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Submodule.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, Yaël Dillies -/ import Mathlib.Algebra.Module.Submodule.LinearMap import Mathlib.Analysis.Normed.Group.Basic /-! # Submodules of normed groups -/ var...
generic_quotient.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice. From mathcomp Require Import seq fintype. (*****...
OpenQuotient.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.Maps.Basic /-! # Open quotient maps An open quotient map is an open map `f : X → Y` which is both an open map and a quotient map. Equivale...
NatPrime.lean
/- Copyright (c) 2020 Bryan Gin-ge Chen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Lacker, Bryan Gin-ge Chen -/ import Mathlib.Data.Nat.Prime.Basic import Mathlib.Algebra.Group.Int.Defs import Mathlib.Data.Int.Basic /-! # Lemmas about `Nat.Prime` using `Int...
vcharacter.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path. From mathcomp Require Import div choice fintype...
Basic.lean
/- Copyright (c) 2023 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.Init import Lean.Meta.AppBuilder import Lean.Meta.Basic /-! # Additions to `Lean.Meta.Basic` Likely these already exist somewhere. Pointers welcome. -/ ...
Chevalley.lean
/- Copyright (c) 2025 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.RingTheory.Ideal.GoingDown import Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity /-! # Chevalley's theorem In this file we provide the usual (algebr...
output.v
From mathcomp Require Import all_boot all_order all_algebra all_field all_character all_fingroup all_solvable. Open Scope group_scope. Check @cyclic_pgroup_Aut_structure.
End.lean
/- Copyright (c) 2018 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot, Kevin Buzzard, Kim Morrison, Johan Commelin, Chris Hughes, Johannes Hölzl, Yury Kudryashov -/ import Mathlib.Algebra.Group.Hom.Instances import Mathlib.Algebra.Ring.D...
Lemmas.lean
/- Copyright (c) 2022 Abby J. Goldberg. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Abby J. Goldberg, Mario Carneiro, Heather Macbeth -/ import Mathlib.Algebra.Order.Module.OrderedSMul import Mathlib.Data.Ineq /-! # Lemmas for the linear_combination tactic These s...
perm.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq path. From mathcomp Require Import choice fintype tup...
path.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq. (******************************************************************************) (* ...
Constructions.lean
/- Copyright (c) 2024 Thomas Browning. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Thomas Browning -/ import Mathlib.LinearAlgebra.CrossProduct import Mathlib.LinearAlgebra.Matrix.DotProduct import Mathlib.LinearAlgebra.Projectivization.Basic /-! # Dot Product and...
EpiMono.lean
/- Copyright (c) 2024 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.CategoryTheory.MorphismProperty.Concrete import Mathlib.CategoryTheory.Sites.LocallyBijective /-! # Morphisms of sheaves factor as a locally surjective followed...
Pointwise.lean
/- Copyright (c) 2024 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Nathaniel Thomas, Jeremy Avigad, Johannes Hölzl, Mario Carneiro, Anne Baanen, Frédéric Dupuis, Heather Macbeth, Antoine Chambert-Loir -/ import Mathlib.Algebra.Group.Pointwise.Set.Sc...
finmodule.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path. From mathcomp Require Import div choice fintype...
Successor.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.Algebra.Homology.ShortComplex.ModuleCat import Mathlib.Topology.Category.Profinite.Nobeling.Basic /-! # The successor case in the induction for Nö...
finalg.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import fintype finset f...
TypeCheck.lean
/- Copyright (c) 2022 Jireh Loreaux. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jireh Loreaux -/ import Mathlib.Init import Lean.Elab.Tactic.Basic import Lean.Elab.SyntheticMVars /-! # The `type_check` tactic Define the `type_check` tactic: it type checks a given ...
Basic.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 Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap import Mathlib.RingTheory.IntegralClosure.Algebra.Defs import Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic /-! # ...
EnoughRootsOfUnity.lean
/- Copyright (c) 2024 Michael Stoll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Stoll -/ import Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots /-! # Commutative monoids with enough roots of unity We define a typeclass `HasEnoughRootsOfUnity M n` for a com...
inertia.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq path. From mathcomp Require Import choice fintype div...
Fold.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Data.Finset.Fold import Mathlib.Data.Finset.Sum import Mathlib.Data.Multiset.Lattice import Mathlib.Data.Set.BooleanAlgebra import Mathlib.Order.Hom.Bo...
Multiequalizer.lean
/- Copyright (c) 2021 Adam Topaz. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Adam Topaz, Joël Riou -/ import Mathlib.CategoryTheory.Limits.Shapes.Products import Mathlib.CategoryTheory.Limits.Shapes.Equalizers import Mathlib.CategoryTheory.Limits.ConeCategory /-! ...
Block.lean
/- Copyright (c) 2019 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen, Wen Yang -/ import Mathlib.LinearAlgebra.Matrix.Transvection import Mathlib.LinearAlgebra.Matrix.NonsingularInverse import Mat...
NonIntegrable.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.Analysis.SpecialFunctions.Log.Deriv import Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus /-! # Non integrable functions In this f...
IterateMapComap.lean
/- Copyright (c) 2024 Jz Pan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jz Pan -/ import Mathlib.Algebra.Module.Submodule.Ker /-! # Iterate maps and comaps of submodules Some preliminary work for establishing the strong rank condition for noetherian rings. Giv...
primitive_action.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat. From mathcomp Require Import div seq fintype tuple finset. From mathcomp Require Import fin...
FiniteDimension.lean
/- Copyright (c) 2022 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Analysis.Calculus.SmoothSeries import Mathlib.Analysis.Calculus.BumpFunction.InnerProduct import Mathlib.Analysis.Convolution import Mathlib.Anal...
Basic.lean
/- Copyright (c) 2021 Stuart Presnell. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Stuart Presnell -/ import Mathlib.Algebra.Order.Interval.Finset.SuccPred import Mathlib.Data.Nat.Factorization.Defs import Mathlib.Order.Interval.Finset.Nat /-! # Basic lemmas on pri...
Interval.lean
/- Copyright (c) 2023 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.Algebra.Order.Group.Pointwise.Interval import Mathlib.Order.Interval.Finset.Defs import Mathlib.Algebra.Group.Pointwise.Finset.Basic /-! # Pointwise operati...
Basic.lean
/- Copyright (c) 2017 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Data.Seq.Seq import Mathlib.Util.CompileInductive /-! # Partially defined possibly infinite lists This file provides a `WSeq α` type represent...
FullyFaithful.lean
/- Copyright (c) 2019 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Dagur Asgeirsson -/ import Mathlib.CategoryTheory.Adjunction.Basic import Mathlib.CategoryTheory.MorphismProperty.Basic import Mathlib.CategoryTheory.EpiMono /-! # Adjoint...
Multiset.lean
/- Copyright (c) 2021 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Algebra.Order.Interval.Finset.Basic import Mathlib.Order.Interval.Multiset /-! # Algebraic properties of multiset intervals This file provides results ab...
all_algebra.v
(* N.B. interval_inference is not exported here. To enjoys the automation it provides, you need to explictly "Import interval_inference". *) From mathcomp Require Export ssralg. From mathcomp Require Export ssrnum. From mathcomp Require Export finalg. From mathcomp Require Export countalg. From mathcomp Require Export...
PoissonSummation.lean
/- Copyright (c) 2023 David Loeffler. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Loeffler -/ import Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform import Mathlib.Analysis.Fourier.PoissonSummation /-! # Poisson summation applied to the Gaussian ...
fingraph.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat. From mathcomp Require Import seq path fintype. (******************************************...
List.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.Data.Set.Image import Mathlib.Data.List.Defs /-! # Lemmas about `List`s and `Set.range` In this file we prove lemmas about range of some operations...
MulAction.lean
/- Copyright (c) 2021 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.Algebra.Group.Submonoid.Defs import Mathlib.Algebra.Group.Action.Defs /-! # Actions by `Submonoid`s These instances transfer the action by an element `m : ...
Extension.lean
/- Copyright (c) 2024 Jiedong Jiang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jiedong Jiang, Bichang Lei, María Inés de Frutos-Fernández, Filippo A. E. Nuccio -/ import Mathlib.RingTheory.Valuation.ValuationSubring /-! # Extension of Valuations In this file, we...
SudoSetOption.lean
/- Copyright (c) 2021 Gabriel Ebner. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Gabriel Ebner -/ import Mathlib.Init import Lean.Elab.ElabRules /-! # Defines the `sudo set_option` command. Allows setting undeclared options. -/ open Lean Elab private def setOpti...
EquivMon.lean
/- Copyright (c) 2020 Adam Topaz. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Adam Topaz -/ import Mathlib.CategoryTheory.Monad.Basic import Mathlib.CategoryTheory.Monoidal.End import Mathlib.CategoryTheory.Monoidal.Mon_ /-! # The equivalence between `Monad C` and...
Clean.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Michail Karatarakis, Kyle Miller -/ import Mathlib.Init import Lean.Elab.SyntheticMVars /-! # `clean%` term elaborator Remove identity functions from a term. -/ open...
EssentiallySmall.lean
/- Copyright (c) 2021 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.CategoryTheory.Category.ULift import Mathlib.CategoryTheory.EqToHom import Mathlib.CategoryTheory.Skeletal import Mathlib.Logic.UnivLE import Mathlib.Logic...
Basic.lean
/- Copyright (c) 2020 Adam Topaz. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Adam Topaz -/ import Mathlib.Algebra.FreeAlgebra import Mathlib.Algebra.RingQuot import Mathlib.Algebra.TrivSqZeroExt import Mathlib.Algebra.Algebra.Operations import Mathlib.LinearAlgebra...
primitive_action.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat. From mathcomp Require Import div seq fintype tuple finset. From mathcomp Require Import fin...
WithZeroTopology.lean
/- Copyright (c) 2021 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot -/ import Mathlib.Algebra.Order.GroupWithZero.Canonical import Mathlib.Topology.Algebra.GroupWithZero import Mathlib.Topology.Order.OrderClosed import Mathlib.Topology.S...
Pretty.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Evgenia Karunus, Kyle Miller -/ import Lean.Meta.Basic import Mathlib.Tactic.Explode.Datatypes /-! # Explode command: pretty This file contains UI code to render the ...
Contracting.lean
/- Copyright (c) 2019 Rohan Mitta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rohan Mitta, Kevin Buzzard, Alistair Tucker, Johannes Hölzl, Yury Kudryashov -/ import Mathlib.Analysis.SpecificLimits.Basic import Mathlib.Data.Setoid.Basic import Mathlib.Dynamics.Fixed...
Ring.lean
/- Copyright (c) 2022 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.Algebra.GroupWithZero.Action.Defs import Mathlib.Algebra.Ring.Defs /-! # Commutativity and associativity of action of integers on rings This file proves th...
ring_quotient.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat. From mathcomp Require Import seq ssralg generic_q...
Single.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Kim Morrison -/ import Mathlib.Algebra.Notation.Indicator import Mathlib.Data.Finsupp.Defs /-! # Finitely supported functions on exactly one point This file contains ...
AEval.lean
/- Copyright (c) 2022 Richard M. Hill. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Richard M. Hill -/ import Mathlib.Algebra.Module.Submodule.Invariant import Mathlib.Algebra.Polynomial.AlgebraMap import Mathlib.LinearAlgebra.DFinsupp import Mathlib.RingTheory.Finit...
Free.lean
/- Copyright (c) 2021 Riccardo Brasca. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Riccardo Brasca -/ import Mathlib.LinearAlgebra.Dimension.StrongRankCondition import Mathlib.LinearAlgebra.FreeModule.Finite.Basic import Mathlib.RingTheory.AlgebraTower import Mathli...
Fintype.lean
/- Copyright (c) 2021 . All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes -/ import Mathlib.Data.SetLike.Basic import Mathlib.Data.Fintype.Powerset /-! # Set-like fintype This file contains a fintype instance for set-like objects such as subgroups. If `SetL...
Basic.lean
/- Copyright (c) 2020 Nicolò Cavalleri. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Nicolò Cavalleri, Andrew Yang -/ import Mathlib.Algebra.Polynomial.AlgebraMap import Mathlib.Algebra.Polynomial.Derivative /-! # Derivations This file defines derivation. A derivat...
LocallyRingedSpace.lean
/- Copyright (c) 2020 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.Algebra.Category.Ring.Constructions import Mathlib.Geometry.RingedSpace.Basic import Mathlib.Geometry.RingedSpace.Stalks import Mathlib.RingTheory.Nilp...
SheafOfFunctions.lean
/- Copyright (c) 2020 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Kim Morrison -/ import Mathlib.Topology.Sheaves.PresheafOfFunctions import Mathlib.Topology.Sheaves.SheafCondition.UniqueGluing /-! # Sheaf conditions for presheaves of ...
Encodable.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.Data.Finsupp.ToDFinsupp import Mathlib.Data.DFinsupp.Encodable /-! # `Encodable` and `Countable` instances for `α →₀ β` In this file we provide inst...
Connected.lean
/- Copyright (c) 2020 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta, Joël Riou -/ import Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts import Mathlib.CategoryTheory.Limits.Shapes.Equalizers import Mathlib.CategoryTheory.Limits.Shapes.W...
End.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Yury Kudryashov -/ import Mathlib.Algebra.Group.Action.Hom import Mathlib.Algebra.Group.Equiv.Defs import Mathlib.Algebra.GroupWithZero.Action.Units /-! # Group actions an...
Tuple.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, Yury Kudryashov, Sébastien Gouëzel, Chris Hughes -/ import Mathlib.Algebra.Group.Basic import Mathlib.Algebra.Notation.Pi.Basic import Mathlib.Data.Fin.VecNotation ...
Marginal.lean
/- Copyright (c) 2023 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn, Heather Macbeth -/ import Mathlib.MeasureTheory.Constructions.Pi /-! # Marginals of multivariate functions In this file, we define a convenient way to compute int...
eqtype.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool. (********************************************************************...
Defs.lean
/- Copyright (c) 2019 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Yury Kudryashov -/ import Mathlib.Analysis.Normed.Field.Basic /-! # Asymptotics We introduce these relations: * `IsBigOWith c l f g` : "f is big O of g along l with co...
Partrec.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Computability.Primrec import Mathlib.Data.Nat.PSub import Mathlib.Data.PFun /-! # The partial recursive functions The partial recursive functions are...
StrongRankCondition.lean
/- Copyright (c) 2021 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.LinearAlgebra.Basis.Basic import Mathlib.LinearAlgebra.Basis.Submodule import Mathlib.LinearAlgebra.Dimension.Finrank import Mathlib.LinearAlgebra.Invarian...
Sort.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 Mathlib.Data.Finset.Max import Mathlib.Data.Fintype.EquivFin import Mathlib.Data.Multiset.Sort import Mathlib.Order.RelIso.Set /-! # Construct a sorted list f...
OpenMapping.lean
/- Copyright (c) 2022 Vincent Beffara. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Vincent Beffara -/ import Mathlib.Analysis.Analytic.IsolatedZeros import Mathlib.Analysis.Complex.CauchyIntegral import Mathlib.Analysis.Complex.AbsMax import Mathlib.Topology.MetricS...
Types.lean
/- Copyright (c) 2017 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Stephen Morgan, Kim Morrison, Johannes Hölzl -/ import Mathlib.CategoryTheory.EpiMono import Mathlib.CategoryTheory.Functor.FullyFaithful import Mathlib.Data.Set.CoeSort import Mathlib.T...
PEmpty.lean
/- Copyright (c) 2018 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Bhavik Mehta -/ import Mathlib.CategoryTheory.Discrete.Basic /-! # The empty category Defines a category structure on `PEmpty`, and the unique functor `PEmpty ⥤ C` for an...
Insert.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, Minchao Wu, Mario Carneiro -/ import Mathlib.Data.Finset.Attr import Mathlib.Data.Finset.Dedup import Mathlib.Data.Finset.Empty import Mathlib....
Triangularizable.lean
/- Copyright (c) 2020 Alexander Bentkamp. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Alexander Bentkamp -/ import Mathlib.LinearAlgebra.Eigenspace.Basic import Mathlib.FieldTheory.IsAlgClosed.Spectrum import Mathlib.LinearAlgebra.FreeModule.Finite.Matrix /-! # Tri...
Explode.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Evgenia Karunus, Kyle Miller -/ import Lean.Elab.Command import Lean.PrettyPrinter import Mathlib.Tactic.Explode.Datatypes import Mathlib.Tactic.Explode.Pretty /-! # E...
Dihedral.lean
/- Copyright (c) 2020 Shing Tak Lam. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Shing Tak Lam -/ import Mathlib.Data.Finite.Sum import Mathlib.Data.ZMod.Basic import Mathlib.GroupTheory.Exponent import Mathlib.GroupTheory.GroupAction.CardCommute import Mathlib.Grou...
Message.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 Mathlib.Init import Lean.Message /-! # Additional operations on MessageData and related types -/ open Lean Std MessageData instance {α β : Type} [ToMess...
LiminfLimsup.lean
/- Copyright (c) 2018 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, Johannes Hölzl, Rémy Degenne -/ import Mathlib.Order.ConditionallyCompleteLattice.Indexed import Mathlib.Order.Filter.IsBounded import Mathlib.Order.Hom.CompleteL...
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, Yury Kudryashov -/ import Mathlib.Order.Filter.Interval import Mathlib.Order.Interval.Set.Pi import Mathlib.Order.OrdContinuous import Mathlib.Tactic.TF...
PiLp.lean
/- Copyright (c) 2020 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, Jireh Loreaux -/ import Mathlib.Analysis.MeanInequalities import Mathlib.Data.Fintype.Order import Mathlib.LinearAlgebra.Matrix.Basis import Mathlib.Analysis.Norm...
EssentiallySmall.lean
/- Copyright (c) 2025 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau -/ import Mathlib.Algebra.Category.FGModuleCat.Basic import Mathlib.RingTheory.Finiteness.Cardinality /-! # The category of finitely generated modules over a ring is essentially...
ssrfun.v
From mathcomp Require Import ssreflect. From Corelib Require Export ssrfun. From mathcomp Require Export ssrnotations. #[export] Set Warnings "-overwriting-delimiting-key". (* remove above line when requiring Rocq >= 9.0 *) Set Implicit Arguments. Unset Strict Implicit. Unset Printing Implicit Defensive. (***********...
Submonoid.lean
/- Copyright (c) 2018 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Kenny Lau, Johan Commelin, Mario Carneiro, Kevin Buzzard, Amelia Livingston, Yury Kudryashov -/ import Mathlib.Algebra.Group.Submonoid.Basic import Mathlib.Algebra.Ring...
Operations.lean
/- Copyright (c) 2018 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Kenny Lau, Johan Commelin, Mario Carneiro, Kevin Buzzard, Amelia Livingston, Yury Kudryashov -/ import Mathlib.Algebra.Group.Action.Faithful import Mathlib.Algebra.Grou...
center.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div. From mathcomp Require Import fintype bigop finset fingroup morphism perm. From math...
ZMod.lean
/- Copyright (c) 2024 David Loeffler. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Loeffler -/ import Mathlib.Topology.Order import Mathlib.Data.ZMod.Defs /-! # Topology on `ZMod N` We equip `ZMod N` with the discrete topology. -/ namespace ZMod variable {N...
extraspecial.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div. From mathcomp Require Import choice fintype bigop finset prime binomial. From mathc...
Nat.lean
/- Copyright (c) 2014 Floris van Doorn (c) 2016 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro -/ import Mathlib.Algebra.CharZero.Defs import Mathlib.Algebra.GroupWithZero.Nat imp...
MoveAdd.lean
/- Copyright (c) 2023 Damiano Testa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Arthur Paulino, Damiano Testa -/ import Mathlib.Algebra.Group.Basic import Mathlib.Lean.Meta import Mathlib.Order.Defs.LinearOrder /-! # `move_add` a tactic for moving summands in ex...
Composition.lean
/- Copyright (c) 2023 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.CategoryTheory.Localization.LocalizerMorphism import Mathlib.CategoryTheory.Functor.ReflectsIso.Basic /-! # Composition of localization functors Given two comp...
Basic.lean
/- Copyright (c) 2020 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta -/ import Mathlib.CategoryTheory.Whiskering import Mathlib.CategoryTheory.Iso import Mathlib.CategoryTheory.Functor.FullyFaithful /-! # Functors which reflect isomorphisms ...
Norm.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.LinearAlgebra.Dual.Lemmas import Mathlib.LinearAlgebra.FreeModule.IdealQuotient import Mathlib.RingTheory.AdjoinRoot import Mathlib.RingTheory.Norm.Defs /-! # N...
TypeVec.lean
/- Copyright (c) 2018 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Mario Carneiro, Simon Hudon -/ import Mathlib.Data.Fin.Fin2 import Mathlib.Logic.Function.Basic import Mathlib.Tactic.Common /-! # Tuples of types, and their categorica...
Basic.lean
/- Copyright (c) 2019 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Kenny Lau -/ import Mathlib.Algebra.Order.Antidiag.Finsupp import Mathlib.Data.Finsupp.Weight import Mathlib.Tactic.Linarith import Mathlib.LinearAlgebra.Pi import Mat...
Comp.lean
/- Copyright (c) 2023 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne, Etienne Marion -/ import Mathlib.Probability.Kernel.MeasurableLIntegral /-! # Composition of kernels We define the composition `η ∘ₖ κ` of kernels `κ : Kernel α β` and `η...
Linear.lean
/- Copyright (c) 2022 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.CategoryTheory.Linear.LinearFunctor import Mathlib.CategoryTheory.Monoidal.Preadditive /-! # Linear monoidal categories A monoidal category is `MonoidalL...
Ordered.lean
/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Algebra.CharP.Invertible import Mathlib.Algebra.Order.Module.OrderedSMul import Mathlib.Algebra.Order.Module.Synonym import Mathlib.LinearAlgebra.Aff...
Basic.lean
/- Copyright (c) 2023 Xavier Roblot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Xavier Roblot -/ import Mathlib.Algebra.Module.ZLattice.Covolume import Mathlib.Data.Real.Pi.Bounds import Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody import Mathlib....
StrongTopology.lean
/- Copyright (c) 2022 Anatole Dedecker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anatole Dedecker, Yury Kudryashov -/ import Mathlib.Topology.Algebra.Module.Equiv import Mathlib.Topology.Algebra.Module.UniformConvergence import Mathlib.Topology.Algebra.Separation...
Sheaf.lean
/- Copyright (c) 2020 Kevin Buzzard, Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Buzzard, Bhavik Mehta -/ import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equalizers import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Products import Mathl...
cyclic.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq choice. From mathcomp Require Import div fintype bigo...