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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
ffef1561b7a36df59a33aa850718dcfbf088e50c | 9b9a16fa2cb737daee6b2785474678b6fa91d6d4 | /src/topology/metric_space/cau_seq_filter.lean | 520cd1ee8ad8e9518a1d83d5a79abd1edc1f041e | [
"Apache-2.0"
] | permissive | johoelzl/mathlib | 253f46daa30b644d011e8e119025b01ad69735c4 | 592e3c7a2dfbd5826919b4605559d35d4d75938f | refs/heads/master | 1,625,657,216,488 | 1,551,374,946,000 | 1,551,374,946,000 | 98,915,829 | 0 | 0 | Apache-2.0 | 1,522,917,267,000 | 1,501,524,499,000 | Lean | UTF-8 | Lean | false | false | 16,303 | lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Sébastien Gouëzel
Characterize completeness of metric spaces in terms of Cauchy sequences.
In particular, reconcile the filter notion of Cauchy-ness with the cau_seq ... |
3e35be8513da1fa978fb9255a60e0d36d73aca07 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/termination_by2.lean | cc801d0452c3c301e2cee09ecb17cacbc793ccf5 | [
"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 | 994 | lean | mutual
def f (n : Nat) :=
if n == 0 then 0 else f (n / 2) + 1
termination_by _ => n
end
def g' (n : Nat) :=
match n with
| 0 => 1
| n+1 => g' n * 3
termination_by
g' n => n
_ n => n
mutual
def isEven : Nat → Bool
| 0 => true
| n+1 => isOdd n
def isOdd : Nat → Bool
| 0 => false
| n+1... |
08f1e1af159348e952e60195ab7b9c8a284352e5 | 7b02c598aa57070b4cf4fbfe2416d0479220187f | /algebra/group_constructions.hlean | d7c9a36e118171ab39aef515e8c6a99d5d3afb74 | [
"Apache-2.0"
] | permissive | jdchristensen/Spectral | 50d4f0ddaea1484d215ef74be951da6549de221d | 6ded2b94d7ae07c4098d96a68f80a9cd3d433eb8 | refs/heads/master | 1,611,555,010,649 | 1,496,724,191,000 | 1,496,724,191,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,285 | 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, Egbert Rijke
Constructions with groups
-/
import .free_commutative_group
open eq algebra is_trunc sigma sigma.ops prod trunc function equiv
namespace group
va... |
bdeccfb73dd4f4682291b8a794123770bf0f620a | f20db13587f4dd28a4b1fbd31953afd491691fa0 | /leanpkg/leanpkg/lean_version.lean | 3375e36f37b065f60dfff363f801c787b579457a | [
"Apache-2.0"
] | permissive | AHartNtkn/lean | 9a971edfc6857c63edcbf96bea6841b9a84cf916 | 0d83a74b26541421fc1aa33044c35b03759710ed | refs/heads/master | 1,620,592,591,236 | 1,516,749,881,000 | 1,516,749,881,000 | 118,697,288 | 1 | 0 | null | 1,516,759,470,000 | 1,516,759,470,000 | null | UTF-8 | Lean | false | false | 542 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Gabriel Ebner
-/
namespace leanpkg
def lean_version_string_core :=
let (major, minor, patch) := lean.version in
sformat!("{major}.{minor}.{patch}")
def lean_version_string :=
i... |
b051431800db3ce89947b6e8112c5b08cb8000b1 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/group_power/identities.lean | a5f1ea7d3902b6bf3f161368db793f7839d14ea5 | [
"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 | 3,367 | lean | /-
Copyright (c) 2020 Bryan Gin-ge Chen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bryan Gin-ge Chen, Kevin Lacker
-/
import tactic.ring
/-!
# Identities
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> https://github.com/leanprover-community/mathlib4/pull/531
> Any... |
6da058a80512c2dad8073253719e6a46a92d6ba3 | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/linear_algebra/basic.lean | 5ebcea554dcabbfcaec37110d741bcef4ae687cc | [
"Apache-2.0"
] | permissive | hikari0108/mathlib | b7ea2b7350497ab1a0b87a09d093ecc025a50dfa | a9e7d333b0cfd45f13a20f7b96b7d52e19fa2901 | refs/heads/master | 1,690,483,608,260 | 1,631,541,580,000 | 1,631,541,580,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 122,452 | 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, Kevin Buzzard, Yury Kudryashov
-/
import algebra.big_operators.pi
import algebra.module.prod
import algebra.module.submodule_lattice
import data.dfinsup... |
b63cb0919a3474b616662e99d2f46e8d70e67420 | 137c667471a40116a7afd7261f030b30180468c2 | /src/data/list/basic.lean | 4caf35a1c18e03933a6c042ca44a5c67eaaec68b | [
"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 | 195,128 | 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 control.monad.basic
import data.nat.basic
import order.rel_classes
import algebra.group... |
46ce8d60b0ebe5db484a4c23a40f2212673b46f5 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/playground/gen.lean | 33f4e3715347726fc3870fcb10917f465a476384 | [
"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 | 241 | lean | def main (xs : List String) : IO UInt32 :=
let n := xs.head.toNat in
IO.println "prelude\ninductive Bool : Type\n| ff : Bool\n| tt : Bool\n\n" *>
Nat.mrepeat n (λ i, IO.println ("theorem x" ++ toString i ++ " : Bool := Bool.tt")) *>
pure 0
|
5969beab82fe71f377186a67e76bde616578388e | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/int/dvd/basic.lean | 2905eb1a1494e651784361dc160076d3d2cd807f | [
"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 | 2,636 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
-/
import data.int.order.basic
import data.nat.cast.basic
/-!
# Basic lemmas about the divisibility relation in `ℤ`.
-/
open nat
namespace int
@[norm_cast] theorem coe... |
ea41ba1df2041df84658673b8cf7ef652f2bc092 | f3849be5d845a1cb97680f0bbbe03b85518312f0 | /tests/lean/run/meta_env1.lean | c1ed2743a2e8d1cb12cc07c2a2ca9e85f573446c | [
"Apache-2.0"
] | permissive | bjoeris/lean | 0ed95125d762b17bfcb54dad1f9721f953f92eeb | 4e496b78d5e73545fa4f9a807155113d8e6b0561 | refs/heads/master | 1,611,251,218,281 | 1,495,337,658,000 | 1,495,337,658,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,053 | lean | open list
meta definition e := environment.mk_std 0
definition hints := reducibility_hints.regular 10 tt
#eval environment.trust_lvl e
#eval (environment.add e (declaration.defn `foo []
(expr.sort (level.succ (level.zero)))
(e... |
dbb5b105f261e52ef95535cd2c67ad022f5a7c62 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/topology/uniform_space/compact_convergence.lean | 357eee4ebcf10a620a03fe37a26af688f487563b | [
"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 | 22,082 | 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 topology.compact_open
import topology.uniform_space.uniform_convergence
/-!
# Compact convergence (uniform convergence on compact sets)
Given a topological space `... |
519fbad2b275ddf357ffb83dec3a77a1398b6b94 | 947b78d97130d56365ae2ec264df196ce769371a | /stage0/src/Lean/Compiler/IR/Checker.lean | f6db9b5d6342a47dd2b3175ecae4c08992232e7e | [
"Apache-2.0"
] | permissive | shyamalschandra/lean4 | 27044812be8698f0c79147615b1d5090b9f4b037 | 6e7a883b21eaf62831e8111b251dc9b18f40e604 | refs/heads/master | 1,671,417,126,371 | 1,601,859,995,000 | 1,601,860,020,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,620 | 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.Compiler.IR.CompilerM
import Lean.Compiler.IR.Format
namespace Lean
namespace IR
namespace Checker
structure CheckerContext :=
(env : Environ... |
cc2e41011c6c6f607422ce53f934a3c07fc06dc8 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/elab6.lean | 84caa3b3dfeebfc39b0db810f7a6299ebcbdbdb7 | [
"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 | 286 | lean | constant R : nat → nat → Prop
constant H : transitive R
set_option pp.all true
constant F : ∀ {A : Type*} ⦃a : A⦄ {b : A} (c : A) ⦃e : A⦄, A → A → A
check H
check F
check F tt
check F tt tt
check F tt tt tt
check H
check F
check F tt
check F tt tt
check F tt tt tt
|
b8c464279cd51de8c1fecc043d9401b05028d2b7 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/order/symm_diff.lean | 5ed2553718d3c6328edeba31f8a3a4413432a512 | [
"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 | 9,111 | lean | /-
Copyright (c) 2021 Bryan Gin-ge Chen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz, Bryan Gin-ge Chen
-/
import order.boolean_algebra
/-!
# Symmetric difference
The symmetric difference or disjunctive union of sets `A` and `B` is the set of elements ... |
90d3ef18f8dfee1d89cabdeb58564427c05330bd | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/InternalExceptionId.lean | 0b72bad7ed75f4720820d040a36b5d91d7ea4325 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 1,506 | 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
-/
namespace Lean
/-- Internal exception identifier -/
structure InternalExceptionId where
idx : Nat := 0
deriving Inhabited, BEq
/-- Internal exceptions... |
c2864d23374d583f678fdea161cd7c23fb474e4d | ce6917c5bacabee346655160b74a307b4a5ab620 | /src/ch4/ex0603.lean | d01ac2028e81af1595b301d8c6a1c473b5430899 | [] | no_license | Ailrun/Theorem_Proving_in_Lean | ae6a23f3c54d62d401314d6a771e8ff8b4132db2 | 2eb1b5caf93c6a5a555c79e9097cf2ba5a66cf68 | refs/heads/master | 1,609,838,270,467 | 1,586,846,743,000 | 1,586,846,743,000 | 240,967,761 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 394 | lean | variables (men : Type) (barber : men)
variable (shaves : men → men → Prop)
example (h : ∀ x : men, shaves barber x ↔ ¬ shaves x x) : false :=
have hb : shaves barber barber ↔ ¬ shaves barber barber, from h barber,
have ¬ shaves barber barber, from
assume : shaves barber barber,
hb.mp this this,
‹¬ shave... |
092bb91756cfd85124e07ce1200f8ffc11ea78a5 | f4bff2062c030df03d65e8b69c88f79b63a359d8 | /src/game/topology/continuity.lean | 492b7f56abea9d95846ada3bf65be19c63344607 | [
"Apache-2.0"
] | permissive | adastra7470/real-number-game | 776606961f52db0eb824555ed2f8e16f92216ea3 | f9dcb7d9255a79b57e62038228a23346c2dc301b | refs/heads/master | 1,669,221,575,893 | 1,594,669,800,000 | 1,594,669,800,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,339 | lean | import data.real.basic
import topology.basic
namespace xena -- hide
open function
open real
open set
/-
Classic eps-delta definition of continuity equivalent to topological definition.
Work in progress.
-/
notation `|` x `|` := abs x
def continuous_at_x (f : ℝ → ℝ) (x : ℝ) :=
∀ ε : ℝ, 0 < ε → ∃ δ : ℝ, 0 < δ ... |
dd181b070aef01307e680d326f35699c81ec05b6 | 4a092885406df4e441e9bb9065d9405dacb94cd8 | /src/valuation/field.lean | 0c781cd5366aa7d54aae86ce99cf0647f9d48b1b | [
"Apache-2.0"
] | permissive | semorrison/lean-perfectoid-spaces | 78c1572cedbfae9c3e460d8aaf91de38616904d8 | bb4311dff45791170bcb1b6a983e2591bee88a19 | refs/heads/master | 1,588,841,765,494 | 1,554,805,620,000 | 1,554,805,620,000 | 180,353,546 | 0 | 1 | null | 1,554,809,880,000 | 1,554,809,880,000 | null | UTF-8 | Lean | false | false | 3,902 | lean | import for_mathlib.topological_field
import for_mathlib.topology
import for_mathlib.division_ring
import valuation.topology
local attribute [instance, priority 0] classical.decidable_linear_order
variables {Γ : Type*} [linear_ordered_comm_group Γ]
def valued_ring (R : Type*) [ring R] (v : valuation R Γ) := R
names... |
1bb4604178911bbcbe1589435e530c898b1ed7d9 | 5ae26df177f810c5006841e9c73dc56e01b978d7 | /src/data/set/intervals.lean | 61814df6b8de9a1ff1a334cc4c0335220acfcf92 | [
"Apache-2.0"
] | permissive | ChrisHughes24/mathlib | 98322577c460bc6b1fe5c21f42ce33ad1c3e5558 | a2a867e827c2a6702beb9efc2b9282bd801d5f9a | refs/heads/master | 1,583,848,251,477 | 1,565,164,247,000 | 1,565,164,247,000 | 129,409,993 | 0 | 1 | Apache-2.0 | 1,565,164,817,000 | 1,523,628,059,000 | Lean | UTF-8 | Lean | false | false | 11,989 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot
Intervals
Naming conventions:
`i`: infinite
`o`: open
`c`: closed
Each interval has the name `I` + letter for left side + letter... |
74be7e3d3e362a00ef4d268d80fc6a0773c25794 | d436468d80b739ba7e06843c4d0d2070e43448e5 | /src/algebra/category/CommRing/basic.lean | 1952cb6b49545bb6e2fdf8246a0066394598d207 | [
"Apache-2.0"
] | permissive | roro47/mathlib | 761fdc002aef92f77818f3fef06bf6ec6fc1a28e | 80aa7d52537571a2ca62a3fdf71c9533a09422cf | refs/heads/master | 1,599,656,410,625 | 1,573,649,488,000 | 1,573,649,488,000 | 221,452,951 | 0 | 0 | Apache-2.0 | 1,573,647,693,000 | 1,573,647,692,000 | null | UTF-8 | Lean | false | false | 6,001 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Johannes Hölzl, Yury Kudryashov
-/
import algebra.category.Group
import category_theory.fully_faithful
import algebra.ring
import data.int.basic
/-!
# Category instan... |
945fe11de788a11f27cb50308e2f423e6812caae | e38e95b38a38a99ecfa1255822e78e4b26f65bb0 | /src/certigrad/aevb/mnist.lean | 66edba159e12b91e3d83c51354396084b2279cbf | [
"Apache-2.0"
] | permissive | ColaDrill/certigrad | fefb1be3670adccd3bed2f3faf57507f156fd501 | fe288251f623ac7152e5ce555f1cd9d3a20203c2 | refs/heads/master | 1,593,297,324,250 | 1,499,903,753,000 | 1,499,903,753,000 | 97,075,797 | 1 | 0 | null | 1,499,916,210,000 | 1,499,916,210,000 | null | UTF-8 | Lean | false | false | 2,892 | lean | /-
Copyright (c) 2017 Daniel Selsam. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Daniel Selsam
Script to run AEVB on MNIST.
-/
import system.io ..program ..prove_model_ok .util .prog ..run_utils
namespace certigrad
namespace aevb
open io
meta def load_mnist_datas... |
51cf6d125ebdc1e2ef1ba57e00b85e151fca718b | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Elab/Notation.lean | 4771a3e138ef87036e678c16db1469f6eee1371e | [
"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 | 7,774 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Elab.Syntax
import Lean.Elab.AuxDef
import Lean.Elab.BuiltinNotation
namespace Lean.Elab.Command
open Lean.Syntax
open Lean.Parser.Term hiding ... |
53b2e99225c4465c4673f5f51c479fb259245004 | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/category_theory/opposites.lean | f77dd3381a0d1cc2271405f151e595ac99c0afb6 | [
"Apache-2.0"
] | permissive | agjftucker/mathlib | d634cd0d5256b6325e3c55bb7fb2403548371707 | 87fe50de17b00af533f72a102d0adefe4a2285e8 | refs/heads/master | 1,625,378,131,941 | 1,599,166,526,000 | 1,599,166,526,000 | 160,748,509 | 0 | 0 | Apache-2.0 | 1,544,141,789,000 | 1,544,141,789,000 | null | UTF-8 | Lean | false | false | 9,650 | 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
import data.opposite
universes v₁ v₂ u₁ u₂ -- declare the `v`'s first; see `category_... |
b00efc60088bf16ad7f278f26a1337115e505ca0 | 367134ba5a65885e863bdc4507601606690974c1 | /src/tactic/omega/lin_comb.lean | b263c71427841488d29a293e852d01e4b11fa7be | [
"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 | 2,161 | 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 combination of constraints.
-/
import tactic.omega.clause
namespace omega
/-- Linear combination of constraints. The second
argument is the list of constraints... |
f430d3728aaddb8b6be8cba21cabb26195eaad2c | ddac945a109b79a5c5b9b3b94ecd42f87d9a8e00 | /lean/leftpad.lean | 8bb8f9c00b448fd36d2c54197931ffde11fa35c6 | [
"LicenseRef-scancode-unknown-license-reference",
"CC0-1.0"
] | permissive | cipher1024/lets-prove-leftpad | f21a2caa0d7d7c7881ebab9e8a8d281e01e2f2f0 | a79d7f5c01817ab519f9b489436667d526e5a968 | refs/heads/master | 1,584,568,854,244 | 1,527,612,383,000 | 1,527,612,383,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,632 | lean |
import data.list.basic
section left_pad
variables {α : Type*}
open nat
lemma list.cons_repeat (c : α) :
Π (n : ℕ), c :: list.repeat c n = list.repeat c n ++ [c] :=
by { intro, symmetry, induction n ; simp *, }
lemma list.take_append (xs ys : list α) (n : ℕ)
(h : xs.length = n) :
(xs ++ ys).take n = xs :=
b... |
2e3432fbed4ffaa09dfa8dfab81a9d6eb2160aec | ae1e94c332e17c7dc7051ce976d5a9eebe7ab8a5 | /stage0/src/Init/System/ST.lean | cad11f39bff651af421893e3ca6c3f5e45accbc8 | [
"Apache-2.0"
] | permissive | dupuisf/lean4 | d082d13b01243e1de29ae680eefb476961221eef | 6a39c65bd28eb0e28c3870188f348c8914502718 | refs/heads/master | 1,676,948,755,391 | 1,610,665,114,000 | 1,610,665,114,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,435 | 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
-/
prelude
import Init.Classical
import Init.Control.EState
import Init.Control.Reader
def EST (ε : Type) (σ : Type) : Type → Type := EStateM ε σ
abbrev ST (σ... |
8d1d2500a01a91f683fd16f444db061c9a8bcb21 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/data/nat/sqrt.lean | 1be8fc95f22910920197b5137a31a114219adc50 | [
"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 | 7,196 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Johannes Hölzl, Mario Carneiro
-/
import data.int.basic
/-!
# Square root of natural numbers
An efficient binary implementation of a (`sqrt n`) function that... |
fdd3bc32c9c93d08c19ef0ac950dde75cbf4b226 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/number_theory/ramification_inertia.lean | 25762372a3867e05ed81fa168ffe5631cc18a14a | [
"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 | 7,504 | lean | /-
Copyright (c) 2022 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import algebra.is_prime_pow
import field_theory.separable
import linear_algebra.free_module.finite.rank
import linear_algebra.free_module.pid
import linear_algebra.matrix.... |
bfa0ef5bcad85a4619ae6bc72b71008aaf436785 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/interactive/hover.lean | cc9e69cac5be8bb8299d5e0275a334161bc3a1cc | [
"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 | 6,060 | lean | import Lean
example : True := by
apply True.intro
--^ textDocument/hover
example : True := by
simp [True.intro]
--^ textDocument/hover
example (n : Nat) : True := by
match n with
| Nat.zero => _
--^ textDocument/hover
| n + 1 => _
/-- My tactic -/
macro "mytac" o:"only"? e:term : tactic => ... |
b8d152ec6f16559e1a3d9965263a4e7a8aa5b2c5 | 492a7e27d49633a89f7ce6e1e28f676b062fcbc9 | /src/monoidal_categories_reboot/rigid_monoidal_category.lean | 8157c4b949e5035ac4096e2b16a21d5290566281 | [
"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 | 2,492 | lean | -- Copyright (c) 2018 Michael Jendrusch. All rights reserved.
import .braided_monoidal_category
universes v u
namespace category_theory
open monoidal_category
class right_duality {C : Sort u} (A A' : C) [monoidal_category.{v} C] :=
(right_unit : tensor_unit C ⟶ A ⊗ A')
(right_counit : A' ⊗ A ⟶ tensor_un... |
f4b223e852393a85616718a7474b13b020147bf3 | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/topology/sheaves/sheaf_condition/equalizer_products.lean | e47dd295feb3cbbae53ebf58daba9903dcbb62b4 | [
"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 | 8,454 | 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 topology.sheaves.presheaf
import category_theory.limits.punit
import category_theory.limits.shapes.products
import category_theory.limits.shapes.equalizers
imp... |
41f5cb9487d456e3693b130df108f32261322961 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/lst64.lean | e5736b60ebf43c951c30f80654fa3691825656d4 | [
"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 | 2,817 | lean | def mylist : list ℕ :=
#[
0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31
,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31
,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31
,0,1,2,3,4,5,6,7,8,9,10,11,12,13,... |
8f948211fe34efc19949a5f2c537ee6558b4a450 | a4673261e60b025e2c8c825dfa4ab9108246c32e | /tests/lean/syntaxInNamespacesAndPP.lean | 0bce0325fe0f3e9a674627015688bce8e1055d2c | [
"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 | 278 | lean | namespace Foo
syntax "foo" term : term
macro_rules
| `(foo $x) => x
set_option trace.Elab true in
#check foo true
end Foo
namespace Bla
syntax[bla] "bla" term : term
macro_rules
| `(bla $x) => x
set_option trace.Elab true in
#check bla true
#print Bla.bla
end Bla
|
5c02012d4a3a56aaa3df76c34172d373c4c8e3cc | 3618c6e11aa822fd542440674dfb9a7b9921dba0 | /scratch/lsemidirect_product.lean | cbb23fa4751c591a8cb793ea8d0c05ed01bffd0e | [] | no_license | ChrisHughes24/single_relation | 99ceedcc02d236ce46d6c65d72caa669857533c5 | 057e157a59de6d0e43b50fcb537d66792ec20450 | refs/heads/master | 1,683,652,062,698 | 1,683,360,089,000 | 1,683,360,089,000 | 279,346,432 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,225 | lean | /-
Copyright (c) 2020 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import data.equiv.mul_add logic.function.basic group_theory.subgroup
/-!
# Semidirect product
This file defines semidirect products of groups, and the canonical maps in ... |
bba2dbe2eb3f72066f5b4ddc06a66f071a2c4ccd | d1a52c3f208fa42c41df8278c3d280f075eb020c | /tests/lean/448.lean | aefaf7c764bbd74a0cc20802c0e7d643a475861d | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | cipher1024/lean4 | 6e1f98bb58e7a92b28f5364eb38a14c8d0aae393 | 69114d3b50806264ef35b57394391c3e738a9822 | refs/heads/master | 1,642,227,983,603 | 1,642,011,696,000 | 1,642,011,696,000 | 228,607,691 | 0 | 0 | Apache-2.0 | 1,576,584,269,000 | 1,576,584,268,000 | null | UTF-8 | Lean | false | false | 901 | lean | namespace TryCatchWithAutolift
structure M (α : Type) where
σ : ExceptT String IO α
instance : Monad M where
pure x := { σ := pure x }
bind x f := { σ := do (f (← x.σ)).σ }
map f x := { σ := do f (← x.σ) }
instance : MonadLiftT IO M where
monadLift {α : Type} (act : IO α) : M α :=
{ σ := monadLift a... |
7fcf17fa81499fd88d2cf83d8381af165c0162c4 | 097294e9b80f0d9893ac160b9c7219aa135b51b9 | /instructor/predicate_logic/induction.lean | c21d02f087c7222e1b522b317e93d1e9aced280e | [] | 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 | 4,500 | lean | /-
Proof strategies.
- direct proof: use established facts
- by negation: to prove ¬ P, assume P;
show that this yields a contradiction,
from which a proof of false can then
be derived. This shows P → false, and
that is the definition of ¬ P.
Prove that the square root of two is
irrational.
Prove tha... |
64d448f802cfd5288f6fdf16f19381f6130fd947 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/number_theory/class_number/admissible_card_pow_degree.lean | f654d2a66f7c00a4e8df45ccc0619af799eba1b4 | [
"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 | 13,910 | 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 number_theory.class_number.admissible_absolute_value
import analysis.special_functions.pow
import ring_theory.ideal.local_ring
import data.polynomial.degree.card_pow... |
f2aa9aa134740044532a9c3e2976a2a11c7a2c58 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/algebra/char_p/quotient.lean | 82a92b2177d803182d5620451852228561f395ec | [
"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 | 1,451 | lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Eric Wieser
-/
import algebra.char_p.basic
import algebra.ring_quot
/-!
# Characteristic of quotients rings
-/
universes u v
namespace char_p
theorem quotient (R : Type u) [... |
284f262de3aacf87821130cde9f295fd79b3b435 | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/data/vector2.lean | 103b302bec083bc60745fcf25126537d8437861c | [
"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 | 10,717 | 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
import data.list.nodup
import data.list.of_fn
import control.applicative
universes u
variables {n : ... |
4bc5e9df06586a2109d98871155b29117b2fde0c | 88fb7558b0636ec6b181f2a548ac11ad3919f8a5 | /tests/lean/whnf_core1.lean | c83718c611e812be709223f643404397977064af | [
"Apache-2.0"
] | permissive | moritayasuaki/lean | 9f666c323cb6fa1f31ac597d777914aed41e3b7a | ae96ebf6ee953088c235ff7ae0e8c95066ba8001 | refs/heads/master | 1,611,135,440,814 | 1,493,852,869,000 | 1,493,852,869,000 | 90,269,903 | 0 | 0 | null | 1,493,906,291,000 | 1,493,906,291,000 | null | UTF-8 | Lean | false | false | 337 | lean | open tactic
definition f (a : nat) := a + 2
attribute [reducible]
definition g (a : nat) := a + 2
example (a : nat) : true :=
by do
to_expr `(f a) >>= whnf >>= trace,
to_expr `(g a) >>= whnf >>= trace,
to_expr `(f a) >>= (λ e, whnf e reducible) >>= trace,
to_expr `(g a) >>= (λ e, whnf e reducible) >>= trace,... |
4fbf73e4fc63a843a973912ceb60d0f20582db05 | 94637389e03c919023691dcd05bd4411b1034aa5 | /src/zzz_junk/04_type_library/03_typeUniverses.lean | 8fde435cc2108d111343b3d6d2158c5352a4b248 | [] | no_license | kevinsullivan/complogic-s21 | 7c4eef2105abad899e46502270d9829d913e8afc | 99039501b770248c8ceb39890be5dfe129dc1082 | refs/heads/master | 1,682,985,669,944 | 1,621,126,241,000 | 1,621,126,241,000 | 335,706,272 | 0 | 38 | null | 1,618,325,669,000 | 1,612,374,118,000 | Lean | UTF-8 | Lean | false | false | 2,948 | lean | /-
Lean's type hierarchy
-/
namespace hidden1
structure box (α : Type) : Type :=
(val : α)
def b3 : box nat := box.mk 3
/-
Every term has a type.
Types are terms, too.
The type of 3 is ℕ.
ℕ is a type, so it has a type.
The type of ℕ (#check) is Type.
So here's a picture so far.
Type (aka Type 0)
... |
5dbaed00e7b8478bdd13c8e35ca547cca733eac1 | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/finset/sort.lean | 7ce7a0e0508f8c1b6573bbb3957c96ddb5861c8c | [
"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 | 8,350 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
-/
import data.finset.lattice
import data.multiset.sort
import data.list.nodup_equiv_fin
/-!
# Construct a sorted list from a finset.
-/
namespace finset
open multiset... |
e3b31b2d2ca4cd02ebb2d62b2af8d4f0adc0af81 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/set/finite.lean | d52c32394fa31f41a793ec50cf123e3a4528b5bd | [
"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 | 51,031 | 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, Kyle Miller
-/
import data.finset.sort
import data.set.functor
import data.finite.basic
/-!
# Finite sets
This file defines predicates for finite and ... |
edbf7274abce707b31b9894957f9ed6f2bcfd484 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/model_theory/syntax.lean | 7d7c4c35869aaf3d606a366c944b3d885ad69400 | [
"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 | 35,949 | lean | /-
Copyright (c) 2021 Aaron Anderson, Jesse Michael Han, Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson, Jesse Michael Han, Floris van Doorn
-/
import data.list.prod_sigma
import data.set.prod
import logic.equiv.fin
import model_theory.... |
63ee8c2886c11cd77cd3afcfb0adf5a41f7b1308 | a7dd8b83f933e72c40845fd168dde330f050b1c9 | /src/analysis/asymptotics.lean | d4a76437b72ac817577bebe858ab55080e904ad8 | [
"Apache-2.0"
] | permissive | NeilStrickland/mathlib | 10420e92ee5cb7aba1163c9a01dea2f04652ed67 | 3efbd6f6dff0fb9b0946849b43b39948560a1ffe | refs/heads/master | 1,589,043,046,346 | 1,558,938,706,000 | 1,558,938,706,000 | 181,285,984 | 0 | 0 | Apache-2.0 | 1,568,941,848,000 | 1,555,233,833,000 | Lean | UTF-8 | Lean | false | false | 29,269 | lean | /-
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad
We introduce these relations:
`is_O f g l` : "f is big O of g along l"
`is_o f g l` : "f is little o of g along l"
Here `l` is any filter on the domain of `f` and `g... |
5b933f03af8511ccb1fe87ceddf7535d2de6114d | b32d3853770e6eaf06817a1b8c52064baaed0ef1 | /src/super/inferences/demod.lean | f1da85a6cf70cf7967884e10df31bc048464aecc | [] | no_license | gebner/super2 | 4d58b7477b6f7d945d5d866502982466db33ab0b | 9bc5256c31750021ab97d6b59b7387773e54b384 | refs/heads/master | 1,635,021,682,021 | 1,634,886,326,000 | 1,634,886,326,000 | 225,600,688 | 4 | 2 | null | 1,598,209,306,000 | 1,575,371,550,000 | Lean | UTF-8 | Lean | false | false | 4,721 | lean | import super.inferences.superposition
namespace super
open tactic
variables (gt : term_order)
meta def get_simpl_clauses : prover (list (expr × expr × clause)) := do
act ← get_active,
pure $ do act ← act.values,
clause_type.atom `(%%l = %%r) ← pure act.cls.ty | [],
pure (l,r,act.cls)
variables (... |
e25125217ccefe8816993b403116a03435f6d6de | 1abd1ed12aa68b375cdef28959f39531c6e95b84 | /src/order/lattice_intervals.lean | 5d778cfba13a0e9a879643c1f9e703a0d9a6e5c1 | [
"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 | 7,881 | 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 order.bounded_lattice
import data.set.intervals.basic
/-!
# Intervals in Lattices
In this file, we provide instances of lattice structures on intervals with... |
04512596ea02f7c39009c992c890da8adccea866 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/run/simplify_with_hypotheses.lean | 81cfba8ed41c920bc22e8da13c58e6430d292f2e | [
"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 | 583 | lean | open tactic
example (A : Type) (a₁ a₂ : A) (f : A → A) (H₀ : a₁ = a₂) : f a₁ = f a₂ := by simp_using_hs
example (A : Type) (a₁ a₁' a₂ a₂' : A) (f : A → A) (H₀ : a₁' = a₂') (H₁ : f a₁ = a₁') (H₂ : f a₂ = a₂')
: f a₁ = f a₂ := by simp_using_hs
constants (A : Type.{1}) (x y z w : A) (f : A → A) (H₁ : f (f x) = f y) (H₂... |
5da349978630f437d7bf641c9e52409678d72a97 | 8b9f17008684d796c8022dab552e42f0cb6fb347 | /tests/lean/hott/457.hlean | ae03e8d59f53ae54e2459ede4c61ebc69da826c8 | [
"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 | 189 | hlean | import algebra.group
open eq path_algebra
definition foo {A : Type} (a b c : A) (H₁ : a = c) (H₂ : c = b) : a = b :=
begin
apply concat,
rotate 1,
apply H₂,
apply H₁
end
|
5ebcb32e1e368b8029e1a9cc259379f4315ec9c7 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/data/dfinsupp/interval.lean | ef238ca546402a73c2b5249df31b8d3fa0cac5da | [
"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 | 5,811 | 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.finset.locally_finite
import data.dfinsupp.order
/-!
# Finite intervals of finitely supported functions
This file provides the `locally_finite_order` instan... |
d06b34e2aca6a6621f7572acd56200b6ff435b4d | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/data/equiv/fin.lean | 5531aced375308d68fff5f608e90cfd381581e2d | [
"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 | 11,290 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import data.fin
import data.equiv.basic
import tactic.norm_num
/-!
# Equivalences for `fin n`
-/
universe variables u
variables {m n : ℕ}
/-- Equivalence between `fin 0` an... |
4b626d77c8ea9fd64735447f7602939cda94e598 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/array/lemmas.lean | 15745bf1532134e66d638b8c6b5c96a3fa21f91e | [
"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 | 9,569 | 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.vector.basic
universes u v w
namespace d_array
variables {n : ℕ} {α : fin n → Type u}
instan... |
1c747878e145d14f56098b4cf273b2738098311a | b00eb947a9c4141624aa8919e94ce6dcd249ed70 | /stage0/src/Std/Data/PersistentHashMap.lean | 15a864b6ac27b0634f8a802ebd2cb5eaaee916a0 | [
"Apache-2.0"
] | permissive | gebner/lean4-old | a4129a041af2d4d12afb3a8d4deedabde727719b | ee51cdfaf63ee313c914d83264f91f414a0e3b6e | refs/heads/master | 1,683,628,606,745 | 1,622,651,300,000 | 1,622,654,405,000 | 142,608,821 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 13,304 | 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
-/
namespace Std
universes u v w w'
namespace PersistentHashMap
inductive Entry (α : Type u) (β : Type v) (σ : Type w) where
| entry (key : α) (val : β) : ... |
abdb84460dffc235d9fb66dbbd1693a27a1f8287 | 02005f45e00c7ecf2c8ca5db60251bd1e9c860b5 | /src/data/matrix/notation.lean | f5a8a68b300657296e8e3686b3d9e1709c2257eb | [
"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 | 17,725 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
Notation for vectors and matrices
-/
import data.fintype.card
import data.matrix.basic
import tactic.fin_cases
/-!
# Matrix and vector notation
This file defines notation ... |
b1ee43674fca2b2440c1efa28373de077d4d0602 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/tactic/lint/type_classes.lean | 0b0efafc654f0599bf651cb144c556554ed5ddc0 | [
"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 | 24,729 | 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, Robert Y. Lewis, Gabriel Ebner
-/
import data.bool.basic
import meta.rb_map
import tactic.lint.basic
/-!
# Linters about type classes
This file defines several li... |
f698215b8e11495185201b9cd4917eb33f5aca92 | 97f752b44fd85ec3f635078a2dd125ddae7a82b6 | /hott/algebra/category/limits/limits.hlean | 3a1d5f8fc4b544ffd2986ce4abb23cfe7c9cd912 | [
"Apache-2.0"
] | permissive | tectronics/lean | ab977ba6be0fcd46047ddbb3c8e16e7c26710701 | f38af35e0616f89c6e9d7e3eb1d48e47ee666efe | refs/heads/master | 1,532,358,526,384 | 1,456,276,623,000 | 1,456,276,623,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 17,439 | 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
Limits in a category
-/
import ..constructions.cone ..constructions.discrete ..constructions.product
..constructions.finite_cats ..category ..constructions.... |
31c5056443cdcccdc5d17f864a3bed2026886fc4 | 968e2f50b755d3048175f176376eff7139e9df70 | /examples/prop_logic_theory/unnamed_2023.lean | 6d5f131af897a99f197f1595e6bf3c32a1d66907 | [] | no_license | gihanmarasingha/mth1001_sphinx | 190a003269ba5e54717b448302a27ca26e31d491 | 05126586cbf5786e521be1ea2ef5b4ba3c44e74a | refs/heads/master | 1,672,913,933,677 | 1,604,516,583,000 | 1,604,516,583,000 | 309,245,750 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 127 | lean | variables {p q : Prop}
-- BEGIN
example (h₁ : ¬p) (h₂ : p) : q :=
begin
exfalso,
show false, from h₁ h₂
end
-- END |
be93723255a7235d096cf49bcd757688996c2295 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/ring_theory/multiplicity.lean | b95e5c0e42adbe2c434aca7cdf11ce8e4ae98198 | [
"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 | 19,767 | lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Chris Hughes
-/
import algebra.associated
import algebra.big_operators.basic
import ring_theory.valuation.basic
/-!
# Multiplicity of a divisor
For a commutative mo... |
1609f1d7b1457ed4c592d2d128702adbe3162f2e | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/unreachable_cases.lean | d76eca52f3425fbe4f3ecf1448225fb929658d47 | [
"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 | 566 | lean | open nat prod
inductive ifin : ℕ → Type := -- inductively defined fin-type
| fz : Π n, ifin (succ n)
| fs : Π {n}, ifin n → ifin (succ n)
open ifin
definition foo {N : Type} : Π{n : ℕ}, N → ifin n → (N × ifin n)
| (succ k) n (fz k) := sorry
| (succ k) n (fs x) := sorry
definition bar {N : Type} : Π{n : ℕ}, (N × ifi... |
3db6042c3458a872079f51d84407b13fd0258417 | a7eef317ddec01b9fc6cfbb876fe7ac00f205ac7 | /src/category_theory/limits/shapes/binary_products.lean | 3f6e89bff30118c79b6674bae7fc2328e5dd4c62 | [
"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 | 27,622 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Bhavik Mehta
-/
import category_theory.limits.shapes.terminal
/-!
# Binary (co)products
We define a category `walking_pair`, which is the index category
for a binary ... |
6784097734060e427afb9a210a640c61efd024db | cbb1957fc3e28e502582c54cbce826d666350eda | /fabstract/Cook_S_P_NP/fabstract.lean | a700a8aac19008bbda1b622b2bdaef0b0a4a0ef2 | [
"CC-BY-4.0"
] | permissive | andrejbauer/formalabstracts | 9040b172da080406448ad1b0260d550122dcad74 | a3b84fd90901ccf4b63eb9f95d4286a8775864d0 | refs/heads/master | 1,609,476,417,918 | 1,501,541,742,000 | 1,501,541,760,000 | 97,241,872 | 1 | 0 | null | 1,500,042,191,000 | 1,500,042,191,000 | null | UTF-8 | Lean | false | false | 2,616 | lean | import meta_data
.turing_machines
namespace Cook_S_P_NP
/- Definitions of the complexity classes P and NP -/
def NP_computable (f : list bool → list bool) : Prop :=
∃ s n (TM : NTATM s n) (c k : nat),
computes_fn_in_time
TM
(λ i : fin 1 → list bool, f (i 0))
(λ i, c * ((i 0).length^k + 1))
def ... |
5c6e88e1b4b403cedc22253f6801257bd8dfe004 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/algebra/char_p/pi.lean | b87b8a93d4f30d47c17d07c5df282ba4fdbe8bc4 | [
"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 | 863 | lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import algebra.char_p.basic
import algebra.ring.pi
/-!
# Characteristic of semirings of functions
-/
universes u v
namespace char_p
instance pi (ι : Type u) [hi : nonempty... |
100467afa7b680f96ff348e47096d4b2207367cb | 842b7df4a999c5c50bbd215b8617dd705e43c2e1 | /nat_num_game/src/Advanced_Proposition_World/adv_prop_wrld8.lean | 625a04cee97de6a7054d23d01bc6cf138b4165ca | [] | no_license | Samyak-Surti/LeanCode | 1c245631f74b00057d20483c8ac75916e8643b14 | 944eac3e5f43e2614ed246083b97fbdf24181d83 | refs/heads/master | 1,669,023,730,828 | 1,595,534,784,000 | 1,595,534,784,000 | 282,037,186 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 594 | lean | lemma and_or_distrib_left (P Q R : Prop) : P ∧ (Q ∨ R) ↔ (P ∧ Q) ∨ (P ∧ R) :=
begin
split,
intro fpqr,
cases fpqr with p qr,
cases qr with q r,
have pq : P ∧ Q,
split,
exact p,
exact q,
left,
exact pq,
have pr : P ∧ R,
split,
exact p,
exact r,
right,
exact... |
e716c94f966aa97158771e72cc8240f67e69f34e | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebraic_geometry/presheafed_space.lean | cc379a666307c5d22bb0b1c078888a30217f3359 | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 14,747 | 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.sheaves.presheaf
import category_theory.adjunction.fully_faithful
/-!
# Presheafed spaces
Introduces the category of topological spaces equipped wit... |
ff1a04ef3f22289ed3831831398fd075552de64f | 18425d4bab0b5e4677ef791d0065e16639493248 | /equipotent.lean | 3481fba47fa4b23f1d9f6dab1b122b8b1903283c | [
"MIT"
] | permissive | tizmd/lean-finitary | 5feb94a2474b55c0f23e4b61b9ac42403bf222f7 | 8958fdb3fa3d9fcc304e116fd339448875025e95 | refs/heads/master | 1,611,397,193,043 | 1,497,517,825,000 | 1,497,517,825,000 | 93,048,842 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,308 | lean | import function.bijection
import data.fin.misc
universes u v
open function
class equipotent (α : Sort u) (β : Sort v) :=
(map : α → β)
(bijection : bijection map)
namespace equipotent
variables {α : Sort u} {β : Sort v}
@[refl]
instance rfl : equipotent α α :=
{
map := id,
bijection := bijection... |
46187620d3a8ff4a076bf7bd3437c3f6771e9205 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebraic_topology/fundamental_groupoid/induced_maps.lean | 1536082abcf65ac0e9d4769c42a9df5a0500c3dc | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 8,816 | lean | /-
Copyright (c) 2022 Praneeth Kolichala. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Praneeth Kolichala
-/
import topology.homotopy.equiv
import category_theory.equivalence
import algebraic_topology.fundamental_groupoid.product
/-!
# Homotopic maps induce naturall... |
505f551f52cdb6d932601e17c15e87225713e0ee | 4bcaca5dc83d49803f72b7b5920b75b6e7d9de2d | /stage0/src/Lean/MetavarContext.lean | 2f7ecc85c02704040eec4c7800de60a1e36c64b9 | [
"Apache-2.0"
] | permissive | subfish-zhou/leanprover-zh_CN.github.io | 30b9fba9bd790720bd95764e61ae796697d2f603 | 8b2985d4a3d458ceda9361ac454c28168d920d3f | refs/heads/master | 1,689,709,967,820 | 1,632,503,056,000 | 1,632,503,056,000 | 409,962,097 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 54,606 | 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.Util.MonadCache
import Lean.LocalContext
namespace Lean
/-
The metavariable context stores metavariable declarations and their
assignments. It... |
fb7ab0819e97de5a5abc18f98476e61e1e8787a8 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/ppbug.lean | 2d05286affdee3a7b8918e5edbe476205da6f8f2 | [
"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 | 19 | lean | #check list.rec_on
|
72931842359a565644bb69f8fca909cd69a047c8 | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /tests/lean/run/structure.lean | c00bd5bdaab7e8a69794835990194c3488077eb9 | [
"Apache-2.0"
] | permissive | walterhu1015/lean4 | b2c71b688975177402758924eaa513475ed6ce72 | 2214d81e84646a905d0b20b032c89caf89c737ad | refs/heads/master | 1,671,342,096,906 | 1,599,695,985,000 | 1,599,695,985,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,184 | lean | import Lean
open Lean
structure S1 :=
(x y : Nat)
structure S2 extends S1 :=
(z : Nat)
structure S3 :=
(w : Nat)
structure S4 extends S2, S3 :=
(s : Nat)
def check (b : Bool) : CoreM Unit :=
unless b $ throwError "check failed"
class S5 :=
(x y : Nat)
inductive D
| mk (x y z : Nat) : D
def tst : CoreM Unit :=
d... |
550c4a3eec815352b3e382750897c17a95b596c6 | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /stage0/src/Lean/Server/FileWorker.lean | 6010e8f49fb050b389fa6d36f74eee425dd4858f | [
"Apache-2.0"
] | permissive | WojciechKarpiel/lean4 | 7f89706b8e3c1f942b83a2c91a3a00b05da0e65b | f6e1314fa08293dea66a329e05b6c196a0189163 | refs/heads/master | 1,686,633,402,214 | 1,625,821,189,000 | 1,625,821,258,000 | 384,640,886 | 0 | 0 | Apache-2.0 | 1,625,903,617,000 | 1,625,903,026,000 | null | UTF-8 | Lean | false | false | 17,804 | lean | /-
Copyright (c) 2020 Marc Huisinga. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Marc Huisinga, Wojciech Nawrocki
-/
import Init.System.IO
import Std.Data.RBMap
import Lean.Environment
import Lean.Data.Lsp
import Lean.Data.Json.FromToJson
import Lean.Server.Util... |
207769164f194c5bb5a6dd8dda5ac4ab6062beb1 | e00ea76a720126cf9f6d732ad6216b5b824d20a7 | /src/group_theory/subgroup.lean | 96589bef7453cbe837c99ea6e96dc3daf726cb9a | [
"Apache-2.0"
] | permissive | vaibhavkarve/mathlib | a574aaf68c0a431a47fa82ce0637f0f769826bfe | 17f8340912468f49bdc30acdb9a9fa02eeb0473a | refs/heads/master | 1,621,263,802,637 | 1,585,399,588,000 | 1,585,399,588,000 | 250,833,447 | 0 | 0 | Apache-2.0 | 1,585,410,341,000 | 1,585,410,341,000 | null | UTF-8 | Lean | false | false | 29,177 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mitchell Rowett, Scott Morrison, Johan Commelin, Mario Carneiro,
Michael Howes
-/
import group_theory.submonoid
open set function
variables {G : Type*} {H : Type*} {... |
dfbc4a1d8f3002eb22f6425eafb4e7985b321bf2 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/analysis/complex/isometry.lean | c20b7eb7f6ec9375e2fd6583cc6ff465c81b951a | [
"Apache-2.0"
] | permissive | kbuzzard/mathlib | 2ff9e85dfe2a46f4b291927f983afec17e946eb8 | 58537299e922f9c77df76cb613910914a479c1f7 | refs/heads/master | 1,685,313,702,744 | 1,683,974,212,000 | 1,683,974,212,000 | 128,185,277 | 1 | 0 | null | 1,522,920,600,000 | 1,522,920,600,000 | null | UTF-8 | Lean | false | false | 6,723 | lean | /-
Copyright (c) 2021 François Sunatori. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: François Sunatori
-/
import analysis.complex.circle
import linear_algebra.determinant
import linear_algebra.matrix.general_linear_group
/-!
# Isometries of the Complex Plane
The l... |
2f8680362d7106122e0db491db0b82c0677bc007 | 8f209eb34c0c4b9b6be5e518ebfc767a38bed79c | /code/src/internal/phi/utils.lean | e4cbb9d4497bf647e942f1eeb39d36592b13c632 | [] | no_license | hediet/masters-thesis | 13e3bcacb6227f25f7ec4691fb78cb0363f2dfb5 | dc40c14cc4ed073673615412f36b4e386ee7aac9 | refs/heads/master | 1,680,591,056,302 | 1,617,710,887,000 | 1,617,710,887,000 | 311,762,038 | 4 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,427 | lean | import tactic
import ...definitions
import data.finset
meta def stable_macro: tactic unit := `[
rw stable,
assume ty1 ty2 h,
ext env,
simp [Φ.eval, h]
]
variable [GuardModule]
open GuardModule
def stable (f: Φ → Φ) := ∀ ty1 ty2: Φ, (ty1.eval = ty2.eval) → (f ty1).eval = (f ty2).eval
lemma stable.id:... |
a8cb458e074b7b269f631c8132a94a583cff73a4 | 94935fb4ab68d4ce640296d02911624a93282575 | /src/hints/thursday/afternoon/category_theory/exercise18/hint2.lean | 3ca3ce5a3362f966df1977e48dc6f5534ed151a9 | [] | permissive | marius-leonhardt/lftcm2020 | 41c0d7fe3457c1cf3b72cbb1c312b48fc94b85d2 | a3eb53f18d9be9a5be748dfe8fe74d0d31a0c1f7 | refs/heads/master | 1,668,623,789,936 | 1,594,710,949,000 | 1,594,710,949,000 | 279,514,936 | 0 | 0 | MIT | 1,594,711,916,000 | 1,594,711,916,000 | null | UTF-8 | Lean | false | false | 1,324 | lean | import category_theory.limits.shapes.pullbacks
/-!
Thanks to Markus Himmel for suggesting this question.
-/
open category_theory
open category_theory.limits
/-!
Let C be a category, X and Y be objects and f : X ⟶ Y be a morphism. Show that f is an epimorphism
if and only if the diagram
X --f--→ Y
| |
f ... |
8b91e5242255941c0119a19e3f0bed4eb19ff8ed | 4b846d8dabdc64e7ea03552bad8f7fa74763fc67 | /tests/lean/run/1315b.lean | f4cad702ab827d92d1e3bb4e18c309aaf763aade | [
"Apache-2.0"
] | permissive | pacchiano/lean | 9324b33f3ac3b5c5647285160f9f6ea8d0d767dc | fdadada3a970377a6df8afcd629a6f2eab6e84e8 | refs/heads/master | 1,611,357,380,399 | 1,489,870,101,000 | 1,489,870,101,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,239 | lean | open nat
def k : ℕ := 0
def fails : Π (n : ℕ) (m : ℕ), ℕ
| 0 m := 0
| (succ n) m :=
match k with
| 0 := 0
| (succ i) :=
let val := m+1 in
match fails n val with
| 0 := 0
| (succ l) := 0
end
end
def test (k : ℕ) : Π (n : ℕ) (m : ℕ), ℕ
| 0 m := 0
| (succ n) m :=
match k with
| 0 := 1
... |
17adcd3f8054e6789da4ad79265bebc17540ca2e | d436468d80b739ba7e06843c4d0d2070e43448e5 | /src/measure_theory/integration.lean | 4db136f0419d466f17cb9078f80eae57d2a9bd0a | [
"Apache-2.0"
] | permissive | roro47/mathlib | 761fdc002aef92f77818f3fef06bf6ec6fc1a28e | 80aa7d52537571a2ca62a3fdf71c9533a09422cf | refs/heads/master | 1,599,656,410,625 | 1,573,649,488,000 | 1,573,649,488,000 | 221,452,951 | 0 | 0 | Apache-2.0 | 1,573,647,693,000 | 1,573,647,692,000 | null | UTF-8 | Lean | false | false | 54,754 | 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
Lebesgue integral on `ennreal`.
We define simple functions and show that each Borel measurable function on `ennreal` can be
approximated by a sequence ... |
b07515d96a9cfa1df3bbed412858f035e45edb63 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/data/rbtree/find_auto.lean | dc1982c4bf5bdb599f95416310c2747dc07162ea | [] | 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 | 2,613 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.Lean3Lib.data.rbtree.basic
universes u
namespace Mathlib
namespace rbnode
t... |
f85a67d5746fec6745b7bead25aeb349210f12c5 | 4f9ca1935adf84f1bae9c5740ec1f2ad406716fa | /src/analysis/asymptotics.lean | b34fa1fd85589d2fbcd7850e42858ac4ca76379d | [
"Apache-2.0"
] | permissive | matthew-hilty/mathlib | 36fd7db866365e9ee4a0ba1d6f8ad34d068cec6c | 585e107f9811719832c6656f49e1263a8eef5380 | refs/heads/master | 1,607,100,509,178 | 1,578,151,707,000 | 1,578,151,707,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 30,725 | lean | /-
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad
-/
import analysis.normed_space.basic
/-!
# Asymptotics
We introduce these relations:
`is_O f g l` : "f is big O of g along l"
`is_o f g l` : "f is little o of g al... |
32b0d4ec30f551bd7bd04b61af039738f7fe1eda | 8cb37a089cdb4af3af9d8bf1002b417e407a8e9e | /tests/lean/pp_links.lean | 44e5293689c908a054d9e1bfbcc631602501c2c1 | [
"Apache-2.0"
] | permissive | kbuzzard/lean | ae3c3db4bb462d750dbf7419b28bafb3ec983ef7 | ed1788fd674bb8991acffc8fca585ec746711928 | refs/heads/master | 1,620,983,366,617 | 1,618,937,600,000 | 1,618,937,600,000 | 359,886,396 | 1 | 0 | Apache-2.0 | 1,618,936,987,000 | 1,618,936,987,000 | null | UTF-8 | Lean | false | false | 192 | lean | open tactic
structure point (α : Type*) :=
(x : α) (y : α)
example : ∀ i : ℤ, (i, i).snd = i + 0 + (point.mk 0 i).x := by do
os ← get_options,
set_options (os.set_bool `pp.links tt) |
20755b66d4b1cbd44a973c7702b8ffa09371ee16 | f618aea02cb4104ad34ecf3b9713065cc0d06103 | /src/data/complex/exponential.lean | 4f3692187f89ffce09bc6bcc6ae3e550d09b9083 | [
"Apache-2.0"
] | permissive | joehendrix/mathlib | 84b6603f6be88a7e4d62f5b1b0cbb523bb82b9a5 | c15eab34ad754f9ecd738525cb8b5a870e834ddc | refs/heads/master | 1,589,606,591,630 | 1,555,946,393,000 | 1,555,946,393,000 | 182,813,854 | 0 | 0 | null | 1,555,946,309,000 | 1,555,946,308,000 | null | UTF-8 | Lean | false | false | 47,503 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir
-/
import algebra.archimedean
import data.nat.choose data.complex.basic
import tactic.linarith
local attribute [instance, priority 0] nat... |
879d5746fe9c51e7d32ffb5f3f77819671802959 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/algebra/direct_sum/finsupp.lean | 279482cfa0cb2a0751f06418664600c03844109c | [
"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 | 1,469 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import algebra.direct_sum.module
import data.finsupp.to_dfinsupp
/-!
# Results on direct sums and finitely supported functions.
1. The linear equivalence between fi... |
87230473cdf431cd8a5965ecb6bb52c55398f59d | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/star/star_alg_hom.lean | 93139df49b5415f636ac1ae2d03af63eddc18de9 | [
"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 | 28,351 | lean | /-
Copyright (c) 2022 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import algebra.hom.non_unital_alg
import algebra.star.prod
import algebra.algebra.prod
/-!
# Morphisms of star algebras
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> ... |
af47dc0d9dbe41076f40f21c0b4a8c4da0658d61 | 4950bf76e5ae40ba9f8491647d0b6f228ddce173 | /src/measure_theory/outer_measure.lean | 656d50417634b7d0398a735b66218a7e902a5ed1 | [
"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 | 40,615 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import analysis.specific_limits
import measure_theory.measurable_space
import topology.algebra.infinite_sum
/-!
# Outer Measures
An outer measure is... |
27dfa782bf2ecbfd085bfdeded35d8bce197fdb8 | 6214e13b31733dc9aeb4833db6a6466005763162 | /src/eqdec.lean | a563f31ca8574129c4fa7b1e7b37ba66c2ac46ea | [] | no_license | joshua0pang/esverify-theory | 272a250445f3aeea49a7e72d1ab58c2da6618bbe | 8565b123c87b0113f83553d7732cd6696c9b5807 | refs/heads/master | 1,585,873,849,081 | 1,527,304,393,000 | 1,527,304,393,000 | 154,901,199 | 1 | 0 | null | 1,540,593,067,000 | 1,540,593,067,000 | null | UTF-8 | Lean | false | false | 55,031 | lean | -- decidable equality of values, terms, expressions, etc.
import .syntax .etc .sizeof
instance : decidable_eq unop := by tactic.mk_dec_eq_instance
instance : decidable_eq binop := by tactic.mk_dec_eq_instance
def wf_measure : has_well_founded
(psum (Σ' (v₁ : value), value)
(psum (Σ' (e₁ : exp), exp)
(psum (Σ' ... |
c294f5aa8c144bb0dfa9527c273deee7893f5cb3 | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/category_theory/fully_faithful.lean | f04d07e7b67e5faf0af2952975fdbc50f2cb05ab | [
"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 | 2,820 | lean | -- Copyright (c) 2018 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Scott Morrison
import category_theory.isomorphism
universes v₁ v₂ v₃ u₁ u₂ u₃ -- declare the `v`'s first; see `category_theory.category` for an explanation
namespace category_... |
b4de842d6b8ab42d27f3dcd2d489a9ab2e34148c | 618003631150032a5676f229d13a079ac875ff77 | /src/category_theory/whiskering.lean | aff7bdfaee451d8183efccfe44c88f3afeec3aab | [
"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 | 5,787 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.natural_isomorphism
namespace category_theory
universes u₁ v₁ u₂ v₂ u₃ v₃ u₄ v₄
section
variables {C : Type u₁} [category.{v₁} C]
... |
0b5056eb289b902ab02f456327d840b8761917a6 | 947b78d97130d56365ae2ec264df196ce769371a | /tests/lean/emptyc.lean | 5ad95b846863578066b025088d97883e95f7dd9a | [
"Apache-2.0"
] | permissive | shyamalschandra/lean4 | 27044812be8698f0c79147615b1d5090b9f4b037 | 6e7a883b21eaf62831e8111b251dc9b18f40e604 | refs/heads/master | 1,671,417,126,371 | 1,601,859,995,000 | 1,601,860,020,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 220 | lean | new_frontend
structure A :=
(x : Nat := 0)
def foo : A :=
{}
theorem ex1 : foo = { x := 0 } :=
rfl
theorem ex2 : foo.x = 0 :=
rfl
instance : HasEmptyc A :=
⟨{ x := 10 }⟩
def boo : A :=
{} -- this is ambiguous
|
c7c837ae836ba6bfd775385095ff4d8bf4c683d0 | 1b8f093752ba748c5ca0083afef2959aaa7dace5 | /src/category_theory/locally_ringed.lean | f8f74355104bbec97ddae9eb2de9043def460ec5 | [] | no_license | khoek/lean-category-theory | 7ec4cda9cc64a5a4ffeb84712ac7d020dbbba386 | 63dcb598e9270a3e8b56d1769eb4f825a177cd95 | refs/heads/master | 1,585,251,725,759 | 1,539,344,445,000 | 1,539,344,445,000 | 145,281,070 | 0 | 0 | null | 1,534,662,376,000 | 1,534,662,376,000 | null | UTF-8 | Lean | false | false | 777 | lean | import category_theory.sheaves
import category_theory.examples.rings.universal
universes v
open category_theory.examples
open category_theory.limits
variables (X : Top.{v})
def structure_sheaf := sheaf.{v+1 v} X CommRing
structure ringed_space :=
(𝒪 : structure_sheaf X)
structure locally_ringed_space extends ri... |
2f01d7020684d8d9ba19fb64eb8a2c41a7a325af | 4727251e0cd73359b15b664c3170e5d754078599 | /src/analysis/locally_convex/bounded.lean | 5fc941f541e5e72474155ccfde9c95287ce596f0 | [
"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 | 5,365 | lean | /-
Copyright (c) 2022 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll
-/
import analysis.locally_convex.basic
import topology.bornology.basic
import topology.algebra.uniform_group
import analysis.locally_convex.balanced_core_hull
/-!
# Von Neum... |
697ce46b9faf69b3f0b6059226ba5ccff8487358 | 560745f5fc6d6dc9a83825cf9709cf565d1f158e | /src/compact_unit_ball.lean | 57694a69287eec6cb6ce48b547c39a8afc50aaf1 | [] | no_license | LAC1213/compact_unit_ball | 335efe663dcb0d2f4e69762677ba314828b701c8 | b4ce16961cb57a4a242d67fb96b41bea2ef1f3a3 | refs/heads/lean-3.4.2 | 1,600,937,389,835 | 1,575,749,508,000 | 1,575,749,508,000 | 225,719,174 | 11 | 2 | null | 1,575,631,335,000 | 1,575,408,323,000 | Lean | UTF-8 | Lean | false | false | 12,517 | lean | import analysis.normed_space.banach
import analysis.normed_space.basic
import linear_algebra.basic
import linear_algebra.basis
import linear_algebra.dimension
import linear_algebra.finite_dimensional
import topology.subset_properties
import set_theory.cardinal
import data.real.basic
import topology.sequences
import ord... |
bb4c455abac728ecc70ac9e2bbdde028fe3db3fb | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/ring_theory/power_basis.lean | be88af1e6a32a22be9a1a3b79e1e2ec5ebb2b6fb | [
"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 | 20,419 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import field_theory.minpoly
/-!
# Power basis
This file defines a structure `power_basis R S`, giving a basis of the
`R`-algebra `S` as a finite list of powers `1, x, ...... |
3aff7e5e6f816cc415a04e436486f84c8d5a8663 | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/ring_theory/adjoin.lean | 194325eef721b9e3cb2f4683726e675bbb07cc42 | [
"Apache-2.0"
] | permissive | agjftucker/mathlib | d634cd0d5256b6325e3c55bb7fb2403548371707 | 87fe50de17b00af533f72a102d0adefe4a2285e8 | refs/heads/master | 1,625,378,131,941 | 1,599,166,526,000 | 1,599,166,526,000 | 160,748,509 | 0 | 0 | Apache-2.0 | 1,544,141,789,000 | 1,544,141,789,000 | null | UTF-8 | Lean | false | false | 9,160 | lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import ring_theory.polynomial.basic
/-!
# Adjoining elements to form subalgebras
This file develops the basic theory of subalgebras of an R-algebra generated
by a set of elem... |
e2f0770822e4e700cf96001bf3c867d7be69559b | 7b66d83f3b69dae0a3dfb684d7ebe5e9e3f3c913 | /src/exercises_sources/tuesday/afternoon/sets.lean | f0f4cdd55880e0dfbc0497c8f7cddd7e087b59c1 | [] | permissive | dpochekutov/lftcm2020 | 58a09e10f0e638075b97884d3c2612eb90296adb | cdfbf1ac089f21058e523db73f2476c9c98ed16a | refs/heads/master | 1,669,226,265,076 | 1,594,629,725,000 | 1,594,629,725,000 | 279,213,346 | 1 | 0 | MIT | 1,594,622,757,000 | 1,594,615,843,000 | null | UTF-8 | Lean | false | false | 7,255 | lean | import data.set.basic data.set.lattice data.nat.parity
import tactic.linarith
open set nat function
open_locale classical
variables {α : Type*} {β : Type*} {γ : Type*} {I : Type*}
/-!
## Set exercises
These are collected from *Mathematics in Lean*.
We will go over the examples together, and then let you
work on t... |
94d8ef70e282081244cb7d061c50e6a55bd4d5a2 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/1725.lean | aaea049f4a1d0733915ad3f42c1ded7ea5a930fe | [
"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 | 692 | lean | structure Fun (α β : Type) : Type where
toFun : α → β
instance : CoeFun (Fun α β) (fun _ => α → β) where
coe := Fun.toFun
example (f : Fun α α) : α → α :=
f ∘ f
example (f : Fun α β) : (γ δ : Type) × (γ → δ) :=
⟨_, _, f⟩
structure Equiv (α : Sort _) (β : Sort _) :=
(toFun : α → β)
(invFun : β → α)
loc... |
5cce700356a7b7f1a93b2ecd9d92567cd4ef863c | 4fa161becb8ce7378a709f5992a594764699e268 | /src/analysis/special_functions/trigonometric.lean | a858b1c41ec86976794aed6f24d22dc1109e8529 | [
"Apache-2.0"
] | permissive | laughinggas/mathlib | e4aa4565ae34e46e834434284cb26bd9d67bc373 | 86dcd5cda7a5017c8b3c8876c89a510a19d49aad | refs/heads/master | 1,669,496,232,688 | 1,592,831,995,000 | 1,592,831,995,000 | 274,155,979 | 0 | 0 | Apache-2.0 | 1,592,835,190,000 | 1,592,835,189,000 | null | UTF-8 | Lean | false | false | 65,697 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne
-/
import analysis.special_functions.exp_log
/-!
# Trigonometric functions
## Main definitions
This file contains the foll... |
42b7d982d97afe8e93689ae8e714b6f894c49d1a | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/topology/metric_space/emetric_space.lean | c11d19a2cb2f880fbf31aa6daf47ab278129bd21 | [
"Apache-2.0"
] | permissive | stjordanis/mathlib | 51e286d19140e3788ef2c470bc7b953e4991f0c9 | 2568d41bca08f5d6bf39d915434c8447e21f42ee | refs/heads/master | 1,631,748,053,501 | 1,627,938,886,000 | 1,627,938,886,000 | 228,728,358 | 0 | 0 | Apache-2.0 | 1,576,630,588,000 | 1,576,630,587,000 | null | UTF-8 | Lean | false | false | 45,838 | 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... |
b46c93dce38207449bce1c19168da0e280858733 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/logic/relation.lean | b9793edf6f6b460655811e1b9e5446f65eab0504 | [] | 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 | 13,477 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Transitive reflexive as well as reflexive closure of relations.
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.tactic.basic
import Mathli... |
4568ad9e08580bb8c7dd01446fab7ec47b3404d0 | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /tests/lean/file_not_found.lean | 0ec53f2fe01927a741ea74346a5cfa7393d5a87a | [
"Apache-2.0"
] | permissive | mhuisi/lean4 | 28d35a4febc2e251c7f05492e13f3b05d6f9b7af | dda44bc47f3e5d024508060dac2bcb59fd12e4c0 | refs/heads/master | 1,621,225,489,283 | 1,585,142,689,000 | 1,585,142,689,000 | 250,590,438 | 0 | 2 | Apache-2.0 | 1,602,443,220,000 | 1,585,327,814,000 | C | UTF-8 | Lean | false | false | 582 | lean | prelude
import Init.System.IO
open IO.FS
#eval (IO.FS.Handle.mk "non-existent-file.txt" Mode.read *> pure () : IO Unit)
#eval do condM (IO.fileExists "readonly.txt")
(pure ())
(IO.FS.withFile "readonly.txt" Mode.write $ fun _ => pure ());
IO.setAccessRights "readonly.txt" { user... |
2e9c83500b86f6c227f351eba337c6b95ec6105b | 7c92a46ce39266c13607ecdef7f228688f237182 | /src/valuation/field.lean | a928e5dfa279b007762f202aa6126acf9e4a74b1 | [
"Apache-2.0"
] | permissive | asym57/lean-perfectoid-spaces | 3217d01f6ddc0d13e9fb68651749469750420767 | 359187b429f254a946218af4411d45f08705c83e | refs/heads/master | 1,609,457,937,251 | 1,577,542,616,000 | 1,577,542,675,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,654 | lean | import for_mathlib.topological_field
import for_mathlib.topology
import for_mathlib.uniform_space.uniform_field
import valuation.topology
import valuation.with_zero_topology
import topology.algebra.ordered
/-!
In this file we study the topology of a field `K` endowed with a valuation (in our application
to adic spaces... |
5bfdf6c47e81f777447ac687905cd185cec9533c | 7b02c598aa57070b4cf4fbfe2416d0479220187f | /algebra/graded.hlean | e7a5053748fa39b4f6040e892ada3c056d467856 | [
"Apache-2.0"
] | permissive | jdchristensen/Spectral | 50d4f0ddaea1484d215ef74be951da6549de221d | 6ded2b94d7ae07c4098d96a68f80a9cd3d433eb8 | refs/heads/master | 1,611,555,010,649 | 1,496,724,191,000 | 1,496,724,191,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 27,667 | hlean | /- Graded (left-) R-modules for a ring R. -/
-- Author: Floris van Doorn
import .left_module .direct_sum .submodule --..heq
open is_trunc algebra eq left_module pointed function equiv is_equiv prod group sigma sigma.ops nat
trunc_index
namespace left_module
definition graded [reducible] (str : Type) (I : Type) : ... |
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