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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...
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.
CPolynomial.lean
/- Copyright (c) 2021 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Analysis.Calculus.FDeriv.Analytic import Mathlib.Analysis.Calculus.ContDiff.Defs /-! # Higher smoothness of continuously polynomial functions We pr...
Pi.lean
/- Copyright (c) 2018 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl -/ import Mathlib.Data.Finset.Card import Mathlib.Data.Finset.Union import Mathlib.Data.Multiset.Pi import Mathlib.Logic.Function.DependsOn /-! # The cartesian product ...
interval.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 div fintype bigo...
GCongr.lean
import Mathlib.MeasureTheory.Measure.MeasureSpace /-! # Testing for the `gcongr` tactic -/ namespace GCongrTests /- Test that `gcongr` lemmas are applied in the `reducible` transparency by default. Previously, `DFunLike.coe` would be unfolded when applying a `@[gcongr]` lemma. -/ section transparency open MeasureThe...
LeftExactFunctor.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.Algebra.Category.Grp.CartesianMonoidal import Mathlib.Algebra.Category.Grp.EquivalenceGroupAddGroup import Mathlib.CategoryTheory.Monoidal.Internal.Types...
Basic.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.Algebra.Algebra.Tower import Mathlib.LinearAlgebra.Pi import Mathlib.LinearAlgebra.Quotient.Defs import Mathlib.RingTheory.Finiteness.Defs /-! # Basic...
TotalComplex.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.CategoryTheory.Linear.Basic import Mathlib.Algebra.Homology.ComplexShapeSigns import Mathlib.Algebra.Homology.HomologicalBicomplex import Mathlib.Algebra.Module....
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...
Affine.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.Convex.Between import Mathlib.Analysis.Normed.Group.AddTorsor import Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic import Mat...
Basic.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.CharP.IntermediateField import Mathlib.FieldTheory.SeparableClosure /-! # Basic results about purely inseparable extensions This file contains basic definit...
Arborescence.lean
/- Copyright (c) 2021 David Wärn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Wärn -/ import Mathlib.Combinatorics.Quiver.Path import Mathlib.Combinatorics.Quiver.Subquiver import Mathlib.Order.WellFounded /-! # Arborescences A quiver `V` is an arborescence ...
SpecificFunctions.lean
/- Copyright (c) 2020 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, Floris van Doorn -/ import Mathlib.Geometry.Manifold.MFDeriv.FDeriv /-! # Differentiability of specific functions In this file, we establish differentiability r...
TypeTags.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.Group.TypeTags.Hom import Mathlib.Algebra.Group.Equiv.Defs import Mathlib.Algebra.Notation.Prod import Mathlib....
Image.lean
/- Copyright (c) 2022 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang, Joël Riou -/ import Mathlib.CategoryTheory.Subpresheaf.Basic import Mathlib.CategoryTheory.Limits.FunctorCategory.EpiMono import Mathlib.CategoryTheory.Limits.Types.Colimits ...
abelian.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path. From mathcomp Require Import choice div fintype finfun bigop finset prime. From ma...
Finrank.lean
/- Copyright (c) 2019 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Anne Baanen -/ import Mathlib.LinearAlgebra.Dimension.Subsingleton import Mathlib.SetTheory.Cardinal.ToNat /-! # Finite dimension of vector spaces Definition of the rank ...
Coinduced.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.CategoryTheory.Preadditive.Projective.Preserves import Mathlib.RepresentationTheory.Rep /-! # Coinduced representations Given a commutative rin...
DenselyOrdered.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.Topology.Order.IsLUB /-! # Order topology on a densely ordered set -/ open Set Filter TopologicalSpace Topology Func...
MapFloor.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.Algebra.Order.Round import Mathlib.Algebra.Order.Group.PiLex import Mathlib.Algebra.Order.Hom.Ring import Mathlib.Algebra.Polynomial.Reverse /-! # Floors ...
Topology.lean
/- Copyright (c) 2022 David Kurniadi Angdinata. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Kurniadi Angdinata -/ import Mathlib.RingTheory.Spectrum.Maximal.Basic import Mathlib.RingTheory.Spectrum.Prime.Topology /-! # The Zariski topology on the maximal spec...
WithoutCDot.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 Lean.Elab.SyntheticMVars import Mathlib.Init /-! # The `without_cdot()` elaborator -/ namespace Lean.Elab.Term open Parser private def withoutCDotContents : Pars...
SesquilinearForm.lean
/- Copyright (c) 2018 Andreas Swerdlow. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andreas Swerdlow -/ import Mathlib.LinearAlgebra.Basis.Basic import Mathlib.LinearAlgebra.BilinearMap import Mathlib.LinearAlgebra.LinearIndependent.Lemmas /-! # Sesquilinear maps ...
Power.lean
/- Copyright (c) 2014 Robert Y. Lewis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Robert Y. Lewis, Leonardo de Moura, Mario Carneiro, Floris van Doorn, Sabbir Rahman -/ import Mathlib.Algebra.Order.Ring.Abs import Mathlib.Algebra.Order.Ring.Pow import Mathlib.Algeb...
Archimedean.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.SuccPred.Basic /-! # Archimedean successor and predecessor * `IsSuccArchimedean`: `SuccOrder` where `succ` iterated to an element gives all the gre...
IsMonicOfDegree.lean
/- Copyright (c) 2025 Michael Stoll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Stoll -/ import Mathlib.Algebra.Polynomial.AlgebraMap import Mathlib.Algebra.Polynomial.Monic /-! # Monic polynomials of given degree This file defines the predicate `Polynomi...
TMConfig.lean
/- Copyright (c) 2020 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Computability.Halting import Mathlib.Computability.PostTuringMachine import Mathlib.Tactic.DeriveFintype /-! # Modelling partial recursive functions u...
Identities.lean
/- Copyright (c) 2020 Bryan Gin-ge Chen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bryan Gin-ge Chen, Kevin Lacker -/ import Mathlib.Tactic.Ring /-! # Identities This file contains some "named" commutative ring identities. -/ variable {R : Type*} [CommRing R] ...
Int.lean
/- Copyright (c) 2021 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.Analysis.Normed.Ring.Lemmas /-! # The integers as normed ring This file contains basic facts about the integers as normed ring. Recall that `‖n‖` de...
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...
gfunctor.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 bigop finset fingroup morphism automorphism. From math...
Polynomial.lean
/- Copyright (c) 2021 Benjamin Davidson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Benjamin Davidson, Yury Kudryashov -/ import Mathlib.Analysis.Calculus.LocalExtr.Rolle import Mathlib.Analysis.Calculus.Deriv.Polynomial import Mathlib.Topology.Algebra.Polynomial ...
Basic.lean
/- Copyright (c) 2018 Robert Y. Lewis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Robert Y. Lewis, Matthew Robert Ballard -/ import Mathlib.NumberTheory.Divisors import Mathlib.NumberTheory.Padics.PadicVal.Defs import Mathlib.Data.Nat.MaxPowDiv import Mathlib.Data....
PadicIntegers.lean
/- Copyright (c) 2018 Robert Y. Lewis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Robert Y. Lewis, Mario Carneiro, Johan Commelin -/ import Mathlib.NumberTheory.Padics.PadicNumbers import Mathlib.RingTheory.DiscreteValuationRing.Basic /-! # p-adic integers This f...
Tower.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.FieldTheory.LinearDisjoint import Mathlib.FieldTheory.PurelyInseparable.PerfectClosure /-! # Tower law for purely inseparable extensions This file contains results ...
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...
Piecewise.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.Data.Finset.BooleanAlgebra import Mathlib.Data.Set.Piecewise import Mathlib.Order.Interval.Set.Basic /-! # Functions defined piecewise on a fins...
EulerIdentity.lean
/- Copyright (c) 2024 Junyan Xu. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Junyan Xu -/ import Mathlib.Algebra.MvPolynomial.PDeriv import Mathlib.RingTheory.MvPolynomial.Homogeneous /-! # Euler's homogeneous identity ## Main results * `IsHomogeneous.sum_X_mul_p...
Portmanteau.lean
/- Copyright (c) 2021 Kalle Kytölä. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kalle Kytölä -/ import Mathlib.MeasureTheory.Measure.ProbabilityMeasure import Mathlib.MeasureTheory.Measure.Lebesgue.Basic import Mathlib.MeasureTheory.Integral.Layercake import Mathlib...
TakeDrop.lean
/- Copyright (c) 2014 Parikshit Khanna. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro -/ import Mathlib.Data.List.Defs import Mathlib.Tactic.Common /-! # `Take` and `Drop` lemmas for...
RadiusLiminf.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.Analysis.Analytic.ConvergenceRadius import Mathlib.Analysis.SpecialFunctions.Pow.NNReal /-! # Representation of `FormalMultilinearSeries.radius` as ...
cancel_denoms.lean
import Mathlib.Algebra.Order.Field.Rat import Mathlib.Tactic.CancelDenoms import Mathlib.Tactic.Ring private axiom test_sorry : ∀ {α}, α universe u section variable {α : Type u} [Field α] [LinearOrder α] [IsStrictOrderedRing α] (a b c d : α) -- prior to https://github.com/leanprover-community/mathlib4/pull/12083, `ca...
WeakDual.lean
/- Copyright (c) 2021 Kalle Kytölä. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kalle Kytölä, Moritz Doll -/ import Mathlib.LinearAlgebra.BilinearMap import Mathlib.Topology.Algebra.Module.LinearMap import Mathlib.Topology.Algebra.Module.WeakBilin /-! # Weak dual t...
presentation.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. From mathcomp Require Import fintype finset fingroup morphism. (**********************...
MinimalAxioms.lean
/- Copyright (c) 2023 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes -/ import Mathlib.Algebra.Group.Defs /-! # Minimal Axioms for a Group This file defines constructors to define a group structure on a Type, while proving only three equal...
Calculus.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.Analysis.InnerProductSpace.PiL2 import Mathlib.Analysis.SpecialFunctions.Sqrt import Mathlib.Analysis.NormedSpace.HomeomorphBall import Mathlib.Analy...
GaloisConnection.lean
/- Copyright (c) 2024 Lagrange Mathematics and Computing Research Center. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anthony Bordg -/ import Mathlib.Data.Rel /-! # The Galois Connection Induced by a Relation In this file, we show that an arbitrary relation `R` be...
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...
fieldext.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 tupl...
Manifold.lean
/- Copyright (c) 2022 Chris Birkbeck. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Birkbeck, David Loeffler -/ import Mathlib.Analysis.Complex.CauchyIntegral import Mathlib.Analysis.Complex.UpperHalfPlane.Topology import Mathlib.Geometry.Manifold.Algebra.Struct...
Coskeletal.lean
/- Copyright (c) 2024 Emily Riehl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Emily Riehl, Joël Riou -/ import Mathlib.AlgebraicTopology.SimplicialObject.Coskeletal import Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal import Mathlib.CategoryTh...
Datatypes.lean
/- Copyright (c) 2024 Yuma Mizuno. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yuma Mizuno -/ import Mathlib.Tactic.CategoryTheory.Coherence.Datatypes import Mathlib.Tactic.CategoryTheory.MonoidalComp /-! # Expressions for monoidal categories This file converts le...
Combination.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.Algebra.BigOperators.Group.Finset.Indicator import Mathlib.Algebra.Module.BigOperators import Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic import...
Sigma.lean
/- Copyright (c) 2025 Christian Merten. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christian Merten -/ import Mathlib.AlgebraicGeometry.Morphisms.Basic /-! # Collapsing covers We define the endofunctor on `Scheme.Cover P` that collapses a cover to a single object...
Bimon_.lean
/- Copyright (c) 2024 Lean FRO LLC. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.CategoryTheory.Monoidal.Comon_ /-! # The category of bimonoids in a braided monoidal category. We define bimonoids in a braided monoidal category `C` as ...
ConjAct.lean
/- Copyright (c) 2022 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.Algebra.Field.Defs import Mathlib.Algebra.GroupWithZero.Action.ConjAct import Mathlib.Algebra.GroupWithZero.Action.Defs /-! # Conjugation action on a field ...
Notation.lean
/- Copyright (c) 2024 Peter Nelson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Peter Nelson -/ import Mathlib.Util.Notation3 import Mathlib.Lean.Expr.ExtraRecognizers /-! # Set Notation This file defines two pieces of scoped notation related to sets and subtypes....
Adjunction.lean
/- Copyright (c) 2019 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Bhavik Mehta -/ import Mathlib.CategoryTheory.Adjunction.Reflective import Mathlib.CategoryTheory.Monad.Algebra /-! # Adjunctions and (co)monads We develop the basic rela...
Option.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.Control.EquivFunctor import Mathlib.Data.Option.Basic import Mathlib.Data.Subtype import Mathlib.Logic.Equiv.Defs /-! # Equivalences for `Option α` We def...
UniformConvergenceTopology.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.Coherent import Mathlib.Topology.UniformSpace.Equiv import Mathlib.Topology.UniformSpace.Pi import Mathlib.Topology.UniformSpace.UniformAp...
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...
Geometric.lean
/- Copyright (c) 2024 Josha Dekker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Josha Dekker -/ import Mathlib.Probability.ProbabilityMassFunction.Basic import Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic /-! # Geometric distributions over ℕ Define the...
Normalize.lean
import Mathlib.Tactic.CategoryTheory.Monoidal.Normalize open CategoryTheory Mathlib.Tactic BicategoryLike open MonoidalCategory namespace CategoryTheory.MonoidalCategory /-- `normalize% η` is the normalization of the 2-morphism `η`. 1. The normalized 2-morphism is of the form `α₀ ≫ η₀ ≫ α₁ ≫ η₁ ≫ ... αₘ ≫ ηₘ ≫ αₘ₊₁`...
Defs.lean
/- Copyright (c) 2021 Damiano Testa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damiano Testa -/ import Mathlib.Algebra.Group.Basic import Mathlib.Order.Basic import Mathlib.Order.Monotone.Defs /-! # Covariants and contravariants This file contains general lemma...
Arithmetic.lean
/- Copyright (c) 2025 Pim Otte. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Pim Otte -/ import Mathlib.Algebra.BigOperators.Finprod import Mathlib.Data.Set.Card import Mathlib.SetTheory.Cardinal.Arithmetic /-! # Results using cardinal arithmetic This file contain...
Composition.lean
/- Copyright (c) 2024 Yunzhou Xie. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Buzzard, Yunzhou Xie, Eric Wieser -/ import Mathlib.Data.Matrix.Basic import Mathlib.Data.Matrix.Basis /-! # Composition of matrices This file shows that Mₙ(Mₘ(R)) ≃ Mₙₘ(R), Mₙ(R...
Basic.lean
/- Copyright (c) 2021 Justus Springer. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Justus Springer, Andrew Yang -/ import Mathlib.Algebra.Category.Ring.Colimits import Mathlib.Algebra.Category.Ring.FilteredColimits import Mathlib.Algebra.Category.Ring.Limits import ...
SiegelsLemma.lean
/- Copyright (c) 2024 Fabrizio Barroero. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Fabrizio Barroero, Laura Capuano, Amos Turchet -/ import Mathlib.Analysis.Matrix import Mathlib.Data.Pi.Interval import Mathlib.Tactic.Rify /-! # Siegel's Lemma In this file we in...
Bundle.lean
/- Copyright (c) 2021 Nicolò Cavalleri. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Nicolò Cavalleri -/ import Mathlib.Data.Set.Basic /-! # Bundle Basic data structure to implement fiber bundles, vector bundles (maybe fibrations?), etc. This file should contain all...
Basic.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.Control.Combinators import Mathlib.Data.Option.Defs import Mathlib.Logic.IsEmpty import Mathlib.Logic.Relator import Mathlib.Util.CompileInductive impo...
Support.lean
/- Copyright (c) 2022 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn -/ import Mathlib.Analysis.Calculus.Deriv.Basic /-! # Support of the derivative of a function In this file we prove that the (topological) support of a function in...
Prelax.lean
/- Copyright (c) 2024 Calle Sönne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yuma Mizuno, Calle Sönne -/ import Mathlib.CategoryTheory.Bicategory.Basic /-! # Prelax functors This file defines lax prefunctors and prelax functors between bicategories. The point ...
Closeds.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.Analysis.SpecificLimits.Basic import Mathlib.Topology.MetricSpace.HausdorffDistance import Mathlib.Topology.Sets.Compacts /-! # Closed subsets ...
Inv.lean
/- Copyright (c) 2022 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Tactic.NormNum.Basic import Mathlib.Data.Rat.Cast.CharZero import Mathlib.Algebra.Field.Basic /-! # `norm_num` plugins for `Rat.cast` and `⁻¹`. -/ va...
cyclic.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 bigo...
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...
Fold.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.Finset.Basic import Mathlib.Data.Finset.Image import Mathlib.Data.Multiset.Fold /-! # The fold operation for a commutative associative operation ...
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...
IsomorphismClasses.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.CategoryTheory.Category.Cat import Mathlib.CategoryTheory.Groupoid import Mathlib.CategoryTheory.Types /-! # Objects of a category up to an isomorph...
Lemmas.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.Control.Bitraversable.Basic /-! # Bitraversable Lemmas ## Main definitions * tfst - traverse on first functor argument * tsnd - traverse on second func...
polydiv.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import fintype bigop ssralg poly. (**********************...
Module.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.Order.Nonneg.Module import Mathlib.Topology.Algebra.ConstMulAction import Mathlib.Topology.Algebra.MulAction /-! # Continuous nonnegative scalar m...
MeasureSpace.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Mario Carneiro -/ import Mathlib.MeasureTheory.MeasurableSpace.MeasurablyGenerated import Mathlib.MeasureTheory.Measure.NullMeasurable import Mathlib.Order.Interval.Set...
Basic.lean
/- Copyright (c) 2020 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne, Sébastien Gouëzel -/ import Mathlib.Analysis.NormedSpace.OperatorNorm.NNNorm import Mathlib.MeasureTheory.Function.LpSeminorm.ChebyshevMarkov import Mathlib.MeasureTheory.F...
Count.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.Algebra.Order.Ring.Nat import Mathlib.Data.List.Chain /-! # List of booleans In this file we prove lemmas about the number of `false`s and `true`s ...
HomogeneousPrimeNotPrime.lean
/- Copyright (c) 2022 Jujian Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Eric Wieser, Jujian Zhang -/ import Mathlib.Algebra.Divisibility.Finite import Mathlib.Algebra.Divisibility.Prod import Mathlib.Data.Fintype.Units import Mathlib.RingTheo...
Adjunction.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.CategoryTheory.CatCommSq import Mathlib.CategoryTheory.Localization.Predicate import Mathlib.CategoryTheory.Adjunction.FullyFaithful /-! # Localization of adjun...
TacticAnalysis.lean
import Mathlib.Tactic.TacticAnalysis.Declarations section rwMerge set_option linter.tacticAnalysis.rwMerge true def x := 1 def y := 1 def z := 1 theorem xy : x = y := rfl theorem yz : y = z := rfl example : x = y := by rw [xy] /-- warning: Try this: rw [xy, yz] -/ #guard_msgs in example : x = z := by rw [xy] ...
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_...
Kernels.lean
/- Copyright (c) 2023 Moritz Firsching. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Kurniadi Angdinata, Moritz Firsching, Nikolas Kuhn -/ import Mathlib.Algebra.Category.Grp.EpiMono import Mathlib.Algebra.Category.Grp.Preadditive import Mathlib.CategoryTheory....
imset2_gproduct.v
From mathcomp Require Import all_boot all_fingroup. Set Implicit Arguments. Unset Strict Implicit. Unset Printing Implicit Defensive. Import GroupScope. Open Scope group_scope. Check @ker_sdprodm.
Equiv.lean
/- Copyright (c) 2017 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Ralf Stephan, Neil Strickland, Ruben Van de Velde -/ import Mathlib.Data.PNat.Defs import Mathlib.Logic.Equiv.Defs /-! # The equivalence between `ℕ+` and `ℕ` -/...
CommutingProbability.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.BigOperators.Fin import Mathlib.GroupTheory.Abelianization.Finite import Mathlib.GroupTheory.SpecificGroups.Dihedral import Mathlib.Tactic.Fi...
slow_simp.lean
import Mathlib import Mathlib.Topology.Category.TopCat.Basic /-! This test file serves as a sentinel against bad simp lemmas. When this test file was first setup, the final declaration of this file took 12,000 heartbeats with the minimal import of `Mathlib/Topology/Category/TopCat/Basic.lean`, but took over 260,000 h...
Defs.lean
/- Copyright (c) 2022 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.Algebra.Ring.Hom.Defs import Mathlib.Algebra.Ring.InjSurj import Mathlib.GroupTheory.Congruence.Defs import Mathlib.Tactic.FastInstance /-! # Congruence rel...
MasonStothers.lean
/- Copyright (c) 2024 Jineon Baek and Seewoo Lee. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jineon Baek, Seewoo Lee -/ import Mathlib.RingTheory.Polynomial.Radical /-! # Mason-Stothers theorem This file states and proves the Mason-Stothers theorem, which is a po...
Commute.lean
/- Copyright (c) 2014 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Yury Kudryashov, Neil Strickland -/ import Mathlib.Algebra.Ring.Semiconj import Mathlib.Algebra.Ring.Units import Mathlib.Algebra.Gro...
tuple.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. From mathcomp Require Import seq choice fintype path. S...
ConcreteSheafification.lean
import Mathlib.Algebra.Category.ModuleCat.Colimits import Mathlib.Algebra.Category.ModuleCat.Limits import Mathlib.Algebra.Category.ModuleCat.FilteredColimits import Mathlib.CategoryTheory.Sites.Equivalence universe u open CategoryTheory attribute [local instance] Types.instFunLike Types.instConcreteCategory sectio...