filename stringlengths 5 42 | content stringlengths 15 319k |
|---|---|
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... |
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