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mxalgebra.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 fintype finfun b...
maximal.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 choice. From mathcomp Require Import div fintype finfun bigop finset prime binomial. Fro...
SequentialProduct.lean
/- Copyright (c) 2024 Dagur Asgeirsson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Dagur Asgeirsson -/ import Mathlib.CategoryTheory.Functor.OfSequence import Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts import Mathlib.CategoryTheory.Limits.Shapes.Countabl...
UniqueFactorizationDomain.lean
/- Copyright (c) 2018 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Anderson -/ import Mathlib.RingTheory.Noetherian.Defs import Mathlib.RingTheory.UniqueFactorizationDomain.Ideal /-! # Noetherian domains have unique factorization ## Main result...
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...
CountableInter.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.Order.Filter.Curry import Mathlib.Data.Set.Countable /-! # Filters with countable intersection property In this file we define `CountableInterFilte...
Defs.lean
/- Copyright (c) 2025 Yunzhou Xie. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yunzhou Xie, Jujian Zhang -/ import Mathlib.Algebra.Module.Projective import Mathlib.RingTheory.Finiteness.Defs import Mathlib.RingTheory.TensorProduct.Basic /-! # Azumaya Algebras An A...
ssralg.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 div seq. From mathcomp Require Import choice fintype finf...
LinearMap.lean
/- Copyright (c) 2023 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.LinearAlgebra.FreeModule.Finite.Basic import Mathlib.LinearAlgebra.FreeModule.PID import Mathlib.LinearAlgebra.Eigenspace.Basic import Mathlib.LinearAlgebra....
StructureSheaf.lean
/- Copyright (c) 2022 Jujian Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jujian Zhang -/ import Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology import Mathlib.Topology.Sheaves.LocalPredicate import Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalizatio...
Constructions.lean
/- Copyright (c) 2020 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, Floris van Doorn, Michael Rothgang -/ import Mathlib.Geometry.Manifold.ContMDiff.Basic /-! ## Smoothness of standard maps associated to the product of manifolds ...
FreeCommRing.lean
/- Copyright (c) 2023 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes -/ import Mathlib.ModelTheory.Algebra.Ring.Basic import Mathlib.RingTheory.FreeCommRing /-! # Making a term in the language of rings from an element of the FreeCommRing T...
Pi.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.Prod import Mathlib.CategoryTheory.Localization.Equivalence import Mathlib.Data.Fintype.Option /-! # Localization of product categor...
Irrational.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.Data.Real.Irrational import Mathlib.Data.Rat.Encodable import Mathlib.Topology.Separation.GDelta import Mathlib.Topology.Instances.Real.Lemmas /-! #...
Basic.lean
/- Copyright (c) 2020 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, Yury Kudryashov, Heather Macbeth, Patrick Massot -/ import Mathlib.Topology.Algebra.Module.Alternating.Topology import Mathlib.Analysis.NormedSpace.Multilinear.Ba...
Invariant.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.GroupTheory.GroupAction.Hom import Mathlib.Algebra.Ring.Subring.Defs /-! # Subrings invariant under an action If a monoid acts on a ring via a `MulSemiring...
BohrMollerup.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.Gamma.Deriv import Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral /-! # Convexity properties of the Gamma funct...
seq.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. (******************************************************...
Lattice.lean
/- Copyright (c) 2021 Christopher Hoskin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christopher Hoskin -/ import Mathlib.Analysis.Normed.Group.Constructions import Mathlib.Analysis.Normed.Group.Rat import Mathlib.Analysis.Normed.Group.Uniform import Mathlib.Topolo...
Preserves.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.CategoryTheory.Limits.Preserves.Shapes.Products import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq import Mathlib.CategoryTheory.Sites.Equ...
Localization.lean
/- Copyright (c) 2022 David Kurniadi Angdinata. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Kurniadi Angdinata -/ import Mathlib.RingTheory.Localization.AsSubring import Mathlib.RingTheory.Spectrum.Maximal.Basic import Mathlib.RingTheory.Spectrum.Prime.RingHom...
MonoidAlgebra.lean
/- Copyright (c) 2025 Amelia Livingston. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Amelia Livingston -/ import Mathlib.RingTheory.Bialgebra.MonoidAlgebra import Mathlib.RingTheory.HopfAlgebra.Basic /-! # The Hopf algebra structure on group algebras Given a group...
Coloring.lean
/- Copyright (c) 2021 Arthur Paulino. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Arthur Paulino, Kyle Miller -/ import Mathlib.Combinatorics.SimpleGraph.Clique import Mathlib.Data.ENat.Lattice import Mathlib.Data.Nat.Lattice import Mathlib.Data.Setoid.Partition imp...
Complex.lean
/- Copyright (c) 2022 Xavier Roblot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Xavier Roblot -/ import Mathlib.Analysis.Complex.Basic import Mathlib.Data.Complex.FiniteDimensional import Mathlib.FieldTheory.IntermediateField.Basic import Mathlib.LinearAlgebra.Fini...
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.Limits.Shapes.Images import Mathlib.CategoryTheory.MorphismProperty.Concrete import Mathlib.CategoryTheory.Types import Mathlib.CategoryTheory.Lim...
Subspace.lean
/- Copyright (c) 2022 Michael Blyth. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Blyth -/ import Mathlib.LinearAlgebra.Projectivization.Basic /-! # Subspaces of Projective Space In this file we define subspaces of a projective space, and show that the subs...
Defs.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Jeremy Avigad, Yury Kudryashov, Patrick Massot -/ import Mathlib.Data.Set.Piecewise import Mathlib.Order.Filter.Basic /-! # Definition of `Filter.atTop` and `Filter.at...
WeylGroup.lean
/- Copyright (c) 2024 Scott Carnahan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Scott Carnahan -/ import Mathlib.LinearAlgebra.RootSystem.Hom import Mathlib.RepresentationTheory.Basic /-! # The Weyl group of a root pairing This file defines the Weyl group of a ro...
algebraics_fundamentals.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 ssrnat eqtype seq choice. From mathcomp Require Import div fintype path...
Length.lean
/- Copyright (c) 2024 Mitchell Lee. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mitchell Lee -/ import Mathlib.Data.ZMod.Basic import Mathlib.GroupTheory.Coxeter.Basic import Mathlib.Tactic.Linarith import Mathlib.Tactic.Zify /-! # The length function, reduced word...
Finiteness.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.Algebra.Group.Pointwise.Set.Finite import Mathlib.Algebra.Group.Subgroup.Pointwise import Mathlib.GroupTheory.QuotientGroup.Defs /-! # Finitely gene...
Monoidal.lean
/- Copyright (c) 2024 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou, Dagur Asgeirsson -/ import Mathlib.CategoryTheory.Localization.Trifunctor import Mathlib.CategoryTheory.Monoidal.Functor /-! # Localization of monoidal categories Let `C` be a ...
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.
pgroup.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 prime fingroup morphism. From mat...
MorphismProperty.lean
/- Copyright (c) 2025 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.CategoryTheory.Abelian.SerreClass.Basic import Mathlib.CategoryTheory.Abelian.DiagramLemmas.KernelCokernelComp import Mathlib.CategoryTheory.MorphismProperty.Com...
Basic.lean
/- Copyright (c) 2025 Jujian Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jujian Zhang, Yunzhou Xie -/ import Mathlib.Algebra.Category.ModuleCat.ChangeOfRings import Mathlib.CategoryTheory.Linear.LinearFunctor import Mathlib.Algebra.Category.ModuleCat.Basic im...
Enum.lean
/- Copyright (c) 2022 Violeta Hernández Palacios. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Violeta Hernández Palacios -/ import Mathlib.SetTheory.Ordinal.Family /-! # Enumerating sets of ordinals by ordinals The ordinals have the peculiar property that every su...
FunctionData.lean
/- Copyright (c) 2024 Tomáš Skřivan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Tomáš Skřivan -/ import Qq import Mathlib.Tactic.FunProp.Mor import Mathlib.Tactic.FunProp.ToBatteries /-! ## `funProp` data structure holding information about a function `FunctionD...
PseudometrizableLindelof.lean
/- Copyright (c) 2023 Josha Dekker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Josha Dekker -/ import Mathlib.Topology.Metrizable.Basic import Mathlib.Topology.Compactness.Lindelof /-! # Second-countability of pseudometrizable Lindelöf spaces Factored out from `...
Basic.lean
/- Copyright (c) 2023 Peter Nelson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Peter Nelson -/ import Mathlib.Data.Finite.Prod import Mathlib.Data.Matroid.Init import Mathlib.Data.Set.Card import Mathlib.Data.Set.Finite.Powerset import Mathlib.Order.UpperLower.Clos...
Subalgebra.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.Algebra.Lie.Basic import Mathlib.RingTheory.Artinian.Module /-! # Lie subalgebras This file defines Lie subalgebras of a Lie algebra and provides basic rel...
Division.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.MonoidAlgebra.Division import Mathlib.Algebra.MvPolynomial.Basic /-! # Division of `MvPolynomial` by monomials ## Main definitions * `MvPolynomial...
algnum.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...
mxpoly.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 seq. From mathcomp Require Import div fintype tupl...
Coequalizer.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.Limits.Shapes.Reflexive import Mathlib.CategoryTheory.Limits.Shapes.SplitCoequalizer import Mathlib.CategoryTheory.Monad.Algebra /-! # Spec...
Imo1982Q3.lean
/- Copyright (c) 2024 Violeta Hernández Palacios. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Violeta Hernández Palacios, Alex Brodbelt -/ import Mathlib.Algebra.Order.Field.GeomSum import Mathlib.Data.NNReal.Basic /-! # IMO 1982 Q3 Consider infinite sequences $\{...
ExponentialBounds.lean
/- Copyright (c) 2020 Joseph Myers. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Joseph Myers -/ import Mathlib.Data.Complex.Exponential import Mathlib.Analysis.SpecialFunctions.Log.Deriv /-! # Bounds on specific values of the exponential -/ namesp...
Density.lean
/- Copyright (c) 2022 Yaël Dillies, Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Bhavik Mehta -/ import Mathlib.Algebra.Order.Field.Basic import Mathlib.Combinatorics.SimpleGraph.Basic import Mathlib.Data.Rat.Cast.Order import Mathlib.Orde...
prime.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 path. From mathcomp Require Import choice fintype div bigop. (*************************...
AddCircleMulti.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.Fourier.AddCircle import Mathlib.MeasureTheory.Integral.Pi /-! # Multivariate Fourier series In this file we define the Fourier series of an...
cyclotomic.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 path. From mathcomp Require Import div choice fintype tuple finfun bigop prime. From mat...
jordanholder.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 big...
trace.lean
import Mathlib.Tactic.Trace set_option linter.unusedTactic false /-- info: 7 -/ #guard_msgs in example : True := by trace 2 + 2 + 3 trivial /-- info: hello world -/ #guard_msgs in example : True := by trace "hello" ++ " world" trivial
Support.lean
/- Copyright (c) 2022 Damiano Testa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damiano Testa -/ import Mathlib.Algebra.Group.Embedding import Mathlib.Algebra.MonoidAlgebra.Module import Mathlib.LinearAlgebra.Finsupp.Supported import Mathlib.Algebra.Group.Pointwise...
SwapVar.lean
/- Copyright (c) 2022 Arthur Paulino. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Arthur Paulino -/ import Mathlib.Tactic.Basic import Mathlib.Tactic.SwapVar example {P Q : Prop} (q : P) (p : Q) : P ∧ Q := by swap_var p ↔ q exact ⟨p, q⟩ example {a b : Nat} (h...
Directed.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Yaël Dillies -/ import Mathlib.Data.Set.Image /-! # Directed indexed families and sets This file defines directed indexed families and directed sets. An indexed famil...
galois.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 div. From mathcomp Require Import choice fintype tupl...
Basic.lean
/- Copyright (c) 2020 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Johan Commelin, Andrew Yang, Joël Riou -/ import Mathlib.Algebra.Group.Basic import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero import Mathlib.CategoryTheory.Monoid...
ssrmatching.v
From Corelib Require Export ssrmatching.
Fin.lean
/- Copyright (c) 2025 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.CategoryTheory.Limits.Shapes.IsTerminal import Mathlib.Order.Fin.Basic /-! # Limits and colimits indexed by `Fin` In this file, we show that `0 : Fin (n + 1)` ...
burnside_app.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 div. From mathcomp Require Import choice fintype tupl...
NormPow.lean
/- Copyright (c) 2024 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.Analysis.InnerProductSpace.Calculus import Mathlib.Analysis.SpecialFunctions.Pow.Deriv /-! # Properties about the powers of the n...
WithSeminorms.lean
/- Copyright (c) 2022 Moritz Doll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Moritz Doll, Anatole Dedecker -/ import Mathlib.Analysis.LocallyConvex.Bounded import Mathlib.Analysis.Seminorm import Mathlib.Data.Real.Sqrt import Mathlib.Topology.Algebra.Equicontinuit...
Hom.lean
/- Copyright (c) 2019 Amelia Livingston. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Amelia Livingston -/ import Mathlib.Algebra.Group.Hom.Defs import Mathlib.GroupTheory.Congruence.Defs /-! # Congruence relations and homomorphisms This file contains elementary de...
ExpLog.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.Analysis.Normed.Module.FiniteDimension import Mathlib.Analysis.SpecialFunctions.Complex.LogDeriv import Mathlib.Data.Complex.FiniteDimensional import Mat...
mxabelem.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...
SingleFunctors.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.Algebra.Homology.HomotopyCategory.Shift import Mathlib.CategoryTheory.Shift.SingleFunctors /-! # Single functors from the homotopy category Let `C` be a preadd...
RationalMap.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.AlgebraicGeometry.SpreadingOut import Mathlib.AlgebraicGeometry.FunctionField import Mathlib.AlgebraicGeometry.Morphisms.Separated /-! # Rational maps betwe...
Hilbert90.lean
/- Copyright (c) 2023 Amelia Livingston. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Amelia Livingston -/ import Mathlib.FieldTheory.Fixed import Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree /-! # Hilbert's Theorem 90 Let `L/K` be a finite ex...
Mul.lean
/- Copyright (c) 2019 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Sébastien Gouëzel, Yury Kudryashov -/ import Mathlib.Analysis.Analytic.Constructions import Mathlib.Analysis.Calculus.FDeriv.Analytic import Mathlib.Analysis.Calculus.FDe...
AlexandrovDiscrete.lean
/- Copyright (c) 2025 Miyahara Kō. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Miyahara Kō -/ import Mathlib.Topology.Separation.Basic import Mathlib.Topology.AlexandrovDiscrete /-! # T1 Alexandrov-discrete topology is discrete -/ open Filter variable {X : Type*...
Pow.lean
/- Copyright (c) 2025 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.Analysis.Calculus.FDeriv.Mul import Mathlib.Analysis.Calculus.FDeriv.Comp /-! # Fréchet Derivative of `f x ^ n`, `n : ℕ` In this file we prove that the Fré...
Basic.lean
/- Copyright (c) 2014 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Mario Carneiro -/ import Mathlib.Data.Subtype import Mathlib.Order.Defs.LinearOrder import Mathlib.Order.Notation import Mathlib.Tactic.GCongr.Core import Mathlib.Tactic....
Path.lean
/- Copyright (c) 2021 Kyle Miller. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kyle Miller -/ import Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected import Mathlib.Combinatorics.SimpleGraph.Paths deprecated_module (since := "2025-06-13")
falgebra.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...
Basis.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 -/ import Mathlib.LinearAlgebra.Basis.Submodule import Mathlib.LinearAlgebra.Matrix.Reindex import Mathlib.LinearAlgebra.Matrix...
qpoly.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import fintype tuple bigop binomial finset finfun ssralg. From mathcomp Require Import countalg finalg poly polydiv perm fingroup matrix. From mathcomp Require Import mxalgebra mxpoly...
CompatibleSheafification.lean
/- Copyright (c) 2021 Adam Topaz. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Adam Topaz -/ import Mathlib.CategoryTheory.Sites.CompatiblePlus import Mathlib.CategoryTheory.Sites.ConcreteSheafification /-! In this file, we prove that sheafification is compatible w...
Convolution.lean
/- Copyright (c) 2023 Josha Dekker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Josha Dekker -/ import Mathlib.MeasureTheory.Measure.MeasureSpace import Mathlib.MeasureTheory.Measure.Prod /-! # The multiplicative and additive convolution of measures In this file w...
sylow.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 prime bigop finset fingroup morphism. From mat...
AlgebraMap.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Johannes Hölzl, Kim Morrison, Jens Wagemaker -/ import Mathlib.Algebra.Algebra.Pi import Mathlib.Algebra.Algebra.Prod import Mathlib.Algebra.Algebra.Subalgebra.Lattice impo...
UniformConvergence.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.Analysis.LocallyConvex.Bounded import Mathlib.Topology.Algebra.FilterBasis import Mathlib.Topology.Algebra.UniformConvergence /-! # Algebraic fact...
SesquilinearForm.lean
/- Copyright (c) 2020 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen, Kexing Ying, Moritz Doll -/ import Mathlib.Algebra.GroupWithZero.Action.Opposite import Mathlib.LinearAlgebra.Finsupp.VectorSpace import Mathlib.LinearAlgebra.Matrix.Basis im...
Matrix.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.Algebra.Lie.OfAssociative import Mathlib.LinearAlgebra.Matrix.Reindex import Mathlib.LinearAlgebra.Matrix.ToLinearEquiv /-! # Lie algebras of matrices An i...
AbsoluteValue.lean
/- Copyright (c) 2021 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen -/ import Mathlib.Algebra.Module.Basic import Mathlib.Algebra.Order.AbsoluteValue.Basic /-! # Absolute values and the integers This file contains some results on absolute va...
Fintype.lean
/- Copyright (c) 2022 Kyle Miller. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kyle Miller -/ import Mathlib.Data.Fintype.Card import Mathlib.Algebra.BigOperators.Group.Finset.Basic /-! # Multiset coercion to type This module defines a `CoeSort` instance for multi...
WeightedHomogeneous.lean
/- Copyright (c) 2022 María Inés de Frutos-Fernández. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Antoine Chambert-Loir, María Inés de Frutos-Fernández -/ import Mathlib.Algebra.BigOperators.Finprod import Mathlib.Algebra.DirectSum.Decomposition import Mathlib.Algeb...
Basic.lean
/- Copyright (c) 2023 Michael Stoll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Stoll -/ import Mathlib.Analysis.Normed.Ring.InfiniteSum import Mathlib.Analysis.SpecificLimits.Normed import Mathlib.NumberTheory.ArithmeticFunction import Mathlib.NumberTheory...
burnside_app.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 div. From mathcomp Require Import choice fintype tupl...
LocalCohomology.lean
/- Copyright (c) 2023 Emily Witt. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Emily Witt, Kim Morrison, Jake Levinson, Sam van Gool -/ import Mathlib.Algebra.Category.ModuleCat.Colimits import Mathlib.Algebra.Category.ModuleCat.Projective import Mathlib.CategoryTheo...
lpSpace.lean
/- Copyright (c) 2021 Heather Macbeth. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Heather Macbeth -/ import Mathlib.Analysis.MeanInequalities import Mathlib.Analysis.MeanInequalitiesPow import Mathlib.Analysis.SpecialFunctions.Pow.Continuity import Mathlib.Data.Set...
test_ssrAC.v
From mathcomp Require Import all_boot ssralg. Section Tests. Lemma test_orb (a b c d : bool) : (a || b) || (c || d) = (a || c) || (b || d). Proof. time by rewrite orbACA. Abort. Lemma test_orb (a b c d : bool) : (a || b) || (c || d) = (a || c) || (b || d). Proof. time by rewrite (AC (2*2) ((1*3)*(2*4))). Abort. Lemma ...
vector.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 bigop fi...
Symmetric.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.Analysis.Analytic.IteratedFDeriv import Mathlib.Analysis.Calculus.Deriv.Pow import Mathlib.Analysis.Calculus.MeanValue import Mathlib.Analysis.Ca...
alt.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 tupl...
Dedup.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.List.Nodup import Mathlib.Data.List.Lattice import Batteries.Data.List.Pairwise /-! # Erasure of duplicates in a list This file proves basic res...
module.lean
/- Copyright (c) 2024 Heather Macbeth. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Heather Macbeth -/ import Mathlib.Algebra.Order.Field.Defs import Mathlib.Tactic.FieldSimp import Mathlib.Tactic.LinearCombination import Mathlib.Tactic.Module import Mathlib.Tactic.N...
Rademacher.lean
/- Copyright (c) 2023 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Analysis.Calculus.LineDeriv.Measurable import Mathlib.Analysis.Normed.Module.FiniteDimension import Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar...
TietzeExtension.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.Order.Interval.Set.IsoIoo import Mathlib.Topology.ContinuousMap.Bounded.Normed import Mathlib.Topology.UrysohnsBounded /-! # Tietze extension theore...
MonoOver.lean
/- Copyright (c) 2020 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta, Kim Morrison -/ import Mathlib.CategoryTheory.Comma.Over.Pullback import Mathlib.CategoryTheory.Adjunction.Reflective import Mathlib.CategoryTheory.Adjunction.Restrict impo...