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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
fd520d04326f10a1dd00093bd6b465fdc683ec87 | 0c1546a496eccfb56620165cad015f88d56190c5 | /library/init/category/monad.lean | cb7fb54437ebe2333ccc894b961e5aab3d52f5c0 | [
"Apache-2.0"
] | permissive | Solertis/lean | 491e0939957486f664498fbfb02546e042699958 | 84188c5aa1673fdf37a082b2de8562dddf53df3f | refs/heads/master | 1,610,174,257,606 | 1,486,263,620,000 | 1,486,263,620,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,314 | lean | /-
Copyright (c) Luke Nelson and Jared Roesch. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Luke Nelson and Jared Roesch
-/
prelude
import init.category.applicative
universe variables u v
class pre_monad (m : Type u → Type v) :=
(bind : Π {a b : Type u}, m a → (a → ... |
6be4920acd24f20f5d31903e116eb477092061b5 | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/measure_theory/measure/stieltjes.lean | a3c89a5a418443fc2da319284bace038e52f2f01 | [
"Apache-2.0"
] | permissive | hikari0108/mathlib | b7ea2b7350497ab1a0b87a09d093ecc025a50dfa | a9e7d333b0cfd45f13a20f7b96b7d52e19fa2901 | refs/heads/master | 1,690,483,608,260 | 1,631,541,580,000 | 1,631,541,580,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 16,744 | lean | /-
Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yury Kudryashov, Sébastien Gouëzel
-/
import measure_theory.constructions.borel_space
/-!
# Stieltjes measures on the real line
Consider a function `f : ℝ → ℝ` whi... |
77935da4eb294605c847fdea6a6a70a92a27480e | bb31430994044506fa42fd667e2d556327e18dfe | /src/number_theory/pell.lean | 5fed9482d43e136a838dd9c688b9b2dad93e23ca | [
"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 | 36,709 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import data.nat.modeq
import number_theory.zsqrtd.basic
/-!
# Pell's equation and Matiyasevic's theorem
This file solves Pell's equation, i.e. integer solutions to... |
043f50e2104d77e1b7510133bf1635f6c69994ac | 0845ae2ca02071debcfd4ac24be871236c01784f | /library/init/control/id.lean | 95d289a03df26a7bb124890e174369014bbb7e0d | [
"Apache-2.0"
] | permissive | GaloisInc/lean4 | 74c267eb0e900bfaa23df8de86039483ecbd60b7 | 228ddd5fdcd98dd4e9c009f425284e86917938aa | refs/heads/master | 1,643,131,356,301 | 1,562,715,572,000 | 1,562,715,572,000 | 192,390,898 | 0 | 0 | null | 1,560,792,750,000 | 1,560,792,749,000 | null | UTF-8 | Lean | false | false | 678 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Ullrich
The identity Monad.
-/
prelude
import init.control.lift
universe u
def Id (type : Type u) : Type u := type
@[inline] def Id.pure {α : Type u} (x : α) : Id α... |
e81ecb76b9bd502a3f0cc83d971d56cc9108b654 | f5f7e6fae601a5fe3cac7cc3ed353ed781d62419 | /src/data/set/finite.lean | 30b1a0de30fac6f072e84f21287c8ddb00819a89 | [
"Apache-2.0"
] | permissive | EdAyers/mathlib | 9ecfb2f14bd6caad748b64c9c131befbff0fb4e0 | ca5d4c1f16f9c451cf7170b10105d0051db79e1b | refs/heads/master | 1,626,189,395,845 | 1,555,284,396,000 | 1,555,284,396,000 | 144,004,030 | 0 | 0 | Apache-2.0 | 1,533,727,664,000 | 1,533,727,663,000 | null | UTF-8 | Lean | false | false | 18,082 | 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
Finite sets.
-/
import logic.function
import data.nat.basic data.fintype data.set.lattice data.set.function
open set lattice function
universes u v w
... |
a0b3e4dda1c29c163ef28252e37cef6c2df2284e | d1a52c3f208fa42c41df8278c3d280f075eb020c | /src/Lean/PrettyPrinter/Formatter.lean | fa407525f7e862023352f84496fed4467c64745d | [
"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 | 23,174 | lean | /-
Copyright (c) 2020 Sebastian Ullrich. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Ullrich
-/
import Lean.CoreM
import Lean.Parser.Extension
import Lean.KeyedDeclsAttribute
import Lean.ParserCompiler.Attribute
import Lean.PrettyPrinter.Basic
/-!
The for... |
e1062bbde692931890f0c13f799bd493a52399f9 | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /stage0/src/Init.lean | d87f6604ad35fb2bb260d467bd460c62a363b409 | [
"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 | 441 | 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
-/
prelude
import Init.Prelude
import Init.Notation
import Init.Core
import Init.Control
import Init.Data.Basic
import Init.WF
import Init.Data
import Init.Sys... |
b0e2cfc9ddafc83ee5bef4f1caa9b74715db6b9e | 453dcd7c0d1ef170b0843a81d7d8caedc9741dce | /data/array/lemmas.lean | 4ceaf6dc574f55e982a4a98886be96dc867eab6d | [
"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 | 9,086 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Mario Carneiro
-/
import data.list.basic data.buffer category.traversable.equiv data.vector2
universes u w
namespace d_array
variables {n : nat} {α : fin n ... |
4c8a0ee509fc0efd9c680c42b9962b0b8a797006 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/homology/homology.lean | 30166c8f1f5ef7fc4d46bcd70c0ce58872b1f31a | [
"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 | 10,408 | 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 algebra.homology.image_to_kernel
import algebra.homology.homological_complex
import category_theory.graded_object
/-!
# The homology of a complex
Given `C : ... |
2988e315b6d2a6c5ea2996f04589bb19ca63ef4d | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/set/prod.lean | be7358befe8d0ed370fc9986525df8919c06677c | [
"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 | 26,452 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johannes Hölzl, Patrick Massot
-/
import data.set.basic
/-!
# Sets in product and pi types
This file defines the product of sets in `α × β` and in `Π i, α i` along wi... |
ec83899c081e20e1c1bb5a405abc888222ce7db0 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/algebra/group/with_one.lean | 947969d1a122b0089185e42f9beda47ac0be2863 | [
"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 | 12,725 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johan Commelin
-/
import algebra.hom.equiv
import algebra.ring.basic
import logic.equiv.basic
import logic.equiv.option
/-!
# Adjoining a zero/one to semigroups and re... |
483ad605b026e9c5d2b88f50f0e31d422c378faa | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/init/algebra/order_auto.lean | 371d24082a9b887dbe796badc4269635e3a17829 | [] | 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 | 12,060 | 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
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.logic
import Mathlib.Lean3Lib.init.classical
import Mathlib.Lean3Lib.init.meta.name
import Mathlib.Lean3... |
ab794ab27e9b96a58f93fb555da3076d4446d429 | 31f556cdeb9239ffc2fad8f905e33987ff4feab9 | /src/Lean/KeyedDeclsAttribute.lean | be7634ffbb1f26913f55e797afa64a7df7520b95 | [
"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 | 7,198 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Sebastian Ullrich
-/
import Lean.Compiler.InitAttr
import Lean.ScopedEnvExtension
import Lean.Compiler.IR.CompilerM
/-!
A builder for attributes that are app... |
9dc1068420c6cb5d41446d4e22c91726230436d5 | 59a4b050600ed7b3d5826a8478db0a9bdc190252 | /src/category_theory/preorder.lean | 800fabf37736c53498266258452e55b7914361ff | [] | no_license | rwbarton/lean-category-theory | f720268d800b62a25d69842ca7b5d27822f00652 | 00df814d463406b7a13a56f5dcda67758ba1b419 | refs/heads/master | 1,585,366,296,767 | 1,536,151,349,000 | 1,536,151,349,000 | 147,652,096 | 0 | 0 | null | 1,536,226,960,000 | 1,536,226,960,000 | null | UTF-8 | Lean | false | false | 351 | lean | import category_theory.category
import category_theory.tactics.obviously
universes u₁
namespace category_theory
variables (α : Type u₁)
instance [preorder α] : small_category α :=
{ hom := λ U V, ulift (plift (U ≤ V)),
id := by tidy,
comp := begin tidy, transitivity Y; assumption end } -- automate, via mono?... |
a01e7a5a35ab2293625423e35de8f74ca8ae6d0e | 46125763b4dbf50619e8846a1371029346f4c3db | /src/geometry/manifold/mfderiv.lean | a1ba5f37e421420e1c24bc633a9ad4904476b359 | [
"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 | 68,471 | 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 geometry.manifold.basic_smooth_bundle
/-!
# The derivative of functions between smooth manifolds
Let `M` and `M'` be two smooth manifolds with corners... |
e64a42cd36bf3a7a467cc7779c5a074f6e533d8e | 618003631150032a5676f229d13a079ac875ff77 | /src/category_theory/endomorphism.lean | fffb8c1fac69225a649ec5a9c1cde51a033461ba | [
"Apache-2.0"
] | permissive | awainverse/mathlib | 939b68c8486df66cfda64d327ad3d9165248c777 | ea76bd8f3ca0a8bf0a166a06a475b10663dec44a | refs/heads/master | 1,659,592,962,036 | 1,590,987,592,000 | 1,590,987,592,000 | 268,436,019 | 1 | 0 | Apache-2.0 | 1,590,990,500,000 | 1,590,990,500,000 | null | UTF-8 | Lean | false | false | 2,824 | lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Scott Morrison, Simon Hudon
Definition and basic properties of endomorphisms and automorphisms of an object in a category.
-/
import category_theory.category
import ... |
1db224692451509207556508664717e5d4248e76 | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/slow/tactic1.lean | 4aa9f5fe6fcf48cb696743abe82ead836e8b1be6 | [
"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 | 1,329 | lean | import Int.
definition double {A : Type} (f : A -> A) : A -> A := fun x, f (f x).
definition big {A : Type} (f : A -> A) : A -> A := (double (double (double (double (double (double (double f))))))).
(*
-- Tactic for trying to prove goal using Reflexivity, Congruence and available assumptions
local congr_tac = Repeat... |
74442bd9ac966fa93e6f13fccea51a51e6e82828 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/data/real/liouville.lean | 71c6e558a4a9c48a5683387c3b5f94e79c98aba1 | [
"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 | 12,343 | lean | /-
Copyright (c) 2020 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
import analysis.calculus.mean_value
import data.polynomial.denoms_clearable
import data.real.irrational
import ring_theory.algebraic
import topology.algebra.polynomial
/-... |
61009c43e0365637e1450578d132fe8a997a16da | a339bc2ac96174381fb610f4b2e1ba42df2be819 | /hott/homotopy/join.hlean | dce4ed436fc9434ba7d6d1858beb542b4a007115 | [
"Apache-2.0"
] | permissive | kalfsvag/lean2 | 25b2dccc07a98e5aa20f9a11229831f9d3edf2e7 | 4d4a0c7c53a9922c5f630f6f8ebdccf7ddef2cc7 | refs/heads/master | 1,610,513,122,164 | 1,483,135,198,000 | 1,483,135,198,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 22,760 | hlean | /-
Copyright (c) 2015 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer, Ulrik Buchholtz
Declaration of a join as a special case of a pushout
-/
import hit.pushout .sphere cubical.cube
open eq function prod equiv is_trunc bool sigma.o... |
a5d598f7b90d27d16ffd7994d411f70d5f8082ea | d31b9f832ff922a603f76cf32e0f3aa822640508 | /src/hott/init/pointed.lean | bbcf4d20d921db37dc55493d2345f1fcdcd80305 | [
"Apache-2.0"
] | permissive | javra/hott3 | 6e7a9e72a991a2fae32e5764982e521dca617b16 | cd51f2ab2aa48c1246a188f9b525b30f76c3d651 | refs/heads/master | 1,585,819,679,148 | 1,531,232,382,000 | 1,536,682,965,000 | 154,294,022 | 0 | 0 | Apache-2.0 | 1,540,284,376,000 | 1,540,284,375,000 | null | UTF-8 | Lean | false | false | 7,694 | lean | /-
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
The definition of pointed types. This file is here to avoid circularities in the import graph
-/
import .trunc
universes u v w
namespace hott
hott_theory
open eq ... |
8992566bfa56c7374191993190bfe555671b8c3a | 1437b3495ef9020d5413178aa33c0a625f15f15f | /tactic/simpa.lean | 2f29e66e11fcb3a603371e72745f7aa961dd34b1 | [
"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 | 1,681 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
namespace tactic
namespace interactive
open interactive interactive.types expr lean.parser
local postfix `?`:9001 := optional
/--
This is a "finishing" tactic modi... |
c75e0158fde1baecacf48ca226caf5fd837952eb | fcf3ffa92a3847189ca669cb18b34ef6b2ec2859 | /src/world6/level7.lean | fa2a0b5e50a0da19e68b5de7ef08f8817c2f3b24 | [
"Apache-2.0"
] | permissive | nomoid/lean-proofs | 4a80a97888699dee42b092b7b959b22d9aa0c066 | b9f03a24623d1a1d111d6c2bbf53c617e2596d6a | refs/heads/master | 1,674,955,317,080 | 1,607,475,706,000 | 1,607,475,706,000 | 314,104,281 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 139 | lean | example (P Q R : Prop) : (P → Q) → ((Q → R) → (P → R)) :=
begin
intros pq qf p,
apply qf,
apply pq,
exact p,
end
|
7032b0b70c907e6a31ac96d838fb007bad8a7a49 | 05b503addd423dd68145d68b8cde5cd595d74365 | /src/tactic/linarith.lean | 015d63d7ff8990f0f818522f9580a83df1c3ef4e | [
"Apache-2.0"
] | permissive | aestriplex/mathlib | 77513ff2b176d74a3bec114f33b519069788811d | e2fa8b2b1b732d7c25119229e3cdfba8370cb00f | refs/heads/master | 1,621,969,960,692 | 1,586,279,279,000 | 1,586,279,279,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 35,581 | lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Robert Y. Lewis
-/
import tactic.ring data.nat.gcd data.list.defs meta.rb_map data.tree
/-!
# `linarith`
A tactic for discharging linear arithmetic goals using Fourier-Motzkin elimi... |
02d9a4f63d4434c550c8a36bca3518ea67dc312e | 9ad8d18fbe5f120c22b5e035bc240f711d2cbd7e | /src/undergraduate/MAS114/fiber.lean | e3a60df9eb1ffe176434c0b74853ea7431fc1cff | [] | no_license | agusakov/lean_lib | c0e9cc29fc7d2518004e224376adeb5e69b5cc1a | f88d162da2f990b87c4d34f5f46bbca2bbc5948e | refs/heads/master | 1,642,141,461,087 | 1,557,395,798,000 | 1,557,395,798,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,658 | lean | import data.fintype
import tactic.squeeze
namespace MAS114
universes u v
variables {α : Type u} {β : Type v} (p : α → β)
variables [fintype α] [fintype β] [decidable_eq α] [decidable_eq β]
def fiber (b : β) : Type* := { a : α // p a = b }
instance (b : β) : fintype (fiber p b) :=
by { dsimp[fiber], apply_instan... |
adcde7a097f1433ecdfe7a82fc5ac71672d005bf | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/data/polynomial/derivative.lean | 4b71af02ec0ae64e9350bc1933191229ab1c5646 | [
"Apache-2.0"
] | permissive | AntoineChambert-Loir/mathlib | 64aabb896129885f12296a799818061bc90da1ff | 07be904260ab6e36a5769680b6012f03a4727134 | refs/heads/master | 1,693,187,631,771 | 1,636,719,886,000 | 1,636,719,886,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 15,239 | 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.eval
/-!
# The derivative map on polynomials
## Main definitions
* `polynomial.derivative`: The ... |
aa38183195c40d2e70795fe77d921a4f8d10f1f9 | 947b78d97130d56365ae2ec264df196ce769371a | /stage0/src/Lean/Compiler/Specialize.lean | 5626752321841b0093563b900d1686062751ccd8 | [
"Apache-2.0"
] | permissive | shyamalschandra/lean4 | 27044812be8698f0c79147615b1d5090b9f4b037 | 6e7a883b21eaf62831e8111b251dc9b18f40e604 | refs/heads/master | 1,671,417,126,371 | 1,601,859,995,000 | 1,601,860,020,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,462 | 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.Attributes
import Lean.Compiler.Util
namespace Lean
namespace Compiler
inductive SpecializeAttributeKind
| specialize | nospecialize
namespac... |
046c585fc0e6289eeb78f64f69eb64842fe27a1e | ad0c7d243dc1bd563419e2767ed42fb323d7beea | /data/set/lattice.lean | e3254a623d182e1e453aa76ea3b48fb00f6b171a | [
"Apache-2.0"
] | permissive | sebzim4500/mathlib | e0b5a63b1655f910dee30badf09bd7e191d3cf30 | 6997cafbd3a7325af5cb318561768c316ceb7757 | refs/heads/master | 1,585,549,958,618 | 1,538,221,723,000 | 1,538,221,723,000 | 150,869,076 | 0 | 0 | Apache-2.0 | 1,538,229,323,000 | 1,538,229,323,000 | null | UTF-8 | Lean | false | false | 26,270 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors Jeremy Avigad, Leonardo de Moura, Johannes Hölzl, Mario Carneiro
-- QUESTION: can make the first argument in ∀ x ∈ a, ... implicit?
-/
import logic.basic data.set.basic data.equiv.basic... |
cf82ab6925f25cce788fcdc7d36afaba64602561 | aa3f8992ef7806974bc1ffd468baa0c79f4d6643 | /library/standard/tools/tactic.lean | eb68a7a19e0875b220042c3b66de9188ce920722 | [
"Apache-2.0"
] | permissive | codyroux/lean | 7f8dff750722c5382bdd0a9a9275dc4bb2c58dd3 | 0cca265db19f7296531e339192e9b9bae4a31f8b | refs/heads/master | 1,610,909,964,159 | 1,407,084,399,000 | 1,416,857,075,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,963 | 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
-----------------------------------------------------... |
2f2a8f73e641805c0964b1b6b52326a3cc1c0337 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /tests/lean/run/specbug.lean | f410424247615b1dbf9648785875527d6c3cc001 | [
"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 | 801 | lean | @[noinline] def f (x : Bool) := x
@[noinline] def g (x y : Bool) := x
def h (x : Bool) (xs : List Nat) : List Bool :=
match x with
| true =>
let z := f true
let y := f false
xs.map fun x => g y z
| false =>
let y := f false
let z := f true
xs.map fun x => g y z
theorem ex1 : h true [1]... |
36a3caaa94d6d2a2ca20043aa6af8faa9e934897 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/topology/category/Profinite/basic.lean | 8f71fdef069dc9198d985061843f12737aa8db1e | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 11,440 | lean | /-
Copyright (c) 2020 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Calle Sönne
-/
import topology.category.CompHaus.basic
import topology.connected
import topology.subset_properties
import topology.locally_constant.basic
import category... |
e41446590375f49eec852a7643a30b07a893520a | 4727251e0cd73359b15b664c3170e5d754078599 | /src/topology/continuous_function/weierstrass.lean | 87b9b01092a8fb4f822820d1d30e51235ec00376 | [
"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 | 5,412 | 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 analysis.special_functions.bernstein
import topology.algebra.algebra
/-!
# The Weierstrass approximation theorem for continuous functions on `[a,b]`
We've al... |
69b420e95a86795762c0465d1a1c02929a6a17ff | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /library/algebra/group_bigops.lean | dde566b5c38e50b8cc5ff76cb8cbd516552068ac | [
"Apache-2.0"
] | permissive | davidmueller13/lean | 65a3ed141b4088cd0a268e4de80eb6778b21a0e9 | c626e2e3c6f3771e07c32e82ee5b9e030de5b050 | refs/heads/master | 1,611,278,313,401 | 1,444,021,177,000 | 1,444,021,177,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,979 | lean | /-
Copyright (c) 2015 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad
Finite products on a monoid, and finite sums on an additive monoid.
We have to be careful with dependencies. This theory imports files from finset and... |
a4e912ce7111484e4bd3811bf34916a540a05cda | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/run/struc_names.lean | feaa79d0fcfc566f7188af80d0494c723b9aede4 | [
"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 | 187 | lean | namespace foo
structure [class] structA :=
mk :: (a : nat)
structure [class] structB extends structA :=
mk :: (b : nat)
check @structA.a
check @structB.to_structA
end foo
|
2deea58c1a8452eb3d8e7f025ba8d9c04b0db3e8 | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/linear_algebra/quadratic_form.lean | 397ea4af81010eb1f959be027352697716530844 | [
"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 | 38,956 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Kexing Ying
-/
import algebra.invertible
import linear_algebra.bilinear_form
import linear_algebra.matrix.determinant
import linear_algebra.special_linear_group
import analy... |
e61fe5a5a0eb9fc846425979ae0202df38791d7b | b3fced0f3ff82d577384fe81653e47df68bb2fa1 | /src/data/matrix/basic.lean | c7a30600fd6f51d6e9e1c9f7fbfcaa24ae10caf1 | [
"Apache-2.0"
] | permissive | ratmice/mathlib | 93b251ef5df08b6fd55074650ff47fdcc41a4c75 | 3a948a6a4cd5968d60e15ed914b1ad2f4423af8d | refs/heads/master | 1,599,240,104,318 | 1,572,981,183,000 | 1,572,981,183,000 | 219,830,178 | 0 | 0 | Apache-2.0 | 1,572,980,897,000 | 1,572,980,896,000 | null | UTF-8 | Lean | false | false | 12,054 | lean | /-
Copyright (c) 2018 Ellen Arlt. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ellen Arlt, Blair Shi, Sean Leather, Mario Carneiro, Johan Commelin
Matrices
-/
import algebra.module algebra.pi_instances
import data.fintype
universes u v
def matrix (m n : Type u) [f... |
d5461aabb0a5ec4fac1e42cb69f7f3862db60ea7 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/robinson.lean | 97230e854fa28fefd93f9d2f0b400d9082e3c56d | [
"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 | 2,037 | lean | inductive Term
| Var (i : Nat)
| Cons (l : Term) (r : Term)
def Subst := Nat → Nat
def depth : Term → Nat
| .Var _ => 0
| .Cons l r => 1 + depth l + depth r
def act (f : Subst) (t : Term) := match t with
| .Var i => Term.Var (f i)
| .Cons l r => Term.Cons (act f l) (act f r)
def strangers (u v : Term) :... |
37a7ef77e72722051e07c3e1bbf92ff7c87f5b88 | 37a833c924892ee3ecb911484775a6d6ebb8984d | /src/category_theory/presheaves/sheaves.lean | 3b4afe1d7b88003984cf201747067d033db4cb41 | [] | no_license | silky/lean-category-theory | 28126e80564a1f99e9c322d86b3f7d750da0afa1 | 0f029a2364975f56ac727d31d867a18c95c22fd8 | refs/heads/master | 1,589,555,811,646 | 1,554,673,665,000 | 1,554,673,665,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,773 | lean | import category_theory.opposites
import category_theory.full_subcategory
import category_theory.limits.types
import category_theory.examples.topological_spaces
import category_theory.limits.obviously
open category_theory
open category_theory.limits
open category_theory.examples
open topological_space
universes u v u... |
00b5920ed1a25ea87eb1c1128f46b1ecee3db470 | 367134ba5a65885e863bdc4507601606690974c1 | /src/ring_theory/integral_closure.lean | 5d08130adab5bf65e674dc00a89948634b038b5a | [
"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 | 25,900 | 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 ring_theory.adjoin.basic
import ring_theory.polynomial.scale_roots
import ring_theory.polynomial.tower
/-!
# Integral closure of a subring.
If A is an R-algebra then `... |
83709345878c8339edfdb0ce5bc95032fbe55714 | d5bef83c55d40cb88f9a01b755c882a93348a847 | /library/init/algebra/classes.lean | b829e618bef84b131363630eeacc7a30116e9959 | [
"Apache-2.0"
] | permissive | urkud/lean | 587d78216e1f0c7f651566e9e92cf8ade285d58d | 3526539070ea6268df5dd373deeb3ac8b9621952 | refs/heads/master | 1,660,171,634,921 | 1,657,873,466,000 | 1,657,873,466,000 | 249,789,456 | 0 | 0 | Apache-2.0 | 1,585,075,263,000 | 1,585,075,263,000 | null | UTF-8 | Lean | false | false | 13,788 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.logic init.data.ordering.basic
universes u v
/-!
# Unbundled algebra classes
These classes and the `@[algebra]` attribute are part of ... |
70b9e6a608f46ff56381d437d41a47f13bff0344 | 3aad12fe82645d2d3173fbedc2e5c2ba945a4d75 | /src/tactic/nursery.lean | cf7c477dce4b752d3f9ac48b1768aa8a6def2ca6 | [] | no_license | seanpm2001/LeanProver-Community_MathLIB-Nursery | 4f88d539cb18d73a94af983092896b851e6640b5 | 0479b31fa5b4d39f41e89b8584c9f5bf5271e8ec | refs/heads/master | 1,688,730,786,645 | 1,572,070,026,000 | 1,572,070,026,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,911 | 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 data.list.basic
import tactic.basic
namespace level
meta def fold_mvar {α} : level → (name → α → α) → α → α
| zero f := id
| (succ a) f := fold_mvar a f
| (param a)... |
925b215339437ccd7ffdc5aeb95f7e19fa3f6c74 | 1a61aba1b67cddccce19532a9596efe44be4285f | /library/algebra/field.lean | 5599bad8fcc88c580904aa70e57694356c5f34a5 | [
"Apache-2.0"
] | permissive | eigengrau/lean | 07986a0f2548688c13ba36231f6cdbee82abf4c6 | f8a773be1112015e2d232661ce616d23f12874d0 | refs/heads/master | 1,610,939,198,566 | 1,441,352,386,000 | 1,441,352,494,000 | 41,903,576 | 0 | 0 | null | 1,441,352,210,000 | 1,441,352,210,000 | null | UTF-8 | Lean | false | false | 19,648 | lean | /-
Copyright (c) 2014 Robert Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Lewis
Structures with multiplicative and additive components, including division rings and fields.
The development is modeled after Isabelle's library.
-/
import logic.eq logic.c... |
e7f577b09c00f5cf7bf227dfec0cfb82f7e55e73 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/data/rat/cast.lean | db2a8da7fe2577808e8f5d796b831e07987420ca | [
"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 | 13,290 | 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
import data.int.char_zero
/-!
# Casts for Rational Numbers
## Summary
We define the canonical injection from ℚ into an arbitr... |
93140dc7d3e25a5fbe55b06b1785149523422c5b | 853df553b1d6ca524e3f0a79aedd32dde5d27ec3 | /src/topology/metric_space/baire.lean | b364d06fb2005247a6eba4c52555b3eb2897f416 | [
"Apache-2.0"
] | permissive | DanielFabian/mathlib | efc3a50b5dde303c59eeb6353ef4c35a345d7112 | f520d07eba0c852e96fe26da71d85bf6d40fcc2a | refs/heads/master | 1,668,739,922,971 | 1,595,201,756,000 | 1,595,201,756,000 | 279,469,476 | 0 | 0 | null | 1,594,696,604,000 | 1,594,696,604,000 | null | UTF-8 | Lean | false | false | 17,152 | 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.specific_limits
import order.filter.countable_Inter
/-!
# Baire theorem
In a complete metric space, a countable intersection of dense open sub... |
f7542e474077170c83f20eb9a1c5c8725f401cea | c777c32c8e484e195053731103c5e52af26a25d1 | /src/topology/subset_properties.lean | d37fdbf1062bcc44cb4d0bb2eb5b2a0714235c18 | [
"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 | 89,273 | 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 order.filter.pi
import topology.bases
import data.finset.order
import data.set.accumulate
import data.set.bool_indicator
impor... |
91294c5d3d6cdf633957c7c04766ad117bc5aeb6 | 137c667471a40116a7afd7261f030b30180468c2 | /src/analysis/mean_inequalities.lean | 033a4cbfafa35cd9d9758f93c9f602775d7726c8 | [
"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 | 33,176 | lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Sébastien Gouëzel, Rémy Degenne
-/
import analysis.convex.specific_functions
import analysis.special_functions.pow
import data.real.conjugate_exponents
import tactic.... |
83756b90d7f6e130001f4f441fbc5d8466432bfc | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/tactic/wlog.lean | 1de77cf9c167af3a23abd8181f1fdfb526a913ce | [
"Apache-2.0"
] | permissive | waynemunro/mathlib | e3fd4ff49f4cb43d4a8ded59d17be407bc5ee552 | 065a70810b5480d584033f7bbf8e0409480c2118 | refs/heads/master | 1,693,417,182,397 | 1,634,644,781,000 | 1,634,644,781,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,146 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Without loss of generality tactic.
-/
import data.list.perm
open expr tactic lean lean.parser
local postfix `?`:9001 := optional
local postfix *:9001 := many
namespa... |
bd50765ba06fc516c6394c0816a87bfc01d99bc3 | e21db629d2e37a833531fdcb0b37ce4d71825408 | /alt/hoare.lean | 61bb1fa35c06ac93d5bc0cb00e82e9f7c95b51af | [] | no_license | fischerman/GPU-transformation-verifier | 614a28cb4606a05a0eb27e8d4eab999f4f5ea60c | 75a5016f05382738ff93ce5859c4cfa47ccb63c1 | refs/heads/master | 1,586,985,789,300 | 1,579,290,514,000 | 1,579,290,514,000 | 165,031,073 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,540 | lean | import aux
import parlang.def
import parlang.lemmas_exec
import data.bool
namespace parlang
variables {σ : Type} {ι : Type} {τ : ι → Type} [decidable_eq ι]
/-
because this holds for all n and ac the pre- and postcondition probably contain ite or forall quantifiers
-/
def hoare (P : thread_state σ τ → Prop) (k :... |
81c17bb1f4416f202311d6a2c12de69c3fdb1789 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/category_theory/limits/shapes/constructions/pullbacks.lean | f800d846ca1f7cfbee2e01f658b4db6922361cc7 | [
"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 | 3,933 | lean | /-
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import category_theory.limits.shapes.binary_products
import category_theory.limits.shapes.equalizers
import category_theory.limits.shapes.pullbacks
universes v u
/-!
... |
b081f42f0f1cc58967336664ffbdea0f50017b95 | b87641ffb6358d6508ccbfa54e67c87070cb28d8 | /ap_cat/src/Preorders.lean | e370c218ab46e3119efc525672372c2e58c3a8bd | [] | no_license | Nolrai/LeanGiggle | a4b628745ae3f5a36ae79b673ee8543e18ed4899 | 8326b2a6685b60a3529ee0fe26bd86f5d849b071 | refs/heads/master | 1,545,396,766,168 | 1,538,238,458,000 | 1,538,238,458,000 | 105,524,473 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,424 | lean | namespace preorder
section preorder
variable T : Type
def is_upper_bound [preorder T] : set T -> T -> Prop :=
λ S x, ∀ y, y ∈ S -> y ≤ x
structure Op := op :: (unop : T)
variable {T}
def op (x : T) : Op T := Op.op x
def unop (x : Op T) : T := Op.unop x
def op_rel (R : T -> T -> Prop) (x y : Op T) :=
R (unop... |
07829b14dbbaa59f190c30682778bf2497ff3878 | 54d7e71c3616d331b2ec3845d31deb08f3ff1dea | /library/init/category/functor.lean | 4db4ec3fa17d845dddaf09f049ccfae51e451819 | [
"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 | 1,158 | lean | /-
Copyright (c) Luke Nelson and Jared Roesch. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Luke Nelson, Jared Roesch, Sebastian Ullrich
-/
prelude
import init.core init.function init.meta.name
open function
universes u v
section
set_option auto_param.check_exists f... |
9b6552bcb9ee14da89f093dbcc0a13d95707516c | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/probability/martingale/optional_stopping.lean | 86c7f5f882d4b32d1344e9ee49b6eff340608cd7 | [
"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 | 12,122 | lean | /-
Copyright (c) 2022 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
import probability.martingale.basic
/-! # Optional stopping theorem (fair game theorem)
The optional stopping theorem states that an adapted integrable process `f` is a ... |
7ead96be57f95284853508a4ee26315ecd6f1fb8 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/topology/algebra/uniform_ring.lean | e253b4d355bbc0ae2321bc4b87056ac358ba865e | [
"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 | 7,240 | lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl
Theory of topological rings with uniform structure.
-/
import topology.algebra.group_completion topology.algebra.ring
open classical set lattice filte... |
8ac3ce54a5646956bac0c07459fbe251ceef872a | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /tests/lean/run/getline_crash.lean | a98170c8e8f18411d05330a50a912c28478175fe | [
"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 | 2,227 | lean | def tstGetLine (str : String) : IO Unit := do
let path := "tmp_file";
IO.FS.withFile path IO.FS.Mode.write $ λ (h : IO.FS.Handle) =>
h.putStrLn str;
IO.FS.withFile path IO.FS.Mode.read $ λ (h : IO.FS.Handle) => do
str' ← h.getLine;
IO.println str.length;
IO.println str'.length;
IO.print str';
unless (str'.l... |
9e99191a13e4dabfe4ce296c734602e0a9b0023c | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Meta/CollectFVars.lean | f787070eea90ea92dc81deedc11a608b5b461005 | [
"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 | 2,385 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Sebastian Ullrich
-/
import Lean.Util.CollectFVars
import Lean.Meta.Basic
namespace Lean
open Meta
def Expr.collectFVars (e : Expr) : StateRefT CollectFVar... |
ab1c5239e9a1bad0dc2366457fc65f7a2994cbdf | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/limits/constructions/limits_of_products_and_equalizers.lean | c022171b26cb247bc841b17ed09a2d415a24c9bf | [
"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 | 18,283 | lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Scott Morrison
-/
import data.fintype.prod
import data.fintype.sigma
import category_theory.limits.shapes.equalizers
import category_theory.limits.shapes.finite_products
im... |
642bd43573d9f8199b156e107c730d421ac27872 | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/data/real/pi.lean | a8cdff6ec19757d43fdf5449a320991c831c9fdd | [
"Apache-2.0"
] | permissive | lacker/mathlib | f2439c743c4f8eb413ec589430c82d0f73b2d539 | ddf7563ac69d42cfa4a1bfe41db1fed521bd795f | refs/heads/master | 1,671,948,326,773 | 1,601,479,268,000 | 1,601,479,268,000 | 298,686,743 | 0 | 0 | Apache-2.0 | 1,601,070,794,000 | 1,601,070,794,000 | null | UTF-8 | Lean | false | false | 7,374 | lean | /-
Copyright (c) 2019 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import analysis.special_functions.trigonometric
namespace real
lemma pi_gt_sqrt_two_add_series (n : ℕ) : 2 ^ (n+1) * sqrt (2 - sqrt_two_add_series 0 n) < pi :=
... |
4a67d0df43ef7861e62bda1704d3d8f436bae728 | 0845ae2ca02071debcfd4ac24be871236c01784f | /library/init/lean/position.lean | 847a9e1a839e6a6d42b35a1255cc83aa8cd292e6 | [
"Apache-2.0"
] | permissive | GaloisInc/lean4 | 74c267eb0e900bfaa23df8de86039483ecbd60b7 | 228ddd5fdcd98dd4e9c009f425284e86917938aa | refs/heads/master | 1,643,131,356,301 | 1,562,715,572,000 | 1,562,715,572,000 | 192,390,898 | 0 | 0 | null | 1,560,792,750,000 | 1,560,792,749,000 | null | UTF-8 | Lean | false | false | 2,787 | lean | /-
Copyright (c) 2018 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Sebastian Ullrich
-/
prelude
import init.data.nat init.data.rbmap init.lean.format
namespace Lean
structure Position :=
(line : Nat)
(column : Nat)
names... |
c3c008284196888b4a248f22e3c629b1713006e0 | 968e2f50b755d3048175f176376eff7139e9df70 | /examples/prop_logic_theory/unnamed_1520.lean | 95790f8c7df4a5dca44941b57356e3ac2b681bae | [] | no_license | gihanmarasingha/mth1001_sphinx | 190a003269ba5e54717b448302a27ca26e31d491 | 05126586cbf5786e521be1ea2ef5b4ba3c44e74a | refs/heads/master | 1,672,913,933,677 | 1,604,516,583,000 | 1,604,516,583,000 | 309,245,750 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 158 | lean | import data.nat.basic
variables x y z : ℕ
-- BEGIN
example : x * y + x * z = (z + y) * x :=
begin
rw ←mul_add,
rw add_comm,
rw mul_comm,
end
-- END |
f856213f6c33567cef02489edbd5b2da4529c8b1 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/topology/sheaves/sheaf_condition/equalizer_products_auto.lean | e1e7baa0269f66ac12335d005ff5cf33f98b89ce | [] | 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 | 12,684 | 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.presheaf
import Mathlib.category_theory.limits.punit
import Mathlib.catego... |
d0106ff4a806be742294e20864c39c5db7e46b45 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/special_functions/trigonometric/complex_deriv.lean | 2ab19256c1269f15cb38c234799cf9898e1e83f5 | [
"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 | 2,652 | 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, Benjamin Davidson
-/
import analysis.special_functions.trigonometric.complex
/-!
# Complex trigonometric functions
> THIS ... |
9412649adafbaf84030ea5d38b51cd14608b752c | c8d830ce6c7de4840cf0c892d8b58e7e8df97e37 | /src/property_catalogue/LTL/pattern_meta.lean | fcda87a7f588b00fe5247b32a8f9105a470c644e | [] | no_license | loganrjmurphy/lean-strategies | 4b8dd54771bb421c929a8bcb93a528ce6c1a70f1 | 020e2a65dc2ab475696dfea5ad8935a0a4085918 | refs/heads/main | 1,682,732,168,860 | 1,614,820,630,000 | 1,614,820,630,000 | 278,458,841 | 3 | 0 | null | 1,613,755,728,000 | 1,594,324,763,000 | Lean | UTF-8 | Lean | false | false | 1,141 | lean | import property_catalogue.LTL.sat.absent
import property_catalogue.LTL.sat.precedes
import common_meta
variable {α : Type}
meta def switch (s : string) : tactic unit :=
do
tgt ← tactic.target, ctx ← tactic.local_context,
match tgt with
| `(sat (precedes.globally %%e₁ %%e₂) _) :=
precedes.globally.sol... |
7cf216f0600177d4f2d5af8a8cbc6a4c1cc4d272 | f4bff2062c030df03d65e8b69c88f79b63a359d8 | /src/game/order/level09.lean | 848d9ccd12db21aebb766d5f4864f1bf06f72b37 | [
"Apache-2.0"
] | permissive | adastra7470/real-number-game | 776606961f52db0eb824555ed2f8e16f92216ea3 | f9dcb7d9255a79b57e62038228a23346c2dc301b | refs/heads/master | 1,669,221,575,893 | 1,594,669,800,000 | 1,594,669,800,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,806 | lean | import game.order.level08
open real
namespace xena -- hide
/-
# Chapter 2 : Order
## Level 9
This level invites you to work out a property of the absolute value.
In Lean the absolute value of $x$ is denoted by `abs x`.
For ease of use, a notation can be used around that definition as below.
Feel free to use the tr... |
b0c651da3df85f530bc72adb34a29a112473cb78 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/zmod/basic.lean | a475e39eee6bc4d1d07c3bfef1162d629ca75286 | [
"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 | 33,981 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import algebra.char_p.basic
import algebra.group.conj_finite
import tactic.fin_cases
/-!
# Integers mod `n`
Definition of the integers mod n, and the field structure o... |
329ba1fb78789a08b1d5d5bc2eda9d8366601d1b | ae1e94c332e17c7dc7051ce976d5a9eebe7ab8a5 | /src/Lean/Elab/Deriving/BEq.lean | 09abe7097a8b72cde9ecbd72026ad37f19011dce | [
"Apache-2.0"
] | permissive | dupuisf/lean4 | d082d13b01243e1de29ae680eefb476961221eef | 6a39c65bd28eb0e28c3870188f348c8914502718 | refs/heads/master | 1,676,948,755,391 | 1,610,665,114,000 | 1,610,665,114,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,438 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Meta.Transform
import Lean.Elab.Deriving.Basic
import Lean.Elab.Deriving.Util
namespace Lean.Elab.Deriving.BEq
open Lean.Parser.Term
open Meta
... |
b0c30f1c2a5dc80459066ee04656ea445791a64a | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/probability/martingale/convergence.lean | d29bc0750b90a236c41bc94fe5ec365f516c43f5 | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 25,477 | lean | /-
Copyright (c) 2022 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
import probability.martingale.upcrossing
import measure_theory.function.uniform_integrable
import measure_theory.constructions.polish
/-!
# Martingale convergence theorem... |
fb59d3d7b716804f933f261201005098193e1060 | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /src/Lean/Elab/Tactic/Induction.lean | b71cac0011275a89e5a87d67f65d751d5833757a | [
"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 | 26,057 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Sebastian Ullrich
-/
import Lean.Util.CollectFVars
import Lean.Parser.Term
import Lean.Meta.RecursorInfo
import Lean.Meta.CollectMVars
import Lean.Meta.Tactic... |
842bba12d7e75ee6a49bf1bc72dfc6d1026729d9 | 9ad8d18fbe5f120c22b5e035bc240f711d2cbd7e | /src/combinatorics/partition/basic.lean | 137ef522f907c8dcd0706740017615ecdf9c2d4c | [] | no_license | agusakov/lean_lib | c0e9cc29fc7d2518004e224376adeb5e69b5cc1a | f88d162da2f990b87c4d34f5f46bbca2bbc5948e | refs/heads/master | 1,642,141,461,087 | 1,557,395,798,000 | 1,557,395,798,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 72,500 | 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 data.fintype tactic.squeeze tactic.fin_cases
import data.finset_transfer data.unique_element
namespace combinatorics
/-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~... |
d8fff3c7cdcec4e1f4f9b390900027a149c931be | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /archive/sensitivity.lean | a14cead730779f7ca1ef3765ce06d97a61d02611 | [
"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 | 15,592 | lean | /-
Copyright (c) 2019 Reid Barton, Johan Commelin, Jesse Han, Chris Hughes, Robert Y. Lewis,
Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Johan Commelin, Jesse Han, Chris Hughes, Robert Y. Lewis, Patrick Massot
-/
import tactic.fin_cases... |
2853bf1e50520a75ece7b892718d7b182f47800c | d450724ba99f5b50b57d244eb41fef9f6789db81 | /src/mywork/lectures/lecture_21.lean | 50f150910ab553f48f719cbfd44c187981d932a0 | [] | no_license | jakekauff/CS2120F21 | 4f009adeb4ce4a148442b562196d66cc6c04530c | e69529ec6f5d47a554291c4241a3d8ec4fe8f5ad | refs/heads/main | 1,693,841,880,030 | 1,637,604,848,000 | 1,637,604,848,000 | 399,946,698 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,661 | lean |
import data.set
namespace hidden
/-
PROPERTIES OF RELATIONS
-/
section relation
/-
For any types, α and β we will refine a
relation, r, to be a predicate on values
of these types. It will implicitly define
the set of all such pairs, also called a
relation, that satisfy the predicate (by
yielding a proposition f... |
79fdd73f06d4a6c16e3e6546e90c139a51c72464 | 46125763b4dbf50619e8846a1371029346f4c3db | /src/algebra/free_monoid.lean | a362b6d5b9f9ebaab0995e9f183cd6713ac03e2c | [
"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 | 3,702 | lean | /-
Copyright (c) 2019 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Yury Kudryashov
-/
import algebra.group.hom data.equiv.algebra data.list.basic
/-!
# Free monoid over a given alphabet
## Main definitions
* `free_monoid α`: free monoid o... |
b686b42d5ddd301dc330e4247e1542f5d0f51d43 | d436468d80b739ba7e06843c4d0d2070e43448e5 | /src/algebra/order_functions.lean | 44714b2555b2d227ef1c0e4472f0bbdc102bf9ef | [
"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 | 11,367 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import algebra.ordered_group order.lattice
open lattice
universes u v
variables {α : Type u} {β : Type v}
attribute [simp] max_eq_left max_eq_right min_eq_left min... |
0ed7380649cde82ba5afb1356f72c02c640b4b22 | c17c60327eee1622a8d7defa5af340e08619107f | /src/snippets/tactics/inegalites.lean | df98055c88a5248b6fbd6eeae3f048b0c4ecc780 | [] | no_license | FredericLeRoux/dEAduction-lean2 | 277e3aad5102ff155fb04b188dbd01568ceea005 | bf7d7d88c2511ecfda5a98ed96e4ca3bc7ae1151 | refs/heads/master | 1,667,931,697,036 | 1,593,174,880,000 | 1,593,174,880,000 | 275,150,842 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,002 | lean | import tactic.linarith
/- Tactique écrite par Mario, qui aojute au contexte que les carrés sont positifs
et que les produits de nb positifs sont positifs avant d'essayer linarith
AFER : ajouter les inverses de positifs
-/
namespace tactic
meta def find_squares : expr → tactic unit
| e@`(%%a ^ 2) := do
find_squar... |
220dbff69ec318c1043e3aaf41d728e5ad372c78 | 95dcf8dea2baf2b4b0a60d438f27c35ae3dd3990 | /src/category_theory/comma.lean | 86d18ad61ed958803daaa0e41ce638566699e3a4 | [
"Apache-2.0"
] | permissive | uniformity1/mathlib | 829341bad9dfa6d6be9adaacb8086a8a492e85a4 | dd0e9bd8f2e5ec267f68e72336f6973311909105 | refs/heads/master | 1,588,592,015,670 | 1,554,219,842,000 | 1,554,219,842,000 | 179,110,702 | 0 | 0 | Apache-2.0 | 1,554,220,076,000 | 1,554,220,076,000 | null | UTF-8 | Lean | false | false | 11,561 | lean | -- Copyright (c) 2018 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Scott Morrison, Johan Commelin
import category_theory.types
import category_theory.isomorphism
import category_theory.whiskering
import category_theory.opposites
import category... |
324c6e25c5eda7fedd24ae1e183e840b7e079019 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/category/Group/filtered_colimits.lean | 52be1744411f11d770674ad6b55353117c1b1e79 | [
"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 | 8,557 | lean | /-
Copyright (c) 2021 Justus Springer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Justus Springer
-/
import algebra.category.Group.basic
import algebra.category.Mon.filtered_colimits
/-!
# The forgetful functor from (commutative) (additive) groups preserves filter... |
bcd45c710b7382e6f1386e835af1e9714d71817b | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /src/Lean/PrettyPrinter/Basic.lean | 2743c66af78ae8f50069724a64a39fd449407a76 | [
"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 | 1,097 | lean | /-
Copyright (c) 2020 Sebastian Ullrich. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Ullrich
-/
import Lean.InternalExceptionId
import Lean.KeyedDeclsAttribute
namespace Lean
namespace PrettyPrinter
/- Auxiliary internal exception for backtracking the pr... |
faef9f080ce8e7ac9378598aa246eb0ff27f4207 | 968e2f50b755d3048175f176376eff7139e9df70 | /examples/prop_logic_theory/unnamed_2274.lean | 9eb66c8bb20afc30e82e1d69bd75a758b1662869 | [] | no_license | gihanmarasingha/mth1001_sphinx | 190a003269ba5e54717b448302a27ca26e31d491 | 05126586cbf5786e521be1ea2ef5b4ba3c44e74a | refs/heads/master | 1,672,913,933,677 | 1,604,516,583,000 | 1,604,516,583,000 | 309,245,750 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 300 | lean | variables {p q : Prop}
-- BEGIN
theorem not_and_not_of_not_or : ¬(p ∨ q) → ¬p ∧ ¬q :=
begin
intro h₁, -- Assume `h₁ : ¬(p ∨ q)`. It suffices to prove `¬p ∧ ¬q`.
split, -- By and introduction, it suffices to prove 1. `¬p` and 2. `¬q`.
{ sorry },
{ sorry },
end
-- END |
4680afdbf69892a5673d070b804c37ab0d29002a | 206422fb9edabf63def0ed2aa3f489150fb09ccb | /src/ring_theory/integral_closure.lean | eaf02569eb938436eb22e59b5f0ccca4f35c41f1 | [
"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 | 26,301 | 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 ring_theory.algebra_tower
import ring_theory.polynomial.scale_roots
/-!
# Integral closure of a subring.
If A is an R-algebra then `a : A` is integral over R if it is ... |
3317c1d5fc10dc7360b94f0a4c2a5306a072bf16 | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /stage0/src/Lean/Expr.lean | bde632e56e8f2d22cfbfea8df6b4f9780be91fc4 | [
"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 | 36,669 | lean | /-
Copyright (c) 2018 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Data.KVMap
import Lean.Level
namespace Lean
inductive Literal
| natVal (val : Nat)
| strVal (val : String)
instance Literal.inhabited : Inhab... |
424941d28527c1d9296840a5f724cec06bf66e93 | 5749d8999a76f3a8fddceca1f6941981e33aaa96 | /src/measure_theory/measurable_space.lean | b191a97979afe2486c94387546352270e6e86a37 | [
"Apache-2.0"
] | permissive | jdsalchow/mathlib | 13ab43ef0d0515a17e550b16d09bd14b76125276 | 497e692b946d93906900bb33a51fd243e7649406 | refs/heads/master | 1,585,819,143,348 | 1,580,072,892,000 | 1,580,072,892,000 | 154,287,128 | 0 | 0 | Apache-2.0 | 1,540,281,610,000 | 1,540,281,609,000 | null | UTF-8 | Lean | false | false | 42,998 | 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
Measurable spaces -- σ-algberas
-/
import data.set.disjointed order.galois_connection data.set.countable
/-!
# Measurable spaces and measurable functio... |
62a111804a90578f48a6982a1fef5cd9c641f0c1 | abd85493667895c57a7507870867b28124b3998f | /src/topology/uniform_space/completion.lean | 444681f8c08751db06ca959854300ac5a41c2ce3 | [
"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 | 23,194 | lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl
Hausdorff completions of uniform spaces.
The goal is to construct a left-adjoint to the inclusion of complete Hausdorff uniform spaces
into all uniform... |
bca5c2ed73d9838a0f0dd7c6b99a49af3a067484 | a0a027e4a00cdb315527e8922122f2a4411fd01c | /4.1-the-universal-quantifier.lean | 83573b2f8dce889243d99d2c6a25bb9857103bd5 | [] | no_license | spl/lean-tutorial | 96a1ef321d06b9b28d044eeb6bf1ff9a86761a6e | 35c0250004d75d8ae58f6192b649744545116022 | refs/heads/master | 1,610,250,012,890 | 1,454,259,122,000 | 1,454,259,122,000 | 49,971,362 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,561 | lean | /-------------------------------------------------------------------------------
- Section 4.1 The Universal Quantifier
------------------------------------------------------------------------------/
variables (A : Type) (p q : A → Prop)
example : (∀ x, p x ∧ q x) ↔ (∀ x, p x) ∧ (∀ x, q x) :=
have fwd : (∀ x, p ... |
16964dae8117736bcfeed42548154cd9e791f59f | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/calculus/parametric_interval_integral.lean | 0d9494850c02e0a19f5ab1dc9cb211785b286c3f | [
"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 | 6,596 | 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.calculus.parametric_integral
import measure_theory.integral.interval_integral
/-!
# Derivatives of interval integrals depending on parameters
> TH... |
43156c88e657823ee77e446a9cad6f2352787b76 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/analysis/normed_space/operator_norm.lean | cd5de39b2371a590d17127cb82f11631339816fd | [
"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 | 42,293 | lean | /-
Copyright (c) 2019 Jan-David Salchow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo
-/
import linear_algebra.finite_dimensional
import analysis.normed_space.riesz_lemma
import analysis.asymptotics
/-!
# Operator norm o... |
899884b8987969d3256067873f34deda0eea6584 | c3f2fcd060adfa2ca29f924839d2d925e8f2c685 | /hott/init/wf.hlean | 79ae373f5c2d3f0bd8758033f8be39c2897012d6 | [
"Apache-2.0"
] | permissive | respu/lean | 6582d19a2f2838a28ecd2b3c6f81c32d07b5341d | 8c76419c60b63d0d9f7bc04ebb0b99812d0ec654 | refs/heads/master | 1,610,882,451,231 | 1,427,747,084,000 | 1,427,747,429,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,850 | hlean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: init.wf
Author: Leonardo de Moura
-/
prelude
import init.relation init.tactic
inductive acc.{l₁ l₂} {A : Type.{l₁}} (R : A → A → Type.{l₂}) : A → Type.{max l₁ l₂} :=
intro : ∀... |
da961dfcd66c378aa1bf8091555d9135ad03a3f9 | 367134ba5a65885e863bdc4507601606690974c1 | /src/measure_theory/ae_eq_fun_metric.lean | a656d28e273f513d03589e0711d83c53aa82ed13 | [
"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 | 4,325 | 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.ae_eq_fun
/-!
# Emetric space structure on almost everywhere equal functions
Emetric on `L⁰` :
If `β` is an ... |
b7c36ff43e90e023293086212ff43dfa0c02277d | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebraic_topology/dold_kan/p_infty.lean | 7b1c539dca8bfc6ba0e623e9e88484f51f9ea26c | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 7,984 | 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.dold_kan.projections
import category_theory.idempotents.functor_categories
import category_theory.idempotents.functor_extension
/-!
# Construction ... |
b44f4a62279d4f09d63487c2843d1b054b365f17 | 64874bd1010548c7f5a6e3e8902efa63baaff785 | /library/algebra/category/natural_transformation.lean | dc77986552a7edcb25cd42736278a240d987fcdb | [
"Apache-2.0"
] | permissive | tjiaqi/lean | 4634d729795c164664d10d093f3545287c76628f | d0ce4cf62f4246b0600c07e074d86e51f2195e30 | refs/heads/master | 1,622,323,796,480 | 1,422,643,069,000 | 1,422,643,069,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,193 | lean | /-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.category.natural_transformation
Author: Floris van Doorn
-/
import .functor
open category eq eq.ops functor
inductive natural_transformation {C D : Category} (F G : C ⇒ D) ... |
3db3512b79fe1bd90af0a17596b22236e6603348 | 2de8c1580f92bb6c28b60135f589fe9d0513faba | /src/rtc.lean | f3df72669484cb92b654a1d3300c3ca1c95da0ca | [] | no_license | FCL-lean/verification | 44a52e40ab78b18654b8d61bb55c2c912a40d2f4 | be02c698c0ca78b18762e3fe7749cdc72a55d197 | refs/heads/master | 1,585,960,207,309 | 1,560,259,990,000 | 1,560,259,990,000 | 155,650,137 | 0 | 0 | null | 1,541,039,704,000 | 1,541,038,972,000 | Lean | UTF-8 | Lean | false | false | 742 | lean | section relation
inductive rtc {α : Sort*} (r : α → α → Prop) : α → α → Prop
| refl : ∀ a, rtc a a
| base : ∀ a b, r a b → rtc a b
| trans : ∀ a b c, rtc a b → rtc b c → rtc a c
section
variables {α : Sort*} {r : α → α → Prop} {a b c : α}
lemma rtc.refl' : rtc r a a := rtc.refl _ _
lemma rtc.base' (h :... |
e752fe0752320dfe76ada24fec31a426dcf1b44d | c9b68131de1dfe4e7f0ea5749b11e67a774bc839 | /src/final_correctness.lean | 355671feaff3f4cd565a29c52e0a722649728af8 | [] | no_license | congge666/formal-proofs | 2013f158f310abcfc07c156bb2a5113fb78f7831 | b5f6964d0220c8f89668357f2c08e44861128fe3 | refs/heads/master | 1,691,374,567,671 | 1,632,704,604,000 | 1,632,706,366,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,523 | lean | /-
This is the final correctenss theorem, stated in terms of the autogenerated constraints.
The statements of the theorems only depend on the data and constraints specified in
`constraints_autogenerated.lean` and the machine semantics in `cpu.lean`.
-/
import correctness glue
noncomputable theory
open_locale classica... |
4acc8d707a9b4b93afdcadd6ee31843438783718 | 592ee40978ac7604005a4e0d35bbc4b467389241 | /Library/generated/mathscheme-lean/Right0.lean | 3dee9f2365a69591934ee523bff5e668f9920c78 | [] | 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 | 6,524 | 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 Right0
structure Right0 (A : Type) : Type :=
(zero : A)
(op : (A → (A → A)))
(rightZero_op_zero : (∀ {x : A} , (op x zero) = zero))
open Right0
s... |
0cb1c301c1e61231f21c9e5ab5ab929ac65a6b60 | 17d3c61bf162bf88be633867ed4cb201378a8769 | /library/init/util.lean | 3b9a9b713e1a527e2b0a3f04404315f0594aa579 | [
"Apache-2.0"
] | permissive | u20024804/lean | 11def01468fb4796fb0da76015855adceac7e311 | d315e424ff17faf6fe096a0a1407b70193009726 | refs/heads/master | 1,611,388,567,561 | 1,485,836,506,000 | 1,485,836,625,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,071 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.data.string.basic
universe variables u
/- This function has a native implementation that tracks time. -/
def timeit {α : Type u} (s : s... |
5ebade349101283164de20f96464f354476864a9 | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /src/Lean/Compiler/Util.lean | 8ab110b0b6189416d7b3ff205e52224891269a26 | [
"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 | 3,904 | 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.Meta.Match.MatcherInfo
namespace Lean.Compiler
/--
Return `true` if `mdata` should be preserved.
Right now, we don't preserve any `MData`, but... |
4e2f947c6307ec51773518fb3870dd7ecc26a461 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/ring_quot.lean | 7d70ddb62fe7720f5670a01e48aad76e63103359 | [
"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 | 17,975 | 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.algebra.basic
import ring_theory.ideal.quotient
/-!
# Quotients of non-commutative rings
Unfortunately, ideals have only been developed in the commut... |
e908cde919fdecee86fcdad157fec2b80021019b | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/algebra/char_zero.lean | e66dd4f86d20c407a09186f25ba398e4a9155f28 | [
"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 | 6,384 | lean | /-
Copyright (c) 2014 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import data.nat.cast
import data.fintype.basic
import tactic.wlog
/-!
# Characteristic zero
A ring `R` is called of characteristic zero if every natural number `n`... |
260aaba216a3b5c369441df90ebca6e0acc8ebdf | 87fd6b43d22688237c02b87c30d2a524f53bab24 | /src/game/sets/sets_level03.lean | ce61a5ba9cf656923001720978f8705561c58d0b | [
"Apache-2.0"
] | permissive | grthomson/real-number-game | 66142fedf0987db90f66daed52f9c8b42b70f909 | 8ddc15fdddc241c246653f7bb341df36e4e880a8 | refs/heads/master | 1,668,059,330,605 | 1,592,873,454,000 | 1,592,873,454,000 | 262,025,764 | 0 | 0 | null | 1,588,849,107,000 | 1,588,849,106,000 | null | UTF-8 | Lean | false | false | 1,344 | lean | import game.sets.sets_level02 -- hide
namespace xena -- hide
open_locale classical -- hide
variable X : Type -- hide
/-
# Chapter 1 : Sets
## Level 3 : intersection (∩)
-/
/-
Now prove that for any two sets $A$ and $B$, $A ∩ B ⊆ A$.
You will need to rewrite the following term:
```
mem_inter_iff : x ∈ A ∩ B... |
8e1bafea7cef56804723ce2515de5194fb264fc6 | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/data/fin2.lean | 8976a129fc023b96b9cba25c99f5c38d45da4522 | [
"Apache-2.0"
] | permissive | lacker/mathlib | f2439c743c4f8eb413ec589430c82d0f73b2d539 | ddf7563ac69d42cfa4a1bfe41db1fed521bd795f | refs/heads/master | 1,671,948,326,773 | 1,601,479,268,000 | 1,601,479,268,000 | 298,686,743 | 0 | 0 | Apache-2.0 | 1,601,070,794,000 | 1,601,070,794,000 | null | UTF-8 | Lean | false | false | 2,926 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
open nat
universes u
/-- An alternate definition of `fin n` defined as an inductive type
instead of a subtype of `nat`. This is useful for its induction
princip... |
a13787d4a9700032f01bef84e8a904ca9999cc6a | c76cc4eaee3c806716844e49b5175747d1aa170a | /src/problem_sheet_two.lean | b71b740762556566b444c4473b319a1c14c36dcf | [] | no_license | ImperialCollegeLondon/M40002 | 0fb55848adbb0d8bc4a65ca5d7ed6edd18764c28 | a499db70323bd5ccae954c680ec9afbf15ffacca | refs/heads/master | 1,674,878,059,748 | 1,607,624,828,000 | 1,607,624,828,000 | 309,696,750 | 3 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,924 | lean | import tactic
import data.real.basic
import data.nat.choose.sum -- binomial theorem
import data.real.ereal
import data.pnat.basic
section Q2
/-!
# Q2
-/
/-
2. Fix nonempty sets S_n ⊆ R, n= 1,2,3,....
Prove that sup{sup S1,sup S2,sup S3,...} = sup(⋃_{n=1}^{infty} S_n),
in the sense that if either exists then so ... |
088c61c01033e9f1ca7d696b102b551449780711 | 8e6cad62ec62c6c348e5faaa3c3f2079012bdd69 | /src/algebra/lie/solvable.lean | c380006b32ffd9cec4934200aff6948474fc6be3 | [
"Apache-2.0"
] | permissive | benjamindavidson/mathlib | 8cc81c865aa8e7cf4462245f58d35ae9a56b150d | fad44b9f670670d87c8e25ff9cdf63af87ad731e | refs/heads/master | 1,679,545,578,362 | 1,615,343,014,000 | 1,615,343,014,000 | 312,926,983 | 0 | 0 | Apache-2.0 | 1,615,360,301,000 | 1,605,399,418,000 | Lean | UTF-8 | Lean | false | false | 14,007 | 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.ideal_operations
import algebra.lie.abelian
import order.preorder_hom
/-!
# Solvable Lie algebras
Like groups, Lie algebras admit a natural concept of ... |
5693b2ebfa12407acf0726463a48cb070f0be8ed | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/init/meta/ac_tactics_auto.lean | 7958b089f1bc93f8fadabdace4eda5b22ee02c4d | [] | 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 | 394 | 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
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.meta.tactic
namespace Mathlib
namespace tactic
/- (flat_assoc op assoc e) -/
/- (perm_ac op assoc c... |
ca6080e5de570315697559cfffcd22e151fdf519 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/hom/group_action.lean | 4bc204da1c7d45e341ce9dfdca1fa658f7b076c5 | [
"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 | 14,356 | lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import algebra.group_ring_action.invariant
import group_theory.group_action.defs
import group_theory.subgroup.basic
/-!
# Equivariant homomorphisms
## Main definitions
* `mu... |
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