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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1ad0cc25a5529f26ad59fa34e21a6de581db0e9b | 271e26e338b0c14544a889c31c30b39c989f2e0f | /stage0/src/Init/Control/Monad.lean | 237ff3839274694eaf65b69be996782c1e65b90b | [
"Apache-2.0"
] | permissive | dgorokho/lean4 | 805f99b0b60c545b64ac34ab8237a8504f89d7d4 | e949a052bad59b1c7b54a82d24d516a656487d8a | refs/heads/master | 1,607,061,363,851 | 1,578,006,086,000 | 1,578,006,086,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,648 | lean | /-
Copyright (c) Luke Nelson and Jared Roesch. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Luke Nelson, Jared Roesch, Sebastian Ullrich
-/
prelude
import Init.Control.Applicative
universes u v w
open Function
class HasBind (m : Type u → Type v) ... |
f609be4c8678fc155255611ec0ef3a446c065bb3 | 32da3d0f92cab08875472ef6cacc1931c2b3eafa | /src/algebra/lie/basic.lean | 98b040512c71b011a4b6f218712e5d89b74110f6 | [
"Apache-2.0"
] | permissive | karthiknadig/mathlib | b6073c3748860bfc9a3e55da86afcddba62dc913 | 33a86cfff12d7f200d0010cd03b95e9b69a6c1a5 | refs/heads/master | 1,676,389,371,851 | 1,610,061,127,000 | 1,610,061,127,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 59,541 | 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 data.bracket
import algebra.algebra.basic
import linear_algebra.bilinear_form
import linear_algebra.matrix
import tactic.noncomm_ring
/-!
# Lie algebras
This file ... |
cd637cb00e9c4a26f67e80cb84166f6eb9ae69d7 | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/group_theory/perm/basic.lean | 10a04b5d6ab296e0257350c6db5845eb566dfd08 | [
"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 | 16,280 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Mario Carneiro
-/
import algebra.group.pi
import algebra.group_power
/-!
# The group of permutations (self-equivalences) of a type `α`
This file defines the... |
fb7f2ee56d14b0725962574f2380ff7b897ee24f | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /tests/lean/interactive/533.lean | 8f2cbf60832a2f43097e70d4f1ba5d64338d6109 | [
"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 | 104 | lean | set_option relaxedAutoImplicit false
inductive Foo where
| bar : F
--^ textDocument/completion
|
872d10a12d5b17032f8352ecc0209361fe188e14 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/order/complete_lattice.lean | cc6b7b520a2edd7845df73457cf30a15e7e3a96e | [
"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 | 53,172 | 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 order.bounds
import data.set.bool
/-!
# Theory of complete lattices
## Main definitions
* `Sup` and `Inf` are the supremum and the infimum of a set;
* `supr... |
1724498950c5c4a466b9092cda5d7bfbdf441db6 | 9028d228ac200bbefe3a711342514dd4e4458bff | /src/data/real/basic.lean | 7322f1f2b5a2a498502df7b5168dd5ba1027e2f1 | [
"Apache-2.0"
] | permissive | mcncm/mathlib | 8d25099344d9d2bee62822cb9ed43aa3e09fa05e | fde3d78cadeec5ef827b16ae55664ef115e66f57 | refs/heads/master | 1,672,743,316,277 | 1,602,618,514,000 | 1,602,618,514,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 26,775 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Floris van Doorn
The (classical) real numbers ℝ. This is a direct construction
from Cauchy sequences.
-/
import order.conditionally_complete_lattice
import data.real.c... |
efd061cc03383abce705e83ed3cddbda1c2074dc | bd30db067473b7b7ccac89486f0faf854379c3f8 | /mm_basic_defs.lean | d0609654a047c268a0d21d41b7d1eb082b3b8d30 | [] | no_license | danieljmchugh/lean_arm_memory_model | e661a986f933d4868928062cb47e9d88f0316c7d | bf53a6c1509d22127f990b030d6f3ab57266dc92 | refs/heads/main | 1,687,711,084,222 | 1,626,487,537,000 | 1,626,487,537,000 | 386,810,582 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,681 | lean | -- Armv8 memory model: Basic defintions
/- ######################## Elements ######################## -/
def observer := Type
@[reducible]
def location := ℕ
@[reducible]
def program_order_instruction_index := ℕ
@[derive decidable_eq]
inductive instruction
| write
| read
structure event :=
(id : ℕ)
(ob : ob... |
0a21e3c92f289f1ca6600eb4b9032f5c3ed41889 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/control/bifunctor.lean | e1b572faf1738ad64cfcff897d3d180b314f6679 | [] | 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 | 7,503 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Simon Hudon
Functors with two arguments
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.logic.function.basic
import Mathlib.control.functor
import Mathlib.ta... |
b2a0923a0af0e9989017d2af854a60205c24efeb | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/data/nat/squarefree.lean | 3a25b67b1f9228977c64833f4d364d5ebc031fd4 | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 22,044 | lean | /-
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import ring_theory.int.basic
import data.nat.factorization.prime_pow
import algebra.squarefree
/-!
# Lemmas about squarefreeness of natural numbers
A number is squar... |
ca319d35378ce68997ef03a3e7abbffc7303ab39 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/algebra/module/ulift.lean | ae139a21f1d4f0f127d23b9cd63fbcaabf598ad4 | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 3,341 | 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 linear_algebra.basic
import algebra.ring.ulift
/-!
# `ulift` instances for module and multiplicative actions
This file defines instances for module, mul_acti... |
1f1b2ef4c8f374ab6a5257f10a00904a59154652 | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/data/real/hyperreal.lean | 8a8c5a35aa4120c8ac29a4325c0ba9138351297f | [
"Apache-2.0"
] | permissive | fpvandoorn/mathlib | b21ab4068db079cbb8590b58fda9cc4bc1f35df4 | b3433a51ea8bc07c4159c1073838fc0ee9b8f227 | refs/heads/master | 1,624,791,089,608 | 1,556,715,231,000 | 1,556,715,231,000 | 165,722,980 | 5 | 0 | Apache-2.0 | 1,552,657,455,000 | 1,547,494,646,000 | Lean | UTF-8 | Lean | false | false | 4,635 | lean | /-
Copyright (c) 2019 Abhimanyu Pallavi Sudhir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Abhimanyu Pallavi Sudhir
Construction of the hyperreal numbers as an ultraproduct of real sequences.
-/
import data.real.basic algebra.field order.filter.filter_product anal... |
85dfd382d2d3a09266df284d2eeb3628d03298b7 | 874a8d2247ab9a4516052498f80da2e32d0e3a48 | /Congruences_(Fermat_little).lean | 8e31ff980e31a94c4ea50e5ef16fa042d2af5607 | [] | no_license | AlexKontorovich/Spring2020Math492 | 378b36c643ee029f5ab91c1677889baa591f5e85 | 659108c5d864ff5c75b9b3b13b847aa5cff4348a | refs/heads/master | 1,610,780,595,457 | 1,588,174,859,000 | 1,588,174,859,000 | 243,017,788 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 2,280 | lean | import data.nat.gcd
import algebra.big_operators
import data.int.gcd
import algebra.euclidean_domain
import data.zmod.basic
def divides (d n: ℤ):= ∃l:ℤ, n = d*l
def is_congruent_mod_n (a b n: ℤ) := divides n (b-a)
def relatively_prime(a b:ℤ) := nat.coprime (int.nat_abs a) (int.nat_abs b)
theorem relatively_prime_su... |
727aeef89df45cbad98b47ea54714f5a713bbde4 | cc060cf567f81c404a13ee79bf21f2e720fa6db0 | /lean/20170429-eblast-regression.lean | 3bf0493c273496a8a44ed1335f2a30d779254f67 | [
"Apache-2.0"
] | permissive | semorrison/proof | cf0a8c6957153bdb206fd5d5a762a75958a82bca | 5ee398aa239a379a431190edbb6022b1a0aa2c70 | refs/heads/master | 1,610,414,502,842 | 1,518,696,851,000 | 1,518,696,851,000 | 78,375,937 | 2 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 1,762 | lean | structure Category :=
( Obj : Type )
( Hom : Obj → Obj → Type )
(compose : Π { X Y Z : Obj }, Hom X Y → Hom Y Z → Hom X Z)
(associativity : ∀ { W X Y Z : Obj } (f : Hom W X) (g : Hom X Y) (h : Hom Y Z),
compose (compose f g) h = compose f (compose g h))
attribute [ematch] Category.associativity
structur... |
202c664e66005b20eb5346b983949bf31c20171c | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/data/mv_polynomial/rename.lean | 61c3d9ea1492ad9a7144f2c04e3570827a154829 | [
"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 | 7,857 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
-/
import data.mv_polynomial.basic
/-!
# Renaming variables of polynomials
This file establishes the `rename` operation on multivariat... |
86eca11a47bdb22aea8aa5c127f0e843728eb0c8 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/topology/metric_space/pi_nat.lean | fc54cfe6d20ddb4bbf36b7c0811ff579ed9e959a | [
"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 | 41,441 | lean | /-
Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import tactic.ring_exp
import topology.metric_space.hausdorff_distance
/-!
# Topological study of spaces `Π (n : ℕ), E n`
When `E n` are topological spaces, t... |
4f2d450ea8c326c2cc5064b9bf56fe551c1346e0 | 1abd1ed12aa68b375cdef28959f39531c6e95b84 | /src/order/complete_lattice.lean | b9127d6a93dc27fd18efa76ccf90cf0330154bce | [
"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 | 53,611 | 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 order.bounds
import data.set.bool
import data.nat.basic
/-!
# Theory of complete lattices
## Main definitions
* `Sup` and `Inf` are the supremum and the inf... |
f52c4ed5f2fdb3f462cd084bf959a0337e706b83 | 6b45072eb2b3db3ecaace2a7a0241ce81f815787 | /algebra/lattice/basic.lean | 1fbb94935c719da3cfe005de5a29736aa0508aeb | [] | no_license | avigad/library_dev | 27b47257382667b5eb7e6476c4f5b0d685dd3ddc | 9d8ac7c7798ca550874e90fed585caad030bbfac | refs/heads/master | 1,610,452,468,791 | 1,500,712,839,000 | 1,500,713,478,000 | 69,311,142 | 1 | 0 | null | 1,474,942,903,000 | 1,474,942,902,000 | null | UTF-8 | Lean | false | false | 8,610 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Defines the inf/sup (semi)-lattice with optionally top/bot type class hierarchy.
-/
import ..order
set_option old_structure_cmd true
universes u v w
/- TODO: automa... |
d5055e9fc7c5e6277b07cfa48adf7c0905c79b42 | 46125763b4dbf50619e8846a1371029346f4c3db | /src/group_theory/congruence.lean | c857a118cb6c006fdfeffe599be9bd8ede4d4159 | [
"Apache-2.0"
] | permissive | thjread/mathlib | a9d97612cedc2c3101060737233df15abcdb9eb1 | 7cffe2520a5518bba19227a107078d83fa725ddc | refs/heads/master | 1,615,637,696,376 | 1,583,953,063,000 | 1,583,953,063,000 | 246,680,271 | 0 | 0 | Apache-2.0 | 1,583,960,875,000 | 1,583,960,875,000 | null | UTF-8 | Lean | false | false | 43,489 | lean | /-
Copyright (c) 2019 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
import group_theory.submonoid
import data.setoid
import algebra.pi_instances
/-!
# Congruence relations
This file defines congruence relations: equivalence r... |
6a2e17cac93cde81f958bb6203de48ebe3a4b5df | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/compiler/foreign/Main.lean | 4e8cab93a90cb9eb63478d0900e2795d9b8ebaaa | [
"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 | 277 | lean | import Main.S
def main : IO Unit := do
IO.println (mkS 10 20 "hello").addXY
IO.println (mkS 10 20 "hello").string
appendToGlobalS "foo"
appendToGlobalS "bla"
getGlobalString >>= IO.println
updateGlobalS (mkS 0 0 "world")
getGlobalString >>= IO.println
pure ()
|
14acbd8153ee4a6d4b6b0a45f9fc5767796a7cc7 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/category_theory/essential_image.lean | d360b4140a6170dc075bde785627eaa8ab7f5f98 | [
"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 | 4,722 | 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.natural_isomorphism
import category_theory.full_subcategory
/-!
# Essential image of a functor
The essential image `ess_image` of a functor consi... |
ae6f355609bfeff077a0997b5eaeecaba2c7c946 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/tactic/nth_rewrite/basic.lean | 933a5b657793fd51636808f6d5bfe074ed8b3567 | [
"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 | 1,316 | lean | /-
Copyright (c) 2018 Keeley Hoek. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Keeley Hoek, Scott Morrison
-/
import meta.expr_lens
namespace tactic
open expr
namespace nth_rewrite
/-- Configuration options for nth_rewrite. -/
meta structure cfg e... |
77e3412359c4977d7117d5286d3a1b026d9d1c97 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/match3.lean | c031c6ddb93a262cded400636b95ee3c1dab4cb7 | [
"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 | 1,042 | lean | open nat
definition foo (a : nat) : nat :=
match a with
| 0 := 0
| (succ n) := n
end
example : foo 3 = 2 := rfl
open decidable
protected def dec_eq : ∀ x y : nat, decidable (x = y)
| 0 0 := is_true rfl
| (succ x) 0 := is_false (λ h, nat.no_confusion h)
| 0 (succ y) := is_false (λ h... |
923a5789c6adfa74c6aac606b51577ad17a24b2f | d1a52c3f208fa42c41df8278c3d280f075eb020c | /tests/lean/run/simpMatchDiscr.lean | f67e8e856720d00a0418919f8dd0ecb3848ee960 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | cipher1024/lean4 | 6e1f98bb58e7a92b28f5364eb38a14c8d0aae393 | 69114d3b50806264ef35b57394391c3e738a9822 | refs/heads/master | 1,642,227,983,603 | 1,642,011,696,000 | 1,642,011,696,000 | 228,607,691 | 0 | 0 | Apache-2.0 | 1,576,584,269,000 | 1,576,584,268,000 | null | UTF-8 | Lean | false | false | 1,381 | lean | inductive Vec (α : Type u) : Nat → Type u
| nil : Vec α 0
| cons : α → {n : Nat} → Vec α n → Vec α (n+1)
def Vec.repeat (a : α) (n : Nat) : Vec α n :=
match n with
| 0 => nil
| n+1 => cons a (repeat a n)
instance [Inhabited α] : Inhabited (Vec α n) where
default := Vec.repeat arbitrary n
def Vec.map (... |
81a26de291b4bdd8110a83b7e360742629006c8b | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/topology/semicontinuous.lean | 77d500b3aa5975703a2fb8c280c1dcd9d53b17e9 | [
"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 | 37,528 | lean | /-
Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import topology.continuous_on
import data.indicator_function
import topology.algebra.group
import topology.algebra.ordered.liminf_limsup
import topology.instanc... |
dda42ca7f27989dc9361aa52c1d277958f220d4e | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/data/string/basic.lean | 99053d13e7486a28de51120bde23696d2c325cb3 | [
"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 | 2,563 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
Supplementary theorems about the `string` type.
-/
import data.list.basic data.char
namespace string
def ltb : iterator → iterator → bool
| s₁ s₂ := begin
cases s₂.h... |
700227c4a20ccf385aa6a00183ab8bb76f6ac68a | 36938939954e91f23dec66a02728db08a7acfcf9 | /lean/deps/galois_stdlib/src/galois/logic.lean | 1fd6857810c052ce24aef70ba836ff1a4449e82b | [
"Apache-2.0"
] | permissive | pnwamk/reopt-vcg | f8b56dd0279392a5e1c6aee721be8138e6b558d3 | c9f9f185fbefc25c36c4b506bbc85fd1a03c3b6d | refs/heads/master | 1,631,145,017,772 | 1,593,549,019,000 | 1,593,549,143,000 | 254,191,418 | 0 | 0 | null | 1,586,377,077,000 | 1,586,377,077,000 | null | UTF-8 | Lean | false | false | 735 | lean | -- Definitions
--- Use type-class resolution to find a decidable instance.
def decide (p:Prop) [h:decidable p] : decidable p := h
--- Use decidable instance to prove any theorem is we have a proof of the theorem, but it is false.
theorem of_as_false {P : Prop} [h:decidable P] (p:P) (q : as_false P) {α : Prop} : α :... |
4d8b50b30d430ad6fa19ca13cc94cade40559dc8 | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/order/ideal.lean | e92b3fdc429fbff13c48a80e874c61d022699988 | [
"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 | 16,097 | lean | /-
Copyright (c) 2020 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn
-/
import order.basic
import data.equiv.encodable.basic
import order.atoms
/-!
# Order ideals, cofinal sets, and the Rasiowa–Sikorski lemma
## Main definitions
Throughout thi... |
4653fa1e204e52729aaad752e4829ddaeb47c330 | 8c9f90127b78cbeb5bb17fd6b5db1db2ffa3cbc4 | /workshop.lean | 01604b6db14646a2ee6fd5f5cded5a0d13fe5800 | [] | no_license | picrin/lean | 420f4d08bb3796b911d56d0938e4410e1da0e072 | 3d10c509c79704aa3a88ebfb24d08b30ce1137cc | refs/heads/master | 1,611,166,610,726 | 1,536,671,438,000 | 1,536,671,438,000 | 60,029,899 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,024 | lean | -- Like almost any programming language, lean has functions. `double` for example is a function.
def double : nat → nat :=
λ a : nat, a + a
-- `nat → nat` is the function's type signature. It means that `double` accepts a non-negative integer (we'll call those "nat") and it produces another nat.
-- It's possible... |
f9d959c039cdeb8a5d2d09eee1bc560cb43f522c | 35b83be3126daae10419b573c55e1fed009d3ae8 | /_target/deps/mathlib/data/nat/gcd.lean | 25cbfde8d68ed1d77663844cacda25607ee417f0 | [] | no_license | AHassan1024/Lean_Playground | ccb25b72029d199c0d23d002db2d32a9f2689ebc | a00b004c3a2eb9e3e863c361aa2b115260472414 | refs/heads/master | 1,586,221,905,125 | 1,544,951,310,000 | 1,544,951,310,000 | 157,934,290 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 12,045 | 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
Definitions and properties of gcd, lcm, and coprime.
-/
import data.nat.basic
namespace nat
/- gcd -/
theorem gcd_dvd (m n : ℕ) : (gcd m n ∣ m) ∧ (g... |
882d6a9e210bfb286a67724afd6cb3566c12562a | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/category_theory/abelian/injective.lean | c4dabce7e96aaf6f295d414e6776c764ccd03f6a | [
"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 | 1,444 | lean | /-
Copyright (c) 2022 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer
-/
import category_theory.abelian.exact
import category_theory.preadditive.injective
import category_theory.preadditive.yoneda
/-!
# Injective objects in abelian c... |
6bc9788be9c11c03ef42b4200d600e38d9137236 | 367134ba5a65885e863bdc4507601606690974c1 | /src/analysis/asymptotics/asymptotics.lean | fda236c5fafd6d6f991ce38b7928972f6c22ed5b | [
"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 | 59,789 | lean | /-
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Yury Kudryashov
-/
import analysis.normed_space.basic
import topology.local_homeomorph
/-!
# Asymptotics
We introduce these relations:
* `is_O_with c f g l` : "f is bi... |
9fd3521c337cfa354b2b81ec80aa312f05990d92 | a46d86797f98e604c71128429409acba8288c1f8 | /abstract_interpretation.lean | 91875ef0b1402b713c085982e0db18ff8c819a36 | [] | no_license | tizmd/lean-abstract-interpretation | 655213d76e84e093910bb6378796cdb4e1ae3565 | ad69622adc082e7009f12b17568662a599779260 | refs/heads/master | 1,610,518,429,734 | 1,498,128,216,000 | 1,498,128,216,000 | 94,891,623 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,079 | lean | import algebra.lattice.basic algebra.lattice.dcpo algebra.lattice.fixed_points
universes u v
open lattice
variables {α : Type u} {γ : Type v} [directed_complete_partial_order α][directed_complete_partial_order γ]
def specification α [order_bot α] := Σ' (f : α → α) (h : monotone f), h.ascending_chain.is_stationary
d... |
2ae17a7498ac31177ccaff832b5d8795cda16b97 | e0f9ba56b7fedc16ef8697f6caeef5898b435143 | /src/data/real/basic.lean | e5fc1b717c9e9c62f59fa4ea740aca6df52c4574 | [
"Apache-2.0"
] | permissive | anrddh/mathlib | 6a374da53c7e3a35cb0298b0cd67824efef362b4 | a4266a01d2dcb10de19369307c986d038c7bb6a6 | refs/heads/master | 1,656,710,827,909 | 1,589,560,456,000 | 1,589,560,456,000 | 264,271,800 | 0 | 0 | Apache-2.0 | 1,589,568,062,000 | 1,589,568,061,000 | null | UTF-8 | Lean | false | false | 26,275 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Floris van Doorn
The (classical) real numbers ℝ. This is a direct construction
from Cauchy sequences.
-/
import order.conditionally_complete_lattice
import data.real.c... |
dd50eaa53edcfe0512edba1bfd8f0ebabc593b2b | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/tactic/omega/lin_comb.lean | bead77095b69a5fa642499daea356ffa8a5221b9 | [
"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 | 2,155 | lean | /- Copyright (c) 2019 Seul Baek. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Seul Baek
Linear combination of constraints. -/
import tactic.omega.clause
namespace omega
/-- Linear combination of constraints. The second
argument is the list of constraints, and ... |
43b4353da0f345fcfa4e99ce518e637ad91fb9f6 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/linear_algebra/std_basis.lean | 1b47691c937d71c69451cffd634cb2e039d487bd | [
"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 | 10,834 | 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.matrix.basis
import linear_algebra.basis
import linear_algebra.pi
/-!
# The standard basis
This file defines the standard basis `pi.basis (s : ∀ j, basi... |
a7ee95e58045907c4242604ea143f8c48ef50117 | eb586f8ae80b7045ba4ff08f1c7ba69403d61081 | /src/liouville_theorem.lean | 0dcc0a4875b4f9842a0479ba01f1903325d8d525 | [] | no_license | bryangingechen/transcendental | 926584f58c47d766b304d39d1aa6814284535394 | 3692ac5ebe85e49c5f65bc7f2ea4f873a973bac2 | refs/heads/master | 1,668,733,660,442 | 1,594,269,161,000 | 1,594,269,161,000 | 278,266,099 | 0 | 0 | null | 1,594,270,314,000 | 1,594,270,313,000 | null | UTF-8 | Lean | false | false | 57,708 | lean | import ring_theory.algebraic
import topology.algebra.polynomial
import analysis.calculus.mean_value
import small_things
noncomputable theory
open_locale classical
open small_things
/--
- a number is transcendental ↔ a number is not algebraic
- a Liouville's number $x$ is a number such that
for every natural number,... |
a0e193f46fc37368863a958c76f7d1bcb096fa3a | b04a2b9331022307985cb4dee8a75dd804625569 | /identities.lean | 60fbd497201de89ebf9fd55f88d23dc2ab3464ff | [] | no_license | tjhance/lean-project | 558de3b6f88b5b12241ec8d0803027a32eaea13f | c00a01e02ae2fee4e90d48bfd8504d2d45fdb43c | refs/heads/master | 1,588,096,917,016 | 1,556,580,095,000 | 1,556,580,106,000 | 175,465,730 | 3 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 23,373 | lean | import data.nat.choose
import data.set
import data.set.finite
import data.multiset
import data.list
import data.list.perm
/- Collaboration between
Travis Hance (thance)
Katherine Cordwell (kcordwell)
-/
/-
Machinery for bijective proofs.
`has_card` is a Prop that indicates a set is finite
and has a ... |
5b443e892ed66d17e64ff4bb82cb22dbf957f606 | 471bedbd023d35c9d078c2f936dd577ace7f5813 | /library/init/data/nat/bitwise.lean | 03d4def49ba205b8cdfc9c6803c5a1a9b78b465d | [
"Apache-2.0"
] | permissive | lambdaxymox/lean | e06f0fa503666df827edd9867d7f49ca017aae64 | fc13c8c72a15dab71a2c2b31410c2cadc3526bd7 | refs/heads/master | 1,666,785,407,985 | 1,666,153,673,000 | 1,666,153,673,000 | 310,165,986 | 0 | 0 | Apache-2.0 | 1,604,542,096,000 | 1,604,542,095,000 | null | UTF-8 | Lean | false | false | 10,080 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
-/
prelude
import init.data.nat.lemmas init.meta.well_founded_tactics
universe u
namespace nat
def bodd_div2 : ℕ → bool × ℕ
| 0 := (ff, 0)
| (succ n) :=... |
eccd0b8080d0064034b429dd10652417f0a20464 | 097294e9b80f0d9893ac160b9c7219aa135b51b9 | /instructor/propositional_logic/satisfiability/rules_of_reasoning.lean | 428e701141cf9e0bd424c0abc612ccb21d045c4d | [] | no_license | AbigailCastro17/CS2102-Discrete-Math | cf296251be9418ce90206f5e66bde9163e21abf9 | d741e4d2d6a9b2e0c8380e51706218b8f608cee4 | refs/heads/main | 1,682,891,087,358 | 1,621,401,341,000 | 1,621,401,341,000 | 368,749,959 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,765 | lean | import .propositional_logic_syntax_and_semantics
open pExp
/-
This file defines three propositional logic variables
and then defines a list of fundamental rules of logical
reasoning. Most of these rules are valid, but a few are
not. It is a homework assignment to use pEval to prove
that the ones that are valid really... |
82dad0c9b4c2bd1721e9a553915105ac90f7b38e | ac2987d8c7832fb4a87edb6bee26141facbb6fa0 | /Mathlib/Tactic/RunTac.lean | 023f91d787529527762a12948bea428fe240700b | [
"Apache-2.0"
] | permissive | AurelienSaue/mathlib4 | 52204b9bd9d207c922fe0cf3397166728bb6c2e2 | 84271fe0875bafdaa88ac41f1b5a7c18151bd0d5 | refs/heads/master | 1,689,156,096,545 | 1,629,378,840,000 | 1,629,378,840,000 | 389,648,603 | 0 | 0 | Apache-2.0 | 1,627,307,284,000 | 1,627,307,284,000 | null | UTF-8 | Lean | false | false | 1,084 | lean | /-
Copyright (c) 2018 Sebastian Ullrich. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Sebastian Ullrich
-/
import Lean.Elab.SyntheticMVars
open Lean Elab Tactic
unsafe def evalRunTacUnsafe (term : Syntax) : TacticM Unit := do
let n := `_runTac
let type := mkApp (... |
7d70fddf6445ebcc7ed825c5e621ddcadb25f74a | 86f6f4f8d827a196a32bfc646234b73328aeb306 | /examples/basics/unnamed_1836.lean | 8dfaaa48bc02bcc393d26dde941aac9d8f42d710 | [] | no_license | jamescheuk91/mathematics_in_lean | 09f1f87d2b0dce53464ff0cbe592c568ff59cf5e | 4452499264e2975bca2f42565c0925506ba5dda3 | refs/heads/master | 1,679,716,410,967 | 1,613,957,947,000 | 1,613,957,947,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 371 | lean | import order.lattice
variables {α : Type*} [lattice α]
variables x y z : α
#check x ⊓ y
#check (inf_le_left : x ⊓ y ≤ x)
#check (inf_le_right : x ⊓ y ≤ y)
#check (le_inf : z ≤ x → z ≤ y → z ≤ x ⊓ y)
#check x ⊔ y
#check (le_sup_left : x ≤ x ⊔ y)
#check (le_sup_right: y ≤ x ⊔ y)
#check (sup_le : x ≤ z → y ≤ z → x ⊔ y ... |
0a2ab1a80e9ed85c75f413c89c19e18f59981345 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/ring_theory/power_basis.lean | dc20629d3bab03a6dbd43647c6df833111fb961e | [] | 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 | 15,686 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.field_theory.adjoin
import Mathlib.field_theory.minpoly
import Mathlib.ring_theory.adjoin
import ... |
c6ca6d0c9af405efed4ee42fb99b1c25155269cc | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /tests/pkg/prv/lakefile.lean | d22d58719d554693e1836ee06461dd6b9083e9fc | [
"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 | 76 | lean | import Lake
open System Lake DSL
package prv
@[defaultTarget] lean_lib Prv
|
8c7956671ec9e968cefc3c9db715c165522fe54b | d6124c8dbe5661dcc5b8c9da0a56fbf1f0480ad6 | /Papyrus/IR/GlobalRefs.lean | 676137db766d389c3167a6ca7a7189860635d8c0 | [
"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 | 4,572 | lean | import Papyrus.Context
import Papyrus.IR.TypeRefs
import Papyrus.IR.ConstantRef
import Papyrus.IR.AddressSpace
import Papyrus.IR.GlobalModifiers
namespace Papyrus
--------------------------------------------------------------------------------
-- # Global Value References
---------------------------------------------... |
176124a778a96216f0b9df2714b795fecff4b05c | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/data/list/defs.lean | d7d3904ed695eea615c73105063a7fdcdcae7d8d | [
"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 | 27,963 | 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... |
56a8f70e2e57d771cce32c8c9d3bf9fa723ccbde | 6df8d5ae3acf20ad0d7f0247d2cee1957ef96df1 | /notes/10.1.19.Polymorphism/boxedTests.lean | a8fc6eb5d063c113fbfc67dfdba8159f88a723bf | [] | no_license | derekjohnsonva/CS2102 | 8ed45daa6658e6121bac0f6691eac6147d08246d | b3f507d4be824a2511838a1054d04fc9aef3304c | refs/heads/master | 1,648,529,162,527 | 1,578,851,859,000 | 1,578,851,859,000 | 233,433,207 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 234 | lean | import .boxed
open boxed_adt
def b1 : boxed nat := boxed.box 3
def b2 : boxed string := boxed.box "Hello"
def b3 : boxed bool := boxed.box tt
def b1' := boxed.box 3 --lean is using type inference
#reduce unbox b1
#reduce unbox b3
|
eb56c56ba8133b5f3ed061f9ffadea874b86dced | e4def7044cdf5942eed78db25d2daa58d80eed64 | /_target/deps/mathlib/src/analysis/calculus/mean_value.lean | 71338b56f004bad5140fff58a51f8b0c1c152211 | [
"Apache-2.0"
] | permissive | kevinsullivan/dm.s20.old | 3f8f736b9a792cca8dd44a73a98ade0b534ed084 | a240be0a53961ac25b5f4426fe7bc8d4dbe7013f | refs/heads/master | 1,607,522,498,471 | 1,579,058,084,000 | 1,579,058,084,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,369 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import analysis.calculus.deriv
/-!
# The mean value inequality
A bound on the derivative of a function implies that this function
is Lipschitz continuous for... |
2dbb4f6512f246ace8ebf87cfa4873a8e4d9757a | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/rbmap/basic.lean | f83f5aeaf436bc44cd1de93664256b4e3fa4e7e3 | [
"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 | 2,928 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import data.rbtree.init
universes u v w
def rbmap_lt {α : Type u} {β : Type v} (lt : α → α → Prop) (a b : α × β) : Prop :=
lt a.1 b.1
set_option auto_par... |
5197c5162976d2c9d0d48f2a1bccbeac1048f6f7 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/is_class_timeout.lean | 8be13fc7c318b5ccd136a7cbddf713336c64e768 | [
"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 | 82 | lean | def c : ℕ := if 999999999 < 9999999999 then 0 else 1
#eval tactic.is_class `(c) |
415e9ac45724b81eba8a4b402254298d3a490459 | 2385ce0e3b60d8dbea33dd439902a2070cca7a24 | /tests/lean/1369.lean | 78bc2f72d59b1aa81209756cb53909f9e489bbd3 | [
"Apache-2.0"
] | permissive | TehMillhouse/lean | 68d6fdd2fb11a6c65bc28dec308d70f04dad38b4 | 6bbf2fbd8912617e5a973575bab8c383c9c268a1 | refs/heads/master | 1,620,830,893,339 | 1,515,592,479,000 | 1,515,592,997,000 | 116,964,828 | 0 | 0 | null | 1,515,592,734,000 | 1,515,592,734,000 | null | UTF-8 | Lean | false | false | 713 | lean | open nat
open tactic
meta def match_le (e : expr) : tactic (expr × expr) :=
match expr.is_le e with
| (some r) := return r
| none := tactic.fail "expression is not a leq"
end
meta def nat_lit_le : tactic unit := do
(base_e, bound_e) ← tactic.target >>= match_le,
base ← tactic.eval_expr ℕ base_e,
skip
exam... |
5f4dc6312ec5b7521b5c01cb15b7c1e15c17da1d | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /test/pretty_cases.lean | 6b930aac0d4401cb4bb397aa1519019984874a9e | [
"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 | 902 | lean | import tactic.pretty_cases
import data.list.perm
example {α} (xs ys : list α) (h : xs ~ ys) : true :=
begin
induction h,
do { x ← tactic.pretty_cases_advice,
guard (x =
"Try this:
case list.perm.nil
{ admit },
case list.perm.cons : h_x h_l₁ h_l₂ h_a h_ih
{ admit },
case list.perm.swap : h_x h_y h_... |
8eb810854724c49f839a6f53bdeb29dca0570dcd | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/ring_theory/polynomial/cyclotomic/basic.lean | 53f19d21e2ae58813b361916c6c9e580297398da | [
"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 | 48,163 | lean | /-
Copyright (c) 2020 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca
-/
import algebra.polynomial.big_operators
import analysis.complex.roots_of_unity
import data.polynomial.lifts
import field_theory.separable
import field_theory.split... |
c0bca8799ad4ce68f1882cb934087cce2b14e14d | 7da5ceac20aaab989eeb795a4be9639982e7b35a | /src/group_theory/presentation.lean | 6fef4b2ca1f16042c7d02eb8a45a86a7f29d5bca | [
"MIT"
] | permissive | formalabstracts/formalabstracts | 46c2f1b3a172e62ca6ffeb46fbbdf1705718af49 | b0173da1af45421239d44492eeecd54bf65ee0f6 | refs/heads/master | 1,606,896,370,374 | 1,572,988,776,000 | 1,572,988,776,000 | 96,763,004 | 165 | 28 | null | 1,555,709,319,000 | 1,499,680,948,000 | Lean | UTF-8 | Lean | false | false | 8,536 | lean | import .basic ..data.dvector
/- Some definitions for specifying normal subgroups generated by group elements and by defining a group by generators and relations -/
open quotient_group set
open category_theory (mk_ob)
variables {α : Type*} [group α]
/-- the subgroup generated by a set is a normal subgroup if the set... |
08e0bc7df9f039bca37907b880fef41f6e61edfe | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/category_theory/idempotents/functor_categories.lean | ca71ecfa055a6849699d71d861fc30c2e4403301 | [
"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 | 5,556 | lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import category_theory.idempotents.karoubi
/-!
# Idempotent completeness and functor categories
In this file we define an instance `functor_category_is_idempotent_complete` ... |
1c65a1686043295adea790eb77403ab7a7f338ef | 8d65764a9e5f0923a67fc435eb1a5a1d02fd80e3 | /src/topology/algebra/infinite_sum.lean | 767517c5145bd276daffa6deb52a4b64ade4872b | [
"Apache-2.0"
] | permissive | troyjlee/mathlib | e18d4b8026e32062ab9e89bc3b003a5d1cfec3f5 | 45e7eb8447555247246e3fe91c87066506c14875 | refs/heads/master | 1,689,248,035,046 | 1,629,470,528,000 | 1,629,470,528,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 57,387 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import algebra.big_operators.intervals
import topology.instances.real
import topology.algebra.module
import algebra.indicator_function
import data.equiv.encodable.lat... |
4139463a05c3554952349691572290b477648ca0 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/topology/algebra/module/basic.lean | dd51e5e7a73db139841f887b93b4b77a8416fe77 | [
"Apache-2.0"
] | permissive | ramonfmir/mathlib | c5dc8b33155473fab97c38bd3aa6723dc289beaa | 14c52e990c17f5a00c0cc9e09847af16fabbed25 | refs/heads/master | 1,661,979,343,526 | 1,660,830,384,000 | 1,660,830,384,000 | 182,072,989 | 0 | 0 | null | 1,555,585,876,000 | 1,555,585,876,000 | null | UTF-8 | Lean | false | false | 92,674 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo, Yury Kudryashov, Frédéric Dupuis,
Heather Macbeth
-/
import topology.algebra.ring
import topology.algebra.mul_action
import topology... |
bc215724093129e32500cf33d68bd2a8e6373b81 | 4aca55eba10c989f0d58647d3c2f371e7da44355 | /src/symmetric_matrix.lean | ff8781dc7d821c62bff83baac63fb534ece5e894 | [] | no_license | eric-wieser/l534zhan-my_project | f9fc75fb5454405e1a2fa9b56cf96c355f6f2336 | febc91e76b7b00fe2517f258ca04d27b7f35fcf3 | refs/heads/master | 1,689,218,910,420 | 1,630,439,440,000 | 1,630,439,440,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,371 | lean | /-
Copyright (c) 2021 Lu-Ming Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Lu-Ming Zhang.
-/
import set_finset_fintype
import matrix_basic
/-!
# Symmetric matrices
This file contains basic results about symmetric matrices.
See `matrix_basic.lean` ... |
122526ce8053282c31ff60ad4f2555df5fe924e7 | 8cb37a089cdb4af3af9d8bf1002b417e407a8e9e | /library/data/lazy_list.lean | e12d6f315a1ad7506ef181a692aedc74f169ad3a | [
"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 | 2,227 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
universes u v w
inductive lazy_list (α : Type u) : Type u
| nil : lazy_list
| cons (hd : α) (tl : thunk lazy_list) : lazy_list
namespace lazy_list
variable... |
b560549fcfa8ea1a4cff0cbe3eb28f4571276415 | e953c38599905267210b87fb5d82dcc3e52a4214 | /library/algebra/ordered_ring.lean | ac364bd0df27449c44bf71be6bec8d3f903b238b | [
"Apache-2.0"
] | permissive | c-cube/lean | 563c1020bff98441c4f8ba60111fef6f6b46e31b | 0fb52a9a139f720be418dafac35104468e293b66 | refs/heads/master | 1,610,753,294,113 | 1,440,451,356,000 | 1,440,499,588,000 | 41,748,334 | 0 | 0 | null | 1,441,122,656,000 | 1,441,122,656,000 | null | UTF-8 | Lean | false | false | 24,180 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
Here an "ordered_ring" is partially ordered ring, which is ordered with respect to both a weak
order and an associated strict order. Our numeric structures (int, rat, and... |
2e7c7c209f2dfe1327b2735d1b4c483930487f86 | 42610cc2e5db9c90269470365e6056df0122eaa0 | /library/theories/finite_group_theory/quotient.lean | e637350a9273f997aff4cb85b06d3b49a7342c5c | [
"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 | 12,757 | lean | -- some extra lemmas about group quotients
import data theories.finite_group_theory.subgroup theories.finite_group_theory.finsubg theories.finite_group_theory.extra_finsubg --algebra.group
-- import theories.group_theory.basic
import theories.finite_group_theory.extra_hom
open group_theory finset subtype
namespace g... |
54ab995eee619e995288045fe53fd07ca13c057d | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/hott/611.hlean | a6271b1ab71cfa2833e4e3e4c7d9d64d5d221b8b | [
"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 | 218 | hlean | open is_trunc
attribute trunc.rec [recursor]
definition my_elim {n : trunc_index} {A : Type} {P : Type}
[Pt : is_trunc n P] (H : A → P) : trunc n A → P :=
begin
intro x, induction x,
apply H, assumption
end
|
9ec00300e0251217c1e41dd12aa6752d7817fde0 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/data/multiset/basic.lean | 3ea06ddf286e6c8cf65c4c7b9419500a3719373b | [
"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 | 98,275 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import data.list.perm
/-!
# Multisets
These are implemented as the quotient of a list by permutations.
## Notation
We define the global infix notation `::ₘ` f... |
603fdf6405a8ddd4d005a56407f344d0ace6a887 | 1e561612e7479c100cd9302e3fe08cbd2914aa25 | /scratch/scratch.lean | e1b2cddd4d46ac087877be0d0b6bc2484d8d8ec5 | [
"Apache-2.0"
] | permissive | kbuzzard/mathlib4_experiments | 8de8ed7193f70748a7529e05d831203a7c64eedb | 87cb879b4d602c8ecfd9283b7c0b06015abdbab1 | refs/heads/master | 1,687,971,389,316 | 1,620,336,942,000 | 1,620,336,942,000 | 353,994,588 | 7 | 4 | Apache-2.0 | 1,622,410,748,000 | 1,617,361,732,000 | Lean | UTF-8 | Lean | false | false | 553 | lean | structure Foo where
x : Nat
y : Nat
structure Boo where
w : Nat
z : Nat
structure Bla extends Foo, Boo where
bit : Bool
#check Bla.mk -- Foo → Boo → Bool → Bla
#check Bla.mk { x := 10, y := 20 } { w := 30, z := 40 } true
#check { x := 10, y := 20, w := 30, z := 40, bit := true : Bla }
#check { toFoo := { x... |
7e9511ad6e498817d13a5fcee41bcbc6e55af765 | b794ca1df49bc5a3bd3fd5552eed3bc4f63b8b93 | /src/mywork/lecture_9.lean | 64bb210f7baef63cac2fd7864d24161a21ce3926 | [] | no_license | akraisinger/cs2120f21 | 8235ac98375e04ffcec504cff5cab7833ee69e54 | 4ef83d7151bb6a284028092aa4f1d509c0eb8237 | refs/heads/main | 1,691,714,771,612 | 1,632,889,465,000 | 1,632,889,465,000 | 399,946,508 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,764 | lean | /-
Negation
-/
/-
Given an proposition, P, we can form a new
proposition, usually written as ¬P, which we
pronounce as "not P," and which we define in
such as way as to assert that P is not true.
-/
/-
So what does it mean when we say that *it is
true that P is not true*?
-/
/-
First, if ¬P is true, there should b... |
d8b9f9aee86fba14a72a2e7e6158644bd2fba7c6 | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/field_theory/adjoin.lean | 4dd8edb153e2d35f00f53a9a2837292dc68815d2 | [
"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 | 5,443 | lean | /-
Copyright (c) 2020 Thomas Browning and Patrick Lutz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning and Patrick Lutz
-/
import field_theory.subfield
import linear_algebra.finite_dimensional
/-!
# Adjoining Elements to Fields
In this file we introd... |
e7b723bbdbe019ec970fb671faa63a3e7ae78e27 | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /tests/compiler/closure_bug7.lean | 7a7f5094d969c2886733e8e0188c126e37d0c5bc | [
"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 | 507 | lean | def f (x : Nat) : Nat × (Nat → String) :=
let x1 := x + 1;
let x2 := x + 2;
let x3 := x + 3;
let x4 := x + 4;
let x5 := x + 5;
let x6 := x + 6;
let x7 := x + 7;
let x8 := x + 8;
let x9 := x + 9;
let x10 := x + 10;
let x11 := x + 11;
let x12 := x + 12;
let x13 := x + 13;
let x14 := x + 14;
let x15 := x + 15;
let x16 := ... |
a6681bfddf2c795339e572de90211faa80dbd49d | 8e6cad62ec62c6c348e5faaa3c3f2079012bdd69 | /src/data/polynomial/coeff.lean | eba1ebf262cc54431705e076f0db43fda7a91324 | [
"Apache-2.0"
] | permissive | benjamindavidson/mathlib | 8cc81c865aa8e7cf4462245f58d35ae9a56b150d | fad44b9f670670d87c8e25ff9cdf63af87ad731e | refs/heads/master | 1,679,545,578,362 | 1,615,343,014,000 | 1,615,343,014,000 | 312,926,983 | 0 | 0 | Apache-2.0 | 1,615,360,301,000 | 1,605,399,418,000 | Lean | UTF-8 | Lean | false | false | 7,485 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Scott Morrison, Jens Wagemaker
-/
import data.polynomial.monomial
import data.finset.nat_antidiagonal
/-!
# Theory of univariate polynomials
The theorems ... |
ad3930f72b58a6d2b9fdefe7a44289814ad54c9d | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /stage0/src/Init/Lean/HeadIndex.lean | 173acb64a4da36afe541b96b4a2c0b595b4b7e42 | [
"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 | 2,480 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
prelude
import Init.Lean.Expr
namespace Lean
inductive HeadIndex
| fvar (fvarId : FVarId)
| mvar (mvarId : MVarId)
| const (constName : Name)
| proj (struc... |
2d66071bfd2ff873f3dd687611a4f8bc2fbd445e | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/computability/DFA.lean | 2bf2fadcda8a24994dd3a450250f1e458cf1a690 | [
"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 | 5,400 | lean | /-
Copyright (c) 2020 Fox Thomson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fox Thomson
-/
import data.fintype.card
import computability.language
import tactic.norm_num
/-!
# Deterministic Finite Automata
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any change... |
ec913f4fd2172a9fff97e836d11d49ec3e16771d | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/meta/expr.lean | 8ba38711156347843fc210a250599f5e22c26773 | [
"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 | 46,689 | lean | /-
Copyright (c) 2019 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Simon Hudon, Scott Morrison, Keeley Hoek, Robert Y. Lewis, Floris van Doorn
-/
import data.string.defs
import tactic.derive_inhabited
/-!
# Additional operations on ex... |
606f9d4f7ade2e0cc03fa0286c330b294a0559a7 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/typeIncorrectPat.lean | d5cd7cdba57fe66dc1293d85322d068fa7b646e2 | [
"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 | 66 | lean | def f : (α : Type) × α → Nat
| ⟨_, true⟩ => 1
| _ => 2
|
75f4ea6aa088e4318a45bf2e227f1ee2114821a4 | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/measure_theory/lebesgue_measure.lean | 0e0ec94e5f19d725a3429c441767850fbe59cdbf | [
"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 | 11,654 | 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 measure_theory.measure_space
import measure_theory.borel_space
/-!
# Lebesgue measure on the real line
-/
noncomputable theory
open classical set filter
open... |
aaee517ef40186c529b0c44860c61b87e3d9ce0d | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /src/Init/Control/Id.lean | 66c07db51368fffd8bb2b3c4b20132766420f35b | [
"Apache-2.0"
] | permissive | WojciechKarpiel/lean4 | 7f89706b8e3c1f942b83a2c91a3a00b05da0e65b | f6e1314fa08293dea66a329e05b6c196a0189163 | refs/heads/master | 1,686,633,402,214 | 1,625,821,189,000 | 1,625,821,258,000 | 384,640,886 | 0 | 0 | Apache-2.0 | 1,625,903,617,000 | 1,625,903,026,000 | null | UTF-8 | Lean | false | false | 487 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Ullrich
The identity Monad.
-/
prelude
import Init.Core
universe u
def Id (type : Type u) : Type u := type
namespace Id
instance : Monad Id where
pure x := x
... |
ac9190e7b6775df9fc1ef5a2e66916c3f17d58d9 | 351a46035517d2a1985619b8cabdf263754d343a | /src/ch9.lean | 1ab4408634cb3637f230e94bc51196145d17ddb7 | [] | no_license | kaychaks/logic_proof | accc212517b613caca92c10db77e6aaf6b7ccfbc | 90f3bf0acbabf558ba2f82dee968255d8bfe2de1 | refs/heads/master | 1,587,001,734,509 | 1,548,235,051,000 | 1,548,235,051,000 | 165,186,786 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,278 | lean | section
variable A : Type
variable f : A → A
variable P : A → Prop
variable h : ∀ x, P x → P (f x)
-- Show the following:
example : ∀ y, P y → P (f (f y)) :=
assume x,
assume h1: P x,
have h2 : P x → P (f x), from h x,
have h3: P (f x), from h2 h1,
have h4 : P (f x) → P (f (f x)), from h (f x),
... |
cc1136adbc970a3dec3216f96c89a05e618984d3 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/run/ind3.lean | be676f4d253d716243d2e99a807572caf0136fff | [
"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 | 437 | lean | exit
inductive tree (A : Type) : Type :=
| node : A → forest A → tree A
with forest : Type :=
| nil : forest A
| cons : tree A → forest A → forest A
check tree.{1}
check forest.{1}
check tree.rec.{1 1}
check forest.rec.{1 1}
print "==============="
inductive group : Type :=
mk_group : Π (carrier : Type) (mul : car... |
046824362a632d171ed45b6c545b342d3e6c0d47 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/data/mv_polynomial/basic.lean | dcaa2de11d7315d3093da886733579948bd94641 | [
"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 | 38,797 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
-/
import data.polynomial.eval
import data.finsupp.antidiagonal
import algebra.algebra.tower
/-!
# Multivariate polynomials
This file ... |
b09ff2d9b71518835ecc8d608800c5738cd2c48a | ebb7367fa8ab324601b5abf705720fd4cc0e8598 | /homotopy/smash.hlean | a8a26ebcc84ea0dbde8f545431f3ee44018011a1 | [
"Apache-2.0"
] | permissive | radams78/Spectral | 3e34916d9bbd0939ee6a629e36744827ff27bfc2 | c8145341046cfa2b4960ef3cc5a1117d12c43f63 | refs/heads/master | 1,610,421,583,830 | 1,481,232,014,000 | 1,481,232,014,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,578 | hlean | -- Authors: Floris van Doorn
import homotopy.smash
open bool pointed eq equiv is_equiv sum bool prod unit circle cofiber prod.ops wedge
/- smash A (susp B) = susp (smash A B) <- this follows from associativity and smash with S¹-/
/- To prove: Σ(X × Y) ≃ ΣX ∨ ΣY ∨ Σ(X ∧ Y) (notation means suspension, wedge, smas... |
9bdcfd2203a69ea2cec25434d31fefb1e4185c74 | 8cb37a089cdb4af3af9d8bf1002b417e407a8e9e | /tests/lean/run/exhaustive_vm_impl_test.lean | eaaf5a6e901ff19afbf646b604ea6f6bfca15fff | [
"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 | 5,227 | lean | instance my_pow : has_pow ℕ ℕ :=
⟨λ x n, nat.rec_on n 1 (λ _ ih, ih * x)⟩
instance nat.decidable_ball (p : ℕ → Prop) [∀ i, decidable (p i)] : ∀ n, decidable (∀ x < n, p x)
| 0 := decidable.is_true begin intros n h, cases h end
| (n+1) :=
match nat.decidable_ball n with
| (decidable.is_false h) :=
decid... |
5ae45c88cfe1656dca58d8640348fd492665d3c3 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/full_subcategory.lean | e80c647354ae7242261360084acd4d2f9a87d885 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 6,761 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Reid Barton
-/
import category_theory.functor.fully_faithful
/-!
# Induced categories and full subcategories
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes ... |
c47d7c3411df6f699c803fb42c943b4fae355406 | d436468d80b739ba7e06843c4d0d2070e43448e5 | /src/order/complete_lattice.lean | d21f3ab4d32815b9f5822c9d6ff115e84d5d1f64 | [
"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 | 34,357 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Theory of complete lattices.
-/
import order.bounded_lattice data.set.basic tactic.pi_instances
set_option old_structure_cmd true
open set
namespace lattice
universes... |
1f52b52e5284a7f8a19318436eb3829bdd910345 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/tactic1.lean | 8f3ed2fbed157dce0e2ce6300044e05c7aea8041 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 1,422 | lean | theorem ex1 (x : Nat) (y : { v // v > x }) (z : Nat) : Nat :=
by {
clear y x;
exact z
}
theorem ex2 (x : Nat) (y : { v // v > x }) (z : Nat) : Nat :=
by {
clear x y;
exact z
}
theorem ex3 (x y z : Nat) (h₁ : x = y) (h₂ : z = y) : x = z :=
by {
have : y = z := h₂.symm;
apply Eq.trans;
exact h₁;
assumpt... |
819c3f58deaf7a5a010599b6e36e09099947d05c | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /stage0/src/Init/Control/EState.lean | cf63b7f58f24224aabcd7c46b861f7a90414bf24 | [
"Apache-2.0"
] | permissive | collares/lean4 | 861a9269c4592bce49b71059e232ff0bfe4594cc | 52a4f535d853a2c7c7eea5fee8a4fa04c682c1ee | refs/heads/master | 1,691,419,031,324 | 1,618,678,138,000 | 1,618,678,138,000 | 358,989,750 | 0 | 0 | Apache-2.0 | 1,618,696,333,000 | 1,618,696,333,000 | null | UTF-8 | Lean | false | false | 1,993 | 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.Control.State
import Init.Control.Except
import Init.Data.ToString.Basic
universes u v
namespace EStateM
variable {ε σ α : Type u}
in... |
4e3cb392c85dda9c0ba73a065b5248fb08a6fb5a | b3fced0f3ff82d577384fe81653e47df68bb2fa1 | /src/data/vector2.lean | 604c7905805b1377952981734c83e2e03ad31a33 | [
"Apache-2.0"
] | permissive | ratmice/mathlib | 93b251ef5df08b6fd55074650ff47fdcc41a4c75 | 3a948a6a4cd5968d60e15ed914b1ad2f4423af8d | refs/heads/master | 1,599,240,104,318 | 1,572,981,183,000 | 1,572,981,183,000 | 219,830,178 | 0 | 0 | Apache-2.0 | 1,572,980,897,000 | 1,572,980,896,000 | null | UTF-8 | Lean | false | false | 10,304 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
Additional theorems about the `vector` type.
-/
import data.vector data.list.basic category.traversable.basic data.set.basic tactic.tauto
universes u
variables {n : ℕ}... |
c43dc32b9088b7584d4fbcaaa4f93ef788f850e4 | ea5678cc400c34ff95b661fa26d15024e27ea8cd | /tactic_scratch.lean | 4bc6b4d10deaf5ee5d040a3c460b827514b2df64 | [] | 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 | 158 | lean | import tactic.interactive
namespace tactic.interactive
meta def get_nat (x : expr) : tactic unit :=
begin
end
end tactic.interactive
lemma (n : ℕ) : |
83cf3caade90155569339e829733ca4978b52cba | 43390109ab88557e6090f3245c47479c123ee500 | /src/M1F/problem_bank/0305/Q0305.lean | 3c07c6c4fe9f7d4fefbff9bb6c4e514d6650f7d9 | [
"Apache-2.0"
] | permissive | Ja1941/xena-UROP-2018 | 41f0956519f94d56b8bf6834a8d39473f4923200 | b111fb87f343cf79eca3b886f99ee15c1dd9884b | refs/heads/master | 1,662,355,955,139 | 1,590,577,325,000 | 1,590,577,325,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 223 | lean | import data.real.basic
variables x t : ℝ
theorem Q0305a (H:t>0) : abs x < t ↔ -t < x ∧ x < t := sorry
theorem Q0305b : abs(x+1)<3 ↔ -4<x ∧ x<2 := sorry
theorem Q0305c : abs (x-2) < abs (x-4) ↔ x < 3 := sorry
|
2907235ec5b2b851967337c525ef52384e401a97 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/topology/metric_space/basic.lean | 391f2292b1fe57b1c4427626c72077b24f4416fc | [
"Apache-2.0"
] | permissive | rmitta/mathlib | 8d90aee30b4db2b013e01f62c33f297d7e64a43d | 883d974b608845bad30ae19e27e33c285200bf84 | refs/heads/master | 1,585,776,832,544 | 1,576,874,096,000 | 1,576,874,096,000 | 153,663,165 | 0 | 2 | Apache-2.0 | 1,544,806,490,000 | 1,539,884,365,000 | Lean | UTF-8 | Lean | false | false | 66,867 | lean | /-
Copyright (c) 2015, 2017 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Metric spaces.
Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
Many definitions and theorems expected on metric spaces are already introduced o... |
51226fd552d10414891ee6dde49e86ca636bfa31 | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/data/int/parity.lean | 60fa977018f717a88a39b9c4535055f8174c6df3 | [
"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 | 6,975 | lean | /-
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Benjamin Davidson
-/
import data.nat.parity
/-!
# Parity of integers
This file contains theorems about the `even` and `odd` predicates on the integers.
## Tags
even, ... |
68acbad3669b18bf51e7923b04bebd91ab05d293 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/ring_theory/nullstellensatz_auto.lean | 06fd9dd741a067ed635e262badd5078f79343e73 | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,827 | lean | /-
Copyright (c) 2021 Devon Tuma. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Devon Tuma
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.ring_theory.jacobson
import Mathlib.field_theory.algebraic_closure
import Mathlib.field_theory.mv_p... |
29fc7f22481c9cd2cce212d874cb8274c1cf6cbd | 4e3bf8e2b29061457a887ac8889e88fa5aa0e34c | /lean/love13_rational_and_real_numbers_exercise_solution.lean | 5d77176f3bda93046fe7a10f70402f73c7212b09 | [] | 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 | 5,532 | lean | /- LoVe Exercise 13: Rational and Real Numbers -/
import .love05_inductive_predicates_demo
import .love13_rational_and_real_numbers_demo
namespace LoVe
set_option pp.beta true
/- Question 1: Rationals -/
/- 1.1. Prove the following lemma.
Hint: The lemma `fraction.mk.inj_eq` might be useful. -/
#check fraction.... |
1e7d9f4326f3867696f5c220d207950a8ef864dd | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/eagerCoeExpansion.lean | 9c72617c5f6697fd2a2b6198b98e920eb6a89989 | [
"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 | 838 | lean | def BV (n : Nat) := { b : Array Bool // b.size = n }
instance : Coe (BV 32) (Array Bool) where
coe bv := bv.val
def f (x : BV n) := x
def g (x : Array Bool) := x
def h (x : BV 32) : Array Bool :=
(fun x => g (f x)) x
#print h
def r (a : Nat) : Prop :=
if a == 0 then (a != 1 : Prop) else a != 2
#print r
se... |
ab68c68dd7bbd41a88f8aa8b92e613a3d92b3618 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/ring_theory/perfection.lean | c7aa8365a1c90380938d2c04a7f974424615f5d2 | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 25,405 | 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.pi
import algebra.char_p.quotient
import algebra.char_p.subring
import algebra.ring.pi
import analysis.special_functions.pow
import field_theory.perfect_... |
1ff809460b0c03155d86584ae7b7e7c3b09f2596 | ebf7140a9ea507409ff4c994124fa36e79b4ae35 | /src/exercises_sources/thursday/category_theory/exercise9.lean | 33c9fbba17eadb84c816a19d36ddee4a35ac1a15 | [] | no_license | fundou/lftcm2020 | 3e88d58a92755ea5dd49f19c36239c35286ecf5e | 99d11bf3bcd71ffeaef0250caa08ecc46e69b55b | refs/heads/master | 1,685,610,799,304 | 1,624,070,416,000 | 1,624,070,416,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,723 | lean | import category_theory.limits.shapes.biproducts
/-!
Let's show that every preadditive category embeds into a preadditive category with biproducts,
and identify a good universal property.
This is a more advanced exercise, for which I've indicated a suggested structure,
but not written a full solution. I hope this stru... |
c2fc8899a387096259a54b63d13134d0621ea9dd | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/algebra/quandle.lean | 75534effef233c6cdc2915372c167ade1578fe3f | [
"Apache-2.0"
] | permissive | ramonfmir/mathlib | c5dc8b33155473fab97c38bd3aa6723dc289beaa | 14c52e990c17f5a00c0cc9e09847af16fabbed25 | refs/heads/master | 1,661,979,343,526 | 1,660,830,384,000 | 1,660,830,384,000 | 182,072,989 | 0 | 0 | null | 1,555,585,876,000 | 1,555,585,876,000 | null | UTF-8 | Lean | false | false | 24,689 | lean | /-
Copyright (c) 2020 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
import algebra.hom.equiv
import data.zmod.basic
import tactic.group
/-!
# Racks and Quandles
This file defines racks and quandles, algebraic structures for sets
that bije... |
84926f4994ac14825c3882bc149962f2e6f99e9c | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/number_theory/legendre_symbol/add_character.lean | 47de7d6d7729b597ee13dfb36a133adeb06480ba | [
"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 | 16,388 | lean | /-
Copyright (c) 2022 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
import number_theory.cyclotomic.primitive_roots
import field_theory.finite.trace
/-!
# Additive characters of finite rings and fields
> THIS FILE IS SYNCHRONIZED WITH... |
1d564ad8470ea1cf770827654ebe4503824e1947 | 592ee40978ac7604005a4e0d35bbc4b467389241 | /Library/generated/mathscheme-lean/LeftPreSemiring.lean | fe4525bfeb25ed7e8393e1b413b12a82fd6ff1d4 | [] | 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 | 9,677 | 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 LeftPreSemiring
structure LeftPreSemiring (A : Type) : Type :=
(times : (A → (A → A)))
(plus : (A → (A → A)))
(associative_times : (∀ {x y z : A} , (time... |
5a8e39a6e187bda7e33783ebf34e1170139a65ce | 8c02fed42525b65813b55c064afe2484758d6d09 | /src/verifyopt.lean | 1b38d33c15f591987e634fb0771fd43c1d371fb2 | [
"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 | 2,126 | lean | -- Copyright (c) Microsoft Corporation. All rights reserved.
-- Licensed under the MIT license.
import .ops
import .lang
import .irsem
namespace opt
section
open irsem
parameter (sem : irsem)
-- uint_like types
variable [ihc:has_comp sem.intty sem.boolty]
variable [ioc:has_overflow_check sem.intty sem.boolty]
vari... |
ed4ad5ce14eb055bcdf958d2e8916384b67062ad | ce6917c5bacabee346655160b74a307b4a5ab620 | /src/ch2/ex0204.lean | dc36b2a0b6b115ba2e84af4da4c8a97c27d8d211 | [] | no_license | Ailrun/Theorem_Proving_in_Lean | ae6a23f3c54d62d401314d6a771e8ff8b4132db2 | 2eb1b5caf93c6a5a555c79e9097cf2ba5a66cf68 | refs/heads/master | 1,609,838,270,467 | 1,586,846,743,000 | 1,586,846,743,000 | 240,967,761 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 52 | lean | constant α : Type
#check list α
#check list nat
|
e23d9af1548c03b5ad4bff2f4b58ca13218e3f75 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /tests/lean/run/def12.lean | 77db02a015e1e9237f561e1b85ebf73042e0ed72 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | cipher1024/lean4 | 6e1f98bb58e7a92b28f5364eb38a14c8d0aae393 | 69114d3b50806264ef35b57394391c3e738a9822 | refs/heads/master | 1,642,227,983,603 | 1,642,011,696,000 | 1,642,011,696,000 | 228,607,691 | 0 | 0 | Apache-2.0 | 1,576,584,269,000 | 1,576,584,268,000 | null | UTF-8 | Lean | false | false | 1,085 | lean | def diag : Bool → Bool → Bool → Nat
| b, true, false => 1
| false, b, true => 2
| true, false, b => 3
| b1, b2, b3 => arbitrary
theorem diag1 (a : Bool) : diag a true false = 1 :=
match a with
| true => rfl
| false => rfl
theorem diag2 (a : Bool) : diag false a true = 2 :=
by cases a; exact rfl; exact rfl
theore... |
b33eb7578412540d4c8835ea86d4927b75811646 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/topology/metric_space/gromov_hausdorff.lean | 787a8b1f5a34616fd22b07cb21cdd4a8cf74d512 | [
"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 | 55,239 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import topology.metric_space.closeds
import set_theory.cardinal
import topology.metric_space.gromov_hausdorff_realized
import topology.metric_space.completion
i... |
7901cbb535cd3414aba7a92a5c2ca11d0add511a | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/category/pairwise.lean | 3d2f139246b46cb8763efc17c4cb30c92e702425 | [] | 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 | 4,206 | 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.category_theory.limits.preserves.basic
import Mathlib.category_theory.limits.lattice
import... |
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