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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
2771cee5f53f8cd102fe8bfd778f51d0c965880d | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/model_theory/direct_limit.lean | 7833595665f8518c6c321e7063617c58b245e6dc | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 14,855 | lean | /-
Copyright (c) 2022 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import data.fintype.order
import algebra.direct_limit
import model_theory.quotients
import model_theory.finitely_generated
/-!
# Direct Limits of First-Order Structu... |
6cf924d780c481c7546f8ec7ce47d8f2eccda3f3 | 6dc0c8ce7a76229dd81e73ed4474f15f88a9e294 | /tests/lean/run/meta4.lean | 2e67b1580fa74a663190e027dc5faf01ab067073 | [
"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 | 1,356 | lean | import Lean.Meta
open Lean
open Lean.Meta
def print (msg : MessageData) : MetaM Unit :=
trace! `Meta.debug msg
def checkM (x : MetaM Bool) : MetaM Unit :=
unless (← x) do throwError "check failed"
axiom Ax : forall (α β : Type), α → β → DecidableEq β
set_option trace.Meta.debug true
def tst1 : MetaM Unit := do
le... |
41a7ab7837e73af1d4d0e795d10aa47ae118ef81 | 137c667471a40116a7afd7261f030b30180468c2 | /src/group_theory/congruence.lean | 026951ec3bb040f96de0654adbe94a8061d9b77a | [
"Apache-2.0"
] | permissive | bragadeesh153/mathlib | 46bf814cfb1eecb34b5d1549b9117dc60f657792 | b577bb2cd1f96eb47031878256856020b76f73cd | refs/heads/master | 1,687,435,188,334 | 1,626,384,207,000 | 1,626,384,207,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 44,887 | 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 data.setoid.basic
import algebra.group.pi
import algebra.group.prod
import data.equiv.mul_add
import group_theory.submonoid.operations
/-!
# Congruence ... |
58454d745b4658980cca1fc5fe1ca7062fc36e24 | 137c667471a40116a7afd7261f030b30180468c2 | /src/algebra/indicator_function.lean | 7aa2fa47888a7a8f0c995f05a84a9dffde582923 | [
"Apache-2.0"
] | permissive | bragadeesh153/mathlib | 46bf814cfb1eecb34b5d1549b9117dc60f657792 | b577bb2cd1f96eb47031878256856020b76f73cd | refs/heads/master | 1,687,435,188,334 | 1,626,384,207,000 | 1,626,384,207,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 20,289 | 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.group.pi
import group_theory.group_action
import algebra.support
import data.finset.lattice
/-!
# Indicator function
- `indicator (s : set α) (f : α → ... |
b267f9edd067ed255016dce51184a70748fb865c | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/finset/slice.lean | 5014f7ed74cc531ff868a8d8ea0758ba3ad93451 | [
"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 | 5,275 | lean | /-
Copyright (c) 2021 Bhavik Mehta, Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Alena Gusakov, Yaël Dillies
-/
import algebra.big_operators.basic
import data.nat.interval
import order.antichain
/-!
# `r`-sets and slice
This file defines... |
ad07484289cb0a3a9dbbf0106d30deb60604058c | d1a52c3f208fa42c41df8278c3d280f075eb020c | /stage0/src/Lean/Elab/Tactic/Injection.lean | d693d317be3356cc445fa87d41a65e32fb232128 | [
"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 | 1,408 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Meta.Tactic.Injection
import Lean.Elab.Tactic.ElabTerm
namespace Lean.Elab.Tactic
-- optional (" with " >> many1 ident')
private def getInjecti... |
2cf2ab8b00bb851f525db5f0a199cc10b99243ea | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /tests/bench/rbmap3.lean | d025d84f9f70f54d08773012f556ea68d3f98fcc | [
"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 | 8,993 | lean | prelude
import init.core init.system.io init.data.ordering
universes u v w
inductive Rbcolor
| red | black
inductive Rbnode (α : Type u) (β : α → Type v)
| leaf {} : Rbnode
| Node (c : Rbcolor) (lchild : Rbnode) (key : α) (val : β key) (rchild ... |
b0b41899f13fbecab0b8b0e69943d798d829a2c4 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/category_theory/monoidal/types.lean | 6412fbbeaa913c12987711df6ee7c652dca1ed7a | [
"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 | 3,071 | lean | /-
Copyright (c) 2018 Michael Jendrusch. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Jendrusch, Scott Morrison
-/
import category_theory.monoidal.of_chosen_finite_products
import category_theory.limits.shapes.finite_products
import category_theory.limits.sha... |
0971ea14128f09f0430dc0719c26928c01ce5a9a | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/topology/algebra/ordered.lean | d598de8e960ec4e6a5cb7b6b6dddd7230294d88d | [
"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 | 43,437 | 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
Theory of ordered topology.
-/
import order.liminf_limsup
import data.set.intervals
import topology.algebra.group
import topology.constructions
open cl... |
66256f57c7441ec2c27aadf96e16a420f1ee9056 | 08bd4ba4ca87dba1f09d2c96a26f5d65da81f4b4 | /src/Lean/PrettyPrinter/Formatter.lean | 80da39d6ff72461307ad14c73a70907264a30d79 | [
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"Apache-2.0",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | gebner/lean4 | d51c4922640a52a6f7426536ea669ef18a1d9af5 | 8cd9ce06843c9d42d6d6dc43d3e81e3b49dfc20f | refs/heads/master | 1,685,732,780,391 | 1,672,962,627,000 | 1,673,459,398,000 | 373,307,283 | 0 | 0 | Apache-2.0 | 1,691,316,730,000 | 1,622,669,271,000 | Lean | UTF-8 | Lean | false | false | 21,865 | 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.CoreM
import Lean.Parser.Extension
import Lean.Parser.StrInterpolation
import Lean.KeyedDeclsAttribute
import Lean.ParserCompiler.Attribute
import L... |
9c33404cb0672d7c0ffacf7b9176d3712c696911 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/linear_algebra/bilinear_form.lean | 1cfd5c3857eb0426cbd4eea22c4c552ad3e07ff9 | [
"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 | 9,062 | lean | /-
Copyright (c) 2018 Andreas Swerdlow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Andreas Swerdlow
-/
import linear_algebra.tensor_product
/-!
# Bilinear form
This file defines a bilinear form over a module. Basic ideas
such as orthogonality are also introduced,... |
b6fcc886851a332089784c84e7ff9c66818f025c | 947b78d97130d56365ae2ec264df196ce769371a | /tests/lean/run/ubscalar.lean | 1e65664a01eedd20f8253a72451461f9e2a7dff3 | [
"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 | 330 | lean | new_frontend
structure Foo :=
(flag : Bool := false)
(x : UInt16 := 0)
(z : UInt32 := 0)
(w : UInt64 := 0)
(h : USize := 0)
(xs : List Nat := [])
set_option trace.compiler.ir.init true
def f (s : Foo) : Foo :=
{ s with x := s.x + 1 }
def g (flag : Bool) : Foo :=
let s : Foo := { x := 10, flag := fl... |
d8c1b5287955d2523576b7280245b6d2bd598ce0 | 5d166a16ae129621cb54ca9dde86c275d7d2b483 | /tests/lean/run/soundness.lean | 55608e3a0215287f2af80cbeb9c23e17da7edd43 | [
"Apache-2.0"
] | permissive | jcarlson23/lean | b00098763291397e0ac76b37a2dd96bc013bd247 | 8de88701247f54d325edd46c0eed57aeacb64baf | refs/heads/master | 1,611,571,813,719 | 1,497,020,963,000 | 1,497,021,515,000 | 93,882,536 | 1 | 0 | null | 1,497,029,896,000 | 1,497,029,896,000 | null | UTF-8 | Lean | false | false | 6,692 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
Define propositional calculus, valuation, provability, validity, prove soundness.
This file is based on Floris van Doorn Coq files.
Similar to soundness.lea... |
26df73cbd1d78e385b5cc1ca615e8b66b0f6e0f5 | c46a17c860913da8a635099f06be3a2416f6cdab | /common_knowledge.lean | 1ca253e8c1f4fafdc8f51df179c6a79ad0af8a79 | [] | no_license | vladfi1/vfds | 4ed0b7fd810218c74eef933364b9aa6be4cc2551 | 664b0d1c8126c93b379115ffe5da7b943f3375d5 | refs/heads/master | 1,585,024,431,435 | 1,535,567,828,000 | 1,535,567,828,000 | 142,457,395 | 0 | 1 | null | 1,532,805,351,000 | 1,532,617,692,000 | Lean | UTF-8 | Lean | false | false | 1,890 | lean | constants p1 p2 : bool
def bool_to_nat : bool -> nat
| ff := 0
| tt := 1
def count (p1 p2 : bool) : nat := bool_to_nat p1 + bool_to_nat p2
inductive person : Type | a | b
def people : list person := [person.a, person.b]
constant color : person -> bool
constant beliefs (p : person) : nat -> set Prop
def is_ration... |
161e0729f2face53d967f380a7036c04e5204d8e | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/testing/slim_check/sampleable.lean | ede25f9a14035568f7901b736988ad7de8fbf738 | [
"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 | 31,386 | 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.lazy_list.basic
import data.tree
import data.int.basic
import control.bifunctor
import tactic.linarith
import testing.slim_check.gen
/-!
# `sampleable` Class
... |
4ecbfbbd4ee52a5dc71f8a20b9bdc3c9d5b37d25 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/combinatorics/simple_graph/ends/properties.lean | 1daaae2a569e205910cca81d65614720710b4e3a | [
"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 | 740 | lean | /-
Copyright (c) 2022 Anand Rao, Rémi Bottinelli. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anand Rao, Rémi Bottinelli
-/
import combinatorics.simple_graph.ends.defs
/-!
# Properties of the ends of graphs
This file is meant to contain results about the ends of (l... |
31b3eebebecc6c383a9d4190d85ce4f212e64742 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/category_theory/adjunction/whiskering.lean | 9d005d33b0cd57b464bc3f50e2cc2d00a4d2bdee | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 2,493 | lean | /-
Copyright (c) 2021 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz
-/
import category_theory.adjunction
import category_theory.whiskering
/-!
Given categories `C D E`, functors `F : D ⥤ E` and `G : E ⥤ D` with an adjunction
`F ⊣ G`, we provid... |
edc1196e4eb9bd5c05c76551b8b0589b5849c3e1 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebraic_geometry/locally_ringed_space.lean | 3e7c3c1bcbcb1c555a201e8e79d681383c6923ef | [
"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 | 10,165 | lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import algebraic_geometry.ringed_space
import algebraic_geometry.stalks
import logic.equiv.transfer_instance
/-!
# The category of locally ringed spaces
We define ... |
a8a2cc2314df947f934a523a95e06899a5654389 | 75c54c8946bb4203e0aaf196f918424a17b0de99 | /src/henkin.lean | 8b5651f71ac3f3e04d0cfeb60cee5fce4a22f77e | [
"Apache-2.0"
] | permissive | urkud/flypitch | 261e2a45f1038130178575406df8aea78255ba77 | 2250f5eda14b6ef9fc3e4e1f4a9ac4005634de5c | refs/heads/master | 1,653,266,469,246 | 1,577,819,679,000 | 1,577,819,679,000 | 259,862,235 | 1 | 0 | Apache-2.0 | 1,588,147,244,000 | 1,588,147,244,000 | null | UTF-8 | Lean | false | false | 52,033 | lean | /-
Copyright (c) 2019 The Flypitch Project. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Han, Floris van Doorn
-/
import .completion .language_extension .colimit
-- local attribute [instance, priority 0] classical.prop_decidable
open fol
universes u v
local... |
05b0b08c6ba5139f3cdf5333b9e5cd3c7ae919fd | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/geometry/manifold/instances/real.lean | f82c76fdf14788d987d5efe5c67d79c71f82a3c1 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 13,823 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import geometry.manifold.smooth_manifold_with_corners
import analysis.inner_product_space.pi_L2
/-!
# Constructing examples of manifolds over ℝ
> THIS FILE IS... |
e2212385b4ea19b23ef9fb3666c085f20787b5c5 | e58fe8dce8abdb027029831196eef44ecb90a19a | /Imperial/pred_prop_example.lean | 560560ad8bc938494ce323a343d1618e61d14dba | [] | no_license | hieule3004/Imperial | 89fc066eded43cf6015e19f6f83677411013b47c | 829d0d96603ff3e68ede818873db4931b8d854da | refs/heads/master | 1,584,834,346,353 | 1,531,250,018,000 | 1,531,250,018,000 | 139,205,362 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,509 | lean | section
open classical
variables (α : Type) (p q : α → Prop)
variable a : α
variable r : Prop
example : (∃ x : α, r) → r :=
λh, exists.elim h (λ_, id)
example : (∃ x : α, r) → r :=
by { intro h, cases h, assumption }
example : r → (∃ x : α, r) :=
exists.intro a
include a
example : r → (∃ x : α, r) :=
by { int... |
6a5bfed889cf20261392c7dcf7bab49211ff46ea | 4e3bf8e2b29061457a887ac8889e88fa5aa0e34c | /lean/love08_operational_semantics_exercise_solution.lean | 5727395175c90fae1cdd9bb7dd7f86a64b379fcf | [] | 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 | 7,404 | lean | /- LoVe Exercise 8: Operational Semantics -/
import .love08_operational_semantics_demo
namespace LoVe
/- Question 1: Program Equivalence -/
/- For this question, we introduce the notation of program equivalence
`p₁ ≈ p₂`. -/
def program_equiv (S₁ S₂ : program) : Prop :=
∀s t, (S₁, s) ⟹ t ↔ (S₂, s) ⟹ t
local infi... |
e8fea1cafaa76df347f4a938d87ad07d828fcf71 | 86d328c7fd9114507f3e8380e2b3d2f83ef6c647 | /repl.lean | 06a2450b3dc867500b9e46fe0a6a05c842723e79 | [] | no_license | forked-from-1kasper/lambda | 05ada15e7abdaa5f453bfe3792c086f04f363f76 | 696363514f3730951a90e86474940135a2339c0b | refs/heads/master | 1,623,388,766,920 | 1,607,249,080,000 | 1,607,249,080,000 | 128,524,636 | 2 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 5,319 | lean | import lambda.parsing lambda.types lambda.unicode
import system.io data.buffer.parser
open parsing types parser (hiding nat)
def mk_env (env : list (string × term)) (t : term) : term :=
match list.unzip env with
| (names, terms) := multi_app (multi_lam names t) terms
end
def add_to_env (env : list (string × term)) :... |
bc37d603a3f24c23178c122827168bf39507dec4 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/ring_theory/norm.lean | 760a5bbe59dd5b6276ceb217aaf225fbc32c7ec9 | [
"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 | 12,055 | 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 field_theory.primitive_element
import linear_algebra.determinant
import linear_algebra.matrix.charpoly.coeff
import linear_algebra.matrix.to_linear_equiv
import fie... |
be57c1e1828527583f54e413498ede056c0d5f95 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/data/sigma/basic.lean | 954537a403716bc524b28ed9dcb0bfbfa063a870 | [
"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 | 9,891 | 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 meta.univs
import tactic.lint
import tactic.ext
/-!
# Sigma types
This file proves basic results about sigma types.
A sigma type is a dependent pair type. L... |
e382cfa93c4be9de56e6607c085322231894926b | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/category_theory/limits/is_limit.lean | 56ce006946f2a9b7e8b953e92fa9609437daf8eb | [
"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 | 38,203 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Mario Carneiro, Scott Morrison, Floris van Doorn
-/
import category_theory.adjunction.basic
import category_theory.limits.cones
/-!
# Limits and colimits
We set up the g... |
e5ac73641e2066ae0aa9ec9890424747b7202317 | 5e3548e65f2c037cb94cd5524c90c623fbd6d46a | /src_icannos_totilas/topologie-espaces-normés/cpge_ten_03.lean | 29ca022794f4258f7e02a3b0100707c02cd254f2 | [] | no_license | ahayat16/lean_exos | d4f08c30adb601a06511a71b5ffb4d22d12ef77f | 682f2552d5b04a8c8eb9e4ab15f875a91b03845c | refs/heads/main | 1,693,101,073,585 | 1,636,479,336,000 | 1,636,479,336,000 | 415,000,441 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 365 | lean | import topology.basic
import algebra.module.basic
import algebra.module.submodule
import analysis.normed_space.basic
-- Montrer que si un sous-espace vectoriel F d'un espace normé E est ouvert alors F = E .
theorem exo {R E: Type*} [normed_field R] [normed_group E] [normed_space R E] (F: subspace R E):
is_open F.c... |
a538c32a48bc9eeafcaf30095ce657725603941a | f20db13587f4dd28a4b1fbd31953afd491691fa0 | /tests/lean/interactive/rb_map_ts.lean | 3ad10741c51960651c778dae6e3e062380c84343 | [
"Apache-2.0"
] | permissive | AHartNtkn/lean | 9a971edfc6857c63edcbf96bea6841b9a84cf916 | 0d83a74b26541421fc1aa33044c35b03759710ed | refs/heads/master | 1,620,592,591,236 | 1,516,749,881,000 | 1,516,749,881,000 | 118,697,288 | 1 | 0 | null | 1,516,759,470,000 | 1,516,759,470,000 | null | UTF-8 | Lean | false | false | 2,177 | lean | meta def mytac :=
state_t (name_map nat) tactic
meta instance : monad mytac :=
state_t.monad _ _
meta instance : monad.has_monad_lift tactic mytac :=
monad.monad_transformer_lift (state_t (name_map nat)) tactic
meta instance (α : Type) : has_coe (tactic α) (mytac α) :=
⟨monad.monad_lift⟩
namespace mytac
meta def s... |
111ec706fb49ce4342828ce75cd53a2a21107e28 | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /06_Inductive_Types.org.5.lean | 033ff5d46e9ae6adb84b0661f01b0f91f17cea25 | [] | no_license | cjmazey/lean-tutorial | ba559a49f82aa6c5848b9bf17b7389bf7f4ba645 | 381f61c9fcac56d01d959ae0fa6e376f2c4e3b34 | refs/heads/master | 1,610,286,098,832 | 1,447,124,923,000 | 1,447,124,923,000 | 43,082,433 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 528 | lean | /- page 78 -/
import standard
import data.nat
open nat
inductive weekday : Type :=
| sunday : weekday
| monday : weekday
| tuesday : weekday
| wednesday : weekday
| thursday : weekday
| friday : weekday
| saturday : weekday
-- BEGIN
namespace weekday
local abbreviation cases_on := @weekday.cases_on
definition numbe... |
801fe2eb3c74115a7f7d1b1c6d2f8d49fb2d7cd5 | 958488bc7f3c2044206e0358e56d7690b6ae696c | /lean/set.lean | a024e02950ae41d15de0ec3513475e832e870a43 | [] | no_license | possientis/Prog | a08eec1c1b121c2fd6c70a8ae89e2fbef952adb4 | d4b3debc37610a88e0dac3ac5914903604fd1d1f | refs/heads/master | 1,692,263,717,723 | 1,691,757,179,000 | 1,691,757,179,000 | 40,361,602 | 3 | 0 | null | 1,679,896,438,000 | 1,438,953,859,000 | Coq | UTF-8 | Lean | false | false | 1,473 | lean | universe u
-- Type of subsets of α. A subset of α is a predicate over α
def set2 (α : Type u) : Type u := α → Prop
--#check @set2
--#check @set
variable α : Type u
def elem (x:α) (a : set α) := a x
notation e ∈ a := elem e a
lemma setext : ∀ {a b : set α}, (∀ (x:α), x ∈ a ↔ x ∈ b) → a = b :=
begin
intros a b H, ... |
6c840f568a1e3f1a0229f497b87c2e27391c25a9 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/analysis/inner_product_space/spectrum.lean | e79c6c18ddf81b422fa9669954451ec8f2aa00c1 | [
"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 | 12,840 | lean | /-
Copyright (c) 2021 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
import analysis.inner_product_space.rayleigh
import analysis.inner_product_space.pi_L2
/-! # Spectral theory of self-adjoint operators
This file covers the spectr... |
9455fec69c3cabcd603eb8310e3ef2129c5a1f7e | d436468d80b739ba7e06843c4d0d2070e43448e5 | /src/topology/uniform_space/basic.lean | 20d976a0e9e3ae4c88e59e2f97cd0093a38992a3 | [
"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 | 41,957 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot
Theory of uniform spaces.
Uniform spaces are a generalization of metric spaces and topological groups. Many concepts directly
generaliz... |
20851bb9d9965d3690315137b02bd4d66ff6778e | 5719a16e23dfc08cdea7a5bf035b81690f307965 | /stage0/src/Init/Lean/Elab/App.lean | 577dd11eb60d4f7e5e4bccd453cc1a0a6da7a0df | [
"Apache-2.0"
] | permissive | postmasters/lean4 | 488b03969a371e1507e1e8a4df9ebf63c7cbe7ac | f3976fc53a883ac7606fc59357d43f4b51016ca7 | refs/heads/master | 1,655,582,707,480 | 1,588,682,595,000 | 1,588,682,595,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 29,014 | 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.Lean.Util.FindMVar
import Init.Lean.Elab.Term
import Init.Lean.Elab.Binders
namespace Lean
namespace Elab
namespace Term
/--
Auxiliar... |
0cf3ca780fd2720e40db1996c68b74aeb722799d | 88fb7558b0636ec6b181f2a548ac11ad3919f8a5 | /library/init/data/list/instances.lean | 6ca265f0d04587de815b7006377b014cbb8b9038 | [
"Apache-2.0"
] | permissive | moritayasuaki/lean | 9f666c323cb6fa1f31ac597d777914aed41e3b7a | ae96ebf6ee953088c235ff7ae0e8c95066ba8001 | refs/heads/master | 1,611,135,440,814 | 1,493,852,869,000 | 1,493,852,869,000 | 90,269,903 | 0 | 0 | null | 1,493,906,291,000 | 1,493,906,291,000 | null | UTF-8 | Lean | false | false | 2,361 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
prelude
import init.data.list.lemmas
import init.meta.mk_dec_eq_instance
open list
universes u v
local attribute [simp] map join ret list.append append_nil... |
9e41b9f84310030087e8b369e4e738f7b8ff6c13 | 26ac254ecb57ffcb886ff709cf018390161a9225 | /src/algebra/category/Group/biproducts.lean | e538a3a229693b12906366265ce77b8db23cbd09 | [
"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 | 3,007 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import algebra.category.Group.basic
import algebra.category.Group.preadditive
import category_theory.limits.shapes.biproducts
import algebra.pi_instances
/-!
# The c... |
5fbe6e42adabd8bdcb16677555f94828ee80958d | abd85493667895c57a7507870867b28124b3998f | /src/geometry/euclidean.lean | b6ef811dfb3e371ef42a612d63cdd0a24033129d | [
"Apache-2.0"
] | permissive | pechersky/mathlib | d56eef16bddb0bfc8bc552b05b7270aff5944393 | f1df14c2214ee114c9738e733efd5de174deb95d | refs/heads/master | 1,666,714,392,571 | 1,591,747,567,000 | 1,591,747,567,000 | 270,557,274 | 0 | 0 | Apache-2.0 | 1,591,597,975,000 | 1,591,597,974,000 | null | UTF-8 | Lean | false | false | 19,060 | lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Joseph Myers.
-/
import analysis.normed_space.real_inner_product
import analysis.normed_space.add_torsor
noncomputable theory
open_locale classical
open_locale real
/-!
# Euclidean spac... |
20b5c541039e90566e70081da076fd957abbfddc | dd24e6c3b8dc14dc504f8a906fc04c51e4312e6b | /src/mywork/lectures/lecture_5.lean | 5e08e65cb52a73fceac1f273aadff1b4ad21d37e | [] | no_license | njeyasingh/CS-2120 | dd781a90dd0645b74e61cee1813483fb7cb4a111 | b3356f665a246f295b3f1e6d61901bfca331810d | refs/heads/main | 1,693,294,711,274 | 1,635,188,659,000 | 1,635,188,659,000 | 399,945,420 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,656 | lean | /-
INTRODUCTION and ELIMINATION RULES
-/
/-
For ∀ x, P x (every x has property P)
- introduction rule: assume arbitrary x, then show P x
- elimination rule: *apply* a proof of ∀ x, P x, as a
kind of function to a specific value of x, say k, to
produce a proof of P k.
-/
theorem silly : ∀ (n : ℕ), true :=
be... |
731d800b5b71d486cb3ed78d928a263e616e53d5 | a4673261e60b025e2c8c825dfa4ab9108246c32e | /tests/lean/run/macroid.lean | 83c661799df540d6f95bdbf3289220c07eaa66fe | [
"Apache-2.0"
] | permissive | jcommelin/lean4 | c02dec0cc32c4bccab009285475f265f17d73228 | 2909313475588cc20ac0436e55548a4502050d0a | refs/heads/master | 1,674,129,550,893 | 1,606,415,348,000 | 1,606,415,348,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 567 | lean | syntax "[" ident "↦" term "]" : term
macro_rules `([$x ↦ $v]) => `(fun $x => $v)
#check [x ↦ x + 1]
syntax "case!" ident ":" term "with" term "," term : term
macro_rules `(case! $h : $c with $t, $e) => `((fun $h => cond $h $t $e) $c)
#check case! h : 0 == 0 with h, not h
syntax "case2!" ident ":" term "with" term "... |
a40d8761b5f387d71c63b94ddd9a7ae850b79d52 | 6f1049e897f569e5c47237de40321e62f0181948 | /src/exercises/06_sub_sequences.lean | 421ff0751f17abae6b5b22eb4f61908a97724f6c | [
"Apache-2.0"
] | permissive | anrddh/tutorials | f654a0807b9523608544836d9a81939f8e1dceb8 | 3ba43804e7b632201c494cdaa8da5406f1a255f9 | refs/heads/master | 1,655,542,921,827 | 1,588,846,595,000 | 1,588,846,595,000 | 262,330,134 | 0 | 0 | null | 1,588,944,346,000 | 1,588,944,345,000 | null | UTF-8 | Lean | false | false | 3,264 | lean | import tuto_lib
/-
This file continues the elementary study of limits of sequences.
It can be skipped if the previous file was too easy, it won't introduce
any new tactic or trick.
Remember useful lemmas:
abs_le (x y : ℝ) : |x| ≤ y ↔ -y ≤ x ∧ x ≤ y
abs_add (x y : ℝ) : |x + y| ≤ |x| + |y|
abs_sub (x y : ℝ) : |x - y... |
e9babc6ec430e42f45bfda67aca866c96ebc5208 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/analysis/normed/group/basic.lean | 67af706a829f8835dfd81d50935ff60591670921 | [
"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 | 55,211 | lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl
-/
import algebra.module.ulift
import analysis.normed.group.seminorm
import order.liminf_limsup
import topology.algebra.uniform_group
import topology.met... |
0771827bf661ec10f1d6c96742c1bbcbed2b3a82 | e8aa886451ad759d8f2621790f1748a9c7d9e820 | /src/category_theory/limits/shapes/binary_products.lean | 0145d00e34d4ace50a813398ede7b207258534ec | [
"Apache-2.0"
] | permissive | siegelzero/mathlib | 04c39faa5d6c1d7799adff1f5cf0710c59def716 | 64fa9a2062bc18cdfac3b1bf03a1f714cb434f86 | refs/heads/master | 1,649,847,954,618 | 1,586,747,318,000 | 1,586,747,318,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 11,859 | 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.limits.shapes.terminal
import category_theory.discrete_category
/-!
# Binary (co)products... |
b1632d7eee2cf399d2cff7c589444cf89bda8b5e | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/logic/nontrivial.lean | 4163cc2d272f6cbef91e5d7ae4e78b7c688c54cd | [
"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 | 10,463 | lean | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import data.pi
import data.prod
import data.subtype
import logic.unique
import logic.function.basic
/-!
# Nontrivial types
A type is *nontrivial* if it contai... |
3b0b14c9f7cc232ef58ac8d795b2490af7ec0d28 | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /06_Inductive_Types.org.40.lean | e8b9473e56e531101ab474394ac897e6e1a798e7 | [] | no_license | cjmazey/lean-tutorial | ba559a49f82aa6c5848b9bf17b7389bf7f4ba645 | 381f61c9fcac56d01d959ae0fa6e376f2c4e3b34 | refs/heads/master | 1,610,286,098,832 | 1,447,124,923,000 | 1,447,124,923,000 | 43,082,433 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 211 | lean | /- page 91 -/
import standard
open nat
namespace hide
-- BEGIN
inductive vector (A : Type) : nat → Type :=
| nil {} : vector A zero
| cons : Π {n}, A → vector A n → vector A (succ n)
-- END
end hide
|
e704ac24e7a46243296396c1b0cc56b687f671bb | 5ca7b1b12d14c4742e29366312ba2c2ef8201b21 | /src/game/world10/level3.lean | 4938b12fe10ac1a87fa8795b0f06030f8a3e3352 | [
"Apache-2.0"
] | permissive | MatthiasHu/natural_number_game | 2e464482ef3001863430b0336133b6697b275ba3 | 2d764f72669ae30861f6a1057fce0257f3e466c4 | refs/heads/master | 1,609,719,110,419 | 1,576,345,737,000 | 1,576,345,737,000 | 240,296,314 | 0 | 0 | Apache-2.0 | 1,581,608,357,000 | 1,581,608,356,000 | null | UTF-8 | Lean | false | false | 2,227 | lean | import game.world10.level2 -- hide
namespace mynat -- hide
/-
# Inequality world.
## Level 3: `le_succ_of_le`
We have seen how the `use` tactic makes progress on goals of the form `⊢ ∃ c, ...`.
But what do we do when we have a *hypothesis* of the form `h : ∃ c, ...`?
The hypothesis claims that there exists some na... |
8510f7652fdbf919dc3e2f5b11890534d42e2941 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/data/finsupp/lattice.lean | 536bb9a1da5b98c7ebb0bb82379c93bd89123d3f | [
"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 | 3,134 | 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 data.finsupp.basic
/-!
# Lattice structure on finsupps
This file provides instances of ordered structures on finsupps.
-/
open_locale classical
noncomputab... |
3ac92111f6515b152d3c99a1f1b1b34859df9785 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/data/list/big_operators.lean | 345c581d5a53a93443ce6f99841dcfa3d00c19aa | [
"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 | 26,072 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Floris van Doorn, Sébastien Gouëzel, Alex J. Best
-/
import algebra.group_power
import data.list.forall2
/-!
# Sums and products from lists
This file provides basic r... |
e238429d4f4ca73aada11b3a67e1cd0b469201e3 | ff5230333a701471f46c57e8c115a073ebaaa448 | /leanpkg/leanpkg/lean_version.lean | 8f91c205d98ddb58c82d71ecc4999fce8145b5e2 | [
"Apache-2.0"
] | permissive | stanford-cs242/lean | f81721d2b5d00bc175f2e58c57b710d465e6c858 | 7bd861261f4a37326dcf8d7a17f1f1f330e4548c | refs/heads/master | 1,600,957,431,849 | 1,576,465,093,000 | 1,576,465,093,000 | 225,779,423 | 0 | 3 | Apache-2.0 | 1,575,433,936,000 | 1,575,433,935,000 | null | UTF-8 | Lean | false | false | 694 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Gabriel Ebner
-/
namespace leanpkg
def lean_version_string_core :=
let (major, minor, patch) := lean.version in
sformat!("{major}.{minor}.{patch}")
def lean_version_string :=
i... |
72f3d50dd785f805e44cb0a9e9b0ba36b2f9e651 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/data/complex/module.lean | 6c3777c3b97a42fd904e2a59f875aa8a43cc07c6 | [
"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 | 11,142 | lean | /-
Copyright (c) 2020 Alexander Bentkamp, Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp, Sébastien Gouëzel, Eric Wieser
-/
import algebra.order.smul
import data.complex.basic
import data.fin.vec_notation
import field_theory.tower
... |
ca92a6a49f5b07c0946b21cb6fa5d3fe8d23d9a6 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/control/functor.lean | b9decb492e97c8417ea21db35149c9511f474f27 | [
"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 | 8,832 | lean | /-
Copyright (c) 2017 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import tactic.lint
import control.basic
/-!
# Functors
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> https://github.com/leanprover-community/mathlib4/pull/612
> Any change... |
e01562b55fe8534ba25c71b05e99f4207d38d259 | 8f67b34bba98f894155dedf263bc8d61c31e89cd | /2ltt/pullbacks.lean | 206874536ca3b57352016034ee4202616cc8af9b | [] | no_license | 5HT/two-level | 3b1523db242cba819681b862fbc8f490d9571a66 | 370f5a91311db3b463b10a31891370721e2476e2 | refs/heads/master | 1,648,254,367,420 | 1,576,269,550,000 | 1,576,269,550,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,653 | lean | import .fibrant .limit data.equiv algebra.category .facts
open function
section pullback
universe variable u
variables {A B C : Type.{u}}
(f : A → C) (g : B → C)
{isfib : is_fibration f}
structure Pullback (f : A → C) (g : B → C):=
(pA : A)
(pB : B)
(pC : C)
(p_law : (f pA = pC) × (g pB ... |
307253e9e2e0f5a212fd9c84829e11c7e243db02 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/group_theory/subgroup.lean | 8962ac03507a661e9503fc3f3167d52c3dcdbd84 | [
"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 | 46,293 | lean | /-
Copyright (c) 2020 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
import group_theory.submonoid
import algebra.group.conj
/-!
# Subgroups
This file defines multiplicative and additive subgroups as an extension of submonoids, in a bundle... |
0ea9c4b15f1e0935ee5a2c8024a80e3f0fc5f9fe | 4727251e0cd73359b15b664c3170e5d754078599 | /src/number_theory/liouville/liouville_with.lean | 9ebc0dcefe9eec41eea2d408994feb1ba854ff36 | [
"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 | 14,953 | lean | /-
Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import analysis.special_functions.pow
import number_theory.liouville.basic
import topology.instances.irrational
/-!
# Liouville numbers with a given exponent... |
cb1fa65932fac63f0ce4419a2a0965f2fcdf7410 | 38bf3fd2bb651ab70511408fcf70e2029e2ba310 | /src/category_theory/concrete_category/basic.lean | 6fc6ce47d28b6a5cdbd31202768a00d88ef0c185 | [
"Apache-2.0"
] | permissive | JaredCorduan/mathlib | 130392594844f15dad65a9308c242551bae6cd2e | d5de80376088954d592a59326c14404f538050a1 | refs/heads/master | 1,595,862,206,333 | 1,570,816,457,000 | 1,570,816,457,000 | 209,134,499 | 0 | 0 | Apache-2.0 | 1,568,746,811,000 | 1,568,746,811,000 | null | UTF-8 | Lean | false | false | 3,967 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Johannes Hölzl, Reid Barton, Sean Leather, Yury Kudryashov
-/
import category_theory.types category_theory.full_subcategory
/-!
# Concrete categories
A concrete categ... |
777a273e87f1ba3eb62b3d4c7dcf790c24d572fb | 28be2ab6091504b6ba250b367205fb94d50ab284 | /src/game/world10/level18a.lean | 20e8b9ede9113172f7e31b529f3aeb3add538f4f | [
"Apache-2.0"
] | permissive | postmasters/natural_number_game | 87304ac22e5e1c5ac2382d6e523d6914dd67a92d | 38a7adcdfdb18c49c87b37831736c8f15300d821 | refs/heads/master | 1,649,856,819,031 | 1,586,444,676,000 | 1,586,444,676,000 | 255,006,061 | 0 | 0 | Apache-2.0 | 1,586,664,599,000 | 1,586,664,598,000 | null | UTF-8 | Lean | false | false | 6,024 | lean | import game.world10.level17 -- hide
namespace mynat -- hide
-- todo INTRODUCE CONGR
lemma lt_irrefl (a : mynat) : ¬ (a < a) :=
begin [nat_num_game]
intro h,
cases h with h1 h2,
apply h2,
exact h1,
end
lemma ne_of_lt (a b : mynat) : a < b → a ≠ b :=
begin [nat_num_game]
intro h,
intro h1,
cases h with h... |
6846b40c831905079b2c67bd9b739cb5cc2e904a | 3dd1b66af77106badae6edb1c4dea91a146ead30 | /tests/lean/bug1.lean | a25db34d03ea29e944eb5671e1ef03796021e5d1 | [
"Apache-2.0"
] | permissive | silky/lean | 79c20c15c93feef47bb659a2cc139b26f3614642 | df8b88dca2f8da1a422cb618cd476ef5be730546 | refs/heads/master | 1,610,737,587,697 | 1,406,574,534,000 | 1,406,574,534,000 | 22,362,176 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 654 | lean | definition bool [inline] : Type.{1} := Type.{0}
definition and [inline] (p q : bool) : bool := ∀ c : bool, (p → q → c) → c
infixl `∧`:25 := and
variable a : bool
-- Error
theorem and_intro (p q : bool) (H1 : p) (H2 : q) : a
:= fun (c : bool) (H : p -> q -> c), H H1 H2
-- Error
theorem and_intro (p q : bo... |
9c13b8f26d055a17e2b64c906c80f62e529b996e | 3f48345ac9bbaa421714efc9872a0409379bb4ae | /src/set_category/limits/Pullback.lean | bb4fe098785b47451c59899454691e86402be989 | [] | no_license | QaisHamarneh/Coalgebra-in-Lean | b4318ee6d83780e5c734eb78fed98b1fe8016f7e | bd0452df98bc64b608e5dfd7babc42c301bb6a46 | refs/heads/master | 1,663,371,200,241 | 1,661,004,695,000 | 1,661,004,695,000 | 209,798,828 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,504 | lean | import tactic.tidy
import set_category.diagram_lemmas
import set_category.category_set
import help_functions
import set_category.limits.Equalizer
import set_category.limits.Product
import category_theory.types
namespace Pullback
open set
diagram_lemmas
classical
function
help_functions
E... |
894555fab8097826c418199f6d65c5edc5e91b41 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /src/Lean/Elab/MutualDef.lean | 12e401d21317df7b8e81f75e037c2f676859f3a4 | [
"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 | 33,362 | 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.Parser.Term
import Lean.Meta.Closure
import Lean.Meta.Check
import Lean.Elab.Command
import Lean.Elab.DefView
import Lean.Elab.PreDefinition
imp... |
36f0c8cc29175b80f578578252e609cd112f476d | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/diamond9.lean | b7cb4b912f505dcfdda566aa6ed85917543504b8 | [
"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 | 395 | lean | class Zero (A : Type u) where zero : A
instance {A} [Zero A] : OfNat A (nat_lit 0) := ⟨Zero.zero⟩
class AddGroup (A : Type u) extends Zero A where
gsmul : Int → A → A
gsmul_zero' : ∀ a, gsmul 0 a = 0
class Ring (R : Type u) extends Zero R, AddGroup R
#print Ring.mk
#check {
zero := 0
gsmul := fun x n => x.t... |
9030ebd7f725ccfd9b714f8ac8be73ea541e8468 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/category/Group/colimits.lean | 362f9ade3e506a3a056083874f0b11fadf7de8b3 | [
"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 | 9,661 | 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 algebra.category.Group.preadditive
import group_theory.quotient_group
import category_theory.limits.shapes.kernels
import category_theory.concrete_category.ele... |
796ee27b88e21490f52b2cdc72b97651c7579f21 | d6124c8dbe5661dcc5b8c9da0a56fbf1f0480ad6 | /Papyrus/IR/BasicBlockRef.lean | 41217ac55850b3b08467c6a810b21eef3fb20531 | [
"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 | 1,214 | lean | import Papyrus.Context
import Papyrus.IR.ValueRef
import Papyrus.IR.InstructionRef
namespace Papyrus
/--
A reference to an external LLVM
[BasicBlock](https://llvm.org/doxygen/classllvm_1_1BasicBlock.html).
-/
structure BasicBlockRef extends ValueRef where
is_basic_block : toValueRef.valueKind = ValueKind.basicB... |
865a19cb2cc3afc43d7ba16801d6cfe9a4226419 | 9028d228ac200bbefe3a711342514dd4e4458bff | /src/algebra/ring/basic.lean | 7d531e6a5b95388869e8f3be4e0af57836679d81 | [
"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 | 38,005 | 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
-/
import algebra.divisibility
import data.set.basic
/-!
# Properties and homomo... |
0869c382dc767295b83610433f226f8a98d1be2e | e39f04f6ff425fe3b3f5e26a8998b817d1dba80f | /meta/rb_map.lean | e09a59b1760d3e2f01e8efb13d261e2745fef492 | [
"Apache-2.0"
] | permissive | kristychoi/mathlib | c504b5e8f84e272ea1d8966693c42de7523bf0ec | 257fd84fe98927ff4a5ffe044f68c4e9d235cc75 | refs/heads/master | 1,586,520,722,896 | 1,544,030,145,000 | 1,544,031,933,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,105 | lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Robert Y. Lewis
Additional operations on native rb_maps and rb_sets.
-/
import data.option
namespace native
namespace rb_set
meta def filter {key} (s : rb_set key) (P : ... |
7434343892967531faa1cd455d04577289ffe4ec | a721fe7446524f18ba361625fc01033d9c8b7a78 | /src/principia/mynat/hcf.lean | 9c670ca1b528ffa22ba9c860e5b991beaaa0ff6a | [] | no_license | Sterrs/leaning | 8fd80d1f0a6117a220bb2e57ece639b9a63deadc | 3901cc953694b33adda86cb88ca30ba99594db31 | refs/heads/master | 1,627,023,822,744 | 1,616,515,221,000 | 1,616,515,221,000 | 245,512,190 | 2 | 0 | null | 1,616,429,050,000 | 1,583,527,118,000 | Lean | UTF-8 | Lean | false | false | 8,264 | lean | import ..myset.basic
import .prime
import ..myint.dvd
import ..logic
/- Noncomputable HCF
In this file we make no attempt to remain computable or
minimise the axioms used.
We construct the HCF of a and b as the smallest positive
integer h for which there exist integers x and y such
that a * x + b * y = h, and then g... |
aa7d9e8f4cf1968b32d661ba09dac0a069b81a57 | 9dd3f3912f7321eb58ee9aa8f21778ad6221f87c | /library/init/meta/interaction_monad.lean | e2f53e8e39233603f1ba51b3b1394758dc838866 | [
"Apache-2.0"
] | permissive | bre7k30/lean | de893411bcfa7b3c5572e61b9e1c52951b310aa4 | 5a924699d076dab1bd5af23a8f910b433e598d7a | refs/heads/master | 1,610,900,145,817 | 1,488,006,845,000 | 1,488,006,845,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,313 | 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, Sebastian Ullrich
-/
prelude
import init.function init.data.option.basic init.util
import init.category.combinators init.category.monad init.category.alternat... |
6584aa93e60cb00d62f57c5a502d2be3bd5a7ff4 | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /09_Type_Classes.org.7.lean | 125d60211d1d06cf247888e243a7b906bbcb16b3 | [] | no_license | cjmazey/lean-tutorial | ba559a49f82aa6c5848b9bf17b7389bf7f4ba645 | 381f61c9fcac56d01d959ae0fa6e376f2c4e3b34 | refs/heads/master | 1,610,286,098,832 | 1,447,124,923,000 | 1,447,124,923,000 | 43,082,433 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 666 | lean | import standard
namespace hide
inductive inhabited [class] (A : Type) : Type :=
mk : A → inhabited A
definition Prop.is_inhabited [instance] : inhabited Prop :=
inhabited.mk true
definition bool.is_inhabited [instance] : inhabited bool :=
inhabited.mk bool.tt
definition nat.is_inhabited [instance] : inhabited nat :... |
bfd887cae69b47b8a9c736e048cf08af462fc812 | e151e9053bfd6d71740066474fc500a087837323 | /src/hott/types/sum.lean | 3315008c75757bc834e8d261a3fba2154e640339 | [
"Apache-2.0"
] | permissive | daniel-carranza/hott3 | 15bac2d90589dbb952ef15e74b2837722491963d | 913811e8a1371d3a5751d7d32ff9dec8aa6815d9 | refs/heads/master | 1,610,091,349,670 | 1,596,222,336,000 | 1,596,222,336,000 | 241,957,822 | 0 | 0 | Apache-2.0 | 1,582,222,839,000 | 1,582,222,838,000 | null | UTF-8 | Lean | false | false | 19,954 | lean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Floris van Doorn, Jakob von Raumer
Theorems about sums/coproducts/disjoint unions
-/
import .pi .equiv hott.cubical.square
open /-hott.lift-/ hott hott.eq hott.is_equiv hott.equiv
... |
25c4ded3961b1b6e84683c7f7819fc78764a1c7e | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/dynamics/ergodic/conservative.lean | b83f718535a37029fc72186eb8599394beeceea4 | [
"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 | 10,016 | lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import dynamics.ergodic.measure_preserving
import combinatorics.pigeonhole
/-!
# Conservative systems
In this file we define `f : α → α` to be a *conservative* sy... |
0e4551478cb8e08a86290f436ab72b1a9e9eaa21 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/category_theory/limits/shapes/types.lean | 1fb3086376ac7c03654368aacf810655790d53b5 | [
"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 | 18,498 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.limits.types
import category_theory.limits.shapes.products
import category_theory.limits.shapes.binary_products
import category_theory.limits.s... |
637f83fe076538c772b9f4f2a25cd80f60b03b1f | 94e33a31faa76775069b071adea97e86e218a8ee | /src/combinatorics/additive/behrend.lean | 872e74b79b0ac9effba7557d684f8ad1cf3d6893 | [
"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 | 8,382 | lean | /-
Copyright (c) 2022 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
import analysis.inner_product_space.pi_L2
import combinatorics.additive.salem_spencer
/-!
# Behrend's bound on Roth numbers
This file proves... |
06e225a8196bcd4e498c0fdd76e491868311b1bf | 8b0adce7bd4e8e06a22dbf65d3ef29169133227b | /inClassNotes/04_type_library/option_test.lean | a39fd6d63166a8fc06293bff6fe407666f0b11ae | [] | no_license | parvahujauva/complogic-s21 | 5420bce9c456cd9dafcb4965719d2e45fb53437a | ba8d38bfb9000420e0051bc07195026b0e39a29c | refs/heads/master | 1,677,682,663,658 | 1,613,232,309,000 | 1,613,232,309,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,017 | lean | /-
The nat type in Lean is defined just as it
is in our nat.lean file, so we just use Lean's
definition here. For reference, here's Lean's
definition.
inductive nat : Type
| zero : nat
| succ : nat → nat
That's it. To fully understand how this
definition produces a set of terms that
we can view interpret as represen... |
382d783dddd23209b39d49b94d68b1befa4538c5 | bb31430994044506fa42fd667e2d556327e18dfe | /src/data/polynomial/degree/lemmas.lean | f9f10db9a956309b85f98fe749a04b730a1cdabf | [
"Apache-2.0"
] | permissive | sgouezel/mathlib | 0cb4e5335a2ba189fa7af96d83a377f83270e503 | 00638177efd1b2534fc5269363ebf42a7871df9a | refs/heads/master | 1,674,527,483,042 | 1,673,665,568,000 | 1,673,665,568,000 | 119,598,202 | 0 | 0 | null | 1,517,348,647,000 | 1,517,348,646,000 | null | UTF-8 | Lean | false | false | 12,622 | 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.eval
/-!
# Theory of degrees of polynomials
Some of the main results include
- `nat_degree_comp_l... |
51fd4e54f49abff9990a125ca9dca0d17031d18e | 94e33a31faa76775069b071adea97e86e218a8ee | /src/data/real/cau_seq_completion.lean | c0a9f7d2c86968b9035b71987f923ff668bf03b5 | [
"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 | 11,166 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Robert Y. Lewis
-/
import data.real.cau_seq
/-!
# Cauchy completion
This file generalizes the Cauchy completion of `(ℚ, abs)` to the completion of a commutative ring
... |
44dd8a2a110b38b5aadd47220fbf3f0ef5dac1f8 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/tactic/rewrite.lean | 999a97888bc63764655621415b03a2fc706d300e | [
"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 | 7,345 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import data.dlist tactic.core
namespace tactic
open expr list
meta def match_fn (fn : expr) : expr → tactic (expr × expr)
| (app (app fn' e₀) e₁) := unify fn fn' $> (e₀, ... |
ade1b86fede8e86bf0aa741f32db6c923d12e863 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/topology/local_homeomorph.lean | c1e6159edd901de24ef30a866985714665d330c9 | [
"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 | 47,444 | 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 data.equiv.local_equiv
import topology.opens
/-!
# Local homeomorphisms
This file defines homeomorphisms between open subsets of topological spaces. An... |
62fa7ff8d1ab004691405821e03da6807d151c91 | 46125763b4dbf50619e8846a1371029346f4c3db | /src/algebra/punit_instances.lean | 3309000cd32b04eeefb7ba35be798a56212a20cc | [
"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 | 3,456 | lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
Instances on punit.
-/
import algebra.module
universes u
open lattice
namespace punit
variables (x y : punit.{u+1}) (s : set punit.{u+1})
@[to_additive add_comm_group]
insta... |
75f5c8a98d5f312fbe1db8ff4bc1734f02806625 | 1a2aed113dcb5f1c07ae98040953fba5e6563624 | /lean_root/src/scratch.lean | 9bff8e89107e01c9a04f812e27bf4eff97ee63a4 | [
"Apache-2.0"
] | permissive | kevindoran/lean | 61d9fb90363b04587624036136482b29e3c16ebd | 77e755095a31e3a214010eb48a61e48d65dfdec9 | refs/heads/master | 1,670,372,072,769 | 1,598,920,365,000 | 1,598,920,365,000 | 264,824,992 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,793 | lean | import data.real.basic
import data.set
namespace my_closure
universes u
variables {α : Type u}
variables P Q Q' : α Prop
local notation `|`x`|` := abs x
def is_adherent (x : ℝ) (X : set ℝ) : Prop :=
∀ ε > 0, ∃y ∈ X, |x - y| < ε
def closure(X : set ℝ) : set ℝ :=
{x : ℝ | is_adherent x X }
lemma closure_inter_su... |
3f44c766f6c2dda75b30091fffd53ee2e8dae1e3 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/ring_theory/subsemiring/basic.lean | 90dc42f73b607870e5fa43153412259437d333ee | [
"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 | 42,563 | 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 algebra.module.basic
import algebra.ring.equiv
import algebra.ring.prod
import data.set.finite
import group_theory.submonoid.centralizer
import group_theory.... |
67842cf9bba265acb07ed4cba2264d2a8be1e179 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/logic/encodable/basic.lean | aed8d48bed5b749d883a6ab12a04c044cf10a810 | [
"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 | 18,899 | 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 logic.equiv.nat
import order.directed
import order.rel_iso
/-!
# Encodable types
This file defines encodable (constructively counta... |
2d10c8de4a2df4b0ddd5470cc417374cc771d6c2 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/algebra/lie/classical.lean | 41deb49cc1a8e41d957993a37308643ff032e359 | [
"Apache-2.0"
] | permissive | stjordanis/mathlib | 51e286d19140e3788ef2c470bc7b953e4991f0c9 | 2568d41bca08f5d6bf39d915434c8447e21f42ee | refs/heads/master | 1,631,748,053,501 | 1,627,938,886,000 | 1,627,938,886,000 | 228,728,358 | 0 | 0 | Apache-2.0 | 1,576,630,588,000 | 1,576,630,587,000 | null | UTF-8 | Lean | false | false | 13,935 | lean | /-
Copyright (c) 2020 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import algebra.invertible
import algebra.lie.skew_adjoint
import algebra.lie.abelian
import linear_algebra.matrix.trace
/-!
# Classical Lie algebras
This file is the plac... |
8b15c7c70efbc8557e6faaa08116b4f30724502a | bb31430994044506fa42fd667e2d556327e18dfe | /src/linear_algebra/pi_tensor_product.lean | d50bc7c91cf76ed37b93588755399f5f07def82b | [
"Apache-2.0"
] | permissive | sgouezel/mathlib | 0cb4e5335a2ba189fa7af96d83a377f83270e503 | 00638177efd1b2534fc5269363ebf42a7871df9a | refs/heads/master | 1,674,527,483,042 | 1,673,665,568,000 | 1,673,665,568,000 | 119,598,202 | 0 | 0 | null | 1,517,348,647,000 | 1,517,348,646,000 | null | UTF-8 | Lean | false | false | 24,378 | lean | /-
Copyright (c) 2020 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis, Eric Wieser
-/
import group_theory.congruence
import linear_algebra.multilinear.tensor_product
/-!
# Tensor product of an indexed family of modules over commutative... |
49f9f98a493e241210d26dc2934c737066e3ab88 | ea5678cc400c34ff95b661fa26d15024e27ea8cd | /zmod_as_fin2.lean | 8c830ec67f475098e56d069b4fce06fd57131dc4 | [] | 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 | 8,564 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Chris Hughes
-/
import data.int.modeq data.int.basic data.nat.modeq data.fintype data.nat.prime data.nat.gcd
lemma int.coe_nat_ne_zero_of_pos {n : ℕ} (hn : 0 < n) : (n : ℤ) ≠ 0 :=
(ne_... |
efe070bfc74fe46fe30c5a443d28b4cc1283685f | 1fbca480c1574e809ae95a3eda58188ff42a5e41 | /src/util/meta/tactic/search.lean | f9c58ab977d6265bb39c72374c2c1dc834e74256 | [] | no_license | unitb/lean-lib | 560eea0acf02b1fd4bcaac9986d3d7f1a4290e7e | 439b80e606b4ebe4909a08b1d77f4f5c0ee3dee9 | refs/heads/master | 1,610,706,025,400 | 1,570,144,245,000 | 1,570,144,245,000 | 99,579,229 | 5 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,817 | lean | import meta.expr
open tactic environment
meta def search_some (s : expr → tactic bool) (hide_prefixed : bool := tt) : tactic unit :=
do env ← get_env,
env.fold (pure ()) $ λ d acc,
do acc,
try $ do
declaration.thm n _ ty _ ← pure d | skip,
when (¬ hide_prefixed ∨ n.last.front ≠ '_') $ do
... |
0e595cc3b9b3f784c491713323ae397d712ca14d | 31f556cdeb9239ffc2fad8f905e33987ff4feab9 | /stage0/src/Lean/ScopedEnvExtension.lean | 475da37e77403ea72e1fddd39756bb78092b39b5 | [
"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 | 8,494 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Environment
import Lean.Data.NameTrie
import Lean.Attributes
namespace Lean
namespace ScopedEnvExtension
inductive Entry (α : Type) where
|... |
89d4366ebea6cefdff75c765fac94379badb6332 | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /src/Lean/Data/PrefixTree.lean | e02b3011f8c0c724a303f6ddbcc00bc23722c34e | [
"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 | 3,841 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Std.Data.RBMap
namespace Lean
open Std
/- Similar to trie, but for arbitrary keys -/
inductive PrefixTreeNode (α : Type u) (β : Type v) where
| N... |
2390e475251c3b60d9d240e82e5801afe79800f2 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/set_theory/ordinal/principal.lean | b2c7bbd834b5bfcb6d6d53dbbc0669332eaea547 | [
"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 | 16,438 | lean | /-
Copyright (c) 2022 Violeta Hernández Palacios. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Violeta Hernández Palacios
-/
import set_theory.ordinal.fixed_point
/-!
### Principal ordinals
We define principal or indecomposable ordinals, and we prove the standard ... |
00538560333d3eb2f0c96631e220db45891e457a | 367134ba5a65885e863bdc4507601606690974c1 | /src/ring_theory/witt_vector/init_tail.lean | 51d35727805c36877304c4537eef789e5d07dec0 | [
"Apache-2.0"
] | permissive | kodyvajjha/mathlib | 9bead00e90f68269a313f45f5561766cfd8d5cad | b98af5dd79e13a38d84438b850a2e8858ec21284 | refs/heads/master | 1,624,350,366,310 | 1,615,563,062,000 | 1,615,563,062,000 | 162,666,963 | 0 | 0 | Apache-2.0 | 1,545,367,651,000 | 1,545,367,651,000 | null | UTF-8 | Lean | false | false | 6,405 | lean | /-
Copyright (c) 2020 Johan Commelin and Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Robert Y. Lewis
-/
import ring_theory.witt_vector.basic
import ring_theory.witt_vector.is_poly
/-!
# `init` and `tail`
Given a Witt vector `x`, ... |
84bb63d1808b58bf58e9a18fd0315d42036bce84 | 34c1747a946aa0941114ffca77a3b7c1e4cfb686 | /src/spectrum_of_a_ring/spec_locally_ringed_space.lean | cab1689e80ae2acb9f48f2250830133468e6173d | [] | no_license | martrik/lean-scheme | 2b9edd63550c4579a451f793ab289af9fc79a16d | 033dc47192ba4c61e4e771701f5e29f8007e6332 | refs/heads/master | 1,588,866,287,405 | 1,554,922,682,000 | 1,554,922,682,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 287 | lean | import spectrum_of_a_ring.structure_sheaf
import spectrum_of_a_ring.strucutre_sheaf_stalks
universe u
variables (R : Type u) [comm_ring R]
def Spec.locally_ringeed_space : locally_ringed_space (Spec R) :=
{ O := structure_sheaf R,
Hstalks := λ P, structure_sheaf.stalk_local P, }
|
806dbcc071eda2fbcb0e587b43433df64e3431e4 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /library/init/meta/environment.lean | 285c5920eea23d0a85fd173226c30a5754cad582 | [
"Apache-2.0"
] | permissive | soonhokong/lean-osx | 4a954262c780e404c1369d6c06516161d07fcb40 | 3670278342d2f4faa49d95b46d86642d7875b47c | refs/heads/master | 1,611,410,334,552 | 1,474,425,686,000 | 1,474,425,686,000 | 12,043,103 | 5 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 4,109 | 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.declaration init.meta.exceptional
meta_constant environment : Type
namespace environment
/- Create a standard environment using t... |
6fcbfdd9332359f23523c012cc8673fc4fccbd16 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/complex/exponential.lean | 4bdb7cd7d4d5c2ccf954ba0bd16e757150d5ae99 | [
"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 | 67,133 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir
-/
import algebra.geom_sum
import data.complex.basic
import data.nat.choose.sum
/-!
# Exponential, trigonometric and hyperbolic trigonometric func... |
faf0ecb85df0fcb14777b58d4302ab09f84cab66 | 351a46035517d2a1985619b8cabdf263754d343a | /src/ch12.lean | bc77208ec502efe68f91ccb39801d3952447e432 | [] | 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 | 3,565 | lean | section
variable {U : Type}
variables {A B C : set U}
example : ∀ x, x ∈ A ∩ C → x ∈ A ∪ B :=
assume x : U,
assume : x ∈ A ∩ C,
show x ∈ A ∪ B, from or.inl (and.left this)
example : ∀ x, x ∈ -(A ∪ B) → x ∈ -A :=
assume x,
assume h1 : x ∈ -(A ∪ B),
show x ∈ -A, from
assume : x ∈ A,
show fal... |
74ea826dbe86c1cde62953f24b02ced4ea708295 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/blast_cc_heq3.lean | 17569f1db6faede269b6b26b1f1a30ee08977584 | [
"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 | 857 | lean | set_option blast.strategy "cc"
set_option blast.cc.heq true -- make sure heterogeneous congruence lemmas are enabled
axiom vector.{l} : Type.{l} → nat → Type.{l}
axiom app : Π {A : Type} {n m : nat}, vector A m → vector A n → vector A (m+n)
example (n1 n2 n3 : nat) (v1 w1 : vector nat n1) (w1' : vector nat n3) (v2 w2... |
5c9a974bcb7169d09c76f56c77215c611251aa40 | bb31430994044506fa42fd667e2d556327e18dfe | /src/ring_theory/algebraic.lean | d91e2bb41c483d1867fc1f4e2ec818cdcfd3ab65 | [
"Apache-2.0"
] | permissive | sgouezel/mathlib | 0cb4e5335a2ba189fa7af96d83a377f83270e503 | 00638177efd1b2534fc5269363ebf42a7871df9a | refs/heads/master | 1,674,527,483,042 | 1,673,665,568,000 | 1,673,665,568,000 | 119,598,202 | 0 | 0 | null | 1,517,348,647,000 | 1,517,348,646,000 | null | UTF-8 | Lean | false | false | 17,620 | lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import linear_algebra.finite_dimensional
import ring_theory.integral_closure
import data.polynomial.integral_normalization
/-!
# Algebraic elements and algebraic ex... |
311521a47bf331f74ad96e4df4e02bfc1a873294 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/continued_fractions/convergents_equiv.lean | d1a1803aceb7dba144acae613603fd4717b9a798 | [
"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 | 19,973 | lean | /-
Copyright (c) 2020 Kevin Kappelmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
-/
import algebra.continued_fractions.continuants_recurrence
import algebra.continued_fractions.terminated_stable
import tactic.field_simp
import tactic.ring
/-!
# ... |
c4784944be3493734c58d0ab81dd54ee81d55e4a | ad0c7d243dc1bd563419e2767ed42fb323d7beea | /data/equiv/basic.lean | 4e431125bb2084b4aab5c6932ea8a118dbfc4162 | [
"Apache-2.0"
] | permissive | sebzim4500/mathlib | e0b5a63b1655f910dee30badf09bd7e191d3cf30 | 6997cafbd3a7325af5cb318561768c316ceb7757 | refs/heads/master | 1,585,549,958,618 | 1,538,221,723,000 | 1,538,221,723,000 | 150,869,076 | 0 | 0 | Apache-2.0 | 1,538,229,323,000 | 1,538,229,323,000 | null | UTF-8 | Lean | false | false | 28,534 | 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
In the standard library we cannot assume the univalence axiom.
We say two types are equivalent if they are isomorphic.
Two equivalent types h... |
30bfad413d8578a739ae08a02abf4f1ca160f76b | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/analysis/calculus/deriv.lean | e33b7ae3be98c491c0fc8c8dd9ac2346221bfa9b | [
"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 | 86,255 | lean | /-
Copyright (c) 2019 Gabriel Ebner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner, Sébastien Gouëzel
-/
import analysis.calculus.fderiv
import data.polynomial.derivative
/-!
# One-dimensional derivatives
This file defines the derivative of a function... |
51c407bf6be9d62faeff33d50e2e6c6d5fc7d8af | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/algebra/star/basic.lean | 23802f8886ae38912a540e4b4cf5347fbb6ce1f8 | [
"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 | 5,349 | 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 tactic.apply_fun
import algebra.ordered_ring
import algebra.big_operators.basic
import data.equiv.ring
/-!
# Star monoids and star rings
We introduce the bas... |
9eedd798bf39a914dcb7dd2f33c0fef90e8b4e40 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/analysis/complex/polynomial.lean | ac65b124c24681012100e233e7429a29232ecb61 | [
"Apache-2.0"
] | permissive | stjordanis/mathlib | 51e286d19140e3788ef2c470bc7b953e4991f0c9 | 2568d41bca08f5d6bf39d915434c8447e21f42ee | refs/heads/master | 1,631,748,053,501 | 1,627,938,886,000 | 1,627,938,886,000 | 228,728,358 | 0 | 0 | Apache-2.0 | 1,576,630,588,000 | 1,576,630,587,000 | null | UTF-8 | Lean | false | false | 5,586 | 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 analysis.special_functions.pow
import field_theory.algebraic_closure
/-!
# The fundamental theorem of algebra
This file proves that every nonconstant complex poly... |
9c69a49611594478f3c259d42c1f26573c6f4559 | 9d2e3d5a2e2342a283affd97eead310c3b528a24 | /src/solutions/thursday/afternoon/category_theory/exercise2.lean | c179781435d40d674bed8ef3c11bb94a18c95181 | [] | permissive | Vtec234/lftcm2020 | ad2610ab614beefe44acc5622bb4a7fff9a5ea46 | bbbd4c8162f8c2ef602300ab8fdeca231886375d | refs/heads/master | 1,668,808,098,623 | 1,594,989,081,000 | 1,594,990,079,000 | 280,423,039 | 0 | 0 | MIT | 1,594,990,209,000 | 1,594,990,209,000 | null | UTF-8 | Lean | false | false | 3,775 | lean | import algebra.category.CommRing.basic
import data.polynomial
/-!
Let's show that taking polynomials over a ring is functor `Ring ⥤ Ring`.
-/
noncomputable theory -- the default implementation of polynomials is noncomputable
-- Just ignore this for now: it's a hack that prevents an annoying problem,
-- and a cleaner... |
a95cfb805852a72022ba25d6860408abcba91e2e | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/exists_intro1.lean | eadef6ded94f25a05ecc009d0079d9613c5fadf1 | [
"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 | 673 | lean | example : ∃ x : nat, x = x :=
Exists.intro 0 rfl
example : ∃ x : nat, x = x :=
exists.intro 0 rfl
lemma ex1 : ∃ x : nat, x = x :=
Exists.intro 0 rfl
lemma ex2 : ∃ x : nat, x = x :=
exists.intro 0 rfl
lemma ex3 : ∃ x y : nat, x = y :=
exists.intro 0 (exists.intro 0 rfl)
lemma ex4 : ∃ x y : nat, x = y + 1 :=
exists.... |
38c0cbecfa84152667baa6cfa868d9c5261bfdcf | 680b0d1592ce164979dab866b232f6fa743f2cc8 | /library/algebra/ordered_group.lean | 43f51d5c0a0d4d0c393e35ec4e56e9533e2deafa | [
"Apache-2.0"
] | permissive | syohex/lean | 657428ab520f8277fc18cf04bea2ad200dbae782 | 081ad1212b686780f3ff8a6d0e5f8a1d29a7d8bc | refs/heads/master | 1,611,274,838,635 | 1,452,668,188,000 | 1,452,668,188,000 | 49,562,028 | 0 | 0 | null | 1,452,675,604,000 | 1,452,675,602,000 | null | UTF-8 | Lean | false | false | 32,084 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
Partially ordered additive groups, modeled on Isabelle's library. These classes can be refined
if necessary.
-/
import logic.eq data.unit data.sigma data.prod
import alge... |
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