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Semiring.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.Algebra.Order.Kleene import Mathlib.Algebra.Order.Ring.Canonical import Mathlib.Data.Set.BooleanAlgebra import Mathlib.Algebra.Group.Pointwise.Set....
Centralizer.lean
/- Copyright (c) 2023 Antoine Chambert-Loir. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Antoine Chambert-Loir -/ import Mathlib.GroupTheory.Perm.Centralizer import Mathlib.GroupTheory.SpecificGroups.Alternating /-! # Centralizer of an element in the alternating gr...
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.
AscendingDescendingSequences.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.Data.Finset.Max import Mathlib.Data.Finset.Prod import Mathlib.Data.Fintype.Powerset /-! # Erdős–Szekeres theorem This file proves Theorem 73 from the [1...
Piecewise.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.BigOperators.Group.Finset.Basic import Mathlib.Data.Finset.Piecewise /-! # Interaction of big operators with piecewise functions This file pr...
Embeddings.lean
/- Copyright (c) 2024 Riccardo Brasca. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Riccardo Brasca -/ import Mathlib.NumberTheory.Cyclotomic.PrimitiveRoots import Mathlib.NumberTheory.NumberField.InfinitePlace.Basic /-! # Cyclotomic extensions of `ℚ` are totally c...
Defs.lean
/- Copyright (c) 2023 Jireh Loreaux. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jireh Loreaux -/ import Mathlib.Algebra.Group.Subgroup.Defs import Mathlib.RingTheory.NonUnitalSubsemiring.Defs import Mathlib.Tactic.FastInstance /-! # `NonUnitalSubring`s Let `R` be...
Manifold.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.Complex.UpperHalfPlane.Manifold import Mathlib.Geometry.Manifold.MFDeriv.FDeriv import Mathlib.NumberTheory.ModularForms.JacobiTheta.OneVariab...
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...
RealSqrt.lean
/- Copyright (c) 2025 Frédéric Dupuis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Frédéric Dupuis -/ import Mathlib.Data.Real.Sqrt /-! # `norm_num` extension for `Real.sqrt` This module defines a `norm_num` extension for `Real.sqrt` and `NNReal.sqrt`. -/ namespa...
Derivative.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.Polynomial.Degree.Domain import Mathlib.Algebra.Polynomial.Degree.Support import Mathlib.Algebra.Poly...
LaurentSeries.lean
/- Copyright (c) 2021 Aaron Anderson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Anderson, María Inés de Frutos-Fernández, Filippo A. E. Nuccio -/ import Mathlib.Data.Int.Interval import Mathlib.FieldTheory.RatFunc.AsPolynomial import Mathlib.RingTheory.Binom...
morphism.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 fintype finfun bigop finset fingroup. (***********...
Pairwise.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.Logic.Function.Basic import Mathlib.Data.Set.Defs /-! # Relations holding pairwise This file defines pairwise relations. ## Main declarations * `Pa...
ChosenFiniteProducts.lean
import Mathlib.Algebra.Category.Grp.CartesianMonoidal deprecated_module (since := "2025-05-15")
ScopedNS.lean
/- Copyright (c) 2021 Gabriel Ebner. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Gabriel Ebner, Mario Carneiro -/ import Mathlib.Util.WithWeakNamespace /-! # `scoped[NS]` syntax This is a replacement for the `localized` command in mathlib. It is similar to `scoped...
MapFold.lean
/- Copyright (c) 2015 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Data.List.Perm.Basic import Mathlib.Data.Multiset.Replicate import Mathlib.Data.Set.List /-! # Mapping and folding multisets ## Main definitio...
Elab.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 Mathlib.Tactic.FunProp.Core /-! ## `funProp` tactic syntax -/ namespace Mathlib open Lean Meta Elab Tactic namespace Meta.FunProp open Lean.Parser.Tactic /-...
ExactFunctor.lean
/- Copyright (c) 2023 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou, Jujian Zhang -/ import Mathlib.Algebra.Homology.ShortComplex.PreservesHomology import Mathlib.Algebra.Homology.ShortComplex.ShortExact import Mathlib.Algebra.Homology.ShortComple...
LimitsOfProductsAndEqualizers.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.Limits.Constructions.BinaryProducts import Mathlib.CategoryTheory.Limits.Constructions.Equalizers import Mathlib.CategoryTheor...
Lemmas.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.Field.Rat import Mathlib.Algebra.Group.Indicator import Mathlib.Algebra.GroupWithZero.Action.End import Mathlib.Algebra...
Linear.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.Analytic.Basic import Mathlib.Analysis.Analytic.CPolynomialDef /-! # Linear functions are analytic In this file we prove that a `Continuou...
StandardSmooth.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.RingTheory.LocalProperties.Basic import Mathlib.RingTheory.Smooth.StandardSmooth import Mathlib.Tactic.Algebraize /-! # Standard smooth ring homom...
Asymptotics.lean
/- Copyright (c) 2024 Lawrence Wu. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Lawrence Wu -/ import Mathlib.MeasureTheory.Group.Measure import Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap /-! # Bounding of integrals by asymptotics We establish integ...
Add.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Johannes Hölzl -/ import Mathlib.MeasureTheory.Constructions.BorelSpace.Real import Mathlib.MeasureTheory.Integral.Lebesgue.Basic /-! # Monotone convergence theorem an...
Floor.lean
/- Copyright (c) 2022 Yuyang Zhao. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yuyang Zhao -/ import Mathlib.Algebra.Order.Floor.Semiring import Mathlib.Order.Filter.AtTopBot.Finite /-! # `a * c ^ n < (n - d)!` holds true for sufficiently large `n`. -/ open Filter...
Convolution.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.Analysis.Convolution import Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension import Mathlib.Analysis.Calculus.BumpFunction.Normed import Math...
Basic.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.Tactic.Abel import Mathlib.Algebra.Ring.Opposite import Mathlib.GroupTheory.GroupAction.SubMulAction import Mathlib.RingTheory.Congruence.Opposite /-! # ...
ClosureSwap.lean
/- Copyright (c) 2024 Thomas Browning, Junyan Xu. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Thomas Browning, Junyan Xu -/ import Mathlib.Algebra.Group.Subgroup.Ker import Mathlib.GroupTheory.GroupAction.Basic import Mathlib.GroupTheory.GroupAction.FixedPoints impo...
IsIntegrallyClosed.lean
/- Copyright (c) 2019 Riccardo Brasca. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Riccardo Brasca, Paul Lezeau, Junyan Xu -/ import Mathlib.RingTheory.AdjoinRoot import Mathlib.FieldTheory.Minpoly.Field import Mathlib.RingTheory.Polynomial.GaussLemma /-! # Minimal...
AlexandrovDiscrete.lean
/- Copyright (c) 2023 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Data.Set.Image import Mathlib.Topology.Bases import Mathlib.Topology.Inseparable import Mathlib.Topology.Compactness.NhdsKer /-! # Alexandrov-discrete top...
IsCoprime.lean
/- Copyright (c) 2023 Kyle Miller. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kyle Miller -/ import Mathlib.RingTheory.Coprime.Lemmas import Mathlib.Tactic.NormNum.GCD /-! # `norm_num` extension for `IsCoprime` This module defines a `norm_num` extension for `IsCo...
div.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. (******************************************************************************) (* Th...
Definitions.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.MonoidAlgebra.Degree import Mathlib.Algebra.Order.Ring.WithTop import Mathlib.Algebra.Polynomial.Basi...
Basic.lean
/- Copyright (c) 2018 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Johan Commelin, Bhavik Mehta -/ import Mathlib.CategoryTheory.Iso import Mathlib.CategoryTheory.Functor.Category import Mathlib.CategoryTheory.EqToHom import Mathlib.Catego...
Monoidal.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.BigOperators.Fin import Mathlib.CategoryTheory.Monoidal.Linear import Mathlib.CategoryTheory.Monoidal.Rigid.FunctorCategory import Mathlib.Category...
AsTensorProduct.lean
/- Copyright (c) 2024 Judith Ludwig, Christian Merten. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Judith Ludwig, Christian Merten -/ import Mathlib.Algebra.Homology.ShortComplex.ModuleCat import Mathlib.CategoryTheory.Abelian.DiagramLemmas.Four import Mathlib.Linea...
character.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 choice ssrnat seq. From mathcomp Require Import path div fintype...
Stability.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.RingTheory.Flat.Basic import Mathlib.RingTheory.IsTensorProduct import Mathlib.LinearAlgebra.TensorProduct.Tower import Mathlib.RingTheory.Localiza...
Basic.lean
/- Copyright (c) 2019 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau -/ import Mathlib.Algebra.CharP.Defs import Mathlib.Algebra.MvPolynomial.CommRing import Mathlib.Algebra.MvPolynomial.Equiv import Mathlib.Algebra.Polynomial.BigOperators import M...
Polynomial.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.RingTheory.Kaehler.Basic import Mathlib.Algebra.MvPolynomial.PDeriv import Mathlib.Algebra.Polynomial.Derivation /-! # The Kaehler differential module of po...
HomEquiv.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.Embedding.Restriction import Mathlib.Algebra.Homology.Embedding.Extend import Mathlib.Algebra.Homology.Embedding.Boundary import Mathlib.Categor...
Yoneda.lean
/- Copyright (c) 2018 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.Limits.Types.Limits /-! # Cones and limits In this file, we give the natural isomorphism between cones on `F` with cone point...
OfFixingSubgroup.lean
/- Copyright (c) 2025 Antoine Chambert-Loir. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Antoine Chambert-Loir -/ import Mathlib.Data.Finite.Card import Mathlib.Data.Set.Card import Mathlib.GroupTheory.GroupAction.FixingSubgroup import Mathlib.GroupTheory.GroupActi...
NormLeOne.lean
/- Copyright (c) 2025 Xavier Roblot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Xavier Roblot -/ import Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone import Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord import Mathlib.NumberTh...
Basic.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl -/ import Mathlib.Logic.Function.Defs import Mathlib.Logic.Function.Iterate import Aesop import Mathlib.Tactic.Inhabit /-! # Extra facts about `Prod` This file proves ...
ENNReal.lean
/- Copyright (c) 2024 Edward van de Meent. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Edward van de Meent -/ import Mathlib.Data.Real.ENatENNReal import Mathlib.Data.Set.Card import Mathlib.Topology.Instances.ENNReal.Lemmas /-! # Infinite sums of ENNReal and Set.e...
Exact.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.Algebra.Exact import Mathlib.LinearAlgebra.Basis.Basic /-! # Basis from a split exact sequence Let `0 → K → M → P → 0` be a split exact sequence ...
derive_encodable.lean
import Mathlib.Tactic.DeriveEncodable /-! # Tests for the `Encodable` deriving handler -/ /-! Structures -/ structure Struct where x : Nat y : Bool deriving Encodable example : Encodable Struct := inferInstance /-! Inductive types with parameters -/ inductive T (α : Type) where | a (x : α) (y : Bool) (z :...
Construction.lean
import Mathlib.Algebra.Algebra.Rat import Mathlib.FieldTheory.SplittingField.Construction universe u v w open Polynomial variable {F : Type u} {K : Type v} {L : Type w} variable [Field K] [Field L] [Field F] variable (f : K[X]) -- The algebra instance deriving from `K` should be definitionally equal to that -- de...
eqtype.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool. (********************************************************************...
IndicatorFunction.lean
/- Copyright (c) 2020 Zhouhang Zhou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Zhouhang Zhou, Yury Kudryashov -/ import Mathlib.Algebra.Group.Indicator import Mathlib.Order.CompleteLattice.Finset import Mathlib.Order.ConditionallyCompleteLattice.Basic import Mathl...
ContDiff.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 Mathlib.Analysis.Calculus.IteratedDeriv.Lemmas import Mathlib.Analysis.SpecialFunctions.ExpDeriv import Mathlib.Analysis.SpecialFunctions.Log.Deriv import Mathli...
eqtype.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool. (********************************************************************...
BigOperators.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.BigOperators.Group.Multiset.Basic import Mathlib.Algebra.BigOperators.Group.List.Lemmas import Mathlib.GroupTheory.Congruence.Defs impor...
FiniteMeasureExt.lean
/- Copyright (c) 2024 Jakob Stiefel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jakob Stiefel -/ import Mathlib.Analysis.RCLike.BoundedContinuous import Mathlib.Analysis.SpecialFunctions.MulExpNegMulSqIntegral import Mathlib.MeasureTheory.Measure.HasOuterApproxClos...
StdSimplex.lean
/- Copyright (c) 2021 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Kim Morrison, Adam Topaz, Joël Riou -/ import Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex import Mathlib.CategoryTheory.Subpresheaf.OfSection import Mathlib.Catego...
Basic.lean
import Mathlib.CategoryTheory.Monoidal.Cartesian.Basic deprecated_module (since := "2025-05-08")
Conv.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.Tactic.Conv.Basic import Lean.Elab.Command /-! Additional `conv` tactics. -/ namespace Mathlib.Tactic.Conv open Lean Parser.Tacti...
Unitary.lean
/- Copyright (c) 2025 Jireh Loreaux. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jireh Loreaux -/ import Mathlib.Algebra.Star.Unitary import Mathlib.Topology.Algebra.Group.Defs import Mathlib.Topology.Algebra.Star import Mathlib.Topology.Algebra.Monoid /-! # `unita...
Limits.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.Limits.Shapes.Pullback.CommSq /-! # Lifting properties and (co)limits In this file, we show some consequences of lifting properties in the p...
Saturated.lean
/- Copyright (c) 2021 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.Algebra.Group.Subgroup.Ker import Mathlib.Algebra.NoZeroSMulDivisors.Defs /-! # Saturated subgroups ## Tags subgroup, subgroups -/ namespace Subgr...
Sigma.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.EquivFin import Mathlib.Data.Fintype.Sigma /-! # Finiteness of sigma types -/ variable {α : Type*} namespace Finite instance {β : α → Type*}...
Measurability.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.Measurability.Init import Mathlib.Algebra.Group.Defs /-! # Measurability We define the `measurability` tactic using `aesop`. -/ open Lean.Parser.T...
Combinators.lean
/- Copyright (c) 2016 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Leonardo de Moura -/ import Mathlib.Init /-! # Monad combinators, as in Haskell's Control.Monad. -/ universe u v w /-- Collapses two layers of monadic structur...
finalg.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import fintype finset f...
Skolem.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.ElementarySubstructures /-! # Skolem Functions and Downward Löwenheim–Skolem ## Main Definitions - `FirstOrder.Language.skolem₁` is a la...
morphism.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 fintype finfun bigop finset fingroup. (***********...
Int.lean
/- Copyright (c) 2025 María Inés de Frutos-Fernández, Filippo A. E. Nuccio. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: María Inés de Frutos-Fernández, Filippo A. E. Nuccio -/ import Mathlib.Algebra.Group.Int.Defs import Mathlib.Algebra.GroupWithZero.WithZero /-! #...
PID.lean
/- Copyright (c) 2024 Riccardo Brasca. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Riccardo Brasca -/ import Mathlib.NumberTheory.NumberField.ClassNumber import Mathlib.NumberTheory.Cyclotomic.Rat import Mathlib.NumberTheory.Cyclotomic.Embeddings /-! # Cyclotomic ...
Defs.lean
/- Copyright (c) 2020 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Logic.Function.Defs import Mathlib.Tactic.TypeStar /-! # Nontrivial types A type is *nontrivial* if it contains at least two elements. This is ...
Mat.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.Algebra.BigOperators.Group.Finset.Pi import Mathlib.Algebra.BigOperators.Pi import Mathlib.Algebra.Opposites import Mathlib.Algebra.Ring.Opposite import Ma...
ULift.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.Logic.Function.ULift import Mathlib.Order.Basic /-! # Ordered structures on `ULift.{v} α` Once these basic instances are setup, the instances of more compl...
HopkinsLevitzki.lean
/- Copyright (c) 2025 Junyan Xu. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Junyan Xu -/ import Mathlib.Algebra.Module.Torsion import Mathlib.RingTheory.FiniteLength import Mathlib.RingTheory.Noetherian.Nilpotent import Mathlib.RingTheory.Spectrum.Prime.Noetherian ...
Algebra.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.Defs import Mathlib.Algebra.Polynomial.Eval.Defs /-! # Evaluation of polynomials in an algeb...
Pullback.lean
/- Copyright (c) 2024 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Analysis.Calculus.VectorField import Mathlib.Geometry.Manifold.ContMDiffMFDeriv import Mathlib.Geometry.Manifold.MFDeriv.NormedSpace import Mathl...
Prod.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.Ring.Prod import Mathlib.Algebra.Star.Basic /-! # Basic Results about Star on Product Type This file provides basic results about the star on produ...
Rat.lean
/- Copyright (c) 2019 Robert Y. Lewis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Kim Morrison -/ import Mathlib.Init import Batteries.Data.Rat.Basic import Batteries.Tactic.Alias /-! # Additional operations on Expr and rational numbers This file ...
IsConjRoot.lean
/- Copyright (c) 2024 Jiedong Jiang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jiedong Jiang -/ import Mathlib.FieldTheory.Extension import Mathlib.FieldTheory.IntermediateField.Adjoin.Basic import Mathlib.FieldTheory.Minpoly.Basic import Mathlib.FieldTheory.Norma...
frobenius.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 div. From mathcomp Require Import fintype bigop prime finset fingroup morphism. From mathcom...
Defs.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Yury Kudryashov -/ import Mathlib.Algebra.Group.Action.Opposite import Mathlib.Algebra.GroupWithZero.Hom import Mathlib.Algebra.GroupWithZero.Opposite import Mathlib.Algebr...
Union.lean
/- Copyright (c) 2025 Oliver Butterley. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Butterley -/ import Mathlib.Data.Finset.Range import Mathlib.Data.Set.Lattice import Mathlib.Order.Interval.Set.LinearOrder /-! # Extra lemmas about unions of intervals This...
quotient.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq div. From mathcomp Require Import choice fintype prim...
Basic.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.Hom import Mathlib.RingTheory.LocalRing.MaximalIdeal.Basic import Mathlib.RingTheory.Ideal.Maps /-! # Local r...
Ideal.lean
/- Copyright (c) 2021 Jujian Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jujian Zhang, Eric Wieser -/ import Mathlib.LinearAlgebra.Finsupp.SumProd import Mathlib.RingTheory.GradedAlgebra.Basic import Mathlib.RingTheory.Ideal.Basic import Mathlib.RingTheory.Id...
IntegralNormalization.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, Andrew Yang, Yuyang Zhao -/ import Mathlib.Algebra.Polynomial.Monic import Mathlib.RingTheory.Polynomial.ScaleRoots /-! # The...
Separation.lean
/- Copyright (c) 2022 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta, Yaël Dillies -/ import Mathlib.Analysis.Convex.Cone.Extension import Mathlib.Analysis.Convex.Gauge import Mathlib.Topology.Algebra.Module.FiniteDimension import Mathlib.Top...
Lemmas.lean
/- Copyright (c) 2021 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne, Sébastien Gouëzel -/ import Mathlib.Analysis.Normed.Operator.BoundedLinearMaps import Mathlib.Dynamics.Ergodic.MeasurePreserving import Mathlib.MeasureTheory.Function.Stron...
ComposableArrows.lean
/- Copyright (c) 2024 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou, Andrew Yang -/ import Mathlib.CategoryTheory.ComposableArrows import Mathlib.CategoryTheory.Localization.CalculusOfFractions /-! # Essential surjectivity of the functor induced ...
Path.lean
/- Copyright (c) 2021 David Wärn,. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Wärn, Kim Morrison, Matteo Cipollina -/ import Mathlib.Combinatorics.Quiver.Prefunctor import Mathlib.Logic.Lemmas import Batteries.Data.List.Basic /-! # Paths in quivers Given a...
Closure.lean
/- Copyright (c) 2019 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Yaël Dillies -/ import Mathlib.GroupTheory.Perm.Cycle.Basic /-! # Closure results for permutation groups * This file contains several closure results: * `closure_isCycle...
Colimits.lean
/- Copyright (c) 2019 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.Algebra.Category.MonCat.Basic import Mathlib.CategoryTheory.Limits.HasLimits import Mathlib.CategoryTheory.ConcreteCategory.Elementwise /-! # The category...
character.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 choice ssrnat seq. From mathcomp Require Import path div fintype...
ssrnotations.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) (******************************************************************************) (* - Reserved notation for various arithmetic and algebraic operations: ...
Defs.lean
/- Copyright (c) 2019 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau -/ import Mathlib.Algebra.Polynomial.Degree.Definitions import Mathlib.Algebra.Polynomial.Eval.Defs import Mathlib.Tactic.Algebraize /-! # Integral closure of a subring. If A is...
MulOppositeLemmas.lean
/- Copyright (c) 2022 Alex Kontorovich. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Alex Kontorovich, Eric Wieser -/ import Mathlib.Algebra.Group.Subgroup.Basic import Mathlib.Algebra.Group.Subgroup.MulOpposite import Mathlib.Algebra.Group.Submonoid.MulOpposite impo...
fingraph.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat. From mathcomp Require Import seq path fintype. (******************************************...
Presheaf.lean
/- Copyright (c) 2023 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Joël Riou -/ import Mathlib.Algebra.Category.ModuleCat.ChangeOfRings import Mathlib.Algebra.Category.Ring.Basic /-! # Presheaves of modules over a presheaf of rings. Give...
all_order.v
Require Export order.
Defs.lean
/- Copyright (c) 2014 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Leonardo de Moura, Simon Hudon, Mario Carneiro -/ import Batteries.Logic import Mathlib.Algebra.Regular.Defs import Mathlib.Data.Int.Notation import Mathlib.Data.Nat.Bina...