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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. (***********...
Over.lean
/- Copyright (c) 2018 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Reid Barton, Bhavik Mehta -/ import Mathlib.CategoryTheory.Comma.Over.Basic import Mathlib.CategoryTheory.Limits.Comma import Mathlib.CategoryTheory.Limits.ConeCategory...
EuclideanDist.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.InnerProductSpace.Calculus import Mathlib.Analysis.InnerProductSpace.PiL2 import Mathlib.Topology.MetricSpace.ProperSpace.Lemmas /-! # Eucl...
Basic.lean
/- Copyright (c) 2019 Simon Hudon. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Simon Hudon -/ import Mathlib.Logic.Equiv.Defs /-! # Monad ## Attributes * ext * functor_norm * monad_norm ## Implementation Details Set of rewrite rules and automation for monads in...
Equiv.lean
/- Copyright (c) 2022 Anatole Dedecker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Patrick Massot, Sébastien Gouëzel, Zhouhang Zhou, Reid Barton, Anatole Dedecker -/ import Mathlib.Logic.Equiv.Fin.Basic import Mathlib.Topology.UniformSpace.UniformEm...
finfun.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 tuple. ...
integral_char.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...
finmodule.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...
EquivFunctor.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.Logic.Equiv.Defs import Mathlib.Tactic.Convert /-! # Functions functorial with respect to equivalences An `EquivFunctor` is a function from `Type → Type`...
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...
InitialSeg.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Floris van Doorn, Violeta Hernández Palacios -/ import Mathlib.Data.Sum.Order import Mathlib.Order.Hom.Lex import Mathlib.Order.RelIso.Set import Mathlib.Order.UpperLow...
Hom.lean
/- Copyright (c) 2022 Heather Macbeth. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Heather Macbeth, Floris van Doorn -/ import Mathlib.Topology.VectorBundle.Basic /-! # The vector bundle of continuous (semi)linear maps We define the (topological) vector bundle of ...
Finite.lean
/- Copyright (c) 2018 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot, Johannes Hölzl -/ import Mathlib.GroupTheory.OrderOfElement import Mathlib.Algebra.Group.AddChar import Mathlib.Algebra.Group.TypeTags.Finite import Mathlib.Analysis.No...
FiniteType.lean
/- Copyright (c) 2025 Christian Merten, Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christian Merten, Andrew Yang -/ import Mathlib.Algebra.Category.CommAlgCat.Basic import Mathlib.CategoryTheory.MorphismProperty.Comma import Mathlib.RingTheory.FinitePr...
Basic.lean
/- Copyright (c) 2022 Pierre-Alexandre Bazin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Pierre-Alexandre Bazin -/ import Mathlib.Algebra.Module.PID import Mathlib.Algebra.Group.TypeTags.Finite import Mathlib.Data.ZMod.QuotientRing /-! # Structure of finite(ly gen...
Real.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.Topology.Metrizable.Basic import Mathlib.Topology.Order.MonotoneContinuity import Mathlib.Topology.Order.Real /-! # `ENNReal` is metri...
RankAndCardinality.lean
/- Copyright (c) 2021 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes -/ import Mathlib.FieldTheory.IntermediateField.Adjoin.Basic import Mathlib.FieldTheory.MvRatFunc.Rank import Mathlib.RingTheory.Algebraic.Cardinality import Mathlib.RingThe...
Prod.lean
/- Copyright (c) 2018 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau, Yury Kudryashov -/ import Mathlib.Algebra.Algebra.Equiv import Mathlib.Algebra.Algebra.Hom import Mathlib.Algebra.Module.Prod /-! # The R-algebra structure on products of R-alge...
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...
Trunc.lean
/- Copyright (c) 2019 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Kenny Lau -/ import Mathlib.RingTheory.MvPowerSeries.Basic import Mathlib.Data.Finsupp.Interval import Mathlib.Algebra.MvPolynomial.Eval /-! # Formal (multivariate) ...
Matrix.lean
/- Copyright (c) 2021 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.LinearAlgebra.AffineSpace.Basis import Mathlib.LinearAlgebra.Matrix.NonsingularInverse /-! # Matrix results for barycentric co-ordinates Results about the ...
bigop.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 fintype tuple ...
CentroidHom.lean
/- Copyright (c) 2024 Christopher Hoskin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christopher Hoskin -/ import Mathlib.Algebra.Ring.CentroidHom import Mathlib.Algebra.Star.StarRingHom import Mathlib.Algebra.Star.Subsemiring import Mathlib.Algebra.Star.Basic /-...
Lemmas.lean
/- Copyright (c) 2019 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Topology.GDelta.Basic /-! # Baire spaces A topological space is called a *Baire space* if a countable intersection of dense open subsets is den...
PropEncodable.lean
/- Copyright (c) 2019 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad -/ import Mathlib.Data.W.Basic import Mathlib.Data.Fin.VecNotation /-! # W types The file `Mathlib/Data/W/Basic.lean` shows that if `α` is an encodable fintype and for e...
NonZeroDivisors.lean
/- Copyright (c) 2020 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau, Devon Tuma, Oliver Nash -/ import Mathlib.Algebra.Group.Submonoid.Membership import Mathlib.Algebra.GroupWithZero.Associated import Mathlib.Algebra.GroupWithZero.Regular import M...
Opposite.lean
/- Copyright (c) 2025 Markus Himmel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Markus Himmel -/ import Mathlib.CategoryTheory.Abelian.Yoneda import Mathlib.CategoryTheory.Generator.Abelian import Mathlib.CategoryTheory.Abelian.GrothendieckCategory.EnoughInjectives...
Epi.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.Limits.Shapes.SequentialProduct import Mathlib.CategoryTheory.Sites.Coherent.SequentialLimit import Mathlib.Condensed.Light.Limits /...
Subring.lean
/- Copyright (c) 2025 Michal Staromiejski. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michal Staromiejski -/ import Mathlib.Algebra.Ring.Subsemiring.Basic import Mathlib.Algebra.GroupWithZero.NonZeroDivisors import Mathlib.RingTheory.LocalRing.Defs /-! # Subrings ...
Defs.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Simon Hudon, Yury Kudryashov -/ import Mathlib.Data.Nat.Notation import Mathlib.Order.TypeTags /-! # Definition and notation for extended natural numbers -/ /-- Exte...
Ideal.lean
/- Copyright (c) 2020 Devon Tuma. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau, Devon Tuma, Wojciech Nawrocki -/ import Mathlib.RingTheory.Ideal.IsPrimary import Mathlib.RingTheory.Ideal.Quotient.Operations import Mathlib.RingTheory.TwoSidedIdeal.Operations...
Int.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.Module.LocalizedModule.Basic import Mathlib.Algebra.Module.Submodule.Pointwise /-! # Integer elements of a localized module This is a mi...
docs.lean
import docs.Conv.Guide import docs.Conv.Introduction
Prespectral.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.Order.Ideal import Mathlib.Topology.Sets.Compacts import Mathlib.Topology.Sets.OpenCover import Mathlib.Topology.Spectral.Hom /-! # Prespectral spaces In ...
Exponential.lean
/- Copyright (c) 2017 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Floris van Doorn, Violeta Hernández Palacios -/ import Mathlib.SetTheory.Ordinal.Family /-! # Ordinal exponential In this file we define the power function and the lo...
Exponential.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Abhimanyu Pallavi Sudhir -/ import Mathlib.Algebra.CharP.Defs import Mathlib.Algebra.Order.CauSeq.BigOperators import Mathlib.Algebra.Order.Star.Basic import Mathlib.Data.C...
Injective.lean
/- Copyright (c) 2022 Jujian Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jujian Zhang -/ import Mathlib.Algebra.Category.ModuleCat.EpiMono import Mathlib.Algebra.Category.Grp.ZModuleEquivalence import Mathlib.Algebra.EuclideanDomain.Int import Mathlib.Algebra...
Circumcenter.lean
/- Copyright (c) 2020 Joseph Myers. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joseph Myers -/ import Mathlib.Geometry.Euclidean.Projection import Mathlib.Geometry.Euclidean.Sphere.Basic import Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid import Mathlib.Linea...
EquationalCriterion.lean
/- Copyright (c) 2024 Mitchell Lee. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mitchell Lee, Junyan Xu -/ import Mathlib.RingTheory.Flat.Basic import Mathlib.LinearAlgebra.TensorProduct.Vanishing import Mathlib.Algebra.Module.FinitePresentation /-! # The equationa...
Uniformity.lean
/- Copyright (c) 2022 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Data.Nat.Lattice import Mathlib.Data.NNReal.Basic import Mathlib.Topology.Metrizable.Basic /-! # Metrizable uniform spaces In this file we prove th...
Character.lean
/- Copyright (c) 2022 Antoine Labelle. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Antoine Labelle -/ import Mathlib.RepresentationTheory.FDRep import Mathlib.LinearAlgebra.Trace import Mathlib.RepresentationTheory.Invariants /-! # Characters of representations Th...
Bifunctor.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.TotalComplex import Mathlib.CategoryTheory.GradedObject.Bifunctor /-! # The action of a bifunctor on homological complexes Given a bifunctor `...
path.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. (******************************************************************************) (* ...
ModEq.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.Algebra.Field.Basic import Mathlib.Algebra.NoZeroSMulDivisors.Basic import Mathlib.Data.Int.ModEq import Mathlib.GroupTheory.QuotientGroup.Defs import Math...
NeZero.lean
/- Copyright (c) 2014 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Gabriel Ebner -/ import Mathlib.Data.Nat.Cast.Defs /-! # Lemmas about nonzero elements of an `AddMonoidWithOne` -/ open Nat namespace NeZero theorem one_le {n : ℕ} ...
Finsupp.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.Algebra.BigOperators.Finsupp.Basic /-! # Connection between `Submonoid.closure` and `Finsupp.prod` -/ assert_not_exists Field namespace Submonoid variabl...
Zero.lean
/- Copyright (c) 2024 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.Algebra.Order.Archimedean.Basic import Mathlib.LinearAlgebra.Charpoly.ToMatrix import Mathlib.LinearAlgebra.Determinant import Mathlib.LinearAlgebra.Ei...
VolumeOfBalls.lean
/- Copyright (c) 2023 Xavier Roblot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Xavier Roblot -/ import Mathlib.Data.Complex.FiniteDimensional import Mathlib.MeasureTheory.Constructions.HaarToSphere import Mathlib.MeasureTheory.Integral.Gamma import Mathlib.Measure...
Exact.lean
/- Copyright (c) 2022 Jujian Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang, Jujian Zhang -/ import Mathlib.Algebra.Exact import Mathlib.Algebra.Module.LocalizedModule.Basic /-! # Localization of modules is an exact functor ## Main definitions - `...
Galois.lean
/- Copyright (c) 2024 Yongle Hu. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yongle Hu, Jiedong Jiang -/ import Mathlib.NumberTheory.RamificationInertia.Basic import Mathlib.RingTheory.Invariant.Basic /-! # Ramification theory in Galois extensions of Dedekind domai...
Perfect.lean
/- Copyright (c) 2022 Felix Weilacher. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Felix Weilacher -/ import Mathlib.Topology.Perfect import Mathlib.Topology.MetricSpace.Polish import Mathlib.Topology.MetricSpace.CantorScheme import Mathlib.Topology.Metrizable.Real...
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...
Basic.lean
/- Copyright (c) 2020 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.Algebra.Algebra.Subalgebra.Basic import Mathlib.Algebra.FreeAlgebra import Mathlib.Algebra.Category.Ring.Basic import Mathlib.Algebra.Category.ModuleCat.Ba...
ConcreteCategory.lean
/- Copyright (c) 2023 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.Algebra.Homology.HomologySequence import Mathlib.Algebra.Homology.ShortComplex.ConcreteCategory /-! # Homology of complexes in concrete categories The homology...
Nth.lean
/- Copyright (c) 2021 Vladimir Goryachev. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Vladimir Goryachev, Kyle Miller, Kim Morrison, Eric Rodriguez -/ import Mathlib.Data.List.GetD import Mathlib.Data.Nat.Count import Mathlib.Data.Nat.SuccPred import M...
DualNumber.lean
/- Copyright (c) 2021 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.Algebra.TrivSqZeroExt /-! # Dual numbers The dual numbers over `R` are of the form `a + bε`, where `a` and `b` are typically elements of a commutative ring...
Sequence.lean
/- Copyright (c) 2025 Julian Berman. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Hill, Julian Berman, Austin Letson, Matej Penciak -/ import Mathlib.Algebra.Polynomial.Monic import Mathlib.LinearAlgebra.Basis.Basic /-! # Polynomial sequences We define polyn...
Finite.lean
/- Copyright (c) 2018 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau, Michael Howes, Antoine Chambert-Loir -/ import Mathlib.GroupTheory.Abelianization.Defs import Mathlib.GroupTheory.Coset.Card /-! # The abelianization of a finite group is finite...
Flag.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.Algebra.Group.Action.Pointwise.Set.Basic import Mathlib.Algebra.Order.Group.Action.End import Mathlib.Order.Preorder.Chain /-! # Action on flags Order is...
Opposite.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.Opposites /-! # Results about `IsRegular` and `MulOpposite` -/ variable {R} [Mul R] open MulOpposite @[to_additive (attr := simp)] theorem isLeftR...
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...
Triplewise.lean
/- Copyright (c) 2025 Joseph Myers, Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joseph Myers, Yaël Dillies -/ import Aesop import Mathlib.Tactic.Lemma import Mathlib.Tactic.MkIffOfInductiveProp /-! # Triplewise predicates on list. ## Main definitions...
Ker.lean
/- Copyright (c) 2020 Kexing Ying. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kexing Ying -/ import Mathlib.Algebra.Group.Subgroup.Map import Mathlib.Tactic.ApplyFun /-! # Kernel and range of group homomorphisms We define and prove results about the kernel and ra...
FixedPointFree.lean
/- Copyright (c) 2024 Thomas Browning. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Thomas Browning -/ import Mathlib.GroupTheory.Perm.Cycle.Type /-! # Fixed-point-free automorphisms This file defines fixed-point-free automorphisms and proves some basic properties....
LeftRightNhds.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, Yury Kudryashov -/ import Mathlib.Algebra.Ring.Pointwise.Set import Mathlib.Order.Filter.AtTopBot.CompleteLattice import Mathlib.Order.Filter.AtTopBot.G...
End.lean
/- Copyright (c) 2018 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Callum Sutton, Yury Kudryashov -/ import Mathlib.Algebra.Ring.Action.Group import Mathlib.Algebra.Ring.Aut /-! # Ring automorphisms This file defines the automorphism...
Schnirelmann.lean
/- Copyright (c) 2023 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Bhavik Mehta, Doga Can Sertbas -/ import Mathlib.Algebra.Order.Ring.Abs import Mathlib.Data.Nat.ModEq import Mathlib.Data.Nat.Prime.Defs import Mathlib.Data.Real.Archimedea...
Hadamard.lean
/- Copyright (c) 2023 Xavier Généreux. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Xavier Généreux -/ import Mathlib.Analysis.SpecialFunctions.Pow.Deriv import Mathlib.Analysis.Complex.PhragmenLindelof /-! # Hadamard three-lines Theorem In this file we present a ...
Functoriality.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.RepresentationTheory.Homological.GroupHomology.LowDegree /-! # Functoriality of group homology Given a commutative ring `k`, a group homomorphi...
Positivity.lean
/- Copyright (c) 2024 Michael Stoll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Birkbeck, David Loeffler, Michael Stoll -/ import Mathlib.Analysis.Complex.TaylorSeries import Mathlib.Analysis.Complex.Positivity import Mathlib.NumberTheory.ArithmeticFunction i...
MappingCone.lean
/- Copyright (c) 2023 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.Algebra.Homology.HomotopyCategory.HomComplex import Mathlib.Algebra.Homology.HomotopyCofiber /-! # The mapping cone of a morphism of cochain complexes In this ...
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: ...
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...
MeasurableEquiv.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.MeasureTheory.Group.Arithmetic /-! # (Scalar) multiplication and (vector) addition as measurable equivalences In this file we define the following ...
CommandStart.lean
/- Copyright (c) 2025 Damiano Testa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damiano Testa -/ import Mathlib.Tactic.Linter.Header /-! # The `commandStart` linter The `commandStart` linter emits a warning if * either a command does not start at the beginning ...
Terminal.lean
/- Copyright (c) 2020 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta -/ import Mathlib.CategoryTheory.Limits.Shapes.Terminal import Mathlib.CategoryTheory.Limits.Preserves.Basic /-! # Preserving terminal object Constructions to relate the n...
finfun.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 tuple. ...
all_boot.v
Require Export ssreflect. Require Export ssrbool. Require Export ssrfun. Require Export eqtype. Require Export ssrnat. Require Export seq. Require Export choice. Require Export monoid. Require Export nmodule. Require Export path. Require Export div. Require Export fintype. Require Export fingraph. Require Export tuple....
InteractiveUnfold.lean
/- Copyright (c) 2023 Jovan Gerbscheid. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jovan Gerbscheid -/ import Batteries.Lean.Position import Mathlib.Tactic.NthRewrite import Mathlib.Tactic.Widget.SelectPanelUtils import Mathlib.Lean.GoalsLocation import Mathlib.Lea...
Variance.lean
/- Copyright (c) 2022 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, Kexing Ying -/ import Mathlib.Probability.Moments.Covariance /-! # Variance of random variables We define the variance of a real-valued random variable as `Var[...
Rename.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro -/ import Mathlib.Algebra.MvPolynomial.Eval /-! # Renaming variables of polynomials This file establishes the `rename` operation on mul...
ContinuousFunctionalCalculus.lean
/- Copyright (c) 2024 Jireh Loreaux. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jireh Loreaux -/ import Mathlib.Tactic.Core import Mathlib.Tactic.FunProp import Aesop /-! # Tactics for the continuous functional calculus At the moment, these tactics are just wra...
attribute.lean
/- Copyright (c) 2024 Geoffrey Irving. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Geoffrey Irving -/ import Mathlib.Algebra.Order.Field.Basic import Mathlib.Tactic.Bound /-! ## Tests for the `@bound` attribute Verify that our heuristic for the priority of a decl...
ssrint.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq. From mathcomp Require Import fintype finfun b...
all.v
From mathcomp Require Export all_boot. From mathcomp Require Export all_order. From mathcomp Require Export all_fingroup. From mathcomp Require Export all_algebra. From mathcomp Require Export all_solvable. From mathcomp Require Export all_field. From mathcomp Require Export all_character.
EquivFin.lean
/- Copyright (c) 2017 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Data.Fintype.Card import Mathlib.Data.List.NodupEquivFin /-! # Equivalences between `Fintype`, `Fin` and `Finite` This file defines the bijection bet...
Predicate.lean
/- Copyright (c) 2022 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.CategoryTheory.Localization.Construction /-! # Predicate for localized categories In this file, a predicate `L.IsLocalization W` is introduced for a functor `...
Imo1960Q2.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.Data.Real.Sqrt /-! # IMO 1960 Q2 For what values of the variable $x$ does the following inequality hold: \[\dfrac{4x^2}{(1 - \sqrt {2x + 1})^2} < ...
IsBounded.lean
/- Copyright (c) 2018 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, Johannes Hölzl, Rémy Degenne -/ import Mathlib.Algebra.BigOperators.Group.Finset.Basic import Mathlib.Algebra.Order.Group.Unbundled.Abs import Mathlib.Algebra.Ord...
Limits.lean
/- Copyright (c) 2022 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.Algebra.Category.FGModuleCat.Basic import Mathlib.Algebra.Category.ModuleCat.EpiMono import Mathlib.Algebra.Category.ModuleCat.Limits import Mathlib.Algebr...
NatCast.lean
/- Copyright (c) 2016 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro, Johannes Hölzl, Yuyang Zhao -/ import Mathlib.Algebra.Order.Monoid.Unbundled.Basic import Mathlib.Algebra.Order.ZeroLEOne import Mathli...
Clopen.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, Yury Kudryashov -/ import Mathlib.Data.Set.Subset import Mathlib.Topology.Clopen import Mathlib.Topology.Connected.Basic /-! # Connected subsets and th...
ZMod.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes -/ import Mathlib.Algebra.Field.Basic import Mathlib.Data.ZMod.Basic /-! # `ZMod p` is a field -/ namespace ZMod variable (p : ℕ) [hp : Fact p.Prime] private theorem mul_...
Slope.lean
/- Copyright (c) 2019 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Analysis.Calculus.Deriv.Add import Mathlib.LinearAlgebra.AffineSpace.Slope import Mathlib.Topology.Algebra.Module.PerfectSpace /-! # Derivative as t...
Hofer.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.Analysis.SpecificLimits.Basic /-! # Hofer's lemma This is an elementary lemma about complete metric spaces. It is motivated by an application to the ...
Order.lean
/- Copyright (c) 2024 Antoine Chambert-Loir, María Inés de Frutos Fernandez. 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.Data.ENat.Basic import Mathlib.Data.Finsupp.Weight import Mathlib.RingTh...
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_...
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...
CharZero.lean
/- Copyright (c) 2017 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Algebra.Notation.Support import Mathlib.Data.Int.Cast.Field import Mathlib.Data.Int.Cast.Lemmas import Mathlib.Data.Int.Cast.Pi /-! # Injectivity of `...
Transfer.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.GroupTheory.Complement import Mathlib.GroupTheory.Sylow /-! # The Transfer Homomorphism In this file we construct the transfer homomorphism. ## Ma...