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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
7ca723ed2738836b34abaa3a73ba68b91d4e0cf6 | 5749d8999a76f3a8fddceca1f6941981e33aaa96 | /src/data/set/lattice.lean | fb584b34ba2b964b685bf69eb23a039ebe6cc2e0 | [
"Apache-2.0"
] | permissive | jdsalchow/mathlib | 13ab43ef0d0515a17e550b16d09bd14b76125276 | 497e692b946d93906900bb33a51fd243e7649406 | refs/heads/master | 1,585,819,143,348 | 1,580,072,892,000 | 1,580,072,892,000 | 154,287,128 | 0 | 0 | Apache-2.0 | 1,540,281,610,000 | 1,540,281,609,000 | null | UTF-8 | Lean | false | false | 34,987 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Johannes Hölzl, Mario Carneiro
-- QUESTION: can make the first argument in ∀ x ∈ a, ... implicit?
-/
import logic.basic data.set.basic data.equiv.basi... |
4c5a70cc34023ff49e25e003ee09a6a2c7685354 | 7da4b05ff6af3f2cd178a7c188a45934cee1cce5 | /example.lean | 011ff512dd4168f0261c2c6e9fd99419cd080e98 | [] | no_license | KeenS/lean_tutorial | 794793c6da95b4c8b7eb6e30e1721da8c86e88de | e4463ddaac14fb321f79d7138b9822238ea10a8f | refs/heads/master | 1,587,246,479,934 | 1,472,389,890,000 | 1,472,389,890,000 | 66,768,865 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,346 | lean | open classical
variables p q r s: Prop
-- commutativity of ∧ and ∨
example : p ∧ q ↔ q ∧ p :=
iff.intro
(assume Hpq: p ∧ q,
have Hp: p, from and.left Hpq,
have Hq: q, from and.right Hpq,
and.intro Hq Hp)
(assume Hqp: q ∧ p,
have Hp: p, from and.right Hqp,
have Hq: q, from and.l... |
441889c290594ed5d4414f910faa9070d48c6473 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/608.hlean | 6c790b37cf782e3596d9f79247ead0bfcba1a931 | [
"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 | 111 | hlean | import algebra.category.precategory
open function category
print id
print "-----------"
print definition id
|
d396512cc56f8af3b29e4b948bdc26ac4360ca51 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/measure_theory/measure/lebesgue/complex.lean | bc7a45288ab0af5e958f6bbff9cea9421281d9e8 | [
"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 | 1,809 | lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import measure_theory.constructions.borel_space.complex
import measure_theory.measure.lebesgue.basic
import measure_theory.measure.haar.of_basis
/-!
# Lebesgue mea... |
edfa50dbeec9473b7173a9e2cc1d0e05d621a163 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/combinatorics/simple_graph/prod.lean | 0dca3687cb37e33586a41a245234344529abf0eb | [
"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 | 8,749 | lean | /-
Copyright (c) 2022 George Peter Banyard, Yaël Dillies, Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: George Peter Banyard, Yaël Dillies, Kyle Miller
-/
import combinatorics.simple_graph.connectivity
/-!
# Graph products
> THIS FILE IS SYNCHRONIZED WI... |
2198569151b9e5631b92d32cf964546ed3964beb | 59aed81a2ce7741e690907fc374be338f4f88b6f | /src/math-688/lectures/lec-8.lean | ddb514c3b9333a0339b0954f19d60917fc234850 | [] | no_license | agusakov/math-688-lean | c84d5e1423eb208a0281135f0214b91b30d0ef48 | 67dc27ebff55a74c6b5a1c469ba04e7981d2e550 | refs/heads/main | 1,679,699,340,788 | 1,616,602,782,000 | 1,616,602,782,000 | 332,894,454 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 79 | lean | /- 16 Sep 2019 -/
-- catalan numbers
-- recurrence relation
-- interpretations |
675139e28e2679f48411cf213a09dc17e6da4304 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/system/random/basic.lean | e7b03e1d7ec32a8a0e2b02a78ee3f7261c789129 | [
"Apache-2.0"
] | permissive | waynemunro/mathlib | e3fd4ff49f4cb43d4a8ded59d17be407bc5ee552 | 065a70810b5480d584033f7bbf8e0409480c2118 | refs/heads/master | 1,693,417,182,397 | 1,634,644,781,000 | 1,634,644,781,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,939 | lean | /-
Copyright (c) 2020 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import algebra.group_power
import control.uliftable
import control.monad.basic
import data.bitvec.basic
import data.fin.basic
import data.list.basic
import data.set.inter... |
4c40ae40a1e42d9a89900a36ffad14dbe92d84da | 206422fb9edabf63def0ed2aa3f489150fb09ccb | /src/linear_algebra/multilinear.lean | 986a6f64e66adf2c2e841ca73678d44f2b87ebe6 | [
"Apache-2.0"
] | permissive | hamdysalah1/mathlib | b915f86b2503feeae268de369f1b16932321f097 | 95454452f6b3569bf967d35aab8d852b1ddf8017 | refs/heads/master | 1,677,154,116,545 | 1,611,797,994,000 | 1,611,797,994,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 46,613 | 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 linear_algebra.basic
import algebra.algebra.basic
import tactic.omega
import data.fintype.sort
/-!
# Multilinear maps
We define multilinear maps as map... |
4bc0fc2c800e5728cb9c4edf7ada4a10f58adf50 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/algebra/lie/basic.lean | 3facb8bd7805c7e8dc150b260dfe9b5dd34b3ed4 | [
"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 | 42,290 | lean | /-
Copyright (c) 2019 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import algebra.algebra.basic
import linear_algebra.linear_action
import linear_algebra.bilinear_form
import linear_algebra.direct_sum.finsupp
import tactic.noncomm_ring
/-... |
052649dcf885e714766402b079a9df640cb445d5 | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /tests/lean/unique_instances.lean | e929b8cd6e8be8717f5f48bd5b135e65f2c6feb1 | [
"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 | 325 | lean | import logic data.prod
open prod
set_option class.unique_instances true set_option pp.implicit true
theorem tst (A : Type) (H₁ : inhabited A) (H₂ : inhabited A) : inhabited (A × A) :=
_
set_option class.unique_instances false
theorem tst2 (A : Type) (H₁ : inhabited A) (H₂ : inhabited A) : inhabited (A × A) :=
_
|
01d909503c9352515d321afc98b50a9bf06ac909 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/data/list/defs.lean | 5dab131ca3e2832f1bfaff854e8338b645e3208c | [
"Apache-2.0"
] | permissive | waynemunro/mathlib | e3fd4ff49f4cb43d4a8ded59d17be407bc5ee552 | 065a70810b5480d584033f7bbf8e0409480c2118 | refs/heads/master | 1,693,417,182,397 | 1,634,644,781,000 | 1,634,644,781,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 38,557 | lean | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
-/
import data.option.defs
import logic.basic
import tactic.cache
/-!
## Definitions on lists
Th... |
a4caa0006f8e0021e7076016c779b5cb8c66a123 | 17d3c61bf162bf88be633867ed4cb201378a8769 | /library/init/meta/fun_info.lean | 371aa58d335ff39778b27464aa338735ed1b7fde | [
"Apache-2.0"
] | permissive | u20024804/lean | 11def01468fb4796fb0da76015855adceac7e311 | d315e424ff17faf6fe096a0a1407b70193009726 | refs/heads/master | 1,611,388,567,561 | 1,485,836,506,000 | 1,485,836,625,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,554 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.meta.tactic init.meta.format init.function
structure param_info :=
(is_implicit : bool)
(is_inst_implicit : bool)
(is_prop ... |
b893403945c6c953c17ee72f21c0b959cb110006 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /library/init/meta/name.lean | 561742ac38899b88be48a1098729607311672758 | [
"Apache-2.0"
] | permissive | soonhokong/lean-osx | 4a954262c780e404c1369d6c06516161d07fcb40 | 3670278342d2f4faa49d95b46d86642d7875b47c | refs/heads/master | 1,611,410,334,552 | 1,474,425,686,000 | 1,474,425,686,000 | 12,043,103 | 5 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 1,989 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.ordering init.coe
/- Reflect a C++ name object. The VM replaces it with the C++ implementation. -/
inductive name
| anonymous : name
|... |
62694e728079eaa9d22cbc25b31b438d7621f7f7 | ea5678cc400c34ff95b661fa26d15024e27ea8cd | /computable_em.lean | 05399664c1401f85ca999ad67381ff2bcd1b71bc | [] | no_license | ChrisHughes24/leanstuff | dca0b5349c3ed893e8792ffbd98cbcadaff20411 | 9efa85f72efaccd1d540385952a6acc18fce8687 | refs/heads/master | 1,654,883,241,759 | 1,652,873,885,000 | 1,652,873,885,000 | 134,599,537 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,763 | lean | import data.quot tactic
open classical
noncomputable theory
variables (p : Type) {α : Type*} {β : Type*}
inductive eq' (a : α) : α → Type
| refl : eq' a
infix ` =' `:50 := eq'
def eq'.symm : ∀ {a b : α}, a =' b → b =' a
| _ _ (eq'.refl _) := (eq'.refl _)
def eq'.trans : ∀ {a b c : α}, a =' b → b =' c → a =' c
| _ _... |
85c059d26aaf52f023afb6f45e44f9c13c1b1bd4 | f4bff2062c030df03d65e8b69c88f79b63a359d8 | /src/game/order/level06.lean | d545ae97cace5c404c0f9ba3037b956036451e8b | [
"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 | 1,086 | lean | import game.order.level05
import data.real.basic
open real
namespace xena -- hide
/-
# Chapter 2 : Order
## Level 6
An interesting result to prove.
-/
/- Lemma
For any two non-negative real numbers $a$ and $b$, we have that
$$a \le b \iff a^2 \le b^2 $$.
-/
theorem le_iff_sq_le (a b : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b... |
da8d90976f99fc1eba2cc495f5d7d137582f791b | aa2345b30d710f7e75f13157a35845ee6d48c017 | /analysis/topology/topological_structures.lean | a0da44263ceb7f551fbc3fb4be9d383f87e8fbd7 | [
"Apache-2.0"
] | permissive | CohenCyril/mathlib | 5241b20a3fd0ac0133e48e618a5fb7761ca7dcbe | a12d5a192f5923016752f638d19fc1a51610f163 | refs/heads/master | 1,586,031,957,957 | 1,541,432,824,000 | 1,541,432,824,000 | 156,246,337 | 0 | 0 | Apache-2.0 | 1,541,434,514,000 | 1,541,434,513,000 | null | UTF-8 | Lean | false | false | 54,413 | 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
Theory of topological monoids, groups and rings.
TODO: generalize `topological_monoid` and `topological_add_monoid` to semigroups, or add a type class
... |
6d5ab284f792eafc0f921008a61df6b2696cbd29 | 1abd1ed12aa68b375cdef28959f39531c6e95b84 | /src/order/filter/at_top_bot.lean | c0e5d56edb4e2e6cd8e85dfa1c16493ec1552608 | [
"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 | 61,580 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jeremy Avigad, Yury Kudryashov, Patrick Massot
-/
import order.filter.bases
import data.finset.preimage
/-!
# `at_top` and `at_bot` filters on preorded sets, monoids a... |
5cbef1b0a0ffa601fe6dec1c0164698e817cd314 | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/linear_algebra/bilinear_form.lean | ebae86396cb2f4876a27c55ae84f3dacdf577e49 | [
"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 | 69,496 | lean | /-
Copyright (c) 2018 Andreas Swerdlow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andreas Swerdlow, Kexing Ying
-/
import linear_algebra.dual
import linear_algebra.matrix.basis
import linear_algebra.matrix.nonsingular_inverse
import linear_algebra.tensor_product
... |
6dd722c1de383e5ea187258d27d435ea25432e10 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/triv_sq_zero_ext.lean | f2ffc13cfe0068a451ce11cfd4c626ab9ac7a458 | [
"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 | 27,037 | 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.algebra.basic
import linear_algebra.prod
/-!
# Trivial Square-Zero Extension
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this fil... |
2f47375518a745be00dce26fcc4a115fe6e68dc9 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/set/function_auto.lean | 225ff60abbe5a2582648a24ac5f22d84d52a8809 | [] | 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 | 41,662 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad, Andrew Zipperer, Haitao Zhang, Minchao Wu, Yury Kudryashov
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.set.basic
import Mathlib.logi... |
77997fa61fdb204227eb9c3c4b8324b0c3151ae2 | 8cb37a089cdb4af3af9d8bf1002b417e407a8e9e | /library/init/algebra/classes.lean | e1dde01dc479922864624e7bc29460bae2356191 | [
"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 | 13,228 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.logic init.data.ordering.basic
universes u v
@[algebra] class is_symm_op (α : Type u) (β : out_param (Type v)) (op : α → α → β) : Prop ... |
24cd22a7d794854c6979154aa456ee9b31142134 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Data/Xml/Basic.lean | 191251d4ca8a4ba592e04b766819b59d87f4801b | [
"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 | 993 | lean |
/-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Dany Fabian
-/
import Lean.Data.RBMap
namespace Lean
namespace Xml
def Attributes := RBMap String String compare
instance : ToString Attributes := ⟨λ as => as.fold (λ s n v =>... |
a327ff412f808cf2f328aed49ecff6a2623749fa | e94d3f31e48d06d252ee7307fe71efe1d500f274 | /hott/types/pointed2.hlean | 86fa91c685a0acca504cc1afe159ebd8b183bbd8 | [
"Apache-2.0"
] | permissive | GallagherCommaJack/lean | e4471240a069d82f97cb361d2bf1a029de3f4256 | 226f8bafeb9baaa5a2ac58000c83d6beb29991e2 | refs/heads/master | 1,610,725,100,482 | 1,459,194,829,000 | 1,459,195,377,000 | 55,377,224 | 0 | 0 | null | 1,459,731,701,000 | 1,459,731,700,000 | null | UTF-8 | Lean | false | false | 8,226 | hlean | /-
Copyright (c) 2014 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
Ported from Coq HoTT
-/
import .equiv cubical.square
open eq is_equiv equiv pointed is_trunc
-- structure pequiv (A B : Type*) :=
-- (to_pmap : A →* B)
-- (... |
4cec1193e38fcd6366eb464dc99b56f4fd5759e9 | fe84e287c662151bb313504482b218a503b972f3 | /src/commutative_algebra/hahn.lean | 2112591ce78f5ce770b9e2e66e5839bb1af1fa77 | [] | no_license | NeilStrickland/lean_lib | 91e163f514b829c42fe75636407138b5c75cba83 | 6a9563de93748ace509d9db4302db6cd77d8f92c | refs/heads/master | 1,653,408,198,261 | 1,652,996,419,000 | 1,652,996,419,000 | 181,006,067 | 4 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 37,424 | lean | import data.real.basic data.real.nnreal
import data.zmod.basic
import ring_theory.hahn_series
namespace infinite_root
noncomputable theory
local attribute [instance, priority 2000] classical.prop_decidable
lemma zmod_cases (a : zmod 2) : a = 0 ∨ a = 1 :=
begin
fin_cases a, {left, refl}, {right, refl}
end
lemma zm... |
047b2aff53b24f04ba8d81b76bd2685121b70007 | 32fa6b3db8c34b5b2996ed46f2eef23e6cd58023 | /znum_tests.lean | 8eea57e9159dcc32a22b5c6f9791c11fa506423a | [] | no_license | skbaek/strassen | 3568459f9aa85beb9d3a653e92225bd9518985a5 | 396c94805360b10896d436813c1e4d0190885840 | refs/heads/master | 1,587,522,553,720 | 1,549,860,051,000 | 1,549,860,051,000 | 170,051,087 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,522 | lean | import data.num.lemmas .matrix .strassen
open vector matrix tactic
def const_mat (c : znum) : ∀ k, matrix znum (2^k) (2^k)
| 0 := vector.singleton (vector.singleton c)
| (k+1) := quadruple (const_mat k, const_mat k, const_mat k, const_mat k)
def arith_prog : ∀ k m : nat, vector znum m
| k 0 := nil
| k (m+1) := ... |
082a9613f15d69cbed9f1f9e43b1268fd4e4a7e6 | 92bfaf170880e47d55bf51d5a782fffd76db2f5f | /melting_point/geometry.lean | 95e8bd2c5db8e85eb28169d954c3aff516c93fa5 | [] | no_license | forked-from-1kasper/melting_point | d33403e1985d876a2c7c06859962cc0c37570189 | e5ea4a0917de086b7e5b122e8d5aa90d2761d147 | refs/heads/master | 1,624,785,375,577 | 1,618,305,367,000 | 1,618,305,367,000 | 222,729,018 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,680 | lean | namespace melting_point.geometry
universe u
class is_euclidian (S : Type u) :=
(B : S → S → S → Prop)
(cong : S × S → S × S → Prop)
-- Tarski axioms
(cong_refl (x y : S) : cong (x, y) (y, x))
(cong_trans (a b c : S × S) : cong a b → cong a c → cong b c)
(identity_of_congruence (x y z : S) : cong (x, y) (z, z) → x = y... |
b2550416a11380f4ec67c3d94faf05c2a048379f | 22e97a5d648fc451e25a06c668dc03ac7ed7bc25 | /src/linear_algebra/contraction.lean | e0b9147d02b54fb7f49919be52a4a78565618be3 | [
"Apache-2.0"
] | permissive | keeferrowan/mathlib | f2818da875dbc7780830d09bd4c526b0764a4e50 | aad2dfc40e8e6a7e258287a7c1580318e865817e | refs/heads/master | 1,661,736,426,952 | 1,590,438,032,000 | 1,590,438,032,000 | 266,892,663 | 0 | 0 | Apache-2.0 | 1,590,445,835,000 | 1,590,445,835,000 | null | UTF-8 | Lean | false | false | 1,807 | lean | /-
Copyright (c) 2020 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import linear_algebra.dual
/-!
# Contractions
Given modules $M, N$ over a commutative ring $R$, this file defines the natural linear maps:
$M^* \otimes M \to R$, $M \otim... |
7486fd4fb18e2cbd986a278bc7c3170dd6fe41eb | cbb817439c51008d66b37ce6b1964fea61434d35 | /theorem-proving-in-lean/src/chap_3.lean | 82f2e9f922b66d885ce64e03bfbdac21d1bf63c6 | [] | no_license | tomhoule/theorem-proving-in-lean-exercises | a07f99d4f6b41ce003e8a0274c7bc46359fa62b2 | 60ccc71b8a6df6924e7cc90aab713b804f78da9f | refs/heads/master | 1,663,582,321,828 | 1,590,352,467,000 | 1,590,352,476,000 | 257,107,936 | 3 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,089 | lean | -- Exercise 1
section ex1
variables p q r : Prop
-- commutativity of ∧ and ∨
example : p ∧ q ↔ q ∧ p :=
have beep : p ∧ q → q ∧ p, from λ p_and_q : p ∧ q, and.intro p_and_q.2 p_and_q.1,
have boop : q ∧ p → p ∧ q, from λ q_and_p : q ∧ p, and.intro q_and_p.2 q_and_p.1,
show p ∧ q ↔ q ∧ p, from iff.intro beep boop
exa... |
858c280958bb92fcfd2ccf82c8aa0eac15972368 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/category_theory/concrete_category/default.lean | 72e4679426489631898786765d4e2aa644dd0176 | [
"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 | 55 | lean | import category_theory.concrete_category.unbundled_hom
|
b49248c6d0215011747bed618e1e1220c575364e | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/measure_theory/lebesgue_measure.lean | 6a58efd518b894bc7a87b3104eb78b00003b23f8 | [
"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 | 22,439 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yury Kudryashov
-/
import measure_theory.pi
/-!
# Lebesgue measure on the real line and on `ℝⁿ`
-/
noncomputable theory
open classical set filter
open ennreal (of_rea... |
6f481290f4d4c3a6b3e660d14a8b839507b5b37e | 437dc96105f48409c3981d46fb48e57c9ac3a3e4 | /src/category_theory/limits/shapes/zero.lean | 53da66753a7ea16d4d90204e46d52998b4c6dbc4 | [
"Apache-2.0"
] | permissive | dan-c-k/mathlib | 08efec79bd7481ee6da9cc44c24a653bff4fbe0d | 96efc220f6225bc7a5ed8349900391a33a38cc56 | refs/heads/master | 1,658,082,847,093 | 1,589,013,201,000 | 1,589,013,201,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,305 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.limits.shapes.binary_products
import category_theory.epi_mono
import category_theory.punit
/-!
# Zero morphisms and zero objects
A category "... |
be7ecb615207f1ba742f5748f73d091d67d3f5e3 | ee8cdbabf07f77e7be63a449b8483ce308d37218 | /lean/src/test/induction-11div10tonmn1ton.lean | 82dd080a2e812e39304b62d0cb2bbe2fb61ebda8 | [
"MIT",
"Apache-2.0"
] | permissive | zeta1999/miniF2F | 6d66c75d1c18152e224d07d5eed57624f731d4b7 | c1ba9629559c5273c92ec226894baa0c1ce27861 | refs/heads/main | 1,681,897,460,642 | 1,620,646,361,000 | 1,620,646,361,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 244 | lean | /-
Copyright (c) 2021 OpenAI. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kunhao Zheng
-/
import data.real.basic
example (n : ℕ) : 11 ∣ ( 10 ^ n - (-1 : ℤ) ^ n ) :=
begin
sorry
end
|
fdcdfcb6c0aa9fa6a705027522dd63e3dca786fc | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/limits/shapes/pullbacks_auto.lean | 242a2bf3baac0a9f84370993ee79a43b94b3dbf1 | [] | 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 | 37,299 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Markus Himmel, Bhavik Mehta
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.category_theory.limits.shapes.wide_pullbacks
import Mathlib.ca... |
67bf9a902fb458d0afa003780f85af4931e3bc56 | 8b9f17008684d796c8022dab552e42f0cb6fb347 | /library/init/default.lean | 829456fbc263388d338893d2a310f86d38895a97 | [
"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 | 428 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: init.default
Authors: Leonardo de Moura
-/
prelude
import init.datatypes init.reserved_notation init.tactic init.logic
import init.relation init.wf init.nat init.wf_k init.prod ... |
7f68660bd2005d7f55b2e74cfb393ef7280af572 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/tactic/simp_command.lean | 4c60b8a34599be418b6f7e9e66f4aefc0fd6194f | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,428 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Keeley Hoek, Scott Morrison
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.tactic.core
import Mathlib.PostPort
namespace Mathlib
/-!
## #simp
A user co... |
6c43d1700ccb9491f907b66493f9db485384bd54 | 26ac254ecb57ffcb886ff709cf018390161a9225 | /src/ring_theory/ideal_operations.lean | 9940b6081f6bdfcac3c3604f04728726a7446b53 | [
"Apache-2.0"
] | permissive | eric-wieser/mathlib | 42842584f584359bbe1fc8b88b3ff937c8acd72d | d0df6b81cd0920ad569158c06a3fd5abb9e63301 | refs/heads/master | 1,669,546,404,255 | 1,595,254,668,000 | 1,595,254,668,000 | 281,173,504 | 0 | 0 | Apache-2.0 | 1,595,263,582,000 | 1,595,263,581,000 | null | UTF-8 | Lean | false | false | 34,422 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
More operations on modules and ideals.
-/
import data.nat.choose
import data.equiv.ring
import ring_theory.algebra_operations
universes u v w x
open_locale big_operators
names... |
fffd578abc924ee172b24f3d2b7721b6b68b6fba | d709f1c2372202af61bb6c915ab774eb387f2182 | /LeanNixStatic2.lean | 6d0fd3e43fd7e5f1e6f72d1d69be11d81434e333 | [] | no_license | zygi/leannixstatic2 | aab9d7dd60c0d261270f623c67facd8320888520 | 72e2e066796b5e07b9267087156934ab5358833d | refs/heads/master | 1,678,437,777,726 | 1,614,394,696,000 | 1,614,394,696,000 | 342,755,005 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 486 | lean | import LeanNixStatic1.Inline
import LeanNixStatic1.Extern
-- When reducing, we get the Lean implementation
#reduce 0 == ifNative1Else0 0
-- When eval-ing, we get the native implementation. That's the plugin at work.
#eval 1 == ifNative1Else0 0
-- And of course we can use these native implementations when compiling
-... |
8f0418748a01fa429fb240ba47f8a0bdd4fad59f | 3bdd27ffdff3ffa22d4bb010eba695afcc96bc4a | /src/combinatorics/simplicial_complex/to_move/default.lean | a97585c09ce017a859117022d2cfa06e5bff84bf | [] | no_license | mmasdeu/brouwerfixedpoint | 684d712c982c6a8b258b4e2c6b2eab923f2f1289 | 548270f79ecf12d7e20a256806ccb9fcf57b87e2 | refs/heads/main | 1,690,539,793,996 | 1,631,801,831,000 | 1,631,801,831,000 | 368,139,809 | 4 | 3 | null | 1,624,453,250,000 | 1,621,246,034,000 | Lean | UTF-8 | Lean | false | false | 689 | lean | /-
Copyright (c) 2021 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
import combinatorics.simplicial_complex.to_move.affine
import combinatorics.simplicial_complex.to_move.convex
import combinatorics.simplicial_... |
f2cfa550813c40c9fb7fc5a9d0e1dcbac6e7e998 | bb31430994044506fa42fd667e2d556327e18dfe | /src/topology/algebra/group/basic.lean | 7463aa2e243c2d80f1114b8f5e2ca015afef199d | [
"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 | 68,461 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot
-/
import group_theory.group_action.conj_act
import group_theory.group_action.quotient
import group_theory.quotient_group
import topology... |
3b89af4cb4c9caa2d75ebe8f4aacf5bcc8665a7c | a4673261e60b025e2c8c825dfa4ab9108246c32e | /stage0/src/Init/Data/Array/BinSearch.lean | 63fb792440bd948b2254db6c9a946f551fb89129 | [
"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 | 2,762 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import Init.Data.Array.Basic
universes u v
-- TODO: CLEANUP
namespace Array
-- TODO: remove the [Inhabited α] parameters as soon as we have the ta... |
92591b6134e57ceec32404e5de4eb71acee2cc7c | 4fa161becb8ce7378a709f5992a594764699e268 | /src/algebra/group/hom.lean | 432288ece3e68807f74ab2de4f416f3e7b1b2526 | [
"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 | 12,502 | lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Kevin Buzzard, Scott Morrison, Johan Commelin, Chris Hughes,
Johannes Hölzl, Yury Kudryashov
-/
import algebra.group.commute
import tactic.ext
/-!
# monoid and group... |
c294bdc363ecf17617eacc474fbdedab163fe19f | 592ee40978ac7604005a4e0d35bbc4b467389241 | /Library/generated/mathscheme-lean/Zero_Ringoid0Sig.lean | 21141357a89b9e3676b3eac099324437d3b5c90c | [] | no_license | ysharoda/Deriving-Definitions | 3e149e6641fae440badd35ac110a0bd705a49ad2 | dfecb27572022de3d4aa702cae8db19957523a59 | refs/heads/master | 1,679,127,857,700 | 1,615,939,007,000 | 1,615,939,007,000 | 229,785,731 | 4 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,295 | lean | import init.data.nat.basic
import init.data.fin.basic
import data.vector
import .Prelude
open Staged
open nat
open fin
open vector
section Zero_Ringoid0Sig
structure Zero_Ringoid0Sig (A : Type) : Type :=
(zero : A)
(times : (A → (A → A)))
(leftZero_op_zero : (∀ {x : A} , (times zero x) = zer... |
44b42028cdc515dacd92c350ac1d31e7bca35db4 | ae1e94c332e17c7dc7051ce976d5a9eebe7ab8a5 | /stage0/src/Init/Data/String/Basic.lean | 2d8757bba5007d8079242b3f4db65da963e7a5e5 | [
"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 | 16,156 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
prelude
import Init.Data.List.Basic
import Init.Data.Char.Basic
import Init.Data.Option.Basic
universes u
/-- A byte position in a `String`. Internally, `St... |
0fc3ddf92aca55c4032a8cb85ffb6cf2d3d44390 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/linear_algebra/affine_space/affine_subspace.lean | 19d7d019d5e01aa376df3548a47a1fc98748ae4e | [
"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 | 56,620 | lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import data.set.intervals.unordered_interval
import linear_algebra.affine_space.affine_equiv
/-!
# Affine spaces
This file defines affine subspaces (over modules) and t... |
5b7e5972c6e3ce43071393cb039ff7f133cc5d40 | 54d7e71c3616d331b2ec3845d31deb08f3ff1dea | /tests/lean/defeq_simp4.lean | 948ac4bb4699384fa832002aa16fed5da4ce5e26 | [
"Apache-2.0"
] | permissive | pachugupta/lean | 6f3305c4292288311cc4ab4550060b17d49ffb1d | 0d02136a09ac4cf27b5c88361750e38e1f485a1a | refs/heads/master | 1,611,110,653,606 | 1,493,130,117,000 | 1,493,167,649,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 861 | lean | attribute [reducible]
definition nat_has_add2 : has_add nat :=
has_add.mk (λ x y : nat, x + y)
attribute [reducible]
definition nat_has_add3 : nat → has_add nat :=
λ n, has_add.mk (λ x y : nat, x + y)
open tactic
set_option pp.all true
-- Example where instance canonization does not work.
-- Remark: we can "fix" it ... |
9a16d30a55acc62a90e053a3d20ca82db82aa57f | 7bf54883c04ff2856c37f76a79599ceb380c1996 | /non-mathlib/quadratic.lean | 735dcf698c571640c34a8bdb855039fd50b0cdd5 | [] | no_license | anonymousLeanDocsHosting/lean-polynomials | 4094466bf19acc0d1a47b4cabb60d8c21ddb2b00 | 361ef4cb7b68ef47d43b85cfa2d13f2ea0a47613 | refs/heads/main | 1,691,112,899,935 | 1,631,819,522,000 | 1,631,819,522,000 | 405,448,439 | 0 | 2 | null | null | null | null | UTF-8 | Lean | false | false | 22,137 | lean | import field_definition
import field_results
import numbers
import roots
def quadratic_subst (f : Type) [myfld f] : f -> f -> f -> f -> f
| x a b c := (a .* (x .* x)) .+ ((b .* x) .+ c)
lemma complete_the_square (f : Type) [myfld f] (x b : f) :
(x .* x) .+ (((two f) .* b) .* x) =
(square f (x .+ b)) .+ (.-... |
0c2b7be960eb0570348903278b85172b9d4312cb | a4673261e60b025e2c8c825dfa4ab9108246c32e | /src/Lean/Elab/PreDefinition/Main.lean | 3b7429851c5defa725a9d4a472aadf15dcf88aa7 | [
"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 | 3,225 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Elab.PreDefinition.Basic
import Lean.Elab.PreDefinition.Structural
import Lean.Elab.PreDefinition.WF
namespace Lean.Elab
open Meta
open Term
pr... |
6c993fbbe354b65b8a2d57895db9871b2e9d81a8 | 5ae26df177f810c5006841e9c73dc56e01b978d7 | /src/topology/uniform_space/uniform_embedding.lean | 511420b02776ffd5168bae37d7afb13803e747bc | [
"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 | 18,998 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Sébastien Gouëzel, Patrick Massot
Uniform embeddings of uniform spaces. Extension of uniform continuous functions.
-/
import topology.uniform_space.cauchy topology.uni... |
c8682f380d1980d41cfe464e078d6fb623970258 | 53618200bef52920c1e974173f78cd378d268f3e | /hott/cubical/cube.hlean | 67a288031ac895981a214324138022806b423ac9 | [
"Apache-2.0"
] | permissive | sayantangkhan/lean2 | cc41e61102e0fcc8b65e8501186dcca40b19b22e | 0fc0378969678eec25ea425a426bb48a184a6db0 | refs/heads/master | 1,590,323,112,724 | 1,489,425,932,000 | 1,489,425,932,000 | 84,854,525 | 0 | 0 | null | 1,489,425,509,000 | 1,489,425,509,000 | null | UTF-8 | Lean | false | false | 18,953 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Floris van Doorn, Jakob von Raumer
Cubes
-/
import .square
open equiv is_equiv sigma sigma.ops
namespace eq
inductive cube {A : Type} {a₀₀₀ : A} : Π{a₂₀₀ a₀₂₀ a₂₂₀ a₀₀₂ a₂₀₂ a₀... |
d219d904f4aad804298a7327a6abfd5b3b6e9ce5 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/algebraic_topology/simplicial_set.lean | 591d9afe97fcedeb66dd9695586b9e5b57879ae9 | [
"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 | 4,263 | lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Scott Morrison, Adam Topaz
-/
import algebraic_topology.simplicial_object
import category_theory.yoneda
import category_theory.limits.types
/-!
A simplicial set is jus... |
d67371a0b61d583e546e30901d6d04924e900930 | 74caf7451c921a8d5ab9c6e2b828c9d0a35aae95 | /library/init/logic.lean | 3b7433ab48facfb7ccbee359b83cbc8382c6bc3b | [
"Apache-2.0"
] | permissive | sakas--/lean | f37b6fad4fd4206f2891b89f0f8135f57921fc3f | 570d9052820be1d6442a5cc58ece37397f8a9e4c | refs/heads/master | 1,586,127,145,194 | 1,480,960,018,000 | 1,480,960,635,000 | 40,137,176 | 0 | 0 | null | 1,438,621,351,000 | 1,438,621,351,000 | null | UTF-8 | Lean | false | false | 35,879 | 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, Jeremy Avigad, Floris van Doorn
-/
prelude
import init.core
universe variables u v w
@[reducible] def id {α : Type u} (a : α) : α := a
def flip {α : Type u... |
6b282f6372429c1ffabf1809551969d3fa546aa7 | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/data/int/sqrt.lean | feeec0bf0cb6869efbd466c3659fdfa8ee7a19cf | [
"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 | 882 | 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.nat.sqrt
namespace int
/-- `sqrt n` is the square root of an integer `n`. If `n` is not a
perfect square, and is positive, it returns the largest `k:ℤ` such
t... |
022d3b5f6ec59938d874e493f80f5209e0b33b79 | 592ee40978ac7604005a4e0d35bbc4b467389241 | /Library/generated/mathscheme-lean/PointedZero.lean | 4563ccb0f15199beac7591ee4123d9f222a2faca | [] | no_license | ysharoda/Deriving-Definitions | 3e149e6641fae440badd35ac110a0bd705a49ad2 | dfecb27572022de3d4aa702cae8db19957523a59 | refs/heads/master | 1,679,127,857,700 | 1,615,939,007,000 | 1,615,939,007,000 | 229,785,731 | 4 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,217 | lean | import init.data.nat.basic
import init.data.fin.basic
import data.vector
import .Prelude
open Staged
open nat
open fin
open vector
section PointedZero
structure PointedZero (A : Type) : Type :=
(zero : A)
open PointedZero
structure Sig (AS : Type) : Type :=
(zeroS : AS)
structure Pr... |
b929b638d522a1857499e9e1c21ca0e03b9371f5 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/data/set/pairwise.lean | f1a03cac739d7dd1be781302f7b9cf91b9c63761 | [
"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 | 14,112 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import data.set.lattice
import logic.relation
/-!
# Relations holding pairwise
This file defines pairwise relations and pairwise disjoint indexed sets.
## Main dec... |
c11b332839ed8963887ec27ff06f0f02d768037e | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/655.lean | 8e5eee93304138d260f916d1b4ec94e07e3ba6a1 | [
"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 | 247 | lean | structure A := a : Nat
structure B extends A := b : Nat
def B.a (self : B) := self.a + self.b
private def B.a (self : B) := self.a + self.b
namespace B
def a (self : B) := self.a + self.b
end B
def b : B := {a := 1, b := 2}
#eval b.a -- 1
|
e9f733012eea667967b7566c02b676a9a92ba2f6 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/combinatorics/simple_graph/regularity/equitabilise.lean | 008d1b177739208fa50c869f32f0b90598513074 | [
"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 | 10,595 | lean | /-
Copyright (c) 2022 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
import order.partition.equipartition
/-!
# Equitabilising a partition
This file allows to blow partitions up into parts of controlled size. ... |
3abb10f887baeacb250d25302eaea7c556508135 | d7189ea2ef694124821b033e533f18905b5e87ef | /galois/temporal/classical.lean | 2108bb13649d4b13c5957827511cab151d57da1c | [
"Apache-2.0"
] | permissive | digama0/lean-protocol-support | eaa7e6f8b8e0d5bbfff1f7f52bfb79a3b11b0f59 | cabfa3abedbdd6fdca6e2da6fbbf91a13ed48dda | refs/heads/master | 1,625,421,450,627 | 1,506,035,462,000 | 1,506,035,462,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 358 | lean | import .temporal
universes u
namespace temporal
namespace classical
lemma not_always_not_implies_eventually {T : Type u} (P : tProp T)
: ⊩ tNot (□ (tNot P)) => ◇ P
:= begin
intros tr notalways,
apply classical.by_contradiction,
intros contra, apply notalways,
intros n contra', apply contra,
constructor, assumption... |
300ba801ced68b12fbba3560883f597b4df32c16 | 037dba89703a79cd4a4aec5e959818147f97635d | /src/2022/sets/sheet7.lean | ccb5c86cfc8fde0a03ef7ac2a5c2fd97fdafa710 | [] | no_license | ImperialCollegeLondon/M40001_lean | 3a6a09298da395ab51bc220a535035d45bbe919b | 62a76fa92654c855af2b2fc2bef8e60acd16ccec | refs/heads/master | 1,666,750,403,259 | 1,665,771,117,000 | 1,665,771,117,000 | 209,141,835 | 115 | 12 | null | 1,640,270,596,000 | 1,568,749,174,000 | Lean | UTF-8 | Lean | false | false | 5,073 | lean | /-
Copyright (c) 2022 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author : Kevin Buzzard
-/
import tactic -- imports all the Lean tactics
/-!
# Sets in Lean, sheet 7 : the sets API
It might have occurred to you that if you had a prove
things like commutati... |
6c101874d70ec8a2894a4c67b12a7bc30654768b | 8930e38ac0fae2e5e55c28d0577a8e44e2639a6d | /data/set/countable.lean | d9df28fe224ddc40db8153a5336b7a6529bcbf2d | [
"Apache-2.0"
] | permissive | SG4316/mathlib | 3d64035d02a97f8556ad9ff249a81a0a51a3321a | a7846022507b531a8ab53b8af8a91953fceafd3a | refs/heads/master | 1,584,869,960,527 | 1,530,718,645,000 | 1,530,724,110,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,440 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl
Countable sets.
-/
import data.equiv.list data.set.finite logic.function
noncomputable theory
open function set encodable
open classical (hiding some)
local attribute... |
676137ddff5c49e9f67c0c4ae133b8d4331de395 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /roadmap/topology/shrinking_lemma.lean | 5b7f6e108871da989a9a6b1a7a4c6d2c582d1014 | [
"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 | 2,286 | lean | /-
Copyright (c) 2020 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton
-/
import ..todo
import topology.separation
/-!
A formal roadmap for the shrinking lemma for local finite countable covers.
It contains the statement of the lemma, and an i... |
4f98f0ef066acc3654fc40a180b43dfc552fcde6 | a4673261e60b025e2c8c825dfa4ab9108246c32e | /tests/lean/doSeqRightIssue.lean | 497f747d9dc9d3e60d07517dad14fdd8d0655093 | [
"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 | 263 | lean |
universes u
variables {α : Type u}
variables {β : α → Type v}
theorem ex {p₁ p₂ : Sigma (fun a => β a)} (h₁ : p₁.1 = p₂.1) (h : p₁.2 ≅ p₂.2) : p₁ = p₂ :=
match p₁, p₂, h₁, h with
| ⟨_, _⟩, ⟨_, _⟩, rfl, HEq.refl _ => rfl
|
cc4ad04e998955c60804081ac2153f674d57fa06 | a623837965543f72645ad3de4797a693f5c64274 | /src/tidy/command/rfl_lemma.lean | 5499be7988dc7b3ab1b5ec64fef62af684717ba5 | [] | no_license | khoek/lean-tidy | 9e1c8ffebc6a3e4739128e6cf7b7e84cba3a0625 | 995fbf6efa56f6c01cdb3754fc4a84b648a6dd91 | refs/heads/master | 1,619,535,208,982 | 1,549,094,268,000 | 1,549,094,268,000 | 122,460,123 | 0 | 0 | null | 1,534,214,616,000 | 1,519,293,337,000 | Lean | UTF-8 | Lean | false | false | 3,887 | lean | import lib.pretty_print
import lib.name
import lib.expr
open lean.parser
open interactive
open exceptional
open declaration
namespace tidy.command
namespace rfl_lemma
structure config :=
(attrs : list string := ["simp"])
(priv : bool := ff)
(trace : bool := ff)
open tactic
meta def handle_defn (lemma_name : str... |
06b68064b9aaebc3e335aed80e985d674d224f2f | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/category_theory/limits/shapes/images.lean | ad4b9b2a1ca7c5509c2027c78900724d6884cc9f | [
"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 | 25,783 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Markus Himmel
-/
import category_theory.limits.shapes.equalizers
import category_theory.limits.shapes.pullbacks
import category_theory.limits.shapes.strong_epi
/-!
# C... |
1be384eb7cb89ad4b5fc7f5ce8c6c834e832fcf2 | 842b7df4a999c5c50bbd215b8617dd705e43c2e1 | /nat_num_game/src/Advanced_Addition_World/adv_add_wrld10.lean | c179676b9eed6226f7650991ac47a6f6f3b859e6 | [] | 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 | 181 | lean | lemma add_left_eq_zero {{a b : ℕ}} (H : a + b = 0) : b = 0 :=
begin
cases b with d,
refl,
rw nat.add_succ at H,
exfalso,
apply nat.succ_ne_zero (a + d) H,
end |
db1d17357a3d927c5178d66a89f9135049c8f388 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/linear_algebra/matrix/basis.lean | 972b50dded8c5fce10cceec28821fd3775a69466 | [
"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 | 10,047 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
-/
import linear_algebra.matrix.reindex
import linear_algebra.matrix.to_lin
/-!
# Bases and matrices
> THIS FILE IS SYNCHRONI... |
b506b7a4d06833102ad6b6c935f1324169ae45a5 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/data/set/function.lean | 2edeffee57c25c3f90b91671d0e3ea45cbb856a1 | [
"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 | 47,563 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Andrew Zipperer, Haitao Zhang, Minchao Wu, Yury Kudryashov
-/
import data.set.prod
import logic.function.conjugate
/-!
# Functions over sets
## Main definitions
### Pr... |
f736c23c2dc7be52bd5282f745e55daee6c9828e | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/topology/maps.lean | d48d34987f317051e2145439db9b6767304be73d | [
"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 | 23,306 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot
-/
import topology.order
/-!
# Specific classes of maps between topological spaces
This file introduces the following properties of a m... |
bc76b8df5bd5733fa1e05ee4478584ead31ced9a | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Meta/Tactic/LinearArith/Nat.lean | a31bdc1732d14deba700cf7cae8050c6f7739695 | [
"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 | 302 | 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.Meta.Tactic.LinearArith.Nat.Basic
import Lean.Meta.Tactic.LinearArith.Nat.Simp
import Lean.Meta.Tactic.LinearArith.Nat.Solver
|
970e4bb4322a0a82766802200a9b70254d34009d | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /02_Dependent_Type_Theory.org.4.lean | 6a73eddad39d4fd72c55d708a8a3f558fb7c7017 | [] | 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 | 310 | lean | /- page 14 -/
import standard
import standard
open bool nat
-- BEGIN
constants A B : Type
constant F : Type → Type
constant G : Type → Type → Type
check A -- Type
check F A -- Type
check F nat -- Type
check G A -- Type → Type
check G A B -- Type
check G A nat -- Type
-- END
|
bc017da1cce2ce2a53c5a4db7877c84659c64ecb | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /06_Inductive_Types.org.33.lean | 42151d0f2d5ca54764546066e334b18ea02de947 | [] | 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 | 4,328 | lean | /- page 88 -/
import standard
namespace hide
inductive nat : Type :=
| zero : nat
| succ : nat → nat
namespace nat
definition add (m n : nat) : nat :=
nat.rec_on n m (fun n add_m_n, succ add_m_n)
notation 0 := zero
infix `+` := add
theorem add_zero (m : nat) : m + 0 = m := rfl
theorem add_succ (m n : nat) : m + ... |
52d31cb34496d598c408e449b2ad866756959286 | 07c76fbd96ea1786cc6392fa834be62643cea420 | /hott/init/pointed.hlean | e7fad229c2f5126adc440a960451a0582b984312 | [
"Apache-2.0"
] | permissive | fpvandoorn/lean2 | 5a430a153b570bf70dc8526d06f18fc000a60ad9 | 0889cf65b7b3cebfb8831b8731d89c2453dd1e9f | refs/heads/master | 1,592,036,508,364 | 1,545,093,958,000 | 1,545,093,958,000 | 75,436,854 | 0 | 0 | null | 1,480,718,780,000 | 1,480,718,780,000 | null | UTF-8 | Lean | false | false | 5,086 | hlean | /-
Copyright (c) 2016 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
The definition of pointed types. This file is here to avoid circularities in the import graph
-/
prelude
import init.trunc
open eq equiv is_equiv is_trunc
struct... |
ec470f0b96905a9fdf6bf9fb86cc34ff5108bf69 | da23b545e1653cafd4ab88b3a42b9115a0b1355f | /test/tidy.lean | 0b33d3bcc1ad2aebce80fe46f64dbf71a966b46b | [] | no_license | minchaowu/lean-tidy | 137f5058896e0e81dae84bf8d02b74101d21677a | 2d4c52d66cf07c59f8746e405ba861b4fa0e3835 | refs/heads/master | 1,585,283,406,120 | 1,535,094,033,000 | 1,535,094,033,000 | 145,945,792 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 601 | lean | -- Copyright (c) 2017 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Scott Morrison
import tidy.tidy
open tactic
namespace tidy.test
meta def interactive_simp := `[simp]
def tidy_test_0 : ∀ x : unit, x = unit.star :=
begin
success_if_fail ... |
5212014314771a2bf3040ec3b5a19e9756cebef6 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/algebra/char_p/subring.lean | 172058f93ef139a35a9049d248c75d2667b8fea8 | [
"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 | 1,026 | 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 ring_theory.subring.basic
/-!
# Characteristic of subrings
-/
universes u v
namespace char_p
instance subsemiring (R : Type u) [semiring... |
ad557bd574de059c68d3814ff6b3c9b90a9fbda4 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/category_theory/limits/shapes/disjoint_coproduct.lean | 55c611509640fd1ea9562cc2173a6fb3fdefba4e | [
"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 | 5,190 | lean | /-
Copyright (c) 2021 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import category_theory.limits.shapes.binary_products
import category_theory.limits.shapes.pullbacks
/-!
# Disjoint coproducts
Defines disjoint coproducts: coproducts wh... |
ef6257f080f7eac26c73c61a2eceeda909ec2186 | ea5678cc400c34ff95b661fa26d15024e27ea8cd | /PIL.lean | 22afe58c6f4a40a7264dd5b80963d9edc273437f | [] | no_license | ChrisHughes24/leanstuff | dca0b5349c3ed893e8792ffbd98cbcadaff20411 | 9efa85f72efaccd1d540385952a6acc18fce8687 | refs/heads/master | 1,654,883,241,759 | 1,652,873,885,000 | 1,652,873,885,000 | 134,599,537 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,543 | lean | open expr tactic classical
section logical_equivalences
local attribute [instance] prop_decidable
variables {a b : Prop}
theorem not_not_iff (a : Prop) : ¬¬a ↔ a :=
iff.intro classical.by_contradiction not_not_intro
theorem implies_iff_not_or (a b : Prop) : (a → b) ↔ (¬ a ∨ b) :=
iff.intro
(λ h, if ha : a then or.inr ... |
f3b9a8621062097ca2009d60bf6e80cf2bc477f0 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/1102.lean | 0f0a0da8ce0c1dc3224be712e085355455d4b82b | [
"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 | 911 | lean | class cls12 := (u12 : Unit)
class cls11 extends cls12 := (u11 : Unit)
class cls10 extends cls11 := (u10 : Unit)
class cls9 extends cls10 := (u9 : Unit)
class cls8 extends cls9 := (u8 : Unit)
class cls7 extends cls8 := (u7 : Unit)
class cls6 extends cls7 := (u6 : Unit)
class cls5 extends cls6 := (u5 : Unit)
class cls4 e... |
80b6d9b0a56f2274408f78840e907811de0d8b34 | 3b15c7b0b62d8ada1399c112ad88a529e6bfa115 | /src/Lean/Server/FileWorker.lean | 2c09ab6a37a49d494c35067481d72199384218de | [
"Apache-2.0"
] | permissive | stephenbrady/lean4 | 74bf5cae8a433e9c815708ce96c9e54a5caf2115 | b1bd3fc304d0f7bc6810ec78bfa4c51476d263f9 | refs/heads/master | 1,692,621,473,161 | 1,634,308,743,000 | 1,634,310,749,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 21,054 | 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.Util.Paths
... |
2b79b935007eeb9ab6a1529664676a4978c00a35 | 367134ba5a65885e863bdc4507601606690974c1 | /src/tactic/omega/coeffs.lean | 308e09e78ab69bd62c68b713cb998a8e22bfcd73 | [
"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 | 10,613 | lean | /-
Copyright (c) 2019 Seul Baek. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Seul Baek
-/
/-
Non-constant terms of linear constraints are represented
by storing their coefficients in integer lists.
-/
import data.list.func
import tactic.ring
import tactic.omega.mis... |
2a691fee817cbb446d41c7079561e3147ab9cbc7 | 9dd3f3912f7321eb58ee9aa8f21778ad6221f87c | /tests/lean/local_ref_bugs.lean | fcd7a67147548d88ce393031c9e42a23cf72964f | [
"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 | 699 | lean | set_option pp.all true
section
parameter α : Type
inductive foo : Type | a : α → foo | b
check (foo.b : foo)
open foo
check (foo.b : foo)
check (b : foo)
open tactic
include α
example : true :=
by do
e ← to_expr `(b),
t ← infer_type e,
trace "-------",
trace e,
trace t,
trace "-------",
triv
def ex : f... |
f25e25e71400f07233b28e65f8002b89940c7f4e | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /doc/examples/compiler/test.lean | 8ac7b82b7bafc4019826e3ef0d44d5e215c5fa05 | [
"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 | 82 | lean | def main (n : list string) : io uint32 :=
do io.println' (to_string n),
pure 0
|
96eaacb2b5af3d62bdc83ba1450da34a68b69870 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /stage0/src/Lean/Elab/Log.lean | 14ff6f717601c4250c0669b986e46704b35a12f9 | [
"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 | 3,092 | 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.Util
import Lean.Util.Sorry
import Lean.Elab.Exception
namespace Lean.Elab
class MonadLog (m : Type → Type) extends MonadFileMap m where
... |
1d79f69078381ed46aeb8d195bb06c45c7978b9d | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /stage0/src/Init/Lean/Elab/Tactic/Generalize.lean | 1d9d36ecf820914807b3f80dd048cb7ac70a0741 | [
"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 | 2,915 | 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, Sebastian Ullrich
-/
prelude
import Init.Lean.Meta.Tactic.Generalize
import Init.Lean.Meta.Check
import Init.Lean.Meta.Tactic.Intro
import Init.Lean.Elab.Tact... |
c6330b2fc9fc0ad5fbf08d3673d36228be2e4ea8 | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/algebra/homology/image_to_kernel_map.lean | eb7e41007fd7b6613893327dd2f556237da27210 | [
"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 | 2,421 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.limits.shapes.images
import category_theory.limits.shapes.kernels
/-!
# The morphism from `image f` to `kernel g` when `f ≫ g = 0`
We define ... |
2c3edc626ec6ba7989c28dc1ff5d5209bb6f4b5b | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/linear_algebra/finite_dimensional.lean | 28b78adb48481e26eb9c4ad80bfb120d8ce5b40b | [
"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 | 68,712 | lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import algebra.algebra.subalgebra
import field_theory.finiteness
/-!
# Finite dimensional vector spaces
Definition and basic properties of finite dimensional vector spa... |
d4e026afb256e6801928b8793cdae8a16a7e56da | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /library/theories/group_theory/perm.lean | 335e630a2d648cf47503beebcf041732c9b8f129 | [
"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 | 4,087 | lean | /-
Copyright (c) 2015 Haitao Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author : Haitao Zhang
-/
import algebra.group data data.fintype.function
open nat list function
namespace group_theory
open fintype
section perm
variables {A : Type} [fintype A] [decidable_eq... |
178b77c71dab3b435908792b937f3cdfe5e6aa42 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/topology/algebra/affine.lean | c03dd227152cc7e4bb4348d32e8c6fb91522bf3c | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 2,298 | lean | /-
Copyright (c) 2020 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
import linear_algebra.affine_space.affine_map
import topology.algebra.group
import topology.algebra.mul_action
/-!
# Topological properties of affine spaces and ma... |
c5a92b524b72df5b956d392d051bd9532c43fb42 | 02fbe05a45fda5abde7583464416db4366eedfbf | /library/init/meta/type_context.lean | f5112368aa9a344298d7fc441042199ba57f93d7 | [
"Apache-2.0"
] | permissive | jasonrute/lean | cc12807e11f9ac6b01b8951a8bfb9c2eb35a0154 | 4be962c167ca442a0ec5e84472d7ff9f5302788f | refs/heads/master | 1,672,036,664,637 | 1,601,642,826,000 | 1,601,642,826,000 | 260,777,966 | 0 | 0 | Apache-2.0 | 1,588,454,819,000 | 1,588,454,818,000 | null | UTF-8 | Lean | false | false | 6,611 | lean | prelude
import init.control.monad init.meta.local_context init.meta.tactic init.meta.fun_info
namespace tactic.unsafe
/-- A monad that exposes the functionality of the C++ class `type_context_old`.
The idea is that the methods to `type_context` are more powerful but _unsafe_ in the
sense that you can create terms that ... |
b4fea56a4d27f32368de04d7c2745af0eddb9db8 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/algebra/module/pi.lean | c19fb701364b138da700ccbeb51bcc9e06760ef5 | [] | 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 | 4,243 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Patrick Massot
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebra.module.basic
import Mathlib.algebra.ring.pi
import Mathlib.PostPort
univ... |
8547e39fe3e183bfb52140380f9742229f08d2e8 | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /stage0/src/Lean/Elab/Deriving.lean | 33dbbcf598e23b230c1a2e5b72877cfbf0b2e2ae | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | EdAyers/lean4 | 57ac632d6b0789cb91fab2170e8c9e40441221bd | 37ba0df5841bde51dbc2329da81ac23d4f6a4de4 | refs/heads/master | 1,676,463,245,298 | 1,660,619,433,000 | 1,660,619,433,000 | 183,433,437 | 1 | 0 | Apache-2.0 | 1,657,612,672,000 | 1,556,196,574,000 | Lean | UTF-8 | Lean | false | false | 526 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Elab.Deriving.Basic
import Lean.Elab.Deriving.Util
import Lean.Elab.Deriving.Inhabited
import Lean.Elab.Deriving.TypeName
import Lean.Elab.Deriv... |
b244284e2ae21d504e1b90a2384f491bdbf4ab6f | d6df40070de62348d40ffe5d02f9c5e18250e863 | /src/apartness_spaces.lean | 3c882843052d857f10a3fd4ce05d5aa5b4ba95ac | [] | no_license | owen-fool/Elementary-Apartness-Spaces | f1ce08f065092c21c7d179cac5f7527f4fea7e46 | 139029bae2c9f40322ee4c75f8f5299b5bf4f2d5 | refs/heads/master | 1,670,498,775,650 | 1,597,845,090,000 | 1,597,845,090,000 | 293,635,048 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,628 | lean | import tactic
import data.setoid.basic
import data.real.basic
import data.set
import topology.metric_space.basic
namespace apartness
@[class]
structure setoid_ppapart (α : Type) extends setoid α :=
(ar : α → α → Prop)
(ar_not_r : ∀ x y, ar x y → ¬ setoid.r x y)
(ar_symm : ∀ x y, ar x y → ar y x)
variables (α : Type)... |
b8139ea2a7f7480c1f3b935259469192d90828fa | 947b78d97130d56365ae2ec264df196ce769371a | /stage0/src/Std/ShareCommon.lean | e4e1a6b423744cca708af1abb9852c5f502c2e25 | [
"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 | 6,455 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Std.Data.HashSet
import Std.Data.HashMap
import Std.Data.PersistentHashMap
import Std.Data.PersistentHashSet
namespace Std
universes u v
namespace S... |
82db66a5a61bf259c1c229db82886b5cf0a8fa4b | b00eb947a9c4141624aa8919e94ce6dcd249ed70 | /stage0/src/Lean/Server/Watchdog.lean | 190303b4ad378b4d8d513f7815e977e18e94ff05 | [
"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 | 25,409 | 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 Init.Data.ByteArray
import Std.Data.RBMap
import Lean.Elab.Import
import Lean.Data.Lsp
import Lean.Server.FileSource
... |
bfbde487bee031288013a16aaf29e3e76b415f68 | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /tests/lean/run/252.lean | fa47afd32a7b3423d9e68ab697777c5101b13fc2 | [
"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 | 321 | lean | open nat
inductive tree (A : Type) :=
leaf : A → tree A,
node : tree A → tree A → tree A
check tree.node
definition size {A : Type} (t : tree A) :=
tree.rec (λ a, 1) (λ t₁ t₂ n₁ n₂, n₁ + n₂) t
check size
eval size (tree.node (tree.node (tree.leaf 0) (tree.leaf 1))
(tree.leaf 0))
|
3d5d569db7b85469e34d2eb11fd205d6317fa11e | a7eef317ddec01b9fc6cfbb876fe7ac00f205ac7 | /src/topology/uniform_space/cauchy.lean | 2e5d64d9fa87c7b0bf4fa3c876e4660b5dc65248 | [
"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 | 25,883 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import topology.uniform_space.basic
import topology.bases
import data.set.intervals
/-!
# Theory of Cauchy filters in uniform spaces. Complete uniform... |
28e32ee0108007620c6b5a21c67802a9a4b30850 | c780ac8c1c0dd4de0fb63981226f2b53b62fe298 | /src/field.lean | 84eceb1b20c528e026642cf5fab4323608ade2ad | [] | no_license | jmvlangen/finite_fields | 0672670245ccf62b2967d9c5edc2f60c53fc141f | 757bd91636e0b3508ee21c92be775eb9d908391e | refs/heads/master | 1,586,987,952,433 | 1,549,629,122,000 | 1,549,629,122,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 841 | lean | import ring_theory
universe u
namespace field
open ideal
variable {α : Type u}
variable [field α]
lemma ne_bot_is_top : ∀ I : ideal α, I ≠ ⊥ → I = ⊤ :=
assume I : ideal α,
assume h : I ≠ ⊥,
have ∃ x ∈ I, (x : α) ≠ (0 : α), from mem_of_not_bot I h,
let ⟨x, hI, h0⟩ := this in
have is_unit x, from is_unit_of_mul_one ... |
52f7015dd24e42596b08566ca528772e63b79750 | 4e3bf8e2b29061457a887ac8889e88fa5aa0e34c | /lean/love12_basic_mathematical_structures_exercise_sheet.lean | e65f95fbe0febcdf64774c5b9a5ae8fff24eebb7 | [] | no_license | mukeshtiwari/logical_verification_2019 | 9f964c067a71f65eb8884743273fbeef99e6503d | 16f62717f55ed5b7b87e03ae0134791a9bef9b9a | refs/heads/master | 1,619,158,844,208 | 1,585,139,500,000 | 1,585,139,500,000 | 249,906,380 | 0 | 0 | null | 1,585,118,728,000 | 1,585,118,727,000 | null | UTF-8 | Lean | false | false | 2,466 | lean | /- LoVe Exercise 12: Basic Mathematical Structures -/
import .lovelib
import .love12_basic_mathematical_structures_demo
namespace LoVe
set_option pp.beta true
/- Question 1: Type Classes -/
namespace btree
/- Recall the datatype `btree` we introduced earlier: -/
#check btree
/- The following function takes two... |
97514162273f872a450cbd83694cd60e89647b00 | ac49064e8a9a038e07cf5574b4fccd8a70d115c8 | /hott/algebra/homological_algebra/algebraic_lemmas.hlean | c32689a09868b8249fa700bad564e113e3955361 | [
"Apache-2.0"
] | permissive | Bolt64/lean2 | 7c75016729569e04a3f403c7a4fc7c1de4377c9d | 75fd8162488214a959dbe3303a185cbbb83f60f9 | refs/heads/master | 1,611,290,445,156 | 1,493,763,922,000 | 1,493,763,922,000 | 81,566,307 | 0 | 0 | null | 1,486,732,167,000 | 1,486,732,167,000 | null | UTF-8 | Lean | false | false | 2,876 | hlean | /-
Copyright (c) 2017 Sayantan Khan
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sayantan Khan
Proofs of elementary algebraic lemmas.
-/
import algebra.group_theory
open algebra
open group
lemma transport_equality_hom : Π {G₁ G₂ : AbGroup}, Π (φ : homomorphism (G₁) (G₂)), Π {x y : G₁... |
f2c6bcb4c011c66bb19cf7cdf0615b4344cbfd90 | b2fe74b11b57d362c13326bc5651244f111fa6f4 | /src/linear_algebra/multilinear.lean | 2931b86c36716df5a1c83892ea5e5ec389d3fd7c | [
"Apache-2.0"
] | permissive | midfield/mathlib | c4db5fa898b5ac8f2f80ae0d00c95eb6f745f4c7 | 775edc615ecec631d65b6180dbcc7bc26c3abc26 | refs/heads/master | 1,675,330,551,921 | 1,608,304,514,000 | 1,608,304,514,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 45,895 | 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 linear_algebra.basic
import algebra.algebra.basic
import tactic.omega
import data.fintype.sort
/-!
# Multilinear maps
We define multilinear maps as map... |
a272896f7eb0e0129229f52b8edd5db3e083180a | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/finset/order.lean | 188ddc4c162059e5f0cb9b4bed8852674f4bec9a | [
"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 | 1,004 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Kenny Lau
-/
import data.finset.basic
/-!
# Finsets of ordered types
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR... |
5b4cf42690874c15b3b02720fd7e4d265f951e26 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/let3.lean | 3a7890dbca74ab760200c04b148c9d3d80d8d57c | [
"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 | 140 | lean | --
constant f : num → num → num → num
check
let a : num := 10
in f a 10
/-
check
let a := 10,
b := 10
in f a b 10
-/
|
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