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d186c114209bd4539ff62454e81db7e58d264921 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/model_theory/definability.lean | a4ddd753f5059ff31cf39c74710052cf02051346 | [
"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 | 11,343 | lean | /-
Copyright (c) 2021 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import data.set_like.basic
import logic.equiv.fintype
import model_theory.semantics
/-!
# Definable Sets
This file defines what it means for a set over a first-order... |
0d01d7340c4e3d4a05e2cc406aed8873b49656a7 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/logic/embedding.lean | 4f5152b78e9dc65f8186c78acae39f1ff0cfddb8 | [
"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 | 12,437 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import data.equiv.basic
import data.sigma.basic
import algebra.group.defs
/-!
# Injective functions
-/
universes u v w x
namespace function
/-- `α... |
d29be2f02f9df56d3bdcbd24aede502479185031 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/yoneda_auto.lean | 9af10316410da2c9c5cd83d4c1993398fef80431 | [] | 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 | 11,074 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.category_theory.hom_functor
import Mathlib.PostPort
universes u₁ v₁ l
namespace Mathlib
... |
29ec21e63980b0c5d93830cf188a224d79827faa | 9b9a16fa2cb737daee6b2785474678b6fa91d6d4 | /src/data/fintype.lean | e2cf15056cfd6ef2a52a151ceb3a7b234aa1304a | [
"Apache-2.0"
] | permissive | johoelzl/mathlib | 253f46daa30b644d011e8e119025b01ad69735c4 | 592e3c7a2dfbd5826919b4605559d35d4d75938f | refs/heads/master | 1,625,657,216,488 | 1,551,374,946,000 | 1,551,374,946,000 | 98,915,829 | 0 | 0 | Apache-2.0 | 1,522,917,267,000 | 1,501,524,499,000 | Lean | UTF-8 | Lean | false | false | 30,038 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
Finite types.
-/
import data.finset algebra.big_operators data.array.lemmas data.vector2 data.equiv.encodable
universes u v
variables {α : Type*} {β : Type*} {γ : Type*... |
c84a9ab401e03346aa0ec3e028bca9d045d6f380 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/category_theory/monad/kleisli.lean | 68026128c069da73ec9aad2c82791867e58cfd4a | [
"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 | 3,095 | lean | /-
Copyright (c) 2020 Wojciech Nawrocki. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wojciech Nawrocki, Bhavik Mehta
-/
import category_theory.adjunction
import category_theory.monad.adjunction
import category_theory.monad.basic
/-! # Kleisli category on a monad
... |
73293d0514d8f2512a5bffb102d200ba46bd7891 | aa101d73b1a3173c7ec56de02b96baa8ca64c42e | /src/my_exercises/05_sequence_limits.lean | f99a639199c853396bd8434d0aef74b6a7016afa | [
"Apache-2.0"
] | permissive | gihanmarasingha/tutorials | b554d4d53866c493c4341dc13e914b01444e95a6 | 56617114ef0f9f7b808476faffd11e22e4380918 | refs/heads/master | 1,671,141,758,153 | 1,599,173,318,000 | 1,599,173,318,000 | 282,405,870 | 0 | 0 | Apache-2.0 | 1,595,666,751,000 | 1,595,666,750,000 | null | UTF-8 | Lean | false | false | 9,576 | lean | import data.real.basic
import algebra.pi_instances
import tuto_lib
notation `|`x`|` := abs x
/-
In this file we manipulate the elementary definition of limits of
sequences of real numbers.
mathlib has a much more general definition of limits, but here
we want to practice using the logical operators and relations
cov... |
542b82753b040758300f770a73eef3ce9917afa1 | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /src/Lean/Parser/Module.lean | 4f5c7d2ed17faebf9241f49a0e64d0fa9b423a1e | [
"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 | 5,889 | 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.Message
import Lean.Parser.Command
namespace Lean
namespace Parser
namespace Module
def «prelude» := leading_parser "prelu... |
4c5a978c1abcd50ebbe0fee569cafada9941ebc8 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/topology/algebra/affine_auto.lean | 7df18793ab9696cca4036d54720c1931aa94400c | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,531 | lean | /-
Copyright (c) 2020 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.topology.algebra.continuous_functions
import Mathlib.linear_algebra.affine_space.affine_m... |
7c83c978fb72b89f3c9ac95da177e0666fac712e | bdb33f8b7ea65f7705fc342a178508e2722eb851 | /order/basic.lean | 3bf3a0845345ac8f220e74f7915dfec1822ad0b7 | [
"Apache-2.0"
] | permissive | rwbarton/mathlib | 939ae09bf8d6eb1331fc2f7e067d39567e10e33d | c13c5ea701bb1eec057e0a242d9f480a079105e9 | refs/heads/master | 1,584,015,335,862 | 1,524,142,167,000 | 1,524,142,167,000 | 130,614,171 | 0 | 0 | Apache-2.0 | 1,548,902,667,000 | 1,524,437,371,000 | Lean | UTF-8 | Lean | false | false | 12,733 | 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 tactic.interactive logic.basic data.sigma data.sum data.set.basic algebra.order
open function
/- TODO: automatic construction of dual definition... |
5f94e1dd327d5d1d33574e345bfcb45859ff191b | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/tactic/generalizes.lean | 08ef1a66ed67d4e551ed3f8ea3168716a0b31323 | [
"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 | 8,915 | lean | /-
Copyright (c) 2020 Jannis Limperg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jannis Limperg
-/
import tactic.core
/-!
# The `generalizes` tactic
This module defines the `tactic.generalizes'` tactic and its interactive version
`tactic.interactive.generalizes`... |
7baa3dd1d8a1259b8503141238a0e9ec339df97c | 31f556cdeb9239ffc2fad8f905e33987ff4feab9 | /stage0/src/Lean/Compiler/LCNF/InferType.lean | dab9e840284694fe17dca193009fc83c12602911 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | tobiasgrosser/lean4 | ce0fd9cca0feba1100656679bf41f0bffdbabb71 | ebdbdc10436a4d9d6b66acf78aae7a23f5bd073f | refs/heads/master | 1,673,103,412,948 | 1,664,930,501,000 | 1,664,930,501,000 | 186,870,185 | 0 | 0 | Apache-2.0 | 1,665,129,237,000 | 1,557,939,901,000 | Lean | UTF-8 | Lean | false | false | 16,498 | lean | /-
Copyright (c) 2022 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Compiler.LCNF.CompilerM
import Lean.Compiler.LCNF.Types
import Lean.Compiler.LCNF.PhaseExt
namespace Lean.Compiler.LCNF
/-! # Type inference fo... |
c56ca5ba2efa6a4bf624132780ae32e95b87d7c1 | 4b846d8dabdc64e7ea03552bad8f7fa74763fc67 | /tests/lean/run/meta2.lean | 632f0d06c03cfdf0215d06aea750f1a689e920fe | [
"Apache-2.0"
] | permissive | pacchiano/lean | 9324b33f3ac3b5c5647285160f9f6ea8d0d767dc | fdadada3a970377a6df8afcd629a6f2eab6e84e8 | refs/heads/master | 1,611,357,380,399 | 1,489,870,101,000 | 1,489,870,101,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 214 | lean | import system.io
open io
meta definition foo : nat → nat
| a := nat.cases_on a 1 (λ n, foo n + 2)
#eval (foo 10)
meta definition loop : nat → io unit
| a := do put_str ">> ", put a, put_str "\n", loop (a+1)
|
85089407b60b9ed7c28c2b93ec5c19eca93c74c5 | e00ea76a720126cf9f6d732ad6216b5b824d20a7 | /src/computability/primrec.lean | 1b923b46afd1c6a9f990151213611cb534fd4dae | [
"Apache-2.0"
] | permissive | vaibhavkarve/mathlib | a574aaf68c0a431a47fa82ce0637f0f769826bfe | 17f8340912468f49bdc30acdb9a9fa02eeb0473a | refs/heads/master | 1,621,263,802,637 | 1,585,399,588,000 | 1,585,399,588,000 | 250,833,447 | 0 | 0 | Apache-2.0 | 1,585,410,341,000 | 1,585,410,341,000 | null | UTF-8 | Lean | false | false | 50,166 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
The primitive recursive functions are the least collection of functions
nat → nat which are closed under projections (using the mkpair
pairing function), composition, ze... |
acd46e93a040cafcf1e07bcfd68729222f801f60 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/algebra/order/archimedean.lean | 3f4b5d4df0fadfe832f750ad0fe07cd858a6344d | [
"Apache-2.0"
] | permissive | urkud/mathlib | eab80095e1b9f1513bfb7f25b4fa82fa4fd02989 | 6379d39e6b5b279df9715f8011369a301b634e41 | refs/heads/master | 1,658,425,342,662 | 1,658,078,703,000 | 1,658,078,703,000 | 186,910,338 | 0 | 0 | Apache-2.0 | 1,568,512,083,000 | 1,557,958,709,000 | Lean | UTF-8 | Lean | false | false | 13,651 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import algebra.field_power
import data.int.least_greatest
import data.rat.floor
/-!
# Archimedean groups and fields.
This file defines the archimedean property for ... |
1bce0c36afcea161d87a947d8beffda127b3790b | f4bff2062c030df03d65e8b69c88f79b63a359d8 | /src/game/order/level05.lean | 078e9e491909cb02b1ad0989535a5dd4537372f0 | [
"Apache-2.0"
] | permissive | adastra7470/real-number-game | 776606961f52db0eb824555ed2f8e16f92216ea3 | f9dcb7d9255a79b57e62038228a23346c2dc301b | refs/heads/master | 1,669,221,575,893 | 1,594,669,800,000 | 1,594,669,800,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,244 | lean | import game.order.level04
namespace xena -- hide
/-
# Chapter 2 : Order
## Level 5
Another well-known property of the absolute value.
-/
notation `|` x `|` := abs x -- hide
/- Lemma
For any two real numbers $a$ and $b$, we have that
$$| |a| - |b| | ≤ |a - b|$$.
-/
theorem abs_of_sub_le_abs (a b : ℝ) : | |a| - |b|... |
30bc170ae77c93aae88b7c5392e71540ac48c0ec | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/polynomial/degree/trailing_degree.lean | 3974f895e9ba4bbb5cfadd86862e603ce02d58ae | [
"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 | 16,032 | lean | /-
Copyright (c) 2020 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
import data.enat.basic
import data.polynomial.degree.definitions
/-!
# Trailing degree of univariate polynomials
## Main definitions
* `trailing_degree p`: the multi... |
8a8d60e2ad5132baf5e22ae979ceb464663e777f | ec5e5a9dbe7f60fa5784d15211d8bf24ada0825c | /src/Value.lean | 94966315c47dd258be35302f0bb0c3543fe9dfd3 | [] | no_license | pnwamk/lean-llvm | fcd9a828e52e80eb197f7d9032b3846f2e09ef74 | ebc3bca9a57a6aef29529d46394f560398fb5c9c | refs/heads/master | 1,668,418,078,706 | 1,593,548,643,000 | 1,593,548,643,000 | 258,617,753 | 0 | 0 | null | 1,587,760,298,000 | 1,587,760,298,000 | null | UTF-8 | Lean | false | false | 877 | lean | import Init.Data.RBMap
import Galois.Data.Bitvec
import LeanLLVM.AST
import LeanLLVM.PP
import LeanLLVM.TypeContext
namespace LLVM
namespace Sim
inductive Value : Type
| bv {w : Nat} (x:bitvec w)
| vec (eltTp:mem_type) (x:Array Value)
| array (eltTp:mem_type) (values:Array Value)
| struct (fields:Array (fieldInfo ... |
d1004f449e7480e0ac270374292a8100a6db19f6 | 626e312b5c1cb2d88fca108f5933076012633192 | /src/data/set/lattice.lean | d13a1a684e7e09ce773a5ff06130fd20107dcd4b | [
"Apache-2.0"
] | permissive | Bioye97/mathlib | 9db2f9ee54418d29dd06996279ba9dc874fd6beb | 782a20a27ee83b523f801ff34efb1a9557085019 | refs/heads/master | 1,690,305,956,488 | 1,631,067,774,000 | 1,631,067,774,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 60,449 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Johannes Hölzl, Mario Carneiro
-/
import data.nat.basic
import order.complete_boolean_algebra
import order.directed
import order.galois_connection
/-!... |
6e19dccbff2c122061e2833da5c58b66abf82aa3 | 07c76fbd96ea1786cc6392fa834be62643cea420 | /hott/types/unit.hlean | a0b6025561608f526beccc9c4c43a58291899f9f | [
"Apache-2.0"
] | permissive | fpvandoorn/lean2 | 5a430a153b570bf70dc8526d06f18fc000a60ad9 | 0889cf65b7b3cebfb8831b8731d89c2453dd1e9f | refs/heads/master | 1,592,036,508,364 | 1,545,093,958,000 | 1,545,093,958,000 | 75,436,854 | 0 | 0 | null | 1,480,718,780,000 | 1,480,718,780,000 | null | UTF-8 | Lean | false | false | 1,454 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
Theorems about the unit type
-/
open is_equiv equiv option eq pointed is_trunc function
namespace unit
protected definition eta : Π(u : unit), ⋆ = u
| eta ⋆ ... |
78c414ff055c907646d656bbbc73eefb78b987f9 | 77c5b91fae1b966ddd1db969ba37b6f0e4901e88 | /src/algebraic_geometry/sheafed_space.lean | baa7e5101bce00e8fba7dcc4abf1f78f356d4171 | [
"Apache-2.0"
] | permissive | dexmagic/mathlib | ff48eefc56e2412429b31d4fddd41a976eb287ce | 7a5d15a955a92a90e1d398b2281916b9c41270b2 | refs/heads/master | 1,693,481,322,046 | 1,633,360,193,000 | 1,633,360,193,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,990 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import algebraic_geometry.presheafed_space
import topology.sheaves.sheaf
/-!
# Sheafed spaces
Introduces the category of topological spaces equipped with a sheaf (t... |
c1d1841cbb923e955fd0a1e08def7511d353dab5 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/topology/metric_space/cau_seq_filter.lean | 0fc2cd93982c0d39b0b72494c12964e16047ac54 | [
"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 | 3,773 | lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Sébastien Gouëzel
-/
import analysis.normed_space.basic
/-!
# Completeness in terms of `cauchy` filters vs `is_cau_seq` sequences
In this file we apply `metric.comp... |
f31027d1ad141a6e075d7f9385acb3360707a24f | e0f9ba56b7fedc16ef8697f6caeef5898b435143 | /src/data/rat/meta_defs.lean | 024a579ac25a439454023f27aff71af3f7cf8719 | [
"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 | 5,067 | lean | /-
Copyright (c) 2019 Robert Y. Lewis . All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Robert Y. Lewis
-/
import data.rat.basic tactic.core
/-!
# Meta operations on ℚ
This file defines functions for dealing with rational numbers as expressions.
They are not defined e... |
576a395397819c4e6dd7782159bdb2a3f34d488a | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/match_convoy2.lean | e18bbf0716ee83001794e818a3be9bfe38862410 | [
"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 | 296 | lean | inductive vec (A : Type) : nat → Type
| nil {} : vec nat.zero
| cons : ∀ {n}, A → vec n → vec (nat.succ n)
open vec
definition boo (n : nat) (v : vec bool n) : vec bool n :=
match n, v : ∀ (n : _), vec bool n → _ with
| 0, nil := nil
| n+1, cons a v := cons (bnot a) v
end
|
694b5e6e8b30851cafe0ad4b0437d47831d5b2c8 | ea5678cc400c34ff95b661fa26d15024e27ea8cd | /univariate_poly.lean | dabc5ff98f29d48e367d2172dc84abd7cd646208 | [] | 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 | 31,857 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
Theory of univariate polynomials, represented as finsupps, ℕ →₀ α, with α a comm_semiring
mono
-/
import linear_algebra.multivariate_polynomial algebra.euclidean_domain
... |
24e72c27e596d03b3f40b21b869ddccafd62bf43 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/topology/instances/real.lean | 28d5af70a62b1b6a75bab0c24c04c3643d67008a | [
"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 | 12,741 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import topology.metric_space.basic
import topology.algebra.uniform_group
import topology.algebra.uniform_mul_action
import topology.algebra.ring
impor... |
1e8315952575f7a24e31a13cfeba98597364d478 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/category_theory/enriched/basic.lean | 1627a7ae4dd6a7e31934058415c35b1820e6f2f9 | [
"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 | 17,192 | lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.monoidal.types
import category_theory.monoidal.center
/-!
# Enriched categories
We set up the basic theory of `V`-enriched categories,
for `V... |
c1bb5447530f69260cadc2687479fe15ae88dcbf | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/elabissues/equation_compiler_slow_with_many_constructors2.lean | 85ac9a50e58a69dd023ec05fb3665c350f55efa1 | [
"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 | 5,526 | lean | /-
Same setup as in 'equation_compiler_slow_with_many_constructors.lean',
except here we have a function `infer` that takes a single `Proof` object
and that matches on all constructors, each applied only to variables.
Despite the favorable matching regime, the function `infer` still takes ~200ms
to elaborate.
-/
namesp... |
d27e46806f32987c712f603ebadf092ab4de9e8e | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/topology/metric_space/contracting.lean | 6fbe5362f36ad510256ff304cf70c5661433c63f | [] | 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 | 15,671 | lean | /-
Copyright (c) 2019 Rohan Mitta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rohan Mitta, Kevin Buzzard, Alistair Tucker, Johannes Hölzl, Yury Kudryashov
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.analysis.specific_limits
import ... |
6a44cf2b322fe9749bf4ba54083077b6dd6c2b7b | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /stage0/src/Lean/Meta/Tactic/Assumption.lean | d2d47fe85b57e39c74a82fede71094ad7963139a | [
"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 | 773 | 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.Meta.ExprDefEq
import Lean.Meta.Tactic.Util
namespace Lean
namespace Meta
def assumptionAux (mvarId : MVarId) : MetaM Bool :=
withMVarContext ... |
3f90c8fbf6fd76ad7be92794ae367a79481a1dd5 | cf39355caa609c0f33405126beee2739aa3cb77e | /library/init/meta/ac_tactics.lean | 57a4125e7cb6ab535ce02fa9d46fd5f145fa3f5a | [
"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 | 496 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.meta.tactic
namespace tactic
/- (flat_assoc op assoc e) -/
meta constant flat_assoc : expr → expr → expr → tactic (expr × expr)
/- (per... |
529b72809d1ff11c62337693c3336615fd56ceba | c777c32c8e484e195053731103c5e52af26a25d1 | /src/ring_theory/bezout.lean | f2e588af810d156d69357d2e469bd20794d9ef49 | [
"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 | 4,751 | lean | /-
Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import ring_theory.principal_ideal_domain
import algebra.gcd_monoid.integrally_closed
/-!
# Bézout rings
A Bézout ring (Bezout ring) is a ring whose finitely generated ... |
ee3e1c0d5f7d13ccc2fe049a5aeccd046073a16c | 4727251e0cd73359b15b664c3170e5d754078599 | /src/category_theory/monoidal/center.lean | 4ffea5d7850a467a2d69e10183b1c87b72eb433e | [
"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 | 12,239 | lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.monoidal.braided
import category_theory.functor.reflects_isomorphisms
import category_theory.monoidal.coherence
/-!
# Half braidings and the D... |
baf4cbbaad97f9bf49e51fb70a1155c1f877c375 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/topology/shrinking_lemma.lean | 643cc7b5529c949ec2f30a5c213b7a71455d51ea | [
"Apache-2.0"
] | permissive | AntoineChambert-Loir/mathlib | 64aabb896129885f12296a799818061bc90da1ff | 07be904260ab6e36a5769680b6012f03a4727134 | refs/heads/master | 1,693,187,631,771 | 1,636,719,886,000 | 1,636,719,886,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 12,218 | lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Reid Barton
-/
import topology.separation
/-!
# The shrinking lemma
In this file we prove a few versions of the shrinking lemma. The lemma says that in a normal
top... |
1a729aa93ceb22a0d2da16ce6171215c141095d7 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/geometry/euclidean/angle/unoriented/affine.lean | f8e2e5b94f9ace3fa23abae04cc44a5458b9cbfc | [
"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 | 17,851 | lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers, Manuel Candales
-/
import analysis.convex.between
import geometry.euclidean.angle.unoriented.basic
/-!
# Angles between points
This file defines unoriented angles in Eucl... |
6dbcc60271afadd18b67d8f3f17e572c19fcf3e2 | 07c76fbd96ea1786cc6392fa834be62643cea420 | /hott/types/nat/sub.hlean | 8e5f58944e443792e7898d8b9787281d5d56f643 | [
"Apache-2.0"
] | permissive | fpvandoorn/lean2 | 5a430a153b570bf70dc8526d06f18fc000a60ad9 | 0889cf65b7b3cebfb8831b8731d89c2453dd1e9f | refs/heads/master | 1,592,036,508,364 | 1,545,093,958,000 | 1,545,093,958,000 | 75,436,854 | 0 | 0 | null | 1,480,718,780,000 | 1,480,718,780,000 | null | UTF-8 | Lean | false | false | 19,639 | hlean | /-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Jeremy Avigad
Subtraction on the natural numbers, as well as min, max, and distance.
-/
import .order
open eq.ops algebra eq
namespace nat
/- subtraction -/
pro... |
2248613ea598112a55a81e159235b37e061c1025 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/linear_algebra/matrix/zpow.lean | 8e31e3d706ec62e1ff491c0892c929643393b0a7 | [
"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 | 12,444 | lean | /-
Copyright (c) 2021 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
import linear_algebra.matrix.nonsingular_inverse
/-!
# Integer powers of square matrices
In this file, we define integer power of matrices, relying on
the nonsing... |
0ba289c65a737f2254a9ffd369c3ee09a0c9ce86 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/topology/uniform_space/abstract_completion.lean | c419423a9b3db70ec3a01a748075530d4ed13ebb | [
"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 | 11,802 | lean | /-
Copyright (c) 2019 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import topology.uniform_space.uniform_embedding
import topology.uniform_space.equiv
/-!
# Abstract theory of Hausdorff completions of uniform spaces
> THIS FILE IS ... |
73da6a395e578d6b907c4e9a4e2596ca5268c0b2 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/category_theory/additive/basic.lean | c232f535f81d76c9e52fa29594c329f0158324b0 | [
"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 | 972 | lean | /-
Copyright (c) 2021 Luke Kershaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Luke Kershaw
-/
import category_theory.limits.shapes.biproducts
/-!
# Additive Categories
This file contains the definition of additive categories.
TODO: show that finite biproducts i... |
7d1a34c28b31f2614987f428cbe861d98f25f23a | 947b78d97130d56365ae2ec264df196ce769371a | /stage0/src/Lean/Parser/Transform.lean | 82e3073d5363dac737d4cd13c940ecacb2a35146 | [
"Apache-2.0"
] | permissive | shyamalschandra/lean4 | 27044812be8698f0c79147615b1d5090b9f4b037 | 6e7a883b21eaf62831e8111b251dc9b18f40e604 | refs/heads/master | 1,671,417,126,371 | 1,601,859,995,000 | 1,601,860,020,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,564 | 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.Parser.Basic
namespace Lean
namespace Syntax
def manyToSepBy (stx : Syntax) (sepTk : String) : Syntax :=
match stx with
| n... |
eaa428180b8304f81253ddbc61e41c341b8e980f | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/data/zmod/quotient.lean | 05b1df97102f4171d3489fd9d847a2d4e6fd7222 | [
"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 | 2,381 | 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 data.zmod.basic
import group_theory.quotient_group
import ring_theory.int.basic
/-!
# `zmod n` and quotient groups / rings
This file relates `zmod n` to the quotie... |
5030cc3814e5c76c738296579da891cc0f015a84 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/456.lean | 9bc679f12839fbadaffce73c127015be15dd44a7 | [
"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 | 36 | lean | def A : Sort u := { s : Prop // _ }
|
1d4f9ded41535dbb60418f981428ed079cfeca17 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Util/CollectFVars.lean | e0649539487895f89c176a1e754835e4ecf7e51b | [
"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 | 1,280 | 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.Expr
import Lean.LocalContext
namespace Lean.CollectFVars
structure State where
visitedExpr : ExprSet := {}
fvarSet : FVarIdSet :=... |
fe0f61d7cf7fac81bc8bffc10e7963327222e78f | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/algebra/algebra/subalgebra.lean | 6ea58b00192fad3b4263ff6b04896d844473297d | [
"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 | 40,162 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Yury Kudryashov
-/
import algebra.algebra.operations
import data.set.Union_lift
/-!
# Subalgebras over Commutative Semiring
In this file we define `subalgebra`s and the usual o... |
fb80941e2b713d0ed6b820d55364391006a7908d | 5c7fe6c4a9d4079b5457ffa5f061797d42a1cd65 | /src/exercises/src_00_introduction_to_formal_maths.lean | 7db76aae0029ac07c283af0fbf3484923a233dcd | [] | 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 | 5,657 | lean | import tactic.linarith
namespace mth1001
/-
The following is a Lean proof that `10 < 20`.
The line `example : 10 < 20` can be read as, 'Here is a proof of `10 < 20`.
The line `by norm_num` says, 'the result is proved using `norm_num`, a 'tactic'
that can prove many numerical equations and inequalities.
You know the... |
f5284502f8ae1bf6b61f64076ab3cdb95e8c1931 | 8d65764a9e5f0923a67fc435eb1a5a1d02fd80e3 | /src/order/omega_complete_partial_order.lean | b42c2def9d38a1a687ae0d11c87e7d43177ef3f8 | [
"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 | 30,199 | 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 data.pfun
import order.preorder_hom
import tactic.wlog
import tactic.monotonicity
/-!
# Omega Complete Partial Orders
An omega-complete partial order is a partial ... |
e1437021d217d3a79dc901f7743ac2295ee6d1dc | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/measure_theory/integral/set_integral.lean | 47b6f186ee8250ff7aca0e0fa0351bba85041492 | [
"Apache-2.0"
] | permissive | AntoineChambert-Loir/mathlib | 64aabb896129885f12296a799818061bc90da1ff | 07be904260ab6e36a5769680b6012f03a4727134 | refs/heads/master | 1,693,187,631,771 | 1,636,719,886,000 | 1,636,719,886,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 45,106 | lean | /-
Copyright (c) 2020 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Yury Kudryashov
-/
import measure_theory.integral.integrable_on
import measure_theory.integral.bochner
import order.filter.indicator_function
/-!
# Set integral
In this... |
936b3d1c3bc540a5f9d1143a7b044aefd4d7b8ce | d1a52c3f208fa42c41df8278c3d280f075eb020c | /tests/leanpkg/builtin_attr/UserAttr/BlaAttr.lean | 6fb03c4e86d608c389dd22756b604323a49e28a0 | [
"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 | 183 | lean | import Lean
open Lean
-- initialize discard <| registerTagAttribute `foo ""
initialize registerBuiltinAttribute {
name := `bar,
descr := "",
add := fun _ _ _ => ()
}
|
ae208e08b8707d077cd5b8da14c2d1304c7f44a8 | 80d0f8071ea62262937ab36f5887a61735adea09 | /src/certigrad/aevb/prog.lean | 6603a560b32e7d812435117f5a8678c774402a0e | [
"Apache-2.0"
] | permissive | wudcscheme/certigrad | 94805fa6a61f993c69a824429a103c9613a65a48 | c9a06e93f1ec58196d6d3b8563b29868d916727f | refs/heads/master | 1,679,386,475,077 | 1,551,651,022,000 | 1,551,651,022,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,359 | lean | /-
Copyright (c) 2017 Daniel Selsam. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Daniel Selsam
Certigrad code for a naive variational autoencoder.
-/
import ..program .util
namespace certigrad
namespace aevb
section program
open certigrad.program certigrad.program... |
edafae5a047241431fb8c1f3c95d5accdb9f3d3a | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/matrix/auto.lean | 0d75a92737462950dfdf3afeb28da83db677f03b | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 8,612 | lean | /-
Copyright (c) 2022 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import algebra.expr
import data.matrix.reflection
/-! # Automatically generated lemmas for working with concrete matrices
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any... |
af0260726afa5012f150cbce020384882a03b6ee | 6094e25ea0b7699e642463b48e51b2ead6ddc23f | /tests/lean/simplifier_light.lean | 703f8ea14f17f9b5d9083968552e045f1c026ada | [
"Apache-2.0"
] | permissive | gbaz/lean | a7835c4e3006fbbb079e8f8ffe18aacc45adebfb | a501c308be3acaa50a2c0610ce2e0d71becf8032 | refs/heads/master | 1,611,198,791,433 | 1,451,339,111,000 | 1,451,339,111,000 | 48,713,797 | 0 | 0 | null | 1,451,338,939,000 | 1,451,338,939,000 | null | UTF-8 | Lean | false | false | 1,670 | lean | -- Test [light] annotation
-- Remark: it will take some additional work to get ⁻¹ to rewrite well
-- when there is a proof obligation.
import algebra.ring algebra.field data.set data.finset
open algebra
attribute neg [light 3]
attribute inv [light 3]
attribute add.right_inv [simp]
attribute add_neg_cancel_left [simp]
... |
2b86f558e0b2e65eee0d77d94a922059ddf5d03c | 3dc4623269159d02a444fe898d33e8c7e7e9461b | /.github/workflows/project_1_a_decrire/topology/chapitre1.lean | 16f6daecfce565f6c0799cc0b4b057a09f3ff4c7 | [] | no_license | Or7ando/lean | cc003e6c41048eae7c34aa6bada51c9e9add9e66 | d41169cf4e416a0d42092fb6bdc14131cee9dd15 | refs/heads/master | 1,650,600,589,722 | 1,587,262,906,000 | 1,587,262,906,000 | 255,387,160 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 21 | lean | import topology.basic |
3fc585320cd81c1d0855c307270434e62acb0b9c | f3a5af2927397cf346ec0e24312bfff077f00425 | /src/game/world5/level7.lean | d271b1e186c72d3988ecb7f18440d20687cfb235 | [
"Apache-2.0"
] | permissive | ImperialCollegeLondon/natural_number_game | 05c39e1586408cfb563d1a12e1085a90726ab655 | f29b6c2884299fc63fdfc81ae5d7daaa3219f9fd | refs/heads/master | 1,688,570,964,990 | 1,636,908,242,000 | 1,636,908,242,000 | 195,403,790 | 277 | 84 | Apache-2.0 | 1,694,547,955,000 | 1,562,328,792,000 | Lean | UTF-8 | Lean | false | false | 856 | lean | /-
# Function world.
## Level 7: `(P → Q) → ((Q → F) → (P → F))`
Have you noticed that, in stark contrast to earlier worlds,
we are not amassing a large collection of useful theorems?
We really are just constructing abstract levels with sets and
functions, and then solving them and never using the results
ever aga... |
c675454ae2631bf8b64ea93f53bbae89232606bc | 48f4f349e1bb919d14ab7e5921d0cfe825f4c423 | /fabstract/Cook_S_P_NP/fabstract.lean | 3fc82ae898d8425fac201ee8572702efc4eabc76 | [] | no_license | thalesant/formalabstracts-2017 | fdf4ff90d30ab1dcb6d4cf16a068a997ea5ecc80 | c47181342c9e41954aa8d41f5049965b5f332bca | refs/heads/master | 1,584,610,453,925 | 1,528,277,508,000 | 1,528,277,508,000 | 136,299,625 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,708 | lean | import meta_data
.turing_machines
namespace Cook_S_P_NP
/- Definitions of the complexity classes P and NP -/
def NP_computable (f : list bool → list bool) : Prop :=
∃ s n (TM : NTATM s n) (c k : nat),
computes_fn_in_time
TM
(λ i : fin 1 → list bool, f (i 0))
(λ i, c * ((i 0).length^k + 1))
def ... |
285f512c33be40126335cedc2e3da93875c06622 | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /src/Lean/Elab/Util.lean | 3ddfae67b4efc733ba5034bf72efa0c425d3882d | [
"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 | 6,599 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Util.Trace
import Lean.Parser.Extension
import Lean.KeyedDeclsAttribute
import Lean.Elab.Exception
namespace Lean
def Syntax.prettyPrint (stx ... |
0882d0082e595cfccaca978f6d6210276def34ef | 67dc347ff8e6eaa780fd69518f3e69b2fa5eef96 | /src/smt2/lol.lean | db5eb4a3f0678fb3a8e434b9b16eb8d3a59c2c07 | [
"Apache-2.0"
] | permissive | Kha/smt2_interface | 74589568b30d32a500fb3a9abb299a28f19d75e9 | d92be33fbf4d56e3745e255ab423ba8da7d7695b | refs/heads/master | 1,619,785,421,091 | 1,518,453,826,000 | 1,518,453,826,000 | 121,273,425 | 0 | 0 | null | 1,518,453,882,000 | 1,518,453,882,000 | null | UTF-8 | Lean | false | false | 13,241 | lean | import smt2.syntax
import smt2.builder
import .except
open native
namespace lol
structure refinement (T : Type) :=
(refinment : T → T)
mutual inductive type, term
with type : Type
| bool : type
| int : type
| var : string → type
| fn : list type → type → type
| refinement : type → (string → term) → type
with term : ... |
7312fefa730a4d1c14fbaaa8677ebb1e653e3a45 | 682dc1c167e5900ba3168b89700ae1cf501cfa29 | /src/del/semantics/translationlemmas.lean | d39b15a90ac2511098de44fa7dd98a3c817dbb40 | [] | no_license | paulaneeley/modal | 834558c87f55cdd6d8a29bb46c12f4d1de3239bc | ee5d149d4ecb337005b850bddf4453e56a5daf04 | refs/heads/master | 1,675,911,819,093 | 1,609,785,144,000 | 1,609,785,144,000 | 270,388,715 | 13 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 3,082 | lean | /-
Copyright (c) 2021 Paula Neeley. All rights reserved.
Author: Paula Neeley
Following the textbook "Dynamic Epistemic Logic" by
Hans van Ditmarsch, Wiebe van der Hoek, and Barteld Kooi
-/
import del.syntax.syntaxDEL del.syntax.syntaxlemmasPADEL
import del.semantics.translationfunction
variables {agents : Type}
ope... |
13d9b7c2e90b41d8da6f734cda887f0ff17d6ba4 | 77c5b91fae1b966ddd1db969ba37b6f0e4901e88 | /src/group_theory/monoid_localization.lean | 8d11002b3abaa3c55ecf481e0f89a3108ff586e0 | [
"Apache-2.0"
] | permissive | dexmagic/mathlib | ff48eefc56e2412429b31d4fddd41a976eb287ce | 7a5d15a955a92a90e1d398b2281916b9c41270b2 | refs/heads/master | 1,693,481,322,046 | 1,633,360,193,000 | 1,633,360,193,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 60,995 | 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.congruence
import group_theory.submonoid
import algebra.group.units
import algebra.punit_instances
/-!
# Localizations of commutative monoi... |
c09c4249b0d5bb64f6efbfea39ad95e7555b06da | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/system/random.lean | 7441b4d7ada32382eca4e8591b160123329f16af | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,944 | lean | /-
Copyright (c) 2018 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
universes u l
namespace Mathlib
/-
Basic random number generator support based on the one
... |
58a86f1f74d53f4efea702c9501798b21e5fae00 | 618003631150032a5676f229d13a079ac875ff77 | /src/category_theory/isomorphism.lean | 39143c151d16fea4a750c7943c0a6cdeeca2445c | [
"Apache-2.0"
] | permissive | awainverse/mathlib | 939b68c8486df66cfda64d327ad3d9165248c777 | ea76bd8f3ca0a8bf0a166a06a475b10663dec44a | refs/heads/master | 1,659,592,962,036 | 1,590,987,592,000 | 1,590,987,592,000 | 268,436,019 | 1 | 0 | Apache-2.0 | 1,590,990,500,000 | 1,590,990,500,000 | null | UTF-8 | Lean | false | false | 10,548 | 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
/-!
# Isomorphisms
This file defines isomorphisms between objects of a category.
## M... |
bfa21c227c25067adf15fa7a3d5d4daac8df414c | ae1e94c332e17c7dc7051ce976d5a9eebe7ab8a5 | /tests/compiler/reusebug.lean | 0079411b46e452ad8395f683e13a366e15c2e839 | [
"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 | 768 | lean | #lang lean4
inductive Expr
| Val : Int → Expr
| Var : String → Expr
| Add : Expr → Expr → Expr
| Mul : Expr → Expr → Expr
namespace Expr
protected def Expr.toString : Expr → String
| Val n => toString n
| Var x => x
| Add f g => "(" ++ Expr.toString f ++ " + " ++ Expr.toString g ++ ")"
| Mul f g => "(" ++ Exp... |
9e392ddab439c47252d171fcd16c28399e74a470 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/simp1.lean | 6ead77e994f8e78b21155c9bc1ee142c41a75ab9 | [
"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 | 1,311 | lean | import Lean
@[simp] theorem ex1 (x : Nat) : 2 * x = x + x :=
sorry
@[simp] theorem ex2 (xs : List α) : xs ++ [] = xs :=
sorry
@[simp] theorem ex3 (xs ys zs : List α) : (xs ++ ys) ++ zs = xs ++ (ys ++ zs) :=
sorry
@[simp] theorem ex5 (p : Prop) : p ∨ True :=
sorry
@[simp] theorem ex4 (xs : List α) : ¬(x :: ... |
ea48f8f8440bd4299a1ef4b6d9f6fd34100aabb8 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/nat/set.lean | eab9bf116b1ce539d46742c9491c6b4f7cdf21c1 | [
"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 | 1,274 | 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.set.image
/-!
### Recursion on the natural numbers and `set.range`
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a co... |
51d94c58fac714de1d3459cc029341e6378e2df4 | 41ebf3cb010344adfa84907b3304db00e02db0a6 | /uexp/tactic_paper_supplemental_material/gapt_export/grp778_1.opt2.lean | bfcd74de156f99df7a1cf3c4a315a58e12b546c3 | [
"BSD-2-Clause"
] | permissive | ReinierKoops/Cosette | e061b2ba58b26f4eddf4cd052dcf7abd16dfe8fb | eb8dadd06ee05fe7b6b99de431dd7c4faef5cb29 | refs/heads/master | 1,686,483,953,198 | 1,624,293,498,000 | 1,624,293,498,000 | 378,997,885 | 0 | 0 | BSD-2-Clause | 1,624,293,485,000 | 1,624,293,484,000 | null | UTF-8 | Lean | false | false | 123,711 | lean | namespace gapt
open tactic expr
namespace lk
lemma LogicalAxiom {a} (main1 : a) (main2 : ¬a) : false := main2 main1
lemma BottomAxiom (main : false) : false := main
lemma TopAxiom (main : ¬true) : false := main ⟨⟩
lemma ReflexivityAxiom {α : Type} {a : α} (main : a ≠ a) : false := main (eq.refl a)
lemma NegLeftRule ... |
8961b01d15351fadd15a162abfcd1ed74d416f0a | aa3f8992ef7806974bc1ffd468baa0c79f4d6643 | /tests/lean/run/intros.lean | 863ae57cffa90921e619f643add018a53e064109 | [
"Apache-2.0"
] | permissive | codyroux/lean | 7f8dff750722c5382bdd0a9a9275dc4bb2c58dd3 | 0cca265db19f7296531e339192e9b9bae4a31f8b | refs/heads/master | 1,610,909,964,159 | 1,407,084,399,000 | 1,416,857,075,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 596 | lean | import logic tools.tactic
open tactic
theorem tst1 (a b : Prop) : a → b → b :=
by intro Ha; intro Hb; apply Hb
theorem tst2 (a b : Prop) : a → b → a ∧ b :=
by intro Ha; intro Hb; rapply and.intro; apply Hb; apply Ha
theorem tst3 (a b : Prop) : a → b → a ∧ b :=
begin
intro Ha,
intro Hb,
apply and.intro,
apply Ha,... |
427ed50c31d62b103ba1462ee319932964cf0524 | 037dba89703a79cd4a4aec5e959818147f97635d | /src/2020/functions/happy_animals.lean | 5c6fcacf5a226ca310da98b1ee7d73c8ff46601e | [] | no_license | ImperialCollegeLondon/M40001_lean | 3a6a09298da395ab51bc220a535035d45bbe919b | 62a76fa92654c855af2b2fc2bef8e60acd16ccec | refs/heads/master | 1,666,750,403,259 | 1,665,771,117,000 | 1,665,771,117,000 | 209,141,835 | 115 | 12 | null | 1,640,270,596,000 | 1,568,749,174,000 | Lean | UTF-8 | Lean | false | false | 1,816 | lean | import tactic
open function
-- Say we have a collection of animals.
variable (animals : Type)
-- `set Animals` is the type of sets of animals, thought of as photos.
-- Theorem: every way of assigning a photo to each animal is not bijective.
theorem cantor : ∀ f : animals → set animals, ¬ (bijective f) :=
begin
--... |
0b957321ec51710abec0b326f052d8de663ed45f | 626e312b5c1cb2d88fca108f5933076012633192 | /src/testing/slim_check/gen.lean | 79524d88fb84f61430563c7cb1dad8eff25592f2 | [
"Apache-2.0"
] | permissive | Bioye97/mathlib | 9db2f9ee54418d29dd06996279ba9dc874fd6beb | 782a20a27ee83b523f801ff34efb1a9557085019 | refs/heads/master | 1,690,305,956,488 | 1,631,067,774,000 | 1,631,067,774,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,709 | 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... |
19f10e5c53f6f1ddc628ac41f4cd960285528005 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/analysis/normed_space/normed_group_quotient.lean | 9f6cea743dd21ae621bcc80ab4d266effc81fb8e | [
"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 | 20,563 | lean | /-
Copyright (c) 2021 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Riccardo Brasca
-/
import analysis.normed_space.normed_group_hom
/-!
# Quotients of seminormed groups
For any `semi_normed_group M` and any `S : add_subgroup M`, we p... |
8ecb1b8f5032fc572ab26e73e6d438542a0ec9e1 | b2fe74b11b57d362c13326bc5651244f111fa6f4 | /src/category_theory/Fintype.lean | e56df934dd91b2c1e220ef748e51a6128337ed9d | [
"Apache-2.0"
] | permissive | midfield/mathlib | c4db5fa898b5ac8f2f80ae0d00c95eb6f745f4c7 | 775edc615ecec631d65b6180dbcc7bc26c3abc26 | refs/heads/master | 1,675,330,551,921 | 1,608,304,514,000 | 1,608,304,514,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,557 | lean | /-
Copyright (c) 2020 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Adam Topaz
-/
import data.fintype.basic
import data.fin
import category_theory.concrete_category.bundled
import category_theory.concrete_category
import category_theory.full... |
8abd4d57a66c14c53f19c1b066027b2be4248efa | 26ac254ecb57ffcb886ff709cf018390161a9225 | /src/data/indicator_function.lean | b1b57e07d0aec2d026a0af330dcf0734c5265b12 | [
"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 | 11,489 | lean | /-
Copyright (c) 2020 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou
-/
import algebra.pi_instances
import data.set.disjointed
import data.support
/-!
# Indicator function
`indicator (s : set α) (f : α → β) (a : α)` is `f a` if `a ∈ s` an... |
ece3c75df54e07322242fda2e719edf508aedce1 | 80746c6dba6a866de5431094bf9f8f841b043d77 | /src/measure_theory/borel_space.lean | 5309bd53aed76badd4fa29d205cd2718317423bf | [
"Apache-2.0"
] | permissive | leanprover-fork/mathlib-backup | 8b5c95c535b148fca858f7e8db75a76252e32987 | 0eb9db6a1a8a605f0cf9e33873d0450f9f0ae9b0 | refs/heads/master | 1,585,156,056,139 | 1,548,864,430,000 | 1,548,864,438,000 | 143,964,213 | 0 | 0 | Apache-2.0 | 1,550,795,966,000 | 1,533,705,322,000 | Lean | UTF-8 | Lean | false | false | 18,609 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Borel (measurable) space -- the smallest σ-algebra generated by open sets
It would be nice to encode this in the topological space type class, i.e. each topological sp... |
b1d2a2b6fbd14e1032616a5bebc6de142ef88f7f | ae45642d9df02b59b44bba57eb547e04381d3030 | /src/group_theory/representation/basic.lean | ff12d1c4565526ae94ff711e4014f080c44c5c1f | [
"Apache-2.0"
] | permissive | avigad/group-representations | 0e73d899d883676e68f526b4f04b4880b0d39a6a | 0279bcfdc2c1d7465bb09d78a0cc7d713872cc6d | refs/heads/master | 1,657,579,290,731 | 1,589,221,654,000 | 1,589,221,654,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 11,870 | lean | /- Copyright (c) 2020 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Douglas, Floris van Doorn
-/
import linear_algebra.finite_dimensional linear_algebra.bilinear_form
import data.fintype.card tactic.apply_fun
universe variables u v w w'
ope... |
18b7c566f34a9ee07721bbeac2995da0944b6ceb | c777c32c8e484e195053731103c5e52af26a25d1 | /src/number_theory/kummer_dedekind.lean | 0ee9f05a5c58d212edfae20758e7fc084945fc69 | [
"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 | 16,862 | lean | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Paul Lezeau
-/
import ring_theory.dedekind_domain.ideal
import ring_theory.is_adjoin_root
/-!
# Kummer-Dedekind theorem
This file proves the monogenic version of the Kumme... |
5d836150652c9e4b7d27fc8359d2330b0fc3080d | 618003631150032a5676f229d13a079ac875ff77 | /src/category_theory/limits/shapes/terminal.lean | 453c65e2b9fd251ff9e2177945d6c2eda690b512 | [
"Apache-2.0"
] | permissive | awainverse/mathlib | 939b68c8486df66cfda64d327ad3d9165248c777 | ea76bd8f3ca0a8bf0a166a06a475b10663dec44a | refs/heads/master | 1,659,592,962,036 | 1,590,987,592,000 | 1,590,987,592,000 | 268,436,019 | 1 | 0 | Apache-2.0 | 1,590,990,500,000 | 1,590,990,500,000 | null | UTF-8 | Lean | false | false | 3,309 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.limits.shapes.finite_products
import category_theory.pempty
/-!
# Initial and terminal objects in a category.
-/
universes v u
open category... |
cfe41f58dcddb95447c42558f0197bcdd5b23f55 | e00ea76a720126cf9f6d732ad6216b5b824d20a7 | /src/data/pnat/factors.lean | b6cf4739044d731cab9d2b4ca36f180349449aa6 | [
"Apache-2.0"
] | permissive | vaibhavkarve/mathlib | a574aaf68c0a431a47fa82ce0637f0f769826bfe | 17f8340912468f49bdc30acdb9a9fa02eeb0473a | refs/heads/master | 1,621,263,802,637 | 1,585,399,588,000 | 1,585,399,588,000 | 250,833,447 | 0 | 0 | Apache-2.0 | 1,585,410,341,000 | 1,585,410,341,000 | null | UTF-8 | Lean | false | false | 14,008 | lean | /-
Copyright (c) 2019 Neil Strickland. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Neil Strickland
-/
import tactic.basic
import data.pnat.basic data.nat.prime data.multiset data.int.basic data.int.gcd
algebra.group algebra.group_power algebra.ordered_ring
/-- The... |
8095f957127e63ea0c06fe01dc3ed98ea95c20ea | 7565ffb53cc64430691ce89265da0f944ee43051 | /hott/homotopy/LES_of_homotopy_groups.hlean | 6e1a358af7fcb2362457166d2f7a9aa0437e0379 | [
"Apache-2.0"
] | permissive | EgbertRijke/lean2 | cacddba3d150f8b38688e044960a208bf851f90e | 519dcee739fbca5a4ab77d66db7652097b4604cd | refs/heads/master | 1,606,936,954,854 | 1,498,836,083,000 | 1,498,910,882,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 35,594 | hlean | /-
Copyright (c) 2016 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
We define the fiber sequence of a pointed map f : X →* Y. We mostly follow the proof in section 8.4
of the book.
PART 1:
We define a sequence fiber_sequence as in ... |
d50cab5935a31ec8c255289d1fe51b9407750aeb | ba4794a0deca1d2aaa68914cd285d77880907b5c | /src/game/world10/level5.lean | 8cb0d77bacaaab367ee30888c9714d9e8e8ebeda | [
"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 | 616 | lean | import game.world10.level4 -- hide
namespace mynat -- hide
/-
# Inequality world.
## Level 5: `le_trans`
Another straightforward one.
-/
/- Lemma
≤ is transitive. In other words, if $a\leq b$ and $b\leq c$ then $a\leq c$.
-/
theorem le_trans (a b c : mynat) (hab : a ≤ b) (hbc : b ≤ c) : a ≤ c :=
begin [less_le... |
0c39ad54f68f877909e639be526a642d01349ffd | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/list/cycle.lean | 60dc82c3a7e7beb1d7328659cdd573e2924dd76f | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 30,206 | lean | /-
Copyright (c) 2021 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
import data.multiset.sort
import data.fintype.list
import data.list.rotate
/-!
# Cycles of a list
Lists have an equivalence relation of whether they are rotationa... |
4583d9de7014541cf6acb9e68a1dbf647b36ad04 | 96e44fc78cabfc9d646dc37d0e756189b6b79181 | /library/init/wf.lean | ee275eb7a5e017d0fd0b8b5455936e94bf7f8c07 | [
"Apache-2.0"
] | permissive | TwoFX/lean | 23c73c10a340f5a381f6abf27a27f53f1fb7e2e3 | 7e3f336714055869690b7309b6bb651fbc67e76e | refs/heads/master | 1,612,504,908,183 | 1,594,641,622,000 | 1,594,641,622,000 | 243,750,847 | 0 | 0 | Apache-2.0 | 1,582,890,661,000 | 1,582,890,661,000 | null | UTF-8 | Lean | false | false | 7,348 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
prelude
import init.data.nat.basic init.data.prod
universes u v
inductive acc {α : Sort u} (r : α → α → Prop) : α → Prop
| intro (x : α) (h : ∀ y, r y x → ... |
3ed5c7b9e973e34a3e530d189b2f38a5bd929966 | 0a6b214fd60b822ae708d58655b7d2f36091d8f8 | /src/misc.lean | b2ea04ed14aa494a105683ed14fa4dbe24dab2b3 | [
"MIT"
] | permissive | Naomij1/lean-homotopie | de0bf067bc77254deac02aab0184511ce7aaafe7 | 21bd6be53449c61088234ceab7ec63c18628521a | refs/heads/master | 1,613,216,666,817 | 1,591,786,776,000 | 1,591,786,776,000 | 244,693,557 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,773 | lean | import data.set.intervals.basic
import data.real.basic
import topology.instances.real
import tactic.suggest
import tactics
open set
open classical
-- Propriétés de base sur l'ensemble [0,1]
abbreviation I := Icc (0 : ℝ) (1 : ℝ)
instance : has_zero I := ⟨⟨ (0 : ℝ), and.intro (le_refl 0) (zero_le_one)⟩⟩
instance : ... |
e60df657978a4539f3967575d8a33cef35c908e5 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /src/Lean/Elab/Print.lean | 1dd7f6468e953b029a249bdd8e8bf464dd7598c0 | [
"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 | 5,815 | 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.Util.FoldConsts
import Lean.Elab.Command
namespace Lean.Elab.Command
private def throwUnknownId (id : Name) : CommandElabM Unit :=
throwErro... |
583db00bb09620fa00ecfad3e8d6b7cada4186da | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/data/list/func.lean | c6a84f32a0a162c4fbeb2c0f10f81ff4489949a8 | [
"Apache-2.0"
] | permissive | dupuisf/mathlib | 62de4ec6544bf3b79086afd27b6529acfaf2c1bb | 8582b06b0a5d06c33ee07d0bdf7c646cae22cf36 | refs/heads/master | 1,669,494,854,016 | 1,595,692,409,000 | 1,595,692,409,000 | 272,046,630 | 0 | 0 | Apache-2.0 | 1,592,066,143,000 | 1,592,066,142,000 | null | UTF-8 | Lean | false | false | 10,350 | lean | /-
Copyright (c) 2019 Seul Baek. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Seul Baek
-/
import data.nat.basic
open list
universes u v w
variables {α : Type u} {β : Type v} {γ : Type w}
namespace list
namespace func
variables {a : α}
variables {as as1 as2 as3 :... |
0d4a4efb768ebcbf17011739eb9cc2635cf2e66a | e967488e2008f07b0aa7b6b18d4398d02c7460e2 | /src/game/sup_inf/L01defs.lean | e6386286571191a83d63289fe4926a7d4e0eb4ec | [] | no_license | thyrgle/real-number-game | 5c53eefaa815051f3d70ca5782e41d2adb76fd6e | a420eecef62209b729c910c2170d1dd27b74bc9f | refs/heads/master | 1,606,405,407,612 | 1,574,956,743,000 | 1,574,956,743,000 | 229,126,103 | 0 | 0 | null | 1,576,784,273,000 | 1,576,784,272,000 | null | UTF-8 | Lean | false | false | 2,274 | lean | import data.real.basic -- imports the real numbers ℝ
namespace xena -- hide
-- World name : Sup and Inf
/-
# Chapter 1 : Sup and Inf
This chapter assumes you are familiar with the following tactics: `intro`, `apply`, `exact`. -- TODO -- any more?
If you are not, try playing Function World and Proposition World of th... |
8febba512ce4411b87b03c9063ce8ee29183faf6 | 4fa161becb8ce7378a709f5992a594764699e268 | /src/data/setoid/basic.lean | e940c1e58a2e2013b24e7b819df4f24cf5105157 | [
"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 | 16,458 | lean | /-
Copyright (c) 2019 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston, Bryan Gin-ge Chen
-/
import order.galois_connection
/-!
# Equivalence relations
This file defines the complete lattice of equivalence relations on a type, resul... |
c8e2a74ff896c8b4a073587d5c0e3616febc9cf5 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/algebra/lie/free.lean | 8e0d827086590aa85cc6fdc855e25798169238c9 | [
"Apache-2.0"
] | permissive | urkud/mathlib | eab80095e1b9f1513bfb7f25b4fa82fa4fd02989 | 6379d39e6b5b279df9715f8011369a301b634e41 | refs/heads/master | 1,658,425,342,662 | 1,658,078,703,000 | 1,658,078,703,000 | 186,910,338 | 0 | 0 | Apache-2.0 | 1,568,512,083,000 | 1,557,958,709,000 | Lean | UTF-8 | Lean | false | false | 10,917 | lean | /-
Copyright (c) 2021 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import algebra.lie.of_associative
import algebra.lie.non_unital_non_assoc_algebra
import algebra.lie.universal_enveloping
import algebra.free_non_unital_non_assoc_algebra
... |
9b245411c37f62b0acaa1e57c4bdcbf9764da4c1 | bdb33f8b7ea65f7705fc342a178508e2722eb851 | /group_theory/submonoid.lean | d924bba848c3c1dfad04d40682c8fd32382de2e4 | [
"Apache-2.0"
] | permissive | rwbarton/mathlib | 939ae09bf8d6eb1331fc2f7e067d39567e10e33d | c13c5ea701bb1eec057e0a242d9f480a079105e9 | refs/heads/master | 1,584,015,335,862 | 1,524,142,167,000 | 1,524,142,167,000 | 130,614,171 | 0 | 0 | Apache-2.0 | 1,548,902,667,000 | 1,524,437,371,000 | Lean | UTF-8 | Lean | false | false | 2,955 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau
-/
import algebra.group_power
variables {α : Type*} [monoid α] {s : set α}
/-- `s` is a submonoid: a set containing 1 and closed under multiplication. -/
cl... |
26471fd93342c443ef451ef42ecc9d6dc8eb94c6 | b70031c8e2c5337b91d7e70f1e0c5f528f7b0e77 | /src/linear_algebra/determinant.lean | 9bbf48794d9b98fdd8c4c74379422be55aefbaf2 | [
"Apache-2.0"
] | permissive | molodiuc/mathlib | cae2ba3ef1601c1f42ca0b625c79b061b63fef5b | 98ebe5a6739fbe254f9ee9d401882d4388f91035 | refs/heads/master | 1,674,237,127,059 | 1,606,353,533,000 | 1,606,353,533,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 13,561 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Chris Hughes, Tim Baanen
-/
import data.matrix.pequiv
import data.fintype.card
import group_theory.perm.sign
import algebra.algebra.basic
import tactic.ring
universes u v w z
op... |
8cff3fdc7118304c71a3f33c6f1380c41b8b9606 | e00ea76a720126cf9f6d732ad6216b5b824d20a7 | /src/order/pilex.lean | 7772dd71512145eb1b03ad768061123179eac014 | [
"Apache-2.0"
] | permissive | vaibhavkarve/mathlib | a574aaf68c0a431a47fa82ce0637f0f769826bfe | 17f8340912468f49bdc30acdb9a9fa02eeb0473a | refs/heads/master | 1,621,263,802,637 | 1,585,399,588,000 | 1,585,399,588,000 | 250,833,447 | 0 | 0 | Apache-2.0 | 1,585,410,341,000 | 1,585,410,341,000 | null | UTF-8 | Lean | false | false | 4,236 | lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import algebra.order_functions tactic.tauto algebra.pi_instances
variables {ι : Type*} {β : ι → Type*} (r : ι → ι → Prop)
(s : Π {i}, β i → β i → Prop)
def pi.lex (x... |
12c95ba42bf8405bdd37b308328ba54a01a6c4c5 | 6dc0c8ce7a76229dd81e73ed4474f15f88a9e294 | /tests/lean/hygienicIntro.lean | 9a92cdda03a2e5ce55829fe731e9daea0fd6e1f2 | [
"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 | 1,195 | lean | --
set_option hygienicIntro false in
theorem ex1 {a p q r : Prop} : p → (p → q) → (q → r) → r := by
intro _ h1 h2;
apply h2;
apply h1;
exact a_1 -- Bad practice, using name generated by `intro`.
theorem ex2 {a p q r : Prop} : p → (p → q) → (q → r) → r := by
intro _ h1 h2;
apply h2;
apply h1;
exact a_1 -- error "unkno... |
761e00ea9745281f0431cb5584c655f3b6f70420 | 130c49f47783503e462c16b2eff31933442be6ff | /stage0/src/Lean/PrettyPrinter/Delaborator/Builtins.lean | 5c7e21a8d8422104781f9ea936c5eae72b457c5d | [
"Apache-2.0"
] | permissive | Hazel-Brown/lean4 | 8aa5860e282435ffc30dcdfccd34006c59d1d39c | 79e6732fc6bbf5af831b76f310f9c488d44e7a16 | refs/heads/master | 1,689,218,208,951 | 1,629,736,869,000 | 1,629,736,896,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 31,188 | lean | /-
Copyright (c) 2020 Sebastian Ullrich. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Ullrich
-/
import Lean.PrettyPrinter.Delaborator.Basic
import Lean.PrettyPrinter.Delaborator.SubExpr
import Lean.PrettyPrinter.Delaborator.TopDownAnalyze
import Lean.Pars... |
c88a6385af258de4f204c0ea47b1175f07fa3486 | 359199d7253811b032ab92108191da7336eba86e | /src/instructor/lectures/lecture_18.lean | 3a38649609a2956c37d35f90075613e778a27786 | [] | no_license | arte-et-marte/my_cs2120f21 | 0bc6215cb5018a3b7c90d9d399a173233f587064 | 91609c3609ad81fda895bee8b97cc76813241e17 | refs/heads/main | 1,693,298,928,348 | 1,634,931,202,000 | 1,634,931,202,000 | 399,946,705 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,973 | lean | import data.set
-- memorize all defs in this file.
/-
Up to now we have mostly used our
intuition to understand operations
on, and special values (empty and
complete) of sets. Now, to prepare
to state and prove theorems about
sets, we will see how to formalize
these ideas in predicate logic. We
isolate our own definit... |
8c29eeb55781273fca100500820d81c3cfb1a105 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/topology/compact_open.lean | a9dfb8e9df0cdf9a25d0311a96b7480f70ca1f0c | [
"Apache-2.0"
] | permissive | urkud/mathlib | eab80095e1b9f1513bfb7f25b4fa82fa4fd02989 | 6379d39e6b5b279df9715f8011369a301b634e41 | refs/heads/master | 1,658,425,342,662 | 1,658,078,703,000 | 1,658,078,703,000 | 186,910,338 | 0 | 0 | Apache-2.0 | 1,568,512,083,000 | 1,557,958,709,000 | Lean | UTF-8 | Lean | false | false | 17,864 | lean | /-
Copyright (c) 2018 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton
-/
import tactic.tidy
import topology.continuous_function.basic
import topology.homeomorph
import topology.subset_properties
import topology.maps
/-!
# The compact-open topol... |
267f89538aa7c09e1c561bdd49a6775c95f376ef | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/order/filter/archimedean.lean | 199bde5debc9cf554ceeedfffe4494400be14fa9 | [
"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 | 3,975 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yury Kudryashov
-/
import order.filter.at_top_bot
import algebra.archimedean
/-!
# `at_top` filter and archimedean (semi)rings/fields
In this file we prove that for a... |
37025ec1d646b832c220a1fe3073f6ff47e6849a | 618003631150032a5676f229d13a079ac875ff77 | /docs/tutorial/category_theory/intro.lean | d6b7a8a705a21d37860e31158df7b7beebd4251a | [
"Apache-2.0"
] | permissive | awainverse/mathlib | 939b68c8486df66cfda64d327ad3d9165248c777 | ea76bd8f3ca0a8bf0a166a06a475b10663dec44a | refs/heads/master | 1,659,592,962,036 | 1,590,987,592,000 | 1,590,987,592,000 | 268,436,019 | 1 | 0 | Apache-2.0 | 1,590,990,500,000 | 1,590,990,500,000 | null | UTF-8 | Lean | false | false | 11,630 | lean | import category_theory.functor_category -- this transitively imports
-- category_theory.category
-- category_theory.functor
-- category_theory.natural_transformation
/-!
# An introduction to category theory in Lean
This is an introduction to the basic usage of category theory (in the mathematical sense) in Lean.
We c... |
be5dc8e72a094536efc8935bdc29e260c3920ae2 | 4950bf76e5ae40ba9f8491647d0b6f228ddce173 | /src/analysis/asymptotic_equivalent.lean | 01bc3f3dd3838c98a7df62c42efa8fa4f7e890ad | [
"Apache-2.0"
] | permissive | ntzwq/mathlib | ca50b21079b0a7c6781c34b62199a396dd00cee2 | 36eec1a98f22df82eaccd354a758ef8576af2a7f | refs/heads/master | 1,675,193,391,478 | 1,607,822,996,000 | 1,607,822,996,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,270 | lean | /-
Copyright (c) 2020 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-/
import analysis.asymptotics
import analysis.normed_space.ordered
import analysis.normed_space.bounded_linear_maps
/-!
# Asymptotic equivalence
In this file, we ... |
cff3f4f31abf05db44d74b567ebfebc390df00e3 | f3849be5d845a1cb97680f0bbbe03b85518312f0 | /tests/lean/run/confuse_ind.lean | d2ecd0f225863d1117f472b3f625803b5008cf31 | [
"Apache-2.0"
] | permissive | bjoeris/lean | 0ed95125d762b17bfcb54dad1f9721f953f92eeb | 4e496b78d5e73545fa4f9a807155113d8e6b0561 | refs/heads/master | 1,611,251,218,281 | 1,495,337,658,000 | 1,495,337,658,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 222 | lean | attribute [reducible] definition mk_arrow (A : Sort*) (B : Sort*) :=
A → A → B
inductive confuse (A : Type)
| leaf1 : confuse
| leaf2 : num → confuse
| node : mk_arrow A confuse → confuse
#check confuse.cases_on
|
328e4d5f4e36f2e84b373ba7df4382e4d504653c | 3f1a1d97c03bb24b55a1b9969bb4b3c619491d5a | /library/init/data/string/default.lean | 41af8d0c3fbcf57d7f867244f75f19c26cd0319f | [
"Apache-2.0"
] | permissive | praveenmunagapati/lean | 00c3b4496cef8e758396005013b9776bb82c4f56 | fc760f57d20e0a486d14bc8a08d89147b60f530c | refs/heads/master | 1,630,692,342,183 | 1,515,626,222,000 | 1,515,626,222,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 229 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.data.string.basic init.data.string.instances
|
da3d80d02df9ebb994c1661bd5498897cb898278 | 95dcf8dea2baf2b4b0a60d438f27c35ae3dd3990 | /src/category_theory/whiskering.lean | a448bebf6e6f740fa212096c30f2fe3563bb106e | [
"Apache-2.0"
] | permissive | uniformity1/mathlib | 829341bad9dfa6d6be9adaacb8086a8a492e85a4 | dd0e9bd8f2e5ec267f68e72336f6973311909105 | refs/heads/master | 1,588,592,015,670 | 1,554,219,842,000 | 1,554,219,842,000 | 179,110,702 | 0 | 0 | Apache-2.0 | 1,554,220,076,000 | 1,554,220,076,000 | null | UTF-8 | Lean | false | false | 5,580 | lean | -- Copyright (c) 2018 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Scott Morrison
import category_theory.isomorphism
import category_theory.functor_category
namespace category_theory
universes u₁ v₁ u₂ v₂ u₃ v₃ u₄ v₄
section
variables (C : S... |
fc624094026bdce0bb2770a84dc0cf103684d54b | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/tactic/generalizes.lean | fd72edbc198d66fcf3597bea710a5c28d78959b5 | [
"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 | 8,913 | lean | /-
Copyright (c) 2020 Jannis Limperg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jannis Limperg
-/
import tactic.core
/-!
# The `generalizes` tactic
This module defines the `tactic.generalizes'` tactic and its interactive version
`tactic.interactive.generalizes`... |
58b26208196dc801a7410dc021a9880f53a7d24f | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/algebra/divisibility.lean | 8bc0c8096115d8ed47c997b36f4d1cd98bc60f11 | [
"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 | 8,140 | 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, Floris van Doorn, Amelia Livingston, Yury Kudryashov,
Neil Strickland, Aaron Anderson
-/
import algebra.group_with_zero
/-!
# Divisibility
This file... |
a1c85050b6d047c1464fb823f6d09e06a572380a | 1f47e6d7d0805180e1e6bd04292f307a4918df8c | /test/ring_exp.lean | 65640d8f20b63d66c7a85aa8efc06d4f6b197bae | [] | no_license | lean-forward/ring_exp | ec92067a91cfc91755d9b10b235b6876d43d3b0e | 9825dd5076a3f95edf316113357e76609cd78c59 | refs/heads/master | 1,607,680,961,230 | 1,587,145,901,000 | 1,587,145,901,000 | 233,816,878 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,636 | lean | import tactic.ring_exp
universes u
section addition
/-!
### `addition` section
Test associativity and commutativity of `(+)`.
-/
example (a b : ℚ) : a = a := by ring_exp
example (a b : ℚ) : a + b = a + b := by ring_exp
example (a b : ℚ) : b + a = a + b := by ring_exp
example (a b : ℤ) : a + b + b = b + (a + b) :... |
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