path stringlengths 11 71 | content stringlengths 75 124k |
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Tactic\NormNum\Eq.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 Mathlib.Tactic.NormNum.Inv
/-!
# `norm_num` extension for equalities
-/
variable {α : Type*}
open Lean Meta Qq
namespace Mathlib.Meta.NormNum
theorem isNa... |
Tactic\NormNum\GCD.lean | /-
Copyright (c) 2021 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Kyle Miller
-/
import Mathlib.Data.Int.GCD
import Mathlib.Tactic.NormNum
/-! # `norm_num` extensions for GCD-adjacent functions
This module defines some `norm_num` ex... |
Tactic\NormNum\Ineq.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 Mathlib.Tactic.NormNum.Eq
import Mathlib.Algebra.Order.Field.Defs
import Mathlib.Algebra.Order.Invertible
import Mathlib.Algebra.Order.Monoid.WithTop
import Ma... |
Tactic\NormNum\Inv.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 Mathlib.Tactic.NormNum.Basic
import Mathlib.Data.Rat.Cast.CharZero
import Mathlib.Algebra.Field.Basic
/-!
# `norm_num` plugins for `Rat.cast` and `⁻¹`.
-/
va... |
Tactic\NormNum\IsCoprime.lean | /-
Copyright (c) 2023 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
import Mathlib.RingTheory.Coprime.Lemmas
import Mathlib.Tactic.NormNum.GCD
/-! # `norm_num` extension for `IsCoprime`
This module defines a `norm_num` extension for `IsCo... |
Tactic\NormNum\LegendreSymbol.lean | /-
Copyright (c) 2022 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
import Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol
/-!
# A `norm_num` extension for Jacobi and Legendre symbols
We extend the `norm_num` tactic so that it can be... |
Tactic\NormNum\NatFib.lean | /-
Copyright (c) 2023 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller, Mario Carneiro
-/
import Mathlib.Data.Nat.Fib.Basic
import Mathlib.Tactic.NormNum
/-! # `norm_num` extension for `Nat.fib`
This `norm_num` extension uses a strategy paralle... |
Tactic\NormNum\NatSqrt.lean | /-
Copyright (c) 2022 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Kyle Miller
-/
import Mathlib.Data.Nat.Defs
import Mathlib.Tactic.NormNum
/-! # `norm_num` extension for `Nat.sqrt`
This module defines a `norm_num` extension for `Na... |
Tactic\NormNum\OfScientific.lean | /-
Copyright (c) 2021 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Thomas Murrills
-/
import Mathlib.Tactic.NormNum.Basic
import Mathlib.Data.Rat.Cast.Lemmas
/-!
## `norm_num` plugin for scientific notation.
-/
namespace Mathlib
open... |
Tactic\NormNum\Pow.lean | /-
Copyright (c) 2021 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Thomas Murrills
-/
import Mathlib.Data.Int.Cast.Lemmas
import Mathlib.Tactic.NormNum.Basic
/-!
## `norm_num` plugin for `^`.
-/
namespace Mathlib
open Lean hiding Rat... |
Tactic\NormNum\Prime.lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-/
import Mathlib.Tactic.NormNum.Basic
import Mathlib.Data.Nat.Prime.Defs
/-!
# `norm_num` extensions on natural numbers
This ... |
Tactic\NormNum\Result.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 Mathlib.Algebra.Field.Defs
import Mathlib.Algebra.GroupWithZero.Invertible
import Mathlib.Data.Sigma.Basic
import Mathlib.Algebra.Ring.Nat
import Mathlib.Data.... |
Tactic\Positivity\Basic.lean | /-
Copyright (c) 2022 Mario Carneiro, Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Heather Macbeth, Yaël Dillies
-/
import Mathlib.Algebra.Order.Group.PosPart
import Mathlib.Algebra.Order.Ring.Basic
import Mathlib.Algebra.Order.Ring.R... |
Tactic\Positivity\Core.lean | /-
Copyright (c) 2022 Mario Carneiro, Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Heather Macbeth, Yaël Dillies
-/
import Mathlib.Tactic.NormNum.Core
import Mathlib.Tactic.HaveI
import Mathlib.Algebra.Order.Invertible
import Mathlib.... |
Tactic\Positivity\Finset.lean | /-
Copyright (c) 2023 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Data.Finset.Density
import Mathlib.Tactic.Positivity.Core
/-!
# Positivity extensions for finsets
This file provides a few `positivity` extensions that c... |
Tactic\ReduceModChar\Ext.lean | /-
Copyright (c) 2023 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import Lean.Meta.Tactic.Simp.Attr
/-!
# `@[reduce_mod_char]` attribute
This file registers `@[reduce_mod_char]` as a `simp` attribute.
-/
open Lean Meta
/-- `@[reduce_m... |
Tactic\Relation\Rfl.lean | /-
Copyright (c) 2022 Newell Jensen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Newell Jensen
-/
import Lean.Meta.Tactic.Rfl
/-!
# `Lean.MVarId.liftReflToEq`
Convert a goal of the form `x ~ y` into the form `x = y`, where `~` is a reflexive
relation, that is, a r... |
Tactic\Relation\Symm.lean | /-
Copyright (c) 2022 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Lean.Meta.Tactic.Symm
/-!
# `relSidesIfSymm?`
-/
open Lean Meta Symm
namespace Mathlib.Tactic
open Lean.Elab.Tactic
/-- If `e` is the form `@R .. x y`, wh... |
Tactic\Relation\Trans.lean | /-
Copyright (c) 2022 Siddhartha Gadgil. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Siddhartha Gadgil, Mario Carneiro
-/
import Mathlib.Lean.Meta
import Mathlib.Lean.Elab.Tactic.Basic
import Lean.Elab.Tactic.ElabTerm
import Mathlib.Tactic.TypeStar
/-!
# `trans` ta... |
Tactic\Ring\Basic.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Aurélien Saue, Anne Baanen
-/
import Mathlib.Algebra.Order.Ring.Rat
import Mathlib.Tactic.NormNum.Inv
import Mathlib.Tactic.NormNum.Pow
import Mathlib.Util.AtomM
/-!
#... |
Tactic\Ring\PNat.lean | /-
Copyright (c) 2023 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Tactic.Ring.Basic
import Mathlib.Data.PNat.Basic
/-!
# Additional instances for `ring` over `PNat`
This adds some instances which enable `ring` to wo... |
Tactic\Ring\RingNF.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Anne Baanen
-/
import Mathlib.Tactic.Ring.Basic
import Mathlib.Tactic.TryThis
import Mathlib.Tactic.Conv
import Mathlib.Util.Qq
/-!
# `ring_nf` tactic
A tactic which ... |
Tactic\Sat\FromLRAT.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 Mathlib.Algebra.Group.Nat
/-!
# `lrat_proof` command
Defines a macro for producing SAT proofs from CNF / LRAT files.
These files are commonly used in the SAT... |
Tactic\Simps\Basic.lean | /-
Copyright (c) 2022 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import Lean.Elab.Tactic.Simp
import Lean.Elab.App
import Mathlib.Tactic.Simps.NotationClass
import Batteries.Data.String.Basic
import Mathlib.Lean.Expr.Basic
/-!... |
Tactic\Simps\NotationClass.lean | /-
Copyright (c) 2022 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import Lean.Elab.Exception
import Batteries.Lean.NameMapAttribute
import Batteries.Lean.Expr
import Batteries.Tactic.Lint
/-!
# `@[notation_class]` attribute fo... |
Tactic\ToAdditive\Frontend.lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Yury Kudryashov, Floris van Doorn, Jon Eugster
-/
import Mathlib.Data.Nat.Notation
import Mathlib.Data.String.Defs
import Mathlib.Data.Array.Defs
import Mathlib.Lean.Ex... |
Tactic\Widget\Calc.lean | /-
Copyright (c) 2023 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import Lean.Elab.Tactic.Calc
import Mathlib.Data.String.Defs
import Mathlib.Tactic.Widget.SelectPanelUtils
import Batteries.CodeAction.Attr
import Batteries.Lean.Pos... |
Tactic\Widget\CommDiag.lean | /-
Copyright (c) 2022 Wojciech Nawrocki. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wojciech Nawrocki
-/
import ProofWidgets.Component.PenroseDiagram
import ProofWidgets.Presentation.Expr
import Mathlib.CategoryTheory.Category.Basic
/-! This module defines tactic/... |
Tactic\Widget\CongrM.lean | /-
Copyright (c) 2023 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import Mathlib.Tactic.Widget.SelectPanelUtils
import Mathlib.Tactic.CongrM
/-! # CongrM widget
This file defines a `congrm?` tactic that displays a widget panel al... |
Tactic\Widget\Conv.lean | /-
Copyright (c) 2023 Robin Böhne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robin Böhne, Wojciech Nawrocki, Patrick Massot
-/
import Mathlib.Tactic.Widget.SelectPanelUtils
import Mathlib.Data.String.Defs
import Batteries.Tactic.Lint
import Batteries.Lean.Position... |
Tactic\Widget\GCongr.lean | /-
Copyright (c) 2023 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import Mathlib.Tactic.Widget.SelectPanelUtils
import Mathlib.Tactic.GCongr
/-! # GCongr widget
This file defines a `gcongr?` tactic that displays a widget panel all... |
Tactic\Widget\InteractiveUnfold.lean | /-
Copyright (c) 2023 Jovan Gerbscheid. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jovan Gerbscheid
-/
import Batteries.Lean.Position
import Mathlib.Tactic.Widget.SelectPanelUtils
import Mathlib.Lean.GoalsLocation
import Mathlib.Lean.Meta.KAbstractPositions
/-!
#... |
Tactic\Widget\SelectInsertParamsClass.lean | /-
Copyright (c) 2023 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import Lean.Widget.InteractiveGoal
import Lean.Elab.Deriving.Basic
/-! # SelectInsertParamsClass
Defines the basic class of parameters for a select and insert widge... |
Tactic\Widget\SelectPanelUtils.lean | /-
Copyright (c) 2023 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import Lean.Meta.ExprLens
import ProofWidgets.Component.MakeEditLink
import ProofWidgets.Component.OfRpcMethod -- needed in all files using this one.
import Mathlib.T... |
Tactic\Widget\StringDiagram.lean | /-
Copyright (c) 2024 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno
-/
import ProofWidgets.Component.PenroseDiagram
import ProofWidgets.Component.Panel.Basic
import ProofWidgets.Presentation.Expr
import Mathlib.Tactic.CategoryTheory.Monoidal
... |
Testing\SlimCheck\Functions.lean | /-
Copyright (c) 2020 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import Mathlib.Data.List.Sigma
import Mathlib.Data.Int.Range
import Mathlib.Data.Finsupp.Defs
import Mathlib.Data.Finsupp.ToDFinsupp
import Mathlib.Testing.SlimCheck.Sample... |
Testing\SlimCheck\Gen.lean | /-
Copyright (c) 2021 Henrik Böving. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Henrik Böving, Simon Hudon
-/
import Mathlib.Control.Random
import Batteries.Data.List.Perm
/-!
# `Gen` Monad
This monad is used to formulate randomized computations with a parameter
... |
Testing\SlimCheck\Sampleable.lean | /-
Copyright (c) 2022 Henrik Böving. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Henrik Böving, Simon Hudon
-/
import Mathlib.Algebra.Order.Ring.Int
import Mathlib.Init.Data.List.Instances
import Mathlib.Testing.SlimCheck.Gen
/-!
# `SampleableExt` Class
This class... |
Testing\SlimCheck\Testable.lean | /-
Copyright (c) 2022 Henrik Böving. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Henrik Böving, Simon Hudon
-/
import Mathlib.Testing.SlimCheck.Sampleable
import Lean
/-!
# `Testable` Class
Testable propositions have a procedure that can generate counter-examples
... |
Topology\AlexandrovDiscrete.lean | /-
Copyright (c) 2023 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Data.Set.Image
import Mathlib.Topology.Bases
import Mathlib.Topology.Inseparable
import Mathlib.Topology.Compactness.Compact
/-!
# Alexandrov-discrete top... |
Topology\Bases.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import Mathlib.Data.Set.Constructions
import Mathlib.Topology.Constructions
import Mathlib.Topology.ContinuousOn
/-!
# Bases of topologies. Countabil... |
Topology\Basic.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Jeremy Avigad
-/
import Mathlib.Order.Filter.Lift
import Mathlib.Topology.Defs.Filter
/-!
# Basic theory of topological spaces.
The main definition is... |
Topology\Clopen.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 Mathlib.Topology.ContinuousOn
import Mathlib.Data.Set.BoolIndicator
/-!
# Clopen sets
A clopen set is a set that is both clo... |
Topology\ClopenBox.lean | /-
Copyright (c) 2023 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
import Mathlib.Topology.CompactOpen
import Mathlib.Topology.Sets.Closeds
/-!
# Clopen subsets in cartesian products
In general, a clopen subset in a cartesian p... |
Topology\CompactOpen.lean | /-
Copyright (c) 2018 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton
-/
import Mathlib.Topology.ContinuousFunction.Basic
/-!
# The compact-open topology
In this file, we define the compact-open topology on the set of continuous maps between t... |
Topology\CompletelyRegular.lean | /-
Copyright (c) 2023 Matias Heikkilä. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Matias Heikkilä
-/
import Mathlib.Topology.UrysohnsLemma
import Mathlib.Topology.UnitInterval
import Mathlib.Topology.StoneCech
/-!
# Completely regular topological spaces.
This fil... |
Topology\Constructions.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 Mathlib.Topology.Maps.Basic
import Mathlib.Topology.NhdsSet
/-!
# Constructions of new topological spaces from old ones
This ... |
Topology\ContinuousOn.lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Topology.Constructions
/-!
# Neighborhoods and continuity relative to a subset
This file defines relative versions
* `nhdsWithin` of `nhds`... |
Topology\CountableSeparatingOn.lean | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Topology.Separation
import Mathlib.Order.Filter.CountableSeparatingOn
/-!
# Countable separating families of sets in topological spaces
In this fil... |
Topology\Covering.lean | /-
Copyright (c) 2022 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import Mathlib.Topology.IsLocalHomeomorph
import Mathlib.Topology.FiberBundle.Basic
/-!
# Covering Maps
This file defines covering maps.
## Main definitions
* `... |
Topology\DenseEmbedding.lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot
-/
import Mathlib.Topology.Separation
import Mathlib.Topology.Bases
/-!
# Dense embeddings
This file defines three properties of functions... |
Topology\DerivedSet.lean | /-
Copyright (c) 2024 Daniel Weber. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Daniel Weber
-/
import Mathlib.Topology.Perfect
import Mathlib.Tactic.Peel
/-!
# Derived set
This file defines the derived set of a set, the set of all `AccPt`s of its principal filter... |
Topology\DiscreteQuotient.lean | /-
Copyright (c) 2021 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Calle Sönne, Adam Topaz
-/
import Mathlib.Data.Setoid.Partition
import Mathlib.Topology.Separation
import Mathlib.Topology.LocallyConstant.Basic
/-!
# Discrete quotients of a topological... |
Topology\DiscreteSubset.lean | /-
Copyright (c) 2023 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash, Bhavik Mehta
-/
import Mathlib.Topology.Constructions
import Mathlib.Topology.Separation
/-!
# Discrete subsets of topological spaces
This file contains various additional ... |
Topology\ExtendFrom.lean | /-
Copyright (c) 2020 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Anatole Dedecker
-/
import Mathlib.Topology.Separation
/-!
# Extending a function from a subset
The main definition of this file is `extendFrom A f` where `f : X → ... |
Topology\ExtremallyDisconnected.lean | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.Topology.Homeomorph
import Mathlib.Topology.StoneCech
/-!
# Extremally disconnected spaces
An extremally disconnected topological space is a space in... |
Topology\Filter.lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Order.Filter.Lift
import Mathlib.Topology.Separation
import Mathlib.Order.Interval.Set.Monotone
/-!
# Topology on the set of filters on a type
This... |
Topology\GDelta.lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Yury Kudryashov
-/
import Mathlib.Topology.UniformSpace.Basic
import Mathlib.Order.Filter.CountableInter
/-!
# `Gδ` sets
In this file we define `Gδ` sets and pr... |
Topology\Germ.lean | /-
Copyright (c) 2023 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import Mathlib.Order.Filter.Germ.Basic
import Mathlib.Topology.NhdsSet
import Mathlib.Topology.LocallyConstant.Basic
import Mathlib.Analysis.Normed.Module.Basic
/-! ... |
Topology\Gluing.lean | /-
Copyright (c) 2021 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.CategoryTheory.GlueData
import Mathlib.Topology.Category.TopCat.Limits.Pullbacks
import Mathlib.Topology.Category.TopCat.Opens
import Mathlib.Tactic.Generali... |
Topology\Homeomorph.lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Sébastien Gouëzel, Zhouhang Zhou, Reid Barton
-/
import Mathlib.Logic.Equiv.Fin
import Mathlib.Topology.DenseEmbedding
import Mathlib.Topology.Support
impo... |
Topology\IndicatorConstPointwise.lean | /-
Copyright (c) 2023 Kalle Kytölä. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kalle Kytölä
-/
import Mathlib.Topology.Separation
/-!
# Pointwise convergence of indicator functions
In this file, we prove the equivalence of three different ways to phrase that the ... |
Topology\Inseparable.lean | /-
Copyright (c) 2021 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang, Yury G. Kudryashov
-/
import Mathlib.Tactic.TFAE
import Mathlib.Topology.ContinuousOn
/-!
# Inseparable points in a topological space
In this file we prove basic properties... |
Topology\Irreducible.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 Mathlib.Topology.ContinuousOn
import Mathlib.Order.Minimal
/-!
# Irreducibility in topological spaces
## Main definitions
* ... |
Topology\IsLocalHomeomorph.lean | /-
Copyright (c) 2021 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import Mathlib.Topology.PartialHomeomorph
import Mathlib.Topology.SeparatedMap
/-!
# Local homeomorphisms
This file defines local homeomorphisms.
## Main definit... |
Topology\KrullDimension.lean | /-
Copyright (c) 2024 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang, Fangming Li
-/
import Mathlib.Order.KrullDimension
import Mathlib.Topology.Sets.Closeds
/-!
# The Krull dimension of a topological space
The Krull dimension of a topologi... |
Topology\List.lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.Topology.Constructions
import Mathlib.Topology.Algebra.Monoid
import Mathlib.Order.Filter.ListTraverse
import Mathlib.Tactic.AdaptationNote
/-!
# Topolog... |
Topology\LocalAtTarget.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 Mathlib.Topology.Sets.Opens
import Mathlib.Topology.LocallyClosed
/-!
# Properties of maps that are local at the target.
We show that the following properties of c... |
Topology\LocallyClosed.lean | /-
Copyright (c) 2024 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.Topology.Constructions
import Mathlib.Tactic.TFAE
/-!
# Locally closed sets
## Main definitions
* `IsLocallyClosed`: Predicate saying that a set is locall... |
Topology\LocallyFinite.lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Topology.ContinuousOn
import Mathlib.Order.Filter.SmallSets
/-!
### Locally finite families of sets
We say that a family of sets in a topological s... |
Topology\NhdsSet.lean | /-
Copyright (c) 2022 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Patrick Massot
-/
import Mathlib.Topology.Basic
/-!
# Neighborhoods of a set
In this file we define the filter `𝓝ˢ s` or `nhdsSet s` consisting of all neighborho... |
Topology\NoetherianSpace.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 Mathlib.Topology.Sets.Closeds
/-!
# Noetherian space
A Noetherian space is a topological space that satisfies any of the following equivalent conditions:
- `WellFo... |
Topology\OmegaCompletePartialOrder.lean | /-
Copyright (c) 2020 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import Mathlib.Topology.Basic
import Mathlib.Order.UpperLower.Basic
import Mathlib.Order.OmegaCompletePartialOrder
/-!
# Scott Topological Spaces
A type of topological sp... |
Topology\Order.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import Mathlib.Topology.Defs.Induced
import Mathlib.Topology.Basic
/-!
# Ordering on topologies and (co)induced topologies
Topologies on a fixed typ... |
Topology\Partial.lean | /-
Copyright (c) 2018 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
-/
import Mathlib.Order.Filter.Partial
import Mathlib.Topology.Basic
/-!
# Partial functions and topological spaces
In this file we prove properties of `Filter.PTendsto`... |
Topology\PartialHomeomorph.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 Mathlib.Logic.Equiv.PartialEquiv
import Mathlib.Topology.Sets.Opens
/-!
# Partial homeomorphisms
This file defines homeomorphisms between open subsets ... |
Topology\PartitionOfUnity.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 Mathlib.Algebra.BigOperators.Finprod
import Mathlib.SetTheory.Ordinal.Basic
import Mathlib.Topology.ContinuousFunction.Algebra
import Mathlib.Topology.Compac... |
Topology\Perfect.lean | /-
Copyright (c) 2022 Felix Weilacher. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Felix Weilacher
-/
import Mathlib.Topology.Separation
/-!
# Perfect Sets
In this file we define perfect subsets of a topological space, and prove some basic properties,
including a... |
Topology\QuasiSeparated.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 Mathlib.Topology.Separation
import Mathlib.Topology.NoetherianSpace
/-!
# Quasi-separated spaces
A topological space is quasi-separated if the intersections of any... |
Topology\RestrictGenTopology.lean | /-
Copyright (c) 2024 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Topology.Defs.Sequences
import Mathlib.Topology.Compactness.Compact
/-!
# Topology generated by its restrictions to subsets
We say that restriction... |
Topology\Semicontinuous.lean | /-
Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Algebra.GroupWithZero.Indicator
import Mathlib.Topology.ContinuousOn
import Mathlib.Topology.Instances.ENNReal
/-!
# Semicontinuous maps
A func... |
Topology\SeparatedMap.lean | /-
Copyright (c) 2023 Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junyan Xu
-/
import Mathlib.Topology.Connected.Basic
import Mathlib.Topology.Separation
/-!
# Separated maps and locally injective maps out of a topological space.
This module introduces a... |
Topology\Separation.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import Mathlib.Topology.Compactness.Lindelof
import Mathlib.Topology.Compactness.SigmaCompact
import Mathlib.Topology.Connected.TotallyDisconnected
im... |
Topology\Sequences.lean | /-
Copyright (c) 2018 Jan-David Salchow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jan-David Salchow, Patrick Massot, Yury Kudryashov
-/
import Mathlib.Topology.Defs.Sequences
import Mathlib.Topology.UniformSpace.Cauchy
/-!
# Sequences in topological spaces
In t... |
Topology\ShrinkingLemma.lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Reid Barton
-/
import Mathlib.Topology.Separation
/-!
# The shrinking lemma
In this file we prove a few versions of the shrinking lemma. The lemma says that in a no... |
Topology\Sober.lean | /-
Copyright (c) 2021 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.Topology.Separation
import Mathlib.Topology.Sets.Closeds
/-!
# Sober spaces
A quasi-sober space is a topological space where every
irreducible closed subse... |
Topology\Specialization.lean | /-
Copyright (c) 2023 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Order.Category.Preord
import Mathlib.Topology.Category.TopCat.Basic
import Mathlib.Topology.ContinuousFunction.Basic
import Mathlib.Topology.Separation
imp... |
Topology\StoneCech.lean | /-
Copyright (c) 2018 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton
-/
import Mathlib.Topology.Bases
import Mathlib.Topology.DenseEmbedding
/-! # Stone-Čech compactification
Construction of the Stone-Čech compactification using ultrafilters.... |
Topology\Support.lean | /-
Copyright (c) 2022 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Patrick Massot
-/
import Mathlib.Algebra.GroupWithZero.Indicator
import Mathlib.Algebra.Module.Basic
import Mathlib.Topology.Separation
/-!
# The topological suppo... |
Topology\TietzeExtension.lean | /-
Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import Mathlib.Analysis.SpecificLimits.Basic
import Mathlib.Order.Interval.Set.IsoIoo
import Mathlib.Topology.Order.MonotoneContinuity
import Mathlib.Topology... |
Topology\UnitInterval.lean | /-
Copyright (c) 2020 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Scott Morrison
-/
import Mathlib.Algebra.Order.Interval.Set.Instances
import Mathlib.Order.Interval.Set.ProjIcc
import Mathlib.Topology.Instances.Real
/-!
# The unit i... |
Topology\UrysohnsBounded.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 Mathlib.Topology.UrysohnsLemma
import Mathlib.Topology.ContinuousFunction.Bounded
/-!
# Urysohn's lemma for bounded continuous functions
In this file we re... |
Topology\UrysohnsLemma.lean | /-
Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import Mathlib.Analysis.NormedSpace.AddTorsor
import Mathlib.LinearAlgebra.AffineSpace.Ordered
import Mathlib.Topology.ContinuousFunction.Basic
import Mathlib... |
Topology\Algebra\Affine.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 Mathlib.LinearAlgebra.AffineSpace.AffineMap
import Mathlib.Topology.Algebra.Group.Basic
import Mathlib.Topology.Algebra.MulAction
/-!
# Topological properti... |
Topology\Algebra\Algebra.lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Antoine Chambert-Loir, María Inés de Frutos-Fernández
-/
import Mathlib.Algebra.Algebra.Subalgebra.Basic
import Mathlib.Topology.Algebra.Module.Basic
import Mathlib.Rin... |
Topology\Algebra\ConstMulAction.lean | /-
Copyright (c) 2021 Alex Kontorovich, Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Kontorovich, Heather Macbeth
-/
import Mathlib.Topology.Algebra.Constructions
import Mathlib.Topology.Homeomorph
import Mathlib.GroupTheory.GroupAction.Basic
im... |
Topology\Algebra\Constructions.lean | /-
Copyright (c) 2021 Nicolò Cavalleri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolò Cavalleri
-/
import Mathlib.Topology.Homeomorph
/-!
# Topological space structure on the opposite monoid and on the units group
In this file we define `TopologicalSpace` str... |
Topology\Algebra\ContinuousAffineMap.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 Mathlib.LinearAlgebra.AffineSpace.AffineMap
import Mathlib.Topology.ContinuousFunction.Basic
import Mathlib.Topology.Algebra.Module.Basic
/-!
# Continuous affine ma... |
Topology\Algebra\ContinuousMonoidHom.lean | /-
Copyright (c) 2022 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import Mathlib.Topology.Algebra.Equicontinuity
import Mathlib.Topology.Algebra.Group.Compact
import Mathlib.Topology.ContinuousFunction.Algebra
import Mathlib.Topol... |
Topology\Algebra\Equicontinuity.lean | /-
Copyright (c) 2022 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-/
import Mathlib.Topology.Algebra.UniformConvergence
/-!
# Algebra-related equicontinuity criterions
-/
open Function
open UniformConvergence
@[to_additive]
th... |
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