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Basic.lean
/- Copyright (c) 2021 Ashvni Narayanan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Ashvni Narayanan, Anne Baanen -/ import Mathlib.Algebra.Algebra.Rat import Mathlib.Algebra.Ring.Int.Parity import Mathlib.Algebra.Ring.Int.Units import Mathlib.RingTheory.DedekindDom...
IsPerfectClosure.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.FieldTheory.PurelyInseparable.Basic import Mathlib.FieldTheory.PerfectClosure /-! # `IsPerfectClosure` predicate This file contains `IsPerfectClosure` which asserts...
OrdinaryHypergeometric.lean
/- Copyright (c) 2024 Edward Watine. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Edward Watine -/ import Mathlib.Analysis.Analytic.OfScalars import Mathlib.Analysis.SpecificLimits.RCLike /-! # Ordinary hypergeometric function in a Banach algebra In this file, we d...
Grothendieck.lean
/- Copyright (c) 2024 Markus Himmel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Markus Himmel -/ import Mathlib.CategoryTheory.Filtered.Basic import Mathlib.CategoryTheory.Grothendieck /-! # Filteredness of Grothendieck construction We show that if `F : C β₯€ Cat` ...
ExtendToSucc.lean
/- Copyright (c) 2024 JoΓ«l Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: JoΓ«l Riou -/ import Mathlib.CategoryTheory.SmallObject.Iteration.Basic /-! # Extension of a functor from `Set.Iic j` to `Set.Iic (Order.succ j)` Given a linearly ordered type `J` with `S...
Defs.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 Aesop import Mathlib.Data.Multiset.Defs import Mathlib.Data.Set.Pairwise.Basic import Mathlib.Order.Hom.Ba...
ENormedSpace.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.Analysis.Normed.Module.Basic import Mathlib.LinearAlgebra.Basis.VectorSpace /-! # Extended norm **ATTENTION.** This file is deprecated. Mathlib now...
CategoryTheory.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.LinearAlgebra.CliffordAlgebra.Basic import Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat import Mathlib.Algebra.Category.AlgCat.Basic /-! # Categor...
M.lean
/- Copyright (c) 2017 Simon Hudon. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Simon Hudon -/ import Mathlib.Data.PFunctor.Univariate.Basic /-! # M-types M types are potentially infinite tree-like structures. They are defined as the greatest fixpoint of a polynomi...
Resolution.lean
/- Copyright (c) 2022 Amelia Livingston. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Amelia Livingston -/ import Mathlib.Algebra.Category.ModuleCat.Projective import Mathlib.AlgebraicTopology.ExtraDegeneracy import Mathlib.CategoryTheory.Abelian.Ext import Mathlib.R...
finfield.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 div tupl...
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.Algebra.Polynomial.Laurent import Mathlib.RingTheory.Coalgebra.Basic /-! # The coalgebra structure on monoid algebras Given a type `X`, a commu...
FunctorToTypes.lean
/- Copyright (c) 2024 Jack McKoen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jack McKoen -/ import Mathlib.CategoryTheory.Functor.FunctorHom import Mathlib.CategoryTheory.Closed.Monoidal /-! # Functors to Type are closed. Show that `C β₯€ Type max w v u` is monoid...
Basic.lean
/- Copyright (c) 2016 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad -/ import Mathlib.Data.Int.Notation import Mathlib.Data.Nat.Notation import Mathlib.Order.Defs.LinearOrder /-! # The order relation on the integers -/ open Nat namespa...
LocallyFinite.lean
/- Copyright (c) 2023 YaΓ«l Dillies, Sara Rousta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: YaΓ«l Dillies -/ import Mathlib.Data.Set.Finite.Lattice import Mathlib.Order.Interval.Finset.Defs import Mathlib.Order.UpperLower.Closure /-! # Upper and lower sets in a loc...
all_character.v
From mathcomp Require Export character. From mathcomp Require Export classfun. From mathcomp Require Export inertia. From mathcomp Require Export integral_char. From mathcomp Require Export mxabelem. From mathcomp Require Export mxrepresentation. From mathcomp Require Export vcharacter.
Associated.lean
/- Copyright (c) 2018 Johannes HΓΆlzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes HΓΆlzl, Jens Wagemaker -/ import Mathlib.Algebra.Prime.Lemmas import Mathlib.Order.BoundedOrder.Basic /-! # Associated elements. In this file we define an equivalence relatio...
AbstractCompletion.lean
/- Copyright (c) 2019 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot -/ import Mathlib.Topology.UniformSpace.UniformEmbedding import Mathlib.Topology.UniformSpace.Equiv /-! # Abstract theory of Hausdorff completions of uniform spaces Th...
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...
Dedup.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.Defs import Mathlib.Data.Multiset.Dedup import Mathlib.Data.Multiset.Basic /-! # Dedu...
Defs.lean
/- Copyright (c) 2017 Johannes HΓΆlzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes HΓΆlzl -/ import Mathlib.Algebra.BigOperators.Finprod import Mathlib.Order.Filter.AtTopBot.BigOperators import Mathlib.Topology.Separation.Hausdorff /-! # Infinite sum and pro...
norm_num.lean
/- Copyright (c) 2017 Simon Hudon. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Simon Hudon, Mario Carneiro, Thomas Murrills -/ import Mathlib.Tactic.NormNum private axiom test_sorry : βˆ€ {Ξ±}, Ξ± /-! # Tests for `norm_num` extensions -/ set_option autoImplicit true ...
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. (*************************...
Integral.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.RingTheory.LocalProperties.Basic import Mathlib.RingTheory.Localization.Integral /-! # The meta properties of integral ring homomorphisms. -/ namespace ...
action.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun ssrnotations eqtype. From mathcomp Require Import ssrnat div seq prime fintype bigop finset. From mathcomp...
Sum.lean
/- Copyright (c) 2024 Martin Dvorak. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Martin Dvorak -/ import Mathlib.Algebra.Notation.Pi.Defs import Mathlib.Order.Basic /-! # Interaction between `Sum.elim`, `≀`, and `0` or `1` This file provides basic API for part-wis...
Truncated.lean
/- Copyright (c) 2025 Jakob von Raumer. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jakob von Raumer -/ import Mathlib.AlgebraicTopology.SimplexCategory.Basic import Mathlib.CategoryTheory.Limits.Final /-! # Properties of the truncated simplex category We prove th...
ConjTranspose.lean
/- Copyright (c) 2018 Ellen Arlt. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Ellen Arlt, Blair Shi, Sean Leather, Mario Carneiro, Johan Commelin, Lu-Ming Zhang -/ import Mathlib.Algebra.BigOperators.GroupWithZero.Action import Mathlib.Algebra.BigOperators.Ring.Fins...
Rev.lean
/- Copyright (c) 2022 Eric Rodriguez. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Rodriguez, Joel Riou, Yury Kudryashov -/ import Mathlib.Data.Fin.Basic /-! # Reverse on `Fin n` This file contains lemmas about `Fin.rev : Fin n β†’ Fin n` which maps `i` to `n - 1...
Ultraproducts.lean
/- Copyright (c) 2022 Aaron Anderson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Anderson -/ import Mathlib.ModelTheory.Quotients import Mathlib.Order.Filter.Finite import Mathlib.Order.Filter.Germ.Basic import Mathlib.Order.Filter.Ultrafilter.Defs /-! # Ult...
all_character.v
From mathcomp Require Export character. From mathcomp Require Export classfun. From mathcomp Require Export inertia. From mathcomp Require Export integral_char. From mathcomp Require Export mxabelem. From mathcomp Require Export mxrepresentation. From mathcomp Require Export vcharacter.
Basic.lean
/- Copyright (c) 2022 Floris van Doorn, Heather Macbeth. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn, Heather Macbeth -/ import Mathlib.Geometry.Manifold.ContMDiff.Atlas import Mathlib.Geometry.Manifold.VectorBundle.FiberwiseLinear import Mathlib.To...
Kolmogorov.lean
/- Copyright (c) 2025 RΓ©my Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: RΓ©my Degenne -/ import Mathlib.MeasureTheory.Function.SpecialFunctions.Basic import Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable import Mathlib.MeasureTheory.In...
Frobenius.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.FieldTheory.Finite.Basic import Mathlib.RingTheory.Invariant.Basic import Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots import Mathlib.RingTheory.Unramified...
DirectSum.lean
/- Copyright (c) 2020 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.Algebra.DirectSum.Module import Mathlib.Algebra.Lie.OfAssociative import Mathlib.Algebra.Lie.Ideal import Mathlib.Algebra.Lie.Basic /-! # Direct sums of Lie...
commutator.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 fintype. From mathcomp Require Import bigop finset binomial fingroup morphism. From mathcomp...
Lattice.lean
/- Copyright (c) 2024 Jujian Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jujian Zhang -/ import Mathlib.RingTheory.TwoSidedIdeal.Basic /-! # The complete lattice structure on two-sided ideals -/ namespace TwoSidedIdeal variable (R : Type*) [NonUnitalNonAs...
separable.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...
Basis.lean
/- Copyright (c) 2021 Jakob von Raumer. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jakob von Raumer -/ import Mathlib.LinearAlgebra.Basis.Basic import Mathlib.LinearAlgebra.DirectSum.Finsupp import Mathlib.LinearAlgebra.Finsupp.VectorSpace import Mathlib.LinearAlge...
TopComparison.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.Opposites import Mathlib.CategoryTheory.Sites.Coherent.SheafComparison import Mathlib.Condensed.Basic import Mathli...
EisensteinCriterion.lean
/- Copyright (c) 2020 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes -/ import Mathlib.Data.Nat.Cast.WithTop import Mathlib.RingTheory.Ideal.Quotient.Basic import Mathlib.RingTheory.Polynomial.Content import Mathlib.RingTheory.Prime deprecat...
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.Compactness.Bases import Mathlib.Topology.CompactOpen import Mathlib.Topology.Separation.Profinite import Mathlib.Topology.Sets.Closeds /...
Nontriviality.lean
/- Copyright (c) 2020 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel, Mario Carneiro -/ import Mathlib.Tactic.Nontriviality.Core /-! # The `nontriviality` tactic. -/
Coprime.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.Algebra.EuclideanDomain.Int import Mathlib.Data.Nat.Prime.Int import Mathlib.Data.ZMod.Basic import Mathlib.RingTheory.Int.Basic import Mathlib.RingTheor...
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 Kudryashov -/ import Mathlib.Order.UpperLower.Closure import Mathlib.Order.UpperLower.Fibration import Mathlib.Tactic.TFAE import Mathlib.Topology.ContinuousOn import Ma...
slim_check.lean
import Mathlib.Algebra.Group.Fin.Basic import Mathlib.Data.DFinsupp.Defs import Mathlib.Data.Finsupp.Notation import Mathlib.Data.Nat.Prime.Defs import Mathlib.Data.PNat.Basic import Mathlib.Tactic.Have import Mathlib.Tactic.SuccessIfFailWithMsg import Mathlib.Testing.Plausible.Functions import Mathlib.Testing.Plausibl...
numfield.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 ssrAC div fintyp...
Radical.lean
/- Copyright (c) 2024 Jineon Baek, Seewoo Lee. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jineon Baek, Seewoo Lee -/ import Mathlib.Algebra.Polynomial.FieldDivision import Mathlib.RingTheory.Polynomial.Wronskian import Mathlib.RingTheory.Radical import Mathlib.Ring...
Jacobian.lean
/- Copyright (c) 2022 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel -/ import Mathlib.Analysis.Calculus.FDeriv.Congr import Mathlib.MeasureTheory.Constructions.BorelSpace.ContinuousLinearMap import Mathlib.MeasureTheory.Covering.Be...
AsSmall.lean
/- Copyright (c) 2024 Jakob von Raumer. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jakob von Raumer -/ import Mathlib.CategoryTheory.Category.Cat import Mathlib.CategoryTheory.Category.ULift /-! # Functorially embedding `Cat` into the category of small categories ...
matrix.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 f...
NatTrans.lean
/- Copyright (c) 2017 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Tim Baumann, Stephen Morgan, Kim Morrison, Floris van Doorn -/ import Mathlib.Tactic.CategoryTheory.Reassoc /-! # Natural transformations Defines natural transformations between functo...
Attribute.lean
/- Copyright (c) 2024 Geoffrey Irving. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Geoffrey Irving -/ import Mathlib.Tactic.Bound.Init import Qq import Aesop /-! # The `bound` attribute Any lemma tagged with `@[bound]` is registered as an apply rule for the `bound...
qfpoly.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import fintype tuple div bigop binomial finset finfun. From mathcomp Require Import ssralg countalg finalg poly polydiv qpoly perm. From mathcomp Require Import fingroup falgebra fiel...
mxrepresentation.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...
ssrbool.v
From mathcomp Require Import ssreflect ssrfun. From Corelib Require Export ssrbool. Set Implicit Arguments. Unset Strict Implicit. Unset Printing Implicit Defensive. (**********************) (* not yet backported *) (**********************) Lemma homo_mono1 [aT rT : Type] [f : aT -> rT] [g : rT -> aT] [aP : pred ...
ExactSequence.lean
/- Copyright (c) 2023 JoΓ«l Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: JoΓ«l Riou -/ import Mathlib.Algebra.Homology.ShortComplex.Exact import Mathlib.CategoryTheory.ComposableArrows /-! # Exact sequences A sequence of `n` composable arrows `S : ComposableArr...
GoingDown.lean
/- Copyright (c) 2025 Christian Merten, Yi Song, Sihan Su. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christian Merten, Yi Song, Sihan Su -/ import Mathlib.RingTheory.Ideal.GoingUp import Mathlib.RingTheory.Flat.FaithfullyFlat.Algebra import Mathlib.RingTheory.Flat...
byContra.lean
-- tests for by_contra! tactic import Mathlib.Tactic.ByContra import Mathlib.Tactic.Rename import Mathlib.Tactic.Set import Mathlib.Algebra.Notation.Defs import Mathlib.Data.Nat.Basic import Mathlib.Order.Basic set_option autoImplicit true example (a b : β„•) (foo : False) : a < b := by by_contra! guard_hyp this : ...
fingroup.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 div path...
FormallyUnramified.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.AlgebraicGeometry.Morphisms.Separated import Mathlib.RingTheory.Ideal.IdempotentFG import Mathlib.RingTheory.RingHom.Unramified /-! # Formally unramified mo...
ssrAC.v
From HB Require Import structures. From Corelib Require Import PosDef. (* use #[warning="-hiding-delimiting-key"] attribute once we require Coq 8.18 *) (* (the warning was completely removed in 9.0) *) Set Warnings "-hiding-delimiting-key". From mathcomp Require Import ssreflect ssrbool ssrfun ssrnat eqtype seq bigop. ...
Algebraic.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.LocalRing.ResidueField.Ideal import Mathlib.RingTheory.Algebraic.Integral /-! # Algebraic extensions of the residue field -/ instance {R : Type*...
Defs.lean
/- Copyright (c) 2024 Chris Birkbeck. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Birkbeck, David Loeffler -/ import Mathlib.NumberTheory.ModularForms.SlashInvariantForms import Mathlib.NumberTheory.ModularForms.CongruenceSubgroups /-! # Eisenstein Series ##...
gfunctor.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 fintype. From mathcomp Require Import bigop finset fingroup morphism automorphism. From math...
SuccPred.lean
/- Copyright (c) 2025 YaΓ«l Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: YaΓ«l Dillies -/ import Mathlib.Algebra.Order.SuccPred import Mathlib.Order.Interval.Set.SuccPred /-! # Set intervals in an additive successor-predecessor order This file proves relatio...
SumIntegralComparisons.lean
/- Copyright (c) 2022 Kevin H. Wilson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin H. Wilson -/ import Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic import Mathlib.Data.Set.Function /-! # Comparing sums and integrals ## Summary It is often the case ...
HasCardinalLT.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.Subobject.Basic import Mathlib.SetTheory.Cardinal.HasCardinalLT /-! # Cardinality of Subobject If `X ⟢ Y` is a monomorphism, and the cardinality...
FunctorCategories.lean
/- Copyright (c) 2022 JoΓ«l Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: JoΓ«l Riou -/ import Mathlib.CategoryTheory.Idempotents.Karoubi /-! # Idempotent completeness and functor categories In this file we define an instance `functor_category_isIdempotentComple...
HomologySequence.lean
/- Copyright (c) 2023 JoΓ«l Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: JoΓ«l Riou -/ import Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex import Mathlib.Algebra.Homology.ShortComplex.SnakeLemma import Mathlib.Algebra.Homology.ShortComplex.ShortExact ...
CompileInductive.lean
/- Copyright (c) 2023 Parth Shastri. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Parth Shastri, Gabriel Ebner, Mario Carneiro -/ import Mathlib.Init import Lean.Elab.Command import Lean.Compiler.CSimpAttr import Lean.Util.FoldConsts import Lean.Data.AssocList /-! #...
Pairing.lean
/- Copyright (c) 2024 JoΓ«l Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: JoΓ«l Riou -/ import Mathlib.GroupTheory.MonoidLocalization.Basic import Mathlib.LinearAlgebra.Dual.Defs import Mathlib.LinearAlgebra.TensorPower.Basic /-! # The pairing between the tensor ...
TopologicalSpace.lean
/- Copyright (c) 2025 Anatole Dedecker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anatole Dedecker -/ import Mathlib.Topology.Algebra.Group.Pointwise import Mathlib.Topology.Algebra.RestrictedProduct.Basic import Mathlib.Topology.Algebra.Ring.Basic /-! # Restrict...
orderedzmod.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 ssrAC div fintyp...
Basic.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.FreeModule.Finite.Basic import Mathlib.LinearAlgebra.Matrix.Charpoly.Coeff import Mathlib.LinearAlgebra.Determinant import Mathlib.Fiel...
AbelSummation.lean
/- Copyright (c) 2024 Xavier Roblot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Xavier Roblot -/ import Mathlib.MeasureTheory.Function.Floor import Mathlib.MeasureTheory.Integral.Asymptotics import Mathlib.MeasureTheory.Integral.IntegralEqImproper import Mathlib.To...
JordanChevalley.lean
/- Copyright (c) 2024 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.Dynamics.Newton import Mathlib.LinearAlgebra.Semisimple import Mathlib.LinearAlgebra.FreeModule.Finite.Matrix /-! # Jordan-Chevalley-Dunford decomposition ...
Basic.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.LinearAlgebra.PiTensorProduct import Mathlib.Logic.Equiv.Fin.Basic import Mathlib.Algebra.DirectSum.Algebra /-! # Tensor power of a semimodule over a commut...
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...
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...
Defs.lean
/- Copyright (c) 2018 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.Algebra.Algebra.Defs import Mathlib.Algebra.Order.Module.OrderedSMul import Mathlib.Data.Real.Archimedean /-! # Nonnegative real numbers In this file...
Compact.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.Topology.ContinuousMap.Bounded.Star import Mathlib.Topology.ContinuousMap.Star import Mathlib.Topology.UniformSpace.Compact import Mathlib.Topology.Compact...
mxred.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 div. From mathcomp Require Import choice fintype finfun bigop fingroup perm order. From ...
FiniteDimension.lean
/- Copyright (c) 2019 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel -/ import Mathlib.Analysis.Asymptotics.AsymptoticEquivalent import Mathlib.Analysis.Normed.Group.Lemmas import Mathlib.Analysis.Normed.Affine.AddTorsor import Math...
PreorderRestrict.lean
/- Copyright (c) 2024 Etienne Marion. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Etienne Marion -/ import Mathlib.MeasureTheory.MeasurableSpace.Constructions import Mathlib.Order.Restriction /-! # Measurability of the restriction function for functions indexed by ...
closed_field.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 seq. From mathcomp Require Import fintype generic_...
Adjugate.lean
/- Copyright (c) 2019 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen -/ import Mathlib.Algebra.Regular.Basic import Mathlib.LinearAlgebra.Matrix.MvPolynomial import Mathlib.LinearAlgebra.Matrix.Polynomial /-! # Cramer's rule and adjugate matri...
Derivation.lean
/- Copyright (c) 2023 Kevin Buzzard. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Buzzard, Richard M. Hill -/ import Mathlib.Algebra.Polynomial.AlgebraMap import Mathlib.Algebra.Polynomial.Derivative import Mathlib.Algebra.Polynomial.Module.AEval import Mathlib...
JordanSub.lean
/- Copyright (c) 2025 Loic Simon. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Loic Simon -/ import Mathlib.MeasureTheory.Measure.Decomposition.Hahn import Mathlib.MeasureTheory.Measure.Sub import Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan /-! # Jordan...
Decomposition.lean
/- Copyright (c) 2022 JoΓ«l Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: JoΓ«l Riou -/ import Mathlib.AlgebraicTopology.DoldKan.PInfty /-! # Decomposition of the Q endomorphisms In this file, we obtain a lemma `decomposition_Q` which expresses explicitly the p...
OreSet.lean
/- Copyright (c) 2022 Jakob von Raumer. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jakob von Raumer, Kevin Klinge -/ import Mathlib.Algebra.Group.Submonoid.Defs import Mathlib.Algebra.GroupWithZero.Basic import Mathlib.Algebra.Ring.Regular import Mathlib.GroupTheor...
WeierstrassPreparation.lean
/- Copyright (c) 2025 Jz Pan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jz Pan -/ import Mathlib.RingTheory.LocalRing.ResidueField.Basic import Mathlib.RingTheory.Polynomial.Eisenstein.Distinguished import Mathlib.RingTheory.PowerSeries.CoeffMulMem import Mathlib....
OrderIso.lean
/- Copyright (c) 2017 Johannes HΓΆlzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes HΓΆlzl, Mario Carneiro, Patrick Massot, Yury Kudryashov, RΓ©my Degenne -/ import Mathlib.Order.Interval.Set.Basic import Mathlib.Order.Hom.Set /-! # Lemmas about images of inte...
FrameAdjunction.lean
/- Copyright (c) 2023 Anne Baanen, Sam van Gool, Leo Mayer, Brendan Murphy. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen, Sam van Gool, Leo Mayer, Brendan Murphy -/ import Mathlib.Topology.Category.Locale /-! # Adjunction between Locales and Topological ...
Lemmas.lean
/- Copyright (c) 2020 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes HΓΆlzl, Mario Carneiro, Alexander Bentkamp, Anne Baanen -/ import Mathlib.Data.Fin.Tuple.Reflection import Mathlib.LinearAlgebra.Finsupp.SumProd import Mathlib.LinearAlgebra.Linea...
Expand.lean
/- Copyright (c) 2020 Riccardo Brasca. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Riccardo Brasca -/ import Mathlib.Algebra.Algebra.ZMod import Mathlib.RingTheory.Polynomial.Cyclotomic.Roots /-! # Cyclotomic polynomials and `expand`. We gather results relating cy...
SProd.lean
/- Copyright (c) 2023 Miyahara Kō. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Miyahara Kō -/ import Mathlib.Tactic.FBinop /-! # Set Product Notation This file provides notation for a product of sets, and other similar types. ## Main Definitions * `SProd α β γ` ...
Tannery.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.Analysis.RCLike.Basic import Mathlib.Analysis.Normed.Group.InfiniteSum /-! # Tannery's theorem Tannery's theorem gives a sufficient criterion for th...
Lex.lean
/- Copyright (c) 2019 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Minchao Wu -/ import Mathlib.Data.Prod.Basic import Mathlib.Order.Lattice import Mathlib.Order.BoundedOrder.Basic import Mathlib.Tactic.Tauto /-! # Lexicographic order Th...
Elab.lean
/- Copyright (c) 2023 Sebastian Zimmer. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sebastian Zimmer, Mario Carneiro, Heather Macbeth, Jovan Gerbscheid -/ import Mathlib.Tactic.GRewrite.Core /-! # The generalized rewriting tactic This file defines the tactics tha...