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Localization.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.Shift.Induced import Mathlib.CategoryTheory.Localization.HasLocalization import Mathlib.CategoryTheory.Localization.LocalizerMorphism /-! # The s...
CDF.lean
/- Copyright (c) 2023 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Probability.Kernel.Disintegration.CondCDF /-! # Cumulative distribution function of a real probability measure The cumulative distribution function (cdf)...
Ring.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.Defs import Mathlib.Algebra.Ring.InjSurj import Mathlib.Tactic.FastInstance /-! # Algebraic structures on the set of positive num...
Units.lean
/- Copyright (c) 2016 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad -/ import Mathlib.Algebra.Ring.Int.Defs import Mathlib.Algebra.Ring.Units import Mathlib.Algebra.Group.Int.Units /-! # Basic lemmas for `ℤˣ`. This file contains lemmas o...
NormedValued.lean
/- Copyright (c) 2024 María Inés de Frutos-Fernández. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: María Inés de Frutos-Fernández -/ import Mathlib.Analysis.Normed.Field.Basic import Mathlib.Analysis.Normed.Group.Ultra import Mathlib.RingTheory.Valuation.RankOne impo...
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.Basic import Mathlib.CategoryTheory.Functor.KanExtension.Adjunction import Mathlib.CategoryTheo...
LocalExtr.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.Algebra.Group.Defs import Mathlib.Order.Filter.Extr import Mathlib.Topology.ContinuousOn /-! # Local extrema of functions on topological spaces ## ...
Cardinality.lean
/- Copyright (c) 2022 Eric Rodriguez. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Rodriguez -/ import Mathlib.Algebra.Field.TransferInstance import Mathlib.Algebra.Field.ULift import Mathlib.Algebra.MvPolynomial.Cardinal import Mathlib.Data.Rat.Encodable import...
Maximal.lean
/- Copyright (c) 2018 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau, Chris Hughes, Mario Carneiro -/ import Mathlib.RingTheory.Ideal.Prime import Mathlib.RingTheory.Ideal.Span /-! # Ideals over a ring This file contains an assortment of definit...
Equiv.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, Kevin Buzzard, Yury Kudryashov, Frédéric Dupuis, Heather Macbeth -/ import Mathlib.Algebra.Module.Submodule.Range /-! ### Linear equivalences involvi...
ZModuleEquivalence.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.Category.ModuleCat.Basic /-! The forgetful functor from ℤ-modules to additive commutative groups is an equivalence of categories. TODO: either us...
Finite.lean
/- Copyright (c) 2020 Aaron Anderson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Anderson -/ import Mathlib.Data.Set.Finite.Lattice import Mathlib.Order.Atoms import Mathlib.Order.Interval.Finset.Defs import Mathlib.Order.Preorder.Finite /-! # Atoms, Coatoms...
Laurent.lean
/- Copyright (c) 2022 Damiano Testa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damiano Testa -/ import Mathlib.Algebra.Polynomial.AlgebraMap import Mathlib.Algebra.Polynomial.Reverse import Mathlib.Algebra.Polynomial.Inductions import Mathlib.RingTheory.Localizati...
Preord.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.CategoryTheory.Category.Cat import Mathlib.CategoryTheory.Category.Preorder import Mathlib.CategoryTheory.Elementwise import Mathlib.Order.Hom.Basic im...
polyXY.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 tuple fi...
CliffordAlgebraNotInjective.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.CharP.Pi import Mathlib.Algebra.CharP.Quotient import Mathlib.LinearAlgebra.CliffordAlgebra.Contraction import Mathlib.RingTheory.MvPolynomial.Basic ...
Monoidal.lean
/- Copyright (c) 2024 Sina Hazratpour. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sina Hazratpour -/ import Mathlib.CategoryTheory.Closed.Monoidal import Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts import Mathlib.CategoryTheory.Limits.Preserves.Fu...
AhlswedeZhang.lean
/- Copyright (c) 2023 Yaël Dillies, Vladimir Ivanov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Vladimir Ivanov -/ import Mathlib.Algebra.BigOperators.Intervals import Mathlib.Algebra.BigOperators.Ring.Finset import Mathlib.Algebra.Order.BigOperators....
TrivSqZeroExt.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.Algebra.TrivSqZeroExt import Mathlib.Topology.Algebra.InfiniteSum.Basic import Mathlib.Topology.Algebra.Module.LinearMapPiProd /-! # Topology on `TrivSqZero...
Polynomial.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 -/ import Mathlib.Algebra.Polynomial.AlgebraMap import Mathlib.Algebra.Polynomial.Inductions import Mathlib.Algebra.Polynomial.Splits import Mathlib.RingTheory.Polynom...
action.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun ssrnotations eqtype. From mathcomp Require Import ssrnat div seq prime fintype bigop finset. From mathcomp...
Shapiro.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.Resolution import Mathlib.RepresentationTheory.Homological.GroupHomology.Basic import Mathlib.Representatio...
preorder.v
(* (c) Copyright 2006-2019 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq. From mathcomp Require Import path fintype tup...
Hom.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Yury Kudryashov -/ import Mathlib.Algebra.Group.Action.Pretransitive import Mathlib.Algebra.Group.Hom.Defs /-! # Homomorphisms and group actions -/ assert_not_exists Mono...
Restrict.lean
/- Copyright (c) 2019 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.CategoryTheory.Adjunction.Basic import Mathlib.CategoryTheory.HomCongr /-! # Restricting adjunctions `Adjunction.restrictFullyFaithful` shows that an adj...
NatCast.lean
/- Copyright (c) 2025 Antoine Chambert-Loir, María Inés de Frutos-Fernández. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Antoine Chambert-Loir, María Inés de Frutos-Fernández -/ import Mathlib.Algebra.Algebra.Defs import Mathlib.Algebra.CharP.Invertible import Math...
Ostrowski.lean
/- Copyright (c) 2024 María Inés de Frutos-Fernández. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Kurniadi Angdinata, Fabrizio Barroero, Laura Capuano, Nirvana Coppola, María Inés de Frutos-Fernández, Sam van Gool, Silvain Rideau-Kikuchi, Amos Turchet, Frances...
Grading.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.LinearAlgebra.CliffordAlgebra.Basic import Mathlib.RingTheory.GradedAlgebra.Basic /-! # Results about the grading structure of the clifford algebra The mai...
OmegaCompletePartialOrder.lean
/- Copyright (c) 2020 Simon Hudon. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Simon Hudon -/ import Mathlib.Order.OmegaCompletePartialOrder import Mathlib.Topology.Order.ScottTopology /-! # Scott Topological Spaces A type of topological spaces whose notion of con...
Tripartite.lean
/- Copyright (c) 2023 Yaël Dillies, Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Bhavik Mehta -/ import Mathlib.Combinatorics.SimpleGraph.Triangle.Basic /-! # Construct a tripartite graph from its triangles This file contains the constru...
Arithmetic.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, Floris van Doorn -/ import Mathlib.SetTheory.Cardinal.Aleph /-! # Cardinal arithmetic Arithmetic operations on cardinals are defined in `SetTheory/Car...
SumsProducts.lean
/- Copyright (c) 2025 Robin Carlier. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Robin Carlier -/ import Mathlib.CategoryTheory.Discrete.Basic import Mathlib.CategoryTheory.Sums.Basic import Mathlib.CategoryTheory.Products.Basic /-! # Sums and products of discrete ...
Asymptotics.lean
/- Copyright (c) 2025 Xavier Roblot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Xavier Roblot -/ import Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne import Mathlib.NumberTheory.NumberField.ClassNumber /-! # Asymptotics on integral ideals of a numb...
LeftExact.lean
/- Copyright (c) 2022 Jakob von Raumer. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Markus Himmel, Jakob von Raumer -/ import Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels impo...
RingHoms.lean
/- Copyright (c) 2020 Johan Commelin, Robert Y. Lewis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Robert Y. Lewis -/ import Mathlib.Algebra.Field.ZMod import Mathlib.NumberTheory.Padics.PadicIntegers import Mathlib.RingTheory.LocalRing.ResidueField....
Divisible.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.Group.ULift import Mathlib.Algebra.GroupWithZero.Subgroup import Mathlib.Algebra.Module.NatInt import Mathlib.GroupTheory.QuotientGroup.Defs import...
CongrM.lean
/- Copyright (c) 2023 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot -/ import Mathlib.Tactic.Widget.SelectPanelUtils import Mathlib.Tactic.CongrM import Batteries.Lean.Position /-! # CongrM widget This file defines a `congrm?` tactic ...
all_algebra.v
(* N.B. interval_inference is not exported here. To enjoys the automation it provides, you need to explictly "Import interval_inference". *) From mathcomp Require Export ssralg. From mathcomp Require Export ssrnum. From mathcomp Require Export finalg. From mathcomp Require Export countalg. From mathcomp Require Export...
sesquilinear.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq div. From mathcomp Require Import choice fintype tuple bigop ssralg finset fingroup. From mathcomp Require Import zmodp poly order ssrnum matrix mxalgebra vector. (************************************************...
pgroup.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div. From mathcomp Require Import fintype bigop finset prime fingroup morphism. From mat...
Monoidal.lean
/- Copyright (c) 2024 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou, Kim Morrison -/ import Mathlib.Algebra.Homology.BifunctorAssociator import Mathlib.Algebra.Homology.Single import Mathlib.CategoryTheory.GradedObject.Monoidal import Mathlib.Cate...
Prod.lean
/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Chris Hughes, Mario Carneiro, Yury Kudryashov -/ import Mathlib.Data.Int.Cast.Prod import Mathlib.Algebra.GroupWithZero.Prod import Mathlib.Algebra.Ring.CompTypeclasse...
classfun.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path. From mathcomp Require Import div choice fintype...
Prod.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.Prod import Mathlib.Data.Fintype.EquivFin /-! # fintype instance for the product of two fintypes. -/ open Function universe u v varia...
Rat.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.Algebra.Order.Module.Basic import Mathlib.Data.NNRat.Lemmas import Mathlib.Data.Rat.Cast.Order /-! # Monotonicity of the action by rational numbers -/ va...
FilteredColimitCommutesFiniteLimit.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.CategoryTheory.Limits.ColimitLimit import Mathlib.CategoryTheory.Limits.Preserves.FunctorCategory import Mathlib.CategoryTheory.Limits.Preserves.Finite imp...
PreservesSheafification.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 GrothendieckTopology attribute [local instance] Types.instFunLike Types.instCon...
NegOnePow.lean
/- Copyright (c) 2023 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou, Johan Commelin -/ import Mathlib.Algebra.Ring.Int.Parity import Mathlib.Algebra.Ring.Int.Units import Mathlib.Data.ZMod.IntUnitsPower /-! # Integer powers of (-1) This file def...
Nat.lean
/- Copyright (c) 2018 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Jens Wagemaker, Aaron Anderson -/ import Mathlib.Data.ENat.Basic import Mathlib.Data.Nat.Factors import Mathlib.RingTheory.UniqueFactorizationDomain.NormalizedFactors ...
Rearrangement.lean
/- Copyright (c) 2022 Mantas Bakšys. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mantas Bakšys -/ import Mathlib.Algebra.Order.Module.OrderedSMul import Mathlib.Algebra.Order.Module.Synonym import Mathlib.Algebra.Order.Monoid.OrderDual import Mathlib.Data.Finset.Max...
Over.lean
/- Copyright (c) 2025 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.CategoryTheory.Limits.Preserves.Filtered /-! # Forgetful functor from `Over X` preserves cofiltered limits Note that `Over.forget X : Over X ⥤ C` already ...
UniqueProds.lean
/- Copyright (c) 2022 Damiano Testa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damiano Testa -/ import Mathlib.Algebra.FreeMonoid.Basic import Mathlib.Algebra.Group.UniqueProds.Basic import Mathlib.Algebra.Order.Group.Nat /-! # Free monoids have unique products -...
mxred.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 div. From mathcomp Require Import choice fintype finfun bigop fingroup perm order. From ...
Pretopology.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.Sites.Grothendieck /-! # Grothendieck pretopologies Definition and lemmas about Grothendieck pretopologies. A Grothendieck pretopology for...
ENNReal.lean
/- Copyright (c) 2021 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Topology.Order.LiminfLimsup import Mathlib.Topology.Metrizable.Real /-! # Limsup and liminf of reals This file compiles filter-related results about `ℝ`,...
NormalizedTrace.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.RingTheory.Trace.Basic /-! # Normalized trace This file defines *normalized trace* map, that is, an `F`-linear map from the algebraic clos...
Intervals.lean
/- Copyright (c) 2024 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.Order.CompleteLatticeIntervals import Mathlib.Order.CompactlyGenerated.Basic /-! # Results about compactness properties for intervals in complete lattices ...
Basic.lean
/- Copyright (c) 2017 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Stephen Morgan, Kim Morrison -/ import Mathlib.CategoryTheory.Functor.Const import Mathlib.CategoryTheory.Opposites import Mathlib.Data.Prod.Basic /-! # Cartesian products of categories...
VonMangoldt.lean
/- Copyright (c) 2022 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta -/ import Mathlib.Analysis.SpecialFunctions.Log.Basic import Mathlib.Data.Nat.Cast.Field import Mathlib.NumberTheory.ArithmeticFunction /-! # The von Mangoldt Function In ...
Quaternion.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.Algebra.Star.SelfAdjoint import Mathlib.LinearAlgebra.Dimension.StrongRankCondition import Mathlib.LinearAlgebra.FreeModule.Finite.Basic /-! # Quate...
LinearTopology.lean
/- Copyright (c) 2024 Antoine Chambert-Loir, María Inés de Frutos-Fernández. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Antoine Chambert-Loir, María Inés de Frutos-Fernández -/ import Mathlib.Data.Finsupp.Interval import Mathlib.RingTheory.Ideal.Quotient.Defs impor...
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. (**********************...
Free.lean
/- Copyright (c) 2024 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.Algebra.Category.ModuleCat.Presheaf.Colimits import Mathlib.Algebra.Category.ModuleCat.Sheaf.Colimits /-! # Free sheaves of modules In this file, we construct ...
order.v
(* (c) Copyright 2006-2019 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq. From mathcomp Require Import path fintype tup...
numfield.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...
MulAntidiagonal.lean
/- Copyright (c) 2020 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn, Yaël Dillies -/ import Mathlib.Algebra.Order.Monoid.Defs import Mathlib.Data.Set.MulAntidiagonal import Mathlib.Algebra.Group.Pointwise.Set.Basic /-! # Multiplicat...
NonsingularInverse.lean
/- Copyright (c) 2019 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen, Lu-Ming Zhang -/ import Mathlib.Data.Matrix.Invertible import Mathlib.Data.Matrix.Kronecker import Mathlib.LinearAlgebra.FiniteDimensional.Basic import Mathlib.LinearAlgebra....
Basic.lean
/- Copyright (c) 2022 Xavier Roblot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Xavier Roblot -/ import Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings import Mathlib.NumberTheory.NumberField.Norm import Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots impo...
irreducibleDef.lean
import Mathlib.Tactic.IrreducibleDef import Mathlib.Util.WhatsNew set_option autoImplicit true /-- Add two natural numbers, but not during unification. -/ irreducible_def frobnicate (a b : Nat) := a + b example : frobnicate a 0 = a := by simp [frobnicate] example : frobnicate a 0 = a := frobnicate_def a 0 irr...
MinImports.lean
import Mathlib.Tactic.NormNum.Basic import Mathlib.Tactic.FunProp.Attr open Lean.Elab.Command Mathlib.Command.MinImports in run_cmd liftTermElabM do guard ([`A, `A.B.C_3, `A.B.C_2, `A.B.C_1, `A.B.C_0, `A.B.C].map previousInstName == [`A, `A.B.C_2, `A.B.C_1, `A.B.C, `A.B.C, `A.B.C]) run_cmd let stx ← `(v...
Concrete.lean
/- Copyright (c) 2021 Yakov Pechersky. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yakov Pechersky -/ import Mathlib.Data.List.Cycle import Mathlib.GroupTheory.Perm.Cycle.Type import Mathlib.GroupTheory.Perm.List /-! # Properties of cyclic permutations constructed...
Preorder.lean
/- Copyright (c) 2025 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.CategoryTheory.Limits.Shapes.Preorder.WellOrderContinuous import Mathlib.CategoryTheory.Limits.Shapes.Preorder.HasIterationOfShape import Mathlib.CategoryTheory....
Limits.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.Category.MonCat.Basic import Mathlib.Algebra.Group.Pi.Basic import Mathlib.Algebra.Group.Shrink import Mathlib.Algebra.Group.Submonoid.Defs import ...
FieldSimp.lean
/- Copyright (c) 2022 Jon Eugster. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jon Eugster, David Renshaw, Heather Macbeth, Michael Rothgang -/ import Mathlib.Tactic.FieldSimp import Mathlib.Tactic.Positivity import Mathlib.Tactic.Ring /-! # Tests for the `field_si...
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. (**********************...
Interval.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.Data.Finset.Sum import Mathlib.Data.Sum.Order import Mathlib.Order.Interval.Finset.Defs /-! # Finite intervals in a disjoint union This file provides the...
test_regular_conv.v
From mathcomp Require Import all_boot all_order all_algebra all_field. Section regular. Import GRing. Goal forall R : ringType, [the lalgType R of R^o] = R :> ringType. Proof. by move=> [? []]. Qed. Goal forall R : comRingType, [the algType R of R^o] = R :> ringType. Proof. by move=> [? []]. Qed. Goal forall R : c...
ProperSpace.lean
/- Copyright (c) 2024 Yakov Pechersky. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yakov Pechersky -/ import Mathlib.Analysis.Normed.Field.Lemmas import Mathlib.Analysis.SpecificLimits.Basic import Mathlib.Topology.MetricSpace.ProperSpace /-! # Proper nontrivially...
Basic.lean
/- Copyright (c) 2019 Reid Barton. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Reid Barton, Kim Morrison -/ import Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits /-! # Filtered categories A category is filtered if every finite diagram admits a cocone. We give a...
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...
ImageToKernel.lean
/- Copyright (c) 2021 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.CategoryTheory.Subobject.Limits /-! # Image-to-kernel comparison maps Whenever `f : A ⟶ B` and `g : B ⟶ C` satisfy `w : f ≫ g = 0`, we have `image_le_ker...
CrossProduct.lean
/- Copyright (c) 2020 Vedant Gupta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Vedant Gupta, Thomas Browning, Eric Wieser -/ import Mathlib.Analysis.InnerProductSpace.PiL2 import Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic import Mathlib.LinearAlgebra.CrossPr...
Dilation.lean
/- Copyright (c) 2022 Hanting Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Hanting Zhang -/ import Mathlib.Topology.MetricSpace.Antilipschitz import Mathlib.Topology.MetricSpace.Isometry import Mathlib.Topology.MetricSpace.Lipschitz import Mathlib.Data.FunLike...
Complete.lean
/- Copyright (c) 2025 Jiedong Jiang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jiedong Jiang -/ import Mathlib.RingTheory.WittVector.Domain import Mathlib.RingTheory.WittVector.Truncated import Mathlib.RingTheory.AdicCompletion.Basic /-! # The ring of Witt vector...
Finiteness.lean
/- Copyright (c) 2025 Jinzhao Pan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jinzhao Pan -/ import Mathlib.Order.RelSeries import Mathlib.RingTheory.Ideal.AssociatedPrime.Basic import Mathlib.RingTheory.Noetherian.Basic import Mathlib.RingTheory.Spectrum.Prime.Def...
Untop0.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.AddGroupWithTop import Mathlib.Algebra.Order.Ring.WithTop /-! # Conversion from WithTop to Base Type For types α that are instances of...
Chain.lean
/- Copyright (c) 2024 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.Algebra.DirectSum.LinearMap import Mathlib.Algebra.Lie.Weights.Cartan import Mathlib.RingTheory.Finiteness.Nilpotent import Mathlib.Data.Int.Interval /-! # ...
LocallySmall.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.Comma.StructuredArrow.Basic import Mathlib.CategoryTheory.Comma.Over.Basic import Mathlib.CategoryTheory.EssentiallySmall /-! # Comma categories...
ssralg.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 div seq. From mathcomp Require Import choice fintype finf...
IndicatorCard.lean
/- Copyright (c) 2024 Damien Thomine. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damien Thomine -/ import Mathlib.Algebra.BigOperators.Group.Finset.Indicator import Mathlib.Algebra.Order.Archimedean.Basic import Mathlib.Algebra.Order.BigOperators.Group.Finset impor...
Atoms.lean
/- Copyright (c) 2020 Aaron Anderson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Anderson -/ import Mathlib.Data.Set.Lattice import Mathlib.Data.SetLike.Basic import Mathlib.Order.ModularLattice import Mathlib.Order.SuccPred.Basic import Mathlib.Order.WellFou...
Birkhoff.lean
/- Copyright (c) 2024 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta -/ import Mathlib.Analysis.Convex.Combination import Mathlib.Analysis.Convex.Extreme import Mathlib.Analysis.Convex.Jensen import Mathlib.Analysis.Normed.Module.Convex impo...
sylow.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 prime bigop finset fingroup morphism. From mat...
Basic.lean
/- Copyright (c) 2022 Jireh Loreaux. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jireh Loreaux -/ import Mathlib.Order.Filter.Cofinite /-! # Basic theory of bornology We develop the basic theory of bornologies. Instead of axiomatizing bounded sets and defining bor...
InjectiveProjective.lean
/- Copyright (c) 2025 Sophie Morel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sophie Morel -/ import Mathlib.RingTheory.SimpleModule.Basic import Mathlib.Algebra.Module.Injective import Mathlib.Algebra.Module.Projective /-! If `R` is a semisimple ring, then any `...
Fix.lean
/- Copyright (c) 2018 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Simon Hudon -/ import Mathlib.Data.PFunctor.Multivariate.W import Mathlib.Data.QPF.Multivariate.Basic /-! # The initial algebra of a multivariate qpf is again a qpf. Fo...
Invariants.lean
/- Copyright (c) 2023 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.MeasureTheory.MeasurableSpace.Defs /-! # σ-algebra of sets invariant under a self-map In this file we define `MeasurableSpace.invariants (f : α → α)...
FiniteGrp.lean
/- Copyright (c) 2024 Jujian Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jujian Zhang, Nailin Guan, Yuyang Zhao -/ import Mathlib.Data.Finite.Defs import Mathlib.Algebra.Category.Grp.Basic /-! ## Main definitions and results * `FiniteGrp` is the category o...
galois.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div. From mathcomp Require Import choice fintype tupl...
TransferInstance.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.Algebra.Algebra.Equiv import Mathlib.Algebra.Module.TransferInstance import Mathlib.Algebra.Ring.TransferInstance /-! # Transfer algebraic structures ...