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fintype.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 ssrnotations eqtype. From mathcomp Require Import ssrnat seq choice pat...
Locus.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.Spectrum.Prime.Topology import Mathlib.RingTheory.Etale.Kaehler import Mathlib.RingTheory.Support /-! # Unramified locus of an algebra ## Main r...
CommMon_.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.CategoryTheory.Monoidal.Cartesian.Mon_ /-! # Yoneda embedding of `CommMon_ C` -/ assert_not_exists MonoidWithZero open CategoryTheory MonoidalCategory Lim...
FreeNonUnitalNonAssocAlgebra.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.Free import Mathlib.Algebra.MonoidAlgebra.Basic /-! # Free algebras Given a semiring `R` and a type `X`, we construct the free non-unital, non-asso...
EssentialImage.lean
/- Copyright (c) 2020 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta -/ import Mathlib.CategoryTheory.NatIso import Mathlib.CategoryTheory.ObjectProperty.ClosedUnderIsomorphisms import Mathlib.CategoryTheory.ObjectProperty.FullSubcategory /-...
superscript.lean
import Mathlib.Util.Superscript import Mathlib.Tactic.UnsetOption import Lean.PrettyPrinter section local syntax:arg term:max noWs superscript(term) : term local macro_rules | `($a:term$b:superscript) => `($a ^ $b) variable (foo : Nat) example : 2² = 4 := rfl example : 2¹⁶ = 65536 := rfl example (n : Nat) : n⁽²⁻¹⁾ ⁺...
Sqrt.lean
/- Copyright (c) 2014 Floris van Doorn (c) 2016 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro -/ import Mathlib.Data.Nat.Basic import Batteries.Data.Nat.Basic /-! # Properties o...
Coeff.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.CharP.Defs import Mathlib.Algebra.MonoidAlgebra.Support import Mathlib.Algebra.Polynomial.Basic impor...
Final.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.Join.Basic import Mathlib.CategoryTheory.Limits.Final import Mathlib.CategoryTheory.Limits.IsConnected /-! # (Co)Finality of the inclusio...
gproduct.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 bigo...
Continuity.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.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Isometric import Mathlib.Topology.MetricSpace.UniformConvergence import Mathlib.Topology.UniformSpace...
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...
Basic.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, Andrew Yang -/ import Mathlib.GroupTheory.OreLocalization.OreSet import Mathlib.Tactic.Common import Mathlib.Algebra.Group.Submonoid.MulAction import ...
Pointwise.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.Group.Finsupp import Mathlib.Algebra.Module.Defs import Mathlib.Algebra.Ring.InjSurj import Mathlib.Algebra.Ring.Pi /-! # The pointwise product on...
Qq.lean
/- Copyright (c) 2023 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Alex J. Best, Yaël Dillies -/ import Mathlib.Init import Qq /-! # Extra `Qq` helpers This file contains some additional functions for using the quote4 library more conven...
algC.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun ssrnat eqtype seq choice. From mathcomp Require Import div fintype path...
NatFib.lean
/- Copyright (c) 2023 Kyle Miller. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kyle Miller, Mario Carneiro -/ import Mathlib.Data.Nat.Fib.Basic import Mathlib.Tactic.NormNum /-! # `norm_num` extension for `Nat.fib` This `norm_num` extension uses a strategy paralle...
ThickenedIndicator.lean
/- Copyright (c) 2022 Kalle Kytölä. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kalle Kytölä -/ import Mathlib.Data.ENNReal.Lemmas import Mathlib.Topology.MetricSpace.Thickening import Mathlib.Topology.ContinuousMap.Bounded.Basic /-! # Thickened indicators This fi...
ApplyCongr.lean
/- Copyright (c) 2020 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Lucas Allen, Kim Morrison -/ import Mathlib.Tactic.Conv /-! ## Introduce the `apply_congr` conv mode tactic. `apply_congr` will apply congruence lemmas inside `conv` mode. It is parti...
Analytic.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.CPolynomial import Mathlib.Analysis.Analytic.Inverse import Mathlib.Analysis.Analytic.Within import Mathlib.Analysis.Calculus.Deriv...
HasIterationOfShape.lean
/- Copyright (c) 2024 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.CategoryTheory.Limits.Comma import Mathlib.CategoryTheory.Limits.FunctorCategory.Basic import Mathlib.CategoryTheory.Limits.Shapes.Preorder.Basic import Mathlib....
LowerUpperTopology.lean
/- Copyright (c) 2023 Christopher Hoskin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christopher Hoskin -/ import Mathlib.Order.Hom.CompleteLattice import Mathlib.Topology.Homeomorph.Defs import Mathlib.Topology.Order.Lattice /-! # Lower and Upper topology This f...
Commutator.lean
/- Copyright (c) 2022 Thomas Browning. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Thomas Browning -/ import Mathlib.Algebra.Group.Defs import Mathlib.Data.Bracket /-! # The bracket on a group given by commutator. -/ assert_not_exists MonoidWithZero DenselyOrdered...
Change.lean
/- Copyright (c) 2023 Damiano Testa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damiano Testa -/ import Mathlib.Init import Lean.Elab.Tactic.ElabTerm import Lean.Meta.Tactic.TryThis /-! # Tactic `change? term` This tactic is used to suggest a replacement of the ...
finsupp_notation.lean
import Mathlib.Data.Finsupp.Notation import Mathlib.Data.DFinsupp.Notation -- to ensure it does not interfere import Mathlib.Data.Nat.Factorization.Basic example : (fun₀ | 1 => 3) 1 = 3 := by simp example : (fun₀ | 1 | 2 | 3 => 3 | 3 => 4) 1 = 3 := by simp example : (fun₀ | 1 | 2 | 3 => 3 | 3 => 4) 2 = 3 := by ...
Char.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Data.Nat.Basic import Mathlib.Order.Defs.LinearOrder /-! # More `Char` instances This file provides a `LinearOrder` instance on `Char`. `Char` is the...
Continuous.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.Action.Basic import Mathlib.Topology.Algebra.MulAction import Mathlib.Topology.Category.TopCat.Basic import Mathlib.Topology.Algebra...
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...
PowerBasis.lean
/- Copyright (c) 2021 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen -/ import Mathlib.RingTheory.Adjoin.Basic import Mathlib.RingTheory.PowerBasis import Mathlib.LinearAlgebra.Matrix.Basis /-! # Power basis for `Algebra.adjoin R {x}` This fi...
InducedMaps.lean
/- Copyright (c) 2022 Praneeth Kolichala. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Praneeth Kolichala -/ import Mathlib.Topology.Homotopy.Equiv import Mathlib.CategoryTheory.Equivalence import Mathlib.AlgebraicTopology.FundamentalGroupoid.Product /-! # Homotopic...
Basic.lean
/- Copyright (c) 2020 Joseph Myers. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joseph Myers, Manuel Candales -/ import Mathlib.Analysis.InnerProductSpace.Subspace import Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse /-! # Angles between vectors This fil...
Tensor.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.Module.Presentation.Basic import Mathlib.LinearAlgebra.TensorProduct.Basic /-! # Presentation of the tensor product of two modules Given presentations ...
Equalizer.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.Reflexive import Mathlib.CategoryTheory.Limits.Shapes.SplitEqualizer import Mathlib.CategoryTheory.Monad.Algebra /-! # Special ...
Monotone.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.Order.BoundedOrder.Basic import Mathlib.Order.Monotone.Basic /-! # Monotone functions on bounded orders -/ assert_not_exists SemilatticeSup open Fu...
ProperConstSMul.lean
/- Copyright (c) 2023 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Topology.Algebra.ConstMulAction import Mathlib.Topology.Maps.Proper.Basic /-! # Actions by proper maps In this file we define `ProperConstSMul M X` ...
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...
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...
Inversion.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.MeasureTheory.Integral.PeakFunction import Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform /-! # Fourier inversion formula In a fin...
Basic.lean
/- Copyright (c) 2018 Mario Carneiro, Kevin Buzzard. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Kevin Buzzard -/ import Mathlib.Algebra.Order.PartialSups import Mathlib.LinearAlgebra.Quotient.Basic import Mathlib.RingTheory.Noetherian.Defs import Ma...
Equicontinuity.lean
/- Copyright (c) 2022 Anatole Dedecker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anatole Dedecker -/ import Mathlib.Topology.UniformSpace.Equicontinuity import Mathlib.Topology.MetricSpace.Pseudo.Lemmas /-! # Equicontinuity in metric spaces This files contains ...
ExistsUnique.lean
/- Copyright (c) 2014 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Leonardo de Moura, Jeremy Avigad, Floris van Doorn -/ import Mathlib.Tactic.TypeStar import Batteries.Tactic.Alias /-! # `ExistsUnique` This file defines the `ExistsUnique` pr...
ProjectiveFamilyContent.lean
/- Copyright (c) 2025 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne, Peter Pfaffelhuber -/ import Mathlib.MeasureTheory.Constructions.Projective import Mathlib.MeasureTheory.Measure.AddContent import Mathlib.MeasureTheory.SetAlgebra /-! # A...
Bitwise.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.Algebra.Ring.Int.Defs import Mathlib.Data.Nat.Bitwise import Mathlib.Data.Nat.Size import Batteries.Data.Int /-! # Bitwise operations on integers Possi...
Sigma.lean
/- Copyright (c) 2023 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Topology.CompactOpen /-! # Equivalence between `C(X, Σ i, Y i)` and `Σ i, C(X, Y i)` If `X` is a connected topological space, then for every contin...
Basic.lean
/- Copyright (c) 2019 Alexander Bentkamp. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Alexander Bentkamp, Yury Kudryashov, Yaël Dillies -/ import Mathlib.Algebra.Order.BigOperators.Ring.Finset import Mathlib.Algebra.Order.Module.OrderedSMul import Mathlib.Algebra.Or...
AnalyticManifold.lean
/- Copyright (c) 2023 Michael Lee. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Lee, Geoffrey Irving -/ import Mathlib.Deprecated.AnalyticManifold deprecated_module "Analytic manifolds are deprecated, use `IsManifold I ω M`" (since := "2025-04-13") set_op...
Monomorphisms.lean
/- Copyright (c) 2025 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.CategoryTheory.Abelian.GrothendieckCategory.Basic import Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Colim import Mathlib.CategoryTheory.MorphismProperty.T...
Yoneda.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.Limits.Preserves.Ulift import Mathlib.CategoryTheory.Limits.FunctorToTypes /-! # Yoneda preserves certain colimits Given a bifunctor `F ...
Complex.lean
/- Copyright (c) 2022 Heather Macbeth. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Heather Macbeth -/ import Mathlib.Analysis.Complex.AbsMax import Mathlib.Analysis.LocallyConvex.WithSeminorms import Mathlib.Geometry.Manifold.MFDeriv.Basic import Mathlib.Topology.Lo...
Evaluation.lean
/- Copyright (c) 2024 Antoine Chambert-Loir, María Inés de Frutos Fernández. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Antoine Chambert-Loir, María Inés de Frutos-Fernández -/ import Mathlib.Algebra.MvPolynomial.CommRing import Mathlib.RingTheory.Ideal.BigOperato...
Guide.lean
/- Copyright (c) 2023 Kyle Miller. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kyle Miller -/ /-! # Guide: Conversion mode tactic This is a curated guide to point you toward how `conv` mode works and what tactics are available. It is not meant to be comprehensive,...
Ulift.lean
/- Copyright (c) 2023 Dagur Asgeirsson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Dagur Asgeirsson, Junyan Xu, Sophie Morel -/ import Mathlib.CategoryTheory.Limits.Creates import Mathlib.CategoryTheory.Limits.Types.Limits import Mathlib.CategoryTheory.Limits.Types...
Curry.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.Analysis.NormedSpace.Multilinear.Basic import Mathlib.LinearAlgebra.Multilinear.Curry /-! # Currying and uncurrying continuous multilinear maps ...
Basic.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Michael Stoll -/ import Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.Basic /-! # Legendre symbol This file contains results about Legendre symbols. We define the Le...
order.v
(* (c) Copyright 2006-2019 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq. From mathcomp Require Import path fintype tup...
InfiniteSum.lean
/- Copyright (c) 2021 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, Heather Macbeth, Johannes Hölzl, Yury Kudryashov -/ import Mathlib.Algebra.BigOperators.Intervals import Mathlib.Analysis.Normed.Group.Uniform import Mathlib.Topo...
AtPrime.lean
/- Copyright (c) 2025 Yongle Hu. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yongle Hu -/ import Mathlib.Algebra.Module.LocalizedModule.Basic import Mathlib.RingTheory.Ideal.Prime /-! # Localizations of modules at the complement of a prime ideal -/ /-- Given a pri...
Finite.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.Module.Presentation.Basic import Mathlib.Algebra.Module.FinitePresentation /-! # Characterization of finitely presented modules A module is finitely pr...
HasColimits.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.Geometry.RingedSpace.PresheafedSpace import Mathlib.Topology.Category.TopCat.Limits.Basic import Mathlib.Topology.Sheaves.Limits import Mathlib.CategoryThe...
Reflection.lean
/- Copyright (c) 2024 Dagur Asgeirsson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Dagur Asgeirsson -/ import Mathlib.CategoryTheory.Adjunction.Restrict import Mathlib.CategoryTheory.Closed.Monoidal import Mathlib.CategoryTheory.Monad.Adjunction import Mathlib.Cate...
CharPZeroNeCharZero.lean
/- Copyright (c) 2022 Damiano Testa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damiano Testa, Eric Wieser -/ import Mathlib.Algebra.CharP.Lemmas import Mathlib.Algebra.Ring.PUnit /-! # `CharP R 0` and `CharZero R` need not coincide for semirings For rings, the t...
Monadicity.lean
/- Copyright (c) 2020 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta -/ import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equalizers import Mathlib.CategoryTheory.Limits.Shapes.Reflexive import Mathlib.CategoryTheory.Monad.Coequalizer imp...
LTSeries.lean
/- Copyright (c) 2025 Yongle Hu. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yongle Hu -/ import Mathlib.RingTheory.Ideal.KrullsHeightTheorem /-! # Lemmas about `LTSeries` in the prime spectrum ## Main results * `PrimeSpectrum.exist_ltSeries_mem_one_of_mem_last`:...
Indicator.lean
/- Copyright (c) 2020 Zhouhang Zhou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Zhouhang Zhou -/ import Mathlib.Algebra.Notation.Support import Mathlib.Data.Set.Piecewise /-! # Indicator function This file defines the indicator function of a set. More lemmas can ...
AddTorsorBases.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.Analysis.Normed.Module.FiniteDimension import Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional /-! # Bases in normed affine spaces. This file contains r...
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...
LinearLowerBound.lean
/- Copyright (c) 2024 Yaël Dillies, Patrick Luo, Eric Rodriguez. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Patrick Luo, Eric Rodriguez -/ import Mathlib.Algebra.Group.Action.Pointwise.Finset import Mathlib.Algebra.Group.Subgroup.Pointwise import Math...
ssrnum.v
From mathcomp Require Export orderedzmod. From mathcomp Require Export numdomain. From mathcomp Require Export numfield. Module Num. Export orderedzmod.Num. Export numdomain.Num. Export numfield.Num. Module Theory. Export orderedzmod.Num.Theory. Export numdomain.Num.Theory. Export numfield.Num.Theory. End Theory. Mo...
Imo2024Q1.lean
/- Copyright (c) 2024 Joseph Myers. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joseph Myers -/ import Mathlib.Algebra.BigOperators.Intervals import Mathlib.Algebra.BigOperators.Ring.Finset import Mathlib.Algebra.Order.BigOperators.Group.LocallyFinite import Mathlib...
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, Joey van Langen, Casper Putz -/ import Mathlib.Data.Nat.Cast.Basic import Mathlib.Data.Nat.Find import Mathlib.Data.Nat.Prime.Defs import Mathlib.Data.Int.Cast.Basic import Mathl...
Balance.lean
/- Copyright (c) 2023 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.BigOperators.Expect /-! # Balancing a function This file defines the balancing of a function `f`, defined as `f` minu...
Basic.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.Order.ConditionallyCompleteLattice.Basic import Mathlib.Order.Cover import Mathlib.Order.Iterate /-! # Successor and predecessor This file defines succes...
Slice.lean
import Mathlib.Tactic.CategoryTheory.Slice open CategoryTheory variable (C : Type) [Category C] (X Y Z W U : C) variable (f₁ f₂ : X ⟶ Y) (g g₁ g₂ : Y ⟶ Z) (h : Z ⟶ W) (l : W ⟶ U) set_option linter.unusedTactic false in example (hyp : f₁ ≫ g₁ = f₂ ≫ g₂) : f₁ ≫ g₁ ≫ h ≫ l = (f₂ ≫ g₂) ≫ (h ≫ l) := by conv => rhs ...
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...
galois.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div. From mathcomp Require Import choice fintype tupl...
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.RepresentationTheory.Homological.Resolution deprecated_module (since := "2025-06-14")
Symmetric.lean
/- Copyright (c) 2020 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Buzzard, Kim Morrison, Jakob von Raumer -/ import Mathlib.CategoryTheory.Monoidal.Braided.Basic import Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic /-! # The symmetric monoid...
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, Yaël Dillies, Michał Mrugała -/ import Mathlib.RingTheory.Bialgebra.Hom import Mathlib.RingTheory.Coalgebra.MonoidAlgebra /-! # The bialgebra structure on monoid...
Spread.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.Binders /-! # Macro for spread syntax (`__ := instSomething`) in structures. -/ open Lean Parser.Term Macro /- This adds support...
DiscreteValuativeRel.lean
/- Copyright (c) 2025 Yakov Pechersky. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yakov Pechersky -/ import Mathlib.Algebra.GroupWithZero.Range import Mathlib.GroupTheory.ArchimedeanDensely import Mathlib.RingTheory.Valuation.RankOne /-! # Discrete Valuative Rel...
Pushforward.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.Category.ModuleCat.Presheaf.ChangeOfRings /-! # Pushforward of presheaves of modules If `F : C ⥤ D`, the precomposition `F.op ⋙ _` induces a functor fr...
IsCardinalForSmallObjectArgument.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.SmallObject.Construction import Mathlib.CategoryTheory.SmallObject.TransfiniteIteration import Mathlib.CategoryTheory.SmallObject.TransfiniteCompo...
DiscreteTopologyNonDiscreteUniformity.lean
/- Copyright (c) 2024 Filippo A. E. Nuccio. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Filippo A. E. Nuccio -/ import Mathlib.Analysis.SpecificLimits.Basic import Mathlib.Order.Interval.Set.Basic import Mathlib.Topology.MetricSpace.Pseudo.Defs import Mathlib.Topol...
NewtonIdentities.lean
/- Copyright (c) 2023 Michael Lee. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Lee -/ import Mathlib.Algebra.Algebra.Subalgebra.Basic import Mathlib.Algebra.MvPolynomial.CommRing import Mathlib.Algebra.MvPolynomial.Rename import Mathlib.Data.Fintype.Basic im...
NoetherianSpace.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.Homeomorph.Lemmas import Mathlib.Topology.Sets.Closeds /-! # Noetherian space A Noetherian space is a topological space that satisfies any of the ...
archimedean.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import fintype bigop or...
poly.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 bigop fi...
Dist.lean
/- Copyright (c) 2014 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn, Jeremy Avigad -/ import Mathlib.Algebra.Order.Group.Nat import Mathlib.Algebra.Order.Ring.Canonical /-! # Distance function on ℕ This file defines a simple dista...
ExistsOfLE.lean
/- Copyright (c) 2021 Peter Nelson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Peter Nelson, Yaël Dillies -/ import Mathlib.Algebra.Order.Monoid.Unbundled.Basic import Mathlib.Order.MinMax /-! # Unbundled and weaker forms of canonically ordered monoids This file ...
Basis.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.Polynomial.Basic import Mathlib.LinearAlgebra.Basis.Defs /-! # Basis of a polynomial ring -/ open Module universe u variable (R : Type u) [Semiring R] n...
ZMod.lean
/- Copyright (c) 2023 Lawrence Wu. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Lawrence Wu -/ import Mathlib.Algebra.Module.LinearMap.Defs import Mathlib.Algebra.Module.Submodule.Defs import Mathlib.GroupTheory.Sylow /-! # The `ZMod n`-module structure on Abelian g...
HasCardinalLT.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.SetTheory.Cardinal.Regular /-! # The property of being of cardinality less than a cardinal Given `X : Type u` and `κ : Cardinal.{v}`, we introduce a predicate ...
Pi.lean
/- Copyright (c) 2025 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.Algebra.Regular.SMul /-! # Results about `IsRegular` and pi types -/ variable {ι α : Type*} {R : ι → Type*} namespace Pi section variable [∀ i, Mul (R i)...
classfun.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...
FunctorCategory.lean
/- Copyright (c) 2025 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.CategoryTheory.Limits.FunctorCategory.EpiMono import Mathlib.CategoryTheory.MorphismProperty.Retract import Mathlib.CategoryTheory.MorphismProperty.Limits import...
GeometryOfNumbers.lean
/- Copyright (c) 2021 Alex J. Best. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Alex J. Best -/ import Mathlib.Analysis.Convex.Body import Mathlib.Analysis.Convex.Measure import Mathlib.MeasureTheory.Group.FundamentalDomain /-! # Geometry of numbers In this file w...
Convex.lean
/- Copyright (c) 2023 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Yaël Dillies -/ import Mathlib.Analysis.Complex.ReImTopology import Mathlib.Analysis.Convex.Combination import Mathlib.Analysis.Convex.PathConnected /-! # Theorems a...
generic_quotient.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice. From mathcomp Require Import seq fintype. (*****...
Hom.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.Group.Equiv.Defs import Mathlib.Algebra.Order.Sub.Unbundled.Basic import Mathlib.Algebra.Ring.Basic import Mathlib.Order.Hom.Basic /-! # Le...
Continuous.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, Jeremy Avigad -/ import Mathlib.Topology.ClusterPt /-! # Continuity in topological spaces For topological spaces `X` and `Y`, a function `f : X → Y` a...