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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
6f42fbbf4a9934112b77f1feaceb306cf34749b6 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/topology/order/lower_topology.lean | 0ed69357c94a12c601225f35a4d9eb43420c31f8 | [
"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 | 9,420 | lean | /-
Copyright (c) 2023 Christopher Hoskin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Hoskin
-/
import topology.homeomorph
import topology.order.lattice
import order.hom.complete_lattice
/-!
# Lower topology
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
>... |
5d7c75ff00cedda4470e447e96164358a356027a | cb3da1b91380e7462b579b426a278072c688954a | /src/iteration.lean | 46166b9e528db34fa5ca9d976374f074cd374103 | [] | no_license | hcheval/tikhonov-mann | 35c93e46a8287f6479a848a9d4f02013e0bc2035 | 6ab7fcefe9e1156c20bd5d1998a7deabd1eeb018 | refs/heads/master | 1,689,232,126,344 | 1,630,182,255,000 | 1,630,182,255,000 | 399,859,996 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 26,319 | lean | import wspace
import rates
import xu
import utils
open metric_space
local notation `|` x `|` := abs x
@[simp]
def tikhonov_mann {X : Type*} [whyperbolic_space X] (T : X → X) (o : X) (l β : ℕ → ℝ) (x₀ : X) : ℕ → X
| 0 := x₀
| (n + 1) := wmap (l n) (wmap (β n) o (tikhonov_mann n)) (T (wmap (β n) o (tikhonov_mann n))... |
bb17823f259d2ea6150258c766fc8977b23e5bb2 | 83c8119e3298c0bfc53fc195c41a6afb63d01513 | /library/init/function.lean | 81d9fe80ce53ff10b4952b2f54fe1d97d619bea3 | [
"Apache-2.0"
] | permissive | anfelor/lean | 584b91c4e87a6d95f7630c2a93fb082a87319ed0 | 31cfc2b6bf7d674f3d0f73848b842c9c9869c9f1 | refs/heads/master | 1,610,067,141,310 | 1,585,992,232,000 | 1,585,992,232,000 | 251,683,543 | 0 | 0 | Apache-2.0 | 1,585,676,570,000 | 1,585,676,569,000 | null | UTF-8 | Lean | false | false | 5,622 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura, Jeremy Avigad, Haitao Zhang
General operations on functions.
-/
prelude
import init.data.prod init.funext init.logic
universes u₁ u₂ u₃ u₄
namespace function... |
fc78dad6a879ffede029edc0abe900c524add68e | 618003631150032a5676f229d13a079ac875ff77 | /src/set_theory/cardinal.lean | 001e2abdb2f32ce7b9449a071fe9f48bc5aad21e | [
"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 | 45,166 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl, Mario Carneiro
-/
import data.set.countable
import set_theory.schroeder_bernstein
import data.fintype.card
/-!
# Cardinal Numbers
We define cardinal numbers as a quoti... |
150f8a27f78ee0ff052eec35b461ca5dcaa4b2f7 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/topology/metric_space/closeds_auto.lean | b6d5fe61027e171a727afa74cbeedbfbc082ba70 | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,244 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Sébastien Gouëzel
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.topology.metric_space.hausdorff_distance
import Mathlib.analysis.specific_limits
impor... |
c051334d62c93ccdccafe84571285ac6bfc0df3d | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/unfold_crash.lean | 1155aee4f19d5c418893ca3ed198f61f39c957ae | [
"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 | 306 | lean | --
open nat tactic
example (a b : nat) : a = succ b → a = b + 1 :=
by do
H ← intro `H,
try (dunfold_hyp [`nat.succ] H),
dunfold_target [`add, `has_add.add, `has_one.one, `nat.add, `one],
trace_state,
t ← target,
expected ← to_expr ```(a = succ b),
guard (t = expected),
assumption
|
4af3e6d1076b5e37fa5bae074191e47f7a0bfa84 | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/topology/metric_space/pi_Lp.lean | c77fac10786bfd2a3a5f987ab95d9b6deab95700 | [
"Apache-2.0"
] | permissive | ilitzroth/mathlib | ea647e67f1fdfd19a0f7bdc5504e8acec6180011 | 5254ef14e3465f6504306132fe3ba9cec9ffff16 | refs/heads/master | 1,680,086,661,182 | 1,617,715,647,000 | 1,617,715,647,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 15,364 | lean | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import analysis.mean_inequalities
/-!
# `L^p` distance on finite products of metric spaces
Given finitely many metric spaces, one can put the max distance on t... |
1a0a28e169818dff9f8217c8955ad2b2e8875b23 | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/data/finset/basic.lean | 20cda225f8b52b0b87b21eb9a5e8b5d1fd2f2835 | [
"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 | 128,767 | 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, Jeremy Avigad, Minchao Wu, Mario Carneiro
-/
import data.multiset.finset_ops
import tactic.apply
import tactic.monotonicity
import tactic.nth_rewrite
/-!
# F... |
e38fd4a5d165b4722798e4b26951718ae540fb25 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/data/list/duplicate.lean | 8aec14aa72b7a247a2521147155dba7b5d406824 | [
"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 | 4,345 | lean | /-
Copyright (c) 2021 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky, Chris Hughes
-/
import data.fin.basic
import data.list.nodup
/-!
# List duplicates
## Main definitions
* `list.duplicate x l : Prop` is an inductive property that ... |
9441877b1e56a1b708cfd08751547e59b8456861 | fe208a542cea7b2d6d7ff79f94d535f6d11d814a | /src/Dedekind_cuts/jean_lo.lean | 3f04d363d317464cb912acc713f9010c77528bb4 | [] | no_license | ImperialCollegeLondon/M1F_room_342_questions | c4b98b14113fe900a7f388762269305faff73e63 | 63de9a6ab9c27a433039dd5530bc9b10b1d227f7 | refs/heads/master | 1,585,807,312,561 | 1,545,232,972,000 | 1,545,232,972,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,792 | lean | import data.rat data.set.basic order.bounds
structure dedekind_real :=
(carrier: set ℚ)
(nonemp: ∃ a, a ∈ carrier)
(nonrat: ∃ a, a ∉ carrier)
(down: ∀ p ∈ carrier, ∀ q, q < p → q ∈ carrier)
(init: ∀ p ∈ carrier, ∀ q ∉ carrier, p < q)
notation `ℝ` := dedekind_real
instance: has_coe ℝ (set ℚ) := ⟨λ r, r.carrier⟩
name... |
58cbc474a499fc39ca1461813ab6c48134101259 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/noncomputable_example.lean | de4542d7ef3c984f0453b36c3d598f4bd2940205 | [
"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 | 396 | lean | universe u
open classical psum
variables (A : Type u) (h : (A → false) → false)
-- both noncomputable example...
noncomputable example : A :=
match type_decidable A with
| (inl ha) := ha
| (inr hna) := false.rec _ (h hna)
end
-- ... and noncomputable theory should work
noncomputable theory
example : A :=
match type_... |
3aef0c0a96e1f91d3934b884d20499e958da044c | c777c32c8e484e195053731103c5e52af26a25d1 | /src/data/finset/n_ary.lean | 3a0db131eab7b99e1bcdca12111b69be2216e544 | [
"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 | 20,035 | lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import data.finset.prod
import data.set.finite
/-!
# N-ary images of finsets
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a correspondi... |
d9cee38a14320c28d08bf26085de8ce672378a19 | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /src/Lean/Data/Json/FromToJson.lean | 34dc91118be777a5d243acc9e4f60f68fde999ad | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | EdAyers/lean4 | 57ac632d6b0789cb91fab2170e8c9e40441221bd | 37ba0df5841bde51dbc2329da81ac23d4f6a4de4 | refs/heads/master | 1,676,463,245,298 | 1,660,619,433,000 | 1,660,619,433,000 | 183,433,437 | 1 | 0 | Apache-2.0 | 1,657,612,672,000 | 1,556,196,574,000 | Lean | UTF-8 | Lean | false | false | 5,325 | lean | /-
Copyright (c) 2019 Gabriel Ebner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner, Marc Huisinga
-/
import Lean.Data.Json.Basic
import Lean.Data.Json.Printer
namespace Lean
universe u
class FromJson (α : Type u) where
fromJson? : Json → Except Str... |
9e6075248104a7dc2dca4cc643ad99d57808652e | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/topology/basic.lean | 55d0359b83892fcb239f9b9741421717f52bd520 | [
"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 | 55,957 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Jeremy Avigad
-/
import order.filter.ultrafilter
import order.filter.partial
import data.support
/-!
# Basic theory of topological spaces.
The main de... |
54cf9dd7fbc956d23b43dd22d186c3b27e465bfe | 01ae0d022f2e2fefdaaa898938c1ac1fbce3b3ab | /categories/full_subcategory.lean | 418b03f2e5a565bd150ad8c94376eadbf2989a27 | [] | no_license | PatrickMassot/lean-category-theory | 0f56a83464396a253c28a42dece16c93baf8ad74 | ef239978e91f2e1c3b8e88b6e9c64c155dc56c99 | refs/heads/master | 1,629,739,187,316 | 1,512,422,659,000 | 1,512,422,659,000 | 113,098,786 | 0 | 0 | null | 1,512,424,022,000 | 1,512,424,022,000 | null | UTF-8 | Lean | false | false | 1,076 | 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 .functor
open categories.functor
namespace categories
definition {u v w} FullSubcategory ( C : Category.{u v} ) ( Z : C.Obj → Sort w ) : Category.{(max ... |
e97269131f3c7622bb8d06aab37a5ae272a03e6d | df561f413cfe0a88b1056655515399c546ff32a5 | /5-advanced-proposition-world/l9.lean | 9822b1dc9207fa8c1b87660e631b7ac0e1c8505a | [] | no_license | nicholaspun/natural-number-game-solutions | 31d5158415c6f582694680044c5c6469032c2a06 | 1e2aed86d2e76a3f4a275c6d99e795ad30cf6df0 | refs/heads/main | 1,675,123,625,012 | 1,607,633,548,000 | 1,607,633,548,000 | 318,933,860 | 3 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 149 | lean | lemma contra (P Q : Prop) : (P ∧ ¬ P) → Q :=
begin
intro h,
cases h with p notp,
rw not_iff_imp_false at notp,
exfalso,
apply notp,
exact p,
end |
ea6ae52e36c3633b2aaab942c842f385836c103f | 6dc0c8ce7a76229dd81e73ed4474f15f88a9e294 | /stage0/src/Lean/Elab/Deriving/Util.lean | 3c4ef885aa1df3c458406af174f9d16b05f56395 | [
"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 | 5,768 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Parser.Term
import Lean.Elab.Term
namespace Lean.Elab.Deriving
open Meta
def implicitBinderF := Parser.Term.implicitBinder
def instBinderF ... |
2b74801163179ae9c1dec7dd66f3bd1e123efc19 | d796eac6dc113f68ec6fc0579c13e8eae2bdef6c | /Resources/Code/Category+Theory-Github-Topic/monoidal-categories-reboot/src/monoidal_categories_reboot/braided_monoidal_category.lean | 9f4a444873f8ee53e0a13115dee754f0b540ce1f | [
"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 | 3,017 | lean | import category_theory.category
import category_theory.functor
import category_theory.products
import category_theory.natural_isomorphism
import .monoidal_category
open category_theory
open tactic
universes v u
open category_theory.category
open category_theory.functor
open category_theory.prod
open category_theory.f... |
c8d1dc97c06e7bcb572671f507783162298ce32a | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/tactic/elide.lean | 14e2eb2f31b722d091229c81caee4523cffdbe08 | [
"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 | 2,175 | lean | import logic.basic tactic.basic
namespace tactic
namespace elide
meta def replace : ℕ → expr → tactic expr
| 0 e := do
t ← infer_type e,
expr.sort u ← infer_type t,
return $ (expr.const ``hidden [u]).app t e
| (i+1) (expr.app f x) := do
f' ← replace (i+1) f,
x' ← replace i x,
return (f' x')
| (i+1) (expr.... |
cc0b648f85fb1034896a66a08812c2a63febd597 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/simplifier11.lean | bf8907258244440dda202b8ecda9f86bc41396ad | [
"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 | 1,957 | lean | -- Conditional congruence
import logic.connectives logic.quantifiers
-- TODO(dhs): add this to the library
lemma not_false_true [simp] : (¬ false) ↔ true := sorry
namespace if_congr
constants {A : Type} {b c : Prop} (dec_b : decidable b) (dec_c : decidable c)
{x y u v : A} (h_c : b ↔ c) (h_t : x = u) (h_e :... |
3b871f29ccc61bea9722a92c328b78833da0f5ae | 7a468d7c7c0949ab8b191bb62ff6d4d2af9f3917 | /test/inconsistent_context.lean | e1da3c5b3921db4d9193b154eb37770bcd9a05d9 | [
"Apache-2.0"
] | permissive | seanpm2001/LeanProver_SMT2_Interface | c15b2fba021c406d965655b182eef54a14121b82 | 7ff0ce248b68ea4db2a2d4966a97b5786da05ed7 | refs/heads/master | 1,688,599,220,366 | 1,547,825,187,000 | 1,547,825,187,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 130 | lean | import smt2
import .test_tactics
lemma P_and_not_P_false (P : Prop) (p : P) (np : not P) : false :=
begin
intros,
z3
end
|
c1a116f977f51fd169eb74a8c1d8c65c3215d044 | 6f510b1ed724f95a55b7d26a8dcd13e1264123dd | /src/page01.lean | fdb80378e32a92a8e7a8d7bd9bd99ca745a3ff94 | [] | no_license | jcommelin/oberharmersbach2019 | adaf2e54ba4eff7c178c933978055ff4d6b0593b | d2cdf780a10baa8502a9b0cae01c7efa318649a6 | refs/heads/master | 1,587,558,516,731 | 1,550,558,213,000 | 1,550,558,213,000 | 170,372,753 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 241 | lean | import data.real.basic
/- Type theory -/
#check "hello, world!"
#check 3
#check ℤ
#check 3 = 4
#check false
#check ℤ = "hi"
#check real.sqrt
--- --- --- --- --- --- --- --- --- --- --- --- --- ---
#eval 1 + 1
#eval real.sqrt 2 |
8864e5c9f1c69cecef106edba3a954f944b85a80 | 05b503addd423dd68145d68b8cde5cd595d74365 | /src/tactic/lint/default.lean | 54231d2e1c3e17ff9bc30f6dfa42354b35a35fcf | [
"Apache-2.0"
] | permissive | aestriplex/mathlib | 77513ff2b176d74a3bec114f33b519069788811d | e2fa8b2b1b732d7c25119229e3cdfba8370cb00f | refs/heads/master | 1,621,969,960,692 | 1,586,279,279,000 | 1,586,279,279,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,754 | lean | /-
Copyright (c) 2020 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Robert Y. Lewis, Gabriel Ebner
-/
import tactic.lint.frontend
tactic.lint.simp
tactic.lint.type_classes
tactic.lint.misc
open tactic
add_tactic_doc
{ name ... |
8db00c94099022999148dac6b225896dfe401551 | f3a5af2927397cf346ec0e24312bfff077f00425 | /src/mynat/definition.lean | 4615797071776cdbabb38c8fe88df4f444b94e84 | [
"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 | 846 | lean | import tactic.structure_helper
import tactic.nat_num_game
/-
mynat/definition.lean -- definition of mynat.
Supplies:
constants zero : mynat and one : mynat
function S : mynat → mynat
notation 0 for zero and 1 for one.
The below code will be *invisible to the player*
-/
-- definition of "the natural numb... |
a6aa1f9ee4d7f03dd14bdfa3cef52e8d352ae5c3 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/category_theory/limits/shapes/normal_mono.lean | 80ddba688e31b4bc3359a1825ab48a113243f063 | [
"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 | 8,866 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Bhavik Mehta
-/
import category_theory.limits.shapes.regular_mono
import category_theory.limits.shapes.kernels
import category_theory.limits.preserves.basic
/-!
# Defi... |
5f580f349e321d59e500fc59071e6f53e00ea42d | 3dd1b66af77106badae6edb1c4dea91a146ead30 | /tests/lean/run/root.lean | a28906a1fc14547c4c75abd0b8c3f11943845f9e | [
"Apache-2.0"
] | permissive | silky/lean | 79c20c15c93feef47bb659a2cc139b26f3614642 | df8b88dca2f8da1a422cb618cd476ef5be730546 | refs/heads/master | 1,610,737,587,697 | 1,406,574,534,000 | 1,406,574,534,000 | 22,362,176 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 249 | lean | import standard
using num
variable foo : Prop
namespace N1
variable foo : Prop
check N1.foo
check _root_.foo
namespace N2
variable foo : Prop
check N1.foo
check N1.N2.foo
print raw foo
print raw _root_.foo
end
end
|
ac0b6b5d8ed0569a080b13bec88b37513ab050e2 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/analysis/normed/group/quotient.lean | a8f5f4110438c65ee373ac10cdeccf9071785883 | [
"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 | 21,911 | lean | /-
Copyright (c) 2021 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Riccardo Brasca
-/
import analysis.normed.group.hom
/-!
# Quotients of seminormed groups
For any `semi_normed_group M` and any `S : add_subgroup M`, we provide a `sem... |
77f6078b8f9acb3e27be4f2465e19219319d96dc | 94e33a31faa76775069b071adea97e86e218a8ee | /src/measure_theory/function/continuous_map_dense.lean | 80df4cea7918fdc68cc889be2a64a6bfa16a12b1 | [
"Apache-2.0"
] | permissive | urkud/mathlib | eab80095e1b9f1513bfb7f25b4fa82fa4fd02989 | 6379d39e6b5b279df9715f8011369a301b634e41 | refs/heads/master | 1,658,425,342,662 | 1,658,078,703,000 | 1,658,078,703,000 | 186,910,338 | 0 | 0 | Apache-2.0 | 1,568,512,083,000 | 1,557,958,709,000 | Lean | UTF-8 | Lean | false | false | 10,073 | lean | /-
Copyright (c) 2021 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
import measure_theory.measure.regular
import measure_theory.function.simple_func_dense_lp
import topology.urysohns_lemma
import measure_theory.function.l1_space
/... |
f1c34f3c3aa0f11ed12ea5925a97ae3a5b95e401 | e00ea76a720126cf9f6d732ad6216b5b824d20a7 | /src/data/real/nnreal.lean | 0474c82c98b21d092a36ca2bf328eeee79362f45 | [
"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 | 24,483 | lean | /-
Copyright (c) 2018 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
Nonnegative real numbers.
-/
import data.real.basic order.lattice algebra.field
noncomputable theory
open_locale classical
/-- Nonnegative real numbers. -/
def nnrea... |
8d942ebf72f91eab96cfc8b734b53a82131bd5ea | a7dd8b83f933e72c40845fd168dde330f050b1c9 | /src/category_theory/instances/Top/default.lean | 59d1ec93de610dc9ec46a3e3a59dac3e2e969dad | [
"Apache-2.0"
] | permissive | NeilStrickland/mathlib | 10420e92ee5cb7aba1163c9a01dea2f04652ed67 | 3efbd6f6dff0fb9b0946849b43b39948560a1ffe | refs/heads/master | 1,589,043,046,346 | 1,558,938,706,000 | 1,558,938,706,000 | 181,285,984 | 0 | 0 | Apache-2.0 | 1,568,941,848,000 | 1,555,233,833,000 | Lean | UTF-8 | Lean | false | false | 397 | 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.instances.Top.basic
import category_theory.instances.Top.limits
import category_theory.instances.Top.epi_mono
import category_theory.instan... |
c3c68c525e511275bb36a00ffae56959fdb8ada8 | b3fced0f3ff82d577384fe81653e47df68bb2fa1 | /src/data/nat/parity.lean | 5c2f98aecdaeb597b915ccd0e5ba08cdfb67ce5b | [
"Apache-2.0"
] | permissive | ratmice/mathlib | 93b251ef5df08b6fd55074650ff47fdcc41a4c75 | 3a948a6a4cd5968d60e15ed914b1ad2f4423af8d | refs/heads/master | 1,599,240,104,318 | 1,572,981,183,000 | 1,572,981,183,000 | 219,830,178 | 0 | 0 | Apache-2.0 | 1,572,980,897,000 | 1,572,980,896,000 | null | UTF-8 | Lean | false | false | 2,714 | lean | /-
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
The `even` predicate on the natural numbers.
-/
import .modeq
namespace nat
@[simp] theorem mod_two_ne_one {n : nat} : ¬ n % 2 = 1 ↔ n % 2 = 0 :=
by cases mod_two_eq_ze... |
650ff347abd0ba53d1db3b462282a6889848f3ba | 3dc4623269159d02a444fe898d33e8c7e7e9461b | /.github/workflows/geo/src/over.lean | 401dd205093f494573e5cff01cb878e4de3923f3 | [] | no_license | Or7ando/lean | cc003e6c41048eae7c34aa6bada51c9e9add9e66 | d41169cf4e416a0d42092fb6bdc14131cee9dd15 | refs/heads/master | 1,650,600,589,722 | 1,587,262,906,000 | 1,587,262,906,000 | 255,387,160 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,680 | lean | import category_theory.comma
import category_theory.adjunction.basic
import category_theory.limits.shapes
import category_theory.epi_mono
import category_theory.limits.over
import cartesian_closed
import pullbacks
import comma
import to_mathlib
/-!
# Properties of the over category.
We can interpret the forgetful fun... |
9b9395d9cc59189976458919aed60a5d036ac125 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/data/finset.lean | 8ed3d1baa68317957aa19937761d9494ff94e5cc | [
"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 | 116,002 | 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, Jeremy Avigad, Minchao Wu, Mario Carneiro
Finite sets.
-/
import logic.embedding algebra.order_functions
data.multiset data.sigma.basic data.set.lattice
t... |
15fd98fbbbbf252a158c86573e534131a93242b1 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/measure_theory/function/jacobian.lean | c36c5707b59b6fb4754e0423a7a7ad568c0e3abc | [
"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 | 68,583 | lean | /-
Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import measure_theory.covering.besicovitch_vector_space
import measure_theory.measure.haar_lebesgue
import analysis.normed_space.pointwise
import measure_theory... |
4dc916fda473ffc6d4a9c2f713e89041f15304eb | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/category_theory/limits/shapes/binary_products.lean | 76698c5a4a4829c44fdb315f4002b676a00a27e8 | [
"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 | 41,952 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Bhavik Mehta
-/
import category_theory.limits.shapes.terminal
import category_theory.discrete_category
import category_theory.epi_mono
import category_theory.over
/-!
... |
cdfba66c8ec1fed109c7f9489a45afdf95698879 | 4fc5f02f6ed9423b87987589bcc202f985d7e9ff | /src/game/intro.lean | 3a2f77739e75c6b6ee301a39d2743d63a1ae77e4 | [
"Apache-2.0"
] | permissive | grthomson/natural_number_game | 2937533df0b83e73e6a873c0779ee21e30f09778 | 0a23a327ca724b95406c510ee27c55f5b97e612f | refs/heads/master | 1,599,994,591,355 | 1,588,869,073,000 | 1,588,869,073,000 | 222,750,177 | 0 | 0 | Apache-2.0 | 1,574,183,960,000 | 1,574,183,960,000 | null | UTF-8 | Lean | false | false | 2,992 | lean | /-
# The Natural Number Game, version 1.3.2
## By Kevin Buzzard and Mohammad Pedramfar.
# What is this game?
Welcome to the natural number game -- a part-book part-game which shows the power of induction.
Blue nodes on the graph are ones that you are ready to enter. Grey nodes you should stay away
from -- a grey no... |
190bd9ea1642a1f5178544109f1931185793f146 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/topology/homotopy/basic.lean | ce67a22a6d9bdb56b3fa7e064a6c59e15f15f5e1 | [
"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 | 18,962 | lean | /-
Copyright (c) 2021 Shing Tak Lam. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shing Tak Lam
-/
import topology.unit_interval
import topology.algebra.ordered.proj_Icc
import topology.continuous_function.basic
import topology.compact_open
/-!
# Homotopy between f... |
80450eb1057e26c402777066d642ead652aa0d8c | 38a6d5def645a1887e1306ceb4da06ff71452096 | /common/shannon_theory.lean | 80506d23346e39fe7ea990fb3722de00dc581fc1 | [] | no_license | QTM3x/Quantum-Internet | bcc2d61e2ae7233bb2b369fedaed22a1feb6fba1 | f90e09fb6c03d35043654d8b1bec1c63d6012268 | refs/heads/master | 1,609,224,401,937 | 1,599,911,583,000 | 1,599,911,583,000 | 238,495,221 | 45 | 33 | null | 1,603,625,079,000 | 1,580,919,815,000 | Jupyter Notebook | UTF-8 | Lean | false | false | 3,496 | lean | import algebra.big_operators
import data.real.basic
import tactic
import analysis.special_functions.exp_log
import measure_theory.probability_mass_function
-- open_locale big_operators -- this enables the notation
noncomputable theory -- without this there is an error
---- HELPER LEMMAS
lemma multiset.map_repeat {α... |
d4a0d7ad788498bd3c2d62b8e04df3764528dd5f | b3fced0f3ff82d577384fe81653e47df68bb2fa1 | /src/category_theory/endomorphism.lean | fc3587a693dab9ec3cba1bdc8c5a3fb9041330b1 | [
"Apache-2.0"
] | permissive | ratmice/mathlib | 93b251ef5df08b6fd55074650ff47fdcc41a4c75 | 3a948a6a4cd5968d60e15ed914b1ad2f4423af8d | refs/heads/master | 1,599,240,104,318 | 1,572,981,183,000 | 1,572,981,183,000 | 219,830,178 | 0 | 0 | Apache-2.0 | 1,572,980,897,000 | 1,572,980,896,000 | null | UTF-8 | Lean | false | false | 2,816 | lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Scott Morrison, Simon Hudon
Definition and basic properties of endomorphisms and automorphisms of an object in a category.
-/
import category_theory.category catego... |
c74e21e22956d6ac8eba1dc917eb20e7efb3da0e | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/nat/totient_auto.lean | e769f2fd0f9ce4400a4332ac05a30760f8c13a0c | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,018 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebra.big_operators.basic
import Mathlib.PostPort
namespace Mathlib
namespace nat
/-- Eul... |
370ecc904eebaffa4b1f8833a0ae0bd26c3f0f7e | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/analysis/special_functions/integrals.lean | 392fffb9c7455074fcca34f5dd4388053eade7cb | [
"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 | 25,925 | lean | /-
Copyright (c) 2021 Benjamin Davidson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Benjamin Davidson
-/
import measure_theory.integral.interval_integral
import analysis.special_functions.trigonometric.arctan_deriv
/-!
# Integration of specific interval integrals
... |
cb759d9a5f6625fe3b98e8dac0bf6d8a9ce288c7 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/hott/def_bug1.hlean | f37e9c92172f1cc994d4898e176501890f2d5f39 | [
"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 | 485 | hlean | open eq eq.ops
variable {A : Type}
definition trans : Π {x y z : A} (p : x = y) (q : y = z), x = z
| trans (refl a) (refl a) := refl a
set_option pp.purify_locals false
definition con_inv_cancel_left : Π {x y z : A} (p : x = y) (q : x = z), p ⬝ (p⁻¹ ⬝ q) = q
| con_inv_cancel_left (refl a) (refl a) := refl (refl a)
... |
7221d3433a8f2733180266140eef5265f886a7ce | f7c63613a4933f66368ef2802a50c417a46cddfc | /library/init/meta/mk_has_reflect_instance.lean | 785d29b3ec3c79dca39bd21b1b9e5f4efff53be3 | [
"Apache-2.0"
] | permissive | avigad/lean | 28cef71cd8c4eae53f342c87f81ca78d7cc75874 | 5410178203ab5ae854b5804586ace074ffd63aae | refs/heads/master | 1,608,801,379,340 | 1,504,894,459,000 | 1,505,174,163,000 | 22,361,408 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,595 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Ullrich
Helper tactic for constructing a has_reflect instance.
-/
prelude
import init.meta.rec_util
namespace tactic
open expr environment list
/- Retrieve the name... |
80ca967277f9dbbba2cf28829923d8e45406b698 | ad0c7d243dc1bd563419e2767ed42fb323d7beea | /ring_theory/principal_ideal_domain.lean | 39c15cd082a4542d3b59c782a7acfbbb71e52348 | [
"Apache-2.0"
] | permissive | sebzim4500/mathlib | e0b5a63b1655f910dee30badf09bd7e191d3cf30 | 6997cafbd3a7325af5cb318561768c316ceb7757 | refs/heads/master | 1,585,549,958,618 | 1,538,221,723,000 | 1,538,221,723,000 | 150,869,076 | 0 | 0 | Apache-2.0 | 1,538,229,323,000 | 1,538,229,323,000 | null | UTF-8 | Lean | false | false | 4,446 | 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 algebra.euclidean_domain ring_theory.ideals
variables {α : Type*} [comm_ring α]
open set function is_ideal
local attribute [instance] classical.... |
1a5034eb5c4459fa3e2c1ce8dae907130f71a774 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/number_theory/pythagorean_triples.lean | 98342e8198626c9ab6e22bc053eb3bace186d37a | [
"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 | 25,741 | lean | /-
Copyright (c) 2020 Paul van Wamelen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Paul van Wamelen
-/
import algebra.field.basic
import ring_theory.int.basic
import algebra.group_with_zero.power
import tactic.ring
import tactic.ring_exp
import tactic.field_simp
im... |
998e4f36a42bc4975b79bbf58f48fe24643d2420 | 1abd1ed12aa68b375cdef28959f39531c6e95b84 | /src/analysis/normed_space/enorm.lean | 88477248844b66b0355e2b445031e047a984a4fc | [
"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 | 7,751 | lean | /-
Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import analysis.normed_space.basic
/-!
# Extended norm
In this file we define a structure `enorm 𝕜 V` representing an extended norm (i.e., a norm that can
... |
3a24ab14f1a0fdb54613d6e1080cf5ff1f9841f9 | 8c02fed42525b65813b55c064afe2484758d6d09 | /src/spec/closed.lean | 6ae42b0995ac5fa6065d89468c0146f7e7d3e41c | [
"LicenseRef-scancode-generic-cla",
"MIT"
] | permissive | microsoft/AliveInLean | 3eac351a34154efedd3ffc4fe2fa4ec01b219e0d | 4b739dd6e4266b26a045613849df221374119871 | refs/heads/master | 1,691,419,737,939 | 1,689,365,567,000 | 1,689,365,568,000 | 131,156,103 | 23 | 18 | NOASSERTION | 1,660,342,040,000 | 1,524,747,538,000 | Lean | UTF-8 | Lean | false | false | 21,661 | lean | -- Copyright (c) Microsoft Corporation. All rights reserved.
-- Licensed under the MIT license.
import ..smtexpr
import ..bitvector
import .spec
--import .lemmas
import .irstate
import .freevar
import .equiv
import smt2.syntax
import system.io
import init.meta.tactic
import init.meta.interactive
namespace spec
open... |
6bd9c25d585e2400dd90a0edf453d24bbecc9899 | 82b86ba2ae0d5aed0f01f49c46db5afec0eb2bd7 | /tests/lean/run/inj2.lean | c20d5c1f64814b39e492601b4a6d1293e532f55c | [
"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 | 1,120 | lean | universes u v
inductive Vec2 (α : Type u) (β : Type v) : Nat → Type (max u v)
| nil : Vec2 α β 0
| cons : α → β → forall {n}, Vec2 α β n → Vec2 α β (n+1)
inductive Fin2 : Nat → Type
| zero (n : Nat) : Fin2 (n+1)
| succ {n : Nat} (s : Fin2 n) : Fin2 (n+1)
theorem test1 {α β} {n} (a₁ a₂ : α) (b₁ b₂ : β) ... |
e5ffed49f19a0c1422e5ad1b7b3287dc03f821c0 | 6305b69bc7636a761e1a1947508bb5ebad93cb7e | /library/init/meta/simp_tactic.lean | 66f179a10a4713bb733ee980cc49a889565b63c9 | [
"Apache-2.0"
] | permissive | HGldJ1966/lean | e7f0068f8a69fde3593b77d8a44609ae446d7738 | 049d940167c419cd5935d12b459c0695d8615ae9 | refs/heads/master | 1,611,340,395,700 | 1,503,103,829,000 | 1,503,103,829,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 22,027 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.meta.tactic init.meta.attribute init.meta.constructor_tactic
import init.meta.relation_tactics init.meta.occurrences
import init.data.op... |
cf992ad8a6d2a71c5549c9550294cab9219b3d1b | 618003631150032a5676f229d13a079ac875ff77 | /src/tactic/omega/prove_unsats.lean | 45708ce72e434b1bff803776f19b8b2f74fabc24 | [
"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 | 2,078 | lean | /- Copyright (c) 2019 Seul Baek. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Seul Baek
A tactic which constructs exprs to discharge
goals of the form `clauses.unsat cs`. -/
import tactic.omega.find_ees
import tactic.omega.find_scalars
import tactic.omega.lin_comb
n... |
1833c7262e9bfd74f5333c3f2cca9e260c24bd92 | ccb7cdf8ebc2d015a000e8e7904952a36b910425 | /src/heap/basic.lean | 93aabb3ab92e0310aaed1436012c98beb7e81439 | [] | no_license | cipher1024/lean-pl | f7258bda55606b75e3e39deaf7ce8928ed177d66 | 829680605ac17e91038d793c0188e9614353ca25 | refs/heads/master | 1,592,558,951,987 | 1,565,043,356,000 | 1,565,043,531,000 | 196,661,367 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,283 | lean |
import data.finmap
run_cmd mk_simp_attr `separation_logic
open finmap
namespace memory
variables value : Type
@[reducible]
def ptr := ℕ
@[reducible]
def heap := finmap (λ _ : ptr, value)
variables {value}
def add (x y : option (heap value)) : option (heap value) :=
do x ← x,
y ← y,
if disjoint x y then p... |
7d986a9db901a7dd9d892af7a933e31af3d18700 | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/topology/instances/ereal.lean | 54e64c041113d23fcc8446f1d7eb1b5c449da180 | [
"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 | 13,315 | lean | /-
Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import topology.instances.ennreal
import data.real.ereal
/-!
# Topological structure on `ereal`
We endow `ereal` with the order topology, and prove basic prop... |
521b75611c6b0cec5cba96b4d98c969aa09dce2c | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /tests/lean/run/openInScopeBug.lean | 52f4fc5f73777886010b02d6a7122c4ecbfd457d | [
"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 | 807 | lean | constant f : Nat → Nat
constant g : Nat → Nat
namespace Foo
@[scoped simp] axiom ax1 (x : Nat) : f (g x) = x
@[scoped simp] axiom ax2 (x : Nat) : g (g x) = g x
end Foo
theorem ex1 : f (g (g (g x))) = x := by
simp -- does not use ax1 and ax2
simp [Foo.ax1, Foo.ax2]
theorem ex2 : f (g (g (g x))) = x :=
have h₁... |
0f0f1a471569bc8c9e97b86472b3dd19e097c8b0 | a4673261e60b025e2c8c825dfa4ab9108246c32e | /stage0/src/Lean/Util/CollectLevelParams.lean | e4afca6126f9558093283adad429742e74790886 | [
"Apache-2.0"
] | permissive | jcommelin/lean4 | c02dec0cc32c4bccab009285475f265f17d73228 | 2909313475588cc20ac0436e55548a4502050d0a | refs/heads/master | 1,674,129,550,893 | 1,606,415,348,000 | 1,606,415,348,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,372 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Expr
namespace Lean
namespace CollectLevelParams
structure State :=
(visitedLevel : LevelSet := {})
(visitedExpr : ExprSet := {})
... |
fd51f1e5ff7b6e248d960635c4739144ecde3b4e | ce6917c5bacabee346655160b74a307b4a5ab620 | /src/ch3/ex0703.lean | 3b5eca7a5f3fb9d59b0cabd0c24b3b88dda44b56 | [] | no_license | Ailrun/Theorem_Proving_in_Lean | ae6a23f3c54d62d401314d6a771e8ff8b4132db2 | 2eb1b5caf93c6a5a555c79e9097cf2ba5a66cf68 | refs/heads/master | 1,609,838,270,467 | 1,586,846,743,000 | 1,586,846,743,000 | 240,967,761 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 128 | lean | variable p : Prop
example : ¬(p ↔ ¬p) :=
assume h,
suffices hnp : ¬p, from hnp (h.mpr hnp),
assume hp,
h.mp hp hp
|
f4a2b517c55b6741e7d91df9cdc85fb5bb2cd6bc | c777c32c8e484e195053731103c5e52af26a25d1 | /src/linear_algebra/std_basis.lean | 0cc92187283bb71134f1e566c3036131c483a4fe | [
"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 | 10,863 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import data.matrix.basis
import linear_algebra.basis
import linear_algebra.pi
/-!
# The standard basis
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to t... |
2d65f8ce4672672127229e4cdd16b509986d2ae8 | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/data/int/basic.lean | 1aaf655304910a50b8b376ca8c54b8d3a7578b43 | [
"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 | 47,767 | 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
import algebra.order_functions
open nat
namespace int
instance : inhabited ℤ := ... |
32b8bb7db3d7a687f10d0c681403d828b6f34c89 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/number_theory/sum_two_squares.lean | 7156185247eb79f18b6a05438ba87d5b2cf140f2 | [
"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 | 819 | lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import number_theory.zsqrtd.gaussian_int
/-!
# Sums of two squares
Proof of Fermat's theorem on the sum of two squares. Every prime congruent to 1 mod 4 is the sum
of tw... |
73c2e23b73dab445275276d2f9eb2654fb955f28 | 130c49f47783503e462c16b2eff31933442be6ff | /src/Lean/Server/Watchdog.lean | 52227bcff43bb07f281b697fd376aee38f36ec0a | [
"Apache-2.0"
] | permissive | Hazel-Brown/lean4 | 8aa5860e282435ffc30dcdfccd34006c59d1d39c | 79e6732fc6bbf5af831b76f310f9c488d44e7a16 | refs/heads/master | 1,689,218,208,951 | 1,629,736,869,000 | 1,629,736,896,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 25,282 | 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 Init.System.IO
import Init.Data.ByteArray
import Std.Data.RBMap
import Lean.Elab.Import
import Lean.Data.Lsp
import Lean.Server.Utils
impor... |
1e114499653c718d8f549902d5fcb4618cfbbd8f | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/linear_algebra/alternating.lean | 2d3cd2ddb8b22e42d4ece3b23ac9da21e5ad1b49 | [
"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 | 30,460 | lean | /-
Copyright (c) 2020 Zhangir Azerbayev. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Zhangir Azerbayev
-/
import linear_algebra.multilinear.tensor_product
import linear_algebra.linear_independent
import group_theory.perm.sign
import group_theory.perm.s... |
b77bc7dae8c2dacc969c9f77047cc0cd85ad5f44 | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/topology/sheaves/stalks.lean | 4c6458ba50c01410b8abf1b9b47294709bfdf36d | [
"Apache-2.0"
] | permissive | hikari0108/mathlib | b7ea2b7350497ab1a0b87a09d093ecc025a50dfa | a9e7d333b0cfd45f13a20f7b96b7d52e19fa2901 | refs/heads/master | 1,690,483,608,260 | 1,631,541,580,000 | 1,631,541,580,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 16,062 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Justus Springer
-/
import topology.category.Top.open_nhds
import topology.sheaves.presheaf
import topology.sheaves.sheaf_condition.unique_gluing
import category_theory.... |
c16747774f00500f3238c10a7c5e5a80c2315dd4 | bdb33f8b7ea65f7705fc342a178508e2722eb851 | /tactic/rcases.lean | 52202692c285b17c5f01404fc6aac76411358cf4 | [
"Apache-2.0"
] | permissive | rwbarton/mathlib | 939ae09bf8d6eb1331fc2f7e067d39567e10e33d | c13c5ea701bb1eec057e0a242d9f480a079105e9 | refs/heads/master | 1,584,015,335,862 | 1,524,142,167,000 | 1,524,142,167,000 | 130,614,171 | 0 | 0 | Apache-2.0 | 1,548,902,667,000 | 1,524,437,371,000 | Lean | UTF-8 | Lean | false | false | 3,793 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import data.dlist tactic.basic
open lean lean.parser
namespace tactic
inductive rcases_patt : Type
| one : name → rcases_patt
| many : list (list rcases_patt) → rc... |
6737279739bbc5fd2346ce993202da8266c617f1 | 6f1049e897f569e5c47237de40321e62f0181948 | /src/exercises/02_iff_if_and.lean | 0c4c79824f83f2fc49882205be0b9bef3059d68b | [
"Apache-2.0"
] | permissive | anrddh/tutorials | f654a0807b9523608544836d9a81939f8e1dceb8 | 3ba43804e7b632201c494cdaa8da5406f1a255f9 | refs/heads/master | 1,655,542,921,827 | 1,588,846,595,000 | 1,588,846,595,000 | 262,330,134 | 0 | 0 | null | 1,588,944,346,000 | 1,588,944,345,000 | null | UTF-8 | Lean | false | false | 13,534 | lean | import data.real.basic
/-
In the previous file, we saw how to rewrite using equalities.
The analogue operation with mathematical statements is rewriting using
equivalences. This is also done using the rw tactic.
Lean uses ↔ to denote equivalence instead of ⇔.
In the following exercises we will use the lemma:
sub_... |
7664cced180866d02fb5b48d67053ad1a469c834 | 2a70b774d16dbdf5a533432ee0ebab6838df0948 | /_target/deps/mathlib/src/data/real/ennreal.lean | e22f28bdd19616a244dacb3b564ba60f7ba3defc | [
"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 | 55,686 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl, Yury Kudryashov
-/
import data.real.nnreal
import data.set.intervals
/-!
# Extended non-negative reals
We define `ennreal := with_no ℝ≥0` to be the type of extended no... |
a9f01b90d5034de34491c269a3a94503d234fc2d | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/algebra/continued_fractions/default.lean | 6355a0bead4ef2860fbd11329b029568de98a525 | [
"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 | 354 | lean | /-
Copyright (c) 2019 Kevin Kappelmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
-/
import algebra.continued_fractions.basic
import algebra.continued_fractions.translations
import algebra.continued_fractions.continuants_recurrence
/-!
# Default E... |
3982365ccd022ee49a32034d8756a7c0bc83d6ae | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/list/sections.lean | 74326e1a4bb2afe4a82be78c962f56c469fda84f | [
"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 | 1,283 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import data.list.forall2
universes u v
open nat function
variables {α : Type u} {β : Type v}
namespace list
/- sections -/
theorem mem_sections {L : list (list α... |
0de1c6f0b1fc2c817930cf54eae73c10788e5370 | c3de33d4701e6113627153fe1103b255e752ed7d | /tools/auto/finish.lean | e6a2a42a1ef148f7f1a14d2ea64c21d6e64cc8ca | [] | 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 | 13,683 | lean | /-
Copyright (c) 2017 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
These tactics do straightforward things: they call the simplifier, split conjunctive assumptions,
eliminate existential quantifiers on the left, and look for contradictio... |
0ed9578a5a59c1f3fe790b528f1e085dd8646c0c | e1da55f4222dac91b940ca052928eaace09762da | /src/increment.lean | 54d5ff577e85c6ea9997e431e0dffa96f65d6ad4 | [] | no_license | b-mehta/regularity-lemma | c5826e22c280d0b073a4e62dba731f4dd3d1b69f | cf26082b0c88fa54276e6fdc3338c15e607c52c6 | refs/heads/master | 1,658,209,524,267 | 1,644,406,456,000 | 1,644,406,456,000 | 457,327,371 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,483 | lean | /-
Copyright (c) 2021 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
import .chunk
import .energy
/-!
# Increment
-/
universes u v
open finset fintype simple_graph
open_locale big_operators classical
variabl... |
4edefc31560d460303441f9bcbe622b59746b6ae | 92b1c7f0343a6a5cd36bc0f623a7490da3f1e0f3 | /src/stump/sample_complexity.lean | 5bdc705147da0798864d079df4d1de746faa5e49 | [
"Apache-2.0"
] | permissive | jtristan/stump-learnable | 717453eb590af16e60c7d3806cc9e66492fab091 | aa3c089f41602efa08d31ef6b41e549456186d57 | refs/heads/master | 1,625,630,634,360 | 1,607,552,106,000 | 1,607,552,106,000 | 218,629,406 | 15 | 2 | null | null | null | null | UTF-8 | Lean | false | false | 1,698 | lean | /-
Copyright © 2019, Oracle and/or its affiliates. All rights reserved.
-/
import analysis.complex.exponential
import ..lib.util
open real
noncomputable
def complexity (ε: ℝ) (δ: ℝ) : ℝ := (log(δ) / log(1 - ε)) - (1: nat)
lemma complexity_enough:
∀ ε: nnreal, ∀ δ: nnreal, ∀ n: ℕ,
ε > (0: nnreal) → ε < (1: nnre... |
e0266a5e343d7c165a6f8e99df095d88c06f7b8a | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/protected_test.lean | 1288abb6c48a9cf16654c5c10af3983eb0347f32 | [
"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 | 279 | lean | namespace nat
#check induction_on -- ERROR
#check rec_on -- ERROR
#check less_than_or_equal.rec_on -- OK
#check nat.less_than_or_equal.rec_on
namespace le
#check rec_on -- ERROR
#check less_than_or_equal.rec_on
end le
end nat
|
73ba06ef1394d92919dec88ce1435da77dfd78f3 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/algebra/order/pi.lean | 1b4e1f3e1ac5cba460af38bf7ebb32379d29083b | [
"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 | 2,379 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Patrick Massot
-/
import algebra.group.pi
import algebra.order.group
import tactic.pi_instances
/-!
# Pi instances for ordered groups and monoids
This file defines instances... |
00b7ef3ab9e56926729b3e8e28484f0caa1bcf47 | ba4794a0deca1d2aaa68914cd285d77880907b5c | /src/game/world8/level3.lean | 33c1cc4c397fdaf8095e833a211ba50259ca7fa4 | [
"Apache-2.0"
] | permissive | ChrisHughes24/natural_number_game | c7c00aa1f6a95004286fd456ed13cf6e113159ce | 9d09925424da9f6275e6cfe427c8bcf12bb0944f | refs/heads/master | 1,600,715,773,528 | 1,573,910,462,000 | 1,573,910,462,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 637 | lean | import mynat.definition -- hide
import mynat.add -- hide
import game.world8.level2 -- hide
namespace mynat -- hide
/-
# Advanced Addition World
## Level 3: `succ_eq_succ_of_eq`.
-/
/-
We are going to prove something completely obvious: if $a=b$ then
$succ(a)=succ(b)$. This is *not* `succ_inj`!
This is trivial -- we... |
ec16dbc7942f638e093d3b9794413a131f580fe2 | 8b9f17008684d796c8022dab552e42f0cb6fb347 | /tests/lean/run/congr_imp_bug.lean | 50ce6df7c6c337b13789c89a60ea2f471bc86c29 | [
"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 | 2,140 | lean | ----------------------------------------------------------------------------------------------------
--- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
--- Released under Apache 2.0 license as described in the file LICENSE.
--- Author: Jeremy Avigad
------------------------------------------------------... |
c0212be667097ff4e512077cc18445f4978c6eb3 | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/ring_theory/ideal_operations.lean | b20f495c825e71b4aa4fe44b64f8d776e7c04e44 | [
"Apache-2.0"
] | permissive | dupuisf/mathlib | 62de4ec6544bf3b79086afd27b6529acfaf2c1bb | 8582b06b0a5d06c33ee07d0bdf7c646cae22cf36 | refs/heads/master | 1,669,494,854,016 | 1,595,692,409,000 | 1,595,692,409,000 | 272,046,630 | 0 | 0 | Apache-2.0 | 1,592,066,143,000 | 1,592,066,142,000 | null | UTF-8 | Lean | false | false | 35,121 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
More operations on modules and ideals.
-/
import data.nat.choose
import data.equiv.ring
import ring_theory.algebra_operations
import ring_theory.ideals
universes u v w x
open_l... |
e61e4659e7628c2a64415bd6399288049150fe54 | 26ac254ecb57ffcb886ff709cf018390161a9225 | /src/algebra/ring.lean | dc597798e193136164e6bcdac250d9047c6e6557 | [
"Apache-2.0"
] | permissive | eric-wieser/mathlib | 42842584f584359bbe1fc8b88b3ff937c8acd72d | d0df6b81cd0920ad569158c06a3fd5abb9e63301 | refs/heads/master | 1,669,546,404,255 | 1,595,254,668,000 | 1,595,254,668,000 | 281,173,504 | 0 | 0 | Apache-2.0 | 1,595,263,582,000 | 1,595,263,581,000 | null | UTF-8 | Lean | false | false | 38,314 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Amelia Livingston, Yury Kudryashov,
Neil Strickland
-/
import algebra.group.hom
import algebra.group.units
import algebra.group_with_... |
5a139a71fbf0b28b46f5a9c0efef3179a0084290 | 8e381650eb2c1c5361be64ff97e47d956bf2ab9f | /src/spectrum_of_a_ring/structure_sheaf_condition.lean | bcad7fef7dfbefd3f0a7ce3fc9a3b6f047fbbe7f | [] | no_license | alreadydone/lean-scheme | 04c51ab08eca7ccf6c21344d45d202780fa667af | 52d7624f57415eea27ed4dfa916cd94189221a1c | refs/heads/master | 1,599,418,221,423 | 1,562,248,559,000 | 1,562,248,559,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 13,774 | lean | /-
If (fᵢ) = R, the sequene R → Π R[1/fᵢ] → Π R[1/fᵢfⱼ] is exact.
https://stacks.math.columbia.edu/tag/00EJ
TODO : Factor out all the finset sum lemmas and clean up the main proof.
-/
import ring_theory.localization
import algebra.pi_instances
import linear_algebra.linear_combination
import to_mathlib.localiza... |
699ac60212b0d64c954138ce14a7be844999718d | d1bbf1801b3dcb214451d48214589f511061da63 | /src/group_theory/subgroup.lean | 7665077f035a16e1a30480a7f1268f062968d988 | [
"Apache-2.0"
] | permissive | cheraghchi/mathlib | 5c366f8c4f8e66973b60c37881889da8390cab86 | f29d1c3038422168fbbdb2526abf7c0ff13e86db | refs/heads/master | 1,676,577,831,283 | 1,610,894,638,000 | 1,610,894,638,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 50,896 | lean | /-
Copyright (c) 2020 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
import group_theory.submonoid
import algebra.group.conj
/-!
# Subgroups
This file defines multiplicative and additive subgroups as an extension of submonoids, in a bundle... |
ebcbfe28afcab9a5f346a0f12699b543f86ba4cc | 49bd2218ae088932d847f9030c8dbff1c5607bb7 | /src/topology/metric_space/basic.lean | d2e08ae0782f33b5b3fb56e1ec197ba50745a22c | [
"Apache-2.0"
] | permissive | FredericLeRoux/mathlib | e8f696421dd3e4edc8c7edb3369421c8463d7bac | 3645bf8fb426757e0a20af110d1fdded281d286e | refs/heads/master | 1,607,062,870,732 | 1,578,513,186,000 | 1,578,513,186,000 | 231,653,181 | 0 | 0 | Apache-2.0 | 1,578,080,327,000 | 1,578,080,326,000 | null | UTF-8 | Lean | false | false | 68,125 | lean | /-
Copyright (c) 2015, 2017 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Metric spaces.
Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
Many definitions and theorems expected on metric spaces are already introduced o... |
0d96850712a124cefd597016a973f77850a69460 | f4bff2062c030df03d65e8b69c88f79b63a359d8 | /src/game/limits/seq_limitZeroProd.lean | 90e30ab70fc29f552fddc4610901a2f80c11e649 | [
"Apache-2.0"
] | permissive | adastra7470/real-number-game | 776606961f52db0eb824555ed2f8e16f92216ea3 | f9dcb7d9255a79b57e62038228a23346c2dc301b | refs/heads/master | 1,669,221,575,893 | 1,594,669,800,000 | 1,594,669,800,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,353 | lean | import game.limits.L01defs
import game.limits.seq_limitLinear
open real
namespace xena -- hide
notation `|` x `|` := abs x -- hide
/-
Use previous results to obtain the limit of a product if individual limits
for the factors are both zero.
-/
/- Lemma
If $\lim_{n \to \infty} a_n = 0$ and $\lim_{n \to \infty} b_n ... |
b935780b8197cbcfee156a243fdfb933c94cc158 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/finite/basic.lean | d38068956d901f82ae63bb3184feaa249da85b9a | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 5,039 | lean | /-
Copyright (c) 2022 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
import data.fintype.powerset
import data.fintype.prod
import data.fintype.sigma
import data.fintype.sum
import data.fintype.vector
/-!
# Finite types
In this file we prov... |
c2f07ada0753c3a46fe4812b54e20b6de178a55c | 3dd1b66af77106badae6edb1c4dea91a146ead30 | /tests/lean/run/tactic29.lean | 0f12a64c8a401d023645f07828b21c867841e028 | [
"Apache-2.0"
] | permissive | silky/lean | 79c20c15c93feef47bb659a2cc139b26f3614642 | df8b88dca2f8da1a422cb618cd476ef5be730546 | refs/heads/master | 1,610,737,587,697 | 1,406,574,534,000 | 1,406,574,534,000 | 22,362,176 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 323 | lean | import standard
using tactic
section
set_option pp.universes true
set_option pp.implicit true
parameter {A : Type}
parameters {a b : A}
parameter H : a = b
parameters H1 H2 : b = a
check H1
check H
check H2
theorem test : a = b ∧ a = a
:= by apply and_intro; apply H; apply refl
end
check @tes... |
66ec10bce772774af9b7bc0d73320976d9d0ac11 | 92e157ec9825b5e4597a6d715a8928703bc8e3b2 | /src/mywork/practice_2.lean | dc4af590c86680b55b416d5a6004c1184ce63480 | [] | no_license | exb3dg/cs2120f21 | 9e566bc508762573c023d3e70f83cb839c199ec8 | 319b8bf0d63bf96437bf17970ce0198d0b3525cd | refs/heads/main | 1,692,970,909,568 | 1,634,584,540,000 | 1,634,584,540,000 | 399,947,025 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,002 | lean | /-
chameleon
exb3dg; https://github.com/exb3dg/cs2120f21.git
-/
/-
Prove the following simple logical conjectures.
Give a formal and an English proof of each one.
Your English language proofs should be complete
in the sense that they identify all the axioms
and/or theorems that you use.
-/
/- true as defined in lean... |
6e9036f4ac94eb304c8484a63cdeae7c01be7cc3 | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/ty2.lean | da1d2c0073643856631fd1b6ca28288c0232d2d9 | [
"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 | 121 | lean | definition B : Type := Bool
definition T : (Type 1) := Type
variable N : T
variable x : N
variable a : B
axiom H : a
|
8dee143116f323b53fb06991a01cef84d46974cc | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/topology/locally_constant/algebra.lean | 007c2f047bd8bc3a6105d92d8bd255eaefe78977 | [
"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 | 9,594 | 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 algebra.algebra.pi
import topology.locally_constant.basic
/-!
# Algebraic structure on locally constant functions
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
... |
a5ae56b0a7548c70ed309814e40402e4120f7ebc | 75db7e3219bba2fbf41bf5b905f34fcb3c6ca3f2 | /hott/init/logic.hlean | bd1d19d3caadbf73cdcb0a79c6b5edfff6d26e98 | [
"Apache-2.0"
] | permissive | jroesch/lean | 30ef0860fa905d35b9ad6f76de1a4f65c9af6871 | 3de4ec1a6ce9a960feb2a48eeea8b53246fa34f2 | refs/heads/master | 1,586,090,835,348 | 1,455,142,203,000 | 1,455,142,277,000 | 51,536,958 | 1 | 0 | null | 1,455,215,811,000 | 1,455,215,811,000 | null | UTF-8 | Lean | false | false | 24,230 | hlean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Floris van Doorn
-/
prelude
import init.reserved_notation
open unit
definition id [reducible] [unfold_full] {A : Type} (a : A) : A :=
a
/- not -/
definiti... |
77a28735bc1bed635d886e4574c6ce3d54fe9643 | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/data/vector/basic.lean | 66bab293ae7152ea17f2153a90bef5e0b2a254ff | [
"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 | 20,121 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import data.vector
import data.list.nodup
import data.list.of_fn
import control.applicative
/-!
# Additional theorems and definitions about the `vector` type
This fi... |
83894691561887ea0375efdb06ec09b1bc2251dc | d1a52c3f208fa42c41df8278c3d280f075eb020c | /tests/bench/rbmap_checkpoint.lean | cb0bb75e931c2bfbe040126b04a78ed2b98d48c3 | [
"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 | 3,428 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import Init.Data.Option.Basic
import Init.Data.List.BasicAux
import Init.Data.String
import Init.System.IO
universe u v w w'
inductive color
| Red... |
4ccf0a566421067ee1771d19c5dacdd83d02bb24 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/algebra/ring/aut.lean | 642a865bbe7c99bdd71ab5e8b29a6cc76e630d32 | [
"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 | 2,174 | 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.hom.aut
import algebra.ring.equiv
/-!
# Ring automorphisms
This file defines the automorphism group structure on `rin... |
fe4832ccaa31a1d00b23e3b2f427b37d9a3a2ad2 | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/implicit5.lean | 0a47e5eaddd8847022bd7f1d73ac2d5e035271c8 | [
"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 | 315 | lean | import Int.
import Real.
variable f {A : Type} (a1 a2 : A) : A
variable g : Int -> Int -> Int
variable h : Int -> Int -> Real -> Int
variable p {A B : Type} (a1 a2 : A) (b : B) : A
infix ++ : f
infix ++ : g
infix ++ : h
infix ++ : p
variable p2 {A B : Type} (a1 a2 : A) (b : B) {C : Type} (c : C) : A
infix ++ : p2
|
7d11694c7c4177d502555d3f51dd1ab268f3bd47 | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/analysis/p_series.lean | 50ab921921ef63703346acf3625979fa1a675f8c | [
"Apache-2.0"
] | permissive | ilitzroth/mathlib | ea647e67f1fdfd19a0f7bdc5504e8acec6180011 | 5254ef14e3465f6504306132fe3ba9cec9ffff16 | refs/heads/master | 1,680,086,661,182 | 1,617,715,647,000 | 1,617,715,647,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,269 | lean | /-
Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import analysis.special_functions.pow
/-!
# Convergence of `p`-series
In this file we prove that the series `∑' k in ℕ, 1 / k ^ p` converges if and only if ... |
b0e086bea53f930451124a71398153a4c628306f | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/linear_algebra/determinant.lean | 9555be081c7c008a3162ed55bc535aab039f8fcc | [
"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 | 5,494 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Chris Hughes
-/
import data.matrix
import group_theory.perm.sign
universes u v
open equiv equiv.perm finset function
namespace matrix
variables {n : Type u} [fintype n] [decid... |
ef183dd1314282420cb6a376bac4811754da017a | 31f556cdeb9239ffc2fad8f905e33987ff4feab9 | /src/Lean/Widget/Diff.lean | b4de3948acb637fed7ad846989b7fe6653b7a0da | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | tobiasgrosser/lean4 | ce0fd9cca0feba1100656679bf41f0bffdbabb71 | ebdbdc10436a4d9d6b66acf78aae7a23f5bd073f | refs/heads/master | 1,673,103,412,948 | 1,664,930,501,000 | 1,664,930,501,000 | 186,870,185 | 0 | 0 | Apache-2.0 | 1,665,129,237,000 | 1,557,939,901,000 | Lean | UTF-8 | Lean | false | false | 12,797 | lean | /-
Copyright (c) 2022 E.W.Ayers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: E.W.Ayers
-/
import Lean.Meta.PPGoal
import Lean.Widget.InteractiveCode
import Lean.Widget.InteractiveGoal
import Lean.Data.Lsp.Extra
import Lean.Elab.InfoTree
namespace Lean.Widget
regi... |
b20313aec36b0afdf9a9e159310089a7476d1be5 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/linear_algebra/basis.lean | dfad04351c8844849a761253529906723bbb86f0 | [
"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 | 50,124 | 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 algebra.big_operators.finsupp
import algebra.big_operators.finprod
import data.fintype.card
import linear_algebra.finsupp
i... |
5d88d34a9616b6d309793f1e153c8310f2de7a09 | e0f9ba56b7fedc16ef8697f6caeef5898b435143 | /src/data/pnat/xgcd.lean | 1b8b380488e1f75a629cac12af91db94217944c9 | [
"Apache-2.0"
] | permissive | anrddh/mathlib | 6a374da53c7e3a35cb0298b0cd67824efef362b4 | a4266a01d2dcb10de19369307c986d038c7bb6a6 | refs/heads/master | 1,656,710,827,909 | 1,589,560,456,000 | 1,589,560,456,000 | 264,271,800 | 0 | 0 | Apache-2.0 | 1,589,568,062,000 | 1,589,568,061,000 | null | UTF-8 | Lean | false | false | 13,399 | lean | /-
Copyright (c) 2019 Neil Strickland. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Neil Strickland
This file sets up a version of the Euclidean algorithm that works
only with natural numbers. Given a, b > 0, it computes the unique
system (w, x, y, z, d) such that ... |
ae41695809a9d9f88923ab1b46cbfd12c9eb3cd9 | 6b10c15e653d49d146378acda9f3692e9b5b1950 | /examples/basic_skills/unnamed_670.lean | bd6c68af167f87455c9062a9af2c50ee14043eda | [] | no_license | gebner/mathematics_in_lean | 3cf7f18767208ea6c3307ec3a67c7ac266d8514d | 6d1462bba46d66a9b948fc1aef2714fd265cde0b | refs/heads/master | 1,655,301,945,565 | 1,588,697,505,000 | 1,588,697,505,000 | 261,523,603 | 0 | 0 | null | 1,588,695,611,000 | 1,588,695,610,000 | null | UTF-8 | Lean | false | false | 233 | lean | namespace my_ring
variables {R : Type*} [ring R]
-- BEGIN
theorem mul_zero (a : R) : a * 0 = 0 :=
begin
have h : a * 0 + a * 0 = a * 0 + 0,
{ rw [←mul_add, add_zero, add_zero] },
rw add_left_cancel h
end
-- END
end my_ring |
d2b47fe56929595a66bd74caa2823768d3ecc725 | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /stage0/src/Init/System/IOError.lean | c51cae9547a228d1407903d915063af81447dd5d | [
"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 | 8,665 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
prelude
import Init.Core
import Init.Data.UInt
import Init.Data.ToString.Basic
import Init.Data.String.Basic
/-
Imitate the structure of IOErrorType in Haskell:... |
0fcad111116912ddc82ea8fbf14778343d19a04e | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/playground/pge.lean | c14f53c8ecc823889403e3051ba0a6b87791d6ee | [
"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 | 12,168 | lean | -- This module defines
namespace Nat
-- `forallRange i n f` is true if f holds for all indices j from i to n-1.
def forallRange (i:Nat) (n:Nat) (f: ∀ (j:Nat), j < n → Bool) : Bool :=
if h:i < n then
f i h && forallRange (i+1) n f
else
true
termination_by forallRange i n f => n-i
-- `forallRange` correct... |
d780a68517846750d8f91dc8b2a56fef5ef14fba | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/polynomial/div.lean | 414337e97976b029e20d5e8919304f0740fb0208 | [
"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 | 23,111 | 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.inductions
import data.polynomial.monic
import ring_theory.multi... |
53caecd45b382cbe846ade64f643581cfe78dfac | 90edd5cdcf93124fe15627f7304069fdce3442dd | /src/Lean/Aesop/Util.lean | d4c7e6b570216c77456e94761715f228b9adc059 | [
"Apache-2.0"
] | permissive | JLimperg/lean4-aesop | 8a9d9cd3ee484a8e67fda2dd9822d76708098712 | 5c4b9a3e05c32f69a4357c3047c274f4b94f9c71 | refs/heads/master | 1,689,415,944,104 | 1,627,383,284,000 | 1,627,383,284,000 | 377,536,770 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 13,278 | lean | /-
Copyright (c) 2021 Jannis Limperg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jannis Limperg, Asta Halkjær From
-/
import Lean.Elab.Syntax
import Lean.Elab.Tactic.Basic
import Lean.Message
import Lean.Meta.DiscrTree
import Lean.Meta.Tactic.Simp.SimpLemmas
impor... |
82213234ff5f970a2a3bfc6f83bc23ab7d7b70ee | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/ring_theory/multiplicity.lean | 5bf0efe12486fa771e87abd8ac9c01e63e55396a | [
"Apache-2.0"
] | permissive | waynemunro/mathlib | e3fd4ff49f4cb43d4a8ded59d17be407bc5ee552 | 065a70810b5480d584033f7bbf8e0409480c2118 | refs/heads/master | 1,693,417,182,397 | 1,634,644,781,000 | 1,634,644,781,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 19,693 | 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, Chris Hughes
-/
import algebra.associated
import algebra.big_operators.basic
import ring_theory.valuation.basic
/-!
# Multiplicity of a divisor
For a commutative mo... |
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