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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
890db783560a670afceac2e6c8c5cd30c13ee27b | 60bf3fa4185ec5075eaea4384181bfbc7e1dc319 | /src/game/sets/sets_level06.lean | 750d01c421f0f9d9dcdd7925ae3f18c694637ef6 | [
"Apache-2.0"
] | permissive | anrddh/real-number-game | 660f1127d03a78fd35986c771d65c3132c5f4025 | c708c4e02ec306c657e1ea67862177490db041b0 | refs/heads/master | 1,668,214,277,092 | 1,593,105,075,000 | 1,593,105,075,000 | 264,269,218 | 0 | 0 | null | 1,589,567,264,000 | 1,589,567,264,000 | null | UTF-8 | Lean | false | false | 1,108 | lean | import game.sets.sets_level05 -- hide
import tactic -- hide
namespace xena -- hide
variable X : Type
open_locale classical -- hide
/-
# Chapter 1 : Sets
## Level 6 : `sdiff` and `neg`
-/
/-
The set-theoretic difference `A \ B` satisfies the following property:
```
lemma mem_sdiff_iff : x ∈ A \ B ↔ x ∈ A ∧ x ∉ ... |
ce502e02e72f736350774fad71a2799afccba848 | 6de8ea38e7f58ace8fbf74ba3ad0bf3b3d1d7ab5 | /solutions2/Problem1/solutions.lean | 54971da0f396f67738d07a9a739b1aff3ed1e5a2 | [] | no_license | KinanBab/CS591K1-Labs | 72f4e2c7d230d4e4f548a343a47bf815272b1f58 | d4569bf99d20c22cd56721024688cda247d1447f | refs/heads/master | 1,587,016,758,873 | 1,558,148,366,000 | 1,558,148,366,000 | 165,329,114 | 5 | 2 | null | 1,550,689,848,000 | 1,547,252,664,000 | TeX | UTF-8 | Lean | false | false | 2,862 | lean | -- Problem 1: filtering elements of a list (30 points)
-- Part A: Implement a filter (5 points)
-- only keeps elements that satisfy the condition F
@[simp] def filter{T} : (T -> bool) -> list T -> list T
| F list.nil := list.nil
| F (list.cons h l') :=
if F h
then list.cons h (filter F l')
else filter F l'
-... |
81e15807e8ae95c8de64ebbf8eb063be0e5c24cf | 41ebf3cb010344adfa84907b3304db00e02db0a6 | /uexp/src/uexp/rules/commonexp.lean | 051c1fc49f641d2675b12c56f85f387d06ea6ce3 | [
"BSD-2-Clause"
] | permissive | ReinierKoops/Cosette | e061b2ba58b26f4eddf4cd052dcf7abd16dfe8fb | eb8dadd06ee05fe7b6b99de431dd7c4faef5cb29 | refs/heads/master | 1,686,483,953,198 | 1,624,293,498,000 | 1,624,293,498,000 | 378,997,885 | 0 | 0 | BSD-2-Clause | 1,624,293,485,000 | 1,624,293,484,000 | null | UTF-8 | Lean | false | false | 1,181 | lean | import ..sql
import ..tactics
import ..u_semiring
import ..extra_constants
import ..meta.ucongr
import ..meta.TDP
import ..meta.cosette_tactics
-- NOTE: this one cannot solved by ucongr, need to be revisited
open Expr
open Proj
open Pred
open SQL
open binary_operators
theorem rule :
forall (Γ s1 : Schema) (a : ... |
8556ed62d5a193dbd3dcbf5fd690bc742203ecff | a0a027e4a00cdb315527e8922122f2a4411fd01c | /6.8-automatically-generated-constructions.lean | 806920c8945c95a24ef5b782b469f43b2e25b5d7 | [] | no_license | spl/lean-tutorial | 96a1ef321d06b9b28d044eeb6bf1ff9a86761a6e | 35c0250004d75d8ae58f6192b649744545116022 | refs/heads/master | 1,610,250,012,890 | 1,454,259,122,000 | 1,454,259,122,000 | 49,971,362 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 593 | lean | inductive tree (A : Type) : Type :=
| leaf : A → tree A
| node : tree A → tree A → tree A
open tree
variable {A : Type}
theorem leaf_ne_node {a : A} {l r : tree A}
(h : leaf a = node l r) : false :=
tree.no_confusion h
theorem leaf_inj {a b : A} (h : leaf a = leaf b) : a = b :=
tree.no_confusion h id
theor... |
8ba84ddeab33d164b0fbbf62b0cd3f1effabdc23 | 618003631150032a5676f229d13a079ac875ff77 | /src/topology/homeomorph.lean | aab3893b1e538b55c128e9662e194c0654e381fb | [
"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 | 8,643 | lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Sébastien Gouëzel, Zhouhang Zhou, Reid Barton
-/
import topology.dense_embedding
open set
variables {α : Type*} {β : Type*} {γ : Type*} {δ : Type*}
/-- ... |
035e6236084f8b6a6587b4ba1958dd05967163c6 | 4e3bf8e2b29061457a887ac8889e88fa5aa0e34c | /lean/love04_functional_programming_exercise_sheet.lean | 81381a57f7024ce4e6c214ef3e92088dc92fc9e1 | [] | no_license | mukeshtiwari/logical_verification_2019 | 9f964c067a71f65eb8884743273fbeef99e6503d | 16f62717f55ed5b7b87e03ae0134791a9bef9b9a | refs/heads/master | 1,619,158,844,208 | 1,585,139,500,000 | 1,585,139,500,000 | 249,906,380 | 0 | 0 | null | 1,585,118,728,000 | 1,585,118,727,000 | null | UTF-8 | Lean | false | false | 5,907 | lean | /- LoVe Exercise 4: Functional Programming -/
import .love04_functional_programming_demo
namespace LoVe
/- Question 1: Reverse of a List -/
/- We define a new accumulator-based version of `reverse`. The first argument
serves as the accumulator. This definition is _tail-recursive_, meaning that
compilers and interp... |
7ba9b611672d93df4c7a3680a10b720fa8303b80 | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/data/dlist/instances.lean | b1d2b8576ede9be71021126a49d1f98cf554eddc | [
"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 | 682 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
Traversable instance for dlists.
-/
import data.dlist category.traversable.equiv category.traversable.instances
namespace dlist
variables (α : Type*)
open function equiv
... |
db13c23572020ca1634a63bc1489d3ee7d6bbd2f | ae1e94c332e17c7dc7051ce976d5a9eebe7ab8a5 | /stage0/src/Init/Coe.lean | a551c061bcc7a68da94f4381cc1db3989c7e47fa | [
"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 | 6,076 | 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
-/
prelude
import Init.Core
universes u v w w'
class Coe (α : Sort u) (β : Sort v) where
coe : α → β
/-- Auxiliary class that contains the transitive clos... |
8e4ee915cb342077ff2061863f3dc84e58ac9f53 | 8e2026ac8a0660b5a490dfb895599fb445bb77a0 | /library/init/data/char/basic.lean | 2cbf476499991f3e9ea43574ff2c11f38f050322 | [
"Apache-2.0"
] | permissive | pcmoritz/lean | 6a8575115a724af933678d829b4f791a0cb55beb | 35eba0107e4cc8a52778259bb5392300267bfc29 | refs/heads/master | 1,607,896,326,092 | 1,490,752,175,000 | 1,490,752,175,000 | 86,612,290 | 0 | 0 | null | 1,490,809,641,000 | 1,490,809,641,000 | null | UTF-8 | Lean | false | false | 729 | 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.fin.basic
open nat
def char_sz : nat := succ 255
def char := fin char_sz
namespace char
/- We cannot use tactic dec_trivial here ... |
a395fc64694b121209a538d4342cc6ba9f13205f | 8e6cad62ec62c6c348e5faaa3c3f2079012bdd69 | /src/data/mv_polynomial/rename.lean | 2a0b539c5274c4ab716e11d7df602c917826be4b | [
"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 | 9,104 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
-/
import data.mv_polynomial.basic
/-!
# Renaming variables of polynomials
This file establishes the `rename` operation on multivariat... |
9e6930cad34e417a64ffce534bab088f46c02af2 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/apply_failure.lean | 245bcbeb6806b6b0316ed2ab1e8aa75edd87db17 | [
"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 | 146 | lean | example (a b c : Prop) : a ∧ b → b ∧ a :=
begin
intro H,
repeat (apply or.elim H | apply and.elim H | intro H | split | assumption)
end
|
9c0f3f61e6f4d186e82ffd374d14cf3b8c9424f1 | dfbb669f3f58ceb57cb207dcfab5726a07425b03 | /vscode-lean4/test/test-fixtures/simple/Test/Version.lean | dd3a5bb806002e5ef06f6243ae6b569973fb4b7c | [
"Apache-2.0"
] | permissive | leanprover/vscode-lean4 | 8bcf7f06867b3c1d42007fe6da863a7a17444dbb | 6ef0bfa668bdeaad0979e6df10551d42fcc01094 | refs/heads/master | 1,692,247,771,767 | 1,691,608,804,000 | 1,691,608,804,000 | 325,845,305 | 64 | 24 | Apache-2.0 | 1,694,176,429,000 | 1,609,435,614,000 | TypeScript | UTF-8 | Lean | false | false | 146 | lean | import Lake
def getLeanVersion :=
Lean.versionString
#eval s!"Lean Version: {getLeanVersion}"
#eval s!"Lake Version: {Lake.versionString}"
|
431118ae33e6e2bfdf8874f69b2ec1de5dc16d85 | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/algebra/group/defs.lean | 33ea9b47fb1dee49d679925c328d02db1ae32004 | [
"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 | 14,416 | 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, Simon Hudon, Mario Carneiro
-/
import algebra.group.to_additive
import tactic.basic
/-!
# Typeclasses for (semi)groups and monoid
In this file we def... |
c48de712b0aa9f4bfa74ecd9ebf1311a21f725f0 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/class6.lean | 4b1bde26727cf8f754845cbfc75fdaaa2077a34f | [
"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 | 308 | lean | open tactic
inductive t1 : Type
| mk1 : t1
inductive t2 : Type
| mk2 : t2
def inhabited_t1 : inhabited t1
:= inhabited.mk t1.mk1
def inhabited_t2 : inhabited t2
:= inhabited.mk t2.mk2
attribute [instance] inhabited_t1
attribute [instance] inhabited_t2
def T : inhabited (t1 × t2)
:= by apply_instance
|
c3106c106bf66d00a277499eb1f5c27272a15cec | d1a52c3f208fa42c41df8278c3d280f075eb020c | /src/Lean/Widget/InteractiveCode.lean | 972fa3541f9ba9a095f521dfa7baf8c9ea205418 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | cipher1024/lean4 | 6e1f98bb58e7a92b28f5364eb38a14c8d0aae393 | 69114d3b50806264ef35b57394391c3e738a9822 | refs/heads/master | 1,642,227,983,603 | 1,642,011,696,000 | 1,642,011,696,000 | 228,607,691 | 0 | 0 | Apache-2.0 | 1,576,584,269,000 | 1,576,584,268,000 | null | UTF-8 | Lean | false | false | 5,009 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wojciech Nawrocki
-/
import Lean.PrettyPrinter.Delaborator.Basic
import Lean.Server.Rpc.Basic
import Lean.Widget.TaggedText
/-! RPC infrastructure for storing and formatting c... |
79eed9a5454f026c2304a94f5dc2fa8cbbdd4317 | 618003631150032a5676f229d13a079ac875ff77 | /src/category_theory/monoidal/types.lean | 82f2ded8dc834dbdb435b7cd3fa0ed30f3aacd28 | [
"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 | 557 | 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_has_finite_products
open category_theory
open tactic
universes u v
namespace category_theory.monoidal
loc... |
cceeb1c139a227d4762928b3fd23b46e8aabadbe | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Compiler/IR/CtorLayout.lean | 94c9d2ed6eedc38e0a47a23c0b5edebd502607a3 | [
"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 | 954 | 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.Environment
import Lean.Compiler.IR.Format
namespace Lean
namespace IR
inductive CtorFieldInfo where
| irrelevant
| object (i : Nat)
| u... |
c454997f88844175dd38d910694a774677013576 | 3446e92e64a5de7ed1f2109cfb024f83cd904c34 | /src/game/world4/level6.lean | cd79d2914d679feb1993065f2f218031175a61d3 | [] | no_license | kckennylau/natural_number_game | 019f4a5f419c9681e65234ecd124c564f9a0a246 | ad8c0adaa725975be8a9f978c8494a39311029be | refs/heads/master | 1,598,784,137,722 | 1,571,905,156,000 | 1,571,905,156,000 | 218,354,686 | 0 | 0 | null | 1,572,373,319,000 | 1,572,373,318,000 | null | UTF-8 | Lean | false | false | 673 | lean | import game.world4.level5 -- hide
namespace mynat -- hide
/-
# World 4 : Power World
## Level 6 of 7: `mul_pow`
You might find `mul_right_comm` useful in this one. Remember `rw mul_right_comm (m ^ t)` will
rewrite the first occurrence of `(m ^ t) * x * y = (m ^ t) * y * x`.
-/
/- Lemma
For all naturals $m$, $n$,... |
b11701f18a5de07ad436b8b4ee8aa47fcfacc940 | 1717bcbca047a0d25d687e7e9cd482fba00d058f | /src/topology/instances/ennreal.lean | 67ff29a58fbbbb11cfd03e78eee88a984e8858cf | [
"Apache-2.0"
] | permissive | swapnilkapoor22/mathlib | 51ad5804e6a0635ed5c7611cee73e089ab271060 | 3e7efd4ecd5d379932a89212eebd362beb01309e | refs/heads/master | 1,676,467,741,465 | 1,610,301,556,000 | 1,610,301,556,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 43,947 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl
-/
import topology.instances.nnreal
/-!
# Extended non-negative reals
-/
noncomputable theory
open classical set filter metric
open_locale classical topological_space e... |
19af6bd7a38afdbd14faac83cc1f970ceb4186c6 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/linear_algebra/vandermonde.lean | 5e64aa124f3fe50755a21a3b135e06500716b264 | [
"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 | 4,281 | 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 algebra.big_operators.fin
import algebra.geom_sum
import group_theory.perm.fin
import linear_algebra.matrix.determinant
import tactic.ring_exp
/-!
# Vandermonde ma... |
d51b90e3a0eaf25315fae67920c467ce26279dff | d796eac6dc113f68ec6fc0579c13e8eae2bdef6c | /Resources/Code/Category+Theory-Github-Topic/monoidal-categories-reboot/src/monoidal_categories_reboot/monoidal_functor.lean | 29d69726e2788763b33d5ae2a01296e1923122fb | [
"Apache-2.0"
] | permissive | paddlelaw/functional-discipline-content-cats | 5a7e13e8adedd96b94f66b0b3cbf1847bc86d7f6 | d93b7aa849b343c384cec40c73ee84a9300004e8 | refs/heads/master | 1,675,541,859,508 | 1,607,251,766,000 | 1,607,251,766,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,883 | lean | -- Copyright (c) 2018 Michael Jendrusch. All rights reserved.
import category_theory.category
import category_theory.functor
import category_theory.products
import category_theory.natural_isomorphism
import .tensor_product
import .monoidal_category
import tactic.rewrite_search
import tactic.interactive
open category_... |
8e0d84ea8c354a91dc93e6e60886159006d54bc7 | 8b9f17008684d796c8022dab552e42f0cb6fb347 | /library/init/reserved_notation.lean | 8867ef0ac167d1186c593d13f5a1f5832b0f4fea | [
"Apache-2.0"
] | permissive | chubbymaggie/lean | 0d06ae25f9dd396306fb02190e89422ea94afd7b | d2c7b5c31928c98f545b16420d37842c43b4ae9a | refs/heads/master | 1,611,313,622,901 | 1,430,266,839,000 | 1,430,267,083,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,409 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: init.reserved_notation
Authors: Leonardo de Moura, Jeremy Avigad
-/
prelude
import init.datatypes
notation `assume` binders `,` r:(scoped f, f) := r
notation `take` binders `... |
9f01f132bf0746bac6a0b2a6524c401e708c23ad | 7a76361040c55ae1eba5856c1a637593117a6556 | /src/lectures/love01_definitions_and_statements_demo.lean | 090ab700506340277480c37ce77b98a4f2720c52 | [] | 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 | 7,553 | lean | import ..lovelib
/-!
# LoVe Demo 1: Definitions and Statements
We introduce the basics of Lean and proof assistants, without trying to carry
out actual proofs yet. We focus on specifying objects and statements of their
intended properties. -/
set_option pp.beta true
set_option pp.generalized_field_notation false
... |
28231f7ecb1e534611862b89b118d33924a14dd4 | 737dc4b96c97368cb66b925eeea3ab633ec3d702 | /src/Lean/Meta/Basic.lean | 59b42c5d2812179e230f64e7832696c39ea5a4a5 | [
"Apache-2.0"
] | permissive | Bioye97/lean4 | 1ace34638efd9913dc5991443777b01a08983289 | bc3900cbb9adda83eed7e6affeaade7cfd07716d | refs/heads/master | 1,690,589,820,211 | 1,631,051,000,000 | 1,631,067,598,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 49,189 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Data.LOption
import Lean.Environment
import Lean.Class
import Lean.ReducibilityAttrs
import Lean.Util.Trace
import Lean.Util.RecDepth
import Lea... |
f80e103f2a2bd0f2f0201f3846024c749c20cbe3 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/measure_theory/integral/mean_inequalities.lean | 970d8d1085a2324fd0ddd0c17bdd872601e8773d | [
"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 | 20,814 | lean | /-
Copyright (c) 2020 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
import measure_theory.integral.lebesgue
import analysis.mean_inequalities
import analysis.mean_inequalities_pow
import measure_theory.function.special_functions.basic
/-... |
884a5f0c10a95fdb0a16ceaf822a3684376065ae | b9a81ebb9de684db509231c4469a7d2c88915808 | /test/super_tests.lean | ac7c3793d14a7b22b781875a5e50549acf3730eb | [] | no_license | leanprover/super | 3dd81ce8d9ac3cba20bce55e84833fadb2f5716e | 47b107b4cec8f3b41d72daba9cbda2f9d54025de | refs/heads/master | 1,678,482,996,979 | 1,676,526,367,000 | 1,676,526,367,000 | 92,215,900 | 12 | 6 | null | 1,513,327,539,000 | 1,495,570,640,000 | Lean | UTF-8 | Lean | false | false | 2,992 | lean | import super
section
open super tactic
example (i : Type) (a b : i) (p : i → Prop) (H : a = b) (Hpa : p a) : true := by do
H ← get_local `H >>= clause.of_classical_proof,
Hpa ← get_local `Hpa >>= clause.of_classical_proof,
a ← get_local `a,
try_sup (λx y, ff) H Hpa 0 0 [0] tt ff ``super.sup_ltr >>= clause.validate,
to... |
57870857fadba4cc469369868a4643938616e279 | efce24474b28579aba3272fdb77177dc2b11d7aa | /src/homotopy_theory/formal/i_category/cofibration_category.lean | 061f7e533e4bc6da67a6e04a92d043cdcbb322ad | [
"Apache-2.0"
] | permissive | rwbarton/lean-homotopy-theory | cff499f24268d60e1c546e7c86c33f58c62888ed | 39e1b4ea1ed1b0eca2f68bc64162dde6a6396dee | refs/heads/lean-3.4.2 | 1,622,711,883,224 | 1,598,550,958,000 | 1,598,550,958,000 | 136,023,667 | 12 | 6 | Apache-2.0 | 1,573,187,573,000 | 1,528,116,262,000 | Lean | UTF-8 | Lean | false | false | 7,600 | lean | import tactic.slice
import category_theory.colimit_lemmas
import category_theory.pushout_fold
import homotopy_theory.formal.cofibrations.cofibration_category
import homotopy_theory.formal.cofibrations.cylinder
import homotopy_theory.formal.cofibrations.factorization_from_cylinder
import homotopy_theory.formal.cofibrati... |
e69166716ea4b448806915cecf50f1f5292de2f5 | 8e6cad62ec62c6c348e5faaa3c3f2079012bdd69 | /src/data/complex/basic.lean | 2cbb0bddfd9086037fc107917c7bc80d540884de | [
"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 | 26,676 | lean | /-
Copyright (c) 2017 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Mario Carneiro
-/
import data.real.sqrt
/-!
# The complex numbers
The complex numbers are modelled as ℝ^2 in the obvious way and it is shown that they form a field
of c... |
dbc4b2bf3afdc47909531dee72041a7cd253885a | f57749ca63d6416f807b770f67559503fdb21001 | /library/data/set/basic.lean | ab7d1701354df5c203047df1ad9af8f2cf8013e0 | [
"Apache-2.0"
] | permissive | aliassaf/lean | bd54e85bed07b1ff6f01396551867b2677cbc6ac | f9b069b6a50756588b309b3d716c447004203152 | refs/heads/master | 1,610,982,152,948 | 1,438,916,029,000 | 1,438,916,029,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,287 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad, Leonardo de Moura
-/
import logic algebra.binary
open eq.ops binary
definition set [reducible] (X : Type) := X → Prop
namespace set
variable {X : Type}
/- membership a... |
36163b7aaa00e20910b301bec856e904603ef7db | c5b07d17b3c9fb19e4b302465d237fd1d988c14f | /src/tmp/zipper.lean | 44ed22ce6cdc5c1d0f11158e0fe2c62b86638d88 | [
"MIT"
] | permissive | skaslev/papers | acaec61602b28c33d6115e53913b2002136aa29b | f15b379f3c43bbd0a37ac7bb75f4278f7e901389 | refs/heads/master | 1,665,505,770,318 | 1,660,378,602,000 | 1,660,378,602,000 | 14,101,547 | 0 | 1 | MIT | 1,595,414,522,000 | 1,383,542,702,000 | Lean | UTF-8 | Lean | false | false | 1,026 | lean | import data.iso
import category.comonad
def U := Type
def UU := Type → Type
axiom deriv : UU → UU
-- The generating function of `zipper f` is T(x) = x f'(x)
def zipper (f : UU) (A) := A × deriv f A
-- The logarithmic derivative of f(x) is g(x) such that f'(x) = f(x) g(x)
-- that is g(x) = (ln f(x))' = f'(x)/f(x)
de... |
55195b6348ed860599925222e4ccf59d5bd10b5c | c31182a012eec69da0a1f6c05f42b0f0717d212d | /src/system_of_complexes/truncate.lean | dcbac5e4f0007b5f34567f10d582ded8296ee8fb | [] | no_license | Ja1941/lean-liquid | fbec3ffc7fc67df1b5ca95b7ee225685ab9ffbdc | 8e80ed0cbdf5145d6814e833a674eaf05a1495c1 | refs/heads/master | 1,689,437,983,362 | 1,628,362,719,000 | 1,628,362,719,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,114 | lean | import category_theory.preadditive.additive_functor
import system_of_complexes.basic
/-!
# Truncation
In this file we define a truncation functors for (systems of) complexes of seminormed groups.
This operation takes a complex `C` indexed by `ℕ`, and creates a new complex whose objects are
* in degree `0`: the co... |
57518249c804cff5798c369151c28552fbf84a0d | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/analysis/normed_space/normed_group_hom.lean | 344d230bae0d6cd4ff4262406922645212c1cbb6 | [
"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 | 22,368 | lean | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import analysis.normed_space.basic
import topology.sequences
/-!
# Normed groups homomorphisms
This file gathers definitions and elementary constructions about bou... |
4dca7da2a15339c7e66cfbcbc23fab9e5d178535 | 649957717d58c43b5d8d200da34bf374293fe739 | /src/category_theory/discrete_category.lean | 0635033c17caaec5bc7d1f42dc540c4a873e0b7e | [
"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 | 2,423 | 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, Floris van Doorn
import data.ulift
import category_theory.opposites category_theory.equivalence
namespace category_theory
universes v₁ v₂ u₁ u₂... |
f7b8e41ae022858522ce244422f9febb2cdea272 | 43390109ab88557e6090f3245c47479c123ee500 | /src/M1F/problem_bank/0504/Q0504.lean | 9a4c410d4e8b6ea57bb7aae58cf412128c9a03a0 | [
"Apache-2.0"
] | permissive | Ja1941/xena-UROP-2018 | 41f0956519f94d56b8bf6834a8d39473f4923200 | b111fb87f343cf79eca3b886f99ee15c1dd9884b | refs/heads/master | 1,662,355,955,139 | 1,590,577,325,000 | 1,590,577,325,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 211 | lean | import algebra.group_power tactic.norm_num algebra.big_operators
def factorial : ℕ → ℕ
| 0 := 1
| (n+1) := (factorial n) * (n+1)
theorem Q4 (n : ℕ) (H : n > 0) : factorial n < 3^n ↔ n ≤ 6 := sorry
|
07d77268afb9809c9268126d9ad996404e93064a | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/geometry/manifold/vector_bundle/fiberwise_linear.lean | d2253f00b568dd2cace2d8d5b88c3ea3f2ffbcf2 | [
"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 | 15,128 | lean | /-
Copyright (c) 2022 Floris van Doorn, Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Heather Macbeth
-/
import geometry.manifold.cont_mdiff
/-! # The groupoid of smooth, fiberwise-linear maps
> THIS FILE IS SYNCHRONIZED WITH MATHL... |
1c9db72effbe9a3e9254d81d26fb55b1b0acb62d | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/topology/topological_fiber_bundle.lean | 9997aceba5bcc23662f9c5c4b22d782e7fd1edd4 | [
"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 | 23,772 | 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.local_homeomorph
/-!
# Fiber bundles
A topological fiber bundle with fiber F over a base B is a space projecting on B for which the
fibers ar... |
e8f5a8f851772f45f83ece23d3a4d9d676c29aec | 8b9f17008684d796c8022dab552e42f0cb6fb347 | /library/algebra/ordered_group.lean | d64ababbfa39f126447bb1bccea8471285325b0b | [
"Apache-2.0"
] | permissive | chubbymaggie/lean | 0d06ae25f9dd396306fb02190e89422ea94afd7b | d2c7b5c31928c98f545b16420d37842c43b4ae9a | refs/heads/master | 1,611,313,622,901 | 1,430,266,839,000 | 1,430,267,083,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 21,329 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.ordered_group
Authors: Jeremy Avigad
Partially ordered additive groups, modeled on Isabelle's library. We could refine the structures,
but we would have to declare more inherit... |
a408f45d8c15e19118950f397fcfe07cee8d5c90 | 87d5955e1100ba73f6b56149b659e85116fa215b | /group_theory/action.lean | bafeb082cd91d633c1bc57d39f435376036875d9 | [
"Apache-2.0"
] | permissive | avigad/leanproved | 4d15a05f8544a67b9f589c5e656358e1485aef3c | 3cf0f5dda3ace82f6b7cdc159528ce3ebaef159f | refs/heads/master | 1,611,368,103,158 | 1,433,589,072,000 | 1,433,589,072,000 | 36,843,899 | 0 | 0 | null | 1,433,385,918,000 | 1,433,385,918,000 | null | UTF-8 | Lean | false | false | 8,188 | lean | /-
Copyright (c) 2015 Haitao Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author : Haitao Zhang
-/
import algebra.group data .extra .hom .perm .finsubg
namespace group
open finset algebra function
local attribute perm.f [coercion]
section def
variable... |
33bd6ec98c260af97bd8e67e7f62fd2189d95e75 | 1dd482be3f611941db7801003235dc84147ec60a | /src/data/equiv/algebra.lean | 1d1475318407e31df148d81376ac761a99685be8 | [
"Apache-2.0"
] | permissive | sanderdahmen/mathlib | 479039302bd66434bb5672c2a4cecf8d69981458 | 8f0eae75cd2d8b7a083cf935666fcce4565df076 | refs/heads/master | 1,587,491,322,775 | 1,549,672,060,000 | 1,549,672,060,000 | 169,748,224 | 0 | 0 | Apache-2.0 | 1,549,636,694,000 | 1,549,636,694,000 | null | UTF-8 | Lean | false | false | 14,441 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import data.equiv.basic data.polynomial linear_algebra.multivariate_polynomial
universes u v w x
variables {α : Type u} {β : Type v} {γ : Type w} {δ : Type x}
names... |
92dfe4c46a0874b35e594c92a9999faca840f4d2 | 9b9a16fa2cb737daee6b2785474678b6fa91d6d4 | /src/category_theory/limits/cones.lean | 0e6d9972821198e64f791857c3f5ca260f47becb | [
"Apache-2.0"
] | permissive | johoelzl/mathlib | 253f46daa30b644d011e8e119025b01ad69735c4 | 592e3c7a2dfbd5826919b4605559d35d4d75938f | refs/heads/master | 1,625,657,216,488 | 1,551,374,946,000 | 1,551,374,946,000 | 98,915,829 | 0 | 0 | Apache-2.0 | 1,522,917,267,000 | 1,501,524,499,000 | Lean | UTF-8 | Lean | false | false | 10,550 | 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
import category_theory.natural_isomorphism
import category_theory.whiskering
import category_theory.const
import category_theory.opposites
import ... |
e675b6828c537b89f08962a78d1d30fff1beedce | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /stage0/src/Lean/Meta/IndPredBelow.lean | f88ce50193c0bd8624f817f328ee7b868923a819 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | EdAyers/lean4 | 57ac632d6b0789cb91fab2170e8c9e40441221bd | 37ba0df5841bde51dbc2329da81ac23d4f6a4de4 | refs/heads/master | 1,676,463,245,298 | 1,660,619,433,000 | 1,660,619,433,000 | 183,433,437 | 1 | 0 | Apache-2.0 | 1,657,612,672,000 | 1,556,196,574,000 | Lean | UTF-8 | Lean | false | false | 25,714 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dany Fabian
-/
import Lean.Meta.Constructions
import Lean.Meta.Transform
import Lean.Meta.Tactic
import Lean.Meta.Match.Match
import Lean.Meta.Reduce
namespace Lean.Meta.IndPr... |
7a3cbbd2fa3fe57657acad15f90dbc932265a7cb | c777c32c8e484e195053731103c5e52af26a25d1 | /src/geometry/manifold/local_invariant_properties.lean | 8e07981ff9550fbfc32236b04a1911169311c246 | [
"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 | 33,826 | lean | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Floris van Doorn
-/
import geometry.manifold.charted_space
/-!
# Local properties invariant under a groupoid
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any ch... |
3c6458db33088f76f64015e62955ecc1252df9d1 | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /tests/lean/diamond5.lean | c08e3189880428b8b082ce61e50765e8e5efdc0c | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | EdAyers/lean4 | 57ac632d6b0789cb91fab2170e8c9e40441221bd | 37ba0df5841bde51dbc2329da81ac23d4f6a4de4 | refs/heads/master | 1,676,463,245,298 | 1,660,619,433,000 | 1,660,619,433,000 | 183,433,437 | 1 | 0 | Apache-2.0 | 1,657,612,672,000 | 1,556,196,574,000 | Lean | UTF-8 | Lean | false | false | 305 | lean | class A (α : Type) where
one : α
zero : α
class B (α : Type) extends A α where
add : α → α → α
class C (α : Type) extends A α where
mul : α → α → α
set_option structureDiamondWarning false
def D.toC (x : Nat) := x
class D (α : Type) extends B α, C α
#check @D.toC_1
|
f58c673c50d7ed01610334b37096de1ef92a4422 | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/explicit2.lean | 35b10020d2ffa792899b160d1bcc966b9ab8ee1f | [
"Apache-2.0"
] | permissive | codyroux/lean0.1 | 1ce92751d664aacff0529e139083304a7bbc8a71 | 0dc6fb974aa85ed6f305a2f4b10a53a44ee5f0ef | refs/heads/master | 1,610,830,535,062 | 1,402,150,480,000 | 1,402,150,480,000 | 19,588,851 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 54 | lean | variable f {A : Type} : A → A
eval (@f Bool)
eval @f |
2b8a553480d81a64860a9ac1ba516b63f45418d8 | 07f5f86b00fed90a419ccda4298d8b795a68f657 | /library/init/meta/name.lean | e86e57ffe361157db527074c3c5289aa54cdb91f | [
"Apache-2.0"
] | permissive | VBaratham/lean | 8ec5c3167b4835cfbcd7f25e2173d61ad9416b3a | 450ca5834c1c35318e4b47d553bb9820c1b3eee7 | refs/heads/master | 1,629,649,471,814 | 1,512,060,373,000 | 1,512,060,469,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,731 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.data.ordering.basic init.coe init.data.to_string
/-- Reflect a C++ name object. The VM replaces it with the C++ implementation. -/
indu... |
91de9e8220457fce35fda5c898e292fbf12f5e89 | 02fbe05a45fda5abde7583464416db4366eedfbf | /library/init/data/nat/basic.lean | 1dd96225de7224dd4dd391c7c95f5ebeca08b7a8 | [
"Apache-2.0"
] | permissive | jasonrute/lean | cc12807e11f9ac6b01b8951a8bfb9c2eb35a0154 | 4be962c167ca442a0ec5e84472d7ff9f5302788f | refs/heads/master | 1,672,036,664,637 | 1,601,642,826,000 | 1,601,642,826,000 | 260,777,966 | 0 | 0 | Apache-2.0 | 1,588,454,819,000 | 1,588,454,818,000 | null | UTF-8 | Lean | false | false | 5,920 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Leonardo de Moura
-/
prelude
import init.logic
notation `ℕ` := nat
namespace nat
inductive less_than_or_equal (a : ℕ) : ℕ → Prop
| refl : less_than_or_equal... |
c53bb823d74c2e2a250cd88a2041b37f48db8a82 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/topology/uniform_space/separation.lean | 3f217a1320fd86283c000db98cb0237fad257d4c | [
"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 | 23,260 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot
-/
import tactic.apply_fun
import data.set.pairwise
import topology.uniform_space.basic
import topology.separation
/-!
# Hausdorff properties of unifor... |
8f45ef3201d4363fd67e56d670b99fd223a777c2 | 77c5b91fae1b966ddd1db969ba37b6f0e4901e88 | /src/data/fin/interval.lean | 95d8fb0c2b96a010c6e49d6e6621ded1eaea94ae | [
"Apache-2.0"
] | permissive | dexmagic/mathlib | ff48eefc56e2412429b31d4fddd41a976eb287ce | 7a5d15a955a92a90e1d398b2281916b9c41270b2 | refs/heads/master | 1,693,481,322,046 | 1,633,360,193,000 | 1,633,360,193,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,062 | lean | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import data.nat.interval
/-!
# Finite intervals in `fin n`
This file proves that `fin n` is a `locally_finite_order` and calculates the cardinality of its
intervals as ... |
b6a36b7c30f4f0b4d83446d821e404c2580434e9 | aa3f8992ef7806974bc1ffd468baa0c79f4d6643 | /tests/lean/run/e2.lean | 0d0f059fc519dd0cf5c4f3031efde57e213774dc | [
"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 | 39 | lean | definition Prop := Type.{0}
check Prop
|
0981be48510bf414f1cfaca4c501154563b76250 | 3f7026ea8bef0825ca0339a275c03b911baef64d | /src/order/filter/basic.lean | 2d0d5237591116fe03d1a2f32e33a3c55911a0e6 | [
"Apache-2.0"
] | permissive | rspencer01/mathlib | b1e3afa5c121362ef0881012cc116513ab09f18c | c7d36292c6b9234dc40143c16288932ae38fdc12 | refs/heads/master | 1,595,010,346,708 | 1,567,511,503,000 | 1,567,511,503,000 | 206,071,681 | 0 | 0 | Apache-2.0 | 1,567,513,643,000 | 1,567,513,643,000 | null | UTF-8 | Lean | false | false | 82,021 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jeremy Avigad
Theory of filters on sets.
-/
import order.galois_connection order.zorn
import data.set.finite
open lattice set
universes u v w x y
local attribute [in... |
5bb44aac7a696771d465cd5cb8aef91064e6b885 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/algebra/category/Module/adjunctions.lean | 2392e6e9b8352e11f224e43148ffd89a45893799 | [
"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 | 10,122 | lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Johan Commelin
-/
import algebra.category.Module.monoidal
import category_theory.monoidal.functorial
import category_theory.monoidal.types
import linear_algebra.direct_... |
ebec6e462b0b7be2542241a741707f24b0d9aed1 | 367134ba5a65885e863bdc4507601606690974c1 | /src/category_theory/limits/preserves/shapes/binary_products.lean | ff3f562bf77266c52a0e8a69a25aeac167a4e07b | [
"Apache-2.0"
] | permissive | kodyvajjha/mathlib | 9bead00e90f68269a313f45f5561766cfd8d5cad | b98af5dd79e13a38d84438b850a2e8858ec21284 | refs/heads/master | 1,624,350,366,310 | 1,615,563,062,000 | 1,615,563,062,000 | 162,666,963 | 0 | 0 | Apache-2.0 | 1,545,367,651,000 | 1,545,367,651,000 | null | UTF-8 | Lean | false | false | 3,462 | 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.binary_products
import category_theory.limits.preserves.basic
/-!
# Preserving binary products
Constructions to relate the notions ... |
e9746df5e9a77b51246cfc7e3f974f57c55a3eab | 4e3bf8e2b29061457a887ac8889e88fa5aa0e34c | /lean/love09_hoare_logic_homework_sheet.lean | 6a82c2640e066820f476109e5e180f9eabd2076f | [] | 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 | 2,539 | lean | /- LoVe Homework 9: Hoare Logic -/
import .love08_operational_semantics_exercise_sheet
import .love09_hoare_logic_demo
namespace LoVe
/- Question 1: Hoare Logic for Dijkstra's Guarded Command Language -/
/- Recall the definition of GCL from exercise 8: -/
#check gcl
namespace gcl
#check big_step
/- The definit... |
f2c8b331e4cd43699dd3e9f861e0f5875f0aba9f | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/algebra/big_operators/finprod.lean | 6ab0a5ecbcbf0d6c68d5266834a9c285856b2c4b | [
"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 | 43,629 | lean | /-
Copyright (c) 2020 Kexing Ying and Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying, Kevin Buzzard, Yury Kudryashov
-/
import algebra.big_operators.order
import algebra.indicator_function
/-!
# Finite products and sums over types and sets
... |
7fbf931f1884424abe8a4be37b3ae58b5b4a8bd1 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/topology/category/Top/basic.lean | 61377c5d6be8f237587d04fd103f189587732e14 | [
"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 | 2,102 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Scott Morrison, Mario Carneiro
-/
import category_theory.concrete_category.unbundled_hom
import topology.continuous_function.basic
import topology.opens
/-!
# Category... |
027547b5a94b648d1e3cc27790f2b843af9fde21 | 75bd9c50a345718d735a7533c007cf45f9da9a83 | /src/measure_theory/l1_space.lean | 42294ebe32b9a5e5112b13273b660a6ca13aaa6b | [
"Apache-2.0"
] | permissive | jtbarker/mathlib | a1a3b1ddc16179826260578410746756ef18032c | 392d3e376b44265ef2dedbd92231d3177acc1fd0 | refs/heads/master | 1,671,246,411,096 | 1,600,801,712,000 | 1,600,801,712,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 36,794 | lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou
-/
import measure_theory.ae_eq_fun
/-!
# Integrable functions and `L¹` space
In the first part of this file, the predicate `integrable` is defined and basic properties o... |
7c37bbf67976e876834418857b14330ebb35f511 | 5d166a16ae129621cb54ca9dde86c275d7d2b483 | /tests/lean/run/aexp.lean | b4dfa099a1d66d6887a164bcee34af32458af879 | [
"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 | 1,712 | lean | namespace imp
open tactic
@[reducible]
def uname := string
inductive aexp
| val : nat → aexp
| var : uname → aexp
| plus : aexp → aexp → aexp
| times : aexp → aexp → aexp
instance : decidable_eq aexp :=
by mk_dec_eq_instance
@[reducible]
def value := nat
def state := uname → value
open aexp
def aval : aexp ... |
99064523c91b0a9f82fb82eb029ab4b05aed983d | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/stream/init.lean | 30c26cbdcd95bbbab4b6acc4f55e88de6fa5f51f | [
"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 | 20,306 | 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
-/
import data.stream.defs
import tactic.ext
import logic.function.basic
/-!
# Streams a.k.a. infinite lists a.k.a. infinite sequences
> THIS FILE IS SYNCHRO... |
0887c042249cd063cc4818833f322e11f7a7b9f7 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/topology/algebra/polynomial.lean | aacfc3ea4b05f7441ab848398f18b8f305cefbc5 | [
"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 | 2,069 | 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
Analytic facts about polynomials.
-/
import topology.algebra.ring
import data.polynomial.div
import data.real.cau_seq
open polynomial is_absolute_value
lemma polynom... |
5e5cdd93657bf104d82c5a512b3b63871cb673b8 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/check_monad_mk.lean | e17c1aaaf87dbb1cd2850f07c30ece43a1aa207a | [
"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 | 59 | lean | #check @monad.mk
#check @functor.mk
#check @applicative.mk
|
1a3d186e5bfae685c55df6e77bed12307a3baffa | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/topology/list.lean | dddaca3c1f0b574d0777a71eb822dc2cbb0339a1 | [
"Apache-2.0"
] | permissive | lacker/mathlib | f2439c743c4f8eb413ec589430c82d0f73b2d539 | ddf7563ac69d42cfa4a1bfe41db1fed521bd795f | refs/heads/master | 1,671,948,326,773 | 1,601,479,268,000 | 1,601,479,268,000 | 298,686,743 | 0 | 0 | Apache-2.0 | 1,601,070,794,000 | 1,601,070,794,000 | null | UTF-8 | Lean | false | false | 8,387 | lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Topology on lists and vectors.
-/
import topology.constructions
open topological_space set filter
open_locale topological_space filter
variables {α : Type*} {β : Type*}
... |
f008237c78e4caf3aafaa644638c998da7e2f7fd | d642a6b1261b2cbe691e53561ac777b924751b63 | /src/topology/metric_space/cau_seq_filter.lean | b8236f2351412734b97984c4bf97c0298ee5dbfa | [
"Apache-2.0"
] | permissive | cipher1024/mathlib | fee56b9954e969721715e45fea8bcb95f9dc03fe | d077887141000fefa5a264e30fa57520e9f03522 | refs/heads/master | 1,651,806,490,504 | 1,573,508,694,000 | 1,573,508,694,000 | 107,216,176 | 0 | 0 | Apache-2.0 | 1,647,363,136,000 | 1,508,213,014,000 | Lean | UTF-8 | Lean | false | false | 19,628 | lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Sébastien Gouëzel
Characterize completeness of metric spaces in terms of Cauchy sequences.
In particular, reconcile the filter notion of Cauchy-ness with the cau_seq ... |
01c341b6389c6dc0711083b119eaf37aebdfa064 | ec5a7ae10c533e1b1f4b0bc7713e91ecf829a3eb | /ijcar16/examples/cc3.lean | 5e2ab496a47481dabd9cfbf8774a66a53fb5bb31 | [
"MIT"
] | permissive | leanprover/leanprover.github.io | cf248934af7c7e9aeff17cf8df3c12c5e7e73f1a | 071a20d2e059a2c3733e004c681d3949cac3c07a | refs/heads/master | 1,692,621,047,417 | 1,691,396,994,000 | 1,691,396,994,000 | 19,366,263 | 18 | 27 | MIT | 1,693,989,071,000 | 1,399,006,345,000 | Lean | UTF-8 | Lean | false | false | 684 | lean | /-
Example/test file for the congruence closure procedure described in the paper:
"Congruence Closure for Intensional Type Theory"
Daniel Selsam and Leonardo de Moura
The tactic `by blast` has been configured in this file to use just
the congruence closure procedure using the command
set_option blast.strategy... |
a042f868c06d67e6c9bc4d147ebfb24543cc98e2 | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/implicit3.lean | 6270f578bbf4cf981c598b561e9e467a1db90b30 | [
"Apache-2.0"
] | permissive | codyroux/lean0.1 | 1ce92751d664aacff0529e139083304a7bbc8a71 | 0dc6fb974aa85ed6f305a2f4b10a53a44ee5f0ef | refs/heads/master | 1,610,830,535,062 | 1,402,150,480,000 | 1,402,150,480,000 | 19,588,851 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 238 | lean | import Int.
print 10 = 20
variable f : Int -> Int -> Int
variable g : Int -> Int -> Int -> Int
notation 10 _ ++ _ : f
notation 10 _ ++ _ : g
set_option pp::implicit true
set_option pp::notation false
print (10 ++ 20)
print (10 ++ 20) 10
|
f9a076258249cdfd3d2119c92604fe3091fd8641 | f618aea02cb4104ad34ecf3b9713065cc0d06103 | /src/field_theory/mv_polynomial.lean | 1107fe1f94df75925c3b0f12f2b417e20a8b8a3d | [
"Apache-2.0"
] | permissive | joehendrix/mathlib | 84b6603f6be88a7e4d62f5b1b0cbb523bb82b9a5 | c15eab34ad754f9ecd738525cb8b5a870e834ddc | refs/heads/master | 1,589,606,591,630 | 1,555,946,393,000 | 1,555,946,393,000 | 182,813,854 | 0 | 0 | null | 1,555,946,309,000 | 1,555,946,308,000 | null | UTF-8 | Lean | false | false | 6,816 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl
Multivariate functions of the form `α^n → α` are isomorphic to multivariate polynomials in
`n` variables.
-/
import linear_algebra.finsupp field_theory.finite
noncomputa... |
7bd49f88521df9b3873ef6e5e1e61586068881f2 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/analysis/convex/basic.lean | afa93ca3e9711a03c00db8ad95b07332e1f6a9a1 | [
"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 | 42,036 | 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, Yaël Dillies
-/
import algebra.order.invertible
import algebra.order.module
import linear_algebra.affine_space.midpoint
import linear_algebra.a... |
2987cc1b98133176f81ee7695b294e68e7bda386 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/1018unknowMVarIssue.lean | 3b36c85e1ac253e73a55b7de5050c8bd6fce8304 | [
"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 | 260 | lean | inductive Fam2 : Type → Type → Type 1 where
| any : Fam2 α α
| nat : Nat → Fam2 Nat Nat
set_option pp.rawOnError true
set_option trace.Elab.info true
example (a : α) (x : Fam2 α β) : β :=
match x with
| Fam2.any => _
| Fam2.nat n => n
|
c42194bd2a9bd7f3784be4c590e0731f4e2d3d70 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/tactic/omega/int/form_auto.lean | 2b66c40a87780ecfc1e82ef7028afe03b28bae7d | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,450 | lean | /-
Copyright (c) 2019 Seul Baek. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Seul Baek
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.tactic.omega.int.preterm
import Mathlib.PostPort
universes l
namespace Mathlib
/-
Linear integer a... |
a07bee8094dd412969fc8ad1901047945a710209 | 8cb37a089cdb4af3af9d8bf1002b417e407a8e9e | /library/init/algebra/order.lean | 201f6574479278a48a0d4cd24105b90f35a7f188 | [
"Apache-2.0"
] | permissive | kbuzzard/lean | ae3c3db4bb462d750dbf7419b28bafb3ec983ef7 | ed1788fd674bb8991acffc8fca585ec746711928 | refs/heads/master | 1,620,983,366,617 | 1,618,937,600,000 | 1,618,937,600,000 | 359,886,396 | 1 | 0 | Apache-2.0 | 1,618,936,987,000 | 1,618,936,987,000 | null | UTF-8 | Lean | false | false | 9,920 | 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.classical init.meta.name init.algebra.classes
/- Make sure instances defined in this file have lower priority than the ones
... |
0441dee1c20707e0c652e51db81cd054be4b8d69 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/topology/algebra/ordered/monotone_convergence.lean | 7a9beeb36bb25df0fc3923572a04a00433fc0201 | [
"Apache-2.0"
] | permissive | AntoineChambert-Loir/mathlib | 64aabb896129885f12296a799818061bc90da1ff | 07be904260ab6e36a5769680b6012f03a4727134 | refs/heads/master | 1,693,187,631,771 | 1,636,719,886,000 | 1,636,719,886,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 12,916 | lean | /-
Copyright (c) 2021 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth, Yury Kudryashov
-/
import topology.algebra.ordered.basic
/-!
# Bounded monotone sequences converge
In this file we prove a few theorems of the form “if the range of... |
f36c4aa4e33797c682350fccd9253309c0f2c105 | 969dbdfed67fda40a6f5a2b4f8c4a3c7dc01e0fb | /src/data/polynomial/coeff.lean | 019a9be24390c5a48efad632ed3a70d13936419f | [
"Apache-2.0"
] | permissive | SAAluthwela/mathlib | 62044349d72dd63983a8500214736aa7779634d3 | 83a4b8b990907291421de54a78988c024dc8a552 | refs/heads/master | 1,679,433,873,417 | 1,615,998,031,000 | 1,615,998,031,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,550 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Scott Morrison, Jens Wagemaker
-/
import data.polynomial.monomial
import data.finset.nat_antidiagonal
/-!
# Theory of univariate polynomials
The theorems ... |
85551a416fddfb4fe90ad249c0901b7a272254d6 | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/univ2.lean | 710088e283c255c2d19ed556ee08cb3dad92e7bc | [
"Apache-2.0"
] | permissive | codyroux/lean0.1 | 1ce92751d664aacff0529e139083304a7bbc8a71 | 0dc6fb974aa85ed6f305a2f4b10a53a44ee5f0ef | refs/heads/master | 1,610,830,535,062 | 1,402,150,480,000 | 1,402,150,480,000 | 19,588,851 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 216 | lean | universe M1 >= 1
universe M2 >= 1
universe Z >= max M1+1 M2+1
print environment
(*
local env = get_environment()
assert(env:get_universe_distance("Z", "M1") == 1)
assert(env:get_universe_distance("Z", "M2") == 1)
*)
|
7f47fdac78001bfc671d4f6a32a531335a67e9d4 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/topology/sheaves/forget.lean | 60e8e07ec58f390ec68f39d69c0cc709ea840d1d | [
"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 | 8,144 | 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.preserves.shapes.products
import topology.sheaves.sheaf
/-!
# Checking the sheaf condition on the underlying presheaf of types.
If `G ... |
6e08df23617f9b9b3b1ece9188d213be715a4da2 | 437dc96105f48409c3981d46fb48e57c9ac3a3e4 | /src/algebra/big_operators.lean | 7e9483523ae4e46f61c7249a080a78f4ae73357e | [
"Apache-2.0"
] | permissive | dan-c-k/mathlib | 08efec79bd7481ee6da9cc44c24a653bff4fbe0d | 96efc220f6225bc7a5ed8349900391a33a38cc56 | refs/heads/master | 1,658,082,847,093 | 1,589,013,201,000 | 1,589,013,201,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 52,133 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import data.finset
import data.nat.enat
import tactic.omega
/-!
# Big operators
In this file we define products and sums indexed by finite sets (specifically, `fin... |
70f2b285836f29ddf8babd317dddeb7303c2da59 | 78630e908e9624a892e24ebdd21260720d29cf55 | /src/logic_first_order/fol_03.lean | 6a06b2837a6ae611caae744794faafe43aa397b4 | [
"CC0-1.0"
] | permissive | tomasz-lisowski/lean-logic-examples | 84e612466776be0a16c23a0439ff8ef6114ddbe1 | 2b2ccd467b49c3989bf6c92ec0358a8d6ee68c5d | refs/heads/master | 1,683,334,199,431 | 1,621,938,305,000 | 1,621,938,305,000 | 365,041,573 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 355 | lean | namespace fol_03
variable A : Type
variables P Q : A → Prop
theorem fol_03 : ((∃ x, P x) → (∀ x, Q x)) → ∀ y, P y → Q y :=
assume h1: (∃ x, P x) → (∀ x, Q x),
assume y: A,
show P y → Q y, from
(assume h2: P y,
have h3: ∃ x, P x, from exists.intro y h2,
have h4: ∀ x, Q x, from h1 h3,
show Q y, from h4 y)
e... |
24336bb34261dbe43b3fda571acb0051ad60b86e | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /hott/init/path.hlean | 8680026961a29effe938960e2fbff4a49b6ceead | [
"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 | 27,972 | hlean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Jakob von Raumer, Floris van Doorn
Ported from Coq HoTT
-/
prelude
import .function .tactic
open function eq
/- Path equality -/
namespace eq
variables {A ... |
15c3a6697a4c975f75e6dcee0fb331151e3d97a2 | 92b50235facfbc08dfe7f334827d47281471333b | /library/data/real/default.lean | 1940618c48462395f53e30524e6a6e56fcd8d447 | [
"Apache-2.0"
] | permissive | htzh/lean | 24f6ed7510ab637379ec31af406d12584d31792c | d70c79f4e30aafecdfc4a60b5d3512199200ab6e | refs/heads/master | 1,607,677,731,270 | 1,437,089,952,000 | 1,437,089,952,000 | 37,078,816 | 0 | 0 | null | 1,433,780,956,000 | 1,433,780,955,000 | null | UTF-8 | Lean | false | false | 182 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Robert Y. Lewis
-/
import .basic .order
|
3c3519e2b60e13b0f755957efee596e3aba87a6c | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/blast_simp_subsingleton2.lean | f8fd199462c800a7cd0c0a46f1bb875fb08c25ef | [
"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 | 312 | lean | import data.unit
open nat unit
constant r {A B : Type} : A → B → A
example (a b c d : unit) : r a b = r c d :=
by simp
example (a b : unit) : a = b :=
by simp
example (a b : unit) : (λ x : nat, a) = (λ y : nat, b) :=
by simp
example (a b : unit) : (λ x : nat, r a b) = (λ y : nat, r b b) :=
by simp
|
b3f35ac18e65734764e6b54e0d9b4650cfe1609f | 206422fb9edabf63def0ed2aa3f489150fb09ccb | /src/category_theory/eq_to_hom.lean | cff79fe70c90b9de0dd7e818e39a9a98c9dae7b3 | [
"Apache-2.0"
] | permissive | hamdysalah1/mathlib | b915f86b2503feeae268de369f1b16932321f097 | 95454452f6b3569bf967d35aab8d852b1ddf8017 | refs/heads/master | 1,677,154,116,545 | 1,611,797,994,000 | 1,611,797,994,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,971 | lean | /-
Copyright (c) 2018 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Scott Morrison
-/
import category_theory.opposites
universes v₁ v₂ u₁ u₂ -- declare the `v`'s first; see `category_theory.category` for an explanation
namespace category_th... |
acef14fefc70bc15313a40d3be3386758b1e8445 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/model_theory/fraisse.lean | 4b8b79d05201fb9d215b7dffdb81c57a6f740b53 | [
"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 | 13,586 | 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 model_theory.finitely_generated
import model_theory.direct_limit
import model_theory.bundled
/-!
# Fraïssé Classes and Fraïssé Limits
This file pertains to ... |
5f6a7413af017571ee6a4a435efad470f810f25d | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/634b.lean | 097699ca2832392b6b9112617c9e6e12bc3749ca | [
"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 | 903 | lean | open nat
namespace foo
section
parameter (X : Type₁)
definition A {n : ℕ} : Type₁ := X
definition B : Type₁ := X
variable {n : ℕ}
check @A n
check foo.A nat
check foo.A (X × B)
check @foo.A (X × B) 10
check @foo.A (@foo.B (@A n)) n
check @foo.A (@foo.B (@foo.A X n)) n
check @foo.A (@foo.B (@foo.A ... |
072329bdff89c9d60c0eaa1ead7532c9b9bdee22 | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/finset/gcd.lean | d8d0ddc7e39ed72a39cf0b5bad0791e659374ce2 | [
"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 | 7,008 | lean | /-
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Aaron Anderson
-/
import data.finset.fold
import data.multiset.gcd
/-!
# GCD and LCM operations on finsets
## Main definitions
- `finset.gcd` - the greatest common denominator of a `... |
0c54829261a844f304e5f037252c71be6461bc83 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/number_theory/cyclotomic/primitive_roots.lean | d7d1218e4a224d0e233686ce388eea4dd3d68a25 | [
"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 | 25,520 | lean | /-
Copyright (c) 2022 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Best, Riccardo Brasca, Eric Rodriguez
-/
import data.pnat.prime
import algebra.is_prime_pow
import number_theory.cyclotomic.basic
import ring_theory.adjoin.power_basis
import ri... |
110851201d377e3f5ae908eeaef448bb91a88afb | 853df553b1d6ca524e3f0a79aedd32dde5d27ec3 | /src/order/zorn.lean | 61c638281a3f0156e3824d41bcc4de21bd61079e | [
"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 | 12,899 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Zorn's lemmas.
Ported from Isabelle/HOL (written by Jacques D. Fleuriot, Tobias Nipkow, and Christian Sternagel).
-/
import data.set.lattice
noncomputable theory
univ... |
27c9e6aca050f33964de5418d97c3ff729520ec8 | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /stage0/src/Lean/Server/Snapshots.lean | 208f650721020fd8c638f75219e436ba9ce8e532 | [
"Apache-2.0"
] | permissive | WojciechKarpiel/lean4 | 7f89706b8e3c1f942b83a2c91a3a00b05da0e65b | f6e1314fa08293dea66a329e05b6c196a0189163 | refs/heads/master | 1,686,633,402,214 | 1,625,821,189,000 | 1,625,821,258,000 | 384,640,886 | 0 | 0 | Apache-2.0 | 1,625,903,617,000 | 1,625,903,026,000 | null | UTF-8 | Lean | false | false | 5,411 | lean | /-
Copyright (c) 2020 Wojciech Nawrocki. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wojciech Nawrocki
-/
import Init.System.IO
import Lean.Elab.Import
import Lean.Elab.Command
/-! One can think of this module as being a partial reimplementation
of Lean.Elab.Fron... |
cd5a85dee841f826e424fe590cde7bfe95fb2acb | d5ecf6c46a2f605470a4a7724909dc4b9e7350e0 | /tests/norm_num.lean | 24039a36afe75a118058570b354a111a5b29f9ea | [
"Apache-2.0"
] | permissive | MonoidMusician/mathlib | 41f79df478987a636b735c338396813d2e8e44c4 | 72234ef1a050eea3a2197c23aeb345fc13c08ff3 | refs/heads/master | 1,583,672,205,771 | 1,522,892,143,000 | 1,522,892,143,000 | 128,144,032 | 0 | 0 | Apache-2.0 | 1,522,892,144,000 | 1,522,890,892,000 | Lean | UTF-8 | Lean | false | false | 1,598 | 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 analysis.real tactic.norm_num
example : 374 + (32 - (2 * 8123) : ℤ) - 61 * 50 = 86 + 32 * 32 - 4 * 5000
∧ 43 ≤ 74 + (33 : ... |
32bfedeb3379fcd5c7378bc03c84a569165d1a75 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/category_theory/limits/bicones.lean | 741c3576f30965c959e870e2e63726ddec9bb4a8 | [
"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 | 4,794 | lean | /-
Copyright (c) 2021 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import category_theory.limits.cones
import category_theory.structured_arrow
import category_theory.fin_category
/-!
# Bicones
Given a category `J`, a walking `bicone J` i... |
e4b1204cc84e1a94a1fcbcce366ab3e3fbadeb9e | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /06_Inductive_Types.org.49.lean | f9a91dcc41349bf4cd3acdd8912816f7e260787a | [] | 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 | 422 | lean | /- page 94 -/
import standard
open nat
variable C : nat → Type
variable fz : C zero
variable fs : Π (n : nat), C n → C (succ n)
eval nat.rec fz fs zero
-- nat.rec_on is defined from nat.rec
eval nat.rec_on zero fz fs
example : nat.rec fz fs zero = fz :=
rfl
variable a : nat
eval nat.rec fz fs (succ a)
eval nat.r... |
79d36099cdbb26cfac27317be2652879c33f1369 | 4bcaca5dc83d49803f72b7b5920b75b6e7d9de2d | /src/Lean/PrettyPrinter/Formatter.lean | e67cc5a877e17378161c9103aaf93d125d567215 | [
"Apache-2.0"
] | permissive | subfish-zhou/leanprover-zh_CN.github.io | 30b9fba9bd790720bd95764e61ae796697d2f603 | 8b2985d4a3d458ceda9361ac454c28168d920d3f | refs/heads/master | 1,689,709,967,820 | 1,632,503,056,000 | 1,632,503,056,000 | 409,962,097 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 21,586 | 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.KeyedDeclsAttribute
import Lean.ParserCompiler.Attribute
import Lean.PrettyPrinter.Basic
/-!
The for... |
0fd89cc9459ee16c702b5fcba02b06c631174d48 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/structInst3.lean | 136a250408cf8ba69b606a8a1f5b37b72495b5b5 | [
"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 | 639 | lean |
universe u
namespace Ex1
structure A (α : Type u) :=
(x : α) (f : α → α := λ x => x)
structure B (α : Type u) extends A α :=
(y : α := f (f x)) (g : α → α → α := λ x y => f x)
structure C (α : Type u) extends B α :=
(z : α := g x y) (x := f z)
end Ex1
open Ex1
def c1 : C Nat := { x := 1 }
#check { c1 with z :=... |
c7ed5d5a223e983318a03a1e028e16dc9fdc10a8 | 432d948a4d3d242fdfb44b81c9e1b1baacd58617 | /src/algebra/module/linear_map.lean | 572797f1c032f1338277979a0eea93a2c4f69031 | [
"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 | 18,637 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nathaniel Thomas, Jeremy Avigad, Johannes Hölzl, Mario Carneiro, Anne Baanen
-/
import algebra.group.hom
import algebra.module.basic
import algebra.group_action_hom
/-!
# Linear maps and... |
264fd74ae3fd626b1b52caf600d58d6077ee80de | b00eb947a9c4141624aa8919e94ce6dcd249ed70 | /stage0/src/Init/Data/Int/Basic.lean | a40b134884b02bad8ad72221a86a998a0ce05891 | [
"Apache-2.0"
] | permissive | gebner/lean4-old | a4129a041af2d4d12afb3a8d4deedabde727719b | ee51cdfaf63ee313c914d83264f91f414a0e3b6e | refs/heads/master | 1,683,628,606,745 | 1,622,651,300,000 | 1,622,654,405,000 | 142,608,821 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,545 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura
The integers, with addition, multiplication, and subtraction.
-/
prelude
import Init.Coe
import Init.Data.Nat.Div
import Init.Data.List.Basic
open Nat
... |
f1be3a800d25d171ff2cd2ab8435408049b6d4e3 | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /archive/imo/imo2006_q3.lean | b9b2f0f3062c9f993f65184dc9413e61ddd0c81b | [
"Apache-2.0"
] | permissive | hikari0108/mathlib | b7ea2b7350497ab1a0b87a09d093ecc025a50dfa | a9e7d333b0cfd45f13a20f7b96b7d52e19fa2901 | refs/heads/master | 1,690,483,608,260 | 1,631,541,580,000 | 1,631,541,580,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,418 | lean | /-
Copyright (c) 2021 Tian Chen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tian Chen
-/
import analysis.special_functions.sqrt
/-!
# IMO 2006 Q3
Determine the least real number $M$ such that
$$
\left| ab(a^2 - b^2) + bc(b^2 - c^2) + ca(c^2 - a^2) \right|
≤ M (a... |
66a0ee58a6e490a1f43e79b4cab0effe417ba705 | 07c6143268cfb72beccd1cc35735d424ebcb187b | /src/algebra/ring.lean | 67b8f006bcf47327dcfcd677d361a6469d7d5110 | [
"Apache-2.0"
] | permissive | khoek/mathlib | bc49a842910af13a3c372748310e86467d1dc766 | aa55f8b50354b3e11ba64792dcb06cccb2d8ee28 | refs/heads/master | 1,588,232,063,837 | 1,587,304,803,000 | 1,587,304,803,000 | 176,688,517 | 0 | 0 | Apache-2.0 | 1,553,070,585,000 | 1,553,070,585,000 | null | UTF-8 | Lean | false | false | 29,195 | 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
-/
import algebra.group.with_one
import deprecated.group
import tactic.norm_cast
/-!
# Properties and homomorphis... |
9108d0052d0156978e5dfca46fabb12e9ab413ac | df7bb3acd9623e489e95e85d0bc55590ab0bc393 | /lean/love02_backward_proofs_exercise_solution.lean | f5e1bb25bbdbcda680078a0a4afc59429fdf75eb | [] | no_license | MaschavanderMarel/logical_verification_2020 | a41c210b9237c56cb35f6cd399e3ac2fe42e775d | 7d562ef174cc6578ca6013f74db336480470b708 | refs/heads/master | 1,692,144,223,196 | 1,634,661,675,000 | 1,634,661,675,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,082 | lean | import .love02_backward_proofs_demo
/- # LoVe Exercise 2: Backward Proofs -/
set_option pp.beta true
set_option pp.generalized_field_notation false
namespace LoVe
namespace backward_proofs
/- ## Question 1: Connectives and Quantifiers
1.1. Carry out the following proofs using basic tactics.
Hint: Some strateg... |
b2b3e6e34a652a28c92f6d45beff5d25c6b54717 | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /stage0/src/Lean/Data/Lsp/Basic.lean | c18758738561caf50933d1e55cfab98ed897ea4f | [
"Apache-2.0"
] | permissive | WojciechKarpiel/lean4 | 7f89706b8e3c1f942b83a2c91a3a00b05da0e65b | f6e1314fa08293dea66a329e05b6c196a0189163 | refs/heads/master | 1,686,633,402,214 | 1,625,821,189,000 | 1,625,821,258,000 | 384,640,886 | 0 | 0 | Apache-2.0 | 1,625,903,617,000 | 1,625,903,026,000 | null | UTF-8 | Lean | false | false | 4,642 | lean | /-
Copyright (c) 2020 Marc Huisinga. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Marc Huisinga, Wojciech Nawrocki
-/
import Lean.Data.Json
import Lean.Data.JsonRpc
/-! Defines most of the 'Basic Structures' in the LSP specification
(https://microsoft.github.io/lan... |
eae8ecdd6189ebb89fbfe8cb27d2f1a185e58653 | cf39355caa609c0f33405126beee2739aa3cb77e | /tmp/debugger_example.lean | b18b57871f4a23360aa4649f9652281dd5fec1db | [
"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 | 235 | lean | import tools.debugger
set_option debugger true
set_option debugger.autorun true
open tactic
local attribute [breakpoint] tactic.constructor
example (p q : Prop) : p → q → p ∧ q :=
by do intros, constructor, repeat assumption
|
0336e79b3e26afa872db76c2c4d4d17dd97fed54 | a45212b1526d532e6e83c44ddca6a05795113ddc | /test/omega.lean | 18dc49c54f41b59d3645f401770f9a1b2a9555b7 | [
"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 | 2,454 | lean | /-
Test cases for omega. Most of the examples are from John Harrison's
Handbook of Practical Logic and Automated Reasoning.
-/
import tactic.omega
example (x : int) : (x = 5 ∨ x = 7) → 2 < x := by omega
example (x : int) : x ≤ -x → x ≤ 0 := by omega
example : ∀ x y : int, (x ≤ 5 ∧ y ≤ 3) → x + y ≤ 8 := by omega
examp... |
472e21d4ba8c05c164860cbdfb7b4305c62e3f93 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/algebra/category/CommRing/basic_auto.lean | b2cc9e06e727c6f18b524b5b8203c7ee7b529449 | [] | 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 | 10,944 | 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, Yury Kudryashov
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebra.category.Group.basic
import Mathlib.data.equiv.rin... |
c3127b283807860069d3e6491d9592e6427a622a | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/algebraic_geometry/prime_spectrum/basic.lean | 543338325925b48320c8ea58a1f91252f7fc51b8 | [
"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 | 30,846 | 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 topology.opens
import ring_theory.ideal.prod
import ring_theory.ideal.over
import linear_algebra.finsupp
import algebra.punit_instances
import ring_theory.nilp... |
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