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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
435b0ab549b188672f29d0ffc8dd26e5817da18a | 13133fade54057ee588bc056e4eaa14a24773d23 | /Proofs/factorial_greater_than_zero.lean | 98d7676e33b8164f0e978d251301a28a97d854dc | [] | no_license | lkloh/lean-project-15815 | 444cbdca1d1a2dfa258c76c41a6ff846392e13d1 | 2cb657c0e41baa318193f7dce85974ff37d80883 | refs/heads/master | 1,611,402,038,933 | 1,432,020,760,000 | 1,432,020,760,000 | 33,372,120 | 0 | 0 | null | 1,431,932,928,000 | 1,428,078,840,000 | Lean | UTF-8 | Lean | false | false | 538 | lean | import data.nat
open nat
-- Asked Jeremy Avigad for help on this
definition fac : nat → nat
| fac 0 := 1
| fac 1 := 1
| fac (n+2) := fac (n+1) * (n+2)
example : fac 0 = 1 :=
rfl
example : fac 1 = 1 :=
rfl
-- fac is always positive
theorem fac_pos : ∀ n, 0 < fac n
| fac_pos 0 := show 0 < 1, from zero_lt_su... |
41e406a28bf81c7e5b1385b2b7fe1e91a2c904df | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/computability/primrec.lean | 402e963f02ba4330b5f9ed642890f69dd93b8b20 | [
"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 | 51,971 | 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.equiv.list
import logic.function.iterate
/-!
# The primitive recursive functions
The primitive recursive functions are the least collection of functions... |
edffef8d9458c8146d520581439ae0917835df85 | e00ea76a720126cf9f6d732ad6216b5b824d20a7 | /src/order/liminf_limsup.lean | b96b25c2628c566cdbae5bac7bb69389b9fb4fff | [
"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 | 19,860 | lean | /-
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Johannes Hölzl
-/
import order.filter order.conditionally_complete_lattice order.bounds
/-!
# liminfs and limsups of functions and filters
Defines the Liminf/L... |
c3ed503b8929e2aa224cc60c3a43abc039984c3b | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/measure_theory/decomposition/signed_hahn.lean | af0b358545896c0b1608e46515303bf64842e17d | [
"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 | 21,640 | lean | /-
Copyright (c) 2021 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
import measure_theory.measure.vector_measure
import order.symm_diff
/-!
# Hahn decomposition
This file proves the Hahn decomposition theorem (signed version). The Hahn de... |
8b80e172425ed865f2b7a6507b619027e84e05dd | 31f556cdeb9239ffc2fad8f905e33987ff4feab9 | /stage0/src/Init/ShareCommon.lean | 2fa5dbff2934336baf23f1b99f1b9424da3c532c | [
"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 | 4,414 | 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, Mario Carneiro
-/
prelude
import Init.Util
namespace ShareCommon
/-
The max sharing primitives are implemented internally.
They use maps and sets of Lean... |
b8ddadaf8207bad54ada2b73c2f258eb2adba6d4 | da23b545e1653cafd4ab88b3a42b9115a0b1355f | /src/tidy/unfold_aux.lean | 26fac41b62ae0923b885e9097234bacd5da111ad | [] | no_license | minchaowu/lean-tidy | 137f5058896e0e81dae84bf8d02b74101d21677a | 2d4c52d66cf07c59f8746e405ba861b4fa0e3835 | refs/heads/master | 1,585,283,406,120 | 1,535,094,033,000 | 1,535,094,033,000 | 145,945,792 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 399 | lean | open tactic
meta def expr.names_with_prefix (pre : name) (r : expr) : list name :=
r.fold [] $ λ e _ l,
match e with
| expr.const n _ := if n.get_prefix = pre then insert n l else l
| _ := l
end
meta def unfold_aux : tactic unit :=
do tgt ← target,
name ← decl_name,
let to_unfold := tgt.names_with_pref... |
1e2c9a17875ca57e7c2c9ab77cefd4f66c650a75 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/geometry/euclidean/triangle.lean | b35cffd796f6a24abe6e51fbf1624cc95255e331 | [] | 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 | 7,682 | lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Joseph Myers.
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.geometry.euclidean.basic
import Mathlib.tactic.interval_cases
import Mathlib.PostPort
universe... |
3c9470826dc07582632941486e40a66399756427 | a047a4718edfa935d17231e9e6ecec8c7b701e05 | /src/analysis/calculus/times_cont_diff.lean | 2058e8e41e58cd480cfda308500a0ba7d8bc0552 | [
"Apache-2.0"
] | permissive | utensil-contrib/mathlib | bae0c9fafe5e2bdb516efc89d6f8c1502ecc9767 | b91909e77e219098a2f8cc031f89d595fe274bd2 | refs/heads/master | 1,668,048,976,965 | 1,592,442,701,000 | 1,592,442,701,000 | 273,197,855 | 0 | 0 | null | 1,592,472,812,000 | 1,592,472,811,000 | null | UTF-8 | Lean | false | false | 81,107 | 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 analysis.calculus.fderiv
/-!
# Higher differentiability
A function is `C^1` on a domain if it is differentiable there, and its derivative is continuous... |
4481e8ce6bb193bb3e105ea06da688db2733ceec | 737dc4b96c97368cb66b925eeea3ab633ec3d702 | /src/Lean/Elab/Tactic/BuiltinTactic.lean | 589d8cd55afb92cccc90a5f20ccb23c2ea8acb99 | [
"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 | 10,507 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Elab.Tactic.Basic
namespace Lean.Elab.Tactic
open Meta
@[builtinTactic Lean.Parser.Tactic.«done»] def evalDone : Tactic := fun _ =>
done
@[... |
dec47a3e2e41b8eceadbab2e2caa60f486680ffa | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /hott/algebra/category/default.hlean | 6fdf85f8c0b50539dca7193e887cbf4c2e0ce2d4 | [
"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 | 209 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import .category .strict .groupoid .constructions
|
cd60f10773725ff3a48d181cbe0890c0250e0b2e | 3268ab3a126f0fef71459fbf170dc38efe5d0506 | /choice.hlean | df700bafd23e4743b79283610b41fca16b646661 | [
"Apache-2.0"
] | permissive | soraismus/Spectral | f043fed1a4e02ddfeba531769b2980eb817471f4 | 32512bf47db3a1b932856e7ed7c7830b1fc07ef0 | refs/heads/master | 1,585,628,705,579 | 1,538,609,948,000 | 1,538,609,974,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,395 | hlean | import types.trunc types.sum types.lift types.unit
open pi prod sum unit bool trunc is_trunc is_equiv eq equiv lift pointed
namespace choice
-- the following brilliant name is from Agda
definition unchoose [unfold 4] (n : ℕ₋₂) {X : Type} (A : X → Type) : trunc n (Πx, A x) → Πx, trunc n (A x) :=
trunc.elim (λf x, tr ... |
640542bad37934bbe502fcf5d11260c3ea4292fc | 08bd4ba4ca87dba1f09d2c96a26f5d65da81f4b4 | /src/Lean/Widget/InteractiveCode.lean | f7a6162320c5a06aa31ab756d6647f12df895774 | [
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"Apache-2.0",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | gebner/lean4 | d51c4922640a52a6f7426536ea669ef18a1d9af5 | 8cd9ce06843c9d42d6d6dc43d3e81e3b49dfc20f | refs/heads/master | 1,685,732,780,391 | 1,672,962,627,000 | 1,673,459,398,000 | 373,307,283 | 0 | 0 | Apache-2.0 | 1,691,316,730,000 | 1,622,669,271,000 | Lean | UTF-8 | Lean | false | false | 3,178 | 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
import Lean.Server.Rpc.Basic
import Lean.Widget.TaggedText
import Lean.Widget.Basic
/-! RPC infrastructure for storing and forma... |
c10f6488c7b4a234865d62b44cfc9a336268170c | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/addDecorationsWithoutPartial.lean | 4c9910c72e881ba7e4bd5744e635fc58b4ab400d | [
"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 | 3,332 | lean | import Lean
namespace Lean
namespace Expr
namespace ReplaceImpl'
abbrev cacheSize : USize := 8192
structure State where
keys : Array Expr -- Remark: our "unsafe" implementation relies on the fact that `()` is not a valid Expr
results : Array Expr
abbrev ReplaceM := StateM State
unsafe def cache (i : USize)... |
6052d8255bdbc7d5c77fe7387858b878788021df | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /src/Lean/Server/FileWorker/WidgetRequests.lean | 067ea372e109c09ef647968aae04f58584701fa0 | [
"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 | 5,264 | 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.Widget.Basic
import Lean.Widget.InteractiveCode
import Lean.Widget.InteractiveGoal
import Lean.Widget.InteractiveDiagnostic
import Lean.Server... |
dbc1e574b02c266cddf49376f44ca729f98200c7 | 5e42295de7f5bcdf224b94603a8ec29b17c2d367 | /tactic.lean | 918b87b684033f90fb3e3383bbedd859cc5dbd9c | [] | no_license | pnmadelaine/lean_polya | 9369e0d87dce773f91383bb58ac6fde0a00a1a40 | 1c62b0b3fa71044b0225ce28030627d251b08ebc | refs/heads/master | 1,590,161,172,243 | 1,515,010,019,000 | 1,515,010,019,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,243 | lean |
#exit
import .blackboard .sum_form .proof_reconstruction
open tactic
namespace polya
meta def polya_tactic := state_t blackboard tactic
meta instance pmt : monad polya_tactic := state_t.monad _ _
meta instance pma : alternative polya_tactic := state_t.alternative _ _
--meta def nfail : polya_tactic unit := state_... |
a32cc3a4c4f4439d118fb86d2a1a5487f96dd953 | 54ce0561cebde424526f41d45f490ed56be2bd0c | /src/game/ch4_Integers_and_Rationals/3_Absolute_Value_and_Exponentiation.lean | c87503abbcfe32d61f0ea8fb703316039efc3541 | [] | no_license | melembroucarlitos/Tao_Analysis-LEAN | cf7b3298d317891a09e4bf21cfe7c7ffcb57b9a9 | 3f4fc7e090d96b6cef64896492fba4bef124794b | refs/heads/master | 1,692,952,385,694 | 1,636,287,522,000 | 1,636,287,522,000 | 400,630,166 | 3 | 0 | null | 1,635,910,807,000 | 1,630,096,823,000 | Lean | UTF-8 | Lean | false | false | 183 | lean | -- Level name : Absolute Value and Exponentiation
/-
# Hey yall
## This is just to a placeholder to make sure all is working
these are some words
and these are some other words
-/
|
f26c266b7e2988e227662a3b3e3d8fcca506f447 | 649957717d58c43b5d8d200da34bf374293fe739 | /src/measure_theory/integration.lean | e1adfd99b26e5aebaa8659e5f2260f3e670f60d5 | [
"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 | 46,156 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johannes Hölzl
Lebesgue integral on `ennreal`.
We define simple functions and show that each Borel measurable function on `ennreal` can be
approximated by a sequence ... |
9154f1a7d0834300108ab7822ea1f9182e7f63f8 | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /04_Quantifiers_and_Equality.org.17.lean | cb259fd5cd1851450707327ec128a4d1e1fdb233 | [] | 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 | 312 | lean | /- page 53 -/
import standard
import data.nat
open nat
variables (a b c d e : nat)
variable H1 : a = b
variable H2 : b = c + 1
variable H3 : c = d
variable H4 : e = 1 + d
theorem T : a = e :=
calc
a = b : H1
... = c + 1 : H2
... = d + 1 : {H3}
... = 1 + d : add.comm d 1
... = e : eq.symm H4
|
01ce65dd7cdcb60d1ca6fb4fbc225e4d5305aad0 | 958488bc7f3c2044206e0358e56d7690b6ae696c | /lean/pattern.lean | 93769e5b4165a8ac5628f4a5b5efc4c63880f9e3 | [] | no_license | possientis/Prog | a08eec1c1b121c2fd6c70a8ae89e2fbef952adb4 | d4b3debc37610a88e0dac3ac5914903604fd1d1f | refs/heads/master | 1,692,263,717,723 | 1,691,757,179,000 | 1,691,757,179,000 | 40,361,602 | 3 | 0 | null | 1,679,896,438,000 | 1,438,953,859,000 | Coq | UTF-8 | Lean | false | false | 5,921 | lean | open nat
def sub1 : ℕ → ℕ
| zero := zero
| (succ x) := x
def is_zero : ℕ → Prop
| zero := true
| (succ x) := false
example : sub1 0 = 0 := rfl
example (n : ℕ) : sub1 (succ n) = n := rfl
example : is_zero 0 = true := rfl
example (n : ℕ) : is_zero (succ n) = false := rfl
example : sub1 7 = 6 := rfl
exampl... |
467dc25488eff254564628f2fb3337bf1ac59896 | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/algebra/associated.lean | b593e0cf410cf0b7b01e27a646f9d8b616480837 | [
"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 | 25,858 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jens Wagemaker
-/
import data.multiset.basic
/-!
# Associated, prime, and irreducible elements.
-/
variables {α : Type*} {β : Type*} {γ : Type*} {δ : Type*}
lemma is... |
be1be236ecbf29290ee08cca76bd1a1770a50f4c | d751a70f46ed26dc0111a87f5bbe83e5c6648904 | /Code/src/inst/exec/algorithms.lean | c00893fe21deaa758214c1103ea648815e56b469 | [] | no_license | marcusrossel/bachelors-thesis | 92cb12ae8436c10fbfab9bfe4929a0081e615b37 | d1ec2c2b5c3c6700a506f2e3cc93f1160e44b422 | refs/heads/main | 1,682,873,547,703 | 1,619,795,735,000 | 1,619,795,735,000 | 306,041,494 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,256 | lean | import topo
import inst.network.basic
-- Cf. inst/primitives.lean
variables (υ : Type*) [decidable_eq υ]
namespace inst
namespace network
-- A function that can generate a well-formed precedence graph for a given instantaneous network.
@[ext]
structure prec_func :=
(func : inst.network υ → prec.graph υ)
... |
1087b3fcbb286aba843fce21b19717e6e8e13051 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/analysis/complex/circle.lean | c34547179b9592b415549c1629c871b08eb5fbc9 | [
"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 | 4,260 | lean | /-
Copyright (c) 2021 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
import analysis.special_functions.exp
import topology.continuous_function.basic
import analysis.normed.field.unit_ball
/-!
# The circle
This file defines `circle`... |
ec0d841546aa03116e825cb4e9edc9f1efa93c88 | a1179fa077c09acc49e4fbc8d67084ba89ac4f4c | /tutorials/src/exercises/09_limits_final.lean | b6da48797fa0ada0adceb4ca61a913a6216a131a | [] | no_license | Seeram/Lean-proof-assistant | 11ca0ca0e0446bacdd1773c4c481a3653b2f1074 | e672d46e0e5f39d8de2933ad4f4cac095ca6094f | refs/heads/master | 1,682,754,224,366 | 1,620,959,431,000 | 1,620,959,431,000 | 299,000,950 | 0 | 1 | null | 1,620,680,462,000 | 1,601,200,258,000 | Lean | UTF-8 | Lean | false | false | 7,228 | lean | import tuto_lib
set_option pp.beta true
set_option pp.coercions false
/-
This is the final file in the series. Here we use everything covered
in previous files to prove a couple of famous theorems from
elementary real analysis. Of course they all have more general versions
in mathlib.
As usual, keep in mind the fol... |
4a0e07b32a74b7eb31828e6d2c078c58628255f7 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/group_theory/sylow.lean | 861713c4025c666631f8df25d00291565e70e346 | [
"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 | 35,205 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Thomas Browning
-/
import data.nat.factorization.basic
import data.set_like.fintype
import group_theory.group_action.conj_act
import group_theory.p_group
import group_theo... |
b0f8e63adba93f6285173a48883e2c2851a2c981 | 4fa161becb8ce7378a709f5992a594764699e268 | /src/linear_algebra/sesquilinear_form.lean | af8d9faf2c5b82bf2abc62ba9741e1773c2c223b | [
"Apache-2.0"
] | permissive | laughinggas/mathlib | e4aa4565ae34e46e834434284cb26bd9d67bc373 | 86dcd5cda7a5017c8b3c8876c89a510a19d49aad | refs/heads/master | 1,669,496,232,688 | 1,592,831,995,000 | 1,592,831,995,000 | 274,155,979 | 0 | 0 | Apache-2.0 | 1,592,835,190,000 | 1,592,835,189,000 | null | UTF-8 | Lean | false | false | 8,795 | lean | /-
Copyright (c) 2018 Andreas Swerdlow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Andreas Swerdlow
-/
import algebra.module
import ring_theory.maps
/-!
# Sesquilinear form
This file defines a sesquilinear form over a module. The definition requires a ring antiaut... |
5e9f425d00c4893fcd6170164239901ca1335117 | 38bf3fd2bb651ab70511408fcf70e2029e2ba310 | /src/tactic/norm_num.lean | 0ecd429414cee4b8f86ae23f8f3a4529f9b1adfb | [
"Apache-2.0"
] | permissive | JaredCorduan/mathlib | 130392594844f15dad65a9308c242551bae6cd2e | d5de80376088954d592a59326c14404f538050a1 | refs/heads/master | 1,595,862,206,333 | 1,570,816,457,000 | 1,570,816,457,000 | 209,134,499 | 0 | 0 | Apache-2.0 | 1,568,746,811,000 | 1,568,746,811,000 | null | UTF-8 | Lean | false | false | 18,865 | 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
Evaluating arithmetic expressions including *, +, -, ^, ≤
-/
import algebra.group_power data.rat.order data.rat.cast data.nat.prime
import tactic.interactive ... |
cec8f5a4dab8b9fea763ac7905e503534ca601dd | c777c32c8e484e195053731103c5e52af26a25d1 | /src/probability/integration.lean | 78a17d30219ded107419cd81c8d6235906047c2c | [
"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 | 17,832 | lean | /-
Copyright (c) 2021 Martin Zinkevich. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Martin Zinkevich, Vincent Beffara
-/
import measure_theory.integral.set_integral
import probability.independence.basic
/-!
# Integration in Probability Theory
Integration results f... |
3b2f3c5ef386366659400ff3efc7b8a63ed07265 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/finsupp/multiset.lean | 924aaa4ca80ebad37db662f386a4a0fa74ee03ca | [
"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 | 7,286 | 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.finsupp.basic
import data.finsupp.order
/-!
# Equivalence between `multiset` and `ℕ`-valued finitely supported functions
This defines `finsupp.to_multis... |
0e8a20083cb204c446b4fec23d70aed9b8b0e939 | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/data/polynomial/eval.lean | 2ea732a6c597c2fe580eb638dc8d7d75d8070a35 | [
"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 | 28,540 | 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.degree.definitions
/-!
# Theory of univariate polynomials
The main defs here are `eval₂`, `eval`,... |
83294c6043fb0da808c0cc0107ba6cf6935deb03 | f3849be5d845a1cb97680f0bbbe03b85518312f0 | /old_library/init/sigma.lean | 86bfdd5f0676ae631ecb4dc6c562c549f6060197 | [
"Apache-2.0"
] | permissive | bjoeris/lean | 0ed95125d762b17bfcb54dad1f9721f953f92eeb | 4e496b78d5e73545fa4f9a807155113d8e6b0561 | refs/heads/master | 1,611,251,218,281 | 1,495,337,658,000 | 1,495,337,658,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 727 | 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, Floris van Doorn
-/
prelude
import init.datatypes init.num init.wf init.logic
definition dpair := @sigma.mk
notation `Σ` binders `, ` r:(scoped... |
94ecc84c96000a2539b982d9c2f95f58de06b1d7 | bb31430994044506fa42fd667e2d556327e18dfe | /src/algebra/module/linear_map.lean | ef23231b5c31566f2c01fd98e8531e20607901d2 | [
"Apache-2.0"
] | permissive | sgouezel/mathlib | 0cb4e5335a2ba189fa7af96d83a377f83270e503 | 00638177efd1b2534fc5269363ebf42a7871df9a | refs/heads/master | 1,674,527,483,042 | 1,673,665,568,000 | 1,673,665,568,000 | 119,598,202 | 0 | 0 | null | 1,517,348,647,000 | 1,517,348,646,000 | null | UTF-8 | Lean | false | false | 37,877 | 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,
Frédéric Dupuis, Heather Macbeth
-/
import algebra.hom.group_action
import algebra.module.pi
import algebra... |
3636cbc9e3617146990184d2337fe2ea74b1878f | 137c667471a40116a7afd7261f030b30180468c2 | /src/topology/metric_space/lipschitz.lean | 9c817be0d8b8368abfe4b29cc013bd026fd1ac51 | [
"Apache-2.0"
] | permissive | bragadeesh153/mathlib | 46bf814cfb1eecb34b5d1549b9117dc60f657792 | b577bb2cd1f96eb47031878256856020b76f73cd | refs/heads/master | 1,687,435,188,334 | 1,626,384,207,000 | 1,626,384,207,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,229 | lean | /-
Copyright (c) 2018 Rohan Mitta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rohan Mitta, Kevin Buzzard, Alistair Tucker, Johannes Hölzl, Yury Kudryashov
-/
import logic.function.iterate
import topology.metric_space.basic
import category_theory.endomorphism
import... |
2cf11d18f27cdc9ab436c1c5f83a48aa64e00344 | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /src/Init/Lean/ToExpr.lean | 998f72b72d5b634d0fed3a3288dc8fb09d4f1a02 | [
"Apache-2.0"
] | permissive | mhuisi/lean4 | 28d35a4febc2e251c7f05492e13f3b05d6f9b7af | dda44bc47f3e5d024508060dac2bcb59fd12e4c0 | refs/heads/master | 1,621,225,489,283 | 1,585,142,689,000 | 1,585,142,689,000 | 250,590,438 | 0 | 2 | Apache-2.0 | 1,602,443,220,000 | 1,585,327,814,000 | C | UTF-8 | Lean | false | false | 2,449 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import Init.Lean.Expr
universe u
namespace Lean
class ToExpr (α : Type u) :=
(toExpr : α → Expr)
(toTypeExpr : Expr)
export ToExpr (toExpr to... |
2727153b6f2466ad0a595a6985e62380e3716c4f | d1a52c3f208fa42c41df8278c3d280f075eb020c | /tests/lean/run/obtain.lean | 875169f969bb4d846610ac85fe44019b45b38454 | [
"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 | 668 | lean |
macro "obtain " p:term " from " d:term "; " body:term : term =>
`(match $d:term with | $p:term => $body:term)
theorem tst1 {p q r} (h : p ∧ q ∧ r) : q ∧ p ∧ r :=
match h with
| ⟨h₁, ⟨h₂, h₃⟩⟩ => ⟨h₂, ⟨h₁, h₃⟩⟩
theorem tst2 {p q r} (h : p ∧ q ∧ r) : q ∧ p ∧ r :=
obtain ⟨h₁, ⟨h₂, h₃⟩⟩ from h;
⟨h₂, ⟨h₁, h₃⟩⟩
macro "o... |
227e72f2b923c32fdbb281c3090dc476afe4fb07 | 246309748072bf9f8da313401699689ebbecd94d | /src/data/finsupp/basic.lean | dce462012fb31b9926b31b12309fa6eaab1fb048 | [
"Apache-2.0"
] | permissive | YJMD/mathlib | b703a641e5f32a996f7842f7c0043bab2b462ee2 | 7310eab9fa8c1b1229dca42682f1fa6bfb7dbbf9 | refs/heads/master | 1,670,714,479,314 | 1,599,035,445,000 | 1,599,035,445,000 | 292,279,930 | 0 | 0 | null | 1,599,050,561,000 | 1,599,050,560,000 | null | UTF-8 | Lean | false | false | 73,126 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Scott Morrison
-/
import algebra.big_operators.order
import algebra.module.basic
import data.fintype.card
import data.set.finite
import data.multiset.antidiagonal
/-!
... |
e743b5699b2a45eafae95eb5cb393d594489018e | 26ac254ecb57ffcb886ff709cf018390161a9225 | /src/measure_theory/l1_space.lean | 49db5524a0cbc7c398162683c440d5dcf44472a5 | [
"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 | 29,451 | 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... |
bea4e5e894a37f1170ce7cfc6c3bc38074c45321 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /tests/lean/run/check.lean | 178193c3a4b63f2f90cf8375f19a3a2dcadb598f | [
"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 | 59 | lean | --
#check And.intro
#check Or.rec
#check Eq
#check Eq.rec
|
1c95d92a7b9b767fa4597d039f47f0e316884a5e | 2fbe653e4bc441efde5e5d250566e65538709888 | /src/topology/bounded_continuous_function.lean | c1a69a1c9f92e99721a5fedfb8826bfb38679622 | [
"Apache-2.0"
] | permissive | aceg00/mathlib | 5e15e79a8af87ff7eb8c17e2629c442ef24e746b | 8786ea6d6d46d6969ac9a869eb818bf100802882 | refs/heads/master | 1,649,202,698,930 | 1,580,924,783,000 | 1,580,924,783,000 | 149,197,272 | 0 | 0 | Apache-2.0 | 1,537,224,208,000 | 1,537,224,207,000 | null | UTF-8 | Lean | false | false | 23,550 | lean | /-
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Mario Carneiro
Type of bounded continuous functions taking values in a metric space, with
the uniform distance.
-/
import analysis.normed_space.basic topology.... |
5db0e6f060162d691c1543c692056ff7c64128ab | bb31430994044506fa42fd667e2d556327e18dfe | /src/analysis/special_functions/gaussian.lean | ef4792ec70e2d3bd58b4d55492075cacad1f7784 | [
"Apache-2.0"
] | permissive | sgouezel/mathlib | 0cb4e5335a2ba189fa7af96d83a377f83270e503 | 00638177efd1b2534fc5269363ebf42a7871df9a | refs/heads/master | 1,674,527,483,042 | 1,673,665,568,000 | 1,673,665,568,000 | 119,598,202 | 0 | 0 | null | 1,517,348,647,000 | 1,517,348,646,000 | null | UTF-8 | Lean | false | false | 16,378 | 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 analysis.special_functions.gamma
import analysis.special_functions.polar_coord
import analysis.convex.complex
/-!
# Gaussian integral
We prove various ... |
eb7607cee04f4a59686a701e7c6cdbc7fed64035 | c3e8fac5ab7ca328e55bccf82a0207a97f96678c | /lean/src/blah.lean | 136bfc1ac5b70aedc354be8fac4736b159f971d0 | [
"Unlicense"
] | permissive | Rotsor/brainfuck | 941bb33862ce3e9d61f0454db5ca02942f4b5775 | 3e6f30f298b8ba76d0bc71b8b5a47cedaf2f0b97 | refs/heads/master | 1,619,718,778,100 | 1,532,913,653,000 | 1,532,913,653,000 | 121,682,141 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 44 | lean | @[reducible]
def a := 10
def x : fin a := 1
|
777ed4406e11d8d792ae25d6f7b5d23bffec24df | 274261f7150b4ed5f1962f172c9357591be8a2b5 | /src/subsets.lean | c0d8a4326941eb89ded0b185e670188ffe367564 | [] | no_license | rspencer01/lean_representation_theory | 219ea1edf4b9897b2997226b54473e44e1538b50 | 2eef2b4b39d99d7ce71bec7bbc3dcc2f7586fcb5 | refs/heads/master | 1,588,133,157,029 | 1,571,689,957,000 | 1,571,689,957,000 | 175,835,785 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,766 | lean | import data.set
import order
import order.zorn
open classical
variables {α : Type} [lattice.complete_lattice α] (S : set α)
variables (inf' : ∀ a b : S, (a : α) ⊓ (b : α) ∈ S)
variables (sup' : ∀ a b : S, (a : α) ⊔ (b : α) ∈ S)
variables (bot' : (⊥ : α) ∈ S)
variables (top' : (⊤ : α) ∈ S)
instance s_has_le : has_le... |
d201f73e7b3c657ccb9cb7c41bdd560d49dd8ec1 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/analysis/mellin_transform.lean | fc32cd4d4c28fe2820d0ef5008628fd252d8d978 | [
"Apache-2.0"
] | permissive | kbuzzard/mathlib | 2ff9e85dfe2a46f4b291927f983afec17e946eb8 | 58537299e922f9c77df76cb613910914a479c1f7 | refs/heads/master | 1,685,313,702,744 | 1,683,974,212,000 | 1,683,974,212,000 | 128,185,277 | 1 | 0 | null | 1,522,920,600,000 | 1,522,920,600,000 | null | UTF-8 | Lean | false | false | 16,710 | lean | /-
Copyright (c) 2023 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
import analysis.special_functions.improper_integrals
import analysis.calculus.parametric_integral
/-! # The Mellin transform
We define the Mellin transform of a lo... |
1354fea3c467524a2a58216c302cf1cd0660118b | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/set/pointwise/basic.lean | 5b100178a201a815d1d65b2d27a909bc3c7d7ec7 | [
"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 | 32,079 | lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Floris van Doorn
-/
import algebra.group_power.basic
import algebra.hom.equiv.basic
import algebra.hom.units
import data.set.lattice
import data.nat.order.basic
/-!
# ... |
05b52ce8b860e442919bc7a9d247c5c664ddb1fa | b2fe74b11b57d362c13326bc5651244f111fa6f4 | /src/analysis/calculus/formal_multilinear_series.lean | dfd31227b23567e418830c08a75220690f6642f7 | [
"Apache-2.0"
] | permissive | midfield/mathlib | c4db5fa898b5ac8f2f80ae0d00c95eb6f745f4c7 | 775edc615ecec631d65b6180dbcc7bc26c3abc26 | refs/heads/master | 1,675,330,551,921 | 1,608,304,514,000 | 1,608,304,514,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,882 | 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 analysis.normed_space.multilinear
import ring_theory.power_series
/-!
# Formal multilinear series
In this file we define `formal_multilinear_series 𝕜 E... |
96f791d5b895aab19e810cf59a0023063deb324b | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /test/derive_fintype.lean | f71e0b8fae307939e5677fd69f83e973718f5254 | [
"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 | 1,219 | lean | /-
Copyright (c) 2020 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import tactic.derive_fintype
@[derive fintype]
inductive alphabet
| a | b | c | d | e | f | g | h | i | j | k | l | m
| n | o | p | q | r | s | t | u | v | w | x | y... |
2d8dc466552afc66edbb6fa8b3902a7e112ea9f3 | d642a6b1261b2cbe691e53561ac777b924751b63 | /src/topology/basic.lean | 2f674d51af5f5a0c006e8141093b77392d51ca53 | [
"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 | 32,985 | 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
/-!
# Basic theory of topological spaces.
The main definition is the type class `topological space α` which endo... |
952fc9fe053dea04a126590c381ed92fb5e55224 | 92e157ec9825b5e4597a6d715a8928703bc8e3b2 | /src/mywork/lecture_1a.lean | 88f24bc264bd34e5c18b3e8e96fa8b01e429ace4 | [] | 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 | 10,273 | lean | -- import definitions of real and rational numbers from mathlib
import data.real.basic
namespace cs2120
/-
The first part of this lesson is in the file, lecture_1.md.
Please start there then return here when you're done with
that document.
-/
/-
NUMBER SYSTEMS
-/
/-
Mathematicians think about operations on many ki... |
1f8b02e58abd681389b376bfbcdfa9e808c9fbc6 | 592ee40978ac7604005a4e0d35bbc4b467389241 | /Library/generated/mathscheme-lean/PrimRingoidSig.lean | cf74637f03f152471ab2b4d0fc65ea18a5caba9d | [] | no_license | ysharoda/Deriving-Definitions | 3e149e6641fae440badd35ac110a0bd705a49ad2 | dfecb27572022de3d4aa702cae8db19957523a59 | refs/heads/master | 1,679,127,857,700 | 1,615,939,007,000 | 1,615,939,007,000 | 229,785,731 | 4 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,971 | lean | import init.data.nat.basic
import init.data.fin.basic
import data.vector
import .Prelude
open Staged
open nat
open fin
open vector
section PrimRingoidSig
structure PrimRingoidSig (A : Type) : Type :=
(times : (A → (A → A)))
(plus : (A → (A → A)))
(prim : (A → A))
open PrimRingoidSig
... |
f269f07b1c9f6e4a506200cb8497d4dff3400ae8 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/data/matrix/dmatrix.lean | 627a0174f8e16ce5c188ad09f872bef0e26c034b | [
"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 | 5,428 | lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import data.fintype.basic
/-!
# Matrices
-/
universes u u' v w z
/-- `dmatrix m n` is the type of dependently typed matrices
whose rows are indexed by the fintype `... |
89763da805209a256676f9717ece47274cf50378 | fe84e287c662151bb313504482b218a503b972f3 | /src/combinatorics/partition/recursive.lean | e3e767348aeeafbfa25986855b69ccb763342d6f | [] | no_license | NeilStrickland/lean_lib | 91e163f514b829c42fe75636407138b5c75cba83 | 6a9563de93748ace509d9db4302db6cd77d8f92c | refs/heads/master | 1,653,408,198,261 | 1,652,996,419,000 | 1,652,996,419,000 | 181,006,067 | 4 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 4,610 | lean | /-
Copyright (c) 2019 Neil Strickland. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Neil Strickland
Let p be a partition of a finite type α with decidable equality.
Then the type α₀ of blocks can be regarded as a quotient of α
in an obvious way, so we can cons... |
a3a328a6d74c27c8cc1f876a38935908fa625eba | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/analysis/complex/upper_half_plane/basic.lean | 7b234162517b4ec821d2eabf8819250bad76433c | [
"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 | 11,525 | lean | /-
Copyright (c) 2021 Alex Kontorovich and Heather Macbeth and Marc Masdeu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Kontorovich, Heather Macbeth, Marc Masdeu
-/
import data.fintype.parity
import linear_algebra.special_linear_group
import analysis.complex.ba... |
b008b2b7d0ce8ab546f0c95cce9a1dc2f04a2774 | 59aed81a2ce7741e690907fc374be338f4f88b6f | /src/math-688/lectures/lec-14.lean | 33cdac89ed19cab249bd0cbb661956707b5a9623 | [] | no_license | agusakov/math-688-lean | c84d5e1423eb208a0281135f0214b91b30d0ef48 | 67dc27ebff55a74c6b5a1c469ba04e7981d2e550 | refs/heads/main | 1,679,699,340,788 | 1,616,602,782,000 | 1,616,602,782,000 | 332,894,454 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 164 | lean | /- 30 Sep 2019 -/
-- graphs and matrices
-- adjacency matrix
-- incidence matrix
-- number of paths of length k
-- adjacency algebra
-- diameter of connected graph |
208bccd12a91dbad5c6a7d5a77edffa1df0222b8 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebraic_topology/nerve.lean | 035a70063220be542730748580f8feab49b11c99 | [
"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 | 1,335 | lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import algebraic_topology.simplicial_set
/-!
# The nerve of a category
This file provides the definition of the nerve of a category `C`,
which is a simplicial set `nerve C`... |
2c2775d73a3c02a380bf97c8a93494d74cef5dcb | 367134ba5a65885e863bdc4507601606690974c1 | /src/algebra/category/Algebra/limits.lean | b69650e215c4400b0c6c7ddad63b60235db59c78 | [
"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 | 5,279 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import algebra.category.Algebra.basic
import algebra.category.Module.limits
import algebra.category.CommRing.limits
/-!
# The category of R-algebras has all limits
... |
3019c85837921041c7a98fe7225eab23d72c134f | e00ea76a720126cf9f6d732ad6216b5b824d20a7 | /src/analysis/normed_space/multilinear.lean | f0b8d1deabea99e4389e7c7c42c65108e3ab48b1 | [
"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 | 48,852 | 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.normed_space.operator_norm topology.algebra.multilinear
import data.fintype.card
/-!
# Operator norm on the space of continuous multilinear ma... |
9835747093d42474ea1b57265c00d96d8d769922 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/group_theory/schreier.lean | c787ff596e72fd6b0c0b56299435e71977b817eb | [
"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 | 6,898 | lean | /-
Copyright (c) 2022 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import data.finset.pointwise
import group_theory.complement
import group_theory.finiteness
import group_theory.index
import tactic.group
/-!
# Schreier's Lemma
I... |
2a708c97e23fc33de4155af31b8b175b1e1f1c41 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/analysis/calculus/fderiv_measurable.lean | 4a080a91fea68acd22698b45b44133f468978e1e | [
"Apache-2.0"
] | permissive | stjordanis/mathlib | 51e286d19140e3788ef2c470bc7b953e4991f0c9 | 2568d41bca08f5d6bf39d915434c8447e21f42ee | refs/heads/master | 1,631,748,053,501 | 1,627,938,886,000 | 1,627,938,886,000 | 228,728,358 | 0 | 0 | Apache-2.0 | 1,576,630,588,000 | 1,576,630,587,000 | null | UTF-8 | Lean | false | false | 21,745 | lean | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Yury Kudryashov
-/
import analysis.calculus.deriv
import measure_theory.borel_space
/-!
# Derivative is measurable
In this file we prove that the derivative of ... |
870b53a838a2cf8f4bb6250c0e57b83aebc95380 | 6065973b1fa7bbacba932011c9e2f32bf7bdd6c1 | /src/topology/algebra/ordered.lean | 8d64921010fae4032a6ac70603cd3b73260bbe8a | [
"Apache-2.0"
] | permissive | khmacdonald/mathlib | 90a0fa2222369fa69ed2fbfb841b74d2bdfd66cb | 3669cb35c578441812ad30fd967d21a94b6f387e | refs/heads/master | 1,675,863,801,090 | 1,609,761,876,000 | 1,609,761,876,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 152,813 | 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, Yury Kudryashov
-/
import tactic.linarith
import tactic.tfae
import algebra.archimedean
import algebra.group.pi
import algebra.ordered_ring
import order... |
5d21f7c3c9cebe6358f1e9579f91acd9eb1555c7 | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /tests/lean/run/bigop.lean | 1d5afb1dcb2400bf98fff8340f8876ade9a96434 | [
"Apache-2.0"
] | permissive | walterhu1015/lean4 | b2c71b688975177402758924eaa513475ed6ce72 | 2214d81e84646a905d0b20b032c89caf89c737ad | refs/heads/master | 1,671,342,096,906 | 1,599,695,985,000 | 1,599,695,985,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,125 | lean | def Seq (α : Type) := List α
def BigBody (β α) := α × (β → β → β) × Bool × β
def applyBig {α β : Type} (body : BigBody β α) (x : β) : β :=
let (_, op, b, v) := body;
if b then op v x else x
def reducebig {α β : Type} (idx : β) (r : Seq α) (body : α → BigBody β α) : β :=
r.foldr (applyBig ∘ body) idx
def bigop := @... |
c69503f7540a946f6ca4f625e390fd97f107b243 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/hom/iterate.lean | 5b5e517f9fca9af674f0b64e1d99d19da4d85588 | [
"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 | 6,058 | lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import logic.function.iterate
import group_theory.perm.basic
import group_theory.group_action.opposite
/-!
# Iterates of monoid and ring homomorphisms
Iterate of... |
299891fa38505c520b9898d8a7d72565bd2ffd75 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/data/set/intervals/monotone.lean | bc11fba75cc5204775f6ccb3f345e4e245735c4a | [
"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 | 12,115 | lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import data.set.intervals.disjoint
import order.succ_pred.basic
import tactic.field_simp
/-!
# Monotonicity on intervals
In this file we prove that a function is ... |
f7ca588345625377ff8ed559c2366f7795fc1aae | 957a80ea22c5abb4f4670b250d55534d9db99108 | /tests/lean/struct_class.lean | c4a0f17d38e2143fd0316211461750ca6220413f | [
"Apache-2.0"
] | permissive | GaloisInc/lean | aa1e64d604051e602fcf4610061314b9a37ab8cd | f1ec117a24459b59c6ff9e56a1d09d9e9e60a6c0 | refs/heads/master | 1,592,202,909,807 | 1,504,624,387,000 | 1,504,624,387,000 | 75,319,626 | 2 | 1 | Apache-2.0 | 1,539,290,164,000 | 1,480,616,104,000 | C++ | UTF-8 | Lean | false | false | 186 | lean | prelude
import init.core
class point (A : Type*) (B : Type*) :=
mk :: (x : A) (y : B)
#print classes
structure point2 (A : Type*) (B : Type*) :=
mk :: (x : A) (y : B)
#print classes
|
384e1bc07f07c7d1a044204bf87493b8d2b75465 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/analysis/special_functions/pow_deriv.lean | e2bb00251748e80ee76683d87255008340d247e1 | [
"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 | 25,713 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Sébastien Gouëzel,
Rémy Degenne
-/
import analysis.special_functions.pow
import analysis.special_functions.complex.log_der... |
7409347fc1220c38ce04b9ea49fd2ae43867aa90 | 618003631150032a5676f229d13a079ac875ff77 | /src/control/applicative.lean | b19fc62e254ff239d3d4df0f8e367ac40e0c0413 | [
"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 | 4,777 | lean | /-
Copyright (c) 2017 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Simon Hudon
Instances for identity and composition functors
-/
import control.functor
import algebra.group.basic
universe variables u v w
section lemmas
open function
variables {F : T... |
91979cb9e6ad79ae67abae29bf797d9b2dda1eb0 | 7d5ad87afb17e514aee234fcf0a24412eed6384f | /src/zfc'.lean | 9e0944eb4114730a84bb2e09410a43f31ac431c2 | [] | no_license | digama0/flypitch | 764f849eaef59c045dfbeca142a0f827973e70c1 | 2ec14b8da6a3964f09521d17e51f363d255b030f | refs/heads/master | 1,586,980,069,651 | 1,547,078,141,000 | 1,547,078,283,000 | 164,965,135 | 1 | 0 | null | 1,547,082,858,000 | 1,547,082,857,000 | null | UTF-8 | Lean | false | false | 387 | lean | import .fol
open fol
/- ZFC in expanded signature -/
namespace zfc'
inductive ZFC'_functions : ℕ → Type
| emptyset : ZFC'_functions 0
| union : ZFC'_functions 1
| pow : ZFC'_functions 1
| pair : ZFC'_functions 2
inductive ZFC'_relations : ℕ → Type
| ϵ : ZFC'_relations 2
| subset : ZFC'_relations 2
def L_ZFC' : L... |
4f9f04d77ad6d2c91f596c8c2d7c8d0bc1911ca5 | 5ae26df177f810c5006841e9c73dc56e01b978d7 | /src/analysis/asymptotics.lean | 12edc04c1750a8ed8450c5d7f2dbf93832ae8e68 | [
"Apache-2.0"
] | permissive | ChrisHughes24/mathlib | 98322577c460bc6b1fe5c21f42ce33ad1c3e5558 | a2a867e827c2a6702beb9efc2b9282bd801d5f9a | refs/heads/master | 1,583,848,251,477 | 1,565,164,247,000 | 1,565,164,247,000 | 129,409,993 | 0 | 1 | Apache-2.0 | 1,565,164,817,000 | 1,523,628,059,000 | Lean | UTF-8 | Lean | false | false | 29,344 | lean | /-
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad
We introduce these relations:
`is_O f g l` : "f is big O of g along l"
`is_o f g l` : "f is little o of g along l"
Here `l` is any filter on the domain of `f` and `g... |
5b7136d89c3a81f9ee657b9546625e0dbde9d342 | 206422fb9edabf63def0ed2aa3f489150fb09ccb | /src/algebra/monoid_algebra.lean | 37cb23ef6dd8be6753ab87e3820910185d90018e | [
"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 | 38,238 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yury G. Kudryashov, Scott Morrison
-/
import algebra.algebra.basic
import linear_algebra.finsupp
/-!
# Monoid algebras
When the domain of a `finsupp` has a multiplica... |
80deafc159dd933eb15b7756bffcc15191699355 | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /stage0/src/Init/Core.lean | 4895795713f78ce5c63333c4fc5453e316c7cd3c | [
"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 | 34,034 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
notation, basic datatypes and type classes
-/
prelude
import Init.Prelude
import Init.SizeOf
universes u v w
def inline {α : Sort u} (a : α) : α := a
@[inl... |
7ec601771e1852e9b91156f09afd79035c3609f2 | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/analysis/calculus/fderiv_measurable.lean | bdc25d4d02ce138baf2bc6c4737a3dbc0996b719 | [
"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 | 21,679 | lean | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Yury Kudryashov
-/
import analysis.calculus.deriv
import measure_theory.constructions.borel_space
/-!
# Derivative is measurable
In this file we prove that the ... |
f5527d6ee5229cac8edd3d07e84d3db4296c4db7 | 957a80ea22c5abb4f4670b250d55534d9db99108 | /tests/lean/run/nat_bug.lean | 83f19bf0c89333cd143f805f5f0cf500e520992f | [
"Apache-2.0"
] | permissive | GaloisInc/lean | aa1e64d604051e602fcf4610061314b9a37ab8cd | f1ec117a24459b59c6ff9e56a1d09d9e9e60a6c0 | refs/heads/master | 1,592,202,909,807 | 1,504,624,387,000 | 1,504,624,387,000 | 75,319,626 | 2 | 1 | Apache-2.0 | 1,539,290,164,000 | 1,480,616,104,000 | C++ | UTF-8 | Lean | false | false | 806 | lean | open decidable open eq
namespace experiment
inductive nat : Type
| zero : nat
| succ : nat → nat
definition refl := @eq.refl
namespace nat
definition pred (n : nat) : nat := nat.rec zero (fun m x, m) n
theorem pred_zero : pred zero = zero := refl _
theorem pred_succ (n : nat) : pred (succ n) = n := refl _
theorem zer... |
59044bf174da3324ec122733819fcd6caaed58d2 | 9dd3f3912f7321eb58ee9aa8f21778ad6221f87c | /library/init/meta/decl_cmds.lean | 0c2eee7f984cd5b1e8801461a092b30833958687 | [
"Apache-2.0"
] | permissive | bre7k30/lean | de893411bcfa7b3c5572e61b9e1c52951b310aa4 | 5a924699d076dab1bd5af23a8f910b433e598d7a | refs/heads/master | 1,610,900,145,817 | 1,488,006,845,000 | 1,488,006,845,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,038 | 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.rb_map
open tactic
private meta def apply_replacement (replacements : name_map name) (e : expr) : expr :=
e^.repl... |
b125f215c2d86462a8a7a5f73ab8bb17ee4fef33 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/ring_theory/polynomial/gauss_lemma.lean | 427d8cca5a60d9ff1a08bea14483b04243c50861 | [
"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 | 12,051 | lean | /-
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import ring_theory.int.basic
import ring_theory.localization.integral
import ring_theory.integrally_closed
/-!
# Gauss's Lemma
Gauss's Lemma is one of a few result... |
3c283ce3bccc062e1039f370483ffc2287d5222e | 31f556cdeb9239ffc2fad8f905e33987ff4feab9 | /stage0/src/Lean/Elab/Extra.lean | d988dff15faa93ed2d83c8ceb8ce128cdab2b4f6 | [
"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 | 21,893 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Elab.App
import Lean.Elab.BuiltinNotation
/-! # Auxiliary elaboration functions: AKA custom elaborators -/
namespace Lean.Elab.Term
open Meta
... |
f48db62ab0c979663c23fcc82273b119293c3e5e | b7f22e51856f4989b970961f794f1c435f9b8f78 | /hott/homotopy/interval.hlean | d9ec4d1fc5d9b94e91015a6d79c74d12c8bd220f | [
"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 | 3,463 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
Declaration of the interval
-/
import .susp types.eq types.prod cubical.square
open eq susp unit equiv is_trunc nat prod
definition interval : Type₀ := susp unit
... |
319ec149bfd5ddbcf7b449d07c34b03b843d2fd9 | 30b012bb72d640ec30c8fdd4c45fdfa67beb012c | /data/nat/modeq.lean | 487119e1b78854e78785f93df5a7c00c3be06d18 | [
"Apache-2.0"
] | permissive | kckennylau/mathlib | 21fb810b701b10d6606d9002a4004f7672262e83 | 47b3477e20ffb5a06588dd3abb01fe0fe3205646 | refs/heads/master | 1,634,976,409,281 | 1,542,042,832,000 | 1,542,319,733,000 | 109,560,458 | 0 | 0 | Apache-2.0 | 1,542,369,208,000 | 1,509,867,494,000 | Lean | UTF-8 | Lean | false | false | 6,623 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
Modular equality relation.
-/
import data.int.gcd algebra.ordered_ring
namespace nat
/-- Modular equality. `modeq n a b`, or `a ≡ b [MOD n]`, means
that `a - b` is ... |
e099a1e40a41693865c6ec400e2762c8c0beb28d | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/nat/factorization/basic.lean | 492f64d1295d48a887ec59ae9ab889f9b85f9ac1 | [
"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 | 37,917 | lean | /-
Copyright (c) 2021 Stuart Presnell. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stuart Presnell
-/
import algebra.big_operators.finsupp
import data.finsupp.multiset
import data.nat.prime_fin
import number_theory.padics.padic_val
import data.nat.interval
import ta... |
1a3f7b80fc7c3c6e5c07bbfe2058ac105467874a | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/category_theory/monoidal/subcategory.lean | 5bf28be48ca431b2ebe64391033ede18d2743649 | [
"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 | 7,356 | lean | /-
Copyright (c) 2022 Antoine Labelle. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Labelle
-/
import category_theory.monoidal.braided
import category_theory.concrete_category.basic
import category_theory.closed.monoidal
/-!
# Full monoidal subcategories
Gi... |
42bcd4bdcf3a6d03ead60d39a57bff3fddb961af | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/category_theory/limits/shapes/zero.lean | d9b79d359e97b6a3ab4ae2e9442feb7d43f6933e | [
"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 | 15,232 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.limits.shapes.terminal
import category_theory.limits.shapes.binary_products
import category_theory.limits.shapes.products
import category_theor... |
482e92261a9bfbdb9cedad4869a6564d7b6288f9 | d1bbf1801b3dcb214451d48214589f511061da63 | /src/data/mv_polynomial/basic.lean | a65a27a9d642c7f8cf8486e6ba3f579ea7bc448c | [
"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 | 36,275 | 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.polynomial.eval
/-!
# Multivariate polynomials
This file defines polynomial rings over a base ring (or even semiring),
... |
ad14bc0ecfb3fe3e2801bd94ebb1169d6b106cee | c1a29ca460720df88ab68dc42d9a1a02e029d505 | /examples/basics/using_theorems_2_3.lean | e0d3c0e04d40ce8812f68fd71680bc3adef8cac7 | [] | no_license | agusakov/mathematics_in_lean | acb5b3d659e4522ae4b4836ea550527f03f6546c | 2539562e4d91c858c73dbecb5b282ce1a7d38b6d | refs/heads/master | 1,665,963,365,241 | 1,592,080,022,000 | 1,592,080,022,000 | 272,078,062 | 0 | 0 | null | 1,592,078,772,000 | 1,592,078,772,000 | null | UTF-8 | Lean | false | false | 9,702 | lean | import data.real.basic
import analysis.special_functions.exp_log
import tactic
variables a b c d e : ℝ
/-Rewriting is great for proving equations, but
what about other sorts of theorems? For example,
how can we prove an inequality, like the fact that
𝑎+𝑒𝑏≤𝑎+𝑒𝑐 holds whenever 𝑏≤𝑐? We have already seen
that... |
3e48833b075ed34b6cf53e5c430052025d730515 | 22e97a5d648fc451e25a06c668dc03ac7ed7bc25 | /src/control/traversable/basic.lean | ea7a47c297ca39dc73d10ced76da5fe3ac41a4b9 | [
"Apache-2.0"
] | permissive | keeferrowan/mathlib | f2818da875dbc7780830d09bd4c526b0764a4e50 | aad2dfc40e8e6a7e258287a7c1580318e865817e | refs/heads/master | 1,661,736,426,952 | 1,590,438,032,000 | 1,590,438,032,000 | 266,892,663 | 0 | 0 | Apache-2.0 | 1,590,445,835,000 | 1,590,445,835,000 | null | UTF-8 | Lean | false | false | 5,761 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Simon Hudon
-/
import control.functor
/-!
# Traversable type class
Type classes for traversing collections. The concepts and laws are taken from
<http://hackage.haskell.org/package/base-... |
19d840b7c8076d48de5b5725a08e99d238f57461 | 076f5040b63237c6dd928c6401329ed5adcb0e44 | /instructor-notes/2019.10.01.Polymorphism/option.lean | 88eeba4a946766949005a822404fa403dfc6af32 | [] | no_license | kevinsullivan/uva-cs-dm-f19 | 0f123689cf6cb078f263950b18382a7086bf30be | 09a950752884bd7ade4be33e9e89a2c4b1927167 | refs/heads/master | 1,594,771,841,541 | 1,575,853,850,000 | 1,575,853,850,000 | 205,433,890 | 4 | 9 | null | 1,571,592,121,000 | 1,567,188,539,000 | Lean | UTF-8 | Lean | false | false | 433 | lean | inductive moption (T : Type) : Type
| some : T → moption
| none : moption
def o1 := moption.some 3
def o2 := moption.none nat
def option_value {T :Type} : moption T → T → T
| (moption.some t) d := t
| (moption.none T) d := d
#reduce option_value o1 0
#reduce option_value o2 0
def just_zero : ℕ → moption nat
| 0 :=... |
a7e8f79ba64a08fcb65acdc4c4c80212937c3575 | abd85493667895c57a7507870867b28124b3998f | /src/data/nat/basic.lean | d0aeb1dc92b488d4c6faabaf1b3f5023e83c2548 | [
"Apache-2.0"
] | permissive | pechersky/mathlib | d56eef16bddb0bfc8bc552b05b7270aff5944393 | f1df14c2214ee114c9738e733efd5de174deb95d | refs/heads/master | 1,666,714,392,571 | 1,591,747,567,000 | 1,591,747,567,000 | 270,557,274 | 0 | 0 | Apache-2.0 | 1,591,597,975,000 | 1,591,597,974,000 | null | UTF-8 | Lean | false | false | 62,442 | lean | /-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-/
import algebra.ordered_ring
import algebra.order_functions
import init_.data.nat.lemmas
/-!
# Basic operations ... |
725aff6c3749e92332f39ee43cf7233c7c4e9ba2 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/algebraic_geometry/structure_sheaf.lean | bf115c0546af011d186f15eecddd660a351644b3 | [
"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 | 43,638 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Scott Morrison
-/
import algebraic_geometry.prime_spectrum
import algebra.category.CommRing.colimits
import algebra.category.CommRing.limits
import topology.sheaves.loc... |
91cc0bee4ffa1ac57a91486cd4b9fb0e5cc6fd8e | 12ba6fe891179eac82e287c24c8812a046221563 | /src/basic.lean | 4c67f4a651fb9476db83003c6b7db85b3d6d8677 | [] | no_license | b-mehta/combinatorics | eca586b4cb7b5e1fd22ec3288f5a2cb4ed6ce4dd | 2a8b30709d35f124f3fc9baa5652d231389e9f63 | refs/heads/master | 1,653,708,057,336 | 1,626,885,184,000 | 1,626,885,184,000 | 228,850,404 | 19 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,831 | 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 data.finset
import data.fintype.basic
open finset
variable {α : Type*}
variable {r : ℕ}
/-!
Basic definitions for finite sets which are useful for combinatori... |
329f705469d006f76702d7cf8a7ce865889b75b7 | 91b8df3b248df89472cc0b753fbe2bac750aefea | /experiments/lean/src/ddl/binary/monad.lean | bde63dfae0b781ebbe7b42810b77d34fc7181ec2 | [
"Apache-2.0",
"LicenseRef-scancode-unknown-license-reference"
] | permissive | yeslogic/fathom | eabe5c4112d3b4d5ec9096a57bb502254ddbdf15 | 3960a9466150d392c2cb103c5cb5fcffa0200814 | refs/heads/main | 1,685,349,769,736 | 1,675,998,621,000 | 1,675,998,621,000 | 28,993,871 | 214 | 11 | Apache-2.0 | 1,694,044,276,000 | 1,420,764,938,000 | Rust | UTF-8 | Lean | false | false | 3,322 | lean | import ddl.binary.basic
namespace ddl.binary.type
open ddl
open ddl.binary
variables {ℓ α β : Type}
def bind : type ℓ α → (α → type ℓ β) → type ℓ β
| (bvar i) f := bvar i
| (fvar x) f := (f x)
| (bit) f := bit
| (union_nil) f := union_nil
... |
f5e916532a3413442a3deed88e7c61745cd219b9 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/data/set/basic.lean | 173dc920e75a918da5bd77c4967506b400cfac2a | [
"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 | 61,140 | 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 tactic.basic tactic.finish data.subtype logic.unique
open function
/-! # Basic properties of sets
This file provides some basic definitions r... |
68b558b009597303ee8741152b7aa9aff0d4afd5 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/blast_ematch_sum.lean | 649805ffc2d4cde8897cbfdedbb2b3614e99c920 | [
"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 | 1,145 | lean | import data.nat
open nat
definition Sum : nat → (nat → nat) → nat :=
sorry
notation `Σ` binders ` < ` n `, ` r:(scoped f, Sum n f) := r
lemma Sum_const [forward] (n : nat) (c : nat) : (Σ x < n, c) = n * c :=
sorry
lemma Sum_add [forward] (f g : nat → nat) (n : nat) : (Σ x < n, f x + g x) = (Σ x < n, f x) + (Σ x < n... |
20105b7a3a086b98ac340e5dbb0401281e45f7d4 | 54f4ad05b219d444b709f56c2f619dd87d14ec29 | /my_project/src/love06_monads_exercise_sheet.lean | 0fa55942069326a3c1ce64e6faf3bb9d2fbbbbbd | [] | no_license | yizhou7/learning-lean | 8efcf838c7276e235a81bd291f467fa43ce56e0a | 91fb366c624df6e56e19555b2e482ce767cd8224 | refs/heads/master | 1,675,649,087,737 | 1,609,022,281,000 | 1,609,022,281,000 | 272,072,779 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,520 | lean | import .love06_monads_demo
/-! # LoVe Exercise 6: Monads -/
set_option pp.beta true
namespace LoVe
/-! ## Question 1: A State Monad with Failure
We introduce a richer notion of lawful monad that provides an `orelse`
operator `<|>` satisfying some laws, given below. `emp` denotes failure.
`x <|> y` tries `x` fir... |
5331ad9e78dd53bba5f88c8e842cbbcbbe4f0f62 | bab2ace2b909818f20ac125499a8dd88ce812721 | /src/2020/relations/partition_challenge_official_solution.lean | 5765d60591fe470269696eef13b9b6a86c5ddf9c | [] | no_license | LaplaceKorea/M40001_lean | 8a3cd411fb821a7665132c09e436f02f674cc666 | 116e9ed1fadf59dc2e78376fca92026859a03bf2 | refs/heads/master | 1,693,347,195,820 | 1,635,517,507,000 | 1,635,517,507,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,964 | lean | import tactic
/-!
# The partition challenge!
Prove that equivalence relations on α are the same as partitions of α.
Three sections:
1) partitions
2) equivalence classes
3) the challenge
Say `α` is a type, and `R` is a binary relation on `α`.
The following things are already in Lean:
reflexive R := ∀ (x : α), R... |
521d2c8f63b38a8fe5a14ce3d24004a550b7bfe4 | 9028d228ac200bbefe3a711342514dd4e4458bff | /src/category_theory/limits/cones.lean | 286c9e49ddce2c4c26c2e8109fa8f0c680cc82d8 | [
"Apache-2.0"
] | permissive | mcncm/mathlib | 8d25099344d9d2bee62822cb9ed43aa3e09fa05e | fde3d78cadeec5ef827b16ae55664ef115e66f57 | refs/heads/master | 1,672,743,316,277 | 1,602,618,514,000 | 1,602,618,514,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 27,176 | 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 category_theory.const
import category_theory.discrete_category
import category_theory.yoneda
import category_theory.reflects_... |
cd8f125fe76f5b33ef99b8e3d45cd918813fcd55 | 695574baef97a204f68217f2dfede8512fd91ff8 | /src/definitions.lean | 13ddeb8a313182502275df464ffb1bb138203cd1 | [] | no_license | JasonKYi/stone-weierstrass | ba463bedc758c4993e922afcc8cf8895a9257bd4 | 390affd1415cf393da55866b82fdf68747dee7a2 | refs/heads/master | 1,680,089,697,789 | 1,617,652,603,000 | 1,617,652,603,000 | 266,203,243 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,286 | lean | import topology.bounded_continuous_function
noncomputable theory
open set classical
local attribute [instance] prop_decidable
variables {X : Type*} [metric_space X] [compact_space X]
-- We adopt the notation of bounded countinuous function from mathlib
local infixr ` →ᵇ ` : 25 := bounded_continuous_function
/- This... |
f2a4f25a400cf2dc2db713471a888492035f5222 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/topology/separation.lean | 7119111c79de598d72032ffd8c7d8a4a4bf66e4b | [
"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 | 78,026 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import topology.subset_properties
import topology.connected
import topology.nhds_set
/-!
# Separation properties of topological spaces.
This file de... |
c54cb05854ac692e4f66592ca2928868d9b6e503 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/analysis/calculus/tangent_cone.lean | cca1f88f166ed31d6f9b0088bea34219793de814 | [
"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 | 16,600 | 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 analysis.convex.basic
import analysis.normed_space.bounded_linear_maps
import analysis.specific_limits
/-!
# Tangent cone
In this file, we define two p... |
d1ff00f5b9a6480279afa8c4a511af1a5f7c25e4 | 8b9f17008684d796c8022dab552e42f0cb6fb347 | /tests/lean/run/tactic13.lean | bf28801f72a6f4e9aafc1af113f06747cab9db78 | [
"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 | 244 | lean | import logic
open tactic
theorem tst (a b : Prop) (H : ¬ a ∨ ¬ b) (Hb : b) : ¬ a ∧ b :=
begin
apply and.intro,
assumption,
assume Ha, or.elim H
(assume Hna, @absurd _ false Ha Hna)
(assume Hnb, @absurd _ false Hb Hnb)
end
|
45390eacc0675d8653f9cacea6661c339f39553c | bf532e3e865883a676110e756f800e0ddeb465be | /tactic/ring.lean | ce9b1971d6b82b4ab0941dde42417638dc2f5f8d | [
"Apache-2.0"
] | permissive | aqjune/mathlib | da42a97d9e6670d2efaa7d2aa53ed3585dafc289 | f7977ff5a6bcf7e5c54eec908364ceb40dafc795 | refs/heads/master | 1,631,213,225,595 | 1,521,089,840,000 | 1,521,089,840,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 17,121 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
Evaluate expressions in the language of (semi-)rings.
Based on http://www.cs.ru.nl/~freek/courses/tt-2014/read/10.1.1.61.3041.pdf .
-/
import algebra.group_power tactic... |
8d10a96360405d9a0eb81f52cbc8a17852d72ef3 | d436468d80b739ba7e06843c4d0d2070e43448e5 | /src/data/finsupp.lean | 380044977e89302908925f01a8c924ec30ed8613 | [
"Apache-2.0"
] | permissive | roro47/mathlib | 761fdc002aef92f77818f3fef06bf6ec6fc1a28e | 80aa7d52537571a2ca62a3fdf71c9533a09422cf | refs/heads/master | 1,599,656,410,625 | 1,573,649,488,000 | 1,573,649,488,000 | 221,452,951 | 0 | 0 | Apache-2.0 | 1,573,647,693,000 | 1,573,647,692,000 | null | UTF-8 | Lean | false | false | 61,657 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Type of functions with finite support.
Functions with finite support provide the basis for the following concrete instances:
* ℕ →₀ α: Polynomials (where α is a ring... |
dac09a1fcce0733437da0232003f907581077327 | a7eef317ddec01b9fc6cfbb876fe7ac00f205ac7 | /src/analysis/normed_space/multilinear.lean | 1970930d3b4c56c056af182dedfaca77b138b4e5 | [
"Apache-2.0"
] | permissive | kmill/mathlib | ea5a007b67ae4e9e18dd50d31d8aa60f650425ee | 1a419a9fea7b959317eddd556e1bb9639f4dcc05 | refs/heads/master | 1,668,578,197,719 | 1,593,629,163,000 | 1,593,629,163,000 | 276,482,939 | 0 | 0 | null | 1,593,637,960,000 | 1,593,637,959,000 | null | UTF-8 | Lean | false | false | 54,557 | 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.normed_space.operator_norm
import topology.algebra.multilinear
/-!
# Operator norm on the space of continuous multilinear maps
When `f` is a c... |
bf96e2c3502b77efa4b3daf9d14277e568d41a81 | d642a6b1261b2cbe691e53561ac777b924751b63 | /src/data/rel.lean | a499a004eb71e7f6b4a9fb464fac24f9ad055975 | [
"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 | 6,041 | lean | /-
Copyright (c) 2018 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
Operations on set-valued functions, aka partial multifunctions, aka relations.
-/
import tactic.basic data.set.lattice order.complete_lattice
variables {α : Type*} {β : ... |
ad3ea953d859a4b28e83a8e18ad6240bd0abae7a | 4727251e0cd73359b15b664c3170e5d754078599 | /src/algebra/geom_sum.lean | 6955c57ae58469de9f55e0cfb96c87afb1bad95a | [
"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 | 21,323 | lean | /-
Copyright (c) 2019 Neil Strickland. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Neil Strickland
-/
import algebra.group_with_zero.power
import algebra.big_operators.order
import algebra.big_operators.ring
import algebra.big_operators.intervals
import tactic.abel... |
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