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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...