb0fe2647ac0b09e4fc87d26824a79ed65e | 31f556cdeb9239ffc2fad8f905e33987ff4feab9 | /src/Lean/Compiler/LCNF/PullLetDecls.lean | 0e3a48205c1bf686cefd22985f1e0726a7586567 | [
"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 | tobiasgrosser/lean4 | ce0fd9cca0feba1100656679bf41f0bffdbabb71 | ebdbdc10436a4d9d6b66acf78aae7a23f5bd073f | refs/heads/master | 1,673,103,412,948 | 1,664,930,501,000 | 1,664,930,501,000 | 186,870,185 | 0 | 0 | Apache-2.0 | 1,665,129,237,000 | 1,557,939,901,000 | Lean | UTF-8 | Lean | false | false | 4,026 | lean | /-
Copyright (c) 2022 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Compiler.LCNF.CompilerM
import Lean.Compiler.LCNF.DependsOn
import Lean.Compiler.LCNF.Types
import Lean.Compiler.LCNF.PassManager
namespace Lea... |
c293f76440def60951c019ee36a0952085061277 | c3f2fcd060adfa2ca29f924839d2d925e8f2c685 | /library/algebra/ordered_ring.lean | b1093d8bffbaf161ca13be55a593983d3ee802a5 | [
"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 | 21,947 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.ordered_ring
Authors: Jeremy Avigad
Here an "ordered_ring" is partially ordered ring, which is ordered with respect to both a weak
order and an associated strict order. Our num... |
c6066e393beabda1a179c2011fa2fa98fdfb987d | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/tactic/omega/nat/form.lean | 54e48c3720628e34f0ffffd81ebe9db7900b18c8 | [
"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 | 5,759 | lean | /- Copyright (c) 2019 Seul Baek. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Seul Baek
Linear natural number arithmetic preformulas in pre-normalized preform. -/
import tactic.omega.nat.preterm
namespace omega
namespace nat
/-- Intermediate shadow syntax for LNA ... |
f72353b18c5df5f7ca404cba4d0ac0aeeb5175be | b794ca1df49bc5a3bd3fd5552eed3bc4f63b8b93 | /src/mywork/lecture_4.lean | d38dab7b94ae1276967e0b1cd6ee084f39cf1ddb | [] | 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 | 3,267 | lean | /-
In this file, we give formal statements (our version)
of the two axioms of equality. We also present Lean's
versions of these rules, and show how you can use them
without giving all of the arguments explicitly.
-/
/-
AXIOMS
Everything is equal to itself. A bit more formally,
if one is given a type, T, and a value,... |
fc1359c9c4a7b7771050de1bc9b3043e2fca8bf7 | 592ee40978ac7604005a4e0d35bbc4b467389241 | /Library/generated/mathscheme-lean/SteinerMagma.lean | e8f381508ba9f92c6d22fecfaf84bef752c815b5 | [] | 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 | 6,023 | 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 SteinerMagma
structure SteinerMagma (A : Type) : Type :=
(op : (A → (A → A)))
(commutative_op : (∀ {x y : A} , (op x y) = (op y x)))
(antiAbsorbent : (∀ ... |
d6f0373b2820d2f44f244dc7ee895b6a2aeb723a | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/data/complex/basic.lean | a9dc4aa5e675350cbec132a3d20c119b7123ae67 | [
"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 | 27,189 | lean | /-
Copyright (c) 2017 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Mario Carneiro
-/
import data.real.sqrt
/-!
# The complex numbers
The complex numbers are modelled as ℝ^2 in the obvious way and it is shown that they form a field
of c... |
6a974f85909c1b4b3dab59b3074f32f91456807c | bf532e3e865883a676110e756f800e0ddeb465be | /algebra/group_power.lean | 83f426114b21d9ac34deed7c3f0647cf128399da | [
"Apache-2.0"
] | permissive | aqjune/mathlib | da42a97d9e6670d2efaa7d2aa53ed3585dafc289 | f7977ff5a6bcf7e5c54eec908364ceb40dafc795 | refs/heads/master | 1,631,213,225,595 | 1,521,089,840,000 | 1,521,089,840,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,898 | lean | /-
Copyright (c) 2015 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Robert Y. Lewis
The power operation on monoids and groups. We separate this from group, because it depends on
nat, which in turn depends on other parts of algebra.
We h... |
3dffccb2b575109ffbdd54c9dd8a185a02400e0b | b7f22e51856f4989b970961f794f1c435f9b8f78 | /hott/algebra/category/constructions/rezk.hlean | bd3e4ec13d975229eb5d26bc714a724766d49cc3 | [
"Apache-2.0"
] | permissive | soonhokong/lean | cb8aa01055ffe2af0fb99a16b4cda8463b882cd1 | 38607e3eb57f57f77c0ac114ad169e9e4262e24f | refs/heads/master | 1,611,187,284,081 | 1,450,766,737,000 | 1,476,122,547,000 | 11,513,992 | 2 | 0 | null | 1,401,763,102,000 | 1,374,182,235,000 | C++ | UTF-8 | Lean | false | false | 17,563 | hlean | /-
Copyright (c) 2016 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer
The Rezk completion
-/
import algebra.category hit.two_quotient types.trunc types.arrow algebra.category.functor.attributes
open eq category equiv trunc_two_quot... |
c6fa4457063123f4d8e55cbc6f7a5e492ae2a1c0 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/finite/default.lean | c30836d0ce0cb3f39c195d6203a707e5234b5231 | [
"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 | 23 | lean | import data.finite.set
|
2cf9c2ea6e9bb7c145fd33a20e1d45a36e8e5b00 | 65d1df074ed9cf826df35e38c866570c4276bea4 | /src/set_theory.lean | a392bf43db54bb727b6f5638e2a1e11ea11deca9 | [
"Apache-2.0"
] | permissive | fpvandoorn/flypitch | 8ad6af930a1f7d95da21669a14f3fb3a59afc8f6 | d09a1f428bdf54c4aebd785f7c842e0fac17b094 | refs/heads/master | 1,585,602,974,244 | 1,575,699,535,000 | 1,575,699,535,000 | 151,622,978 | 1 | 0 | null | 1,538,680,215,000 | 1,538,680,215,000 | null | UTF-8 | Lean | false | false | 34,977 | lean | /-
Copyright (c) 2019 The Flypitch Project. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Han, Floris van Doorn
-/
import .to_mathlib
/-
note: in comment above cofinality, change sentence with
+ `∀ a, ∃ b ∈ S, ¬(b > a)`. It is defined for all ordinals, but
-/... |
3a758233420060216d7692881ae8cb82e5bdca6c | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/coe5.lean | ba310eb1af7d2eb293413782adc6d584e0825215 | [
"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 | 310 | lean | open tactic
attribute [instance]
definition expr_to_app : has_coe_to_fun expr :=
has_coe_to_fun.mk (expr → expr) (λ e, expr.app e)
constants f a b : expr
check f a
check f a b
check f a b a
set_option pp.coercions false
check f a b a
set_option pp.all true
set_option pp.coercions true
check f a b
|
c5e7aed4b410e75dfe1aec070767302d3a04542a | 41ebf3cb010344adfa84907b3304db00e02db0a6 | /uexp/src/uexp/rules/transitiveInferenceComplexPredicate.lean | 7041e03f33b6adc0baea0bab0fdbd1028a68298a | [
"BSD-2-Clause"
] | permissive | ReinierKoops/Cosette | e061b2ba58b26f4eddf4cd052dcf7abd16dfe8fb | eb8dadd06ee05fe7b6b99de431dd7c4faef5cb29 | refs/heads/master | 1,686,483,953,198 | 1,624,293,498,000 | 1,624,293,498,000 | 378,997,885 | 0 | 0 | BSD-2-Clause | 1,624,293,485,000 | 1,624,293,484,000 | null | UTF-8 | Lean | false | false | 3,110 | lean | import ..sql
import ..tactics
import ..u_semiring
import ..extra_constants
import ..meta.ucongr
import ..meta.TDP
set_option profiler true
open Expr
open Proj
open Pred
open SQL
open tree
open binary_operators
notation `int` := datatypes.int
variable integer_1: const datatypes.int
variable integer_2: const datatype... |
c209eeff9d55b0227582a5ca42bd6043d683ab75 | 649957717d58c43b5d8d200da34bf374293fe739 | /src/algebra/CommRing/colimits.lean | 5a5330e486713ae31c92c21dd82926acd320f83a | [
"Apache-2.0"
] | permissive | Vtec234/mathlib | b50c7b21edea438df7497e5ed6a45f61527f0370 | fb1848bbbfce46152f58e219dc0712f3289d2b20 | refs/heads/master | 1,592,463,095,113 | 1,562,737,749,000 | 1,562,737,749,000 | 196,202,858 | 0 | 0 | Apache-2.0 | 1,562,762,338,000 | 1,562,762,337,000 | null | UTF-8 | Lean | false | false | 12,141 | 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 algebra.CommRing.basic
import category_theory.limits.limits
universes u v
open category_theory
open category_theory.limits
-- [ROBOT VOICE]:
-- You shoul... |
58b24ac6f3a9639055a5c16421cfc87893b50333 | e0f9ba56b7fedc16ef8697f6caeef5898b435143 | /src/data/set/intervals/disjoint.lean | 72566e31b01bd649c16bc8e82d70a3cb8ab102bd | [
"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 | 1,353 | lean | /-
Copyright (c) 2019 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Yury Kudryashov
-/
import data.set.lattice
/-! # Extra lemmas about intervals
This file contains lemmas about intervals that cannot be included into `data.set.int... |
82efd3358bde78af195410af110debba5a0a9ebc | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/liftOverLeft.lean | 366a207108ff5b7ecbac2c79773acaaa0d1c2fd3 | [
"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 | 237 | lean | def foo1 : IO Unit := do
let f (x : IO.Ref Nat) : IO Nat :=
pure ((← x.get) + 1)
IO.println (IO.mkRef 10)
def foo2 : IO Unit := do
let rec f (x : IO.Ref Nat) : IO Nat :=
pure ((← x.get) + 1)
IO.println (IO.mkRef 10)
|
43c783062bf888568a7e999eb00cfae865d3fb6a | 367134ba5a65885e863bdc4507601606690974c1 | /src/geometry/manifold/tangent_functor_monad.lean | cec415eef29bbb521c39188d1639a21fc9a9e51f | [
"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 | 2,237 | lean | import geometry.manifold.basic_smooth_bundle
import geometry.manifold.mfderiv
noncomputable theory
universes u v w
section tangent_bundle_monad
variables {𝕜 : Type*} [nondiscrete_normed_field 𝕜]
{E E' : Type*} [normed_group E] [normed_group E'] [normed_space 𝕜 E] [normed_space 𝕜 E']
{H H' : Type*} [topological... |
12ae0ddc14a812c3ac124812f1a13195fbb56691 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/deprecated/subring.lean | ba4f799512f2512e65f6b4e57ce3185413e7299c | [
"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 | 8,083 | lean | /-
Copyright (c) 2018 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import deprecated.subgroup
import deprecated.group
import ring_theory.subring.basic
universes u v
open group
variables {R : Type u} [ring R]
/-- `S` is a subring:... |
9d17d6ceb873efcfd206306ae62eecbc7faca8ff | 46125763b4dbf50619e8846a1371029346f4c3db | /src/tactic/where.lean | 23adae81d8b27df5ca95d7e7ed11545abe187f12 | [
"Apache-2.0"
] | permissive | thjread/mathlib | a9d97612cedc2c3101060737233df15abcdb9eb1 | 7cffe2520a5518bba19227a107078d83fa725ddc | refs/heads/master | 1,615,637,696,376 | 1,583,953,063,000 | 1,583,953,063,000 | 246,680,271 | 0 | 0 | Apache-2.0 | 1,583,960,875,000 | 1,583,960,875,000 | null | UTF-8 | Lean | false | false | 7,995 | lean | /-
Copyright (c) 2019 Keeley Hoek. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Keeley Hoek
-/
import data.list.defs tactic.core
/-!
# The `where` command
When working in a Lean file with namespaces, parameters, and variables,
it can be confusing to identify what ... |
c8a2e68e8e358c20e74137716996ddb18bda1165 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/algebra/ring/ulift.lean | 5aef1a846f5a5deda32ac1a6ab53fccdf44d18f6 | [
"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 | 2,866 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import algebra.group.ulift
import data.equiv.ring
/-!
# `ulift` instances for ring
This file defines instances for ring, semiring and related structures on `ulift` ... |
ea2c56c5288efedc7c3bf55150c247fe8c125b63 | 91b8df3b248df89472cc0b753fbe2bac750aefea | /experiments/lean/src/ddl/embed.lean | c19f85c711e0d97a7c9ba7f5161f1e2c529b829e | [
"Apache-2.0",
"LicenseRef-scancode-unknown-license-reference"
] | permissive | yeslogic/fathom | eabe5c4112d3b4d5ec9096a57bb502254ddbdf15 | 3960a9466150d392c2cb103c5cb5fcffa0200814 | refs/heads/main | 1,685,349,769,736 | 1,675,998,621,000 | 1,675,998,621,000 | 28,993,871 | 214 | 11 | Apache-2.0 | 1,694,044,276,000 | 1,420,764,938,000 | Rust | UTF-8 | Lean | false | false | 1,252 | lean | /- Embedding as Lean terms -/
import ddl.binary.basic
import ddl.binary.kinding
namespace ddl
namespace host
open ddl.host
variables {ℓ : Type} [decidable_eq ℓ]
def type.embed : type ℓ → Type
| type.bool := bool
| type.nat := ℕ
| type.union_nil := empty
| (type.union_cons _ t... |
88651deaa71a48c7fda65c876e33e45aa50fe7b1 | 61ccc57f9d72048e493dd6969b56ebd7f0a8f9e8 | /src/analysis/normed_space/real_inner_product.lean | d33e36c7a78951c6def167c19af1eeec20689843 | [
"Apache-2.0"
] | permissive | jtristan/mathlib | 375b3c8682975df28f79f53efcb7c88840118467 | 8fa8f175271320d675277a672f59ec53abd62f10 | refs/heads/master | 1,651,072,765,551 | 1,588,255,641,000 | 1,588,255,641,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 22,032 | lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou
-/
import algebra.quadratic_discriminant
import analysis.special_functions.pow
import tactic.monotonicity
/-!
# Inner Product Space
This file defines real inner product... |
2d027d854bbff5276d234dbda65812ee30e88268 | a332e4934ff49f6c0a1af6799591f6694d9ccda6 | /sphinx/_Prime_KhanhDT.lean | 129d8616544d32dc49181da132adbed9281ee91a | [
"CC-BY-4.0"
] | permissive | khanhdt/formalabstracts | 295624d43b15275bf1acd03e6835b35d496bde42 | c25503700d85df0a592d681c8fdf3b8af6b9a759 | refs/heads/master | 1,584,616,983,167 | 1,528,963,872,000 | 1,528,963,872,000 | 136,273,754 | 0 | 0 | null | 1,528,260,960,000 | 1,528,260,960,000 | null | UTF-8 | Lean | false | false | 348 | lean | def isPrime (n: ℕ): Prop:=
(n≥2)∧ (∀m:ℕ, m≥1 ∧ m∣n→ (m=1 ∨ m=n))
def GoldBach (n:ℕ): Prop:=
(n>2) ∧ (2∣n)∧ (∃ p q: ℕ, isPrime p ∧ isPrime q ∧ n = p+q)
def TwinPrime: Prop:=
∀n:ℕ, ∃p: ℕ, p>n ∧ isPrime p ∧ isPrime (p+2)
def Opperman: Prop:=
∀n: ℕ, ∃p:ℕ, isPrime p ∧ p>n^2 ∧ p< (n+1)^2
|
b143f9d6bff294acda3876ec972a72f1baaa28a3 | 492a7e27d49633a89f7ce6e1e28f676b062fcbc9 | /src/monoidal_categories_reboot/dagger_category.lean | b9d3cbc3a1e87dc0a5c4364646ef4e3860baa3c7 | [
"Apache-2.0"
] | permissive | semorrison/monoidal-categories-reboot | 9edba30277de48a234b63813cf85b171772ce36f | 48b5f1d535daba4e591672042a298ac36be2e6dd | refs/heads/master | 1,642,472,396,149 | 1,560,587,477,000 | 1,560,587,477,000 | 156,465,626 | 0 | 1 | null | 1,541,549,278,000 | 1,541,549,278,000 | null | UTF-8 | Lean | false | false | 2,232 | lean | -- Copyright (c) 2018 Michael Jendrusch. All rights reserved.
import category_theory.category
import category_theory.functor
import category_theory.products
import category_theory.natural_isomorphism
import category_theory.tactics.obviously -- Give ourselves access to `rewrite_search`
import .braided_monoidal_category... |
0e0a6e1bee4dbdfa90613143a5bbee4095d4903b | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/topology/instances/real_vector_space.lean | e4eb9132a52c20c3103fa04501c3930f8001c062 | [
"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 | 1,524 | lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import topology.algebra.module
import topology.instances.real
/-!
# Continuous additive maps are `ℝ`-linear
In this file we prove that a continuous map `f : E →+ ... |
e1e590bcd6aaf4aacde7e18c408fdd9fce67029f | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/tactic/group.lean | 72f2e4409dd5afcdf2847f68e9f6cbbacd8a35a8 | [] | 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 | 3,243 | lean | /-
Copyright (c) 2020. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Patrick Massot
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.tactic.ring
import Mathlib.tactic.doc_commands
import Mathlib.PostPort
universes u_1
namespace Mathlib
... |
acaf78001805ff790df0b740ec94f99f3861ec98 | 46125763b4dbf50619e8846a1371029346f4c3db | /src/data/rel.lean | 5f6fcc793fd2f082ea597c4df9e80ce99b359651 | [
"Apache-2.0"
] | permissive | thjread/mathlib | a9d97612cedc2c3101060737233df15abcdb9eb1 | 7cffe2520a5518bba19227a107078d83fa725ddc | refs/heads/master | 1,615,637,696,376 | 1,583,953,063,000 | 1,583,953,063,000 | 246,680,271 | 0 | 0 | Apache-2.0 | 1,583,960,875,000 | 1,583,960,875,000 | null | UTF-8 | Lean | false | false | 6,481 | lean | /-
Copyright (c) 2018 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
Operations on set-valued functions, aka partial multifunctions, aka relations.
-/
import tactic.basic data.set.lattice order.complete_lattice logic.relator
variables {α ... |
87825c1fa64062218b97cbea9baeb5be342322b4 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/data/quot.lean | cd789cf1dbb0f6750d2b5ba83d189157527e9d52 | [
"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 | 22,663 | 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
/-!
# Quotient types
This module extends the core library's treatment of quotient types (`init.data.quot`).
## Tags
quotient
-/
variables {α... |
1471165ed8980457d1bd8997872e5273a2b99305 | 137c667471a40116a7afd7261f030b30180468c2 | /src/analysis/calculus/local_extr.lean | 228609e19b91834ca93117668b254d06b933744e | [
"Apache-2.0"
] | permissive | bragadeesh153/mathlib | 46bf814cfb1eecb34b5d1549b9117dc60f657792 | b577bb2cd1f96eb47031878256856020b76f73cd | refs/heads/master | 1,687,435,188,334 | 1,626,384,207,000 | 1,626,384,207,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 18,183 | lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import topology.local_extr
import topology.algebra.ordered.extend_from
import analysis.calculus.deriv
import topology.algebra.polynomial
/-!
# Local extrema of smo... |
83e85f3d91a7856dead2046fb1efc03970c3a374 | 1a9d3677cccdaaccacb163507570e75d34043a38 | /src/week_7/Part_C_back_to_Z.lean | 8b7162d7d4e4c6b3e08f725dfb45d3484d1131cf | [
"Apache-2.0"
] | permissive | alreadydone/formalising-mathematics | 687d386a72065795e784e270f5c05ea3948b67dd | 65869362cd7a2ac74dd1a97c7f9471835726570b | refs/heads/master | 1,680,260,936,332 | 1,616,563,371,000 | 1,616,563,371,000 | 348,780,769 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,758 | lean | import week_7.Part_A_quotients
import week_7.Part_B_universal_property
/-
# `Z ≃ ℤ`
Let's use the previous parts to show that Z and ℤ are isomorphic.
-/
-- Let's define pℤ to be the usual subtraction function ℕ² → ℤ
def pℤ (ab : N2) : ℤ := (ab.1 : ℤ) - ab.2
@[simp] lemma pℤ_def (a b : ℕ) : pℤ (a, b) = (a : ℤ) - ... |
b9b80799c0cfccb839ad15e623305bfa94963561 | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/qpf/multivariate/constructions/cofix.lean | 86158297c0881a460804db571b6a2d6668343e68 | [
"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 | 19,011 | 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 control.functor.multivariate
import data.pfunctor.multivariate.basic
import data.pfunctor.multivariate.M
import data.qpf.multivariate.basic
/-!
# T... |
65744630ddec3932aa4994506069b88670e434ba | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/preadditive/yoneda/basic.lean | 64cd6f6302f84937fef1f452a50abb13ff38307a | [
"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 | 5,462 | lean | /-
Copyright (c) 2022 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import category_theory.limits.yoneda
import category_theory.preadditive.opposite
import algebra.category.Module.basic
import algebra.category.Group.preadditive
/-!
# T... |
cb84fe3dd35049d4c1d826bc17bb66285e0b92c0 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/whenIO.lean | 4656f58c7797ae1d0a01b1da53997534e6ba9646 | [
"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 | 180 | lean | import system.io
open io
def iowhen (b : bool) (a : io unit) : io unit :=
if b = tt then a else return ()
#eval iowhen tt (put_str "hello\n")
#eval iowhen ff (put_str "error\n")
|
747f675a9ba66009e9078d194311ee0b1f136381 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/algebra/monoid_algebra/grading.lean | 66acf8d64ee7e4f6acb342024c6e9bb961d81e17 | [
"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 | 10,296 | lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import linear_algebra.finsupp
import algebra.monoid_algebra.basic
import algebra.direct_sum.internal
/-!
# Internal grading of an `add_monoid_algebra`
In this file, we sh... |
b67ee3f3388ea506f55f31173103bac7f348a56b | fcf3ffa92a3847189ca669cb18b34ef6b2ec2859 | /src/world1/level3.lean | 80c5fa4b2b402495e2f466bbd838f2bf81ad8029 | [
"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 | 171 | lean | import mynat.definition
namespace mynat
lemma example3 (a b : mynat) (h : succ a = b) : succ(succ(a)) = succ(b) :=
begin [nat_num_game]
rw h,
refl
end
end mynat |
ea9ff8ab3332f736cfc4f9f36c612f3a79d9a701 | 274261f7150b4ed5f1962f172c9357591be8a2b5 | /src/simple.lean | b86b60ef7fb37be169609a1b5a207d5829413e5d | [] | no_license | rspencer01/lean_representation_theory | 219ea1edf4b9897b2997226b54473e44e1538b50 | 2eef2b4b39d99d7ce71bec7bbc3dcc2f7586fcb5 | refs/heads/master | 1,588,133,157,029 | 1,571,689,957,000 | 1,571,689,957,000 | 175,835,785 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,866 | lean | import algebra.category.Module.basic
import .lattices
variables (R : Type) [ring R] {M : Module R}
def is_minimal {α : Type} [lattice.bounded_lattice α] (x : α) := x ≠ ⊥ ∧ ∀ y, y < x → y = ⊥
def inf_with_minimal_bot_or_idem {α : Type} [lattice.bounded_lattice α] (x y : α) : is_minimal x → (x ⊓ y = ⊥ ∨ x ⊓ y = x) :=... |
12b0b5a932da4df94cd0856c9c5a98094c3b2799 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/algebra/big_operators/order.lean | 130c609db875270892b57383f03f88225af25d86 | [
"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 | 20,733 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import algebra.big_operators.basic
/-!
# Results about big operators with values in an ordered algebraic structure.
Mostly monotonicity results for the `∏` and `∑`... |
c581f5f83dbfded3a88170c6e439d8a3d36d86f9 | 07f5f86b00fed90a419ccda4298d8b795a68f657 | /library/data/rbtree/min_max.lean | 944e4946da3ad7cc18adea2c35e18ee803939cc1 | [
"Apache-2.0"
] | permissive | VBaratham/lean | 8ec5c3167b4835cfbcd7f25e2173d61ad9416b3a | 450ca5834c1c35318e4b47d553bb9820c1b3eee7 | refs/heads/master | 1,629,649,471,814 | 1,512,060,373,000 | 1,512,060,469,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,804 | 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
-/
import data.rbtree.basic
universe u
/- TODO(Leo): remove after we cleanup stdlib simp lemmas -/
local attribute [-simp] or.comm or.left_comm or.assoc and.c... |
94dab0d3b1f1c047b366c0a408e3f46e7d9e007a | 4727251e0cd73359b15b664c3170e5d754078599 | /src/analysis/normed_space/pointwise.lean | 5868265fa1dc5c638e00e267d44416e5c45cb173 | [
"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 | 16,320 | lean | /-
Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Yaël Dillies
-/
import analysis.normed.group.pointwise
import analysis.normed_space.basic
/-!
# Properties of pointwise scalar multiplication of sets in normed s... |
f51dea17b96e745b48d4d333f2eec14d9f35afcd | 4727251e0cd73359b15b664c3170e5d754078599 | /src/order/bounded_order.lean | a05d1341844d9865d46a876178c442029911a8cb | [
"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 | 54,189 | 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.option.basic
import logic.nontrivial
import order.lattice
import order.max
import tactic.pi_instances
/-!
# ⊤ and ⊥, bounded lattices and variants
This ... |
1c2a267cc16ad5e50137afc381777861fd35824c | da3a76c514d38801bae19e8a9e496dc31f8e5866 | /library/init/meta/pexpr.lean | 35049feea9cd00f870cce62b489a5b4691700ae0 | [
"Apache-2.0"
] | permissive | cipher1024/lean | 270c1ac5781e6aee12f5c8d720d267563a164beb | f5cbdff8932dd30c6dd8eec68f3059393b4f8b3a | refs/heads/master | 1,611,223,459,029 | 1,487,566,573,000 | 1,487,566,573,000 | 83,356,543 | 0 | 0 | null | 1,488,229,336,000 | 1,488,229,336,000 | null | UTF-8 | Lean | false | false | 1,289 | 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.meta.expr
universe u
@[reducible] def pos := nat × nat
/- Quoted expressions. They can be converted into expressions by using a tactic... |
1adfa636aa4992ccf42950cb025a63316d99137f | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/algebra/category/Module/basic.lean | 293a1a9f818013cf389ef3a8f48d81a01480c909 | [
"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 | 5,865 | lean | /-
Copyright (c) 2019 Robert A. Spencer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert A. Spencer, Markus Himmel
-/
import algebra.module
import algebra.punit_instances
import algebra.category.Group.basic
import category_theory.concrete_category
import category... |
3ce17ea77068efcd305c542f1bfdd71928a23193 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/topology/metric_space/lipschitz.lean | cb70388974d66b6ce2bc542cf095e486f7934b01 | [
"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 | 25,226 | lean | /-
Copyright (c) 2018 Rohan Mitta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rohan Mitta, Kevin Buzzard, Alistair Tucker, Johannes Hölzl, Yury Kudryashov
-/
import logic.function.iterate
import data.set.intervals.proj_Icc
import topology.metric_space.basic
import ... |
3796906b6078ee37f30122c5d2df91b982d705de | 4727251e0cd73359b15b664c3170e5d754078599 | /src/algebra/category/Algebra/limits.lean | 19c423b60363eed709b9e8141a090bbc231d39a4 | [
"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 | 5,804 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import algebra.category.Algebra.basic
import algebra.category.Module.limits
import algebra.category.Ring.limits
/-!
# The category of R-algebras has all limits
Furt... |
707c6cd438432a414825b3d293f3e4bd2697a2cd | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/algebra/group_power/lemmas.lean | f0a68fadcf617da412e29fe4f7834012cc33e03b | [
"Apache-2.0"
] | permissive | waynemunro/mathlib | e3fd4ff49f4cb43d4a8ded59d17be407bc5ee552 | 065a70810b5480d584033f7bbf8e0409480c2118 | refs/heads/master | 1,693,417,182,397 | 1,634,644,781,000 | 1,634,644,781,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 35,941 | lean | /-
Copyright (c) 2015 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Robert Y. Lewis
-/
import algebra.group_power.basic
import algebra.invertible
import algebra.opposites
import data.list.basic
import data.int.cast
import data.equiv.basic... |
8a0cb6d88cb4f553d73b3ccbbc93cbf592c2ab8e | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/zsqrtd/gaussian_int_auto.lean | 42fe2887050a91f53eb5533f6ca85d0fd432145d | [] | 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 | 8,824 | lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Chris Hughes
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.zsqrtd.basic
import Mathlib.data.complex.basic
import Mathlib.ring_theory.principal_ideal_d... |
cef321f5aacbd392ff52a5adcf95b8f8446b668b | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/topology/algebra/uniform_filter_basis.lean | 58df1cd45c0b80d746b49873a7c4c0dd89fdfde9 | [
"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 | 1,973 | lean | /-
Copyright (c) 2021 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import topology.algebra.filter_basis
import topology.algebra.uniform_group
/-!
# Uniform properties of neighborhood bases in topological algebra
> THIS FILE IS SYN... |
9aea31114adefe46f30db13dda45d415db4d7bf9 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/data/mv_polynomial/funext.lean | 5d097fb19d654af3d87742433a50b4d96b76d61b | [
"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 | 3,409 | 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 data.polynomial.ring_division
import data.mv_polynomial.rename
import ring_theory.polynomial.basic
/-!
## Function extensionality for multivariate polynomials... |
4873748925b11db1d874e7cf2387defbe7d6c2cc | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/data/fintype/card.lean | ba0f552678cb3c3ce40f4e886d1cd39543484cc4 | [
"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 | 17,310 | 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.fintype.basic
import algebra.big_operators.ring
/-!
Results about "big operations" over a `fintype`, and consequent
results about cardinalities of certai... |
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