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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
bcb382412963de0b1210db6ad54406e1c158a842 | 1437b3495ef9020d5413178aa33c0a625f15f15f | /analysis/measure_theory/integration.lean | 732cdd3cd68574f8a754ef8fd7ec2ec66c49a72b | [
"Apache-2.0"
] | permissive | jean002/mathlib | c66bbb2d9fdc9c03ae07f869acac7ddbfce67a30 | dc6c38a765799c99c4d9c8d5207d9e6c9e0e2cfd | refs/heads/master | 1,587,027,806,375 | 1,547,306,358,000 | 1,547,306,358,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 29,137 | 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 ... |
9af6f8beb3e1cb1f5a8c8fc4d844520abef3b573 | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /08_Building_Theories_and_Proofs.org.21.lean | d06f962773f40c553ff742e979fc7229da0f8ebb | [] | 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 | 52 | lean | import standard
set_option unifier.max_steps 100000
|
9f169b5dceb41dcbe8af288385e3d0de361056ba | 54d7e71c3616d331b2ec3845d31deb08f3ff1dea | /tests/lean/run/dunfold3.lean | c7699e2700bf469472b57574ce44a2269c0d8a35 | [
"Apache-2.0"
] | permissive | pachugupta/lean | 6f3305c4292288311cc4ab4550060b17d49ffb1d | 0d02136a09ac4cf27b5c88361750e38e1f485a1a | refs/heads/master | 1,611,110,653,606 | 1,493,130,117,000 | 1,493,167,649,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 883 | lean | open tactic
def g : nat → nat := λ x, x + 5
example (a b : nat) (p : nat → Prop) (h : p (g (nat.succ (nat.succ a)))) : p (g (a + 2)) :=
begin
unfold g at h,
do { h ← get_local `h >>= infer_type, t ← to_expr `(p (nat.succ (nat.succ a) + 5)), guard (h = t) },
unfold add has_add.add bit0 one nat.add,
unfold g,
... |
faaf1f6915d36735d4a1274465e51cf6d3e0c0f4 | 4b846d8dabdc64e7ea03552bad8f7fa74763fc67 | /library/init/category/state.lean | 42cb19c5335fb288d4a4f48e8edd06a6bc30d643 | [
"Apache-2.0"
] | permissive | pacchiano/lean | 9324b33f3ac3b5c5647285160f9f6ea8d0d767dc | fdadada3a970377a6df8afcd629a6f2eab6e84e8 | refs/heads/master | 1,611,357,380,399 | 1,489,870,101,000 | 1,489,870,101,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,441 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.logic init.category.monad init.category.alternative
def state (σ : Type) (α : Type) : Type :=
σ → α × σ
section
variables {σ : Type} {... |
a08a485cda2c1b25e7d6b4b810d9b76f35752a3e | 969dbdfed67fda40a6f5a2b4f8c4a3c7dc01e0fb | /src/topology/separation.lean | 9494e67abe65b2a023b3d9356ce5847515676647 | [
"Apache-2.0"
] | permissive | SAAluthwela/mathlib | 62044349d72dd63983a8500214736aa7779634d3 | 83a4b8b990907291421de54a78988c024dc8a552 | refs/heads/master | 1,679,433,873,417 | 1,615,998,031,000 | 1,615,998,031,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 43,204 | 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
Separation properties of topological spaces.
-/
import topology.subset_properties
import topology.connected
open set filter
open_locale topological_spa... |
ec9668ae4dfbb1955fda5946ffb7ce5a26bf8e24 | 7b02c598aa57070b4cf4fbfe2416d0479220187f | /homotopy/cohomology.hlean | 38a7e4ccd68e07fa2a6156e270298f3ca31d4510 | [
"Apache-2.0"
] | permissive | jdchristensen/Spectral | 50d4f0ddaea1484d215ef74be951da6549de221d | 6ded2b94d7ae07c4098d96a68f80a9cd3d433eb8 | refs/heads/master | 1,611,555,010,649 | 1,496,724,191,000 | 1,496,724,191,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 12,138 | hlean | /-
Copyright (c) 2016 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
Reduced cohomology of spectra and cohomology theories
-/
import .spectrum ..algebra.arrow_group .fwedge ..choice .pushout ..algebra.product_group
open eq spectrum... |
923e7536d0013e4b734a0ad09c472b98825423df | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/measure_theory/ae_eq_fun.lean | e6ba384cf90ac3449013b7e3279d91bfccc26a60 | [
"Apache-2.0"
] | permissive | gebner/mathlib | eab0150cc4f79ec45d2016a8c21750244a2e7ff0 | cc6a6edc397c55118df62831e23bfbd6e6c6b4ab | refs/heads/master | 1,625,574,853,976 | 1,586,712,827,000 | 1,586,712,827,000 | 99,101,412 | 1 | 0 | Apache-2.0 | 1,586,716,389,000 | 1,501,667,958,000 | Lean | UTF-8 | Lean | false | false | 22,605 | lean | /-
Copyright (c) 2019 Johannes Hölzl, Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Zhouhang Zhou
-/
import measure_theory.integration
/-!
# Almost everywhere equal functions
Two measurable functions are treated as identical if they ... |
746c5fd6770aaaad489bb7c9175e7204e1831f50 | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/data/real/irrational.lean | 5fbe72943cd594d3a089b87e21ed250fda7fd858 | [
"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 | 9,562 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Yury Kudryashov
-/
import data.real.sqrt
import data.rat.sqrt
import ring_theory.int.basic
import data.polynomial.eval
i... |
dcf697bb63617344cb447d63c6915e241c686157 | e00ea76a720126cf9f6d732ad6216b5b824d20a7 | /src/analysis/calculus/fderiv.lean | 9dc5e2e36fdea9a757f4703df8957135f92806f0 | [
"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 | 80,385 | lean | /-
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Sébastien Gouëzel, Yury Kudryashov
-/
import analysis.asymptotics analysis.calculus.tangent_cone
/-!
# The Fréchet derivative
Let `E` and `F` be normed spaces, `f : E ... |
8b127b0b72cae0bc6c44f91cee11ec7270c9ed78 | bb31430994044506fa42fd667e2d556327e18dfe | /src/data/polynomial/field_division.lean | b1a6db3f07905a0f3b359bc771cbf3fadd041ceb | [
"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 | 19,401 | 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.derivative
import data.polynomial.ring_division
import ring_theory.euclidean_domain
/-!
# Theory o... |
4f4b56b6e775fe732f6fbc9fe170cf9e7cf3ccac | f7315930643edc12e76c229a742d5446dad77097 | /tests/lean/run/466.lean | 6716d61fc4f00427209c761d5c370024206886ba | [
"Apache-2.0"
] | permissive | bmalehorn/lean | 8f77b762a76c59afff7b7403f9eb5fc2c3ce70c1 | 53653c352643751c4b62ff63ec5e555f11dae8eb | refs/heads/master | 1,610,945,684,489 | 1,429,681,220,000 | 1,429,681,449,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 179 | lean | open eq
section
parameter (A : Type)
definition foo (a : A) : a = a := refl a
definition bar (a : A) : foo a = refl a :=
begin
unfold foo,
apply rfl
end
end
|
867cc123743a22815534767055edfa36c58826fd | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/int/nat_prime.lean | c49b3c290572401e0824e312a9180a635325ac3b | [
"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 | 1,610 | lean | /-
Copyright (c) 2020 Bryan Gin-ge Chen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Lacker, Bryan Gin-ge Chen
-/
import data.nat.prime
/-!
# Lemmas about nat.prime using `int`s
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a ... |
e3e729e831055b842cba22609fef1817bf4c2070 | 31f556cdeb9239ffc2fad8f905e33987ff4feab9 | /stage0/src/Lean/Compiler/LCNF/ElimDead.lean | 156004bcc23269c9d86cd0d953def3b64f1ebd1e | [
"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 | 2,407 | lean | /-
Copyright (c) 2022 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Compiler.LCNF.CompilerM
namespace Lean.Compiler.LCNF
abbrev UsedLocalDecls := FVarIdHashSet
/--
Collect set of (let) free variables in a LCNF... |
1fb6ff2f33d670eb6e27d80877891a4226933d2a | 7282d49021d38dacd06c4ce45a48d09627687fe0 | /tests/lean/simp17.lean | facb8e33caea68b5fc0d8473cad87eb3ca4389bb | [
"Apache-2.0"
] | permissive | steveluc/lean | 5a0b4431acefaf77f15b25bbb49294c2449923ad | 92ba4e8b2d040a799eda7deb8d2a7cdd3e69c496 | refs/heads/master | 1,611,332,256,930 | 1,391,013,244,000 | 1,391,013,244,000 | 16,361,079 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 343 | lean | rewrite_set simple
add_rewrite and_truer and_truel and_falser and_falsel or_falsel Nat::add_zeror : simple
(*
add_congr_theorem("simple", "and_congrr")
*)
variables a b c : Nat
(*
local t = parse_lean([[c + 0 ≠ b + 1 ∧ b = 0 ∧ c = 1]])
local s, pr = simplify(t, "simple")
print(s)
print(pr)
print(get_environment():t... |
6b3e1027035e8e41098da36c0ae6053c992083a3 | 4bcaca5dc83d49803f72b7b5920b75b6e7d9de2d | /stage0/src/Lean/Meta/Basic.lean | c41eed377fee9a5c3a6d2fe7af2bfa2069d80ad3 | [
"Apache-2.0"
] | permissive | subfish-zhou/leanprover-zh_CN.github.io | 30b9fba9bd790720bd95764e61ae796697d2f603 | 8b2985d4a3d458ceda9361ac454c28168d920d3f | refs/heads/master | 1,689,709,967,820 | 1,632,503,056,000 | 1,632,503,056,000 | 409,962,097 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 49,864 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Data.LOption
import Lean.Environment
import Lean.Class
import Lean.ReducibilityAttrs
import Lean.Util.Trace
import Lean.Util.RecDepth
import Lea... |
9394e2b658e090370961f0ab8ec968c86b2eb7a3 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/nat/sqrt_norm_num.lean | 4ae37dded19f09aac9904f42f6a12983d053a29c | [
"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 | 1,469 | lean | /-
Copyright (c) 2022 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import tactic.norm_num
import data.nat.sqrt
/-! ### `norm_num` plugin for `sqrt`
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a cor... |
ee08a1b2cc79d8e9b2e802205809479a2daf6e6e | 4727251e0cd73359b15b664c3170e5d754078599 | /test/calc.lean | a527971d154fdc34806d6ff08b16d7eee725162c | [
"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 | 1,056 | lean | import analysis.asymptotics.asymptotic_equivalent
import measure_theory.integral.interval_integral
import measure_theory.measure.vector_measure
variables {α β γ δ : Type*}
section is_equivalent
open_locale asymptotics
example {l : filter α} {u v w : α → β} [normed_group β]
(huv : u ~[l] v) (hvw : v ~[l] w) : u ~[... |
2231ddab8da370cf052430d90119ed5f3a34b832 | 61ccc57f9d72048e493dd6969b56ebd7f0a8f9e8 | /src/algebra/category/Group/Z_Module_equivalence.lean | 4b6394d2e5f6d1e9d17984127a905172996426d6 | [
"Apache-2.0"
] | permissive | jtristan/mathlib | 375b3c8682975df28f79f53efcb7c88840118467 | 8fa8f175271320d675277a672f59ec53abd62f10 | refs/heads/master | 1,651,072,765,551 | 1,588,255,641,000 | 1,588,255,641,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,289 | 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.Module.basic
/-!
The forgetful functor from ℤ-modules to additive commutative groups is
an equivalence of categories.
TODO:
either use this ... |
43973d899746e1a509b26a8b0d1ca785b4358949 | e0b0b1648286e442507eb62344760d5cd8d13f2d | /tests/lean/run/decClassical.lean | 821ad9caaae594f8d90d9375e9539c860b9b8abe | [
"Apache-2.0"
] | permissive | MULXCODE/lean4 | 743ed389e05e26e09c6a11d24607ad5a697db39b | 4675817a9e89824eca37192364cd47a4027c6437 | refs/heads/master | 1,682,231,879,857 | 1,620,423,501,000 | 1,620,423,501,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 304 | lean | open Classical
theorem ex : if (fun x => x + 1) = (fun x => x + 2) then False else True := by
have (fun x => x + 1) ≠ (fun x => x + 2) by
intro h
have 1 = 2 from congrFun h 0
contradiction
rw [ifNeg this]
exact True.intro
def tst (x : Nat) : Bool :=
if 1 < 2 then true else false
|
03bc0c999c7eb35a5afe4da686bbeb095f1b2a56 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/category_theory/types.lean | 41c59d98a3a8b492037ad6c173a051d45c05f18e | [
"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 | 11,116 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stephen Morgan, Scott Morrison, Johannes Hölzl
-/
import category_theory.epi_mono
import category_theory.functor.fully_faithful
import logic.equiv.basic
/-!
# The category `Type`.
In... |
fff5ddcddd37566dd30c2011161f3a64376cc889 | 1e3a43e8ba59c6fe1c66775b6e833e721eaf1675 | /src/data/real/ennreal.lean | 46fd9355460ad1cd20fc12e57d79e0f5950c974b | [
"Apache-2.0"
] | permissive | Sterrs/mathlib | ea6910847b8dfd18500486de9ab0ee35704a3f52 | d9327e433804004aa1dc65091bbe0de1e5a08c5e | refs/heads/master | 1,650,769,884,257 | 1,587,808,694,000 | 1,587,808,694,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 44,685 | 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
Extended non-negative reals
-/
import data.real.nnreal
import data.set.intervals
noncomputable theory
open classical set
open_locale classical
variable... |
04feeba07219ea0899c9c802cbdf69db9d3b8200 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/group_theory/eckmann_hilton.lean | 9a60bf7806bf96fe18c459faf7d7736a19dcc205 | [
"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 | 1,910 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Kenny Lau, Robert Y. Lewis
-/
import tactic.basic
universe u
namespace eckmann_hilton
variables {X : Type u}
local notation a `<`m`>` b := m a b
class is_unital (m : X ... |
21275995fc4b05172650469088141c893f3420cc | d1a52c3f208fa42c41df8278c3d280f075eb020c | /stage0/src/Lean/Data/Json/Parser.lean | 1255653ae61bd7200690e96afa97d1c223f29369 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | cipher1024/lean4 | 6e1f98bb58e7a92b28f5364eb38a14c8d0aae393 | 69114d3b50806264ef35b57394391c3e738a9822 | refs/heads/master | 1,642,227,983,603 | 1,642,011,696,000 | 1,642,011,696,000 | 228,607,691 | 0 | 0 | Apache-2.0 | 1,576,584,269,000 | 1,576,584,268,000 | null | UTF-8 | Lean | false | false | 5,433 | 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.Parsec
namespace Lean
open Std (RBNode RBNode.singleton RBNode.leaf)
namespace Json.Parser
open Lean.Pa... |
66cc25151529f3f067e4d254c7cff48dba44dad3 | de8d0cdc3dc15aa390280472764229d0e14e734c | /src/pointwise_convergence.lean | 1c861e0f725adc4387360f34ea17ae16e039ac1e | [] | no_license | amesnard0/lean-topology | 94720ccf0af34961b24b52b96bcfb19df5c8f544 | e8f6a720c435cb59d098579a26f6eb70ea05f91a | refs/heads/main | 1,682,525,569,376 | 1,622,116,766,000 | 1,622,116,766,000 | 358,047,823 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,867 | lean | import tactic
import data.set.finite
import topological_spaces
import neighbourhoods
import topological_spaces2
open set
open_locale classical
open topological_space
-- Convergence simple :
def pointwise_lim {X Y : Type} [topological_space Y] (f : ℕ → (X → Y)) (F : X → Y) : Prop :=
∀ (x : X), seq_lim (λ n, f n x) ... |
ef3844d25dd4bad3b75e9700be265b6b423c02b5 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /archive/imo/imo2008_q4.lean | 8b1db18a76517819a456e16922937d7b34ec43f5 | [
"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 | 5,534 | lean | /-
Copyright (c) 2021 Manuel Candales. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Manuel Candales
-/
import data.real.basic
import data.real.sqrt
import data.real.nnreal
/-!
# IMO 2008 Q4
Find all functions `f : (0,∞) → (0,∞)` (so, `f` is a function from the posit... |
616467ff50b938244156849302bdcc95c7f127f0 | 66a6486e19b71391cc438afee5f081a4257564ec | /heq.hlean | 2fabb7438971760d5579bf81ec1038ea826118e2 | [
"Apache-2.0"
] | permissive | spiceghello/Spectral | c8ccd1e32d4b6a9132ccee20fcba44b477cd0331 | 20023aa3de27c22ab9f9b4a177f5a1efdec2b19f | refs/heads/master | 1,611,263,374,078 | 1,523,349,717,000 | 1,523,349,717,000 | 92,312,239 | 0 | 0 | null | 1,495,642,470,000 | 1,495,642,470,000 | null | UTF-8 | Lean | false | false | 1,801 | hlean | -- Author: Floris van Doorn
open eq is_trunc
variables {I : Set} {P : I → Type} {i j k : I} {x x₁ x₂ : P i} {y y₁ y₂ : P j} {z : P k}
{Q : Π⦃i⦄, P i → Type}
structure heq (x : P i) (y : P j) : Type :=
(p : i = j)
(q : x =[p] y)
namespace eq
notation x ` ==[`:50 P:0 `] `:0 y:50 := @heq _ P _ _ x y
infi... |
cbb37c4cd54f4b9341567a194e063404eac15094 | 5d166a16ae129621cb54ca9dde86c275d7d2b483 | /library/init/meta/smt/smt_tactic.lean | 01c2d6e3a4af159fdb260b9998ffe6a584ba4d94 | [
"Apache-2.0"
] | permissive | jcarlson23/lean | b00098763291397e0ac76b37a2dd96bc013bd247 | 8de88701247f54d325edd46c0eed57aeacb64baf | refs/heads/master | 1,611,571,813,719 | 1,497,020,963,000 | 1,497,021,515,000 | 93,882,536 | 1 | 0 | null | 1,497,029,896,000 | 1,497,029,896,000 | null | UTF-8 | Lean | false | false | 15,312 | 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.category
import init.meta.simp_tactic
import init.meta.smt.congruence_closure
import init.meta.smt.ematch
universe u
run_cmd mk_simp_a... |
7602297153c982b02efb77448ef063569b0e7f99 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/category_theory/subobject/lattice.lean | f56923aeb54e82b92f89c4f478fc857077b29c38 | [
"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 | 22,481 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Scott Morrison
-/
import category_theory.subobject.factor_thru
import category_theory.subobject.well_powered
/-!
# The lattice of subobjects
We provide the `semilattice... |
b9b99dc49302a61bf18defa3535e666ef3b45eb1 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/lie/semisimple.lean | d76852391a9c73700e4e42fd9b7175b82d160a9e | [
"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 | 4,593 | lean | /-
Copyright (c) 2021 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import algebra.lie.solvable
/-!
# Semisimple Lie algebras
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathlib4.
T... |
c68ce65e1b807730536f049d38180a82be7fd253 | 65807aed539a1b7077e26f006d2ee5724004fd5d | /src/chap1.lean | fcfc712326e4e65aab5e58a2a106372f9081d6d3 | [] | no_license | b-mehta/generating-functions | d6c00769c751b3c4e5fd681a33fbcba43ab9243a | 2fc00b2ba7ed92d1e24682124cac146d23b47f92 | refs/heads/master | 1,671,586,110,726 | 1,601,063,036,000 | 1,601,063,036,000 | 296,391,458 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,779 | lean | import ring_theory.power_series
import combinatorics.composition
import data.nat.parity
open power_series
noncomputable theory
variables {α : Type*}
/-- The sequence from section 1.1 of GFology -/
def sequence_one_one : ℕ → ℚ
| 0 := 0
| (n+1) := 2 * sequence_one_one n + 1
/-- Inductive proof of the formula -/
lemma... |
b8615c7a129566d63b50b64bc9ce290e991d34d8 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/algebraic_geometry/presheafed_space.lean | 7438ac454d3b00fc8c925f4a4e2b4b41abe28dba | [] | 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 | 12,903 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.topology.sheaves.presheaf
import Mathlib.PostPort
universes v u l
namespace Mathlib
/-!... |
11b848124c1cfff1d4f48955e6571c8ee5ae521a | 8c02fed42525b65813b55c064afe2484758d6d09 | /src/spec/spec.lean | 1be9ffc8bde6e2a0af152e9df0ecebdf25900aef | [
"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 | 13,095 | lean | -- Copyright (c) Microsoft Corporation. All rights reserved.
-- Licensed under the MIT license.
import ..smtexpr
import ..bitvector
import ..irsem
import ..irsem_exec
import ..irsem_smt
import ..freevar
import ..verifyopt
import .lemmas_basic
import smt2.syntax
import smt2.solvers.z3
import system.io
namespace spec
... |
9acbef9299d05b89ceaffcd5cb2c4dda8e631f23 | 0d22ec5e0205ec4203aae2ddf07e1f695ff21a61 | /src/step3.lean | d7b58a7ffbe526219de5a6cc9544ba9af5fc4d09 | [
"Apache-2.0"
] | permissive | shingtaklam1324/step3-06-q8-lean | 4611fda6b002797d38d3f625253960dcfeb2a987 | 20e5161fab8b5c3c2dd051bd707a26f1dc50dac2 | refs/heads/master | 1,649,936,589,910 | 1,585,242,273,000 | 1,585,242,273,000 | 250,318,324 | 2 | 0 | Apache-2.0 | 1,585,389,271,000 | 1,585,241,690,000 | Lean | UTF-8 | Lean | false | false | 3,068 | lean | /-
2006 STEP 3 Question 8
-/
import data.polynomial
data.real.basic
tactic
open polynomial
/-
Δ is a function takes takes polynomials in x to polynomials in x; that is, given
any polynomial h(x), there is a polynomial called Δh(x) which is obtained from
h(x) using the rules that define Δ.
-/
variable ... |
d590338648c61cd110db9c5821529311a03baf05 | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/multiset/nat_antidiagonal.lean | 7bb1e2b071760fda5e8b733e0b16b68a30cb8302 | [
"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 | 1,487 | lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import data.multiset.nodup
import data.list.nat_antidiagonal
/-!
# The "antidiagonal" {(0,n), (1,n-1), ..., (n,0)} as a multiset.
-/
namespace multiset
namespace na... |
0a9467cdf65b97df374894f3d70e2ed86527998b | 94e33a31faa76775069b071adea97e86e218a8ee | /src/geometry/euclidean/basic.lean | d67d199e4960f098c365402f2578d66a5764cab2 | [
"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 | 56,972 | lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers, Manuel Candales
-/
import analysis.inner_product_space.projection
import analysis.special_functions.trigonometric.inverse
import algebra.quadratic_discriminant
import linea... |
f6268ee7e6b02cf2f409a2d53e908d24ea393dfc | ac89c256db07448984849346288e0eeffe8b20d0 | /stage0/src/Lean/Parser/Basic.lean | a9740fa7d441f3bbb24eee95730d38280b6ac9e6 | [
"Apache-2.0"
] | permissive | chepinzhang/lean4 | 002cc667f35417a418f0ebc9cb4a44559bb0ccac | 24fe2875c68549b5481f07c57eab4ad4a0ae5305 | refs/heads/master | 1,688,942,838,326 | 1,628,801,942,000 | 1,628,801,995,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 76,132 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Sebastian Ullrich
-/
import Lean.Data.Trie
import Lean.Data.Position
import Lean.Syntax
import Lean.ToExpr
import Lean.Environment
import Lean.Attributes
impo... |
487096af27e1b77ec6600801da9c533f53175930 | de7b3dbc03c2200899ec842ca1e7cba570a04fa1 | /src/sort_benchmarks.lean | c9078a51a744689798caffa6294db57c33375995 | [] | no_license | robertylewis/relevance_filter | 4c48a0e02bbeef857f9c67b0f7dc8f3acd5b906a | d11544e08c6d3569410e312baf149412b168ebb4 | refs/heads/master | 1,670,019,263,018 | 1,597,851,640,000 | 1,597,851,640,000 | 105,209,556 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 1,256 | lean | import .sort data.list.sort
open native
meta instance : inhabited float := ⟨0⟩
-- meta constant float.random : float
set_option profiler true
--set_option trace.array.update true
/-
all updates are destructive. I don't know why my array quicksort takes twice the time of list.qsort.
They seem to scale at... |
743f7ee1101a9f541935eeaf48c48bbd4507edf0 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/probability/stopping.lean | b45d42c26a784b5e1aa6bfabc2eb3dd42655ca56 | [
"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 | 61,931 | 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.function.conditional_expectation.real
import topology.instances.discrete
/-!
# Filtration and stopping time
This file defines some standard definiti... |
3313e5242ddf2f0ff2cc2bd9a618ec4c1030f663 | 7bc35d4fbdda0c01e9b22a949940ee5cbb9800d0 | /basis.lean | b0f0f99e1f17e406a2064e06a233a49480e38f47 | [] | no_license | truonghoangle/manifolds | e6c2534dd46579f56ba99a48e2eb7ce51640e7c0 | dcf4815b29ad363ec9712fd00b7756c36cfa7c1c | refs/heads/main | 1,638,501,090,139 | 1,636,918,550,000 | 1,636,918,550,000 | 185,779,631 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 703 | lean | import topology.constructions
import equiv
open topological_space
noncomputable theory
universes u v
variables {α : Type u} {β : Type v}
structure Top :=
(carrier : Type u)
(struct : topological_space carrier)
namespace Top
instance : has_coe_to_sort Top := ⟨Type*, Top.carrier⟩
attribute [instance] Top.st... |
3d51a5387e7dc7dad6d361e4dac88e6613c39a2d | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/dfinsupp/lex.lean | 91aa1fa74b091f01fae8a4532ad24c21a5b8df78 | [
"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 | 6,799 | lean | /-
Copyright (c) 2022 Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa, Junyan Xu
-/
import data.dfinsupp.order
import data.dfinsupp.ne_locus
import order.well_founded_set
/-!
# Lexicographic order on finitely supported dependent functions
This... |
b873621b778877d6636db01d425f46e58505ea66 | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/simple.lean | 8d9e40fe477cb467e4a54884b041e90ce67f9b3d | [
"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 | 45 | lean | import Int.
variable x : Int
variable y : Int |
e2b80aa12db3a6a0c5dc915f15302a7c6e955964 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/order/filter/germ.lean | 74ca4709019a2e859d5f357b4d2e9460bf5a6947 | [
"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 | 22,358 | 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, Abhimanyu Pallavi Sudhir
-/
import order.filter.basic
import algebra.module.pi
/-!
# Germ of a function at a filter
The germ of a function `f : α → β` at a fi... |
5a4ab54aead1ce1312276e07dddb21bba21e6838 | 097294e9b80f0d9893ac160b9c7219aa135b51b9 | /instructor/objects/prod_s_t.lean | e3a871c495b548598048a857e3853117d2837930 | [] | no_license | AbigailCastro17/CS2102-Discrete-Math | cf296251be9418ce90206f5e66bde9163e21abf9 | d741e4d2d6a9b2e0c8380e51706218b8f608cee4 | refs/heads/main | 1,682,891,087,358 | 1,621,401,341,000 | 1,621,401,341,000 | 368,749,959 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 519 | lean | -- Ordered pairs
#eval prod.mk 2 3 -- represents (2, 3)
#eval prod.mk 2 tt -- represents (2, tt)
#eval prod.mk tt ff -- represents (tt, ff)
#eval prod.mk -- a pair of pairs
(prod.mk 2 tt)
(prod.mk "Hello" 3)
-- Notation
#eval (2, 3) -- prod.mk 2 3
#eval (2, tt) -- etc.
#eval (tt, ff)... |
f17e70108e8ed1ec993992f72c043acc60e77114 | 28b6e1a13d35e9b450f65c001660f4ec4713aa10 | /Search/NTactic/Basic.lean | 6b2db43f844f796aa313923e631834b32b693194 | [
"Apache-2.0"
] | permissive | dselsam/search | 14e3af3261a7a70f8e5885db9722b186f96fe1f5 | 67003b859d2228d291a3873af6279c1f61430c64 | refs/heads/master | 1,684,700,794,306 | 1,614,294,810,000 | 1,614,294,810,000 | 339,578,823 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,536 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Daniel Selsam
-/
import Search.Transform.Classic
import Search.SaveRestore
import Search.Heuristic
import Search.Generic.Heuristic
import Search.Algorithm.BestFirst
import Lean
... |
a444712babef731872ec80b341dee7d74f34cbea | d78da34857deb99eac819e7889eae59fdccec754 | /src/article3.lean | a0262387e2440fbd9792731bbc1c9e1346d5d97c | [] | no_license | wudcscheme/conceptual-mathematics-in-lean | 6ef168b69fb28eb25223db10ebb4b2fefad4dbdb | cc7877f528bfaf99a024844744e023acbfcadb1d | refs/heads/master | 1,678,885,284,910 | 1,601,437,497,000 | 1,601,663,206,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 17,428 | lean | import category_theory.category
import category_theory.isomorphism
import category_theory.types
import category_theory.isomorphism
import data.finset.basic
import data.finset.sort
import data.int.parity
import .article2
namespace exercises
universe u
section endomaps
open category_theory
variables {α β: Type*}
va... |
80c0c89a43f66ec90909e724c4fd771d25349ce5 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/analysis/normed_space/hahn_banach/separation.lean | 490875ab9ab2869c241532e98b0a3fa3e717e896 | [
"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 | 10,589 | lean | /-
Copyright (c) 2022 Bhavik Mehta All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Yaël Dillies
-/
import analysis.convex.cone.basic
import analysis.convex.gauge
/-!
# Separation Hahn-Banach theorem
In this file we prove the geometric Hahn-Banach theorem... |
526c1c59a909893212146706be20fa5ad4409076 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/number_theory/sum_four_squares.lean | 4b4ae4d06d78f33a95cd9537e3751cb7ba14fcf2 | [
"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 | 12,015 | lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
## Lagrange's four square theorem
The main result in this file is `sum_four_squares`,
a proof that every natural number is the sum of four square numbers.
# Implementatio... |
b5bee400e96c605beb81690c657d2e76052ebcba | d1a52c3f208fa42c41df8278c3d280f075eb020c | /tests/lean/run/meta3.lean | ed8b1379a1fccc6754b22a6c910c3473013aae63 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | cipher1024/lean4 | 6e1f98bb58e7a92b28f5364eb38a14c8d0aae393 | 69114d3b50806264ef35b57394391c3e738a9822 | refs/heads/master | 1,642,227,983,603 | 1,642,011,696,000 | 1,642,011,696,000 | 228,607,691 | 0 | 0 | Apache-2.0 | 1,576,584,269,000 | 1,576,584,268,000 | null | UTF-8 | Lean | false | false | 1,859 | lean | import Lean.Meta
open Lean
open Lean.Meta
def dbgOpt : Options :=
let opt : Options := {};
let opt := opt.setBool `trace.Meta true;
-- let opt := opt.setBool `trace.Meta.check false;
opt
def print (msg : MessageData) : MetaM Unit := do
trace[Meta.debug] msg
def check (x : MetaM Bool) : MetaM Unit :=
unless (← x) do... |
d11d9c60ef2b12863e433ef98f7be68e9fad9829 | a4673261e60b025e2c8c825dfa4ab9108246c32e | /stage0/src/Lean/Parser/Do.lean | fe3fb0402280972d6b4066c4316cc19ea544f48d | [
"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 | 5,758 | 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
namespace Lean
namespace Parser
builtin_initialize registerBuiltinParserAttribute `builtinDoElemParser `doElem
builtin_initialize ... |
7ec7c008d9d240418531b8b1b65e466cf49f514c | 7cdf3413c097e5d36492d12cdd07030eb991d394 | /world_experiments/world7/level10andathird.lean | 729672e5a3372afdcdfe621598d6689b071bb752 | [] | no_license | alreadydone/natural_number_game | 3135b9385a9f43e74cfbf79513fc37e69b99e0b3 | 1a39e693df4f4e871eb449890d3c7715a25c2ec9 | refs/heads/master | 1,599,387,390,105 | 1,573,200,587,000 | 1,573,200,691,000 | 220,397,084 | 0 | 0 | null | 1,573,192,734,000 | 1,573,192,733,000 | null | UTF-8 | Lean | false | false | 1,587 | lean | import mynat.definition -- hide
import mynat.add -- hide
import game.world2.level10 -- hide
namespace mynat -- hide
/-
# World 2 -- Addition World
## Level 7 -- `succ_ne_zero`
Levels 7 to 16 are some more advanced facts about addition. If you want
to see what theorems or tactics you have, look in the drop-down menu... |
4abfa0e144f4198cacebdf734f3734a3b7caf0b9 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/tactic/reserved_notation.lean | 0f18d64545518ae262de0da086828a670cfdef77 | [
"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 | 1,607 | lean | /-
Copyright (c) 2020 Bryan Gin-ge Chen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bryan Gin-ge Chen
-/
/-!
# Reserved notation
This file is imported by `logic.basic` and `logic.relator` to place it at the top of the
import graph.
We place all of `mathlib`'s re... |
bac8bdd47f106caf7fde6ef11d1ead55b6aba60e | 80746c6dba6a866de5431094bf9f8f841b043d77 | /src/ring_theory/polynomial.lean | 1f8b494ab15384ffab45712500a59201dd3eb64d | [
"Apache-2.0"
] | permissive | leanprover-fork/mathlib-backup | 8b5c95c535b148fca858f7e8db75a76252e32987 | 0eb9db6a1a8a605f0cf9e33873d0450f9f0ae9b0 | refs/heads/master | 1,585,156,056,139 | 1,548,864,430,000 | 1,548,864,438,000 | 143,964,213 | 0 | 0 | Apache-2.0 | 1,550,795,966,000 | 1,533,705,322,000 | Lean | UTF-8 | Lean | false | false | 9,154 | lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
Hilbert basis theorem: if a ring is noetherian then so is its polynomial ring.
-/
import linear_algebra.multivariate_polynomial
import data.polynomial
import ring_theory.princip... |
ca39ef32ec94f53881d36213f389960faf70905e | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /tests/lean/236.lean | 6f6dc59f10274ed1cad166d7c73580fc6132e060 | [
"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 | 214 | lean | structure Foo where
x : Nat
b : Bool
#check { x := 10, b := true : Foo }
set_option pp.all true
#check { x := 10, b := true : Foo }
set_option pp.structure_instances true
#check { x := 10, b := true : Foo }
|
608f415d8b67cea106b3796ea74eb1d63f21cfc6 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/topology/sheaves/presheaf.lean | f0b55bd21d3df37b3b7e0723ba54c0910722b375 | [
"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 | 11,945 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Mario Carneiro, Reid Barton, Andrew Yang
-/
import category_theory.limits.kan_extension
import category_theory.adjunction
import topology.category.Top.opens
/-!
# Pres... |
26afcc2882629bb679962a581776c2774f7ddf61 | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/ring_theory/noetherian.lean | 39b930e2adafad6e8a0379d2b1ddd6a4ca5adf7e | [
"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 | 36,653 | lean | /-
Copyright (c) 2018 Mario Carneiro, Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Kevin Buzzard
-/
import algebraic_geometry.prime_spectrum
import data.multiset.finset_ops
import linear_algebra.linear_independent
import order.order_iso... |
078af4003db35ce81290ef610de4f5146eb6511c | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/algebraic_geometry/morphisms/quasi_compact.lean | ce3b7758ffb832e95c36878995d04ce4e4456f35 | [
"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 | 10,442 | lean | /-
Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import algebraic_geometry.morphisms.basic
import topology.spectral.hom
/-!
# Quasi-compact morphisms
A morphism of schemes is quasi-compact if the preimages of quasi-comp... |
c4bc1883d2497b294ee0e7642dd825027595022c | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/topology/sheaves/sheaf_condition/pairwise_intersections_auto.lean | 558fd0f5c5289a248e4d73a13e7f2f2d0430fbde | [] | 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 | 13,101 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.topology.sheaves.sheaf
import Mathlib.category_theory.limits.preserves.basic
import Mathlib... |
efef72df67aa6e7d41072eeaf0428a90052ff03e | 9cb9db9d79fad57d80ca53543dc07efb7c4f3838 | /src/locally_constant/analysis.lean | b96fc6b0ab56927d619c2c23e524e4703846daa2 | [] | no_license | mr-infty/lean-liquid | 3ff89d1f66244b434654c59bdbd6b77cb7de0109 | a8db559073d2101173775ccbd85729d3a4f1ed4d | refs/heads/master | 1,678,465,145,334 | 1,614,565,310,000 | 1,614,565,310,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,460 | lean | import topology.locally_constant.algebra
import for_mathlib.normed_group_hom
/-!
# Analysis of locally constant maps
This file defines the normed group of locally constant maps into a normed group.
## Main construction
* The instance `locally_constant.normed_group`
* `locally_constant.map_hom`: push-forward of loca... |
d198b4ddd18454b0b95e02b92e7c541f59b300ab | e2c1ee9c02c59b832eb48536755242ce5f9b2c3e | /src/t8.lean | 10376127793d521fb1adde590391cb71f801282b | [] | no_license | yairgueta/Lean | cb5bb16d81674e8a07f85c9dbeb56dc2f543d4eb | af8a4fa24f76edfdd0dd33f013db194e611e6a86 | refs/heads/master | 1,676,275,529,938 | 1,610,289,661,000 | 1,610,289,661,000 | 328,405,309 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,371 | lean | universe u
inductive vector (α : Type u) : nat → Type u
| nil {} : vector 0
| cons : Π {n}, α → vector n → vector (n+1)
namespace vector
local notation h :: t := cons h t
def append_tail {α : Type*} : Π {n : ℕ}, vector α n → α → vector α (n+1)
| 0 nil a := a :: nil
| (n+1) (a::v) b := a::(append_tail v b)
--... |
c9e324e4eea4fc1f6a6fa02a8cdf55b060372ef4 | 76df16d6c3760cb415f1294caee997cc4736e09b | /lean/src/interp/lang/thm.lean | a1a3d263a37dc49a1e19b36670e43320bdbf152a | [
"MIT"
] | permissive | uw-unsat/leanette-popl22-artifact | 70409d9cbd8921d794d27b7992bf1d9a4087e9fe | 80fea2519e61b45a283fbf7903acdf6d5528dbe7 | refs/heads/master | 1,681,592,449,670 | 1,637,037,431,000 | 1,637,037,431,000 | 414,331,908 | 6 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 9,904 | lean | import ...cs.lang
import .defs
import ..tactic
import ...basic.basic
namespace interp
section interp
variables
{D O : Type}
{op : O → list (lang.val D O) → lang.result D O}
open lang
lemma interpVar_evalC
{a : ℕ} {ε : env D O} {v : val D O}
(h : ε.nth a = some v) : evalC op (exp.var a) ε (result.ans v)... |
6dc47524c197c8d0ab06ec91872c7ccaa67eefb2 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/combinatorics/simple_graph/partition.lean | e1f70e32fbb2ab705d3388610775753fb26579ec | [
"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 | 5,105 | lean | /-
Copyright (c) 2021 Arthur Paulino. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Arthur Paulino, Kyle Miller
-/
import combinatorics.simple_graph.coloring
/-!
# Graph partitions
This module provides an interface for dealing with partitions on simple graphs. A pa... |
bf1c0d3edf2d039d58e62ebd9fd09f95f5935203 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/order/hom/complete_lattice.lean | 872fcdd441fbfb8812f8cc66515bc2c149a6668d | [
"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 | 19,072 | 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 order.complete_lattice
import order.hom.lattice
/-!
# Complete lattice homomorphisms
This file defines frame homorphisms and complete lattice homomorphisms.
We ... |
5754803d12f026e040f463185e130f8dca70b9fd | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/123-1.lean | 02988530129745b351e322d8694b43d30e1f0f58 | [
"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 | 898 | lean | /-- notation typeclass not in core. -/
class has_scalar (G : Type) (V : Type) := (smul : G → V → V)
infixr ` • `:73 := has_scalar.smul
structure Ring : Type.
instance : has_coe_to_sort Ring Type :=
⟨λ R, unit⟩
variables {G : Type} [has_mul G] {R : Ring}
class distrib_mul_action' (G : Type) (V : Type)
[has_mul G... |
5098c14bc3f6c2ed8afc86a061283e709dcf0520 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/data/rat/cast.lean | bf1b55d6fa78d47b4b8ac458c3e2e45e077e2c7f | [
"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 | 11,417 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import data.rat.order
/-!
# Casts for Rational Numbers
## Summary
We define the canonical injection from ℚ into an arbitrary division ring and prove... |
e32d49e00e613827dbc4002cbb4520e52b0ad05b | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/data/rat/order.lean | 2157df0da1cf0082f1fc18e9fbf8ce9d48b01983 | [
"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 | 8,207 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import algebra.order.field
import data.rat.basic
/-!
# Order for Rational Numbers
## Summary
We define the order on `ℚ`, prove that `ℚ` is a discre... |
684b3b1bea4049a306d86389cc2d28018b25bd3f | 38bf3fd2bb651ab70511408fcf70e2029e2ba310 | /src/linear_algebra/dual.lean | 75d34abe35868c1760da8c1e550e06280f0118d7 | [
"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 | 6,316 | lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Fabian Glöckle
Dual vector spaces, the spaces of linear functionals to the base field, including the dual basis
isomorphism and evaluation isomorphism in the finite-di... |
c763337bde33e79722baa313af2ad688f6df2bb8 | e00ea76a720126cf9f6d732ad6216b5b824d20a7 | /src/topology/constructions.lean | 43655cf79dd8255840351945fce30598b621946e | [
"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 | 30,225 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot
-/
import topology.maps
/-!
# Constructions of new topological spaces from old ones
This file constructs products, sums, subtypes and q... |
8ad27badd922a09f65fbe9fa69a9540f104bd21c | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/category_theory/core.lean | 8c55b963516401551495965273e58a2419a35fbb | [
"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 | 3,002 | 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 control.equiv_functor
import category_theory.groupoid
import category_theory.whiskering
import category_theory.types
/-!
# The core of a category
The core of ... |
5cb9019778d01a07926a7902215a7ca1d09e0411 | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /stage0/src/Lean/Meta/InferType.lean | 8377d68d74ad0cf3cc273c9dee4016d9d142bb0b | [
"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 | 17,294 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Data.LBool
import Lean.Meta.Basic
namespace Lean
/-
Auxiliary function for instantiating the loose bound variables in `e` with `args[start:sto... |
e9f072f2a3e80389832351eb45bf314d8df361f9 | ecad13897fdb44984cf1968424224d1750040236 | /lean/lean/examples/example05.lean | 5849a3932b1cd34c6c187561cefac84615f72108 | [] | no_license | MetaBorgCube/sdf3-demo | 4899159b1cfb0a95ae3af325035bbba8a1255477 | e831606d5b404eba75b087916a1162923143b98a | refs/heads/master | 1,609,472,086,310 | 1,553,380,857,000 | 1,553,380,857,000 | 59,577,395 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 37 | lean | (z (a : b))(c : d) -> (e)(f : H) -> y |
6a9045978a7a5e34edf50691848335df2f263ca9 | dd4e652c749fea9ac77e404005cb3470e5f75469 | /src/NN.lean | 4bb1fae26d20ed15464282d255861aca154605a6 | [] | no_license | skbaek/cvx | e32822ad5943541539966a37dee162b0a5495f55 | c50c790c9116f9fac8dfe742903a62bdd7292c15 | refs/heads/master | 1,623,803,010,339 | 1,618,058,958,000 | 1,618,058,958,000 | 176,293,135 | 3 | 2 | null | null | null | null | UTF-8 | Lean | false | false | 8,545 | lean | import data.rat tactic.norm_num .misc .string
universes u v
variables {α : Type}
def N (α : Type) : Type := nat → α
def NN (α : Type) : Type := nat → nat → α
def N.eq (n : nat) (a b : N α) : Prop :=
∀ j < n, a j = b j
def NN.eq (m n : nat) (A B : NN α) : Prop :=
∀ i < m, ∀ j < n, A i j = B i j
def NN.mul_aux... |
61f0161da746ca21a3fc7df73a0fe8d8ac590974 | 0c1546a496eccfb56620165cad015f88d56190c5 | /library/data/list/basic.lean | a97e0973293d25b4495e1229a9caa0e78eb55e3c | [
"Apache-2.0"
] | permissive | Solertis/lean | 491e0939957486f664498fbfb02546e042699958 | 84188c5aa1673fdf37a082b2de8562dddf53df3f | refs/heads/master | 1,610,174,257,606 | 1,486,263,620,000 | 1,486,263,620,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,043 | lean | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn
Basic properties of lists.
-/
import init.data.list.basic
universe variables u v w
namespace list
open nat
v... |
1b7cffc03c0b874449c2984e6656bdbbaaa34e45 | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /12_Axioms.org.16.lean | 5be853de4026b48d3e10517f460a82ad5b67a3ce | [] | 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 | 194 | lean | import standard
open subtype nonempty
namespace hide
-- BEGIN
axiom strong_indefinite_description {A : Type} (P : A → Prop) (H : nonempty A) :
{ x | (∃ y : A, P y) → P x}
-- END
end hide
|
66f095d3e457d7a74b86783df7d3328e65d77258 | 076f5040b63237c6dd928c6401329ed5adcb0e44 | /instructor-notes/2019.10.01..poly/boxed.lean | ac26e565a92647592f4843ead16bf91d20c35a77 | [] | 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 | 113 | lean | inductive boxed (T : Type) : Type
| box : T → boxed
def unbox {T : Type} : boxed T → T
| (boxed.box n) := n
|
c2d2d56d966cab9bcd531ea1c193622742c027d5 | a7602958ab456501ff85db8cf5553f7bcab201d7 | /Notes/Logic_and_Proof/Chapter4/4.31.lean | feb5e1312425df00e3658bde66bc713ccad747f5 | [] | no_license | enlauren/math-logic | 081e2e737c8afb28dbb337968df95ead47321ba0 | 086b6935543d1841f1db92d0e49add1124054c37 | refs/heads/master | 1,594,506,621,950 | 1,558,634,976,000 | 1,558,634,976,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 517 | lean | -- Building Natural Deduction Proofs
-- 4.31 Implication
variables A B: Prop
-- Implication introduction (by "assume" keyword).
example: A /\ B -> B /\ A :=
assume h: A /\ B,
show B /\ A, from and.intro (and.right h) (and.left h)
-- (or another example); I actually do not know if this is a legitimate example.
variab... |
3fc6b1740ca331b1e461a022cc299b8d260b2100 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/const.lean | c86f45bf99cbc953a3edc3d5441c8c55bc5597d9 | [
"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 | 301 | lean | --
universe variables u
definition foo {A : Type u} [H : inhabited A] : A :=
inhabited.rec (λa, a) H
constant bla {A : Type u} [H : inhabited A] : Type 1
set_option pp.implicit true
section
variable A : Type u
variable S : inhabited A
variable B : @bla A S
#check B
#check @foo A S
end
|
75985f60aea82530cfb1e14506e5f60d858ca282 | 46125763b4dbf50619e8846a1371029346f4c3db | /src/topology/uniform_space/separation.lean | 8917cb88b5b68c9393cab55020133305e6acd2d4 | [
"Apache-2.0"
] | permissive | thjread/mathlib | a9d97612cedc2c3101060737233df15abcdb9eb1 | 7cffe2520a5518bba19227a107078d83fa725ddc | refs/heads/master | 1,615,637,696,376 | 1,583,953,063,000 | 1,583,953,063,000 | 246,680,271 | 0 | 0 | Apache-2.0 | 1,583,960,875,000 | 1,583,960,875,000 | null | UTF-8 | Lean | false | false | 13,808 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot
Hausdorff properties of uniform spaces. Separation quotient.
-/
import topology.uniform_space.basic
open filter topological_space lattice set classical... |
7fa9d1f40b4219b789295c023bf721a50870f811 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/analysis/asymptotics/asymptotic_equivalent.lean | 914c2fc6e3eacdccd96d8880f5952c2fd740d211 | [
"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 | 10,993 | lean | /-
Copyright (c) 2020 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-/
import analysis.asymptotics.asymptotics
import analysis.normed_space.ordered
/-!
# Asymptotic equivalence
In this file, we define the relation `is_equivalent u ... |
f090bc3c963d7e6c0c76c0baf180da9b1f5ac1b8 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/topology/metric_space/completion.lean | e801ac609b1e741f66903a2c765c9ee9107f9e6d | [
"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 | 8,574 | 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 topology.uniform_space.completion topology.metric_space.isometry
/-!
# The completion of a metric space
Completion of uniform spaces are already define... |
e6a0f4b783541e72a772f472b2a3f53bf95ab264 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/order/monotone/basic.lean | 9ca070071a7ca93fe28a09050a195cd6b584fe20 | [
"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 | 39,308 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Mario Carneiro, Yaël Dillies
-/
import order.compare
import order.max
import order.rel_classes
/-!
# Monotonicity
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any chang... |
b060042ce7df5058955844e92ae9659335000228 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/nested1.lean | 050763629964568492a7d6d394d5813838808685 | [
"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 | 267 | lean | import data.nat
open nat
namespace test
constant foo (a : nat) : a > 0 → nat
definition bla (a : nat) :=
foo
(succ (succ a))
abstract as foo.prf [irreducible] lt.step (zero_lt_succ a) end
print foo.prf
print bla
end test
print test.bla
print test.foo.prf
|
123b43f839c6a01ab1377a8a2b9c6f01814758ce | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/algebra/ordered_smul.lean | bc2dec9084d7dc676662f848a7397f09df583042 | [
"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 | 7,340 | lean | /-
Copyright (c) 2020 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
import algebra.ordered_pi
import algebra.smul_with_zero
import group_theory.group_action.group
/-!
# Ordered scalar product
In this file we define
* `ordered_sm... |
cf9ea946079c9965ada5884c7db6c2ba6d54588d | 737dc4b96c97368cb66b925eeea3ab633ec3d702 | /src/Lean/Util/FindLevelMVar.lean | e84186b7d31b5fcf939fb80f8758c070f33e5bff | [
"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 | 1,619 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Daniel Selsam
-/
import Lean.Expr
namespace Lean
namespace FindLevelMVar
abbrev Visitor := Option MVarId → Option MVarId
mutual
partial def visit (p : MVarId → Bool) (e : Ex... |
1683e6145d7633f8cdb354aac99b94061775a6fb | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/number_theory/l_series.lean | ab291a985295f7de05778775baddb507db7a9361 | [
"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 | 4,844 | lean | /-
Copyright (c) 2021 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import analysis.p_series
import number_theory.arithmetic_function
import topology.algebra.infinite_sum
/-!
# L-series
Given an arithmetic function, we define the co... |
e87f9af3093375a2dbe4c631c352fe2ae7452b79 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/ring_theory/polynomial/basic.lean | 6006fb7de02c0f6174c5ef40cd79dc25afc1c030 | [
"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 | 41,836 | lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import algebra.char_p.basic
import data.mv_polynomial.comm_ring
import data.mv_polynomial.equiv
import data.polynomial.field_division
import ring_theory.principal_ideal_domain... |
4f82ecb77ea898fcbe55d02555fc58d2080d5759 | 453dcd7c0d1ef170b0843a81d7d8caedc9741dce | /category/applicative.lean | b8fa963f28dd48509d50d2122b04b59d6cfb98ec | [
"Apache-2.0"
] | permissive | amswerdlow/mathlib | 9af77a1f08486d8fa059448ae2d97795bd12ec0c | 27f96e30b9c9bf518341705c99d641c38638dfd0 | refs/heads/master | 1,585,200,953,598 | 1,534,275,532,000 | 1,534,275,532,000 | 144,564,700 | 0 | 0 | null | 1,534,156,197,000 | 1,534,156,197,000 | null | UTF-8 | Lean | false | false | 3,086 | 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 category.functor
universe variables u v w
section lemmas
open function
variables {f : Type u → Type v}
variables... |
ebfedb84c10d455a956d2f610d2f433612c8163b | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/measure_theory/measure/hausdorff.lean | 40b9e7863e06fcebd5214371814484c8cb712d25 | [
"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 | 53,579 | 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 analysis.convex.between
import measure_theory.constructions.borel_space.basic
import measure_theory.measure.haar.inner_product_space
import measure_theory.me... |
231890b8478f18e0041a4d37c0e5b5eb5054c8d3 | 8eeb99d0fdf8125f5d39a0ce8631653f588ee817 | /src/algebra/module/basic.lean | a0302427d97425e521ab60a6930fd7823b255295 | [
"Apache-2.0"
] | permissive | jesse-michael-han/mathlib | a15c58378846011b003669354cbab7062b893cfe | fa6312e4dc971985e6b7708d99a5bc3062485c89 | refs/heads/master | 1,625,200,760,912 | 1,602,081,753,000 | 1,602,081,753,000 | 181,787,230 | 0 | 0 | null | 1,555,460,682,000 | 1,555,460,682,000 | null | UTF-8 | Lean | false | false | 22,883 | lean | /-
Copyright (c) 2015 Nathaniel Thomas. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nathaniel Thomas, Jeremy Avigad, Johannes Hölzl, Mario Carneiro
-/
import group_theory.group_action
import tactic.nth_rewrite
/-!
# Modules over a ring
In this file we define
* `s... |
f2684aac5c71cb551b79173845a3692d58b78fc9 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/category_theory/category/preorder.lean | b5ce286ec310621688689bfadcbb042b560423b4 | [
"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 | 5,382 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stephen Morgan, Scott Morrison, Johannes Hölzl, Reid Barton
-/
import category_theory.adjunction.basic
import order.galois_connection
/-!
# Preorders as categories
We install a cate... |
f7048df4b36f1aeaee6f1a1863d8203aade4ceeb | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/normed/group/controlled_closure.lean | e43218e83efbb08ebec339721385064b86610bff | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 6,745 | lean | /-
Copyright (c) 2021 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import analysis.normed.group.hom
import analysis.specific_limits.normed
/-! # Extending a backward bound on a normed group homomorphism from a dense set
> THIS FILE... |
fae5230fd9f3e88810cc3ec405cc2165e2ad2378 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /stage0/src/Lean/Util/FindExpr.lean | 48086e85dbc25c51e13183a8d2016cb7e6d7972b | [
"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 | 2,273 | 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 Expr
namespace FindImpl
abbrev cacheSize : USize := 8192
structure State where
keys : Array Expr -- Remark: ... |
e499104df7c19c4d3fa0431ceadab7e82dc5da6e | 437dc96105f48409c3981d46fb48e57c9ac3a3e4 | /src/data/setoid.lean | 9617ade69025f970aa6a8f86394592638b635b73 | [
"Apache-2.0"
] | permissive | dan-c-k/mathlib | 08efec79bd7481ee6da9cc44c24a653bff4fbe0d | 96efc220f6225bc7a5ed8349900391a33a38cc56 | refs/heads/master | 1,658,082,847,093 | 1,589,013,201,000 | 1,589,013,201,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 24,445 | lean | /-
Copyright (c) 2019 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston, Bryan Gin-ge Chen
-/
import data.set.lattice
/-!
# Equivalence relations
The first section of the file defines the complete lattice of equivalence relations
on ... |
35a7887b9fa8c81346f61a24d4e6b8e308e488ca | 80d0f8071ea62262937ab36f5887a61735adea09 | /src/certigrad/aevb/graph.lean | 5b3f9630065e4ce1a2f9797d24cfe1317e9c8bf1 | [
"Apache-2.0"
] | permissive | wudcscheme/certigrad | 94805fa6a61f993c69a824429a103c9613a65a48 | c9a06e93f1ec58196d6d3b8563b29868d916727f | refs/heads/master | 1,679,386,475,077 | 1,551,651,022,000 | 1,551,651,022,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,857 | lean | /-
Copyright (c) 2017 Daniel Selsam. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Daniel Selsam
The actual graph produced by the naive variational auto-encoder code in aevb/prog.lean.
Note: we include this file as an optimization, to avoid repeatedly simplifying the... |
04458fba6cfc433983da88cef7ef700733334b33 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/topology/continuous_function/basic.lean | fffbb5263bd4c48f3acb4f94a6c839460f5418f1 | [
"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 | 12,647 | lean | /-
Copyright © 2020 Nicolò Cavalleri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolò Cavalleri
-/
import data.set.Union_lift
import topology.homeomorph
/-!
# Continuous bundled maps
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require... |
434652232ef2ede6283f7477b7e2a54659140a98 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/group_theory/group_action/opposite.lean | c7c6e102dc174b38c8caa2d685763957729b0359 | [
"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 | 5,397 | lean | /-
Copyright (c) 2020 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import algebra.group.opposite
import group_theory.group_action.defs
/-!
# Scalar actions on and by `Mᵐᵒᵖ`
This file defines the actions on the opposite type `has_scalar R... |
3fc510bc558aee1b93178a44b606de1c7437c015 | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/group_theory/sylow.lean | 4dc876f0c11a210eab993d6be884649287f3c755 | [
"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 | 11,859 | 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 group_theory.group_action
import group_theory.quotient_group
import group_theory.order_of_element
import data.zmod.basic
import data.fintype.card
import data.list.... |
50e92ce3862d59b7f89a84eb577534c78716b8a1 | ee712cba63470502ae3b6e8fe7e5d109efaa0053 | /src/polygonal_connectedness.lean | e5ec2a80439798ac987a53ae7a9046ee580efdaf | [
"Apache-2.0"
] | permissive | chrisilouseph/Xena-Project-2020 | cf7837b039a113559a2118ccfa6134be43f8ce8a | 5fb76b50ace083a80508f6234887c7d24e1c88c3 | refs/heads/master | 1,670,447,937,865 | 1,598,513,203,000 | 1,598,513,203,000 | 290,692,541 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,723 | lean | /-
Copyright (c) 2020 Chrisil Ouseph. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chrisil Ouseph
-/
import analysis.complex.basic tactic
/-!
# Polygonally-Connected & Step-Connected Sets in Complex Numbers and Regions
This file defines polygonal-connectedness and... |
1f8aa234f7557bdf0e2ce0647746359205440b27 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/topology/category/Top/limits.lean | 205dfcc5d2c07b4a828d0c8de60fa52f22e53b44 | [
"Apache-2.0"
] | permissive | gebner/mathlib | eab0150cc4f79ec45d2016a8c21750244a2e7ff0 | cc6a6edc397c55118df62831e23bfbd6e6c6b4ab | refs/heads/master | 1,625,574,853,976 | 1,586,712,827,000 | 1,586,712,827,000 | 99,101,412 | 1 | 0 | Apache-2.0 | 1,586,716,389,000 | 1,501,667,958,000 | Lean | UTF-8 | Lean | false | false | 2,735 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Scott Morrison, Mario Carneiro
-/
import topology.category.Top.basic
import category_theory.limits.types
import category_theory.limits.preserves
open topological_space... |
037ba6d1fd2398cffff73e5ff60b37cd60c70401 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/category_theory/differential_object.lean | 8ef034bfda0200240cab464eef9dc5a2adff0498 | [
"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 | 8,549 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.shift
/-!
# Differential objects in a category.
A differential object in a category with zero morphisms and a shift is
an object `X` equipped... |
c737cfe01508f72696c189627c80bc6d34d2520e | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/634c.lean | 40c6a6bc6dd180b01d50532cab5c1fe1b1cdbbf4 | [
"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 | 946 | lean | open nat
section
parameter (X : Type₁)
definition A {n : ℕ} : Type₁ := X
definition B : Type₁ := X
variable {n : ℕ}
check @A n
check _root_.A nat
check _root_.A (X × B)
check @_root_.A (X × B) 10
check @_root_.A (_root_.B (@_root_.A X n)) n
check @_root_.A (@_root_.B (@_root_.A nat n)) n
set_opti... |
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