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Lemmas.lean
/- Copyright (c) 2018 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Topology.Order.Compact import Mathlib.Topology.MetricSpace.ProperSpace import Mathlib.Topology.Order.IntermediateValue import Mathlib.Topology.O...
Basic.lean
/- Copyright (c) 2021 Shing Tak Lam. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Shing Tak Lam -/ import Mathlib.Topology.Order.ProjIcc import Mathlib.Topology.ContinuousMap.Ordered import Mathlib.Topology.CompactOpen import Mathlib.Topology.UnitInterval /-! # Homo...
Range.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.Algebra.Group.Embedding import Mathlib.Algebra.Group.Nat.Defs import Mathlib.Data.Finset.Image /-...
LocallyIntegrable.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.MeasureTheory.Integral.IntegrableOn /-! # Locally integrable functions A function is called *locally integrable* (`MeasureTheory.LocallyIntegrabl...
Coherence.lean
/- Copyright (c) 2022 Yuma Mizuno. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yuma Mizuno, Junyan Xu -/ import Mathlib.CategoryTheory.PathCategory.Basic import Mathlib.CategoryTheory.Functor.FullyFaithful import Mathlib.CategoryTheory.Bicategory.Free import Mathlib...
ContinuousAffineMap.lean
/- Copyright (c) 2021 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.LinearAlgebra.AffineSpace.AffineMap import Mathlib.Topology.Algebra.Module.LinearMap /-! # Continuous affine maps. This file defines a type of bundled cont...
Basic.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.Group.End import Mathlib.Data.Set.Function /-! # Fixed points of a self-map In this file we define * the predicate `IsFixedPt f x := f x =...
Thin.lean
/- Copyright (c) 2019 Kim Morrison, Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Bhavik Mehta -/ import Mathlib.CategoryTheory.Functor.Category import Mathlib.CategoryTheory.Iso /-! # Thin categories A thin category (also known as a spars...
FullSubcategory.lean
/- Copyright (c) 2017 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Reid Barton -/ import Mathlib.CategoryTheory.Functor.FullyFaithful deprecated_module "Auto-generated deprecation" (since := "2025-04-23")
nmodule.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq. From mathcomp Require Import bigop fintype finfun monoid. (******************************************************************************) (* Additive group-like structures ...
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.RingTheory.FreeCommRing /-! # Constructing Ring terms from MvPolynomial This file provides tools for constructing ring terms that can be evaluated to p...
Opposite.lean
/- Copyright (c) 2020 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.Algebra.Group.Action.Faithful import Mathlib.Algebra.Group.Action.Opposite import Mathlib.Algebra.GroupWithZero.Action.Defs import Mathlib.Algebra.GroupWithZ...
Projection.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.LinearAlgebra.Quotient.Basic import Mathlib.LinearAlgebra.Prod import Mathlib.Algebra.Module.Submodule.Invariant import Mathlib.LinearAlgebra.General...
Basic.lean
/- Copyright (c) 2021 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Anne Baanen -/ import Mathlib.Algebra.GroupWithZero.Regular import Mathlib.Algebra.GroupWithZero.Units.Lemmas import Mathlib.Algebra.Order.Hom.Basic import Mathlib.Algebra...
QuasiCompact.lean
/- Copyright (c) 2022 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap import Mathlib.Topology.Spectral.Hom import Mathlib.AlgebraicGeometry.Limits /-! # Quasi-compact morphisms A morp...
EpiMono.lean
/- Copyright (c) 2019 Reid Barton. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Reid Barton -/ import Mathlib.Topology.Category.TopCat.Adjunctions import Mathlib.CategoryTheory.Functor.EpiMono /-! # Epi- and monomorphisms in `Top` This file shows that a continuous ...
zmodp.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 choice eqtype ssrnat seq. From mathcomp Require Import div fintype bigo...
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...
Star.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.Analysis.Calculus.Deriv.Basic import Mathlib.Analysis.Calculus.FDeriv.Star /-! # Star operations on derivatives This file contains the usual formulas (and ...
List.lean
/- Copyright (c) 2021 Stuart Presnell. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Stuart Presnell, Daniel Weber -/ import Mathlib.Algebra.BigOperators.Group.List.Defs import Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic /-! # Big operators on a list in order...
NhdsKer.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.Tactic.Peel import Mathlib.Topology.Compactness.Compact import Mathlib.Topology.NhdsKer /-! # Compactness of the neighborhoods kernel of a set In t...
BaseChange.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.LinearAlgebra.Matrix.NonsingularInverse import Mathlib.Algebra.Field.Subfield.Defs /-! # Matrices and base change This file is a home for results about bas...
Core.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.GCongr.Core /-! # The generalized rewriting tactic This module defines the core of the...
Pseudo.lean
/- Copyright (c) 2024 Calle Sönne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Calle Sönne -/ import Mathlib.CategoryTheory.Bicategory.Functor.Pseudofunctor import Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Oplax /-! # Strong transformations of pseud...
Intervals.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl -/ import Mathlib.Algebra.Order.BigOperators.Group.LocallyFinite import Mathlib.Algebra.Order.Interval.Finset.Basic import Mathlib.Algebra.Order.Sub.Basic import Mathlib...
hall.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 choice. From mathcomp Require Import fintype finset prime fingroup morphism. From ma...
Quotient.lean
/- Copyright (c) 2025 Xavier Roblot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen, Xavier Roblot -/ import Mathlib.Data.ZMod.QuotientRing import Mathlib.LinearAlgebra.Dimension.Constructions import Mathlib.LinearAlgebra.FreeModule.PID import Mathlib.Linea...
hall.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 choice. From mathcomp Require Import fintype finset prime fingroup morphism. From ma...
NatAntidiagonal.lean
/- Copyright (c) 2019 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.Data.List.NatAntidiagonal import Mathlib.Data.Multiset.MapFold /-! # Antidiagonals in ℕ × ℕ as multisets This file defines the antidiagonals of ℕ × ℕ...
Angle.lean
/- Copyright (c) 2019 Calle Sönne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Calle Sönne -/ import Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic import Mathlib.Analysis.Normed.Group.AddCircle import Mathlib.Algebra.CharZero.Quotient import Mathlib.Topology...
Fintype.lean
/- Copyright (c) 2022 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen -/ import Mathlib.Data.Fintype.Basic import Mathlib.Data.FunLike.Basic import Mathlib.Data.Finite.Prod /-! # Finiteness of `DFunLike` types We show a type `F` with a `DFunLi...
numdomain.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...
Defs.lean
/- Copyright (c) 2018 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau, Chris Hughes, Mario Carneiro -/ import Mathlib.Algebra.Group.Units.Defs import Mathlib.Algebra.Ring.Defs /-! # Local rings Define local rings as commutative rings having a uni...
Basic.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, Reid Barton -/ import Mathlib.CategoryTheory.Category.Init import Mathlib.Combinatorics.Quiver.Basic import Mathlib.Tactic.PPWithUniv import...
MulOpposite.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.Group.Submonoid.MulOpposite import Mathlib.Algebra.Ring.Subsemiring.Basic import Mathlib.Algebra.Ring.Opposite /-! # Subsemiring of opposite semirings For e...
Int.lean
/- Copyright (c) 2015 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Leonardo de Moura, Jeremy Avigad, Mario Carneiro -/ import Mathlib.Algebra.Ring.Int.Defs import Mathlib.Data.Nat.Prime.Basic import Mathlib.Algebra.Group.Int.Units import Mathli...
Filtration.lean
/- Copyright (c) 2022 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.Algebra.Polynomial.Module.Basic import Mathlib.RingTheory.Finiteness.Nakayama import Mathlib.RingTheory.LocalRing.MaximalIdeal.Basic import Mathlib.RingTheor...
CommSq.lean
/- Copyright (c) 2022 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Joël Riou, Calle Sönne -/ import Mathlib.CategoryTheory.Limits.Constructions.ZeroObjects import Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts import Mathlib.Catego...
Characterization.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.Condensed.Discrete.Colimit import Mathlib.Condensed.Discrete.Module /-! # Characterizing discrete condensed sets and `R`-modules. This file prove...
Restrict.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Mario Carneiro -/ import Mathlib.MeasureTheory.Measure.Comap import Mathlib.MeasureTheory.Measure.QuasiMeasurePreserving /-! # Restricting a measure to a subset or a s...
IncMatrix.lean
/- Copyright (c) 2021 Gabriel Moise. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Gabriel Moise, Yaël Dillies, Kyle Miller -/ import Mathlib.Combinatorics.SimpleGraph.Finite import Mathlib.Data.Finset.Sym import Mathlib.Data.Matrix.Mul /-! # Incidence matrix of a si...
Nontrivial.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.LinearAlgebra.Basis.VectorSpace import Mathlib.RingTheory.Flat.FaithfullyFlat.Basic import Mathlib.RingTheory.Localization.FractionRing /-! # Nontriviality of tensor...
polydiv.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 choice. From mathcomp Require Import fintype bigop ssralg poly. (**********************...
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, Floris van Doorn, Yaël Dillies -/ import Mathlib.Algebra.Group.Equiv.Basic import Mathlib.Algebra.Group.Prod import Mathlib.Algebra.Order.Monoid.Unbundled.Pow import Ma...
Ordinal.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.Order.GameAdd import Mathlib.Order.RelIso.Set import Mathlib.SetTheory.ZFC.Basic /-! # Von Neumann ordinals This file works t...
Path.lean
/- Copyright (c) 2020 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot -/ import Mathlib.Topology.Order.ProjIcc import Mathlib.Topology.CompactOpen import Mathlib.Topology.UnitInterval /-! # Paths in topological spaces This file introduce...
SubGaussian.lean
/- Copyright (c) 2025 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Probability.Kernel.Condexp import Mathlib.Probability.Moments.MGFAnalytic import Mathlib.Probability.Moments.Tilted /-! # Sub-Gaussian random variables T...
Abelian.lean
/- Copyright (c) 2020 Markus Himmel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Markus Himmel -/ import Mathlib.Algebra.Category.Grp.Colimits import Mathlib.Algebra.Category.Grp.Limits import Mathlib.Algebra.Category.Grp.ZModuleEquivalence import Mathlib.Algebra.Ca...
Defs.lean
/- Copyright (c) 2020 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau, Thomas Browning, Patrick Lutz -/ import Mathlib.Algebra.Polynomial.Splits import Mathlib.FieldTheory.IntermediateField.Basic import Mathlib.FieldTheory.Minpoly.Field /-! # Norma...
Opposite.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.Group.Equiv.Basic import Mathlib.Algebra.Group.Opposite /-! # Group isomorphism between a group and its opposite -/ variable {α : Type*} n...
Analytic.lean
/- Copyright (c) 2025 Stefan Kebekus. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Stefan Kebekus -/ import Mathlib.Analysis.Calculus.FDeriv.Symmetric import Mathlib.Analysis.Complex.CauchyIntegral import Mathlib.Analysis.Complex.Conformal import Mathlib.Analysis.Inn...
Cast.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.RingTheory.Polynomial.Pochhammer /-! # Cast of factorials This file allows calculating factorials (including ascending and descending ones) as elements o...
Init.lean
/- Copyright (c) 2023 Jannis Limperg. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jannis Limperg -/ import Mathlib.Init import Aesop /-! # Sym2 Rule Set This module defines the `Sym2` Aesop rule set. Aesop rule sets only become visible once the file in which they...
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 -/ import Mathlib.Algebra.Polynomial.Expand import Mathlib.Algebra.Polynomial.Roots import Mathlib.RingTheory.Adjoin.Polynomial import Mathlib.RingTheory.Algebraic.Defs ...
NatInt.lean
/- Copyright (c) 2015 Nathaniel Thomas. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Nathaniel Thomas, Jeremy Avigad, Johannes Hölzl, Mario Carneiro -/ import Mathlib.Algebra.Module.Defs import Mathlib.Data.Int.Cast.Lemmas /-! # Modules over `ℕ` and `ℤ` This file c...
FinitelyGenerated.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.Data.Set.Finite.Lemmas import Mathlib.ModelTheory.Substructures /-! # Finitely Generated First-Order Structures This file defines what it means for a...
Basic.lean
/- Copyright (c) 2021 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn -/ import Mathlib.Algebra.Order.Sub.Defs import Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE /-! # Lemmas about subtraction in an unbundled canonically ordered...
QuasiSeparated.lean
/- Copyright (c) 2022 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.Topology.Compactness.Bases import Mathlib.Topology.NoetherianSpace /-! # Quasi-separated spaces A topological space is quasi-separated if the intersections...
Basic.lean
/- Copyright (c) 2019 Gabriel Ebner. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Gabriel Ebner, Sébastien Gouëzel -/ import Mathlib.Analysis.Calculus.FDeriv.Const import Mathlib.Analysis.NormedSpace.OperatorNorm.NormedSpace /-! # One-dimensional derivatives This ...
ERealExp.lean
/- Copyright (c) 2024 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Pietro Monticone, Rémy Degenne, Lorenzo Luccioli -/ import Mathlib.Data.Complex.Exponential import Mathlib.Data.EReal.Basic /-! # Extended Nonnegative Real Exponential We define `exp` ...
Frobenius.lean
/- Copyright (c) 2021 Jakob Scholbach. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jakob Scholbach -/ import Mathlib.Algebra.Algebra.Defs import Mathlib.Algebra.CharP.Lemmas /-! ### The Frobenius endomorphism ## Tags Frobenius endomorphism ## Implementation note...
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_...
Basic.lean
/- Copyright (c) 2021 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.CategoryTheory.Sites.Sheaf import Mathlib.CategoryTheory.Sites.CoverLifting import Mathlib.CategoryTheory.Sites.CoverPreserving import Mathlib.CategoryTheory...
ExtraRecognizers.lean
/- Copyright (c) 2023 Kyle Miller. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kyle Miller -/ import Mathlib.Data.Set.Operations /-! # Additional Expr recognizers needing theory imports -/ namespace Lean.Expr /-- If `e` is a coercion of a set to a type, return t...
CartanSubalgebra.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.Nilpotent import Mathlib.Algebra.Lie.Normalizer /-! # Cartan subalgebras Cartan subalgebras are one of the most important concepts in Lie theor...
NegOnePow.lean
/- Copyright (c) 2023 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou, Johan Commelin -/ import Mathlib.Algebra.Field.Defs import Mathlib.Algebra.Ring.NegOnePow import Mathlib.Tactic.NormNum /-! # Integer powers of `-1` in a field -/ namespace Int...
Fin.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Kim Morrison, Johan Commelin -/ import Mathlib.Data.Finset.Card import Mathlib.Data.Fin.Embedding /-! # Finsets in `Fin n` A few constructions for Finsets in `Fin n`. ##...
imset2_gproduct.v
From mathcomp Require Import all_boot all_fingroup. Set Implicit Arguments. Unset Strict Implicit. Unset Printing Implicit Defensive. Import GroupScope. Open Scope group_scope. Check @ker_sdprodm.
FiniteIndex.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.GroupTheory.Index import Mathlib.RepresentationTheory.Coinduced import Mathlib.RepresentationTheory.Induced /-! # (Co)induced representations of...
Monoidal.lean
/- Copyright (c) 2024 Amelia Livingston. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Amelia Livingston -/ import Mathlib.Algebra.Category.AlgCat.Monoidal import Mathlib.Algebra.Category.BialgCat.Basic import Mathlib.Algebra.Category.CoalgCat.Monoidal import Mathlib....
Div.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.Field.IsField import Mathlib.Algebra.Polynomial.Inductions import Mathlib.Algebra.Polynomial.Monic im...
Mon_.lean
/- Copyright (c) 2025 Robin Carlier. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Robin Carlier -/ import Mathlib.CategoryTheory.Monoidal.Opposite import Mathlib.CategoryTheory.Monoidal.Mon_ /-! # Monoid objects internal to monoidal opposites In this file, we recor...
Lemmas.lean
/- Copyright (c) 2021 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.LinearAlgebra.Matrix.ToLin import Mathlib.LinearAlgebra.Quotient.Basic import Mathlib.RingTheory.Ideal.Maps import Mathlib.RingTheory.Nilpotent.Defs /-! # N...
Coe.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 /-! # Additional coercion notation Defines notation for coercions. 1. `↑ t` is defined in core. 2. `(↑)` is equivalent ...
Linearity.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.Algebra.BigOperators.Field import Mathlib.NumberTheory.LSeries.Basic /-! # Linearity of the L-series of `f` as a function of `f` We show that the `LSer...
RegularEpi.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.Shapes.RegularMono import Mathlib.CategoryTheory.EffectiveEpi.Basic /-! # The relationship between effective and regular epi...
OverAdjunction.lean
/- Copyright (c) 2024 Christian Merten. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christian Merten -/ import Mathlib.CategoryTheory.MorphismProperty.Comma import Mathlib.CategoryTheory.Comma.Over.Pullback import Mathlib.CategoryTheory.MorphismProperty.Limits /-! ...
Resolution.lean
/- Copyright (c) 2022 Jujian Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jujian Zhang, Kim Morrison -/ import Mathlib.CategoryTheory.Preadditive.Injective.Resolution import Mathlib.Algebra.Homology.HomotopyCategory import Mathlib.Data.Set.Subsingleton import ...
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...
IntegralCompProd.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.Composition.MeasureComp import Mathlib.Probability.Kernel.MeasurableIntegral /-! # Bochner integral of a function again...
Limits.lean
/- Copyright (c) 2020 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.Algebra.Category.Grp.ForgetCorepresentable import Mathlib.Algebra.Category.Grp.Preadditive import Mathlib.Algebra.Category.MonCat.ForgetCorepresentable imp...
Laurent.lean
/- Copyright (c) 2022 Yakov Pechersky. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yakov Pechersky -/ import Mathlib.Algebra.Polynomial.Taylor import Mathlib.FieldTheory.RatFunc.AsPolynomial /-! # Laurent expansions of rational functions ## Main declarations * `R...
FBinop.lean
/- Copyright (c) 2023 Kyle Miller. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kyle Miller -/ import Lean.Elab.App import Lean.Elab.BuiltinNotation import Mathlib.Tactic.ToExpr /-! # Elaborator for functorial binary operators `fbinop% f x y` elaborates `f x y` for...
Infinite.lean
/- Copyright (c) 2024 Nailin Guan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Nailin Guan -/ import Mathlib.FieldTheory.KrullTopology import Mathlib.FieldTheory.Galois.GaloisClosure import Mathlib.Topology.Algebra.Group.ClosedSubgroup /-! # The Fundamental Theorem...
all_solvable.v
From mathcomp Require Export abelian. From mathcomp Require Export alt. From mathcomp Require Export burnside_app. From mathcomp Require Export center. From mathcomp Require Export commutator. From mathcomp Require Export cyclic. From mathcomp Require Export extraspecial. From mathcomp Require Export extremal. From mat...
Surjective.lean
/- Copyright (c) 2022 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.RingTheory.LocalProperties.Basic /-! # The meta properties of surjective ring homomorphisms. ## Main results Let `R` be a commutative ring, `M` be a subm...
Complex.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.Data.Complex.Module import Mathlib.RingTheory.Norm.Defs import Mathlib.RingTheory.Trace.Defs /-! # Lemmas about `Algebra.trace` and `Algebra.norm` on `ℂ` -/...
Simp.lean
import Mathlib.Algebra.Algebra.Pi import Mathlib.Algebra.Algebra.Defs /-! Tests for the behavior of `simp`. -/ /- Taken from [Zulip](https://leanprover.zulipchat.com/#narrow/stream/270676-lean4/ topic/simp.20.5BX.5D.20fails.2C.20rw.20.5BX.5D.20works) -/ -- Example 1: succeeds example {α R : Type*} [CommRing R] (f :...
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...
CoprodI.lean
/- Copyright (c) 2021 David Wärn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Wärn, Joachim Breitner -/ import Mathlib.Algebra.Group.Action.End import Mathlib.Algebra.Group.Action.Pointwise.Set.Basic import Mathlib.Algebra.Group.Submonoid.Membership import Mat...
Lattice.lean
/- Copyright (c) 2020 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn -/ import Mathlib.Logic.Encodable.Basic import Mathlib.Logic.Pairwise import Mathlib.Data.Set.Subsingleton /-! # Lattice operations on encodable types Lemmas about...
VerySmallDoubling.lean
/- Copyright (c) 2024 Yaël Dillies, Patrick Luo, Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Patrick Luo, Bhavik Mehta -/ import Mathlib.Algebra.BigOperators.Ring.Finset import Mathlib.Algebra.Group.Action.Pointwise.Finset import Mathlib....
StandardBorel.lean
/- Copyright (c) 2024 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Probability.Kernel.Composition.MeasureCompProd import Mathlib.Probability.Kernel.Disintegration.Basic import Mathlib.Probability.Kernel.Disintegration.Cond...
HausdorffDimension.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.Calculus.ContDiff.RCLike import Mathlib.MeasureTheory.Measure.Hausdorff /-! # Hausdorff dimension The Hausdorff dimension of a set `X` in ...
ParametricIntervalIntegral.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.Calculus.ParametricIntegral import Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic /-! # Derivatives of interval integrals depending ...
ssrnat.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From Corelib Require Import PosDef. From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype. #[export] Set Warnings "-ov...
NormedSpace.lean
/- Copyright (c) 2020 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn, Sébastien Gouëzel -/ import Mathlib.MeasureTheory.Measure.Haar.InnerProductSpace import Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar import Mathlib.MeasureTheory.I...
RationalRoot.lean
/- Copyright (c) 2020 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen -/ import Mathlib.RingTheory.IntegralClosure.IntegrallyClosed import Mathlib.RingTheory.Localization.NumDen import Mathlib.RingTheory.Polynomial.ScaleRoots /-! # Rational roo...
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...
PProd.lean
/- Copyright (c) 2020 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.Logic.Function.Defs /-! # Extra facts about `PProd` -/ open Function variable {α β γ δ : Sort*} namespace PProd def mk.injArrow {α : Type*} {β : Type*}...