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b18b3f7eb952928f7182f9213d8a44e5c0667dec | aa3f8992ef7806974bc1ffd468baa0c79f4d6643 | /tests/lean/run/coe7.lean | fda2f4f3b532b69d1cf4ab9b904882b5242e607c | [
"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 | 258 | lean | import logic
namespace experiment
constant nat : Type.{1}
constant int : Type.{1}
constant of_nat : nat → int
coercion of_nat
theorem tst (n : nat) : n = n :=
have H : true, from trivial,
calc n = n : eq.refl _
... = n : eq.refl _
end experiment
|
77fd527f0599180096dc4a723401c11fe4d6db63 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/group_theory/monoid_localization.lean | 2ba1d19fd9e03f630fd033d40b6b09f69c2d33b0 | [
"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 | 54,831 | 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 algebra.group.units
import algebra.punit_instances
/-!
# Localizations of commutative monoids
Localizing a commutative r... |
2925f6233d21ac9a39b8e4bca6d4153e6f9bbc15 | 618003631150032a5676f229d13a079ac875ff77 | /src/analysis/calculus/mean_value.lean | 9b1d690ad080ad37dcc3862e154e56bfcd6bfbec | [
"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 | 41,602 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Yury Kudryashov
-/
import analysis.calculus.local_extr
import analysis.convex.topology
/-!
# The mean value inequality and equalities
In this file we prove the ... |
ae05f3b136f78b8b04f7a988903465f5ec61319a | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/category_theory/limits/preserves/shapes/pullbacks.lean | 6ee4eaea2bf172abe1081aaf1d3cfbc857f90229 | [
"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 | 3,743 | lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import category_theory.limits.shapes.pullbacks
import category_theory.limits.preserves.basic
/-!
# Preserving pullbacks
Constructions to relate the notions of preservin... |
2b07649f483ef2e0b183b24bfcb71f7a6dcf271f | e030b0259b777fedcdf73dd966f3f1556d392178 | /library/data/tuple.lean | 0839af8bb14f18e8438e1a78cc27f50871911d11 | [
"Apache-2.0"
] | permissive | fgdorais/lean | 17b46a095b70b21fa0790ce74876658dc5faca06 | c3b7c54d7cca7aaa25328f0a5660b6b75fe26055 | refs/heads/master | 1,611,523,590,686 | 1,484,412,902,000 | 1,484,412,902,000 | 38,489,734 | 0 | 0 | null | 1,435,923,380,000 | 1,435,923,379,000 | null | UTF-8 | Lean | false | false | 4,241 | 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
Tuples are lists of a fixed size.
It is implemented as a subtype.
-/
import data.list
def tuple (α : Type) (n : ℕ) := {l : list α // list.length l = n}
names... |
4c9fdbe8dd524b3081139245512816dc8eb015e9 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/field_theory/finite/polynomial_auto.lean | 55d6929446a2e6d5e99e6d145f495215d92bc20f | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,293 | lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.field_theory.finite.basic
import Mathlib.field_theory.mv_polynomial
import Mathlib.data.mv_... |
b0e88800f0eddfa8b40fda501af3b24b932b4ce6 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/extract.lean | bbcbaf2b7047b143f466b9ac961f6f49e9555f1b | [
"Apache-2.0"
] | permissive | leanprover-community/lean | 12b87f69d92e614daea8bcc9d4de9a9ace089d0e | cce7990ea86a78bdb383e38ed7f9b5ba93c60ce0 | refs/heads/master | 1,687,508,156,644 | 1,684,951,104,000 | 1,684,951,104,000 | 169,960,991 | 457 | 107 | Apache-2.0 | 1,686,744,372,000 | 1,549,790,268,000 | C++ | UTF-8 | Lean | false | false | 1,629 | lean | #eval "abc"
/- some "a" -/
#eval
let s₁ := "abcde" in
let it₁ := s₁.mk_iterator in
let it₂ := it₁.next in
it₁.extract it₂
/- some "" -/
#eval
let s₁ := "abcde" in
let it₁ := s₁.mk_iterator in
it₁.extract it₁
/- none -/
#eval
let s₁ := "abcde" in
let it₁ := s₁.mk_iterator in
let it₂ := it₁.next in
it₂.e... |
82a34b1a55e7b63013c5944bf4e42b609ae741d3 | fe84e287c662151bb313504482b218a503b972f3 | /src/data/equiv_extra.lean | 6a185d13fcdf8e459031bcd549a3ff4559c8eef5 | [] | no_license | NeilStrickland/lean_lib | 91e163f514b829c42fe75636407138b5c75cba83 | 6a9563de93748ace509d9db4302db6cd77d8f92c | refs/heads/master | 1,653,408,198,261 | 1,652,996,419,000 | 1,652,996,419,000 | 181,006,067 | 4 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 114 | lean | import logic.equiv.basic
lemma equiv.apply {α β : Type*} (f : α ≃ β) (a : α) :
f a = f.to_fun a := rfl
|
03220f4cd29a6431a2e233d871fddabd9a09f36d | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/data/finset/lattice.lean | ec76d88b4391b2750e1888e1968be55d7803a040 | [
"Apache-2.0"
] | permissive | agjftucker/mathlib | d634cd0d5256b6325e3c55bb7fb2403548371707 | 87fe50de17b00af533f72a102d0adefe4a2285e8 | refs/heads/master | 1,625,378,131,941 | 1,599,166,526,000 | 1,599,166,526,000 | 160,748,509 | 0 | 0 | Apache-2.0 | 1,544,141,789,000 | 1,544,141,789,000 | null | UTF-8 | Lean | false | false | 16,123 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
-/
import data.finset.fold
import data.multiset.lattice
/-!
# Lattice operations on multisets
-/
variables {α β γ : Type*}
namespace finset
open multiset
/-! ### sup ... |
9cfc13f8b74e5dfd5847592b3a87c3054fd53932 | 076f5040b63237c6dd928c6401329ed5adcb0e44 | /instructor-notes/2019.10.14.prop_logic/inference_rules.lean | a7a6be443ea4956d53be754ea0160ca1bb4b732f | [] | no_license | kevinsullivan/uva-cs-dm-f19 | 0f123689cf6cb078f263950b18382a7086bf30be | 09a950752884bd7ade4be33e9e89a2c4b1927167 | refs/heads/master | 1,594,771,841,541 | 1,575,853,850,000 | 1,575,853,850,000 | 205,433,890 | 4 | 9 | null | 1,571,592,121,000 | 1,567,188,539,000 | Lean | UTF-8 | Lean | false | false | 1,389 | lean |
--import .prop_logic
import .prop_logic
open prop_logic
open prop_logic.var
open prop_logic.unOp
open prop_logic.binOp
open prop_logic.pExp
/-
Define a few propositional variables.
-/
def P := varExp (mkVar 0)
def Q := varExp (mkVar 1)
def R := varExp (mkVar 2)
/-
Which of the following propositions are valid?
A... |
d54c7e92c62aea42acebecc57395960026b09177 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/analysis/specific_limits.lean | cf34ef54e55c5e33a236cfb8825be8615184102b | [] | 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 | 24,521 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebra.geom_sum
import Mathlib.order.filter.archimedean
import Mathlib.order.iterate
impor... |
81f52891d08ccee10b22174049f36bb63abd2d5c | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/hierarchy_design.lean | 7ba81405e8a939add1cf912084616caedcc8a6f9 | [
"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 | 9,303 | lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Eric Wieser
-/
import tactic.doc_commands
/-!
# Documentation of the algebraic hierarchy
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> https://github.com/leanprover-co... |
f03ed981f741358054cd87dae6553b5f4b0da796 | 50b3917f95cf9fe84639812ea0461b38f8f0dbe1 | /blog/xena_complex.lean | 6acde92d56ebd26268ebad267af7114b9a738822 | [] | no_license | roro47/xena | 6389bcd7dcf395656a2c85cfc90a4366e9b825bb | 237910190de38d6ff43694ffe3a9b68f79363e6c | refs/heads/master | 1,598,570,061,948 | 1,570,052,567,000 | 1,570,052,567,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,314 | lean | -- import the reals...
import data.real.basic
-- ...and now we can build the complex numbers as an ordered pair of reals.
structure complex : Type :=
(re : ℝ) (im : ℝ)
notation `ℂ` := complex
namespace complex
/-
What we have so far:
*) a new type called `complex` or ℂ for short;
*) Two functions `complex.re` and ... |
6dc481b7196d47e58e17e5665d7468feb20435cf | ab1416f6fd6655094298e6c7bab1ac47d2533342 | /samples/Lean/set.hlean | 761cd67d7485de0943ae39ae43d1488d551291dc | [
"MIT",
"LicenseRef-scancode-unknown-license-reference",
"Apache-2.0"
] | permissive | monkslc/hyperpolyglot | 6ddc09e9d10d30bd8ce5c80a3bd755fa5714d621 | a55a3b58eaed09b4314ef93d78e50a80cfec36f4 | refs/heads/master | 1,685,114,774,686 | 1,684,331,491,000 | 1,684,331,491,000 | 248,387,967 | 43 | 11 | Apache-2.0 | 1,684,331,495,000 | 1,584,583,355,000 | RenderScript | UTF-8 | Lean | false | false | 2,293 | hlean | -- Copyright (c) 2015 Jakob von Raumer. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Jakob von Raumer
-- Category of sets
import .basic types.pi trunc
open truncation sigma sigma.ops pi function eq morphism precategory
open equiv
namespace precategory
uni... |
0745d2fa8fb89210016991033299630f73ef2be1 | 4fa161becb8ce7378a709f5992a594764699e268 | /src/linear_algebra/basis.lean | f37bf9f419028c6a665fab51a5963484faab323d | [
"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 | 54,591 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Alexander Bentkamp
-/
import linear_algebra.finsupp
import linear_algebra.projection
import order.zorn
import data.fintype.card
/-!
# Linear independe... |
49f79afe7fb8ced8932a94a8976f767a5a8e3d5e | 82b86ba2ae0d5aed0f01f49c46db5afec0eb2bd7 | /src/Lean/Elab/Attributes.lean | 12436ba273e5c10f2a5dacff5f2caedaeec28811 | [
"Apache-2.0"
] | permissive | banksonian/lean4 | 3a2e6b0f1eb63aa56ff95b8d07b2f851072d54dc | 78da6b3aa2840693eea354a41e89fc5b212a5011 | refs/heads/master | 1,673,703,624,165 | 1,605,123,551,000 | 1,605,123,551,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,739 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Sebastian Ullrich
-/
import Lean.Parser.Basic
import Lean.Attributes
import Lean.MonadEnv
namespace Lean.Elab
structure Attribute :=
(name : Name) (args : Sy... |
97b1b1e15369d2f072e0f13151c218169325ee9e | fe84e287c662151bb313504482b218a503b972f3 | /src/data/power_series.lean | 9eac8926469f209e5643d138118d318c0088ac9b | [] | no_license | NeilStrickland/lean_lib | 91e163f514b829c42fe75636407138b5c75cba83 | 6a9563de93748ace509d9db4302db6cd77d8f92c | refs/heads/master | 1,653,408,198,261 | 1,652,996,419,000 | 1,652,996,419,000 | 181,006,067 | 4 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 8,848 | lean | import algebra.ring algebra.big_operators.basic
import data.birange
universes u v
variables (α : Type u) (β : Type v)
def power_series := ℕ → α
namespace power_series
@[ext]
lemma ext {a b : power_series α} : a = b ↔ ∀ k, (a k) = (b k) :=
⟨λ e, congr_fun e,λ e,funext e⟩
section add_comm_monoid
variable [add_... |
0f7e78ae573b393f458435f6e7321d3e5f310ea8 | 7a76361040c55ae1eba5856c1a637593117a6556 | /src/exercises/love01_definitions_and_statements_exercise_sheet.lean | 011ddd53a77915ef59ceb35f3afa6139480ea3fd | [] | no_license | rgreenblatt/fpv2021 | c2cbe7b664b648cef7d240a654d6bdf97a559272 | c65d72e48c8fa827d2040ed6ea86c2be62db36fa | refs/heads/main | 1,692,245,693,819 | 1,633,364,621,000 | 1,633,364,621,000 | 407,231,487 | 0 | 0 | null | 1,631,808,608,000 | 1,631,808,608,000 | null | UTF-8 | Lean | false | false | 4,368 | lean | import ..lectures.love01_definitions_and_statements_demo
/-! # LoVe Exercise 1: Definitions and Statements
Replace the placeholders (e.g., `:= sorry`) with your solutions. -/
set_option pp.beta true
set_option pp.generalized_field_notation false
namespace LoVe
/-! ## Question 1: Truncated Subtraction
1.1. Defi... |
a48c0471f33dd6692edd21290fd9c35131591fe8 | b70031c8e2c5337b91d7e70f1e0c5f528f7b0e77 | /src/data/complex/is_R_or_C.lean | 4e708545782c43026b5d75f6183c9701ec3eaeb8 | [
"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 | 28,866 | 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 analysis.normed_space.basic
import analysis.complex.basic
/-!
# `is_R_or_C`: a typeclass for ℝ or ℂ
This file defines the typeclass `is_R_or_C` intended t... |
226ad5a9c9aec361b2317361a92b53858f1a71c2 | 1abd1ed12aa68b375cdef28959f39531c6e95b84 | /src/order/closure.lean | 5c9a38a2c2904383a9e08fc60302bc50746b1a4e | [
"Apache-2.0"
] | permissive | jumpy4/mathlib | d3829e75173012833e9f15ac16e481e17596de0f | af36f1a35f279f0e5b3c2a77647c6bf2cfd51a13 | refs/heads/master | 1,693,508,842,818 | 1,636,203,271,000 | 1,636,203,271,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 17,336 | lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Yaël Dillies
-/
import data.set_like.basic
import order.preorder_hom
import order.galois_connection
import tactic.monotonicity
/-!
# Closure operators between preorders
W... |
cb2633a88d9e72cccb3b60aebb9bb10c20ca1cf3 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/filePath.lean | ee4915ada5d8f8c9aef5f6f572ccdc964ce5dc55 | [
"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 | 912 | lean | open System
open System.Platform
def norm (f : FilePath) : String :=
f.toString.map fun c => if c == '\\' then '/' else c
#eval FilePath.isAbsolute (if isWindows then "C:\\foo" else "/foo")
#eval FilePath.isAbsolute "a/b"
#eval norm <| ("a" : FilePath) / "b"
#eval norm <| ("a" : FilePath) / "b" / "c"
#eval norm <|... |
5791279889a679e5c411963f0769c81476565155 | 2a70b774d16dbdf5a533432ee0ebab6838df0948 | /_target/deps/mathlib/src/category_theory/limits/shapes/pullbacks.lean | 63f3788747886c1e3c2f29bbdaf889adde43ef81 | [
"Apache-2.0"
] | permissive | hjvromen/lewis | 40b035973df7c77ebf927afab7878c76d05ff758 | 105b675f73630f028ad5d890897a51b3c1146fb0 | refs/heads/master | 1,677,944,636,343 | 1,676,555,301,000 | 1,676,555,301,000 | 327,553,599 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 29,133 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Markus Himmel, Bhavik Mehta
-/
import category_theory.limits.shapes.wide_pullbacks
import category_theory.limits.shapes.binary_products
/-!
# Pullbacks
We define a ca... |
bc142191e26a2f751d93d68eafd363743d2540b3 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/set_theory/cofinality.lean | 5be2daa072695895d3c5d0a0f713b5c12b0e824a | [
"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 | 22,008 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
Cofinality on ordinals, regular cardinals.
-/
import set_theory.ordinal
noncomputable theory
open function cardinal set
open_locale classical
universes u v w
variables... |
6da30c03fe0fc5335276366bae4a9691b17d9519 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/computability/regular_expressions.lean | bcd047edbcfd60748b72e50b2a7a0c64ce3e14f8 | [
"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 | 12,223 | lean | /-
Copyright (c) 2020 Fox Thomson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fox Thomson
-/
import tactic.rcases
import computability.language
/-!
# Regular Expressions
This file contains the formal definition for regular expressions and basic lemmas. Note these... |
1f1e2182882c8971a35af3bf84e751d0f6425ef6 | 2d34dfb0a1cc250584282618dc10ea03d3fa858e | /src/prereqs.lean | 8521f9ee7aeedc666873ea441e3a6871752256cb | [] | no_license | zeta1999/lean-liquid | 61e294ec5adae959d8ee1b65d015775484ff58c2 | 96bb0fa3afc3b451bcd1fb7d974348de2f290541 | refs/heads/master | 1,676,579,150,248 | 1,610,771,445,000 | 1,610,771,445,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 438 | lean | import linear_algebra.matrix
namespace matrix
open equiv
variables {m n R : Type*} [fintype m] [fintype n] [semiring R] (M : matrix m n R)
lemma reindex_linear_equiv_sum_empty_symm :
(reindex_linear_equiv (sum_empty _) (sum_empty _)).symm M = from_blocks M 0 0 0 :=
begin
ext (i|i) (j|j),
{ simp only [sum_empty... |
17013e03f7051de75faa49e1b263693d9a7b61c8 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/probability/martingale/upcrossing.lean | 40c21806a1d45543b35eb24a14a22a8c5833bedd | [
"Apache-2.0"
] | permissive | ramonfmir/mathlib | c5dc8b33155473fab97c38bd3aa6723dc289beaa | 14c52e990c17f5a00c0cc9e09847af16fabbed25 | refs/heads/master | 1,661,979,343,526 | 1,660,830,384,000 | 1,660,830,384,000 | 182,072,989 | 0 | 0 | null | 1,555,585,876,000 | 1,555,585,876,000 | null | UTF-8 | Lean | false | false | 41,694 | lean | /-
Copyright (c) 2022 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
import probability.hitting_time
import probability.martingale.basic
/-!
# Doob's upcrossing estimate
Given a discrete real-valued submartingale $(f_n)_{n \in \mathbb{N}}... |
5da48910872e4a462e77d1f068699a9d195734cb | 94e33a31faa76775069b071adea97e86e218a8ee | /src/ring_theory/localization/away.lean | 94e5a33c55037753132127514852d486e531b341 | [
"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 | 5,564 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Mario Carneiro, Johan Commelin, Amelia Livingston, Anne Baanen
-/
import ring_theory.localization.basic
/-!
# Localizations away from an element
## Main definitions
* `is_loc... |
f290a8e5818a1c87c2a94b0ff82d0bdda97bc234 | 5749d8999a76f3a8fddceca1f6941981e33aaa96 | /src/analysis/convex.lean | 6970523edd49aa271618f63a32fffd687e67351f | [
"Apache-2.0"
] | permissive | jdsalchow/mathlib | 13ab43ef0d0515a17e550b16d09bd14b76125276 | 497e692b946d93906900bb33a51fd243e7649406 | refs/heads/master | 1,585,819,143,348 | 1,580,072,892,000 | 1,580,072,892,000 | 154,287,128 | 0 | 0 | Apache-2.0 | 1,540,281,610,000 | 1,540,281,609,000 | null | UTF-8 | Lean | false | false | 28,122 | lean | /-
Copyright (c) 2019 Alexander Bentkamp. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp, Yury Kudriashov
-/
import analysis.normed_space.basic
import data.complex.basic
import data.set.intervals
import tactic.interactive
import tactic.linarith
impo... |
dc4f251c08dbf0c6bb719870b41295948c82cbc2 | 8e6cad62ec62c6c348e5faaa3c3f2079012bdd69 | /src/data/polynomial/integral_normalization.lean | dc9f2476988b4632044f3c6f3d3b9c21f0a1d867 | [
"Apache-2.0"
] | permissive | benjamindavidson/mathlib | 8cc81c865aa8e7cf4462245f58d35ae9a56b150d | fad44b9f670670d87c8e25ff9cdf63af87ad731e | refs/heads/master | 1,679,545,578,362 | 1,615,343,014,000 | 1,615,343,014,000 | 312,926,983 | 0 | 0 | Apache-2.0 | 1,615,360,301,000 | 1,605,399,418,000 | Lean | UTF-8 | Lean | false | false | 5,306 | 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.algebra_map
import data.polynomial.monic
/-!
# Theory of monic polynomials
We define `integral_no... |
bfb33a73a406600de7b28ba1c1468816cc9dac51 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/data/set/enumerate.lean | 810ae4f412cc0c938a8082a22b076e91434ca7c3 | [
"Apache-2.0"
] | permissive | gebner/mathlib | eab0150cc4f79ec45d2016a8c21750244a2e7ff0 | cc6a6edc397c55118df62831e23bfbd6e6c6b4ab | refs/heads/master | 1,625,574,853,976 | 1,586,712,827,000 | 1,586,712,827,000 | 99,101,412 | 1 | 0 | Apache-2.0 | 1,586,716,389,000 | 1,501,667,958,000 | Lean | UTF-8 | Lean | false | false | 2,393 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl
Enumerate elements of a set with a select function.
-/
import data.set.lattice tactic.wlog
noncomputable theory
open function set
namespace set
section enumerate
par... |
54ea7e70ad8eded0793c5d9631008242a27dc696 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /library/logic/examples/cont.lean | 9e4db4b600299bf4060a85b186ffd2001fb4aaab | [
"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 | 2,768 | 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
Formalization of Theorem 1 from the following paper:
"The inconsistency of a Brouwerian continuity
principle with the Curry–Howard interpretation"
by Martín E... |
51c362915deee3ef34099e05dbe0c75a72aa5890 | ae1e94c332e17c7dc7051ce976d5a9eebe7ab8a5 | /src/Lean/Compiler/IR/PushProj.lean | 19fbec98b6a96e1fa65845cdceb5e206aeed9f44 | [
"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 | 2,110 | 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.Compiler.IR.Basic
import Lean.Compiler.IR.FreeVars
import Lean.Compiler.IR.NormIds
namespace Lean.IR
partial def pushProjs (bs : Array FnBody)... |
1dab99a54c95838a6f50d1994dce62054eeabda5 | 33340b3a23ca62ef3c8a7f6a2d4e14c07c6d3354 | /dlo/reify.lean | 39f95cd31080e1d0c6a198e318845f087660e17e | [] | no_license | lclem/cooper | 79554e72ced343c64fed24b2d892d24bf9447dfe | 812afc6b158821f2e7dac9c91d3b6123c7a19faf | refs/heads/master | 1,607,554,257,488 | 1,578,694,133,000 | 1,578,694,133,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,680 | lean | import .formula
open tactic expr
meta def expr.to_term_lia : expr → tactic expr
| (expr.var k) := return (app `(term_dlo.var) `(k))
| r := return (app `(term_dlo.cst) r)
meta def expr.to_atom_dlo : expr → tactic expr
| `(%%rx1 < %%rx2) :=
do tx1 ← rx1.to_term_lia,
tx2 ← rx2.to_term_lia,
retur... |
fd027aaa8f703e66e520514b5b09a7d37cb25519 | d7189ea2ef694124821b033e533f18905b5e87ef | /galois/tactic.lean | 32b9cd20025f8679dab1f026e8e9e5291c7c981a | [
"Apache-2.0"
] | permissive | digama0/lean-protocol-support | eaa7e6f8b8e0d5bbfff1f7f52bfb79a3b11b0f59 | cabfa3abedbdd6fdca6e2da6fbbf91a13ed48dda | refs/heads/master | 1,625,421,450,627 | 1,506,035,462,000 | 1,506,035,462,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,677 | lean | universes u v
open tactic lean lean.parser
open interactive interactive.types expr
namespace tactic.interactive
private
meta def specialize_get_name : expr → tactic name
| (app f _) := specialize_get_name f
| (local_const _ n _ _) := pure n
| _ := fail "Not an application of a local constant"
/-- The analogue of Co... |
f30b537e01afe63089cf0323e78165f46d83e077 | 534c92d7322a8676cfd1583e26f5946134561b54 | /src/Exercises/01_Propositions/Q0103/Q0003.lean | 25b2993a8a5f00045a1795e3d2cc5ad2b3ffc2a6 | [
"Apache-2.0"
] | permissive | kbuzzard/mathematics-in-lean | 53f387174f04d6077f434e27c407aee9425837f7 | 3fad7bb7e888dabef94921101af8671b78a4304a | refs/heads/master | 1,586,812,457,439 | 1,546,893,744,000 | 1,546,893,744,000 | 163,450,734 | 8 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 80 | lean | theorem prove_P_implies_Q (P Q : Prop) (HQ : Q) : P → Q :=
begin
sorry,
end
|
32763dc370daad3ad6a33bcdee7ed61555d03e45 | 92c6b42948d74fe325c2d88530f1d36da388b2f7 | /src/cvc4/reflect.lean | f57b27574b6e1faefeac7166b702b895acf1a053 | [
"MIT"
] | permissive | riaqn/smtlean | 8ad65055b6c1600cd03b9e345059a3b24419b6d5 | c11768cfb43cd634340b552f5039cba094701a87 | refs/heads/master | 1,584,569,627,940 | 1,535,314,713,000 | 1,535,314,713,000 | 135,333,334 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 8,121 | lean | import ..smtlib
import .sig.sat
import .sig.smt
import .sig.th_base
namespace reflect
attribute [reducible]
meta def pvar := string
attribute [reducible]
meta def atom := string
@[derive decidable_eq]
meta structure lit := (var : pvar) (pol : bool)
attribute [reducible]
meta def clause := list lit
meta inductive... |
8bdabe8b5073a2d7089e2d9aa1b64653d65ca9f9 | 5ae26df177f810c5006841e9c73dc56e01b978d7 | /src/measure_theory/simple_func_dense.lean | b22fe0ec24a802ff84cc740e72c57f298ce42a3b | [
"Apache-2.0"
] | permissive | ChrisHughes24/mathlib | 98322577c460bc6b1fe5c21f42ce33ad1c3e5558 | a2a867e827c2a6702beb9efc2b9282bd801d5f9a | refs/heads/master | 1,583,848,251,477 | 1,565,164,247,000 | 1,565,164,247,000 | 129,409,993 | 0 | 1 | Apache-2.0 | 1,565,164,817,000 | 1,523,628,059,000 | Lean | UTF-8 | Lean | false | false | 15,141 | lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou
Show that each Borel measurable function can be approximated,
both pointwise and in L¹ norm, by a sequence of simple functions.
-/
import measure_theory.l1_space
noncom... |
86987dc2231047df365a4b1c5ab48d990b2cd12f | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/interactive/plainTermGoal.lean | 0c2082187bb480b6fed4b4cc1ae1b8f37bd54c64 | [
"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 | 1,006 | lean | --
example : 0 < 2 :=
Nat.lt_trans Nat.zero_lt_one (Nat.lt_succ_self _)
--^ $/lean/plainTermGoal
--^ $/lean/plainTermGoal
--^ $/lean/plainTermGoal
--^ $/lean/plainTermGoal
--^ $/lean/plainTermGoal
exampl... |
2a0041b7fc4cf1c315964c869204cb0ec193df83 | 367134ba5a65885e863bdc4507601606690974c1 | /src/ring_theory/matrix_algebra.lean | fbdd8201552f15ca0e009a4c8c1cd51194496169 | [
"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 | 6,736 | 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 ring_theory.tensor_product
/-!
We provide the `R`-algebra structure on `matrix n n A` when `A` is an `R`-algebra,
and show `matrix n n A ≃ₐ[R] (A ⊗[R] matrix ... |
bbedef53dd875e72263d818de496e0e3ce7531b4 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/induction_tac1.lean | eb16fca512dafb2cc26bb2fc838064603193e6e7 | [
"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 | 348 | lean | import data.examples.vector
open vector
set_option pp.implicit true
attribute and.rec_on [recursor 4]
example (a b : Prop) (h : a ∧ b) : a :=
begin
induction h using and.rec_on with ha hb,
exact ha
end
example (A : Type) (n : nat) (v w : vector A n) (h : v = w) : w = v :=
begin
induction v with n a t r,
rew... |
109c4daccf16baabe72d8493e16dae8bfd3df615 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/topology/algebra/continuous_affine_map.lean | 70e8688ec37d79477fbeaabdadf57f71656950c0 | [
"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 | 7,745 | 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 linear_algebra.affine_space.affine_map
import topology.continuous_function.basic
import topology.algebra.module.basic
/-!
# Continuous affine maps.
This file defin... |
680706233c1d42f76f792fc35561ae6096e2a28a | b2e508d02500f1512e1618150413e6be69d9db10 | /src/algebra/direct_limit.lean | abda4a7ce8437c16862546ab5fcd1203ea51de3f | [
"Apache-2.0"
] | permissive | callum-sutton/mathlib | c3788f90216e9cd43eeffcb9f8c9f959b3b01771 | afd623825a3ac6bfbcc675a9b023edad3f069e89 | refs/heads/master | 1,591,371,888,053 | 1,560,990,690,000 | 1,560,990,690,000 | 192,476,045 | 0 | 0 | Apache-2.0 | 1,568,941,843,000 | 1,560,837,965,000 | Lean | UTF-8 | Lean | false | false | 25,122 | lean | /-
Copyright (c) 2019 Kenny Lau, Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Chris Hughes
Direct limit of modules, abelian groups, rings, and fields.
See Atiyah-Macdonald PP.32-33, Matsumura PP.269-270
Generalizes the notion of "union", o... |
3072f7aeb5959c8fb06ee0a10bff645f3d454706 | 5d166a16ae129621cb54ca9dde86c275d7d2b483 | /library/init/algebra/ordered_ring.lean | e620304e2a1798d98761f6214cf5e249d021ad8f | [
"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 | 16,376 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura
-/
prelude
import init.algebra.ordered_group init.algebra.ring
/- Make sure instances defined in this file have lower priority than the ones
... |
1e6726de460f13993e5e036cfc13de6dfac58787 | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /stage0/src/Lean/Util/Path.lean | 87bf7d6951c1cbd43cfda7b0cd50dc82d46b5334 | [
"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 | 3,145 | 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
Management of the Lean search path (`LEAN_PATH`), which is a list of
paths containing package roots: an import `A.B.C` resolves to
`path/A/... |
edc9e7408c54a3c6cc6600727bd3cd3ccd495236 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/linear_algebra/determinant.lean | a90810da6de748408b24179337206f0b69fe847c | [
"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 | 6,151 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
-/
import linear_algebra.free_module
import linear_algebra.matrix.basis
import linear_algebra.matrix.diagonal
import linear_alg... |
08b43bae68b315484a43f764ff9415a5a6d43679 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/apply_tac.lean | a1f9ccc10045c360d497eeaf9a3e54ff452893b4 | [
"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 | 984 | lean | import Lean
open Lean
open Lean.Elab
open Lean.Meta
open Lean.Elab.Tactic
example (a b c : Nat) (h₁ : a = b) (h₂ : b = c) : a = c := by
apply Eq.trans _ h₂ -- the metavars created during elaboration become new goals
trace_state
exact h₁
example (a : Nat) : ∃ x, x = a := by
apply Exists.intro -- the goal for... |
0f69ac499aa1599156cf455935869dfe794801ea | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/data/nat/totient.lean | 999f24b10b7ae2282fc046df3438819868081cbc | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 4,065 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import algebra.big_operators.basic
/-!
# Euler's totient function
This file defines [Euler's totient function][https://en.wikipedia.org/wiki/Euler's_totient_function]
`... |
bafb95c0cafebecf9846afdd25ce018575795ac2 | 649957717d58c43b5d8d200da34bf374293fe739 | /src/category_theory/limits/opposites.lean | 67b45004baa15426be5bd0b1a2f84318947c7d9c | [
"Apache-2.0"
] | permissive | Vtec234/mathlib | b50c7b21edea438df7497e5ed6a45f61527f0370 | fb1848bbbfce46152f58e219dc0712f3289d2b20 | refs/heads/master | 1,592,463,095,113 | 1,562,737,749,000 | 1,562,737,749,000 | 196,202,858 | 0 | 0 | Apache-2.0 | 1,562,762,338,000 | 1,562,762,337,000 | null | UTF-8 | Lean | false | false | 3,446 | lean | -- Copyright (c) 2019 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Scott Morrison, Floris van Doorn
import category_theory.limits.limits category_theory.discrete_category
universes v u
open category_theory
open category_theory.functor
open op... |
88bfb70ca103190d0f617ab261e588afbe6bcfb4 | 00de0c30dd1b090ed139f65c82ea6deb48c3f4c2 | /test/norm_num.lean | 7b8c5a3c7957ad201e512c42e2a0f4e5c454d96f | [
"Apache-2.0"
] | permissive | paulvanwamelen/mathlib | 4b9c5c19eec71b475f3dd515cd8785f1c8515f26 | 79e296bdc9f83b9447dc1b81730d36f63a99f72d | refs/heads/master | 1,667,766,172,625 | 1,590,239,595,000 | 1,590,239,595,000 | 266,392,625 | 0 | 0 | Apache-2.0 | 1,590,257,277,000 | 1,590,257,277,000 | null | UTF-8 | Lean | false | false | 11,913 | lean | /-
Copyright (c) 2017 Simon Hudon All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Mario Carneiro
Tests for norm_num
-/
import tactic.norm_num
import data.complex.basic
-- constant real : Type
-- notation `ℝ` := real
-- @[instance] constant real.linear_or... |
c1d04afb406a06d762b4ee13ddfbaf82d16407a6 | cd221f6f26a5eaa584034502e1f2667c8d5c069c | /src/examples.lean | 6c416b1d3c0863bc5202f79eea258382b452060c | [] | no_license | NeilStrickland/lean_hello_world | 8487b02d463cb148c7ae5e44c7ad6bcced8922ab | f2cd1113e16a7e956e194a66cc3101b7ea324b34 | refs/heads/master | 1,587,743,393,549 | 1,550,847,133,000 | 1,550,847,133,000 | 172,084,162 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,534 | lean | /-
This file shows how to use Lean to perform various kinds of
calculations. The primary purpose of Lean is to deal with proofs,
but nonetheless these calculations serve as a gentle introduction
to some aspects of the system.
All comments in this file assume that you have opened it in the
VS Code editor... |
d40a19be6277669aaa5558ede41fcc60933d70e4 | 6fbf10071e62af7238f2de8f9aa83d55d8763907 | /examples/negation_properties.lean | 0ccba209a83a485f82598cc32fe01f921763f14f | [] | no_license | HasanMukati/uva-cs-dm-s19 | ee5aad4568a3ca330c2738ed579c30e1308b03b0 | 3e7177682acdb56a2d16914e0344c10335583dcf | refs/heads/master | 1,596,946,213,130 | 1,568,221,949,000 | 1,568,221,949,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,902 | lean |
theorem same{P: Prop}: (¬P) = (P → false) := rfl
theorem zneqo : 0 ≠ 1.
#check zneqo
theorem zneqoeqzneqo : (0 ≠ 1) = ¬(0 = 1) := rfl
theorem zneqo' : 0 = 1 → false :=
λ h : (0 = 1),
nat.no_confusion h
theorem zneqo'' : ¬ 0 = 1 :=
begin
assume h : (0 = 1),
show false,
from nat.no_confusi... |
a1ed97d3159ea0bf07418620473db4d0d76d3e20 | 1a61aba1b67cddccce19532a9596efe44be4285f | /hott/algebra/category/constructions/hset.hlean | 56b094f2e14a68a746c9a62073a6468b1e561750 | [
"Apache-2.0"
] | permissive | eigengrau/lean | 07986a0f2548688c13ba36231f6cdbee82abf4c6 | f8a773be1112015e2d232661ce616d23f12874d0 | refs/heads/master | 1,610,939,198,566 | 1,441,352,386,000 | 1,441,352,494,000 | 41,903,576 | 0 | 0 | null | 1,441,352,210,000 | 1,441,352,210,000 | null | UTF-8 | Lean | false | false | 3,605 | 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, Jakob von Raumer
Category of hsets
-/
import ..category types.equiv
--open eq is_trunc sigma equiv iso is_equiv
open eq category equiv iso is_equiv is_trunc func... |
fc75c84733c8a8cbe6cbdf50e8655eac99b8a73e | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/combinatorics/simple_graph/adj_matrix.lean | d4640df5f98441c1713fdba5f6b8e2a82f65c56a | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,007 | lean | /-
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Aaron Anderson, Jalex Stark.
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.linear_algebra.matrix
import Mathlib.data.rel
import Mathlib.combinatorics.si... |
3e2a2c63813a84b93b8a6fcaa6341eb7e7b906f0 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/tactic/omega/coeffs.lean | d4a5f10aab4540e199c799a6f9a7a875a5ab8c7b | [
"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 | 10,496 | lean | /-
Copyright (c) 2019 Seul Baek. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Seul Baek
-/
/-
Non-constant terms of linear constraints are represented
by storing their coefficients in integer lists.
-/
import data.list.func
import tactic.ring
import tactic.omega.mi... |
4cfad93c4fd852baad1255b3242cb1051cdabc20 | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /03_Propositions_and_Proofs.org.29.lean | 07d259ab52c5aeb16bdcf6ffbce8ffa64f169d99 | [] | 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 | 322 | lean | /- page 42 -/
import standard
variables p q : Prop
-- BEGIN
theorem and_swap : p ∧ q ↔ q ∧ p :=
iff.intro
(assume H : p ∧ q,
show q ∧ p, from and.intro (and.right H) (and.left H))
(assume H : q ∧ p,
show p ∧ q, from and.intro (and.right H) (and.left H))
check and_swap p q -- p ∧ q ↔ q ∧ p
-- END
|
c8f06d4f7c8c111f8803b6c03e845a443c64f4cb | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/number_theory/divisors.lean | 2b3bfa30404b64df41519e526049d39573f5afeb | [
"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 | 12,235 | 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 algebra.big_operators.order
import tactic
/-!
# Divisor finsets
This file defines sets of divisors of a natural number. This is particularly useful as backgr... |
a7c085dda90cd64fa2c35a36669a77373998526c | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/ring_theory/principal_ideal_domain.lean | 540562b328d2d956254d704369c177f15b1f00a3 | [
"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 | 8,987 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Chris Hughes, Morenikeji Neri
-/
import ring_theory.noetherian
import ring_theory.unique_factorization_domain
/-!
# Principal ideal rings and principal ideal domains
A principal ideal ri... |
3176cddd1d204cfbab13f95ab373846e99951a9a | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/topology/algebra/open_subgroup.lean | 9af24a08d8007638c6879fd592a1de648dde6dd8 | [
"Apache-2.0"
] | permissive | ayush1801/mathlib | 78949b9f789f488148142221606bf15c02b960d2 | ce164e28f262acbb3de6281b3b03660a9f744e3c | refs/heads/master | 1,692,886,907,941 | 1,635,270,866,000 | 1,635,270,866,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,162 | 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 order.filter.lift
import topology.opens
import topology.algebra.ring
open topological_space
open_locale topological_space
/-- The type of open subgroups of a ... |
aeee17a97f66f99d7acd5d40a0dc1991a6e8e0d9 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/category_theory/limits/shapes/biproducts.lean | 6e3f996250607b172400b5d37ac5018ba03b6677 | [
"Apache-2.0"
] | permissive | ramonfmir/mathlib | c5dc8b33155473fab97c38bd3aa6723dc289beaa | 14c52e990c17f5a00c0cc9e09847af16fabbed25 | refs/heads/master | 1,661,979,343,526 | 1,660,830,384,000 | 1,660,830,384,000 | 182,072,989 | 0 | 0 | null | 1,555,585,876,000 | 1,555,585,876,000 | null | UTF-8 | Lean | false | false | 84,598 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Jakob von Raumer
-/
import algebra.group.ext
import category_theory.limits.shapes.finite_products
import category_theory.limits.shapes.binary_products
import category_t... |
55964441f4c48d5acb9c53e5fc88d990a52e03a7 | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /stage0/src/Init/Data/List/BasicAux.lean | bf698d979540b5aa98a9ea1d836ad45d8f348559 | [
"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 | 2,196 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
prelude
import Init.Data.List.Basic
import Init.Util
universes u
namespace List
/- The following functions can't be defined at `Init.Data.List.Basic`, beca... |
8f84f1394ed3664d4eb8af7a73e5ebe38aa8045c | 4fa161becb8ce7378a709f5992a594764699e268 | /src/data/multiset.lean | fdf080eb96f29fcf0a30b16571dfce812c4a0a64 | [
"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 | 135,138 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
Multisets.
-/
import data.list.sort
import data.list.intervals
import data.list.antidiagonal
import data.string.basic
import algebra.group_power
import algebra.or... |
7029c0e7a4d4f761539e622c30642812e7913924 | 0c1546a496eccfb56620165cad015f88d56190c5 | /library/init/data/set.lean | f10af71c1d19a263a5fe54c98e2157cf66ce77e2 | [
"Apache-2.0"
] | permissive | Solertis/lean | 491e0939957486f664498fbfb02546e042699958 | 84188c5aa1673fdf37a082b2de8562dddf53df3f | refs/heads/master | 1,610,174,257,606 | 1,486,263,620,000 | 1,486,263,620,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,648 | 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.logic init.category.functor
universe variables u v
def set (α : Type u) := α → Prop
def set_of {α : Type u} (p : α → Prop) : set α :=
... |
74a8458f8733ded01b1e3c94dd32c39309efde39 | c45b34bfd44d8607a2e8762c926e3cfaa7436201 | /uexp/src/uexp/sql.lean | 14b4ebdd7571fd75e0d43748e8d73445f44a285a | [
"BSD-2-Clause"
] | permissive | Shamrock-Frost/Cosette | b477c442c07e45082348a145f19ebb35a7f29392 | 24cbc4adebf627f13f5eac878f04ffa20d1209af | refs/heads/master | 1,619,721,304,969 | 1,526,082,841,000 | 1,526,082,841,000 | 121,695,605 | 1 | 0 | null | 1,518,737,210,000 | 1,518,737,210,000 | null | UTF-8 | Lean | false | false | 8,643 | lean | import .u_semiring
open tree
constant relation : Schema → Type
constant aggregator : datatype → datatype → Type
constant const : datatype → Type
constant unary: datatype → datatype → Type
constant binary: datatype → datatype → datatype → Type
noncomputable definition Relation (s : Schema) := Tuple s → usr
definition... |
5c8a88b60a06c19534bfe4c294a6eda0315931f1 | 618003631150032a5676f229d13a079ac875ff77 | /src/algebra/category/CommRing/adjunctions.lean | 431ebf9832a1af5dea1c160b44e24772f2069b5a | [
"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 | 1,609 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Johannes Hölzl
-/
import algebra.category.CommRing.basic
import data.mv_polynomial
/-!
Multivariable polynomials on a type is the left adjoint of the
forgetful functor... |
099b2ca7dbf229769ee2cee4682b4af1adedfaf7 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/set/Union_lift.lean | 017854b0d7b2d1a79eda549ef5591703e6558181 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 7,127 | lean | /-
Copyright (c) 2021 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import data.set.lattice
import order.directed
/-!
# Union lift
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathli... |
4f6be7ca006bf7f65911700d8b944439e583d9c8 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/combinatorics/simple_graph/subgraph.lean | bf9ff81a12cb9e1799ef62d3114a7b88254cc5e3 | [
"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 | 13,654 | lean | /-
Copyright (c) 2021 Hunter Monroe. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Hunter Monroe, Kyle Miller, Alena Gusakov
-/
import combinatorics.simple_graph.basic
/-!
# Subgraphs of a simple graph
A subgraph of a simple graph consists of subsets of the graph's ... |
dfff42626972f18cbfc25dfbfd7a09ca6062921c | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/sums/associator.lean | b9c6c6da17307a1366dea1877dd9e5f166f57f29 | [
"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 | 3,602 | 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.sums.basic
/-!
# Associator for binary disjoint union of categories.
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file re... |
66e6955138564c4eece28d66d4b7789bcfd85c9b | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /tests/lean/run/fold.lean | 07303c04cb35144a36b179ed0e5c24050b0a373d | [
"Apache-2.0"
] | permissive | davidmueller13/lean | 65a3ed141b4088cd0a268e4de80eb6778b21a0e9 | c626e2e3c6f3771e07c32e82ee5b9e030de5b050 | refs/heads/master | 1,611,278,313,401 | 1,444,021,177,000 | 1,444,021,177,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 257 | lean | definition id {A : Type} (a : A) := a
example (a b c : nat) : id a = id b → a = b :=
begin
intro H,
fold [id a, id b],
assumption
end
example (a b c : nat) : id a = id b → a = b :=
begin
intro H,
fold (id a),
fold (id b),
assumption
end
|
1bc63bb85b859a54521d41d8d6cb5ab6dac044f6 | bdc27058d2df65f1c05b3dd4ff23a30af9332a2b | /src/tarski.lean | f1c7935d83ea74748409c4e2e8d29008ae5b1a51 | [] | no_license | bakerjd99/leanteach2020 | 19e3dda4167f7bb8785fe0e2fe762a9c53a9214d | 2160909674f3aec475eabb51df73af7fa1d91c65 | refs/heads/master | 1,668,724,511,289 | 1,594,407,424,000 | 1,594,407,424,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,301 | lean | -- Tarski's axioms formalized
import tactic
noncomputable theory
open_locale classical
constant Point : Type -- There is a type called point
-- There is an infinite hierarchy of types
-- Type 0 == Type
-- Type 1
-- Type 2
-- .....
-- This is the Betweenness relation.
-- This is saying "y" is in between "x" and "z"... |
af545905e2cc67f8bc3f8409a466d42b5c6af6bb | 4b846d8dabdc64e7ea03552bad8f7fa74763fc67 | /tests/lean/bad_inaccessible.lean | b8f360242222b24aae7db95c52f7d879569bc952 | [
"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 | 486 | lean | universe variables u
definition f1 : nat → nat → nat
| a .a := a
definition f2 : ∀ (a b c : nat), a = c → c = a
| a b .b rfl := rfl
inductive vec (A : Type u) : nat → Type (max 1 u)
| nil {} : vec 0
| cons : Π {n}, A → vec n → vec (n+1)
definition foo (A : Type u) (f : A → A → A) : Π {n}, vec A n → vec A n → vec A ... |
78a4ec069eca2cf72bbbeb158b0eb0544fb88cb4 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/group/with_one/defs.lean | 18428357b909cc1dd1d6d543a4b6a40d015f9086 | [
"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 | 11,622 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johan Commelin
-/
import order.with_bot
import algebra.ring.defs
/-!
# Adjoining a zero/one to semigroups and related algebraic structures
> THIS FILE IS SYNCHRONIZED... |
ef368eef79d06535b1c5aa49ac376f6b2e1615e9 | c3de33d4701e6113627153fe1103b255e752ed7d | /tools/super/intuit.lean | 354c5b7b2a249c22faf0e4b51a9dc78b3469ecdf | [] | no_license | jroesch/library_dev | 77d2b246ff47ab05d55cb9706a37d3de97038388 | 4faa0a45c6aa7eee6e661113c2072b8840bff79b | refs/heads/master | 1,611,281,606,352 | 1,495,661,644,000 | 1,495,661,644,000 | 92,340,430 | 0 | 0 | null | 1,495,663,344,000 | 1,495,663,344,000 | null | UTF-8 | Lean | false | false | 2,560 | lean | import tools.super.clausifier tools.super.cdcl tools.super.trim
open tactic super expr monad
-- Intuitionistic propositional prover based on
-- SAT Modulo Intuitionistic Implications, Claessen and Rosen, LPAR 2015
namespace intuit
meta def check_model (intuit : tactic unit) : cdcl.solver (option cdcl.proof_term) :=
... |
a66b2ee3ee941b584f4c29ba15b1a9ef426cd7c0 | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/geometry/manifold/basic_smooth_bundle.lean | e58be4301d3d43a31958d366391b7442d2d9cdca | [
"Apache-2.0"
] | permissive | agjftucker/mathlib | d634cd0d5256b6325e3c55bb7fb2403548371707 | 87fe50de17b00af533f72a102d0adefe4a2285e8 | refs/heads/master | 1,625,378,131,941 | 1,599,166,526,000 | 1,599,166,526,000 | 160,748,509 | 0 | 0 | Apache-2.0 | 1,544,141,789,000 | 1,544,141,789,000 | null | UTF-8 | Lean | false | false | 31,533 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import topology.topological_fiber_bundle
import geometry.manifold.smooth_manifold_with_corners
/-!
# Basic smooth bundles
In general, a smooth bundle is a bun... |
44ce6122612e887a03d6d4543fe3d1b1baf73261 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/init/meta/mk_has_sizeof_instance.lean | 1ac13355c52fc8c55fc01319255167cf8e59a198 | [] | 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 | 457 | 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
Helper tactic for constructing has_sizeof instance.
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.meta.rec_util
import Mathlib.Lean3Lib.init.meta.con... |
69492d6ddf2e892d0c0916c4238a2a6eec7b0b7e | 690889011852559ee5ac4dfea77092de8c832e7e | /src/data/int/basic.lean | 51d4470d262069a66cb05db2a66cec4c490af4a9 | [
"Apache-2.0"
] | permissive | williamdemeo/mathlib | f6df180148f8acc91de9ba5e558976ab40a872c7 | 1fa03c29f9f273203bbffb79d10d31f696b3d317 | refs/heads/master | 1,584,785,260,929 | 1,572,195,914,000 | 1,572,195,913,000 | 138,435,193 | 0 | 0 | Apache-2.0 | 1,529,789,739,000 | 1,529,789,739,000 | null | UTF-8 | Lean | false | false | 51,217 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
The integers, with addition, multiplication, and subtraction.
-/
import data.nat.basic data.list.basic algebra.char_zero algebra.order_functions
open nat
namespace int
... |
5b16029c1457672469c790c1b929d67e241812a4 | 432d948a4d3d242fdfb44b81c9e1b1baacd58617 | /src/ring_theory/power_basis.lean | d079ddc7df14a40e42c083affa2f025a093a7f5e | [
"Apache-2.0"
] | permissive | JLimperg/aesop3 | 306cc6570c556568897ed2e508c8869667252e8a | a4a116f650cc7403428e72bd2e2c4cda300fe03f | refs/heads/master | 1,682,884,916,368 | 1,620,320,033,000 | 1,620,320,033,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 15,131 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import field_theory.minpoly
/-!
# Power basis
This file defines a structure `power_basis R S`, giving a basis of the
`R`-algebra `S` as a finite list of powers `1, x, ...... |
e1e14dc41edcd2407c9091220cccae2791e2dd8a | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/linear_algebra/sesquilinear_form.lean | 68e4ce25da91e44226a74cb0d1a1346ade051a5d | [
"Apache-2.0"
] | permissive | agjftucker/mathlib | d634cd0d5256b6325e3c55bb7fb2403548371707 | 87fe50de17b00af533f72a102d0adefe4a2285e8 | refs/heads/master | 1,625,378,131,941 | 1,599,166,526,000 | 1,599,166,526,000 | 160,748,509 | 0 | 0 | Apache-2.0 | 1,544,141,789,000 | 1,544,141,789,000 | null | UTF-8 | Lean | false | false | 8,792 | 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 algebra.module.basic
import ring_theory.maps
/-!
# Sesquilinear form
This file defines a sesquilinear form over a module. The definition requires a ring a... |
730818c5835a13b6e6737eba0aeafe56ee52d9e4 | 4fa161becb8ce7378a709f5992a594764699e268 | /src/data/fin.lean | 7ad0839fafccfe3c19dc3094fa8e97dc55afffce | [
"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 | 29,871 | lean | /-
Copyright (c) 2017 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Keeley Hoek
-/
import data.nat.cast
/-!
# The finite type with `n` elements
`fin n` is the type whose elements are natural numbers smaller than `n`.
This file expand... |
4b94b85c6e1b73b9dc510d4c8cf85934f48fc0e6 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/KyleAlg.lean | e6171660b2edc2a0dff75fe044e917bcd0413143 | [
"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 | 8,443 | lean | import Lean
/- from core:
class OfNat (α : Type u) (n : Nat) where
ofNat : α
class Mul (α : Type u) where
mul : α → α → α
class Add (α : Type u) where
add : α → α → α
-/
class Inv (α : Type u) where
inv : α → α
postfix:max "⁻¹" => Inv.inv
class One (α : Type u) where
one : α
export One (one)
instance... |
6d2ecb1833290ede983c6c1a71ccfaac14401100 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/data/fin/basic.lean | bd02a922c3d66d246c34f89dd72cf37834bd7d9d | [
"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 | 67,581 | lean | /-
Copyright (c) 2017 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Keeley Hoek
-/
import algebra.ne_zero
import data.nat.cast
import order.rel_iso
import tactic.apply_fun
import tactic.localized
/-!
# The finite type with `n` elemen... |
1abc05e4b082c41f4395251a8a631eb1186bb174 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/algebra/ring/equiv.lean | 968535cee52faf25d341e93aee91a3a9ba9268ba | [
"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 | 23,224 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Callum Sutton, Yury Kudryashov
-/
import algebra.big_operators.basic
import algebra.field.basic
import algebra.hom.equiv
import algebra.ring.opposite
/-!
# (Semi)ring ... |
4043d32d9c03092e9e43cb6f8827ddfa386557eb | c777c32c8e484e195053731103c5e52af26a25d1 | /src/data/is_R_or_C/basic.lean | d3907aa627b28e41ab95c20a4d66baf1b8621f7d | [
"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 | 28,002 | 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 data.real.sqrt
import analysis.normed_space.star.basic
import analysis.normed_space.continuous_linear_map
/-!
# `is_R_or_C`: a typeclass for ℝ or ℂ
This fi... |
bb99f49df58e8e08a885df36c69b11d686a71db4 | 7007bb645068e0b6b859aab9da7cf5c1c79e98be | /library/init/data/nat/lemmas.lean | 2691e897a4ad558e954b1331fdbd0f8da14253ac | [
"Apache-2.0"
] | permissive | EdAyers/lean | 7d3fb852380bc386545ebc119b7d03c128c3ce1c | be72c8dc527a062e243a408480f487a55b06cb0a | refs/heads/master | 1,624,443,179,694 | 1,592,837,958,000 | 1,592,837,958,000 | 154,972,348 | 0 | 0 | Apache-2.0 | 1,557,768,267,000 | 1,540,649,772,000 | C++ | UTF-8 | Lean | false | false | 50,384 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad
-/
prelude
import init.data.nat.basic init.data.nat.div init.meta init.algebra.functions
universes u
namespace nat
attribute [pre_smt] nat_zero... |
c9970b5d19cc0ecd682d79c59aa41f488f6a55c5 | 750acab0c635b67751bcfec43c5411aa3941c441 | /qalgs_scratch.lean | fe033b2bfcbda78b7e3a26662941f63931c8ed47 | [] | no_license | nthomas103/lean_work | 912f8e662cdd73ba97f5d3655ddb8a5d2cd204c9 | 7e9785cae2b60a77b41922fd5d5b159a1fae415c | refs/heads/master | 1,586,739,169,355 | 1,455,759,226,000 | 1,455,759,226,000 | 50,978,095 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 12,840 | lean | import data.real data.complex data.list data.nat algebra.module theories.analysis.normed_space
import data.fintype data.finset data.set algebra.group_bigops data.fin
open complex real list nat algebra prod function finset set fintype fin metric_space
structure star_ring [class] (R : Type) extends ring R :=
(star : R →... |
759a15ada45dc1d65c02a3d18c4320adcc9d389a | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/linear_algebra/exterior_algebra.lean | 6512773c275d6ef31a2adb5a9700552b556fc90c | [] | 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 | 9,608 | lean | /-
Copyright (c) 2020 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhangir Azerbayev, Adam Topaz, Eric Wieser.
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebra.ring_quot
import Mathlib.linear_algebra.tensor_algebra
imp... |
8f26a32ab5b47414bd5e6a030748d656ae455afa | 853df553b1d6ca524e3f0a79aedd32dde5d27ec3 | /src/category_theory/category/default.lean | df501cb43d1142f74fd66a0c232b17e3cefa8056 | [
"Apache-2.0"
] | permissive | DanielFabian/mathlib | efc3a50b5dde303c59eeb6353ef4c35a345d7112 | f520d07eba0c852e96fe26da71d85bf6d40fcc2a | refs/heads/master | 1,668,739,922,971 | 1,595,201,756,000 | 1,595,201,756,000 | 279,469,476 | 0 | 0 | null | 1,594,696,604,000 | 1,594,696,604,000 | null | UTF-8 | Lean | false | false | 8,007 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stephen Morgan, Scott Morrison, Johannes Hölzl, Reid Barton
-/
import tactic.basic
import tactic.tidy
/-!
# Categories
Defines a category, as a type class parametrised by the type of... |
66d59ad1337bfaadaa67ed87b04e11a9294c8e6f | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/adjunction/comma.lean | b4668efc61b2e664a77cf4c2eeea1082967bf3d9 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 6,643 | lean | /-
Copyright (c) 2021 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import category_theory.adjunction.basic
import category_theory.punit
import category_theory.structured_arrow
/-!
# Properties of comma categories relating to adjunctions... |
da0a9b872966a2855680901183eeb443e41751e4 | 36c7a18fd72e5b57229bd8ba36493daf536a19ce | /tests/lean/run/blast21.lean | d840fef2f14c38f33c3f5795566c756c5ffebc23 | [
"Apache-2.0"
] | permissive | YHVHvx/lean | 732bf0fb7a298cd7fe0f15d82f8e248c11db49e9 | 038369533e0136dd395dc252084d3c1853accbf2 | refs/heads/master | 1,610,701,080,210 | 1,449,128,595,000 | 1,449,128,595,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 431 | lean | namespace ex
constant typ : Type₁
constant subtype : typ → typ → Prop
constant subtype_refl : ∀ T, subtype T T
constant subtype_trans : ∀ S T U, subtype S T → subtype T U → subtype S U
attribute subtype_refl subtype_trans [backward]
lemma L1 : ∀ T1 T2 T3 T4 T5 T6, subtype T1 T2 → subtype T2 T3 → subtype T3 T4 → s... |
2cdd22527fe14dbd9a82c8f0c4a1027bd19a045e | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/matrix/hadamard.lean | d8ca3ffc18d9133d969082a05103cdd557631de5 | [
"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 | 3,719 | lean | /-
Copyright (c) 2021 Lu-Ming Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lu-Ming Zhang
-/
import linear_algebra.matrix.trace
/-!
# Hadamard product of matrices
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR... |
82676ceb614a3f7711497d4de70f46908b7d45d1 | e00ea76a720126cf9f6d732ad6216b5b824d20a7 | /src/tactic/hint.lean | 370c9acc6a32730cb83a70a6fd4420b6eb65228b | [
"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 | 3,653 | 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.solve_by_elim
import tactic.interactive
namespace tactic
namespace hint
/-- An attribute marking a `tactic unit` or `tactic string` which should be u... |
d086b977ff8d4cc34df6ac5233b3549cfe5df2cb | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/algebraic_geometry/structure_sheaf.lean | b90842d7fbbf5ea5d087b4c7e20d3c1c95abf16c | [
"Apache-2.0"
] | permissive | ayush1801/mathlib | 78949b9f789f488148142221606bf15c02b960d2 | ce164e28f262acbb3de6281b3b03660a9f744e3c | refs/heads/master | 1,692,886,907,941 | 1,635,270,866,000 | 1,635,270,866,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 44,835 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Scott Morrison
-/
import algebraic_geometry.prime_spectrum
import algebra.category.CommRing.colimits
import algebra.category.CommRing.limits
import topology.sheaves.loc... |
a5b9811a8ec63254914780aef5fcbef062e74866 | ae1e94c332e17c7dc7051ce976d5a9eebe7ab8a5 | /tests/lean/run/elseIfConfusion.lean | c2bc4ac7acb7e9c75745da0450ebb0015f2b5a03 | [
"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 | 187 | lean | #lang lean4
def tst (x : Nat) : IO Unit := do
if x == 0 then
IO.println "x is zero"
else
if x == 1 then
IO.println "x is one"
throw $ IO.userError "x is not zero"
#eval tst 0
|
582ac01d605d8299ded23a8f66b620436816b1df | 4727251e0cd73359b15b664c3170e5d754078599 | /src/order/pfilter.lean | e421064d01b2ac450701d9002a5a47df9999cbfe | [
"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 | 4,068 | lean | /-
Copyright (c) 2020 Mathieu Guay-Paquet. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mathieu Guay-Paquet
-/
import order.ideal
/-!
# Order filters
## Main definitions
Throughout this file, `P` is at least a preorder, but some sections
require more structure, su... |
f0dd0038c57b8398c3f62a9d6a6c41911e772eb6 | 290f65d8de0088e3098f612884d54e5b714d7862 | /src/for_mathlib/mv_polynomial.lean | ebdb04e020a7e6adb70fca54325149a822351235 | [
"Apache-2.0"
] | permissive | auhlmann/M4P33 | ec775fd53610427b35f59ef84d469c30511de24e | dc2586aa3a8e0d916fc0795df592a996c89c85bb | refs/heads/master | 1,607,862,664,432 | 1,579,796,968,000 | 1,579,796,968,000 | 234,415,945 | 0 | 0 | Apache-2.0 | 1,579,210,321,000 | 1,579,210,320,000 | null | UTF-8 | Lean | false | false | 11,861 | lean | import data.mv_polynomial
import data.polynomial
-- workaround for the "open_locale at top of file" issue in Lean 3
example : ℕ := 37
open_locale classical
lemma sum.rec_comp_left (X : Type*) (Y : Type*) (β : Type*) (γ : Type*)
(i : β → X) (j : γ → X) (f : X → Y) (x : β ⊕ γ) :
f (sum.rec i j x) = sum.rec (f ∘ i)... |
c1939ff125cd539e7e9a71911c9e53123ff207c9 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/algebraic_geometry/locally_ringed_space.lean | 3e88bfb7a6cdfd28126c0f4253fa95d980c82243 | [
"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 | 10,013 | 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
/-!
# The category of locally ringed spaces
We define (bundled) locally ringed spaces (as `... |
663b5e53d54e6178c4978b60e0a97de63527364d | 6dc0c8ce7a76229dd81e73ed4474f15f88a9e294 | /src/Lean/Meta/Tactic/Simp/Rewrite.lean | 7a28411d4ab9acc9c4591c6f4198d56cd59640d7 | [
"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 | 6,349 | 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.SynthInstance
import Lean.Meta.Tactic.Simp.Types
namespace Lean.Meta.Simp
def synthesizeArgs (lemmaName : Name) (xs : Array Expr) (bis : ... |
9af5ed6379b2b3fa7211df67fe9fb20a52616f71 | f3a5af2927397cf346ec0e24312bfff077f00425 | /src/game/world9/level4.lean | 9240633aae4111bb0fa9dc14a8feb2d5dfd72173 | [
"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 | 3,686 | lean | import game.world9.level3 -- hide
namespace mynat -- hide
/-
# Advanced Multiplication World
## Level 4: `mul_left_cancel`
This is the last of the bonus multiplication levels.
`mul_left_cancel` will be useful in inequality world.
People find this level hard. I have probably had more questions about this
level than ... |
c758ff542630fa10d9cd0d67ad01897aa2d9e8a3 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/linear_algebra/trace.lean | c7e2673e6080aeb23d38d27cf7b6f8cb32efbd0b | [
"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 | 11,416 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen, Antoine Labelle
-/
import linear_algebra.matrix.to_lin
import linear_algebra.matrix.trace
import linear_algebra.contraction
im... |
2c803cc2b66d34d8e2b127e14e3fd48204313e29 | c09f5945267fd905e23a77be83d9a78580e04a4a | /src/algebra/group.lean | c72a6969179b3e6058e12f7f5565a8a4142a3847 | [
"Apache-2.0"
] | permissive | OHIHIYA20/mathlib | 023a6df35355b5b6eb931c404f7dd7535dccfa89 | 1ec0a1f49db97d45e8666a3bf33217ff79ca1d87 | refs/heads/master | 1,587,964,529,965 | 1,551,819,319,000 | 1,551,819,319,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 35,881 | 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
Various multiplicative and additive structures.
-/
import tactic.interactive data.option.defs
section pending_1857
/- Transport multiplicative to add... |
cd5e57de1ec9b21f85b0f7c8377e64d983be6239 | ea4aee6b11f86433e69bb5e50d0259e056d0ae61 | /src/tidy/chain.lean | 66742586c085fce399f5f7c386daac1a483f3a17 | [] | no_license | timjb/lean-tidy | e18feff0b7f0aad08c614fb4d34aaf527bf21e20 | e767e259bf76c69edfd4ab8af1b76e6f1ed67f48 | refs/heads/master | 1,624,861,693,182 | 1,504,411,006,000 | 1,504,411,006,000 | 103,740,824 | 0 | 0 | null | 1,505,553,968,000 | 1,505,553,968,000 | null | UTF-8 | Lean | false | false | 2,988 | 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 .if_then_else
-- import .hash_target
-- open tactic
-- open nat
-- -- FIXME can we set options? It's annoying to have to pass a configuration... |
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