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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
32e48870420571e83dbbcc7fbe19bda459f783b5 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/topology/category/Compactum.lean | b0a26f2fed396f99f93486262802c1241028c14c | [
"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 | 17,936 | lean | /-
Copyright (c) 2020 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz
-/
import category_theory.monad.types
import category_theory.monad.limits
import category_theory.equivalence
import topology.category.CompHaus.basic
import topology.category.Pr... |
461f097b2dfa4a8a82ae3fe31aa44662c4a783b3 | a4673261e60b025e2c8c825dfa4ab9108246c32e | /src/Lean/Compiler/IR/Format.lean | 1645751fce36c18ce95254d9f86429dcfb5725e2 | [
"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 | 6,950 | 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.Data.FormatMacro
import Lean.Compiler.IR.Basic
namespace Lean
namespace IR
private def formatArg : Arg → Format
| Arg.var id => format i... |
fcdd832e0b3f047a7c010565018bc1572af7ebbf | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/analysis/normed_space/inner_product.lean | 368abee26d03580903cc0faec95e8694f14eee47 | [
"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 | 127,984 | lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Sébastien Gouëzel, Frédéric Dupuis, Heather Macbeth
-/
import linear_algebra.bilinear_form
import linear_algebra.sesquilinear_form
import topology.metric_space.pi_Lp
imp... |
dbdee493869bcada8f6e7fe84f9a3e520cce8440 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/ring_theory/adjoin/power_basis.lean | e400d257dc74d1c4a322aeca4f6ffcab8992d4ac | [
"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 | 7,996 | lean | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import ring_theory.adjoin.basic
import ring_theory.power_basis
import linear_algebra.matrix.basis
/-!
# Power basis for `algebra.adjoin R {x}`
This file defines the cano... |
b87393fb8af2e53a781a1afe22ac449648e236c8 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /src/Lean/Server/Requests.lean | b0ea8fe58b7f8da1cee8dd94ea526656729036ee | [
"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 | 6,353 | lean | /-
Copyright (c) 2021 Wojciech Nawrocki. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wojciech Nawrocki, Marc Huisinga
-/
import Lean.DeclarationRange
import Lean.Data.Json
import Lean.Data.Lsp
import Lean.Server.FileSource
import Lean.Server.FileWorker.Utils
imp... |
791efd0b11fa3fe7a3f2941fc01a6c76cd482675 | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/analysis/normed_space/operator_norm.lean | fedd0062fb2b8817620f04551d053d45a579cad9 | [
"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 | 59,488 | 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... |
0d154c85832209839cd9b3fb554eb073dacd3de2 | d436468d80b739ba7e06843c4d0d2070e43448e5 | /src/analysis/normed_space/basic.lean | f3aef5d6a4dcd6f705a9224654c8289db60603b2 | [
"Apache-2.0"
] | permissive | roro47/mathlib | 761fdc002aef92f77818f3fef06bf6ec6fc1a28e | 80aa7d52537571a2ca62a3fdf71c9533a09422cf | refs/heads/master | 1,599,656,410,625 | 1,573,649,488,000 | 1,573,649,488,000 | 221,452,951 | 0 | 0 | Apache-2.0 | 1,573,647,693,000 | 1,573,647,692,000 | null | UTF-8 | Lean | false | false | 24,966 | lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Normed spaces.
Authors: Patrick Massot, Johannes Hölzl
-/
import algebra.pi_instances
import linear_algebra.basic
import topology.instances.nnreal topology.instances.complex
import topology.a... |
dda28ba7532bd59601f319f5fa288c8c0fabf2bd | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /src/Init/Control/StateRef.lean | fd05a47bd451ed67f51f581afcf1200643abdd28 | [
"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 | 2,528 | 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
The State monad transformer using IO references.
-/
prelude
import Init.System.IO
import Init.Control.State
def StateRefT' (ω : Type) (σ :... |
8ad496b87212f746f9224fa5ae0cdbad4ec87edf | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/order/basic.lean | 47d1bc5ebc1599ae9b75c4db8df61793490af118 | [
"Apache-2.0"
] | permissive | dupuisf/mathlib | 62de4ec6544bf3b79086afd27b6529acfaf2c1bb | 8582b06b0a5d06c33ee07d0bdf7c646cae22cf36 | refs/heads/master | 1,669,494,854,016 | 1,595,692,409,000 | 1,595,692,409,000 | 272,046,630 | 0 | 0 | Apache-2.0 | 1,592,066,143,000 | 1,592,066,142,000 | null | UTF-8 | Lean | false | false | 16,963 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Mario Carneiro
-/
import data.subtype
import data.prod
open function
/-!
# Basic definitions about `≤` and `<`
## Definitions
### Predicates on functions
- `monotone... |
0ce839e1f1be491a93df02f7faf03c6512e96d3b | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/analysis/normed_space/basic_auto.lean | 9e7a5d04f48ac8dfa69db32e4b1d71839865e67b | [] | 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 | 56,714 | lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.topology.instances.nnreal
import Mathlib.topology.algebra.module
import Mat... |
0926518a12f597a9720398a0959a790ca660ba19 | 4fa161becb8ce7378a709f5992a594764699e268 | /src/tactic/ext.lean | a6873c4e839db78d5ce232c47f350b0c60e2b936 | [
"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 | 14,639 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import tactic.rcases
import data.sum
universes u₁ u₂
open interactive interactive.types
open lean.parser nat tactic
/--
`derive_struct_ext_lemma n` generates two extensio... |
2aed1fb9080fd1fc3c86da4e94789b96178dcd9f | ecad13897fdb44984cf1968424224d1750040236 | /lean/lean/examples/example03.lean | da5f3ec36e08fa8aae5fb4208284d98c3bf06eba | [] | no_license | MetaBorgCube/sdf3-demo | 4899159b1cfb0a95ae3af325035bbba8a1255477 | e831606d5b404eba75b087916a1162923143b98a | refs/heads/master | 1,609,472,086,310 | 1,553,380,857,000 | 1,553,380,857,000 | 59,577,395 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 28 | lean | (a : A) -> (z : S) -> x c
|
3f01fdf8d84c8321b75b9cc51b492b26e9000ecf | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/algebra/star/basic_auto.lean | 37885a9745622301961b1bf22bab22804a956d42 | [] | 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 | 4,683 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.tactic.apply_fun
import Mathlib.algebra.ordered_ring
import Mathlib.algebra.big_operators.... |
56c477e2e829f58c4f362878698df5f96dbdaa6e | ae1e94c332e17c7dc7051ce976d5a9eebe7ab8a5 | /stage0/src/Lean/Meta/Tactic/Cases.lean | 3854b02ff2209298a54bbab9e818be82c56e2ec5 | [
"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 | 14,597 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Meta.AppBuilder
import Lean.Meta.Tactic.Induction
import Lean.Meta.Tactic.Injection
import Lean.Meta.Tactic.Assert
import Lean.Meta.Tactic.Subst... |
ee6029c11696913b60e42b72c2e8450846b84122 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/testing/slim_check/gen.lean | 811128a16a335fffec67ab919db90ddc31f70000 | [
"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 | 5,690 | 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 control.uliftable
import system.random
import system.random.basic
/-!
# `gen` Monad
This monad is used to formulate randomized computations with a parameter
to sp... |
7f3dcb34714ca2e3520e74088212acaf5a8b39e9 | 957a80ea22c5abb4f4670b250d55534d9db99108 | /tests/lean/cyclic_default_fields.lean | 3c432f810581fbdb720e40d5bb0c10c80b4e8861 | [
"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 | 179 | lean | class Eq (α : Type) :=
(eq : α → α → Prop := λ a b, ¬ne a b)
(ne : α → α → Prop := λ a b, ¬eq a b)
#check ({eq := (=)} : Eq ℕ)
#check ({ne := (≠)} : Eq ℕ)
|
13106b6e9e04f2a0edea69729809a3e0eb158eb6 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/heap_code.lean | 57e3ee62dfa0051af946b2c10aa9790a0fb9970d | [
"Apache-2.0"
] | permissive | leanprover-community/lean | 12b87f69d92e614daea8bcc9d4de9a9ace089d0e | cce7990ea86a78bdb383e38ed7f9b5ba93c60ce0 | refs/heads/master | 1,687,508,156,644 | 1,684,951,104,000 | 1,684,951,104,000 | 169,960,991 | 457 | 107 | Apache-2.0 | 1,686,744,372,000 | 1,549,790,268,000 | C++ | UTF-8 | Lean | false | false | 2,420 | lean | structure coding :=
(code : Type)
[code_dec_eq : decidable_eq code]
(decode : code → Type)
instance coding_code_has_dec_eq (β : coding) : decidable_eq β.code :=
β.code_dec_eq
@[reducible] def typeof (β : coding) (c : β.code) : Type :=
β.decode c
structure ref {code : Type} (c : code) :=
(idx : nat)
stru... |
e17c49520747882ac1a474affe87e9277178fdd7 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/category/Group/epi_mono.lean | c43176e057940f7ec6eaa8da4f465a34493b831c | [
"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 | 13,484 | lean | /-
Copyright (c) 2022 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
import algebra.category.Group.equivalence_Group_AddGroup
import group_theory.quotient_group
/-!
# Monomorphisms and epimorphisms in `Group`
> THIS FILE IS SYNCHRONIZED ... |
7de64ae80a2c6e73c360ba950cfe354d24d4592e | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/ring_theory/graded_algebra/homogeneous_ideal.lean | 535d934b73de82e1a6a91f4e1e03eec8eedad46d | [
"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 | 21,624 | lean | /-
Copyright (c) 2021 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang, Eric Wieser
-/
import ring_theory.ideal.basic
import ring_theory.ideal.operations
import linear_algebra.finsupp
import ring_theory.graded_algebra.basic
/-!
# Homogeneous id... |
3db1344ad0ef18affac0b0180d3db33a94131777 | 432d948a4d3d242fdfb44b81c9e1b1baacd58617 | /src/ring_theory/valuation/basic.lean | cb27f4ed81d6b70713d46c58dd7d6b97669c692c | [
"Apache-2.0"
] | permissive | JLimperg/aesop3 | 306cc6570c556568897ed2e508c8869667252e8a | a4a116f650cc7403428e72bd2e2c4cda300fe03f | refs/heads/master | 1,682,884,916,368 | 1,620,320,033,000 | 1,620,320,033,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 23,252 | lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Johan Commelin, Patrick Massot
-/
import algebra.linear_ordered_comm_group_with_zero
import algebra.group_power
import ring_theory.ideal.operations
import algebra.punit... |
e212d55e5baf42b4b74cdd2220cbe1af1127c9f5 | 83c8119e3298c0bfc53fc195c41a6afb63d01513 | /library/init/data/list/lemmas.lean | baa54c9de1544de8d4a531efa74773931afb302e | [
"Apache-2.0"
] | permissive | anfelor/lean | 584b91c4e87a6d95f7630c2a93fb082a87319ed0 | 31cfc2b6bf7d674f3d0f73848b842c9c9869c9f1 | refs/heads/master | 1,610,067,141,310 | 1,585,992,232,000 | 1,585,992,232,000 | 251,683,543 | 0 | 0 | Apache-2.0 | 1,585,676,570,000 | 1,585,676,569,000 | null | UTF-8 | Lean | false | false | 10,451 | lean | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn
-/
prelude
import init.data.list.basic init.function init.meta init.data.nat.lemmas
import init.meta.interactive i... |
92787edbda291bc10b5bea2cd02c065880d6a844 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/data/dlist/basic.lean | d241690d7c43743b34a6861c45a52824f22f1d77 | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 1,139 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import data.dlist
/-!
# Difference list
This file provides a few results about `dlist`, which is defined in core Lean.
A difference list is a function that, given a list... |
126019f8a3bc241400e13ef70d29dcadf3fe60ce | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/data/polynomial.lean | 8772e85d2c18f77e217851b93034ce2d1ea5b53b | [
"Apache-2.0"
] | permissive | gebner/mathlib | eab0150cc4f79ec45d2016a8c21750244a2e7ff0 | cc6a6edc397c55118df62831e23bfbd6e6c6b4ab | refs/heads/master | 1,625,574,853,976 | 1,586,712,827,000 | 1,586,712,827,000 | 99,101,412 | 1 | 0 | Apache-2.0 | 1,586,716,389,000 | 1,501,667,958,000 | Lean | UTF-8 | Lean | false | false | 105,169 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Scott Morrison, Jens Wagemaker
Theory of univariate polynomials, represented as `add_monoid_algebra α ℕ`, where α is a commutative semiring.
-/
import data... |
53ce8e5203a9eb98827960eb89e1258cf7f8a968 | 968e2f50b755d3048175f176376eff7139e9df70 | /examples/pred_logic/unnamed_196.lean | f3c3f138705b7d79ab21f626a13d1ac20d0f415b | [] | 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 | 92 | lean | def even (x : ℤ) : Prop := ∃ m : ℤ, x = 2 *m
-- BEGIN
#check even
#check even 5
-- END |
b9df4da5d7b804e729207b6dd05854f514ed302c | 5412d79aa1dc0b521605c38bef9f0d4557b5a29d | /stage0/src/Lean/MonadEnv.lean | 1fbfb87a84079e834e4961684e956d0740b9b208 | [
"Apache-2.0"
] | permissive | smunix/lean4 | a450ec0927dc1c74816a1bf2818bf8600c9fc9bf | 3407202436c141e3243eafbecb4b8720599b970a | refs/heads/master | 1,676,334,875,188 | 1,610,128,510,000 | 1,610,128,521,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,821 | 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.Environment
import Lean.Exception
namespace Lean
def setEnv [MonadEnv m] (env : Environment) : m Unit :=
modifyEnv fun _ => env
def isInduc... |
34762d02fd96d1a347973e6905fe2d3e1ace519f | a7eef317ddec01b9fc6cfbb876fe7ac00f205ac7 | /src/data/matrix/basic.lean | 68c1f6134430ea637f6f3bdaa03fa20e34562617 | [
"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 | 23,828 | lean | /-
Copyright (c) 2018 Ellen Arlt. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ellen Arlt, Blair Shi, Sean Leather, Mario Carneiro, Johan Commelin
-/
import algebra.pi_instances
/-!
# Matrices
-/
universes u v w
open_locale big_operators
@[nolint unused_arguments]
... |
25db0910095ca616d02d97b4f2c3b5255ff531f8 | ba4794a0deca1d2aaa68914cd285d77880907b5c | /src/game/world5/level1.lean | 9754fc69199728d5013a9390c8e20f1e7910ea8a | [
"Apache-2.0"
] | permissive | ChrisHughes24/natural_number_game | c7c00aa1f6a95004286fd456ed13cf6e113159ce | 9d09925424da9f6275e6cfe427c8bcf12bb0944f | refs/heads/master | 1,600,715,773,528 | 1,573,910,462,000 | 1,573,910,462,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,408 | lean | -- World name : Function world
/-
# Function world.
If you have beaten Addition World, then you have got
quite good at manipulating equalities in Lean using the `rw` tactic.
But there are plenty of levels later on which will require you
to manipulate functions, and `rw` is not the tool for you here.
To manipulate ... |
35e41be0fadaa13f4b0fbe1f5f169c1d4ebaecb4 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/cyclic_default_fields.lean | 873683b051cceae0258166993b5dac3fbf379a97 | [
"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 | 205 | lean | class Eq (α : Type) :=
(eq : α → α → Prop)
(ne : α → α → Prop := λ a b, ¬eq a b)
(eq := λ a b, ¬ne a b)
#check ({} : Eq ℕ)
#check ({eq := (=)} : Eq ℕ)
#check ({ne := (≠)} : Eq ℕ)
|
80985ef52ba534d8d50337c168f3617042e96f2b | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/interactive/hoverAt.lean | e523ae9492dbaf149292b94167ef1fe23e1e15c3 | [
"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 | 448 | lean | inductive Palindrome : List α → Prop where
| nil : Palindrome []
| single : (a : α) → Palindrome [a]
| sandwish : (a : α) → Palindrome as → Palindrome ([a] ++ as ++ [a])
theorem palindrome_reverse (h : Palindrome as) : Palindrome as.reverse :=
match h with
| .nil => .nil
| .single a => Palindrome.si... |
76903b382e0b0fb3e87046427906df5e74c115d4 | 30b012bb72d640ec30c8fdd4c45fdfa67beb012c | /tactic/norm_num.lean | d6d04f382dd469001cfb30f2a73dd1df7afe1647 | [
"Apache-2.0"
] | permissive | kckennylau/mathlib | 21fb810b701b10d6606d9002a4004f7672262e83 | 47b3477e20ffb5a06588dd3abb01fe0fe3205646 | refs/heads/master | 1,634,976,409,281 | 1,542,042,832,000 | 1,542,319,733,000 | 109,560,458 | 0 | 0 | Apache-2.0 | 1,542,369,208,000 | 1,509,867,494,000 | Lean | UTF-8 | Lean | false | false | 18,794 | lean | /-
Copyright (c) 2017 Simon Hudon All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Mario Carneiro
Evaluating arithmetic expressions including *, +, -, ^, ≤
-/
import algebra.group_power data.rat data.nat.prime
import tactic.interactive tactic.converter.int... |
347c5eb05eb848336389ca361283d55c2f859136 | 97f752b44fd85ec3f635078a2dd125ddae7a82b6 | /library/data/finset/comb.lean | bc7b16df4cc0c27644a7687148ff25a3035d28de | [
"Apache-2.0"
] | permissive | tectronics/lean | ab977ba6be0fcd46047ddbb3c8e16e7c26710701 | f38af35e0616f89c6e9d7e3eb1d48e47ee666efe | refs/heads/master | 1,532,358,526,384 | 1,456,276,623,000 | 1,456,276,623,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 18,720 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura, Jeremy Avigad
Combinators for finite sets.
-/
import data.finset.basic logic.identities
open list quot subtype decidable perm function
namespace finset
/- i... |
69254f884cdd60e4b3a3529d0837d694ad815a43 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/category_theory/limits/fubini.lean | 858026bbeb8757695102a3da232e3d4ac0b8d3d4 | [
"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 | 10,048 | 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.limits
import category_theory.products.basic
import category_theory.currying
/-!
# A Fubini theorem for categorical limits
We prove th... |
b01f16bee8571649d5ba36f1f3ac6932f2a7cb76 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/analysis/inner_product_space/rayleigh.lean | c90384af7aea6487515c1019d655ac5f2081723f | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 12,730 | lean | /-
Copyright (c) 2021 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth, Frédéric Dupuis
-/
import analysis.inner_product_space.calculus
import analysis.inner_product_space.dual
import analysis.calculus.lagrange_multipliers
import linear_a... |
480a7e9675641996b0ab7aa224f0d29562dd6a01 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/topology/algebra/ring/basic.lean | c3aa31b2889f23811eaccf33ebe182a17e016813 | [
"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 | 17,411 | lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl
-/
import algebra.ring.prod
import ring_theory.subring.basic
import topology.algebra.group.basic
/-!
# Topological (semi)rings
> THIS FILE IS SYNCHRON... |
6cf376d2c70062bf24e2a87cc79650ba57423529 | 38bf3fd2bb651ab70511408fcf70e2029e2ba310 | /src/linear_algebra/basis.lean | 927b51be849f2c518a6241dd5bb5bf8101002505 | [
"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 | 47,906 | 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, Alexander Bentkamp
-/
import linear_algebra.basic linear_algebra.finsupp order.zorn
/-!
# Linear independence and bases
This file defines linear ind... |
bdcdab00629dd88e50c4357f18069475e0d25860 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/category_theory/closed/zero.lean | ae9c89c07b3332552db3b33ee62518354cd8670b | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 2,131 | lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import category_theory.closed.cartesian
import category_theory.limits.shapes.zero
import category_theory.punit
import category_theory.conj
/-!
# A cartesian closed cate... |
c07f0bd54742547c45218ab7eff3989364ef7bfb | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /tests/lean/run/recInfo1.lean | 6451f5786a741716d44c4ab344686f05a76cade6 | [
"Apache-2.0"
] | permissive | walterhu1015/lean4 | b2c71b688975177402758924eaa513475ed6ce72 | 2214d81e84646a905d0b20b032c89caf89c737ad | refs/heads/master | 1,671,342,096,906 | 1,599,695,985,000 | 1,599,695,985,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 522 | lean | import Lean.Meta
open Lean
open Lean.Meta
def print (msg : MessageData) : MetaM Unit :=
trace! `Meta.debug msg
def showRecInfo (declName : Name) (majorPos? : Option Nat := none) : MetaM Unit := do
info ← mkRecursorInfo declName majorPos?;
print (toString info)
set_option trace.Meta true
set_option trace.Meta.isDefE... |
d2a1fcd3a7796d36466cfb388e8f1f08ece1c87c | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /stage0/src/Lean/ResolveName.lean | abdbe3e026c990fe94356dfa8dcd2b7996fa37c0 | [
"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 | 12,427 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Sebastian Ullrich
-/
import Lean.Data.OpenDecl
import Lean.Hygiene
import Lean.Modifiers
import Lean.Exception
namespace Lean
/-!
We use aliases to impleme... |
f10f15ab1cd3c005d0b843a4d61c53f94d31fced | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/tactic/dec_trivial_auto.lean | 64cbf233ee50ecedff998a0f00bbf0e97ba6a22a | [] | 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 | 941 | lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.tactic.interactive
import Mathlib.PostPort
namespace Mathlib
/-!
# `dec_trivial` tactic
... |
428a4ab626aa2e9d4761b4a13d47a8221044646c | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/ring_theory/principal_ideal_domain.lean | b69eb9ce9b1c63c10f8b46c9ef2a0aca8db8a348 | [
"Apache-2.0"
] | permissive | agjftucker/mathlib | d634cd0d5256b6325e3c55bb7fb2403548371707 | 87fe50de17b00af533f72a102d0adefe4a2285e8 | refs/heads/master | 1,625,378,131,941 | 1,599,166,526,000 | 1,599,166,526,000 | 160,748,509 | 0 | 0 | Apache-2.0 | 1,544,141,789,000 | 1,544,141,789,000 | null | UTF-8 | Lean | false | false | 9,158 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Chris Hughes, Morenikeji Neri
-/
import ring_theory.noetherian
import ring_theory.unique_factorization_domain
/-!
# Principal ideal rings and principal ideal domains
A principal ideal ri... |
d23c1d56a312c5cedc0f8f85063fd338967c6fbf | f09e92753b1d3d2eb3ce2cfb5288a7f5d1d4bd89 | /src/for_mathlib/option_inj.lean | d25b263119c1d6050104bca860f934c4430eb74c | [
"Apache-2.0"
] | permissive | PatrickMassot/lean-perfectoid-spaces | 7f63c581db26461b5a92d968e7563247e96a5597 | 5f70b2020b3c6d508431192b18457fa988afa50d | refs/heads/master | 1,625,797,721,782 | 1,547,308,357,000 | 1,547,309,364,000 | 136,658,414 | 0 | 1 | Apache-2.0 | 1,528,486,100,000 | 1,528,486,100,000 | null | UTF-8 | Lean | false | false | 317 | lean | universes u v
open function
theorem option.map_inj
{α : Type u} {β : Type v} {f : α → β} (Hf : injective f) :
injective (option.map f) := λ a₁ a₂ H,
begin
cases h₁ : a₁;cases h₂ : a₂;rw [h₁,h₂] at H; try {exact option.no_confusion H},
congr,apply Hf,apply option.some.inj,exact H
end
|
937a5d94f520123ee167bf96dd655303a2c86094 | b73bd2854495d87ad5ce4f247cfcd6faa7e71c7e | /src/game/world4/level2.lean | ab89fca677b0bb9df9d0ff8b8fee7476643a02c0 | [] | no_license | agusakov/category-theory-game | 20db0b26270e0c95a3d5605498570273d72f731d | 652dd7e90ae706643b2a597e2c938403653e167d | refs/heads/master | 1,669,201,216,310 | 1,595,740,057,000 | 1,595,740,057,000 | 280,895,295 | 12 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,665 | lean | import category_theory.category.default
import category_theory.functor
import category_theory.isomorphism
universes v₁ v₂ u₁ u₂ -- The order in this declaration matters: v often needs to be explicitly specified while u often can be omitted
namespace category_theory
variables (C : Type u₁) [category.{v₁} C]
variabl... |
19461dd22f5643160f97911cc76ab2804d35b14f | 26ac254ecb57ffcb886ff709cf018390161a9225 | /src/data/real/cardinality.lean | 86a9578d6daf5a9f89f62bfc6e293f2b1ce19d7a | [
"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 | 7,818 | lean | /-
Copyright (c) 2019 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
The cardinality of the reals.
-/
import set_theory.ordinal
import analysis.specific_limits
import data.rat.denumerable
import data.set.intervals.image_preimage
ope... |
f659189c35d6f682635a03dc03f6bbc059c59e01 | 5c7fe6c4a9d4079b5457ffa5f061797d42a1cd65 | /src/exercises/src_31_function_surjective_injective_bijective.lean | 7e50e79e24b65a9c1bd10ea52043811f74968e4e | [] | no_license | gihanmarasingha/mth1001_tutorial | 8e0817feeb96e7c1bb3bac49b63e3c9a3a329061 | bb277eebd5013766e1418365b91416b406275130 | refs/heads/master | 1,675,008,746,310 | 1,607,993,443,000 | 1,607,993,443,000 | 321,511,270 | 3 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,224 | lean | import tactic.linarith
import .src_17_even_odd_further
open function
open int
namespace mth1001
/-
We define a functions `p₁` and `p₂` so that `p₁ x = x + 3` and `p₂ x = 2 * x`,
for every `x : ℤ`.
-/
def p₁ (x : ℤ) : ℤ := x + 3
def p₂ (x : ℤ) : ℤ := 2 * x
#eval p₁ 10 -- `p₁ 10` evaluates to `13`.
#eval p₂ 7 -- ... |
d82a9f22fe0f98b961a830424d796b8cb26d019d | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/category_theory/natural_isomorphism.lean | 1f9632e1757b8ddc9d1f513741f3c4974d32fa0d | [
"Apache-2.0"
] | permissive | Lix0120/mathlib | 0020745240315ed0e517cbf32e738d8f9811dd80 | e14c37827456fc6707f31b4d1d16f1f3a3205e91 | refs/heads/master | 1,673,102,855,024 | 1,604,151,044,000 | 1,604,151,044,000 | 308,930,245 | 0 | 0 | Apache-2.0 | 1,604,164,710,000 | 1,604,163,547,000 | null | UTF-8 | Lean | false | false | 7,247 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tim Baumann, Stephen Morgan, Scott Morrison, Floris van Doorn
-/
import category_theory.functor_category
import category_theory.isomorphism
/-!
# Natural isomorphisms
For the most pa... |
6289a81e93bb344a6401c632d8fcb0d351d6adac | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/nat_mod_defeq.lean | c36d59e87d308a2048a315a965840f78db1d402c | [
"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 | 447 | lean | import Init.Data.Nat.Div
/-!
This tests that `0 : Fin (n + 1)` unfolds to `0 : Nat`, which is a property kept for backwards
compatibility with mathlib in Lean 3.
Some Zulip discussion is available
[here](https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Nat.2Emod.200.20n.20.3D.200.20no.20longer.20... |
76b4f209ebf214bdfc889335f652532ebc65e528 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/newfrontend3.lean | d2a80068b3ff3c1e547bd402a02acaecfa135b4d | [
"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 | 762 | lean | --
structure S :=
(g {α} : α → α)
def f (h : Nat → ({α : Type} → α → α) × Bool) : Nat :=
(h 0).1 1
def tst : Nat :=
f fun n => (fun x => x, true)
theorem ex : id (Nat → Nat) :=
by {
intro;
assumption
}
def g (i j k : Nat) (a : Array Nat) (h₁ : i < k) (h₂ : k < j) (h₃ : j < a.size) : Nat :=
let vj := a.get ⟨... |
21c38120ab5a68f310db87f1e7bdb2175181284c | 6065973b1fa7bbacba932011c9e2f32bf7bdd6c1 | /src/measure_theory/lp_space.lean | af60735e5b6dbf3ca408a68d77b4188a3591e478 | [
"Apache-2.0"
] | permissive | khmacdonald/mathlib | 90a0fa2222369fa69ed2fbfb841b74d2bdfd66cb | 3669cb35c578441812ad30fd967d21a94b6f387e | refs/heads/master | 1,675,863,801,090 | 1,609,761,876,000 | 1,609,761,876,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 11,923 | lean | /-
Copyright (c) 2020 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Rémy Degenne.
-/
import measure_theory.l1_space
import analysis.mean_inequalities
/-!
# ℒp space
This file describes properties of measurable functions with finite seminorm `(∫ ∥f a∥^p ... |
05a5794cb005695c02ed09456d1d8e4e109b5376 | 649957717d58c43b5d8d200da34bf374293fe739 | /src/data/polynomial.lean | d79d91b7f928aa29c95a7e7dcef95cb07a960e86 | [
"Apache-2.0"
] | permissive | Vtec234/mathlib | b50c7b21edea438df7497e5ed6a45f61527f0370 | fb1848bbbfce46152f58e219dc0712f3289d2b20 | refs/heads/master | 1,592,463,095,113 | 1,562,737,749,000 | 1,562,737,749,000 | 196,202,858 | 0 | 0 | Apache-2.0 | 1,562,762,338,000 | 1,562,762,337,000 | null | UTF-8 | Lean | false | false | 97,974 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Jens Wagemaker
Theory of univariate polynomials, represented as `ℕ →₀ α`, where α is a commutative semiring.
-/
import data.finsupp algebra.gcd_domain ring... |
d8e9fbcba3d0a08c917aaaf02459323fb0d16e96 | f22a91842f18b5e855075b9becd55d2233756c6a | /src/ch03_01.lean | 0489bfb1a0f6fc9a6d1fa32801feb0a071e617a7 | [] | no_license | kckennylau/tao-analysis-one | 48cef1ee896d6703fcaf47ce5548e44f88901a0e | 2bd2d14c3c722bb36526c5a4e6b87618b2c081b1 | refs/heads/master | 1,621,002,517,963 | 1,514,151,057,000 | 1,514,151,057,000 | 115,971,702 | 0 | 0 | null | 1,514,864,495,000 | 1,514,864,495,000 | null | UTF-8 | Lean | false | false | 10,839 | lean | --------------------------------------------------------------------------------
-- Chapter 3 - Set theory
-- Section 1 - Fundamentals
-- Analysis 1, Third Edition, Tao
--------------------------------------------------------------------------------
import data.set.basic
open set
variable {α : Type}
-- Exercise 3.1... |
feb5df35579807feaaac5a9b1ed83e6cfa32a4ed | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/matchNoPostponing.lean | af7f62e1dc7a0b3580cb2e5ac04a2e50ae109953 | [
"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 | 623 | lean |
/- In the following example, type of `x` and `y` could be any type `α` s.t. `[OfNat α]`.
It relies on `SyntheticMVarKind.withDefault` to set `α := Nat`.
Moreover, we must commit to `α := Nat` before we try to build de `matcher` since
`mkMatcher` assumes `matchType` does not contain metavariables.
We accomp... |
b436db9c14c6002b98fec508f72818057a2bcb2b | 1abd1ed12aa68b375cdef28959f39531c6e95b84 | /src/data/set/equitable.lean | 665a804098b181b3040a585807103118504b57a8 | [
"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 | 3,382 | 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 algebra.big_operators.order
import data.nat.basic
/-!
# Equitable functions
This file defines equitable functions.
A function `f` is... |
17ad28ea070bf6d7439b7c5882288231828f8549 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /doc/monads/except.lean | 75da8cf24cfbbc8766eb5b450486f77570903a42 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 7,038 | lean | /-!
# Except
The `Except` Monad adds exception handling behavior to your functions. Exception handling
in other languages like Python or Java is done with a built in `throw` method that you
can use anywhere. In `Lean` you can only `throw` an exception when your function is
executing in the context of an `Except` mon... |
49763182a7b097c3bd84312a5d39077824782439 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/module/hom.lean | 81b6c29f0738e5eae07447365a221d69bc7d6d90 | [
"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 | 1,926 | lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import algebra.module.pi
/-!
# Bundled hom instances for module and multiplicative actions
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a... |
52ce5322f28abffafca5b002cded030958398ab3 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/pkg/builtin_attr/UserAttr/Tst.lean | 76870872c46d508ef0e5c0acd53dac931f76e6cf | [
"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 | 89 | lean | import UserAttr.BlaAttr
@[bar] def f (x : Nat) := x + 2
@[bar] def g (x : Nat) := x + 1
|
40f617012145b60e44758e5bda0daeccc28b2d81 | 22e97a5d648fc451e25a06c668dc03ac7ed7bc25 | /src/algebra/group/hom.lean | 33f5f41032bc6bfb0adc0a60d6923677b5f3e1cf | [
"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 | 10,534 | 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.basic
import tactic.ext
/-!
# monoid and group h... |
895da6e683c1b58f727b9baf7b3c85c455a5c93b | c777c32c8e484e195053731103c5e52af26a25d1 | /src/measure_theory/measure/stieltjes.lean | 9911b118cab9220a6d45cda2da9c5db05b3bead0 | [
"Apache-2.0"
] | permissive | kbuzzard/mathlib | 2ff9e85dfe2a46f4b291927f983afec17e946eb8 | 58537299e922f9c77df76cb613910914a479c1f7 | refs/heads/master | 1,685,313,702,744 | 1,683,974,212,000 | 1,683,974,212,000 | 128,185,277 | 1 | 0 | null | 1,522,920,600,000 | 1,522,920,600,000 | null | UTF-8 | Lean | false | false | 24,107 | lean | /-
Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yury Kudryashov, Sébastien Gouëzel
-/
import measure_theory.constructions.borel_space
import topology.algebra.order.left_right_lim
/-!
# Stieltjes measures on the r... |
66e0cc2e40335c069f3984ad31ef67f246f6c198 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/331.lean | 32004add7e1b0ac4092a28ce1499611fe908bca9 | [
"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 | 310 | lean | namespace nat
inductive less (a : nat) : nat → Prop
| base : less (succ a)
| step : Π {b}, less b → less (succ b)
end nat
open nat
#check less.rec_on
namespace foo1
protected definition foo2.bar : nat := 10
end foo1
example : foo1.foo2.bar = 10 :=
rfl
open foo1
example : foo2.bar = 10 :=
rfl
|
a15d8526cb8bf429f93c540bfe16e63bf3b0bb40 | d6124c8dbe5661dcc5b8c9da0a56fbf1f0480ad6 | /Papyrus/IR/TypeRefs.lean | 3f70132f25521017a0ba9b6297fa3baa3e6b29df | [
"Apache-2.0"
] | permissive | xubaiw/lean4-papyrus | c3fbbf8ba162eb5f210155ae4e20feb2d32c8182 | 02e82973a5badda26fc0f9fd15b3d37e2eb309e0 | refs/heads/master | 1,691,425,756,824 | 1,632,122,825,000 | 1,632,123,075,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 20,779 | lean | import Papyrus.Context
import Papyrus.IR.TypeRef
import Papyrus.IR.AddressSpace
namespace Papyrus
--------------------------------------------------------------------------------
-- Singleton Type References
--------------------------------------------------------------------------------
-- # Special Types
/-- A re... |
aa162aa4d79480cc83beaac2d4ef4f941c4df4ef | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/data/nat/basic.lean | e1eaeba817a194b28fa0fe4114143116f3e6c41f | [
"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 | 66,697 | 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 algebra.order.ring
import algebra.order.with_zero
/-!
# Basic operations ... |
83c308a48c82457d35e381b16f3ea9cd3b326e01 | 6dc0c8ce7a76229dd81e73ed4474f15f88a9e294 | /tests/lean/run/genindices.lean | b39c35f71837b757033c0084cef771c9d725c12e | [
"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 | 742 | lean | import Lean
universe u
inductive Pred : ∀ (α : Type u), List α → Type (u+1)
| foo {α : Type u} (l1 : List α) (l2 : List (Option α)) : Pred (Option α) l2 → Pred α l1
axiom goal : forall (α : Type u) (xs : List (List α)) (h : Pred (List α) xs), xs ≠ [] → xs = xs
open Lean
open Lean.Meta
def tst1 : MetaM Unit := do
l... |
bde25c89b5cf75e229864e80190489e63cc0cacd | 42610cc2e5db9c90269470365e6056df0122eaa0 | /library/theories/finite_group_theory/cyclic.lean | 8b326798ab500505ce85ba2c98ecee90090faf75 | [
"Apache-2.0"
] | permissive | tomsib2001/lean | 2ab59bfaebd24a62109f800dcf4a7139ebd73858 | eb639a7d53fb40175bea5c8da86b51d14bb91f76 | refs/heads/master | 1,586,128,387,740 | 1,468,968,950,000 | 1,468,968,950,000 | 61,027,234 | 0 | 0 | null | 1,465,813,585,000 | 1,465,813,585,000 | null | UTF-8 | Lean | false | false | 15,834 | 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 data algebra.group algebra.group_power .finsubg .hom .perm
open function finset
open eq.ops
namespace group_theory
section cyclic
open nat fin list
local attr... |
757ea1b1f0cec83c703d5539e90422d06a6bf2b1 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/pnat/prime.lean | 4db050a84b83c58ff852d527b3a49c27442e78bd | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 7,672 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Neil Strickland
-/
import data.nat.prime
import data.pnat.basic
/-!
# Primality and GCD on pnat
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to thi... |
4767f955bb8d39f32fb59bb6295ce909f609615f | 4d3f29a7b2eff44af8fd0d3176232e039acb9ee3 | /LAMR/Examples/using_lean/examples2.lean | 8b4f50d2cdac0ade8b3a2c5638104ac7d1632660 | [] | no_license | marijnheule/lamr | 5fc5d69d326ff92e321242cfd7f72e78d7f99d7e | 28cc4114c7361059bb54f407fa312bf38b48728b | refs/heads/main | 1,689,338,013,620 | 1,630,359,632,000 | 1,630,359,632,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,332 | lean | -- textbook: defining functions
def foo n := 3 * n + 7
#eval foo 3
#eval foo (foo 3)
def bar n := foo (foo n) + 3
#eval bar 3
#eval bar (bar 3)
-- end textbook: defining functions
-- textbook: hello world
def printExample : IO Unit:= do
IO.println "hello"
IO.println "world"
#eval printExample
-- end textbook: ... |
e3de929ac2ec83cef90298fbd7077bdef770d411 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/control/uliftable.lean | 104ed8c3b5399d9dd7737f4d10736ca88ef5b871 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 5,692 | 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 control.monad.basic
import control.monad.cont
import control.monad.writer
import logic.equiv.basic
import tactic.interactive
/-!
# Universe lifting for type familie... |
c9ec40e7e9bd40511a52ba9577ec8aaeff7da324 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/rat/cast.lean | b98a704e023766243d852a73b81330782dac867a | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,462 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.rat.order
import Mathlib.data.int.char_zero
import Mathlib.PostPort
u... |
1c80399e58e919826781be3c5cdbe3dfbf37c4ca | 367134ba5a65885e863bdc4507601606690974c1 | /src/linear_algebra/unitary_group.lean | 5eb311d4bac8d8dd10a712893c872412084ccd6d | [
"Apache-2.0"
] | permissive | kodyvajjha/mathlib | 9bead00e90f68269a313f45f5561766cfd8d5cad | b98af5dd79e13a38d84438b850a2e8858ec21284 | refs/heads/master | 1,624,350,366,310 | 1,615,563,062,000 | 1,615,563,062,000 | 162,666,963 | 0 | 0 | Apache-2.0 | 1,545,367,651,000 | 1,545,367,651,000 | null | UTF-8 | Lean | false | false | 6,375 | lean | /-
Copyright (c) 2021 Shing Tak Lam. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Shing Tak Lam
-/
import linear_algebra.matrix
import linear_algebra.nonsingular_inverse
import data.complex.basic
/-!
# The Unitary Group
This file defines elements of the unitary grou... |
60404d9fc463b5cb110781c13ef2ec2c459e6d7d | 8c02fed42525b65813b55c064afe2484758d6d09 | /src/lang.lean | fd6634e345dd3d84be841ec36908c84d088eb612 | [
"LicenseRef-scancode-generic-cla",
"MIT"
] | permissive | microsoft/AliveInLean | 3eac351a34154efedd3ffc4fe2fa4ec01b219e0d | 4b739dd6e4266b26a045613849df221374119871 | refs/heads/master | 1,691,419,737,939 | 1,689,365,567,000 | 1,689,365,568,000 | 131,156,103 | 23 | 18 | NOASSERTION | 1,660,342,040,000 | 1,524,747,538,000 | Lean | UTF-8 | Lean | false | false | 3,398 | lean | -- Copyright (c) Microsoft Corporation. All rights reserved.
-- Licensed under the MIT license.
-- constant value
inductive const : Type
| int : ℤ → const
-- register
-- Design choice: Let reg store its name, but not
-- its type. Reason is that, if reg contains type,
-- modifying register's type should track all
-- d... |
1ba1c564092d0b29ac4784e4b7781daa273e6aba | 5d76f062116fa5bd22eda20d6fd74da58dba65bb | /src/snarks/sonic/vars.lean | bb1b17e4a67965e76abf0bfbf4649c549bba7b08 | [] | no_license | brando90/formal_baby_snark | 59e4732dfb43f97776a3643f2731262f58d2bb81 | 4732da237784bd461ff949729cc011db83917907 | refs/heads/master | 1,682,650,246,414 | 1,621,103,975,000 | 1,621,103,975,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 105 | lean |
section
@[derive decidable_eq]
inductive vars : Type
| x : vars
| y : vars
| z : vars
| α : vars
end |
cc583086adaf2058e4db26c1934ec083f974015d | c61b91f85121053c627318ad8fcde30dfb8637d2 | /Chapter5/5-1to3.lean | ecd4e2abed706ddec22edce1a2bb988067ff7bf4 | [] | no_license | robkorn/theorem-proving-in-lean-exercises | 9e2256360eaf6f8df6cdd8fd656e63dfb04c8cdb | 9c51da587105ee047a9db55d52709d881a39be7a | refs/heads/master | 1,585,403,341,988 | 1,540,142,619,000 | 1,540,142,619,000 | 148,431,678 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,365 | lean | theorem test (p q : Prop) (hp : p) (hq : q) : p ∧ q ∧ p :=
begin
apply and.intro hp,
exact and.intro hq hp
end
theorem test' (p q : Prop) (hp : p) (hq : q) : p ∧ q ∧ p :=
by exact and.intro hp (and.intro hq hp)
#print test
example (p q r : Prop) : p ∧ (q ∨ r) ↔ (p ∧ q) ∨ (p ∧ r) :=
begin
apply iff.intro,
in... |
b7e6ee3e0d7d28218b69a1f3f49aeb7b943a5f4e | 1b8f093752ba748c5ca0083afef2959aaa7dace5 | /src/category_theory/universal/uniqueness.lean | 5276ad39aa468df3b8a280ab1ae61ce024817d64 | [] | no_license | khoek/lean-category-theory | 7ec4cda9cc64a5a4ffeb84712ac7d020dbbba386 | 63dcb598e9270a3e8b56d1769eb4f825a177cd95 | refs/heads/master | 1,585,251,725,759 | 1,539,344,445,000 | 1,539,344,445,000 | 145,281,070 | 0 | 0 | null | 1,534,662,376,000 | 1,534,662,376,000 | null | UTF-8 | Lean | false | false | 2,056 | lean | import category_theory.limits
universes u v
open category_theory
namespace category_theory.limits
variables {C : Type u} [𝒞 : category.{u v} C]
include 𝒞
section
@[extensionality] lemma homs_to_terminal_ext (X' : C) (X : C) (h : is_terminal.{u v} X) (f g : X' ⟶ X) : f = g :=
begin
rw h.uniq X' f,
rw h.uniq ... |
69e45e76d6105e7eb0d520f5310173e008000fe6 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /library/data/set/map.lean | f313d8bb73818c13957bc47e649bd1e5d7032c89 | [
"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 | 6,148 | 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
Functions between subsets of finite types, bundled with the domain and range.
-/
import data.set.function
open eq.ops
namespace set
record map {X Y : Ty... |
b8540d87ccf369cbb6ece1e55a49586bde0b5c3c | e09201d437062e1f95e6e5360aab0c9f947901aa | /src/automata/epsnfa_triv.lean | dd54126264038bff381b62e285e421720ea0d226 | [] | no_license | VArtem/lean-regular-languages | 34f4b093f28ef2f09ba7e684e642a0f97c901560 | e877243188253d0ac17ccf0ae2da7bf608686ff0 | refs/heads/master | 1,683,590,111,306 | 1,622,307,234,000 | 1,622,307,234,000 | 284,232,653 | 7 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,950 | lean | import data.set.basic
import data.finset.basic
import automata.epsnfa
import languages.basic
import languages.star
open set epsnfa languages
namespace epsnfa.triv
variables {S : Type} [fintype S] [decidable_eq S]
def epsnfa_empty : epsNFA S bool := {
start := ff,
term := tt,
next := λ q c, ∅,
eps :... |
748913abc48bcddb60b4d44e4cb6a34560fcb235 | 205f0fc16279a69ea36e9fd158e3a97b06834ce2 | /HOMEWORK/HW3.lean | cf1fc48defc9228195f275dc872e7c40a9f7f83a | [] | no_license | kevinsullivan/cs-dm-lean | b21d3ca1a9b2a0751ba13fcb4e7b258010a5d124 | a06a94e98be77170ca1df486c8189338b16cf6c6 | refs/heads/master | 1,585,948,743,595 | 1,544,339,346,000 | 1,544,339,346,000 | 155,570,767 | 1 | 3 | null | 1,541,540,372,000 | 1,540,995,993,000 | Lean | UTF-8 | Lean | false | false | 5,789 | lean | /-
This homework assignment will be due in class
on Thursday, September. Edit your answers into
this file and save your answers. Know where
the file is in your file system so that you
can submit it to Collab during class. To be
ready for this homework, you should be sure
to have read all of the class material up to
an... |
eea654f21e93d862de6263e446d94ea39ae57923 | 22e97a5d648fc451e25a06c668dc03ac7ed7bc25 | /src/init_/data/nat/lemmas.lean | 0b50fa3b9aa353be9bffb0cf6e871cc6310373de | [
"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 | 3,545 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad
-/
import algebra.ordered_ring
/-
Results copied from the core library to mathlib by Johan Commelin
-/
namespace nat
instance : zero_ne_one_... |
767e97c7ad7a14afb7752744341b07db3b99646b | e61a235b8468b03aee0120bf26ec615c045005d2 | /stage0/src/Init/Control/Except.lean | 117492c9872487501d03a528d161a9b712806b27 | [
"Apache-2.0"
] | permissive | SCKelemen/lean4 | 140dc63a80539f7c61c8e43e1c174d8500ec3230 | e10507e6615ddbef73d67b0b6c7f1e4cecdd82bc | refs/heads/master | 1,660,973,595,917 | 1,590,278,033,000 | 1,590,278,033,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,082 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jared Roesch, Sebastian Ullrich
The Except monad transformer.
-/
prelude
import Init.Control.Alternative
import Init.Control.Lift
import Init.Data.ToString
universes u v w
ind... |
2a66f6bf0677cebfcd791a99fe948637ee79cce9 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/order/category/PartialOrder.lean | b3991e433bbb9b609ceed7b83736337cb29d7a1e | [
"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 | 2,097 | lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import order.category.Preorder
/-!
# Category of partial orders
This defines `PartialOrder`, the category of partial orders with monotone maps.
-/
open category_t... |
260f07e610d74cd1a9e42612e268b56acc7e1356 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/convex/intrinsic.lean | f3e91c330fe29949b36b4ae620327e734b0ec138 | [
"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 | 14,197 | lean | /-
Copyright (c) 2023 Paul Reichert. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Paul Reichert, Yaël Dillies
-/
import analysis.normed_space.add_torsor_bases
/-!
# Intrinsic frontier and interior
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this fil... |
3835c736df3040d4cbaea7b6682c98bd324f5f57 | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/pnat/basic.lean | 3aaba579670835bdc1e000693e260d68151f8e6e | [
"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 | 15,581 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro, Neil Strickland
-/
import data.nat.basic
/-!
# The positive natural numbers
This file defines the type `ℕ+` or `pnat`, the subtype of natural numbers that are p... |
bcf3845c195f0377d3447a66798e9b727a7352b5 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/nat/multiplicity_auto.lean | b7bea78c6dee0b1bde57fe714f6f494167279fe1 | [] | 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 | 4,971 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.nat.bitwise
import Mathlib.data.nat.parity
import Mathlib.ring_theory.int.basic
import Mat... |
8176493e2718bc00c8971c85a576755a98a29ea6 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/blast_flat.lean | c16b6eea211f6b3f0c6a443e8e6151135c8d7c91 | [
"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 | 645 | lean | open nat subtype
definition f (x : nat) (y : {n : nat | n > x}) : nat :=
x + elt_of y
definition f_flat (x : nat) (y : nat) (H : y > x) : nat :=
f x (tag y H)
lemma f_flat_simp [forward] (x : nat) (y : nat) (H : y > x) : f x (tag y H) = f_flat x y H :=
rfl
set_option trace.simplifier true
set_option trace.blast tru... |
d4757643b0fe3627e98c1e626bb6b865cbfa073d | dc253be9829b840f15d96d986e0c13520b085033 | /heq.hlean | d99aeedf9ee79ffe04e5ff95ee50e94fd743c0eb | [
"Apache-2.0"
] | permissive | cmu-phil/Spectral | 4ce68e5c1ef2a812ffda5260e9f09f41b85ae0ea | 3b078f5f1de251637decf04bd3fc8aa01930a6b3 | refs/heads/master | 1,685,119,195,535 | 1,684,169,772,000 | 1,684,169,772,000 | 46,450,197 | 42 | 13 | null | 1,505,516,767,000 | 1,447,883,921,000 | Lean | UTF-8 | Lean | false | false | 1,815 | hlean | -- Author: Floris van Doorn
open eq is_trunc
variables {I : Type} [is_set I] {P : I → Type} {i j k : I} {x x₁ x₂ : P i} {y y₁ y₂ : P j} {z : P k}
{Q : Π⦃i⦄, P i → Type}
structure heq (x : P i) (y : P j) : Type :=
(p : i = j)
(q : x =[p] y)
namespace eq
notation x ` ==[`:50 P:0 `] `:0 y:50 := @heq _ _ ... |
e09fa00ce236851280bff7464c8c6c97217939c4 | 5ca7b1b12d14c4742e29366312ba2c2ef8201b21 | /src/game/world7/level9.lean | 4f39d63ea85ed5fea1899c2ffb5601a1b16979ab | [
"Apache-2.0"
] | permissive | MatthiasHu/natural_number_game | 2e464482ef3001863430b0336133b6697b275ba3 | 2d764f72669ae30861f6a1057fce0257f3e466c4 | refs/heads/master | 1,609,719,110,419 | 1,576,345,737,000 | 1,576,345,737,000 | 240,296,314 | 0 | 0 | Apache-2.0 | 1,581,608,357,000 | 1,581,608,356,000 | null | UTF-8 | Lean | false | false | 3,023 | lean | import game.world7.level8 -- hide
import tactic.tauto -- useful high-powered tactic
local attribute [instance, priority 10] classical.prop_decidable -- we are mathematicians
/-
# Advanced proposition world.
You already know enough to embark on advanced addition world. But here are just a couple
more things.
## Level... |
57f4b3755b96110f6feb7b4e3fcec5dae161e5da | 9d2e3d5a2e2342a283affd97eead310c3b528a24 | /src/exercises_sources/wednesday/afternoon/algebraic_hierarchy.lean | ba5efbbb4cad4db0754460e078b3c5e7ccd7df6e | [] | permissive | Vtec234/lftcm2020 | ad2610ab614beefe44acc5622bb4a7fff9a5ea46 | bbbd4c8162f8c2ef602300ab8fdeca231886375d | refs/heads/master | 1,668,808,098,623 | 1,594,989,081,000 | 1,594,990,079,000 | 280,423,039 | 0 | 0 | MIT | 1,594,990,209,000 | 1,594,990,209,000 | null | UTF-8 | Lean | false | false | 19,968 | lean | /-
This is a sorry-free file covering the material on Wednesday afternoon
at LFTCM2020. It's how to build some algebraic structures in Lean
-/
import data.rat.basic -- we'll need the rationals at the end of this file
/-
As a mathematician I essentially always start my Lean files with the following line:
-/
import tac... |
e4947a8ec83caf92b5085972839b1d70083bc211 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /stage0/src/Lean/Meta/Basic.lean | 52f0dd45263fb91c30afff6f4061b89c7a6fd23e | [
"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 | 56,525 | 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.Data.LOption
import Lean.Environment
import Lean.Class
import Lean.ReducibilityAttrs
import Lean.Util.Trace
import Lean.Util.RecDepth
import Lea... |
6e83a94575eace8c2375dc1b95bbcc5f04385e70 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/free_algebra.lean | 0dd0cb1a592c4f4917f2353c90bbdf302b4b4acc | [
"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 | 16,409 | lean | /-
Copyright (c) 2020 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Adam Topaz
-/
import algebra.algebra.subalgebra.basic
import algebra.monoid_algebra.basic
/-!
# Free Algebras
Given a commutative semiring `R`, and a type `X`, we constru... |
a62ffbb1593b9a7a5e025faaca351f6f59e5232e | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/init/data/array/default_auto.lean | 61630a986ed9176c14ef4aed3f43ca8551731aaf | [] | 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 | 306 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.data.array.basic
import Mathlib.Lean3Lib.init.data.array.slice
namespace Mathlib
end Mathlib |
814a6748c6167a1e4fd955ff0ffd3e3df01a9723 | 69bc7d0780be17e452d542a93f9599488f1c0c8e | /prop_logic_test.lean | be6d05a7be4517713aa7e6abb9d680ea0c113684 | [] | no_license | joek13/cs2102-notes | b7352285b1d1184fae25594f89f5926d74e6d7b4 | 25bb18788641b20af9cf3c429afe1da9b2f5eafb | refs/heads/master | 1,673,461,162,867 | 1,575,561,090,000 | 1,575,561,090,000 | 207,573,549 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,018 | lean | import .prop_logic
open prop_logic
open prop_logic.var
open prop_logic.unOp
open prop_logic.binOp
open prop_logic.pExp
def varX := mkVar 0
def varY := mkVar 1
def varZ := mkVar 2
def varW := mkVar 3
def X := varExp varX
def Y := varExp varY
def Z := varExp varZ
def W := varExp varW
-- Notes on operator precedence
d... |
d4d4b4a7444a9bb575f6fa71431496baa9b02e6e | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/tactic/ring_exp.lean | 5b502badf58ac671db535fb0b2d9a5bdf7e5543a | [
"Apache-2.0"
] | permissive | gebner/mathlib | eab0150cc4f79ec45d2016a8c21750244a2e7ff0 | cc6a6edc397c55118df62831e23bfbd6e6c6b4ab | refs/heads/master | 1,625,574,853,976 | 1,586,712,827,000 | 1,586,712,827,000 | 99,101,412 | 1 | 0 | Apache-2.0 | 1,586,716,389,000 | 1,501,667,958,000 | Lean | UTF-8 | Lean | false | false | 55,552 | lean | /-
Copyright (c) 2019 Tim Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Tim Baanen.
Solve equations in commutative (semi)rings with exponents.
-/
import tactic.norm_num
/-!
# `ring_exp` tactic
A tactic for solving equations in commutative (semi)rings,
where ... |
aa7a922c0384bf1c0958d6e2fba1a8d82650159f | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /03_Propositions_and_Proofs.org.36.lean | 454eaef2702e7fae6fc02349272e499194435ff9 | [] | 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 | 250 | lean | /- page 44 -/
import standard
open classical
variables p q : Prop
-- BEGIN
example (H : ¬ (p ∧ q)) : ¬ p ∨ ¬ q :=
or.elim (em p)
(assume Hp : p,
or.inr
(show ¬q, from
assume Hq : q,
H (and.intro Hp Hq)))
(assume Hp : ¬p,
or.inl Hp)
-- END
|
652dc949e37e4d5fefab390bf2f7aa2e68eb2910 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/linear_algebra/tensor_product.lean | c7ceca676048e63467db59af31e0c0936b73d624 | [
"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 | 40,645 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Mario Carneiro
-/
import group_theory.congruence
import linear_algebra.basic
/-!
# Tensor product of modules over commutative semirings.
This file constructs the tensor produc... |
6f2bba0d2e9670496020e9b2c00974e555fda5e1 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/category_theory/limits/comma.lean | 6de3508a4374b71ca6ee87e52c147b8e5139e8c2 | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 10,254 | 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.arrow
import category_theory.limits.constructions.epi_mono
import category_theory.limits.creates
import category_theory.limits.unit
import category... |
03b3f3188af2c7dd9ff5f567bef1b0309785ee4c | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/1888.lean | 9e2644a753f02b3909c5b78d3f172e4416f4d87a | [
"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 | 600 | lean | universes u
variables {α : Sort u} {r p q : α → Prop} {P Q : ∀ x, p x → Prop} {a b c d : Prop}
@[simp] theorem exists_prop {p q : Prop} : (∃ h : p, q) ↔ p ∧ q := sorry
@[simp] theorem exists_and_distrib_right {q : Prop} {p : α → Prop} : (∃x, p x ∧ q) ↔ (∃x, p x) ∧ q := sorry
@[simp] theorem and_imp : (a ∧ b → c) ↔ (a ... |
85eeafcb7baa3fd0bb47c7b95c5f0f7c2d79aa44 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/linear_algebra/multilinear.lean | 6cf4ec9be8bef2a4f68f82481041671022ceb09b | [
"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 | 54,255 | 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 algebra.big_operators.order
import algebra.big_operators.ring
import data.fintype.card
import da... |
2778f1fcac3b426df3ac155691b6e5467a47569c | 367134ba5a65885e863bdc4507601606690974c1 | /src/analysis/quaternion.lean | 31621e0082334ae01e475787ba4ec31c5bac3ff5 | [
"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 | 3,367 | lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import data.quaternion
import analysis.normed_space.inner_product
/-!
# Quaternions as a normed algebra
In this file we define the following structures on the spa... |
0afa40650d1d9d045df4326131b4f2a75e23a28e | 92bfaf170880e47d55bf51d5a782fffd76db2f5f | /melting_point/naive.lean | 1575f00836b35e060bc7efd0c037302ae14bd246 | [] | 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 | 6,642 | lean | -- Naive set theory
noncomputable theory
open classical
axiom ens : Type
namespace ens
axiom contains : ens → ens → Prop
instance : has_mem ens ens := ⟨contains⟩
axiom comp : (ens → Prop) → ens
@[simp] axiom compβrule : Π (φ : ens → Prop) (x : ens), (x ∈ comp φ) = φ x
axiom setext.intro : ∀ {α β : ens}, (∀... |
cc8e7a2c1cfbc492f3a45b4873e190bd8e09656c | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/env_errors.lean | bb38e0d41fbeb385929af7b686703b4a2098a0cd | [
"Apache-2.0"
] | permissive | codyroux/lean0.1 | 1ce92751d664aacff0529e139083304a7bbc8a71 | 0dc6fb974aa85ed6f305a2f4b10a53a44ee5f0ef | refs/heads/master | 1,610,830,535,062 | 1,402,150,480,000 | 1,402,150,480,000 | 19,588,851 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 374 | lean | variable x : Nat
set_opaque x true.
print "before import"
(*
local env = get_environment()
env:import("tstblafoo.lean")
*)
print "before load1"
(*
local env = get_environment()
env:load("tstblafoo.lean")
*)
print "before load2"
(*
local env = get_environment()
env:load("fake1.olean")
*)
print "before load3"
(*
loc... |
29879f7aa76f22a5136f0cb312fe26560cac90ed | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/field_theory/primitive_element.lean | 0b0f3776da526374d89ec825d52864794d66f58e | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 8,802 | lean | /-
Copyright (c) 2020 Thomas Browning, Patrick Lutz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning, Patrick Lutz
-/
import field_theory.adjoin
import field_theory.fixed
import field_theory.is_alg_closed.basic
import field_theory.separable
import ring_... |
62a835497070935d5f134d7be38addc91cb0bd52 | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /src/Lean/PrettyPrinter/Meta.lean | 62b8769f84f7bdc2699a85e2babc30f864a11dfe | [
"Apache-2.0"
] | permissive | walterhu1015/lean4 | b2c71b688975177402758924eaa513475ed6ce72 | 2214d81e84646a905d0b20b032c89caf89c737ad | refs/heads/master | 1,671,342,096,906 | 1,599,695,985,000 | 1,599,695,985,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,963 | lean | /-
Copyright (c) 2020 Sebastian Ullrich. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Ullrich
-/
/-!
Set up pretty printer compilers for the next stage.
-/
import Lean.PrettyPrinter.Parenthesizer
import Lean.PrettyPrinter.Formatter
import Lean.ParserCompi... |
85068075fa26e4a5b5be5573697e72f7dc3b757a | 969dbdfed67fda40a6f5a2b4f8c4a3c7dc01e0fb | /src/group_theory/dihedral.lean | 9ba253c6489b44a46e7d5102a71d73acffe49552 | [
"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 | 5,354 | lean | /-
Copyright (c) 2020 Shing Tak Lam. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shing Tak Lam
-/
import data.zmod.basic
import group_theory.order_of_element
/-!
# Dihedral Groups
We define the dihedral groups `dihedral n`, with elements `r i` and `sr i` for `i : ... |
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