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IsSmall.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.MorphismProperty.Basic import Mathlib.Logic.Small.Basic /-! # Small classes of morphisms A class of morphisms `W : MorphismProperty C` is `w`-sm...
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...
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. (********************************************************************...
LieTheorem.lean
/- Copyright (c) 2024 Lucas Whitfield. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Lucas Whitfield, Johan Commelin -/ import Mathlib.Algebra.Lie.Weights.Basic import Mathlib.RingTheory.Finiteness.Nilpotent /-! # Lie's theorem for Solvable Lie algebras. Lie's theor...
LinearMap.lean
/- Copyright (c) 2019 Zhouhang Zhou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Zhouhang Zhou, Sébastien Gouëzel, Frédéric Dupuis -/ import Mathlib.Analysis.InnerProductSpace.Continuous /-! # Linear maps on inner product spaces This file studies linear maps on i...
AB.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.Algebra.Category.Grp.AB import Mathlib.Algebra.Category.ModuleCat.Colimits import Mathlib.Algebra.Module.Shrink import Mathlib.CategoryTheory.Abeli...
Away.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.Group.Submonoid.Membership import Mathlib.GroupTheory.MonoidLocalization.Basic /-! # Localizing commutative monoids away from an element...
Opposite.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.Equivalence /-! # Localization of the opposite category If a functor `L : C ⥤ D` is a localization functor for `W : MorphismProper...
center.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div. From mathcomp Require Import fintype bigop finset fingroup morphism perm. From math...
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.Module.Shrink import Mathlib.LinearAlgebra.LinearPMap import Mathlib.Logic.Small.Basic import Mathlib.RingTheory.Ideal.Defs /-! # Injective module...
ring_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 choice ssrnat. From mathcomp Require Import seq ssralg generic_q...
Limit.lean
/- Copyright (c) 2022 Violeta Hernández Palacios. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Violeta Hernández Palacios -/ import Mathlib.Order.SuccPred.Archimedean import Mathlib.Order.BoundedOrder.Lattice /-! # Successor and predecessor limits We define the pre...
Internal.lean
/- Copyright (c) 2023 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.LinearAlgebra.TensorProduct.Graded.External import Mathlib.RingTheory.GradedAlgebra.Basic /-! # Graded tensor products over graded algebras The graded tens...
mxpoly.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 div fintype tupl...
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...
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, Joey van Langen, Casper Putz -/ import Mathlib.Algebra.CharP.Defs import Mathlib.Algebra.Group.Fin.Basic import Mathlib.Algebra.Ring.ULift import Mathlib.Algebra.Ring.Opposite im...
IntegralClosure.lean
/- Copyright (c) 2020 Kenji Nakagawa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenji Nakagawa, Anne Baanen, Filippo A. E. Nuccio -/ import Mathlib.LinearAlgebra.FreeModule.PID import Mathlib.LinearAlgebra.FreeModule.Finite.Basic import Mathlib.LinearAlgebra.Bilin...
Basic.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.Category.Preorder import Mathlib.CategoryTheory.Limits.FunctorCategory.Basic import Mathlib.CategoryTheory.Limits.Shapes.Preorder.HasIterationOfSh...
Fold.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.LinearAlgebra.CliffordAlgebra.Conjugation /-! # Recursive computation rules for the Clifford algebra This file provides API for a special case `CliffordAlg...
FourierTransform.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.Algebra.Group.AddChar import Mathlib.Analysis.Complex.Circle import Mathlib.MeasureTheory.Group.Integral import Mathlib.MeasureTheory.Integral.Prod imp...
Interval.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.Data.Fintype.BigOperators import Mathlib.Data.DFinsupp.BigOperators import Mathlib.Data.DFinsupp.Order import Mathlib.Order.Interval.Finset.Basic import Ma...
BinaryRec.lean
/- Copyright (c) 2017 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Praneeth Kolichala, Yuyang Zhao -/ import Batteries.Tactic.Alias import Mathlib.Init /-! # Binary recursion on `Nat` This file defines binary recursion on `Nat...
Basic.lean
/- Copyright (c) 2025 Stefan Kebekus. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Stefan Kebekus -/ import Mathlib.Analysis.InnerProductSpace.Laplacian /-! # Harmonic Functions This file defines harmonic functions on real, finite-dimensional, inner product spaces ...
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...
Integral.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Sébastien Gouëzel, Yury Kudryashov -/ import Mathlib.MeasureTheory.Integral.Bochner.Set import Mathlib.MeasureTheory.Measure.Lebesgue.Basic import Mathlib.MeasureTheory...
HomologySequenceLemmas.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.HomologySequence import Mathlib.Algebra.Homology.QuasiIso import Mathlib.CategoryTheory.Abelian.DiagramLemmas.Four /-! # Consequences of the ho...
Defs.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.Group.Defs /-! # The integers form a group This file contains the additive group and multiplicative monoid instances on the integers. See note...
SmoothSeries.lean
/- Copyright (c) 2022 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Analysis.Calculus.ContDiff.Operations import Mathlib.Analysis.Calculus.UniformLimitsDeriv import Mathlib.Topology.Algebra.InfiniteSum.Module impo...
Rectangles.lean
/- Copyright (c) 2024 Lean FRO. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ /-! # Finding the maximal rectangles in a list of points. -/ /-- A rectangle `r` is a product of the left-closed, right-open intervals `[r.left, r.right) × [r.bottom, r.top...
AdjMatrix.lean
/- Copyright (c) 2020 Aaron Anderson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Anderson, Jalex Stark, Kyle Miller, Lu-Ming Zhang -/ import Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkCounting import Mathlib.LinearAlgebra.Matrix.Symmetric import Mathl...
binomial.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq path. From mathcomp Require Import div fintype tuple ...
interval_inference.v
(* mathcomp analysis (c) 2017 Inria and AIST. License: CeCILL-C. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype choice. From mathcomp Require Import order ssralg ssrnum ssrint interval. (**md********************************************************...
Smooth.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.AlgebraicGeometry.Morphisms.RingHomProperties import Mathlib.AlgebraicGeometry.Morphisms.FinitePresentation import Mathlib.RingTheory.RingHom.Stand...
Imo2024Q3.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.Order.Sub.Basic import Mathlib.Algebra.Ring.Parity import Mathlib.Data.Fintype.Pigeonhole import Mathlib.Data.Nat.Nth import Mathlib.Tactic.ApplyFu...
Card.lean
/- Copyright (c) 2022 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, Violeta Hernández Palacios -/ import Mathlib.MeasureTheory.MeasurableSpace.Defs import Mathlib.SetTheory.Cardinal.Regular import Mathlib.SetTheory.Cardinal.Contin...
SingleObj.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.Limits.Types.Colimits import Mathlib.CategoryTheory.Limits.Types.Limits import Mathlib.CategoryTheory.SingleObj import Mathlib.Data....
BooleanSubalgebra.lean
/- Copyright (c) 2024 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Order.Sublattice /-! # Boolean subalgebras This file defines boolean subalgebras. -/ open Function Set variable {ι : Sort*} {α β γ : Type*} variable (...
Injectivity.lean
/- Copyright (c) 2024 Michael Stoll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Stoll -/ import Mathlib.Analysis.InnerProductSpace.Basic import Mathlib.Analysis.Normed.Group.Tannery import Mathlib.NumberTheory.LSeries.Convergence import Mathlib.NumberTheory...
Ideal.lean
/- Copyright (c) 2021 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.Algebra.Lie.Submodule /-! # Lie Ideals This file defines Lie ideals, which are Lie submodules of a Lie algebra over itself. They are defined as a special c...
PathObject.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.AlgebraicTopology.ModelCategory.Basic import Mathlib.AlgebraicTopology.ModelCategory.IsCofibrant /-! # Path objects We introduce a notion of path object for an...
StoneWeierstrass.lean
/- Copyright (c) 2021 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Heather Macbeth -/ import Mathlib.Algebra.Algebra.Subalgebra.Tower import Mathlib.Analysis.RCLike.Basic import Mathlib.Topology.Algebra.Star.Real import Mathlib.Topology.Al...
IsHomeomorphicTrivialBundle.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.Constructions.SumProd /-! # Maps equivariantly-homeomorphic to projection in a product This file contains the definition `IsHomeomorph...
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 -/ import Mathlib.Algebra.Group.Action.End import Mathlib.Algebra.Group.Action.Pointwise.Set.Basic import Mathlib.Algebra.Group.Action.Prod import Mathlib.Algebra.Group.Subg...
StacksAttribute.lean
/- Copyright (c) 2024 Damiano Testa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damiano Testa -/ import Lean.Elab.Command import Mathlib.Init /-! # The `stacks` and `kerodon` attributes This allows tagging of mathlib results with the corresponding tags from the [...
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, Johan Commelin -/ import Mathlib.Algebra.Algebra.RestrictScalars import Mathlib.Algebra.Algebra.Subalgebra.Lattice import Mathlib.Algebra.Module.Rat import Mathlib.LinearAl...
ContinuousAffineEquiv.lean
/- Copyright (c) 2024 Michael Rothgang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Rothgang -/ import Mathlib.LinearAlgebra.AffineSpace.AffineEquiv import Mathlib.Topology.Algebra.Module.Equiv import Mathlib.Topology.Algebra.ContinuousAffineMap /-! # Conti...
Ext.lean
/- Copyright (c) 2018 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Kenny Lau -/ import Mathlib.Algebra.Group.Submonoid.Basic import Mathlib.Data.DFinsupp.Defs /-! # Extensionality principles for `DFinsupp` ## Main results * `DFinsupp.add...
output.v
From mathcomp Require Import all_boot all_order all_algebra all_field all_character all_fingroup all_solvable. Open Scope group_scope. Check @cyclic_pgroup_Aut_structure.
Roots.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, Johan Commelin -/ import Mathlib.Algebra.Polynomial.BigOperators import Mathlib.Algebra.Polynomial.RingDivision import Mathlib...
PrincipalIdealDomainOfPrime.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen -/ import Mathlib.RingTheory.Ideal.Colon import Mathlib.RingTheory.PrincipalIdealDomain /-! # Principal ideal domains and prime ideals # Main results - `IsPrincipalIdeal.o...
SupClosed.lean
/- Copyright (c) 2023 Yaël Dillies, Christopher Hoskin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Christopher Hoskin -/ import Mathlib.Data.Finset.Lattice.Prod import Mathlib.Data.Finset.Powerset import Mathlib.Data.Set.Finite.Basic import Mathlib.Or...
PGroup.lean
/- Copyright (c) 2018 . All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Thomas Browning -/ import Mathlib.GroupTheory.Perm.Cycle.Type import Mathlib.GroupTheory.SpecificGroups.Cyclic /-! # p-groups This file contains a proof that if `G` is a `p`-group ac...
Basic.lean
/- Copyright (c) 2022 Frédéric Dupuis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Frédéric Dupuis -/ import Mathlib.Topology.Algebra.Module.CharacterSpace import Mathlib.Analysis.Normed.Module.WeakDual import Mathlib.Analysis.Normed.Algebra.Spectrum /-! # Normed a...
ssrfun.v
From mathcomp Require Import ssreflect. From Corelib Require Export ssrfun. From mathcomp Require Export ssrnotations. #[export] Set Warnings "-overwriting-delimiting-key". (* remove above line when requiring Rocq >= 9.0 *) Set Implicit Arguments. Unset Strict Implicit. Unset Printing Implicit Defensive. (***********...
Tactic.lean
/- Copyright (c) 2022 Arthur Paulino. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Arthur Paulino, Jannis Limperg -/ import Mathlib.Init import Lean.MetavarContext /-! # Miscellaneous helper functions for tactics. [TODO] Ideally we would find good homes for everyth...
Basic.lean
/- Copyright (c) 2022 Markus Himmel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Markus Himmel -/ import Mathlib.CategoryTheory.Limits.EssentiallySmall import Mathlib.CategoryTheory.Limits.Opposites import Mathlib.CategoryTheory.Subobject.Lattice import Mathlib.Data...
TwoVariable.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.Calculus.SmoothSeries import Mathlib.Analysis.NormedSpace.OperatorNorm.Prod import Mathlib.Analysis.SpecialFunctions.Gaussian.PoissonSummation...
Snoc.lean
/- Copyright (c) 2023 Alex Keizer. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Alex Keizer -/ import Mathlib.Data.Vector.Basic /-! This file establishes a `snoc : Vector α n → α → Vector α (n+1)` operation, that appends a single element to the back of a vector....
Cast.lean
/- Copyright (c) 2021 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Data.Nat.Choose.Basic import Mathlib.Data.Nat.Factorial.Cast /-! # Cast of binomial coefficients This file allows calculating the binomial coefficient `a...
spectral.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat. From mathcomp Require Import seq div fintype bigop ssralg finset fingroup zmodp. From mathcomp Require Import poly polydiv order ssrnum matrix mxalgebra vector. From mathcomp Require Import mxpoly mxred sesqui...
automorphism.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat fintype. From mathcomp Require Import finset fingroup perm morphism. (*********************...
StdBasis.lean
/- Copyright (c) 2019 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen -/ import Mathlib.Data.Matrix.Basis import Mathlib.LinearAlgebra.StdBasis /-! # Standard basis on matrices ## Main results *...
Lattice.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.Submonoid.Operations import Mathlib.Algebra.Group.Subgroup.Defs /-! # Lattice structure of subgroups We prove subgroups of a group form a com...
Archimedean.lean
/- Copyright (c) 2020 Heather Macbeth, Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Heather Macbeth, Patrick Massot -/ import Mathlib.Algebra.Group.Subgroup.Order import Mathlib.Algebra.Order.Archimedean.Basic /-! # Archimedean groups This file prov...
Defs.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.Data.Set.Defs import Mathlib.Order.Defs.PartialOrder /-! # Intervals In any preorder `α`, we define intervals (which on each side can be either infin...
ContinuousCompMeasurePreserving.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.MeasureTheory.Function.SimpleFuncDenseLp import Mathlib.MeasureTheory.Measure.ContinuousPreimage /-! # Continuity of `MeasureTheory.Lp.compMeasurePr...
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, Johannes Hölzl, Kim Morrison, Jens Wagemaker -/ import Mathlib.Algebra.Group.Submonoid.Operations import Mathlib.Algebra.MonoidAlgebra.Module import Mathlib.Algebra.MonoidA...
Constructor.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.Localization.DerivabilityStructure.Basic /-! # Constructor for derivability structures In this file, we provide a constructor for right derivabi...
Lemmas.lean
/- Copyright (c) 2021 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Data.EReal.Inv import Mathlib.Topology.Semicontinuous /-! # Topological structure on `EReal` We prove basic properties of the topology on `ERea...
all_fingroup.v
From mathcomp Require Export action. From mathcomp Require Export automorphism. From mathcomp Require Export fingroup. From mathcomp Require Export gproduct. From mathcomp Require Export morphism. From mathcomp Require Export perm. From mathcomp Require Export presentation. From mathcomp Require Export quotient.
TransferInstance.lean
/- Copyright (c) 2025 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.TransferInstance import Mathlib.Algebra.GroupWithZero.Action.Defs /-! # Transfer algebraic structures across `Equiv`s This continues...
PrimitiveRoots.lean
/- Copyright (c) 2022 Riccardo Brasca. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Alex J. Best, Riccardo Brasca, Eric Rodriguez -/ import Mathlib.Data.Nat.Factorization.LCM import Mathlib.Data.PNat.Prime import Mathlib.NumberTheory.Cyclotomic.Basic import Mathlib.R...
Cone.lean
/- Copyright (c) 2025 Moisés Herradón Cueto. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Moisés Herradón Cueto -/ import Mathlib.CategoryTheory.Comma.Over.Basic import Mathlib.CategoryTheory.WithTerminal.Basic /-! # Relations between `Cone`, `WithTerminal` and `Ove...
automorphism.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat fintype. From mathcomp Require Import finset fingroup perm morphism. (*********************...
falgebra.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq path. From mathcomp Require Import choice fintype div...
ProjectiveLine.lean
/- Copyright (c) 2024 Bjørn Kjos-Hanssen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bjørn Kjos-Hanssen, Oliver Nash -/ import Mathlib.LinearAlgebra.Projectivization.Basic import Mathlib.Topology.Compactification.OnePoint.Basic /-! # One-point compactification and...
algnum.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...
Pointed.lean
/- Copyright (c) 2022 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.CategoryTheory.ConcreteCategory.Basic import Mathlib.CategoryTheory.Adjunction.Basic /-! # The category of pointed types This defines `Pointed`, the cate...
ContinuousMapZero.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.Topology.ContinuousMap.Algebra import Mathlib.Topology.ContinuousMap.Compact /-! # Continuous maps sending zero to zero This is the type of continuous ...
LinOrd.lean
/- Copyright (c) 2020 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.Order.Category.Lat /-! # Category of linear orders This defines `LinOrd`, the category of linear orders with monotone maps. -/ open CategoryTheory ...
Finite.lean
/- Copyright (c) 2025 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Data.Set.Finite.Basic import Mathlib.Order.Minimal /-! # Finite preorders and finite sets in a preorder This file shows that non-empty finite sets in a p...
CommAlgCat.lean
import Mathlib.Algebra.Category.CommAlgCat.Basic universe v u open CategoryTheory CommAlgCat set_option maxHeartbeats 10000 set_option synthInstance.maxHeartbeats 2000 variable (R : Type u) [CommRing R] /- We test if all the coercions and `map_add` lemmas trigger correctly. -/ example (X : Type v) [CommRing X] [A...
Skeleton.lean
/- Copyright (c) 2021 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta -/ import Mathlib.CategoryTheory.Monoidal.Braided.Basic import Mathlib.CategoryTheory.Monoidal.Transport import Mathlib.CategoryTheory.Skeletal /-! # The monoid on the skel...
center.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div. From mathcomp Require Import fintype bigop finset fingroup morphism perm. From math...
Creates.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.Functor.ReflectsIso.Basic import Mathlib.CategoryTheory.Limits.Preserves.Basic /-! # Creating (co)limits We say that `F` creates limits of...
Localization.lean
/- Copyright (c) 2025 Nailin Guan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Nailin Guan -/ import Mathlib.Algebra.Module.LocalizedModule.Basic import Mathlib.RingTheory.Ideal.AssociatedPrime.Basic import Mathlib.RingTheory.Localization.AtPrime.Basic /-! # Assoc...
DivergenceTheorem.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.BoxIntegral.DivergenceTheorem import Mathlib.Analysis.BoxIntegral.Integrability import Mathlib.Analysis.Calculus.Deriv.Basic import Mathlib....
ProximityFunction.lean
/- Copyright (c) 2025 Stefan Kebekus. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Stefan Kebekus -/ import Mathlib.Algebra.Order.WithTop.Untop0 import Mathlib.Analysis.SpecialFunctions.Integrability.LogMeromorphic import Mathlib.MeasureTheory.Integral.CircleAverage ...
Inversion.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.LinearAlgebra.CliffordAlgebra.Contraction /-! # Results about inverses in Clifford algebras This contains some basic results about the inversion of vectors...
RealVectorSpace.lean
/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Topology.Algebra.Module.Equiv import Mathlib.Topology.Instances.Rat import Mathlib.Algebra.Module.Rat /-! # Continuous additive maps are `ℝ`-linear ...
Matrix.lean
/- Copyright (c) 2025 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.LinearAlgebra.PerfectPairing.Basic import Mathlib.LinearAlgebra.Matrix.Dual import Mathlib.LinearAlgebra.Matrix.ToLinearEquiv /-! # Perfect pairings and mat...
ConditionalProbability.lean
/- Copyright (c) 2022 Rishikesh Vaishnav. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rishikesh Vaishnav -/ import Mathlib.MeasureTheory.Measure.Typeclasses.Probability /-! # Conditional Probability This file defines conditional probability and includes basic resu...
Extension.lean
/- Copyright (c) 2020 Thomas Browning. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Thomas Browning, Junyan Xu -/ import Mathlib.Data.Fintype.Order import Mathlib.FieldTheory.IntermediateField.Adjoin.Basic /-! # Extension of field embeddings `IntermediateField.exis...
TensorProduct.lean
/- Copyright (c) 2023 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.LinearAlgebra.BilinearForm.TensorProduct import Mathlib.LinearAlgebra.QuadraticForm.Basic /-! # The quadratic form on a tensor product ## Main definitions ...
spectral.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat. From mathcomp Require Import seq div fintype bigop ssralg finset fingroup zmodp. From mathcomp Require Import poly polydiv order ssrnum matrix mxalgebra vector. From mathcomp Require Import mxpoly mxred sesqui...
Defs.lean
/- Copyright (c) 2020 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Filippo A. E. Nuccio, Andrew Yang -/ import Mathlib.RingTheory.Ideal.Prime /-! # Prime spectrum of a commutative (semi)ring as a type The prime spectrum of a commutat...
Topology.lean
/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Johannes Hölzl -/ import Mathlib.Dynamics.FixedPoints.Basic import Mathlib.Topology.Separation.Hausdorff /-! # Topological properties of fixed points Currently this...
Perm.lean
import Mathlib.GroupTheory.Perm.Cycle.Concrete import Mathlib.Tactic.DeriveFintype open Equiv #guard with_decl_name% ex₁ unsafe (reprStr (1 : Perm (Fin 4))) == "1" #guard with_decl_name% ex₂ unsafe (reprStr (c[0, 1] : Perm (Fin 4))) == "c[0, 1]" #guard with_decl_name% ex₃ unsafe (reprStr (c[0, 1] * c[2, 3] : Perm ...
UnitPartition.lean
/- Copyright (c) 2024 Xavier Roblot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Xavier Roblot -/ import Mathlib.Algebra.Module.ZLattice.Basic import Mathlib.Analysis.BoxIntegral.Integrability import Mathlib.Analysis.BoxIntegral.Partition.Measure import Mathlib.Anal...
Prod.lean
/- Copyright (c) 2018 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Riccardo Brasca -/ import Mathlib.Algebra.Algebra.Prod import Mathlib.Algebra.Algebra.Subalgebra.Lattice /-! # Products of subalgebras In this file we define the product of two subalgebra...