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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...