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Restriction.lean
/- Copyright (c) 2024 Etienne Marion. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Etienne Marion -/ import Mathlib.Data.Finset.Update import Mathlib.Order.Interval.Finset.Basic /-! # Restriction of a function indexed by a preorder Given a preorder `α` and dependen...
Basic.lean
/- Copyright (c) 2020 Anatole Dedecker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anatole Dedecker, Devon Tuma -/ import Mathlib.Algebra.Polynomial.Roots import Mathlib.Analysis.Asymptotics.AsymptoticEquivalent import Mathlib.Analysis.Asymptotics.SpecificAsymptoti...
Pi.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, Eric Wieser -/ import Mathlib.Algebra.Group.Fin.Tuple import Mathlib.Algebra.BigOperators.GroupWithZero.Action import Ma...
VitaliCaratheodory.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.MeasureTheory.Integral.Bochner.VitaliCaratheodory deprecated_module (since := "2025-04-06")
Bounds.lean
/- Copyright (c) 2023 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.Algebra.Order.Monoid.Canonical.Defs import Mathlib.Data.List.Infix import Mathlib.Data.List.MinMax import Mathlib.Data.List.EditDistance.Defs /-! # Lower ...
TypeTags.lean
/- Copyright (c) 2014 Floris van Doorn (c) 2016 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro -/ import Mathlib.Algebra.Group.Nat.Defs import Mathlib.Algebra.Group.TypeTags.Basic...
HomEquiv.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.LocalizerMorphism import Mathlib.CategoryTheory.HomCongr /-! # Bijections between morphisms in two localized categories Given two ...
LinearMaps.lean
/- Copyright (c) 2024 Wanyi He. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Wanyi He, Huanyu Zheng -/ import Mathlib.Algebra.CharP.Algebra import Mathlib.Algebra.Module.Torsion /-! # Characteristic of the ring of linear Maps This file contains properties of the cha...
LongExactSequence.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.Algebra.Homology.ConcreteCategory import Mathlib.Algebra.Homology.HomologicalComplexAbelian import Mathlib.RepresentationTheory.Homological.Group...
Basic.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.Algebra.Group.Action.Pi import Mathlib.Algebra.Group.End import Mathlib.Algebra.Module.NatInt import Mathlib.Algebra.Order.Archimedean.Basic /-! # M...
Decomposition.lean
/- Copyright (c) 2022 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser, Jujian Zhang -/ import Mathlib.Algebra.DirectSum.Module import Mathlib.Algebra.Module.Submodule.Basic /-! # Decompositions of additive monoids, groups, and modules into dire...
algC.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun ssrnat eqtype seq choice. From mathcomp Require Import div fintype path...
Pretriangulated.lean
/- Copyright (c) 2021 Luke Kershaw. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Luke Kershaw, Joël Riou -/ import Mathlib.Algebra.Homology.ShortComplex.Basic import Mathlib.CategoryTheory.Limits.Constructions.FiniteProductsOfBinaryProducts import Mathlib.CategoryThe...
Defs.lean
/- Copyright (c) 2018 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot, Johannes Hölzl -/ import Mathlib.Topology.UniformSpace.DiscreteUniformity import Mathlib.Topology.Algebra.Group.Basic /-! # Uniform structure on topological groups Th...
OfFunctorialResolutions.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.Localization.DerivabilityStructure.Constructor /-! # Functorial resolutions give derivability structures In this file, we provide a constructor ...
Triple.lean
/- Copyright (c) 2024 Dagur Asgeirsson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Dagur Asgeirsson, Ben Eltschig -/ import Mathlib.CategoryTheory.Adjunction.Unique import Mathlib.CategoryTheory.Monad.Adjunction /-! # Adjoint triples This file concerns adjoint tr...
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...
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...
DisjointCover.lean
/- Copyright (c) 2024 David Loeffler. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Loeffler -/ import Mathlib.Algebra.Notation.Indicator import Mathlib.Data.Fintype.BigOperators import Mathlib.Order.Disjointed import Mathlib.Topology.Separation.Profinite import...
Pseudoelement.lean
/- Copyright (c) 2022 Riccardo Brasca. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Riccardo Brasca -/ import Mathlib.CategoryTheory.Abelian.Pseudoelements import Mathlib.Algebra.Category.ModuleCat.Biproducts /-! # Pseudoelements and pullbacks Borceux claims in Prop...
imset2_finset.v
From mathcomp Require Import all_boot. Set Implicit Arguments. Unset Strict Implicit. Unset Printing Implicit Defensive. Check @imset2_pair.
Peel.lean
/- Copyright (c) 2023 Jireh Loreaux. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jireh Loreaux -/ import Mathlib.Tactic.Basic import Mathlib.Order.Filter.Basic /-! # The `peel` tactic `peel h with h' idents*` tries to apply `forall_imp` (or `Exists.imp`, or `Filte...
Basic.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, Johannes Hölzl, Mario Carneiro -/ import Mathlib.Algebra.Field.Defs import Mathlib.Algebra.Ring.GrindInstances import Mathlib.Algebra.Ring.Commute ...
monoid.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq. From mathcomp Require Import bigop fintype finfun. (******************************************************************************) (* Group-like structures ...
Order.lean
/- Copyright (c) 2019 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Minchao Wu -/ import Mathlib.Data.Sigma.Lex import Mathlib.Util.Notation3 import Init.NotationExtra import Mathlib.Data.Sigma.Basic import Mathlib.Order.Lattice import Math...
Ring.lean
/- Copyright (c) 2020 Devon Tuma. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Devon Tuma -/ import Mathlib.RingTheory.Localization.Away.Basic import Mathlib.RingTheory.Ideal.GoingUp import Mathlib.RingTheory.Jacobson.Polynomial import Mathlib.RingTheory.Artinian.Mod...
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...
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...
DeprecatedModule.lean
import Mathlib.Tactic.Linter.DeprecatedModule import Mathlib.Tactic.Linter.DocPrime import Mathlib.Tactic.Linter.DocString deprecated_module (since := "2025-04-10") /-- info: Deprecated modules 'MathlibTest.DeprecatedModule' deprecates to #[Mathlib.Tactic.Linter.DocPrime, Mathlib.Tactic.Linter.DocString] with no mes...
CartanExists.lean
/- Copyright (c) 2024 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.Algebra.Lie.CartanSubalgebra import Mathlib.Algebra.Lie.Rank /-! # Existence of Cartan subalgebras In this file we prove existence of Cartan subalge...
Pi.lean
/- Copyright (c) 2018 Simon Hudon. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Simon Hudon, Patrick Massot -/ import Mathlib.Algebra.Group.Pi.Lemmas import Mathlib.Algebra.GroupWithZero.Pi import Mathlib.Algebra.Ring.CompTypeclasses import Mathlib.Algebra.Ring.Hom.D...
FinitePresentation.lean
/- Copyright (c) 2025 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang, Christian Merten -/ import Mathlib.Algebra.Category.Ring.FilteredColimits import Mathlib.CategoryTheory.Limits.Preserves.Over import Mathlib.CategoryTheory.Limits.Shapes.Fini...
OfFn.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Data.Fin.Tuple.Basic /-! # Lists from functions Theorems and lemmas for dealing with `List.ofFn`, which converts a function on `Fin n` to a list of l...
LittleWedderburn.lean
/- Copyright (c) 2021 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Eric Rodriguez -/ import Mathlib.Algebra.GroupWithZero.Action.Center import Mathlib.GroupTheory.ClassEquation import Mathlib.RingTheory.Polynomial.Cyclotomic.Eval /-! ...
Antidiagonal.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.Multiset.Powerset /-! # The antidiagonal on a multiset. The antidiagonal of a multiset `s` consists of all pairs `(t₁, t₂)` such that `t₁ + t₂ =...
BicategoryCoherence.lean
/- Copyright (c) 2022 Yuma Mizuno. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yuma Mizuno -/ import Mathlib.CategoryTheory.Bicategory.Coherence import Mathlib.Tactic.CategoryTheory.BicategoricalComp /-! # A `coherence` tactic for bicategories We provide a `bicate...
Integration.lean
/- Copyright (c) 2021 Martin Zinkevich. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Martin Zinkevich, Vincent Beffara, Etienne Marion -/ import Mathlib.MeasureTheory.Integral.Pi import Mathlib.Probability.Independence.Integrable import Mathlib.Probability.Notation ...
frobenius.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 div. From mathcomp Require Import fintype bigop prime finset fingroup morphism. From mathcom...
Noetherian.lean
/- Copyright (c) 2020 Filippo A. E. Nuccio. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Filippo A. E. Nuccio, Andrew Yang -/ import Mathlib.RingTheory.Spectrum.Prime.Topology import Mathlib.RingTheory.Ideal.Quotient.Noetherian import Mathlib.RingTheory.Artinian.Modu...
Preserves.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.Monoidal.Braided.Basic import Mathlib.CategoryTheory.Limits.FunctorCategory.Basic /-! # Miscellany about preservations of (co)limits in m...
Grpd.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.SingleObj import Mathlib.CategoryTheory.Limits.Shapes.Products /-! # Category of groupoids This file contains the definition of the ...
GroupRingAction.lean
/- Copyright (c) 2020 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau -/ import Mathlib.Algebra.Polynomial.AlgebraMap import Mathlib.Algebra.Polynomial.Monic import Mathlib.Algebra.Ring.Action.Basic import Mathlib.GroupTheory.Coset.Card import Mathl...
Prime.lean
/- Copyright (c) 2017 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Neil Strickland -/ import Mathlib.Data.Nat.Prime.Defs import Mathlib.Data.PNat.Basic /-! # Primality and GCD on pnat This file extends the theory of `ℕ+` with ...
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_...
FiniteLength.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.RingTheory.Artinian.Module /-! # Modules of finite length We define modules of finite length (`IsFiniteLength`) to be finite iterated extensions of simple modu...
Basic.lean
/- Copyright (c) 2025 Anatole Dedecker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anatole Dedecker -/ import Mathlib.Algebra.Ring.Pi import Mathlib.Algebra.Ring.Subring.Defs import Mathlib.GroupTheory.GroupAction.SubMulAction import Mathlib.Order.Filter.Cofinite -...
matrix.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq choice. From mathcomp Require Import fintype finfun f...
maximal.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq choice. From mathcomp Require Import div fintype finfun bigop finset prime binomial. Fro...
GaussianInt.lean
/- Copyright (c) 2019 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes -/ import Mathlib.Data.Complex.Basic import Mathlib.Data.Nat.Prime.Basic import Mathlib.Data.Real.Archimedean import Mathlib.NumberTheory.Zsqrtd.Basic /-! # Gaussian intege...
MongePoint.lean
/- Copyright (c) 2020 Joseph Myers. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joseph Myers -/ import Mathlib.Geometry.Euclidean.Altitude import Mathlib.Geometry.Euclidean.Circumcenter /-! # Monge point and orthocenter This file defines the orthocenter of a trian...
DownstreamTest.lean
import Mathlib
LiouvilleWith.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.SpecialFunctions.Pow.Asymptotics import Mathlib.NumberTheory.Transcendental.Liouville.Basic import Mathlib.Topology.Instances.Irrational /-...
FormatTable.lean
/- Copyright (c) 2024 Bolton Bailey. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bolton Bailey -/ import Mathlib.Data.String.Defs /-! # Format Table This file provides a simple function for formatting a two-dimensional array of `String`s into a markdown-compliant ...
NoncommRing.lean
/- Copyright (c) 2020 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jireh Loreaux, Kim Morrison, Oliver Nash -/ import Mathlib.Algebra.Group.Action.Defs import Mathlib.Tactic.Abel /-! # The `noncomm_ring` tactic Solve goals in not necessarily commutativ...
LocalRing.lean
/- Copyright (c) 2022 Jon Eugster. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jon Eugster -/ import Mathlib.Algebra.CharP.Defs import Mathlib.Algebra.IsPrimePow import Mathlib.Data.Nat.Factorization.Basic import Mathlib.RingTheory.LocalRing.ResidueField.Defs /-! #...
OfEquivalence.lean
/- Copyright (c) 2022 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.CategoryTheory.Monoidal.Rigid.Basic /-! # Transport rigid structures over a monoidal equivalence. -/ noncomputable section namespace CategoryTheory op...
PluenneckeRuzsa.lean
/- Copyright (c) 2022 Yaël Dillies, George Shakan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, George Shakan -/ import Mathlib.Algebra.Order.Field.Rat import Mathlib.Combinatorics.Enumerative.DoubleCounting import Mathlib.Tactic.FieldSimp import Mathli...
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...
Prod.lean
/- Copyright (c) 2019 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Sébastien Gouëzel, Yury Kudryashov, Eric Wieser -/ import Mathlib.Analysis.Calculus.FDeriv.Comp import Mathlib.Analysis.Calculus.FDeriv.Const import Mathlib.Analysis.Calc...
Nonunits.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.Maximal /-! # The set of non-invertible elements of a monoid ## Main definitions * `nonunits` is the set of non...
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...
alt.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq choice. From mathcomp Require Import div fintype tupl...
AffineMap.lean
/- Copyright (c) 2021 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.Analysis.Normed.Affine.ContinuousAffineMap import Mathlib.Analysis.Calculus.ContDiff.Operations /-! # Smooth affine maps This file contains results about s...
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...
Imo2001Q5.lean
/- Copyright (c) 2025 Jeremy Tan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Tan -/ import Mathlib.Geometry.Euclidean.Triangle /-! # IMO 2001 Q5 Let `ABC` be a triangle. Let `AP` bisect `∠BAC` and let `BQ` bisect `∠ABC`, with `P` on `BC` and `Q` on `AC`. I...
CauchyDavenport.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.Additive.ETransform import Mathlib.GroupTheory.Order.Min /-! # The Cauchy-Davenport theorem This file proves a ...
Explicit.lean
/- Copyright (c) 2023 Dagur Asgeirsson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Dagur Asgeirsson -/ import Mathlib.CategoryTheory.Sites.Coherent.SheafComparison import Mathlib.Condensed.Light.Module /-! # The explicit sheaf condition for light condensed sets W...
Colex.lean
/- Copyright (c) 2020 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta, Alena Gusakov, Yaël Dillies -/ import Mathlib.Algebra.Order.Ring.GeomSum import Mathlib.Data.Finset.Slice import Mathlib.Data.Nat.BitIndices import Mathlib.Order.SupClosed ...
HomeomorphBall.lean
/- Copyright (c) 2021 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Oliver Nash -/ import Mathlib.Topology.PartialHomeomorph import Mathlib.Analysis.Normed.Group.AddTorsor import Mathlib.Analysis.NormedSpace.Pointwise import Mathlib.D...
ProjIcc.lean
/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Patrick Massot -/ import Mathlib.Order.Interval.Set.ProjIcc import Mathlib.Topology.Order.Basic /-! # Projection onto a closed interval In this file we prove that t...
Kernels.lean
/- Copyright (c) 2019 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Markus Himmel -/ import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero /-! # Kernels and cokernels In a category with zero morphisms, the kernel of a morphism `f : X...
Unique.lean
/- Copyright (c) 2020 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta, Thomas Read, Andrew Yang, Dagur Asgeirsson, Joël Riou -/ import Mathlib.CategoryTheory.Adjunction.Mates /-! # Uniqueness of adjoints This file shows that adjoints are uni...
CountingFunction.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.Meromorphic.Divisor import Mathlib.Analysis.SpecialFunctions.Log.Basic /-! # The Counting Function of Value Distribution Theory For nontrivi...
Basic.lean
/- Copyright (c) 2020 Joseph Myers. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joseph Myers -/ import Mathlib.LinearAlgebra.AffineSpace.AffineEquiv import Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs /-! # Affine spaces This file gives further properties...
DinatTrans.lean
/- Copyright (c) 2023 Andrea Laretto. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrea Laretto, Fernando Chu -/ import Mathlib.CategoryTheory.Opposites /-! # Dinatural transformations Dinatural transformations are special kinds of transformations between functors...
PrimesInAP.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.NumberTheory.DirichletCharacter.Orthogonality import Mathlib.NumberTheory.LSeries.Linearity import Mathlib.NumberTheory.LSeries.Nonvanishing import Mathl...
Terminal.lean
/- Copyright (c) 2025 Emily Riehl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Robin Carlier, Emily Riehl -/ import Mathlib.CategoryTheory.Limits.Shapes.Terminal /-! # Terminal categories We prove that a category is terminal if its underlying type has a `Unique` s...
Box.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.Disjointed import Mathlib.Algebra.Order.Ring.Int import Mathlib.Algebra.Order.Ring.Prod import Mathlib.Data.Int.Interval import Mathlib.Tacti...
Constructible.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.BooleanSubalgebra import Mathlib.Topology.Compactness.Bases import Mathlib.Topology.LocalAtTarget import Mathlib.Topology.QuasiSeparated import Mathl...
matrix.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq choice. From mathcomp Require Import fintype finfun f...
CocompactMap.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.Topology.ContinuousMap.Basic /-! # Cocompact continuous maps The type of *cocompact continuous maps* are those which tend to the cocompact filter on th...
Gluing.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.Order.ConditionallyCompleteLattice.Group import Mathlib.Topology.MetricSpace.Isometry /-! # Metric space gluing Gluing two metric spaces along ...
Init.lean
/- Copyright (c) 2023 Jannis Limperg. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jannis Limperg -/ import Mathlib.Init import Aesop /-! # SimpleGraph Rule Set This module defines the `SimpleGraph` Aesop rule set which is used by the `aesop_graph` tactic. Aesop r...
Defs.lean
/- Copyright (c) 2015, 2017 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel -/ import Mathlib.Data.ENNReal.Inv import Mathlib.Topology.UniformSpace.Basic import Mathlib.Topo...
Free.lean
/- Copyright (c) 2019 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau -/ import Mathlib.Algebra.Group.Basic import Mathlib.Algebra.Group.Equiv.Defs import Mathlib.Control.Applicative import Mathlib.Control.Traversable.Basic import Mathlib.Logic.Equi...
Mul.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.Nat.Choose.Basic import Mathlib.Tactic.Ring.RingNF /-! # Two lemm...
Basic.lean
/- Copyright (c) 2021 Aaron Anderson, Jesse Michael Han, Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Anderson, Jesse Michael Han, Floris van Doorn -/ import Mathlib.SetTheory.Cardinal.Basic /-! # Basics on First-Order Structures This file d...
symm.lean
import Mathlib.Algebra.Group.Hom.Defs import Mathlib.Logic.Equiv.Basic set_option autoImplicit true -- testing that the attribute is recognized @[symm] def eq_symm {α : Type} (a b : α) : a = b → b = a := Eq.symm example (a b : Nat) : a = b → b = a := by intros; symm; assumption example (a b : Nat) : a = b → True → b ...
Basic.lean
/- Copyright (c) 2018 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.Algebra.BigOperators.Expect import Mathlib.Algebra.Order.BigOperators.Ring.Finset import Mathlib.Algebra.Order.Field.Canonical import Mathlib.Algebra.O...
ssrmatching.v
From Corelib Require Export ssrmatching.
MayerVietoris.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.Sites.MayerVietorisSquare import Mathlib.CategoryTheory.Sites.Spaces import Mathlib.CategoryTheory.Functor.ReflectsIso.Balanced /-! # Mayer-Viet...
bigop.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path. From mathcomp Require Import div fintype tuple ...
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...
monoid.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq. From mathcomp Require Import bigop fintype finfun. (******************************************************************************) (* Group-like structures ...
Sum.lean
/- Copyright (c) 2025 Robin Carlier. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Robin Carlier -/ import Mathlib.CategoryTheory.Join.Basic import Mathlib.CategoryTheory.Sums.Basic /-! # Embedding of `C ⊕ D` into `C ⋆ D` This file constructs a canonical functor `Jo...
Vec.lean
/- Copyright (c) 2025 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.LinearAlgebra.Matrix.Trace import Mathlib.Data.Matrix.Kronecker import Mathlib.Data.Matrix.Hadamard /-! # Vectorization of matrices This file defines `Matr...
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.Closed.Enrichment import Mathlib.CategoryTheory.Enriched.FunctorCategory /-! # Functor categories are monoidal closed Let `C` be a monoidal clos...
Asymptotics.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Sébastien Gouëzel, Rémy Degenne, David Loeffler -/ import Mathlib.Analysis.SpecialFunctions.Pow.NNReal /-! # Limits and a...
Stabilizer.lean
/- Copyright (c) 2023 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Algebra.Group.Action.Pointwise.Finset import Mathlib.GroupTheory.QuotientGroup.Defs import Mathlib.Order.ConditionallyCompleteLattice.Basic /-! # Stabiliz...
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...