filename stringlengths 5 42 | content stringlengths 15 319k |
|---|---|
Homotopy.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.Algebra.Homology.Linear
import Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex
import Mathlib.Tactic.Abel
/-!
# Chain homotopies
We define chain... |
div.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq.
(******************************************************************************)
(* Th... |
LYM.lean | /-
Copyright (c) 2022 Bhavik Mehta, Yaël Dillies. 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.Field.Basic
import Mathlib.Algebra.Field.Rat
import Mathlib.Combinatorics.Enumerative.DoubleCounting
imp... |
Unit.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.PUnit
import Mathlib.CategoryTheory.Limits.HasLimits
/-!
# `Discrete PUnit` has limits and colimits
Mostly for the sake of constructing tr... |
Pointwise.lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Alex J. Best
-/
import Mathlib.MeasureTheory.Group.Arithmetic
/-!
# Pointwise set operations on `MeasurableSet`s
In this file we prove several versions of the follo... |
Prorepresentability.lean | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
import Mathlib.Algebra.Category.Grp.Limits
import Mathlib.CategoryTheory.CofilteredSystem
import Mathlib.CategoryTheory.Galois.Decomposition
import Mathlib.Catego... |
Identities.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Kim Morrison, Jens Wagemaker
-/
import Mathlib.Algebra.Polynomial.Derivative
import Mathlib.Tactic.LinearCombination
import Mathlib.Tactic.Ring
/-!
# Theor... |
FactorsThrough.lean | /-
Copyright (c) 2025 Etienne Marion. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Etienne Marion
-/
import Mathlib.MeasureTheory.Constructions.Polish.StronglyMeasurable
import Mathlib.Probability.Process.Filtration
/-!
# Factorization of a map from measurability
C... |
interval_inference.v | (* mathcomp analysis (c) 2017 Inria and AIST. License: CeCILL-C. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype choice.
From mathcomp Require Import order ssralg ssrnum ssrint interval.
(**md********************************************************... |
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.Algebra.Homology.ComplexShape
import Mathlib.Algebra.Ring.Int.Defs
import Mathlib.Algebra.Group.Nat.Defs
import Mathlib.Tactic.ByContra
/-! # Embeddings of comp... |
Basic.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.AlgebraicTopology.SimplexCategory.Basic
import Mathlib.CategoryTheory.PathCategory.Basic
/-! # Presentation of the simplex category by generators and rel... |
Imo2020Q2.lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers, Yury Kudryashov
-/
import Mathlib.Analysis.MeanInequalities
/-!
# IMO 2020 Q2
The real numbers `a`, `b`, `c`, `d` are such that `a ≥ b ≥ c ≥ d > 0` and `a + b + c + d = 1... |
Lemmas.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, Kyle Miller
-/
import Mathlib.Data.Finset.Max
import Mathlib.Data.Set.Finite.Basic
import Mathlib.Data.Set.Lattice
import Mathlib.Data.Fintype.Powerset
... |
ZMod.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.Group.EvenFunction
import Mathlib.Analysis.SpecialFunctions.Complex.CircleAddChar
import Mathlib.Analysis.Fourier.FourierTransform
import Mathl... |
Odd.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.Group.Defs
import Mathlib.Algebra.Order.Monoid.OrderDual
import Mathlib.Order.Monotone.Union
/-!
# Monotonicity of odd functions
An o... |
jordanholder.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 big... |
IsTerminal.lean | /-
Copyright (c) 2019 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Bhavik Mehta
-/
import Mathlib.CategoryTheory.PEmpty
import Mathlib.CategoryTheory.Limits.IsLimit
import Mathlib.CategoryTheory.EpiMono
import Mathlib.CategoryTheory.Catego... |
Compatibility.lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.CategoryTheory.Equivalence
/-! Tools for compatibilities between Dold-Kan equivalences
The purpose of this file is to introduce tools which will enable the
con... |
Pi.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 Batteries.Tactic.Alias
import Mathlib.Data.Int.Notation
import Mathlib.Tactic.TypeStar
import Mathlib.Util.AssertExists
/-!
# Cast of integers to function typ... |
KrullTopology.lean | /-
Copyright (c) 2022 Sebastian Monnet. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Monnet
-/
import Mathlib.FieldTheory.Galois.Basic
import Mathlib.Topology.Algebra.FilterBasis
import Mathlib.Topology.Algebra.OpenSubgroup
/-!
# Krull topology
We define ... |
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... |
Field.lean | /-
Copyright (c) 2024 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.FieldTheory.PurelyInseparable.Basic
import Mathlib.RingTheory.Artinian.Ring
import Mathlib.RingTheory.LocalProperties.Basic
import Mathlib.Algebra.Polynomial... |
FunctorCategory.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.Limits.FunctorCategory.Basic
import Mathlib.CategoryTheory.Monoidal.Cartesian.Basic
import Mathlib.CategoryTheory.Monoidal.Types.Basic
/-!
# Func... |
Generators.lean | /-
Copyright (c) 2024 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.RingTheory.Ideal.Cotangent
import Mathlib.RingTheory.Localization.Away.Basic
import Mathlib.RingTheory.MvPolynomial.Tower
import Mathlib.RingTheory.TensorPro... |
T0Sierpinski.lean | /-
Copyright (c) 2022 Ivan Sadofschi Costa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ivan Sadofschi Costa
-/
import Mathlib.Topology.Order
import Mathlib.Topology.Sets.Opens
import Mathlib.Topology.ContinuousMap.Basic
/-!
# Any T0 space embeds in a product of co... |
all.v | From mathcomp Require Export all_boot.
From mathcomp Require Export all_order.
From mathcomp Require Export all_fingroup.
From mathcomp Require Export all_algebra.
From mathcomp Require Export all_solvable.
From mathcomp Require Export all_field.
From mathcomp Require Export all_character.
|
BigOperators.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.Star.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Defs
/-! # Big-operators lemmas about `star` algebraic operations
These results are kep... |
LocallyFinite.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.Order.Filter.SmallSets
import Mathlib.Topology.ContinuousOn
/-!
### Locally finite families of sets
We say that a family of sets in a topological s... |
Card.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
-/
import Mathlib.LinearAlgebra.Quotient.Defs
import Mathlib.SetTheory.Cardinal.Finite
import Mathlib.GroupTheory.Coset.B... |
Atlas.lean | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Floris van Doorn
-/
import Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions
import Mathlib.Geometry.Manifold.VectorBundle.Tangent
/-!
# Differentiability of m... |
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... |
ZMod.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.Analysis.Fourier.ZMod
import Mathlib.Analysis.NormedSpace.Connected
import Mathlib.NumberTheory.LSeries.RiemannZeta
/-!
# L-series of functions on `Z... |
MulAction.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.Algebra.AddTorsor.Defs
import Mathlib.GroupTheory.GroupAction.SubMulAction
import Mathlib.Topology.Algebra.Constructions
import Mathlib.Topology.Alge... |
delaborators.lean | import Mathlib.Util.Delaborators
import Mathlib.Data.Set.Lattice
section PiNotation
variable (P : Nat → Prop) (α : Nat → Type) (s : Set ℕ)
/-- info: ∀ x > 0, P x : Prop -/
#guard_msgs in
#check ∀ x, x > 0 → P x
/-- info: ∀ x > 0, P x : Prop -/
#guard_msgs in
#check ∀ x > 0, P x
/-- info: ∀ x ≥ 0, P x : Prop -/
#gua... |
Mod_.lean | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Paul Lezeau, Robin Carlier
-/
import Mathlib.CategoryTheory.Monoidal.Mon_
import Mathlib.CategoryTheory.Monoidal.Action.Basic
/-!
# The category of module objects over a m... |
tuple.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat.
From mathcomp Require Import seq choice fintype path.
S... |
ArtinianObject.lean | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou, Kim Morrison
-/
import Mathlib.CategoryTheory.Subobject.Lattice
import Mathlib.CategoryTheory.ObjectProperty.ContainsZero
import Mathlib.CategoryTheory.ObjectProperty.EpiMono
imp... |
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... |
List.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.Algebra.Order.Group.Nat
import Mathlib.Data.List.Rotate
import Mathlib.GroupTheory.Perm.Support
/-!
# Permutations from a list
A list `l : List α` ... |
linear_combination.lean | import Mathlib.Tactic.Abel
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.LinearCombination
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.Module
set_option autoImplicit true
private axiom test_sorry : ∀ {α}, α
-- We deliberately mock R here so that we don't have to import the deps
axiom Real : Type
no... |
Basic.lean | /-
Copyright (c) 2022 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import Mathlib.LinearAlgebra.Dimension.DivisionRing
import Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas
import Mathlib.RingTheory.Finiteness.Quotient
import Mathlib.RingT... |
ShiftSequence.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.Shift.InducedShiftSequence
import Mathlib.CategoryTheory.Shift.Localization
import Mathlib.Algebra.Homology.HomotopyCategory.Shift
import Mathlib.... |
Simplex.lean | /-
Copyright (c) 2025 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import Mathlib.Analysis.Normed.Affine.Simplex
import Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine
/-!
# Simplices in Euclidean spaces.
This file defines propertie... |
Instances.lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro, Johannes Hölzl
-/
import Mathlib.Algebra.Order.Group.Defs
import Mathlib.Algebra.Order.Monoid.OrderDual
import Mathlib.Tactic.Linter.De... |
NonUnital.lean | /-
Copyright (c) 2024 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Algebra.Algebra.Spectrum.Quasispectrum
import Mathlib.Topology.ContinuousMap.Compact
import Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Un... |
binomial.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq path.
From mathcomp Require Import div fintype tuple ... |
Ideal.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.RingTheory.Finiteness.Finsupp
import Mathlib.RingTheory.Ideal.Maps
/-!
# Finitely generated ideals
Lemmas about finiteness of ideal operations.
-/
o... |
SymmDiff.lean | /-
Copyright (c) 2021 Bryan Gin-ge Chen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz, Bryan Gin-ge Chen, Yaël Dillies
-/
import Mathlib.Order.BooleanAlgebra.Basic
import Mathlib.Logic.Equiv.Basic
/-!
# Symmetric difference and bi-implication
This file d... |
character.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 choice ssrnat seq.
From mathcomp Require Import path div fintype... |
FreimanHom.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.CharP.Basic
import Mathlib.Algebra.Group.Pointwise.Set.Basic
import Mathlib.Algebra.G... |
CantorSet.lean | /-
Copyright (c) 2024 Jana Göken. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Artur Szafarczyk, Suraj Krishna M S, Jean-Baptiste Stiegler, Isabelle Dubois,
Tomáš Jakl, Lorenzo Zanichelli, Alina Yan, Emilie Uthaiwat, Jana Göken,
Filippo A. E. Nuccio
-/
import Mathlib... |
NatSqrt.lean | /-
Copyright (c) 2022 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Kyle Miller
-/
import Mathlib.Tactic.NormNum
/-! # `norm_num` extension for `Nat.sqrt`
This module defines a `norm_num` extension for `Nat.sqrt`.
-/
namespace Tactic... |
HullKernel.lean | /-
Copyright (c) 2024 Christopher Hoskin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Hoskin
-/
import Mathlib.Data.Set.Subset
import Mathlib.Order.Irreducible
import Mathlib.Topology.Order.LowerUpperTopology
import Mathlib.Topology.Sets.Closeds
/-!
# ... |
Bounded.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.Topology.Order.Compact
import Mathlib.Topology.MetricSpace.ProperSpace
import M... |
Hyperoperation.lean | /-
Copyright (c) 2023 Mark Andrew Gerads. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mark Andrew Gerads, Junyan Xu, Eric Wieser
-/
import Mathlib.Tactic.Ring
/-!
# Hyperoperation sequence
This file defines the Hyperoperation sequence.
`hyperoperation 0 m k = k + ... |
Archive.lean | import Archive.Arithcc
import Archive.Examples.Eisenstein
import Archive.Examples.IfNormalization.Result
import Archive.Examples.IfNormalization.Statement
import Archive.Examples.IfNormalization.WithoutAesop
import Archive.Examples.MersennePrimes
import Archive.Examples.PropEncodable
import Archive.Hairer
import Archiv... |
FailIfNoProgress.lean | /-
Copyright (c) 2023 Thomas Murrills. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Murrills
-/
import Mathlib.Init
import Lean.Elab.Tactic.Basic
import Lean.Meta.Tactic.Util
/-!
# Fail if no progress
This implements the `fail_if_no_progress` tactic, which f... |
Nat.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.GroupWithZero.Defs
i... |
SingleTriangle.lean | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.Algebra.Homology.DerivedCategory.ShortExact
/-!
# The distinguished triangle of a short exact sequence in an abelian category
Given a short exact short complex... |
PosPart.lean | /-
Copyright (c) 2021 Christopher Hoskin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Hoskin, Yaël Dillies
-/
import Mathlib.Algebra.Order.Group.Unbundled.Abs
import Mathlib.Algebra.Notation
/-!
# Positive & negative parts
Mathematical structures posse... |
Order.lean | /-
Copyright (c) 2022 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.Data.NNRat.Defs
import Mathlib.Algebra.Order.Ring.Rat
import Mathlib.Algebra.Order.Nonneg.Ring
/-!
# Bundled ordered algebra s... |
Basic.lean | /-
Copyright (c) 2022 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Geißer, Michael Stoll
-/
import Mathlib.Data.Real.Irrational
import Mathlib.RingTheory.Coprime.Lemmas
import Mathlib.RingTheory.Int.Basic
import Mathlib.Tactic.Basic
/-!
# Diop... |
Preserves.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.EffectiveEpi.Comp
import Mathlib.Data.Fintype.EquivFin
/-!
# Functors preserving effective epimorphisms
This file concerns functor... |
FinitePresentation.lean | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
import Mathlib.RingTheory.Localization.Finiteness
import Mathlib.RingTheory.MvPolynomial.Localization
import Mathlib.RingTheory.RingHom.FiniteType
import Mathlib.... |
ssreflect.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From Corelib Require Export ssreflect.
Global Set SsrOldRewriteGoalsOrder.
Global Set Asymmetric Patterns.
Global Set Bullet Behavior "None".
#[deprecated(sinc... |
StructurePolynomial.lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Robert Y. Lewis
-/
import Mathlib.FieldTheory.Finite.Polynomial
import Mathlib.NumberTheory.Basic
import Mathlib.RingTheory.WittVector.WittPolynomial
/-!
# Witt struct... |
Iso.lean | /-
Copyright (c) 2018 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback
/-!
# The pullback of an isomorphism
This file provides some basic results about the pullback (and push... |
center.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div.
From mathcomp Require Import fintype bigop finset fingroup morphism perm.
From math... |
Complete.lean | /-
Copyright (c) 2024 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
import Mathlib.CategoryTheory.Adjunction.Lifting.Right
import Mathlib.CategoryTheory.Closed.FunctorCategory.Groupoid
import Mathlib.CategoryTheory.Groupoid.Discre... |
hall.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 choice.
From mathcomp Require Import fintype finset prime fingroup morphism.
From ma... |
Degrees.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
-/
import Mathlib.Algebra.MonoidAlgebra.Degree
import Mathlib.Algebra.MvPolynomial.Rename
/-!
# Degrees of polynomials
This file establ... |
all_fingroup.v | From mathcomp Require Export action.
From mathcomp Require Export automorphism.
From mathcomp Require Export fingroup.
From mathcomp Require Export gproduct.
From mathcomp Require Export morphism.
From mathcomp Require Export perm.
From mathcomp Require Export presentation.
From mathcomp Require Export quotient.
|
Basic.lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Kenny Lau
-/
import Mathlib.Algebra.Ring.GeomSum
import Mathlib.RingTheory.Ideal.Quotient.Defs
import Mathlib.RingTheory.Ideal.Span
/-!
# Basic results in number theor... |
Prod.lean | /-
Copyright (c) 2019 Jan-David Salchow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo
-/
import Mathlib.Analysis.NormedSpace.OperatorNorm.Bilinear
/-!
# Operator norm: Cartesian products
Interaction of operator norm wit... |
ring.lean | import Mathlib.Algebra.Order.Field.Defs
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.Ring
private axiom test_sorry : ∀ {α}, α
set_option autoImplicit true
-- We deliberately mock R here so that we don't have to import the deps
axiom Real : Type
notation "ℝ" => Real
@[instance] axiom Real.field : Field ℝ
@[in... |
Solvable.lean | /-
Copyright (c) 2021 Jordan Brown, Thomas Browning, Patrick Lutz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jordan Brown, Thomas Browning, Patrick Lutz
-/
import Mathlib.Data.Fin.VecNotation
import Mathlib.GroupTheory.Abelianization.Defs
import Mathlib.GroupTheor... |
EulerMascheroni.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.Data.Complex.ExponentialBounds
import Mathlib.NumberTheory.Harmonic.Defs
import Mathlib.Analysis.Normed.Order.Lattice
import Mathlib.Analysis.SpecialF... |
SetLike.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.Init
import Aesop
/-!
# SetLike Rule Set
This module defines the `SetLike` and `SetLike!` Aesop rule sets.
Aesop rule sets only become visible once th... |
Int.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.Order.Group.Unbundled.Abs
import Mathlib.Algebra.Group.Int.Defs
import Mathlib.Data.Int.Basic
/-!
# Facts about `ℤ` as an (unbundled) ordered gr... |
FunctorCategory.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.Limits.FunctorCategory.Basic
import Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts
import Mathlib.CategoryTheory.Limits.Prese... |
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.CategoryTheory.Limits.Shapes.Products
import Mathlib.CategoryTheory.Limits.Shapes.Equalizers
import Mathlib.Ca... |
qpoly.v | From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
From mathcomp Require Import fintype tuple bigop binomial finset finfun ssralg.
From mathcomp Require Import countalg finalg poly polydiv perm fingroup matrix.
From mathcomp Require Import mxalgebra mxpoly... |
PartialHomeomorph.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.Logic.Equiv.PartialEquiv
import Mathlib.Topology.Homeomorph.Lemmas
import Mathlib.Topology.Sets.Opens
/-!
# Partial homeomorphisms
This file de... |
IdealQuotient.lean | /-
Copyright (c) 2022 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import Mathlib.LinearAlgebra.FreeModule.Finite.Quotient
/-! # Ideals in free modules over PIDs
## Main results
- `Ideal.quotientEquivPiSpan`: `S ⧸ I`, if `S` is finite f... |
IsKan.lean | /-
Copyright (c) 2023 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno
-/
import Mathlib.CategoryTheory.Bicategory.Extension
/-!
# Kan extensions and Kan lifts in bicategories
The left Kan extension of a 1-morphism `g : a ⟶ c` along a 1-morphis... |
Localization.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.Center.Basic
import Mathlib.CategoryTheory.Localization.Predicate
import Mathlib.CategoryTheory.Preadditive.AdditiveFunctor
/-!
# Localization of... |
EqLocus.lean | /-
Copyright (c) 2022 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.Module.Submodule.Ker
/-!
# The submodule of elements `x : M` such that `f x = g x`
## Main declarations
* `LinearMap.eqLocus`: the submodule of el... |
PartialSups.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.Data.Set.Finite.Lattice
import Mathlib.Order.ConditionallyCompleteLattice.Indexed
import Mathlib.Order.Interval.Finset.Nat
import Mathlib.Order.SuccPred.Ba... |
Tannaka.lean | /-
Copyright (c) 2025 Yacine Benmeuraiem. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yacine Benmeuraiem
-/
import Mathlib.RepresentationTheory.FDRep
/-!
# Tannaka duality for finite groups
In this file we prove Tannaka duality for finite groups.
The theorem can ... |
Subquiver.lean | /-
Copyright (c) 2021 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn
-/
import Mathlib.Order.Notation
import Mathlib.Combinatorics.Quiver.Basic
/-!
## Wide subquivers
A wide subquiver `H` of a quiver `H` consists of a subset of the edge set `a ... |
SmallComplete.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.Limits.Shapes.Products
import Mathlib.SetTheory.Cardinal.Basic
/-!
# Any small complete category is a preorder
We show that any small cate... |
WeakBilin.lean | /-
Copyright (c) 2021 Kalle Kytölä. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kalle Kytölä, Moritz Doll
-/
import Mathlib.Topology.Algebra.Module.LinearMap
import Mathlib.LinearAlgebra.BilinearMap
/-!
# Weak dual topology
This file defines the weak topology give... |
Coequalizer.lean | /-
Copyright (c) 2025 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
import Mathlib.Logic.Function.Defs
/-!
# Coequalizer of a pair of functions
The coequalizer of two functions `f g : α → β` is the pair (`μ`, `p : β → μ`) that
s... |
Injective.lean | /-
Copyright (c) 2024 Andrew Yang, Qi Ge, Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang, Qi Ge, Christian Merten
-/
import Mathlib.RingTheory.RingHomProperties
/-! # Meta properties of injective ring homomorphisms -/
lemma _root_.RingHo... |
Basic.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.Algebra.BigOperators.Associated
import Mathlib.Data.ENat.Basic
import Mathlib.RingTheory.UniqueFactorizationDomain.Defs... |
Integer.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Mario Carneiro, Johan Commelin, Amelia Livingston, Anne Baanen
-/
import Mathlib.Algebra.Group.Pointwise.Set.Scalar
import Mathlib.Algebra.Ring.Subsemiring.Basic
import Mathlib.R... |
extraspecial.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 choice fintype bigop finset prime binomial.
From mathc... |
SynthesizeUsing.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.Init
import Lean.Elab.Tactic.Basic
import Qq
/-!
# `SynthesizeUsing`
This is a slight simplification of the `solve_aux` tactic in Lean3.
-/
open Lean El... |
jordanholder.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 big... |
TwoP.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.CategoryTheory.Category.Bipointed
import Mathlib.Data.TwoPointing
/-!
# The category of two-pointed types
This defines `TwoP`, the category of two-pointe... |
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