blob_id stringlengths 40 40 | directory_id stringlengths 40 40 | path stringlengths 7 139 | content_id stringlengths 40 40 | detected_licenses listlengths 0 16 | license_type stringclasses 2
values | repo_name stringlengths 7 55 | snapshot_id stringlengths 40 40 | revision_id stringlengths 40 40 | branch_name stringclasses 6
values | visit_date int64 1,471B 1,694B | revision_date int64 1,378B 1,694B | committer_date int64 1,378B 1,694B | github_id float64 1.33M 604M ⌀ | star_events_count int64 0 43.5k | fork_events_count int64 0 1.5k | gha_license_id stringclasses 6
values | gha_event_created_at int64 1,402B 1,695B ⌀ | gha_created_at int64 1,359B 1,637B ⌀ | gha_language stringclasses 19
values | src_encoding stringclasses 2
values | language stringclasses 1
value | is_vendor bool 1
class | is_generated bool 1
class | length_bytes int64 3 6.4M | extension stringclasses 4
values | content stringlengths 3 6.12M |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
23dce528fa32fadd88f41620102cea7a8c95cb51 | 38bf3fd2bb651ab70511408fcf70e2029e2ba310 | /src/geometry/manifold/manifold.lean | 50c788b6bc608227c1e1a2860f08b5f7a6e5ee74 | [
"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 | 25,824 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import topology.local_homeomorph
/-!
# Manifolds
A manifold is a topological space M locally modelled on a model space H, i.e., the manifold is
covered by op... |
7a9247a118f4178cc67d233b145fa6af9110316f | 969dbdfed67fda40a6f5a2b4f8c4a3c7dc01e0fb | /src/ring_theory/integral_domain.lean | 8a62e116aebd6f6977f4b4de7a1b0519a434b6a3 | [
"Apache-2.0"
] | permissive | SAAluthwela/mathlib | 62044349d72dd63983a8500214736aa7779634d3 | 83a4b8b990907291421de54a78988c024dc8a552 | refs/heads/master | 1,679,433,873,417 | 1,615,998,031,000 | 1,615,998,031,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,034 | lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Chris Hughes
-/
import data.fintype.card
import data.polynomial.ring_division
import group_theory.order_of_element
import algebra.geom_sum
/-!
# Integral domains
Ass... |
d94299224f0f5f9788817ccd3733faa6c760c46a | f3849be5d845a1cb97680f0bbbe03b85518312f0 | /tests/lean/run/secnot.lean | b400854e65022f84ae147bb41474ad97737b3ac6 | [
"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 | 396 | lean | section
variable {A : Type}
definition f (a b : A) := a
infixl ` ◀ `:65 := f
variables a b : A
#check a ◀ b
end
inductive List (T : Type) : Type
| nil {} : List
| cons : T → List → List
namespace List
section
variable {T : Type}
notation `[` l:(foldr `,` (h t, cons h t) nil) `]` := l
#check [(10:num), 20, 30]
end
e... |
16794b916395129c40283582a30ee7346bc8da65 | 0d2e44896897eda703992595d71a0b19ed30b8a1 | /uexp/src/uexp/extra_constants.lean | 2cfad3f656b0a106d5c337e2c483175e62eaf37d | [
"BSD-2-Clause"
] | permissive | wwombat/Cosette | a87312aabefdb53ea8b67c37731bd58c7485afb6 | 4c5dc6172e24d3546c9818ac1fad06f72fe1c991 | refs/heads/master | 1,619,479,568,051 | 1,520,292,502,000 | 1,520,292,502,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 724 | lean | import .sql
import .u_semiring
open tree
namespace datatypes
constant int : datatype
end datatypes
namespace aggregators
constant count {T} : aggregator T datatypes.int
notation `COUNT` := aggregatorGroupByProj count
constant sum {T} : aggregator T datatypes.int
notation `SUM` := aggregatorGroupByProj sum
const... |
f028a2fca3f041f68dc4e199cf1aa293d1bf71ff | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/control/bitraversable/instances.lean | 8a103289c991ecf5f2b1ea693685af2062369cd6 | [
"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 | 4,385 | lean | /-
Copyright (c) 2019 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author(s): Simon Hudon
-/
import control.bitraversable.lemmas
import control.traversable.lemmas
/-!
# bitraversable instances
## Instances
* prod
* sum
* const
* flip
* bicompl
* bicompr
... |
0b7402be88db8c7fadd3fb19c1fc9b7311377ba1 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/category_theory/limits/preserves/shapes/products.lean | 65c4572c5fcc18c1cd04b629b9a8cee6500d8bbd | [
"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 | 6,484 | lean | /-
Copyright (c) 2020 Scott Morrison, Bhavik Mehta. 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.products
import category_theory.limits.preserves.basic
/-!
# Preserving products
Constructions to r... |
68917625f8161908ade7e48aa6537be908f56103 | b7b549d2cf38ac9d4e49372b7ad4d37f70449409 | /src/LeanLLVM/Simulate.lean | a459708672da49aaf46b7cefbfcd515653bf4304 | [
"Apache-2.0"
] | permissive | GaloisInc/lean-llvm | 7cc196172fe02ff3554edba6cc82f333c30fdc2b | 36e2ec604ae22d8ec1b1b66eca0f8887880db6c6 | refs/heads/master | 1,637,359,020,356 | 1,629,332,114,000 | 1,629,402,464,000 | 146,700,234 | 29 | 1 | Apache-2.0 | 1,631,225,695,000 | 1,535,607,191,000 | Lean | UTF-8 | Lean | false | false | 12,868 | lean | import Galois.Data.Bitvec
import LeanLLVM.AST
import LeanLLVM.Memory
import LeanLLVM.PP
import LeanLLVM.SimMonad
import LeanLLVM.TypeContext
import LeanLLVM.Value
namespace LLVM
namespace Sim
def unreachable {a} : Sim a := throw (IO.userError "unreachable code!")
def int_op (f:∀w, bitvec w -> bitvec w -> Sim Sim.Va... |
20ae3b9efa4915450d7e588ea6272af9100a1a99 | 968e2f50b755d3048175f176376eff7139e9df70 | /examples/prop_logic_theory/unnamed_2088.lean | 31f7e7de4f724c125cf9221c4ab699824fcd7770 | [] | 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 | 293 | lean | variables {p q : Prop}
-- BEGIN
example (h : ¬(p ∨ q)) : ¬p :=
begin
assume h₁ : p, -- It suffices to prove `false`.
apply h, -- By false introduction on `h`, it suffices to prove `p ∨ q`.
exact or.inl h₁, -- This follows by left or introduction on `h₁`.
end
-- END |
ab2a53e156161836afe40dc2cfe84aac8cc2843a | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/category_theory/whiskering.lean | d8d7b8591485eb5c7d8b8f6d5198af5f515de8cf | [
"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 | 7,095 | 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]
... |
aa873f00d961507db1254a55f9bf03a1f7311a87 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/default_field_pi.lean | cd48fa9a5b6e40b501db2e08acc64525a5cd667f | [
"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 | 94 | lean | structure foo :=
(bar : Π n : ℕ, ℕ := id)
(baz : Π {n : ℕ}, ℕ := id)
#check {foo.}
|
170301d234ce5fc8f8f1ff22b3faafe96efe7d33 | 947b78d97130d56365ae2ec264df196ce769371a | /tests/lean/run/csimp_type_error.lean | 79d29ef7f55b876947c1e07f951e5129f9322304 | [
"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 | 317 | lean | new_frontend
namespace scratch
inductive type
| bv (w:Nat) : type
open type
def value : type -> Type
| bv w => {n // n < w}
def tester_fails : ∀ {tp : type}, value tp -> Bool
| bv _, v1 => decide (v1.val = 0)
def tester_ok : ∀ {tp : type}, value tp -> Prop
| bv _, v1 => v1.val = 0
end scratch
|
205dfaaa5bd3573ce83bcfef64791160ff88b9dc | 8e2026ac8a0660b5a490dfb895599fb445bb77a0 | /library/system/process.lean | d2dbb6aa99dc9d7f8fc949bace533eedc1dba958 | [
"Apache-2.0"
] | permissive | pcmoritz/lean | 6a8575115a724af933678d829b4f791a0cb55beb | 35eba0107e4cc8a52778259bb5392300267bfc29 | refs/heads/master | 1,607,896,326,092 | 1,490,752,175,000 | 1,490,752,175,000 | 86,612,290 | 0 | 0 | null | 1,490,809,641,000 | 1,490,809,641,000 | null | UTF-8 | Lean | false | false | 648 | lean | import init.data.list.basic
inductive process.stdio
| piped
| inherit
| null
structure process :=
(cmd : string)
/- Add an argument to pass to the process. -/
(args : list string)
/- Configuration for the process's stdin handle. -/
(stdin := stdio.inherit)
/- Configuration for the process's stdout handle. -/
(stdout ... |
e3d058406e16405b67a585e2528232b9072d0676 | f3a5af2927397cf346ec0e24312bfff077f00425 | /src/game/world7/level1.lean | 26e787ffc1cc81507cd7ee722c64241c17971922 | [
"Apache-2.0"
] | permissive | ImperialCollegeLondon/natural_number_game | 05c39e1586408cfb563d1a12e1085a90726ab655 | f29b6c2884299fc63fdfc81ae5d7daaa3219f9fd | refs/heads/master | 1,688,570,964,990 | 1,636,908,242,000 | 1,636,908,242,000 | 195,403,790 | 277 | 84 | Apache-2.0 | 1,694,547,955,000 | 1,562,328,792,000 | Lean | UTF-8 | Lean | false | false | 1,567 | lean | /-
# Advanced proposition world.
In this world we will learn five key tactics needed to solve all the
levels of the Natural Number Game, namely `split`, `cases`, `left`, `right`, and `exfalso`.
These, and `use` (which we'll get to in Inequality World) are all the
tactics you will need to beat all the levels of the ... |
acab9e0bab18f7fbc709267ddaade0d7a77a1f5e | 94e33a31faa76775069b071adea97e86e218a8ee | /src/analysis/special_functions/log/deriv.lean | 2a95b04277468bb80a29697336410165bfc9d4d2 | [
"Apache-2.0"
] | permissive | urkud/mathlib | eab80095e1b9f1513bfb7f25b4fa82fa4fd02989 | 6379d39e6b5b279df9715f8011369a301b634e41 | refs/heads/master | 1,658,425,342,662 | 1,658,078,703,000 | 1,658,078,703,000 | 186,910,338 | 0 | 0 | Apache-2.0 | 1,568,512,083,000 | 1,557,958,709,000 | Lean | UTF-8 | Lean | false | false | 12,628 | 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.log.basic
import analysis.special_functions.exp_deriv
/-!
# Derivative and series expan... |
7d20256852a4a213c09b72f2cafb2e79c7e0a36c | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/algebra/associated.lean | 9f98272142d867bdb29acdf3e3819dac67355302 | [
"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 | 32,046 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jens Wagemaker
-/
import algebra.divisibility
import algebra.group_power.basic
import algebra.invertible
/-!
# Associated, prime, and irreducible elements.
-/
variabl... |
fed5fb8ea9f35f6a418a262a17544893467d3e8f | 4e3a83d79923bb53bf84b68a2b8217b809b80c1b | /src/fermat.lean | 3f940429e37bcfda26c60b5f1b55a0f68641f65c | [] | no_license | upamanyus/x2ny2-lean | ff4817ccfde5555bb4f0f81636326fe7f3c4353a | 9c8d1d529201ec03ab129d75f0389101f303cc1a | refs/heads/main | 1,685,909,531,125 | 1,624,379,209,000 | 1,624,379,209,000 | 379,085,315 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,178 | lean | import ring_theory.coprime
import data.real.basic
import data.nat.modeq
open nat
noncomputable theory
namespace fermat
def is_sum_of_relprime_squares (n:ℕ) :=
∃ a b, n = a^2 + b^2 ∧ gcd a b = 1.
theorem lem_1_4 (N q: ℕ) :
is_sum_of_relprime_squares N →
nat.prime q → is_sum_of_relprime_squares q → q ∣ N →
is_s... |
ae8bbffe37c315dbdb8ce00c1ddf099bf0bccfc2 | 6b02ce66658141f3e0aa3dfa88cd30bbbb24d17b | /src/Lean/Elab/InfoTree.lean | 1fa0cfaa1209265f8e90c29b175499c64722937a | [
"Apache-2.0"
] | permissive | pbrinkmeier/lean4 | d31991fd64095e64490cb7157bcc6803f9c48af4 | 32fd82efc2eaf1232299e930ec16624b370eac39 | refs/heads/master | 1,681,364,001,662 | 1,618,425,427,000 | 1,618,425,427,000 | 358,314,562 | 0 | 0 | Apache-2.0 | 1,618,504,558,000 | 1,618,501,999,000 | null | UTF-8 | Lean | false | false | 12,337 | lean | /-
Copyright (c) 2020 Wojciech Nawrocki. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wojciech Nawrocki, Leonardo de Moura
-/
import Lean.Data.Position
import Lean.Expr
import Lean.Message
import Lean.Data.Json
import Lean.Meta.Basic
import Lean.Meta.PPGoal
namespa... |
dcfdb90a083fe11c6619457ad950b8c649db6752 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/linear_algebra/matrix/ldl.lean | 55458ac40f91d475e7624da1804d4c276c26f800 | [
"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 | 4,761 | lean | /-
Copyright (c) 2022 Alexander Bentkamp. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp
-/
import analysis.inner_product_space.gram_schmidt_ortho
import linear_algebra.matrix.pos_def
/-! # LDL decomposition
> THIS FILE IS SYNCHRONIZED WITH MATHLIB... |
3a9e6d5dc36d8154e1154b89067f7b13f4f3a5a0 | 437dc96105f48409c3981d46fb48e57c9ac3a3e4 | /src/geometry/manifold/real_instances.lean | 644a5080dc148c919a81e76b365061ab922d0dfa | [
"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 | 14,125 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import geometry.manifold.smooth_manifold_with_corners
import linear_algebra.finite_dimensional
/-!
# Constructing examples of manifolds over ℝ
We introduce th... |
c9da1dd35e0c8c684da5d4c876c6cdbd1616af08 | 367134ba5a65885e863bdc4507601606690974c1 | /src/linear_algebra/alternating.lean | d9a38cc8fe0f67d06e9169526b1fc83e419354e8 | [
"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 | 15,831 | lean | /-
Copyright (c) 2020 Zhangir Azerbayev. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Eric Wieser, Zhangir Azerbayev
-/
import linear_algebra.multilinear
import linear_algebra.linear_independent
import group_theory.perm.sign
/-!
# Alternating Maps
We construct the ... |
d38134b019f61add95e53f37f1e9ca5266cd34a2 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/measure_theory/group/measure.lean | 16c0670da6b6d07f91229b2581312e154e0737d2 | [
"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 | 22,699 | 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 dynamics.ergodic.measure_preserving
import measure_theory.measure.regular
import measure_theory.group.measurable_equiv
import measure_theory.measure.open_p... |
72ec7e7e3c1a5816372a9f5ed300c1ed92d33671 | 957a80ea22c5abb4f4670b250d55534d9db99108 | /tests/lean/run/u_eq_max_u_v.lean | f24e42df5f4fec5f1bb6496ec69fb3dc9d0bebd0 | [
"Apache-2.0"
] | permissive | GaloisInc/lean | aa1e64d604051e602fcf4610061314b9a37ab8cd | f1ec117a24459b59c6ff9e56a1d09d9e9e60a6c0 | refs/heads/master | 1,592,202,909,807 | 1,504,624,387,000 | 1,504,624,387,000 | 75,319,626 | 2 | 1 | Apache-2.0 | 1,539,290,164,000 | 1,480,616,104,000 | C++ | UTF-8 | Lean | false | false | 3,058 | lean | universe variables u v u1 u2 v1 v2
set_option pp.universes true
open smt_tactic
meta def blast : tactic unit := using_smt $ intros >> add_lemmas_from_facts >> repeat_at_most 3 ematch
notation `♮` := by blast
structure semigroup_morphism { α β : Type u } ( s : semigroup α ) ( t: semigroup β ) :=
(map: α → β)
(mul... |
7acdb6e8b7d6b495674e22ab010caf1f6e83d751 | d31b9f832ff922a603f76cf32e0f3aa822640508 | /src/hott/types/nat/order.lean | 09022a51dbfeac03fa42e0d9fd9da5faaf5fa546 | [
"Apache-2.0"
] | permissive | javra/hott3 | 6e7a9e72a991a2fae32e5764982e521dca617b16 | cd51f2ab2aa48c1246a188f9b525b30f76c3d651 | refs/heads/master | 1,585,819,679,148 | 1,531,232,382,000 | 1,536,682,965,000 | 154,294,022 | 0 | 0 | Apache-2.0 | 1,540,284,376,000 | 1,540,284,375,000 | null | UTF-8 | Lean | false | false | 28,339 | lean | /-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad
The order relation on the natural numbers.
-/
import .basic ...algebra.ordered_ring
universes u v w
hott_theory
namespace hott
ope... |
36a13c0dee1e5c350f8536277a62afa58f27e5b7 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/topology/sheaves/limits.lean | 3612b1b8acc3f1d76e076ab721cafb12088ac200 | [
"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 | 1,936 | 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.sheaf_condition.sites
import category_theory.sites.limits
import category_theory.adjunction
import category_theory.limits.functor_category
/-... |
dce60f1dfec875db1d7864528902c4518ddf880a | 4fa161becb8ce7378a709f5992a594764699e268 | /src/control/equiv_functor/instances.lean | 3bc8ea3ee4fe7f6e19b7366dd7a3713b8b3e9c98 | [
"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 | 788 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Scott Morrison
-/
import data.finset
import control.equiv_functor
/-!
# `equiv_functor` instances
We derive some `equiv_functor` instances, to enable `equiv_rw` to rewrite under these... |
36ea0e0c483f9e683a8685283db9c34079ffa906 | 271e26e338b0c14544a889c31c30b39c989f2e0f | /stage0/src/Init/Lean/Level.lean | 262aab73091f520eaa937a810449a043c8d31956 | [
"Apache-2.0"
] | permissive | dgorokho/lean4 | 805f99b0b60c545b64ac34ab8237a8504f89d7d4 | e949a052bad59b1c7b54a82d24d516a656487d8a | refs/heads/master | 1,607,061,363,851 | 1,578,006,086,000 | 1,578,006,086,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,790 | lean | /-
Copyright (c) 2018 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import Init.Data.Option.Basic
import Init.Data.HashMap
import Init.Data.PersistentHashMap
import Init.Lean.Data.Name
import Init.Lean.Data.Format
d... |
a9a591ac2ee5f0973dead9ba861e0d45aa839f65 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/order/rel_iso/group.lean | 0cc4b0c71b19410d6a0625ee8dc31f83a6cd7d0e | [
"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 | 1,142 | 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 algebra.group.defs
import order.rel_iso.basic
/-!
# Relation isomorphisms form a group
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file ... |
75433930b0a8714c7fac8ae3cb97d78ba787d6e7 | 957a80ea22c5abb4f4670b250d55534d9db99108 | /tests/lean/run/kha_inst_bug.lean | 31fa9c3d64c94bbec314aef6e124ba2a756183ba | [
"Apache-2.0"
] | permissive | GaloisInc/lean | aa1e64d604051e602fcf4610061314b9a37ab8cd | f1ec117a24459b59c6ff9e56a1d09d9e9e60a6c0 | refs/heads/master | 1,592,202,909,807 | 1,504,624,387,000 | 1,504,624,387,000 | 75,319,626 | 2 | 1 | Apache-2.0 | 1,539,290,164,000 | 1,480,616,104,000 | C++ | UTF-8 | Lean | false | false | 190 | lean | open nat
example (a b : ℕ) : a - b = a - min a b :=
if h : a ≥ b then by rw [min_eq_right h]
else by rw [sub_eq_zero_of_le (le_of_not_ge h), min_eq_left (le_of_not_ge h), nat.sub_self]
|
8235b64f8c9f4b247c928c33f90380464108f6f8 | 3dc4623269159d02a444fe898d33e8c7e7e9461b | /.github/workflows/project_1_a_decrire/lean-scheme-submission/src/sheaves/covering/covering.lean | 14c004630acc062c49df5c0d0df207ef04714b3f | [] | no_license | Or7ando/lean | cc003e6c41048eae7c34aa6bada51c9e9add9e66 | d41169cf4e416a0d42092fb6bdc14131cee9dd15 | refs/heads/master | 1,650,600,589,722 | 1,587,262,906,000 | 1,587,262,906,000 | 255,387,160 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,295 | lean | /-
Package the definition of an open cover of an open set.
-/
import topology.basic
import topology.opens
import to_mathlib.opens
universes u
open topological_space lattice
section covering
variables {α : Type u} [topological_space α]
-- Open cover.
structure covering (U : opens α) :=
{γ : Type u}
(Uis :... |
1f88ffe4e3f301a992c3652079d402fe57253738 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Compiler/Options.lean | 5ec2f8a0e21d839efe2757bad12481b3f364b571 | [
"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 | 449 | 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.Util.Trace
import Lean.Data.Options
namespace Lean.Compiler
register_builtin_option compiler.check : Bool := {
defValue := true
group :... |
c893f62dbbb0f9c681d90678d981404213972d8f | e38e95b38a38a99ecfa1255822e78e4b26f65bb0 | /src/certigrad/util.lean | f2b556d6901fad9c19c356fcc3c861de38a2c054 | [
"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 | 21,413 | lean | import system.io data.list.set
meta constant io.mkdir (s : string) [io.interface] : io nat
class has_smul (α β : Type) := (smul : α → β → β)
def smul {α β : Type} [has_smul α β] : α → β → β := has_smul.smul
infixl ` ⬝ ` := smul
def pextt {P : Prop} : P → (P = true) := λ Hp, propext (iff_true_intro Hp)
def pextf {P :... |
5c63069789cb065eba7aec7fa93cef72f4ea4986 | aa101d73b1a3173c7ec56de02b96baa8ca64c42e | /src/exercises/02_iff_if_and.lean | 5f28043d86bd7e4656d68494ea1e9932054269fe | [
"Apache-2.0"
] | permissive | gihanmarasingha/tutorials | b554d4d53866c493c4341dc13e914b01444e95a6 | 56617114ef0f9f7b808476faffd11e22e4380918 | refs/heads/master | 1,671,141,758,153 | 1,599,173,318,000 | 1,599,173,318,000 | 282,405,870 | 0 | 0 | Apache-2.0 | 1,595,666,751,000 | 1,595,666,750,000 | null | UTF-8 | Lean | false | false | 13,610 | lean | import data.real.basic
/-
In the previous file, we saw how to rewrite using equalities.
The analogue operation with mathematical statements is rewriting using
equivalences. This is also done using the `rw` tactic.
Lean uses ↔ to denote equivalence instead of ⇔.
In the following exercises we will use the lemma:
su... |
c16f27a9845d8e9c511deaa02383cd2b720f720c | 4727251e0cd73359b15b664c3170e5d754078599 | /src/topology/algebra/uniform_filter_basis.lean | 3fd209f25f00388493d136e0381b57ced7a5a1e0 | [
"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 | 1,857 | 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 files contain... |
e2b293cb2d4f263c22fd7b5ef58d5606e361a5e2 | 367134ba5a65885e863bdc4507601606690974c1 | /src/dynamics/omega_limit.lean | db27d7394b65f70c33dabdf1f99db18b60673a3c | [
"Apache-2.0"
] | permissive | kodyvajjha/mathlib | 9bead00e90f68269a313f45f5561766cfd8d5cad | b98af5dd79e13a38d84438b850a2e8858ec21284 | refs/heads/master | 1,624,350,366,310 | 1,615,563,062,000 | 1,615,563,062,000 | 162,666,963 | 0 | 0 | Apache-2.0 | 1,545,367,651,000 | 1,545,367,651,000 | null | UTF-8 | Lean | false | false | 16,711 | lean | /-
Copyright (c) 2020 Jean Lo. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean Lo
-/
import dynamics.flow
/-!
# ω-limits
For a function `ϕ : τ → α → β` where `β` is a topological space, we
define the ω-limit under `ϕ` of a set `s` in `α` with respect to
filter `f... |
4857aa79c9a891ef82c0d509fc60fbbeb85b9d51 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/endofunctor/algebra.lean | 42a453ec5d005130ac8f5a238afae13c8970f461 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 17,065 | lean | /-
Copyright (c) 2022 Joseph Hua. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Bhavik Mehta, Johan Commelin, Reid Barton, Rob Lewis, Joseph Hua
-/
import category_theory.functor.reflects_isomorphisms
import category_theory.limits.shapes.terminal
/-!
... |
e001e314c83410aa5ac73d6f55ff4d2d2c779a5c | af6139dd14451ab8f69cf181cf3a20f22bd699be | /library/init/native/anf.lean | ef29acefa546d3dcd274063f2e06198fbfb8aa04 | [
"Apache-2.0"
] | permissive | gitter-badger/lean-1 | 1cca01252d3113faa45681b6a00e1b5e3a0f6203 | 5c7ade4ee4f1cdf5028eabc5db949479d6737c85 | refs/heads/master | 1,611,425,383,521 | 1,487,871,140,000 | 1,487,871,140,000 | 82,995,612 | 0 | 0 | null | 1,487,905,618,000 | 1,487,905,618,000 | null | UTF-8 | Lean | false | false | 4,254 | lean | /-
Copyright (c) 2016 Jared Roesch. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jared Roesch
-/
prelude
import init.meta.format
import init.meta.expr
import init.data.string
import init.category.state
import init.native.internal
import init.native.ir
import init.na... |
31616dda5972e67457d6cf690d00b21781652c78 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/core.lean | 2311c8fe3d08512db8bb2c6c50f2fb7542326aa3 | [
"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 | 3,113 | 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 control.equiv_functor
import category_theory.groupoid
import category_theory.whiskering
import category_theory.types
/-!
# The core of a category
> THIS FILE ... |
edfd995193036b79e0c5183e35684425b78f0e77 | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/analysis/normed_space/operator_norm.lean | 637843a43bfb9da56601df9137ccf2845c601995 | [
"Apache-2.0"
] | permissive | ayush1801/mathlib | 78949b9f789f488148142221606bf15c02b960d2 | ce164e28f262acbb3de6281b3b03660a9f744e3c | refs/heads/master | 1,692,886,907,941 | 1,635,270,866,000 | 1,635,270,866,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 59,604 | lean | /-
Copyright (c) 2019 Jan-David Salchow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo
-/
import algebra.algebra.tower
import analysis.normed_space.linear_isometry
import analysis.normed_space.riesz_lemma
import data.equiv... |
bef483e964a8d8bafa4b8b6ae3005bebe8d45c4c | 510e96af568b060ed5858226ad954c258549f143 | /algebra/lattice/complete_lattice.lean | dc89bf7527ede698de5f7dc3e67cca928532bb27 | [] | no_license | Shamrock-Frost/library_dev | cb6d1739237d81e17720118f72ba0a6db8a5906b | 0245c71e4931d3aceeacf0aea776454f6ee03c9c | refs/heads/master | 1,609,481,034,595 | 1,500,165,215,000 | 1,500,165,347,000 | 97,350,162 | 0 | 0 | null | 1,500,164,969,000 | 1,500,164,969,000 | null | UTF-8 | Lean | false | false | 20,238 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Theory of complete lattices.
-/
import .bounded_lattice
set_option old_structure_cmd true
universes u v w w₂
variables {α : Type u} {β : Type v} {ι : Sort w} {ι₂ : So... |
3fa87351fd0f99caeacb4fd669e58f7efad9d3e2 | 9dd3f3912f7321eb58ee9aa8f21778ad6221f87c | /tests/lean/run/1335.lean | 4da99f493eee2759532d961166bf1a317b695adc | [
"Apache-2.0"
] | permissive | bre7k30/lean | de893411bcfa7b3c5572e61b9e1c52951b310aa4 | 5a924699d076dab1bd5af23a8f910b433e598d7a | refs/heads/master | 1,610,900,145,817 | 1,488,006,845,000 | 1,488,006,845,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 615 | lean | import standard
namespace int
private lemma sub_nat_nat_elim (m n : ℕ) (P : ℕ → ℕ → ℤ → Prop)
(hp : ∀i n, P (n + i) n (of_nat i))
(hn : ∀i m, P m (m + i + 1) (-[1+ i])) :
P m n (sub_nat_nat m n) :=
sorry
inductive rel_int_nat_nat : ℤ → ℕ × ℕ → Prop
| pos : ∀m p, rel_int_nat_nat (of_nat p) (m + p, m)
| neg : ∀m ... |
1cd97e93ea067b12bb743ad6f5d73da8a4b7e5e7 | 947b78d97130d56365ae2ec264df196ce769371a | /tests/lean/run/overloaded.lean | 1929fe664b482276f8cdfda2572ac6b996753ca4 | [
"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 | 397 | lean | new_frontend
def A.x : Nat := 10
def B.x : String := "hello"
def f (a : Nat) := a + 1
def g (s : String) := s ++ " world"
open A
open B
#check f x
#check g x
macro "foo!" x:term : term => `($x + 1)
macro "foo!" x:term : term => `($x ++ " world")
#check f (foo! 1)
#check g (foo! "hello")
macro "bla!" : term => `((1 ... |
2a08a3fd5fc4c14c8dd5ae9ac6787d31237c93b0 | 618003631150032a5676f229d13a079ac875ff77 | /test/hint.lean | e1a5109b3002622f90c2b78ae431631a956a23f3 | [
"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 | 1,298 | lean | import tactic.hint
import tactic.split_ifs
import tactic.finish
example : 1 = 1 :=
begin
(do hints ← tactic.hint, guard $ ("refl", 0) ∈ hints),
refl
end
-- `split_ifs` is designated as a `hint_tactic` in its own file
example : if 1 = 1 then true else false :=
begin
(do hints ← tactic.hint, guard $ ("split_ifs",... |
65dd30afe6b2ed06305e7f45df20d3494fdbbc9f | 367134ba5a65885e863bdc4507601606690974c1 | /src/algebra/order_functions.lean | 3fdb37aa29d472c7bcfbe97260824746b2d67be2 | [
"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 | 3,929 | 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 algebra.order
import order.lattice
/-!
# `max` and `min`
This file proves basic properties about maxima and minima on a `linear_order`.
## Tags
min, max
-/... |
2e2bf7666c360e716e547e0e6e3d2128fc0c45dd | 36938939954e91f23dec66a02728db08a7acfcf9 | /lean/deps/x86_semantics/src/x86_semantics/common.lean | 4157c80863a7586d9845e544ab9a5dc7309a15d8 | [
"Apache-2.0"
] | permissive | pnwamk/reopt-vcg | f8b56dd0279392a5e1c6aee721be8138e6b558d3 | c9f9f185fbefc25c36c4b506bbc85fd1a03c3b6d | refs/heads/master | 1,631,145,017,772 | 1,593,549,019,000 | 1,593,549,143,000 | 254,191,418 | 0 | 0 | null | 1,586,377,077,000 | 1,586,377,077,000 | null | UTF-8 | Lean | false | false | 32,739 | lean | /-
This module defines the core datatypes used to represent x86 instruction semantics.
-/
import galois.category.coe1
import galois.sexpr
namespace mc_semantics
------------------------------------------------------------------------
-- arg_index
/- This denotes the index of a variable in a context.
It is equivant ... |
6adc05ad86360767c3f7904014fc371a9474a77c | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/nat/basic.lean | f4f86b7632b89ca1f6afef8834d46e053408db87 | [
"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 | 30,710 | lean | /-
Copyright (c) 2014 Floris van Doorn (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-/
import order.basic
import algebra.group_with_zero.basic
import algebra.ring.defs
... |
a228f018943f127408848b7c0986c24044ce293a | c512f72c3704cbf8f34addab0d4482633dc46bbe | /src/reducibility.lean | 9e73e955b72ca2e5138e0f76819fae54e57a644a | [] | no_license | iehality/abstract-computability | 7479c2786ecac8e00f3d7be00cbd7cd4a4ae43fc | 19c1a32e748e733c65f3e9e6395e4e56e4330cca | refs/heads/main | 1,680,113,399,119 | 1,616,950,483,000 | 1,616,950,483,000 | 346,220,308 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,361 | lean | import pca
import re
namespace pca
universe variable u
variables {α : Type u}
variables [pca α]
namespace reducibility
def m_reducible (f g : α) : Prop := ∃ e : α, e ∈ (ℛ₀ : set α) ∧ (∀ x, ↓e * ↓g * ↓x = ↓f * ↓x)
def i_reducible (f g : α) : Prop :=
∃ e : α, e ∈ (ℛ₀ : set α) ∧ (∀ x, ↓e * ↓g * ↓x = ↓f * ↓x) ∧ (∀ x... |
4326e2d4b8d4f515fcf98d0e38b0e0a1b78db405 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/order/fixed_points.lean | c8511d89f99a52d8d584f4512ada7e043ea8821b | [
"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 | 8,660 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau
Fixed point construction on complete lattices.
-/
import order.complete_lattice
universes u v w
variables {α : Type u} {β : Type v} {γ : Type w}
namespace ... |
430043b69c7055defb9436f3c101b37afcb2d40d | 4727251e0cd73359b15b664c3170e5d754078599 | /src/tactic/lint/type_classes.lean | cd945a06fdc8cdf431d71e02347a82d5d52bd086 | [
"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 | 23,325 | 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... |
853be6c5a8e146af2fa6e13bc5fbd4e81fb4940e | 97c8e5d8aca4afeebb5b335f26a492c53680efc8 | /ground_zero/HITs/circle.lean | 03ee870207bee5edb13827fc9f022580c91462de | [] | no_license | jfrancese/lean | cf32f0d8d5520b6f0e9d3987deb95841c553c53c | 06e7efaecce4093d97fb5ecc75479df2ef1dbbdb | refs/heads/master | 1,587,915,151,351 | 1,551,012,140,000 | 1,551,012,140,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,458 | lean | import ground_zero.HITs.suspension ground_zero.theorems.ua
import ground_zero.types.integers
open ground_zero.types.equiv (subst transport)
open ground_zero.types.eq (renaming refl -> idp)
open ground_zero.structures (hset)
open ground_zero.types
/-
Circle S¹ as Higher Inductive Type.
* HoTT 6.4
π₁(S¹) = ℤ proo... |
5d4cb0cb183acd909201f661e6e449430c9b59d9 | 3dd1b66af77106badae6edb1c4dea91a146ead30 | /tests/lean/run/tactic2.lean | a554983d0666e3650a07ed120841b1b8e9211524 | [
"Apache-2.0"
] | permissive | silky/lean | 79c20c15c93feef47bb659a2cc139b26f3614642 | df8b88dca2f8da1a422cb618cd476ef5be730546 | refs/heads/master | 1,610,737,587,697 | 1,406,574,534,000 | 1,406,574,534,000 | 22,362,176 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 111 | lean | import standard
using tactic
theorem tst {A B : Prop} (H1 : A) (H2 : B) : A
:= by state; assumption
check tst |
1e47f2fba3ecf78350266330f667334046a4d4dc | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/algebra/category/Module/limits.lean | 0aac52b22812167e22170cf304eead94d315cbfe | [
"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 | 4,433 | 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.Module.basic
import algebra.category.Group.limits
/-!
# The category of R-modules has all limits
Further, these limits are preserved by the ... |
472bf23fa0437c39ff23ff1f75770a66a161a764 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/data/real/basic.lean | 113e0afb158dfade519ca221b8d3fe8048712934 | [
"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 | 25,505 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Floris van Doorn
-/
import algebra.module.basic
import algebra.bounds
import algebra.order.archimedean
import algebra.star.basic
import data.real.cau_seq_completion
imp... |
177bf1f324b97da96fea50edeb9cb9970b3aa3a4 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/125.lean | afa97f6a23263e3d64c6487deca6d165df45f4ff | [
"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 | 657 | lean | class HasElems (α : Type) : Type := (elems : Array α)
def elems (α : Type) [HasElems α] : Array α := HasElems.elems
inductive Foo : Type
| mk1 : Bool → Foo
| mk2 : Bool → Foo
open Foo
instance BoolElems : HasElems Bool := ⟨#[false, true]⟩
instance FooElems : HasElems Foo := ⟨(elems Bool).map mk1 ++ (elems Bool).ma... |
64234f31e4ab30579412ba3dabda23192ecd0255 | 367134ba5a65885e863bdc4507601606690974c1 | /src/measure_theory/pi_system.lean | 728bb281585994d70474caaa5c3fab470003b565 | [
"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 | 17,822 | lean | /-
Copyright (c) 2021 Martin Zinkevich. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Martin Zinkevich
-/
import measure_theory.measurable_space
import data.equiv.encodable.lattice
/-!
# Induction principles for measurable sets, related to π-systems a... |
9b524b262a67df8d6ae07c4072e1c8ce508aafc0 | 6094e25ea0b7699e642463b48e51b2ead6ddc23f | /tests/lean/run/blast_meta_bug.lean | ca6e04f1b5bea1359fc520288bffbc21ee2494f3 | [
"Apache-2.0"
] | permissive | gbaz/lean | a7835c4e3006fbbb079e8f8ffe18aacc45adebfb | a501c308be3acaa50a2c0610ce2e0d71becf8032 | refs/heads/master | 1,611,198,791,433 | 1,451,339,111,000 | 1,451,339,111,000 | 48,713,797 | 0 | 0 | null | 1,451,338,939,000 | 1,451,338,939,000 | null | UTF-8 | Lean | false | false | 197 | lean | constants {A : Type.{1}} (P : A → Prop) (Q : A → Prop)
definition H : ∀ a, (: P a :) → Exists Q := sorry
set_option blast.strategy "ematch"
example (a : A) : P a → Exists Q :=
by blast
|
2c28942c189960098592f8d81bed2319d85a342f | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /tests/lean/run/270.lean | 12ff3e314b676524e086d0a1ba871f1bbc500ae4 | [
"Apache-2.0"
] | permissive | collares/lean4 | 861a9269c4592bce49b71059e232ff0bfe4594cc | 52a4f535d853a2c7c7eea5fee8a4fa04c682c1ee | refs/heads/master | 1,691,419,031,324 | 1,618,678,138,000 | 1,618,678,138,000 | 358,989,750 | 0 | 0 | Apache-2.0 | 1,618,696,333,000 | 1,618,696,333,000 | null | UTF-8 | Lean | false | false | 1,071 | lean | class CommAddSemigroup (α : Type u) extends Add α where
addComm : {a b : α} → a + b = b + a
addAssoc : {a b c : α} → a + b + c = a + (b + c)
open CommAddSemigroup
theorem addComm3 [CommAddSemigroup α] {a b c : α} : a + b + c = a + c + b := by {
have h : b + c = c + b := addComm;
have h' := congrArg (a... |
8e50d440a1f1cdfe992dca62dd1a47d101ed21d2 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/group_theory/perm/cycle/type.lean | ea4c53db906c223021e97177f5a1a5f7c9c58ebf | [
"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 | 28,057 | lean | /-
Copyright (c) 2020 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import algebra.gcd_monoid.multiset
import combinatorics.partition
import group_theory.perm.cycle.basic
import ring_theory.int.basic
import tactic.linarith
/-!
# C... |
c2c38c6bb53b78c37e2812745e6c67a8b7da65b3 | c3f2fcd060adfa2ca29f924839d2d925e8f2c685 | /library/logic/axioms/prop_decidable.lean | c1d723b04f697d546b15ccb40aa8b6504cf2b758 | [
"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 | 886 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: logic.axioms.prop_decidable
Author: Leonardo de Moura
-/
import logic.axioms.prop_complete logic.axioms.hilbert
open decidable inhabited nonempty
-- Excluded middle + Hilbert i... |
181b68d1b17f2e8d2c91635bd5e04a7d81168b7e | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/model_theory/bundled.lean | bcbbb232f22c68a2f3a5c61c73c7a62134bbab57 | [
"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 | 6,121 | lean | /-
Copyright (c) 2022 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import model_theory.elementary_maps
import category_theory.concrete_category.bundled
/-!
# Bundled First-Order Structures
This file bundles types together with their ... |
4210834a47ac8ab4dc1db6b48a090dc5961a51e4 | ad0c7d243dc1bd563419e2767ed42fb323d7beea | /analysis/topology/infinite_sum.lean | 1a7812671a57971497e970cf7648eae53ba98fde | [
"Apache-2.0"
] | permissive | sebzim4500/mathlib | e0b5a63b1655f910dee30badf09bd7e191d3cf30 | 6997cafbd3a7325af5cb318561768c316ceb7757 | refs/heads/master | 1,585,549,958,618 | 1,538,221,723,000 | 1,538,221,723,000 | 150,869,076 | 0 | 0 | Apache-2.0 | 1,538,229,323,000 | 1,538,229,323,000 | null | UTF-8 | Lean | false | false | 21,309 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Infinite sum over a topological monoid
This sum is known as unconditionally convergent, as it sums to the same value under all possible
permutations. For Euclidean spa... |
683a233485bc668ea09bc2b01ab5568bb85cbb23 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/run/qexpr1.lean | 7d489543bccc9aafcfc80a8c235048a1af809acf | [
"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 | 590 | lean | open tactic
check
λ (A : Type) (a b c d : A) (H1 : a = b) (H2 : c = b) (H3 : d = c),
have Hac : a = c, by do {
h ← get_local `H2,
hs ← mk_app `eq.symm [h],
x ← to_expr `(eq.trans H1 %%hs),
exact x },
show a = d, by do {
x ← to_expr `(
have aux : a = c, from Hac,
have c = d, by do { symmetry, assumption... |
90f125e711ad8ef07014e01118c5265d3532a4d2 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/char.lean | ae0bf26d899b58082cb26706db85e65624bbf5c8 | [] | 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 | 473 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
Supplementary theorems about the `char` type.
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.PostPort
namespace Mathlib
protected instan... |
d4a732850f97034ff559aefc92cf781288bb21f3 | bb31430994044506fa42fd667e2d556327e18dfe | /src/measure_theory/covering/liminf_limsup.lean | 08303d9914277ea3ad879ebacdbc95a3f0e317d6 | [
"Apache-2.0"
] | permissive | sgouezel/mathlib | 0cb4e5335a2ba189fa7af96d83a377f83270e503 | 00638177efd1b2534fc5269363ebf42a7871df9a | refs/heads/master | 1,674,527,483,042 | 1,673,665,568,000 | 1,673,665,568,000 | 119,598,202 | 0 | 0 | null | 1,517,348,647,000 | 1,517,348,646,000 | null | UTF-8 | Lean | false | false | 16,258 | lean | /-
Copyright (c) 2022 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import measure_theory.covering.density_theorem
/-!
# Liminf, limsup, and doubling measures.
This file is a place to collect lemmas about liminf and limsup for subsets of ... |
388e23e4befddd25f986924cd8aee5e49b93a919 | c86b74188c4b7a462728b1abd659ab4e5828dd61 | /stage0/src/Lean/Elab/Binders.lean | 28dba32e2c7eccec2abf9fc3a0ca8cb38648238b | [
"Apache-2.0"
] | permissive | cwb96/lean4 | 75e1f92f1ba98bbaa6b34da644b3dfab2ce7bf89 | b48831cda76e64f13dd1c0edde7ba5fb172ed57a | refs/heads/master | 1,686,347,881,407 | 1,624,483,842,000 | 1,624,483,842,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 26,104 | 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.Elab.Quotation.Precheck
import Lean.Elab.Term
import Lean.Parser.Term
namespace Lean.Elab.Term
open Meta
open Lean.Parser.Term
/--
Given syn... |
9accd8a8af8a1b76c01b0a41453c06ed79110725 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/analysis/normed_space/pi_Lp.lean | 888405d93df839407eb5ed718b2bd2b4747306fc | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 17,953 | lean | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import analysis.mean_inequalities
/-!
# `L^p` distance on finite products of metric spaces
Given finitely many metric spaces, one can put the max distance on t... |
b3960aa6abe273cb0701d354075af109810e8275 | 1a2aed113dcb5f1c07ae98040953fba5e6563624 | /lean_root/src/demo.lean | 9051f07439283f01b00c2af1d8bfea8477e6f961 | [
"Apache-2.0"
] | permissive | kevindoran/lean | 61d9fb90363b04587624036136482b29e3c16ebd | 77e755095a31e3a214010eb48a61e48d65dfdec9 | refs/heads/master | 1,670,372,072,769 | 1,598,920,365,000 | 1,598,920,365,000 | 264,824,992 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,572 | lean | import data.real.basic
import tactic
namespace logic_example
variable U : Type
variables A B : U → Prop
/-
If you have a proof, h1, which says:
for all x, if the property A(x) is true, then the property B(x) is true.
and you have another proof, h2, which says:
for all x, the property A(X) is true,
Then ... |
bebf00e032ae7287b6a7d52fe9cfeb2510a43836 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/run/mutual_inductive.lean | e8d543dd978c6708bdf0ea0b12038c518c86fffb | [
"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 | 2,865 | lean | namespace X1
mutual_inductive foo, bar
with foo : Type
| mk : foo
with bar : Type
| mk : bar
check @foo
check @bar
check @foo.rec
check @bar.rec
check @foo.has_sizeof_inst
check @bar.has_sizeof_inst
check @foo.mk.sizeof_spec
check @bar.mk.sizeof_spec
end X1
namespace X2
mutual_inductive foo, bar
with foo : Type
| m... |
a980194cf5e18ea1acc5ced5995476928d8df37f | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/enumDecEq.lean | 0aece8c98481fe381458369fb899fec6920b4ee1 | [
"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 | 404 | lean | inductive Foo1 where
| a1
deriving DecidableEq
#print Foo1.ofNat
inductive Foo2 where
| a1 | a2
deriving DecidableEq
#print Foo2.ofNat
inductive Foo3 where
| a1 | a2 | a3
deriving DecidableEq
#print Foo3.ofNat
inductive Foo4 where
| a1 | a2 | a3 | a4
deriving DecidableEq
#print Foo4.ofNat
induct... |
d33225a92de62b2dfc8a07500fe0db14ff77f0e0 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/byStrictIndent.lean | fbaeb666ded1d1bc0041c84d5b1b9f986cf3ca3d | [
"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 | 582 | lean | --
-- no indentation on top-level `by` is still allowed
theorem byTopLevelNoIndent (n : Nat) (h : n > 1) : n > 1 := by
exact h
#print byTopLevelNoIndent
--
theorem byNestedStrictIndent (n : Nat) (h : n > 0) : n > 1 := by
have helper : n > 1 := by
sorry -- expected '{' or strict indentation
sorry
--
theorem by... |
0d94f1c557a79f4183e708c4ea012d9952389513 | 6b10c15e653d49d146378acda9f3692e9b5b1950 | /examples/logic/unnamed_332.lean | e9a5fff458ac44d65475208eb2786b900ee2cba2 | [] | no_license | gebner/mathematics_in_lean | 3cf7f18767208ea6c3307ec3a67c7ac266d8514d | 6d1462bba46d66a9b948fc1aef2714fd265cde0b | refs/heads/master | 1,655,301,945,565 | 1,588,697,505,000 | 1,588,697,505,000 | 261,523,603 | 0 | 0 | null | 1,588,695,611,000 | 1,588,695,610,000 | null | UTF-8 | Lean | false | false | 132 | lean | import tactic
variables A B : Prop
example : A ∧ B → B ∧ A :=
begin
rintros ⟨h₁, h₂⟩,
exact ⟨h₂, h₁⟩
end |
27d0faab58229a7df3e3cf925da6434a85fc83b0 | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/linear_algebra/determinant.lean | 366e1c1957b77963cd81e6b9974ab18850758c0a | [
"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 | 10,628 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Chris Hughes, Tim Baanen
-/
import data.matrix.pequiv
import data.fintype.card
import group_theory.perm.sign
import ring_theory.algebra
import tactic.ring
universes u v w z
open... |
2e96ff2834b67f6c4d16a3ac73238abbcb91841b | 77c5b91fae1b966ddd1db969ba37b6f0e4901e88 | /src/measure_theory/measure/content.lean | 67ffcd4e053549b8bdd2edd49f20fd7859cda57b | [
"Apache-2.0"
] | permissive | dexmagic/mathlib | ff48eefc56e2412429b31d4fddd41a976eb287ce | 7a5d15a955a92a90e1d398b2281916b9c41270b2 | refs/heads/master | 1,693,481,322,046 | 1,633,360,193,000 | 1,633,360,193,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 17,015 | 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.measure.measure_space
import measure_theory.measure.regular
import topology.opens
import topology.compacts
/-!
# Contents
In this file we ... |
2d18813c8ab04f0eab66a091410e44aa99d108dc | b5d813b41740060da28e55b77c69760b7c52760d | /lean_stuff_5.lean | 3e906e2d5f6fefabd904be05c01acad90be3e784 | [] | no_license | ImperialCollegeLondon/SF-solns-zak | 4e85518c5cd4093b995a7593eee8295887e8727e | 7edc4424938e01a6ef4bb518fa8ec1757a2226b1 | refs/heads/master | 1,584,849,829,155 | 1,533,216,269,000 | 1,533,216,269,000 | 139,470,368 | 3 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,273 | lean | --import tactic.ring
theorem m (a b c:ℕ) : (a+b) * c = a * c + b * c := begin
induction c with c H,
{
refl
},
{
have H2 := nat.mul_succ,
rw H2, clear H2,
have H2 := nat.mul_succ a c,
rw H2, clear H2,
have H2 := nat.mul_succ b c,
rw H2, rw H, simp
}
end
theorem m2 (a b c:ℕ) : c * (a+b) = a ... |
1f30bc9715bf5c134eeae4f74cef54fad1b0376a | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/ring_theory/witt_vector/truncated.lean | 1ada6ed1b505347b73cb188838bb2836a31b6553 | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 14,450 | lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Robert Y. Lewis
-/
import ring_theory.witt_vector.init_tail
import tactic.equiv_rw
/-!
# Truncated Witt vectors
The ring of truncated Witt vectors (of length `n`) i... |
104f9144bec4627f7900633253d750796555ce54 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/linear_algebra/basic_auto.lean | f60d6829144209dca3d8b4c2b37b9e70f6da5874 | [] | 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 | 164,231 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebra.big_operators.pi
import Mathlib.alg... |
626f1e1170b4537e116dd5ab787e13f03dc57483 | 302b541ac2e998a523ae04da7673fd0932ded126 | /workspace/more.lean | b48c6d38b7601a68499f7407b3fa7232fe93b767 | [] | no_license | mattweingarten/lambdapure | 4aeff69e8e3b8e78ea3c0a2b9b61770ef5a689b1 | f920a4ad78e6b1e3651f30bf8445c9105dfa03a8 | refs/heads/master | 1,680,665,168,790 | 1,618,420,180,000 | 1,618,420,180,000 | 310,816,264 | 2 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 744 | lean | import Init.Data.BinomialHeap
set_option trace.compiler.ir.init true
abbrev Heap := BinomialHeap Nat (fun a b => a < b)
def mkHeap (n m : Nat) : Heap :=
let hs : List Heap := n.fold (fun i hs =>
let h : Heap := BinomialHeap.empty;
let h : Heap := m.fold (fun j h =>
let v := n*m - j*n - i;
h.ins... |
f0d4467b718e033566749cff27e2eb4e6c8ee6f6 | e37bb385769d6f4ac9931236fd07b708397e086b | /src/library/src_ordered_field.lean | 34ca388f0e7e117f8e43a52030e72f75b8f199d8 | [] | no_license | gihanmarasingha/ems_reals | 5f5d5b9d9dfb5a10da465046336d74995132dff6 | 9df527742db69d0a389add44b506538fdb4d0800 | refs/heads/master | 1,675,327,747,064 | 1,608,036,820,000 | 1,608,036,820,000 | 315,825,726 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,398 | lean | import .src_field_lemmas
namespace mth1001
namespace myreal
class myordered_field (R : Type) extends myfield R :=
(pos : R → Prop)
(decidable_pos : decidable_pred pos)
(trichotomy : ∀ x : R, pos x ∧ ¬x = 0 ∧ ¬pos (-x) ∨ ¬pos x ∧ x = 0 ∧ ¬pos (-x)
∨ ¬pos x ∧ x ≠ 0 ∧ pos (-x))
(pos_add_of_pos_of_pos : ∀ x y, pos x →... |
27ba5f1582043d508eabfa9ce21e969139d725f2 | 6afa22d5eee6e9a56b6a2f1210eca8f7a1067466 | /library/init/core.lean | ea89fd59aed4eda2f8ef6f249f18e70d795dbcd8 | [
"Apache-2.0"
] | permissive | giordano/lean | 72a1fabfeb2f1ccfd38673e2719a719cd6ffbb40 | 56f8877f1efa22215aca0b82f1c0ce2ff975b9c3 | refs/heads/master | 1,663,091,511,168 | 1,590,688,082,000 | 1,590,688,082,000 | 268,183,678 | 0 | 0 | Apache-2.0 | 1,590,885,425,000 | 1,590,885,424,000 | null | UTF-8 | Lean | false | false | 18,791 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
notation, basic datatypes and type classes
-/
prelude
notation `Prop` := Sort 0
notation f ` $ `:1 a:0 := f a
/- Reserving notation. We do this sot that the... |
d4b68b49ed8187e4a6344feb806032519274cb8e | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /hott/algebra/category/precategory.hlean | 490b7a8ed5ece9e55d26d8d1f511a145c3f10c85 | [
"Apache-2.0"
] | permissive | davidmueller13/lean | 65a3ed141b4088cd0a268e4de80eb6778b21a0e9 | c626e2e3c6f3771e07c32e82ee5b9e030de5b050 | refs/heads/master | 1,611,278,313,401 | 1,444,021,177,000 | 1,444,021,177,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 11,377 | 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
-/
import types.trunc types.pi arity
open eq is_trunc pi
namespace category
/-
Just as in Coq-HoTT we add two redundant fields to precategories: assoc' and id_i... |
730fb9824fb911a172c44291471fa4fa0a04de10 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/algebra/category/FinVect/limits.lean | 70188668e71dbc1ad40fa8d6b0c988290f32fe78 | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 2,854 | lean | /-
Copyright (c) 2022 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import algebra.category.FinVect
import algebra.category.Module.limits
import algebra.category.Module.products
import algebra.category.Module.epi_mono
import category_... |
461f5d7e0ec15c5fd85edfb315104a06ef9d35de | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/init/control/reader_auto.lean | 0246841fb14f9363cc940d3e09e8d71827d9f717 | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,298 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Ullrich
The reader monad transformer for passing immutable state.
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.control.lift
import Mathlib.Lean3Lib.init.con... |
ff7aa1a03d832b309479b1ab10cd2cba8eed277f | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/data/fin2.lean | 609c7906521a7107053d8d02c7f92ef9fdbb4fc1 | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 4,068 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
/-!
# Inductive type variant of `fin`
`fin` is defined as a subtype of `ℕ`. This file defines an equivalent type, `fin2`, which is
defined inductively. This is usef... |
2fbf24215ec5e3779234e7c3af00e9490efb9fd4 | 1e3a43e8ba59c6fe1c66775b6e833e721eaf1675 | /src/ring_theory/power_series.lean | 412c5918dfebb4e2e14264971ba3adf30a68894c | [
"Apache-2.0"
] | permissive | Sterrs/mathlib | ea6910847b8dfd18500486de9ab0ee35704a3f52 | d9327e433804004aa1dc65091bbe0de1e5a08c5e | refs/heads/master | 1,650,769,884,257 | 1,587,808,694,000 | 1,587,808,694,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 58,210 | lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Kenny Lau
-/
import data.mv_polynomial
import ring_theory.ideal_operations
/-!
# Formal power series
This file defines (multivariate) formal power series
and develops... |
dfd3039ec8ff15a7e670412f7d86486c150f78f0 | d6aa76a731f5d0a2c72a62729e52996fe8ac81b3 | /src/char_poly.lean | bbfc84909016d18db7b36addd29d7cca50ee17ec | [] | no_license | jalex-stark/friendship-theorem | 88d30d3f4b17cc275a1a4bbc747eeb41f9e1b7a1 | d0e823b0b298c3fcfffe885cd6d2064a5757ef27 | refs/heads/master | 1,668,993,481,235 | 1,595,108,750,000 | 1,595,108,777,000 | 270,936,124 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,876 | lean | /-
Copyright (c) 2020 Aaron Anderson, Jalex Stark. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Aaron Anderson, Jalex Stark.
-/
import linear_algebra.char_poly
import linear_algebra.matrix
import ring_theory.polynomial.basic
import data.zmod.basic
import number_theor... |
e66e7f19d07b11eb0455feb4eed5b87d8ce3c847 | 08bd4ba4ca87dba1f09d2c96a26f5d65da81f4b4 | /src/Lean/Meta/Instances.lean | 87a2bcb941c6c9066265e8b1a032bd04a425f904 | [
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"Apache-2.0",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | gebner/lean4 | d51c4922640a52a6f7426536ea669ef18a1d9af5 | 8cd9ce06843c9d42d6d6dc43d3e81e3b49dfc20f | refs/heads/master | 1,685,732,780,391 | 1,672,962,627,000 | 1,673,459,398,000 | 373,307,283 | 0 | 0 | Apache-2.0 | 1,691,316,730,000 | 1,622,669,271,000 | Lean | UTF-8 | Lean | false | false | 7,209 | 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.ScopedEnvExtension
import Lean.Meta.GlobalInstances
import Lean.Meta.DiscrTree
namespace Lean.Meta
/-
Note: we want to use iota reduction when... |
9abc20d1f294004be63252094d42dcecde5b1eb3 | e39f04f6ff425fe3b3f5e26a8998b817d1dba80f | /category_theory/opposites.lean | eaf07a80d790e94e0a28afcdf005a1cbfbc77fa5 | [
"Apache-2.0"
] | permissive | kristychoi/mathlib | c504b5e8f84e272ea1d8966693c42de7523bf0ec | 257fd84fe98927ff4a5ffe044f68c4e9d235cc75 | refs/heads/master | 1,586,520,722,896 | 1,544,030,145,000 | 1,544,031,933,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,253 | lean | -- Copyright (c) 2017 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Stephen Morgan, Scott Morrison
import category_theory.products
import category_theory.types
namespace category_theory
universes u₁ v₁ u₂ v₂
def op (C : Type u₁) : Type u₁ := ... |
bf1563e4bd884c53c2f34775fa789213343074f8 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/geometry/euclidean/triangle.lean | 97964d71482ecfb0146b6070674c1c6580ec342b | [
"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 | 17,280 | lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Joseph Myers.
-/
import geometry.euclidean.basic
import tactic.interval_cases
noncomputable theory
open_locale big_operators
open_locale classical
open_locale real
open_locale real_inner... |
018c5eeb4a8099af1ddfa4431b594699742b9232 | 3618c6e11aa822fd542440674dfb9a7b9921dba0 | /tests/comparison.lean | 728bbce796870fa3293e0e0862dad7c07e00badc | [] | 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 | 6,741 | lean | import multirelation.approach2.tactic
import tactic.group1r
variables {G : Type} [group G]
(a b c d e f g h i j k l m n o p q r s t u v w x y z : G)
set_option profiler true
-- example (h : a * b * a * b = 1) :
-- (b * a * b * a * b⁻¹ * a⁻¹ * b⁻¹ * a⁻¹ = 1) :=
-- by group1r using h
-- example (h : a * b * a * b... |
2251336613b6d8004da6f7a749b1bdee4ac29183 | 6dc0c8ce7a76229dd81e73ed4474f15f88a9e294 | /stage0/src/Init/Control/Basic.lean | 12e26e63191cfbfc19cc009b1f2dfb5115193148 | [
"Apache-2.0"
] | permissive | williamdemeo/lean4 | 72161c58fe65c3ad955d6a3050bb7d37c04c0d54 | 6d00fcf1d6d873e195f9220c668ef9c58e9c4a35 | refs/heads/master | 1,678,305,356,877 | 1,614,708,995,000 | 1,614,708,995,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,627 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura, Sebastian Ullrich
-/
prelude
import Init.Core
universes u v w
@[reducible] def Functor.mapRev {f : Type u → Type v} [Functor f] {α β : Type u} : f α → (α → β... |
ab42500228363bee4b33e55f491c625c38c396fd | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/number_theory/dioph.lean | 5d7a1451ffebed3736c687e635e9cabeec402555 | [
"Apache-2.0"
] | permissive | ayush1801/mathlib | 78949b9f789f488148142221606bf15c02b960d2 | ce164e28f262acbb3de6281b3b03660a9f744e3c | refs/heads/master | 1,692,886,907,941 | 1,635,270,866,000 | 1,635,270,866,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 28,071 | 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.fin.fin2
import data.pfun
import data.vector3
import number_theory.pell
/-!
# Diophantine functions and Matiyasevic's theorem
Hilbert's tenth problem as... |
b8243e636b9bddccdc8b54311d3cdd1e4594b29e | d1a52c3f208fa42c41df8278c3d280f075eb020c | /tests/lean/run/wfrecUnary.lean | 09b40e17cd683a49c87333c2734244093e3fb2c9 | [
"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 | 191 | lean | def f (n : Nat) : Nat :=
if h : n = 0 then
1
else
2 * f (n-1)
termination_by measure id
decreasing_by
simp [measure, id, invImage, InvImage, Nat.lt_wfRel]
apply Nat.pred_lt h
|
4facaaededda5b158b37a66b7a0db0000994edd8 | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /04_Quantifiers_and_Equality.org.21.lean | db3902ba9a3bf44f0dc4f1b1040f456effbbf0ea | [] | no_license | cjmazey/lean-tutorial | ba559a49f82aa6c5848b9bf17b7389bf7f4ba645 | 381f61c9fcac56d01d959ae0fa6e376f2c4e3b34 | refs/heads/master | 1,610,286,098,832 | 1,447,124,923,000 | 1,447,124,923,000 | 43,082,433 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 431 | lean | /- page 55 -/
import standard
import data.nat
open nat
variable g : ℕ → ℕ → ℕ
variable Hg : g 0 0 = 0
theorem gex1 : ∃ x, g x x = x := exists.intro 0 Hg
theorem gex2 : ∃ x, g x 0 = x := exists.intro 0 Hg
theorem gex3 : ∃ x, g 0 0 = x := exists.intro 0 Hg
theorem gex4 : ∃ x, g x x = 0 := exists.intro 0 Hg
set_option... |
e6e1615d65862f7cceeaf6879e480eab229d20f8 | 74a02dffce22907d2b61b8e226f1d9aa8384c7c0 | /Cli/Basic.lean | 2f4119d02c685c69d103ed7a4584c9a1e90f678b | [
"MIT"
] | permissive | mhuisi/lean4-cli-docker-test | 7e0566c7397746701162e2e22fbad38afcf1e9c4 | 6b3881eaa22596f6f430654f61fc03719ee18c62 | refs/heads/main | 1,680,104,973,886 | 1,616,975,353,000 | 1,616,975,353,000 | 352,411,347 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 57,639 | lean | import Std.Data.RBTree
section Utils
/--
Matches the lengths of lists `a` and `b` by filling the shorter one with
`unit` elements at the tail end. The matched lists are returned in the same order
as they were passed.
-/
def List.matchLength (a : List α) (b : List α) (unit : α) : List α × List α :=
if a... |
04c91e110af4f97013fd78084f1457922c664baa | 31f556cdeb9239ffc2fad8f905e33987ff4feab9 | /tests/pkg/user_attr/UserAttr/Tst.lean | 4c91cb3602a56db0b71a55b38fce3bbd682a0f52 | [
"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 | 2,249 | lean | import Lean
import UserAttr.BlaAttr
@[bla] def f (x : Nat) := x + 2
@[bla] def g (x : Nat) := x + 1
@[foo 10] def h1 (x : Nat) := 2*x + 1
@[foo 20 important] def h2 (x : Nat) := 2*x + 1
open Lean in
def hasBlaAttr (declName : Name) : CoreM Bool :=
return blaAttr.hasTag (← getEnv) declName
#eval hasBlaAttr ``f
#ev... |
a8517ea4fa6b564df5ea1a11d643562a0b36b7cc | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/data/complex/basic.lean | 706716ea7fb1ae7a448ef15e5c78c66bd1226df0 | [
"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 | 27,059 | 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... |
e135adc3ce1dcf18216b192503ddf8b10ed7d27e | a4673261e60b025e2c8c825dfa4ab9108246c32e | /tests/compiler/t2.lean | 5ed5fc44452a5a74835d1c7600d7d20691596c6d | [
"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 | 2,970 | lean | #lang lean4
/- Benchmark for new code generator -/
inductive Expr
| Val : Int → Expr
| Var : String → Expr
| Add : Expr → Expr → Expr
| Mul : Expr → Expr → Expr
| Pow : Expr → Expr → Expr
| Ln : Expr → Expr
namespace Expr
partial def pown : Int → Int → Int
| a, 0 => 1
| a, 1 => a
| a, n =>
let b := pown a (n / 2);... |
62faf40ce5ddc9b96c7aaf611bf8c251310d7f91 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /src/Lean/Data/Lsp/Capabilities.lean | 7d0c3380f71a8ab2372f472c69829c8a0bd64c00 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | cipher1024/lean4 | 6e1f98bb58e7a92b28f5364eb38a14c8d0aae393 | 69114d3b50806264ef35b57394391c3e738a9822 | refs/heads/master | 1,642,227,983,603 | 1,642,011,696,000 | 1,642,011,696,000 | 228,607,691 | 0 | 0 | Apache-2.0 | 1,576,584,269,000 | 1,576,584,268,000 | null | UTF-8 | Lean | false | false | 1,304 | 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 Lean.Data.JsonRpc
import Lean.Data.Lsp.TextSync
import Lean.Data.Lsp.LanguageFeatures
/-! Minimal LSP servers/clients do not have to impleme... |
d01153a5db1dd405fd6a23643a864492d19be0df | 77c5b91fae1b966ddd1db969ba37b6f0e4901e88 | /src/ring_theory/polynomial/content.lean | e0c87de0baeb634cad810e14c6aebde2e21999dd | [
"Apache-2.0"
] | permissive | dexmagic/mathlib | ff48eefc56e2412429b31d4fddd41a976eb287ce | 7a5d15a955a92a90e1d398b2281916b9c41270b2 | refs/heads/master | 1,693,481,322,046 | 1,633,360,193,000 | 1,633,360,193,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 17,052 | 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 ... |
e01724e467aafbfe15a5c4b0ef3f39badcaf24a2 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/algebra/squarefree.lean | 651f91c4259878945e9dcc8d12c9765e2972994a | [
"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 | 9,457 | 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 ring_theory.unique_factorization_domain
import ring_theory.int.basic
import number_theory.divisors
/-!
# Squarefree elements of monoids
An element of a monoid... |
c48a80dc5c85147441b11d516d503ac75eb7c1df | 8cb37a089cdb4af3af9d8bf1002b417e407a8e9e | /tests/lean/run/gcd.lean | 9ea15ab058a4e17bd615915b41f5437a72bdd2c4 | [
"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 | 1,484 | lean | open nat well_founded decidable prod
namespace playground
-- Setup
definition pair_nat.lt := lex nat.lt nat.lt
definition pair_nat.lt.wf : well_founded pair_nat.lt :=
prod.lex_wf lt_wf lt_wf
infixl `≺`:50 := pair_nat.lt
-- Lemma for justifying recursive call
private lemma lt₁ (x₁ y₁ : nat) : (x₁ - y₁, succ y₁) ≺ ... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.