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BinaryProducts.lean
/- Copyright (c) 2020 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta, Andrew Yang -/ import Mathlib.CategoryTheory.Limits.Shapes.Terminal import Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts import Mathlib.CategoryTheory.Limits.Preserve...
Basic.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.Endomorphism /-! # The center of a category Given a category `C`, we introduce an abbreviation `CatCenter C` for the center of the category `C`,...
Smooth.lean
/- Copyright (c) 2025 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.RingTheory.RingHom.FinitePresentation import Mathlib.RingTheory.Smooth.Locus /-! # Smooth ring homomorphisms In this file we define smooth ring homomorphis...
orderedzmod.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import ssrAC div fintyp...
Limits.lean
/- Copyright (c) 2020 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.Algebra.Category.ModuleCat.Basic import Mathlib.Algebra.Category.Grp.Limits import Mathlib.Algebra.Colimit.Module import Mathlib.Algebra.Module.Shrink /-!...
Symmetric.lean
/- Copyright (c) 2022 Anatole Dedecker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Moritz Doll, Frédéric Dupuis, Heather Macbeth -/ import Mathlib.Analysis.InnerProductSpace.Subspace import Mathlib.Analysis.Normed.Operator.Banach import Mathlib.LinearAlgebra.Sesqui...
Expr.lean
import Mathlib.Lean.Expr.ReplaceRec import Mathlib.Data.Nat.Notation import Lean.Elab.Command open Lean Meta Elab Command section replaceRec /-! Test the implementation of `Expr.replaceRec` -/ /-- Reorder the last two arguments of every function in the expression. (The resulting term will generally not be a type-c...
fraction.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat div seq. From mathcomp Require Import ssrAC choice tuple ...
ZMod.lean
/- Copyright (c) 2021 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.Algebra.Algebra.Defs import Mathlib.Data.ZMod.Basic /-! # The `ZMod n`-algebra structure on rings whose characteristic divides `n` -/ assert_not_exis...
Compactum.lean
/- Copyright (c) 2020 Adam Topaz. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Adam Topaz -/ import Mathlib.CategoryTheory.Monad.Types import Mathlib.CategoryTheory.Monad.Limits import Mathlib.CategoryTheory.Equivalence import Mathlib.Topology.Category.CompHaus.Basic...
StoneSeparation.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.Analysis.Convex.Combination import Mathlib.Analysis.Convex.Join /-! # Stone's separation theorem This file proves Stone's separation theorem. This tells ...
Bochner.lean
/- Copyright (c) 2019 Zhouhang Zhou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Zhouhang Zhou, Yury Kudryashov, Sébastien Gouëzel, Rémy Degenne -/ import Mathlib.MeasureTheory.Integral.Bochner.Basic import Mathlib.MeasureTheory.Integral.Bochner.L1 import Mathlib.Me...
Basic.lean
/- Copyright (c) 2024 Violeta Hernández Palacios. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Violeta Hernández Palacios -/ import Mathlib.Data.Nat.Bitwise import Mathlib.SetTheory.Ordinal.Family import Mathlib.Tactic.Linter.DeprecatedModule deprecated_module "Th...
Examples.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.CategoryTheory.Galois.Basic import Mathlib.CategoryTheory.Action.Concrete import Mathlib.CategoryTheory.Action.Limits /-! # Examples of Galois cat...
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...
ParallelPair.lean
/- Copyright (c) 2023 Dagur Asgeirsson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Dagur Asgeirsson, Joël Riou -/ import Mathlib.CategoryTheory.Limits.Final /-! # Conditions for `parallelPair` to be initial In this file we give sufficient conditions on a category...
all_solvable.v
From mathcomp Require Export abelian. From mathcomp Require Export alt. From mathcomp Require Export burnside_app. From mathcomp Require Export center. From mathcomp Require Export commutator. From mathcomp Require Export cyclic. From mathcomp Require Export extraspecial. From mathcomp Require Export extremal. From mat...
Regular.lean
/- Copyright (c) 2017 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Floris van Doorn, Violeta Hernández Palacios -/ import Mathlib.SetTheory.Cardinal.Cofinality import Mathlib.SetTheory.Ordinal.FixedPoint /-! # Regular cardinals This ...
OptionalSampling.lean
/- Copyright (c) 2023 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Order.SuccPred.LinearLocallyFinite import Mathlib.Probability.Martingale.Basic /-! # Optional sampling theorem If `τ` is a bounded stopping time and `σ` ...
Parity.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.Fintype.Card import Mathlib.Algebra.Group.Even /-! # The cardinality of `Fin 2` is even. -/ variable {α : Type*} namespace Fintype instance I...
cc.lean
example (a₁ a₂ b₁ b₂ c d : Nat) : a₁ = c → a₂ = c → b₁ = d → d = b₂ → a₁ + b₁ + a₁ = a₂ + b₂ + c := by grind example (a b c : Prop) : (a ↔ b) → ((a ∧ (c ∨ b)) ↔ (b ∧ (c ∨ a))) := by grind example (a b c d : Prop) [d₁ : Decidable a] [d₂ : Decidable b] [d₃ : Decidable c] [d₄ : Decidable ...
Incenter.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.Geometry.Euclidean.Altitude import Mathlib.Geometry.Euclidean.SignedDist import Mathlib.Geometry.Euclidean.Sphere.Tangent import Mathlib.Tactic.Positivity....
Group.lean
/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Algebra.Order.Group.Basic import Mathlib.Topology.Algebra.Group.Defs import Mathlib.Topology.Order.LeftRightNhds /-! # Topology on a linear ordered ...
Basic.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.Monoid.Unbundled.Basic import Mathlib.Algebra.Order.Sub.Defs import Mathlib.Util.AssertE...
SumTransform.lean
/- Copyright (c) 2023 Frédéric Dupuis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Frédéric Dupuis -/ import Mathlib.Computability.AkraBazzi.GrowsPolynomially import Mathlib.Analysis.Calculus.Deriv.Inv import Mathlib.Analysis.SpecialFunctions.Pow.Continuity import ...
Compact.lean
/- Copyright (c) 2025 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.RingTheory.DedekindDomain.Factorization import Mathlib.RingTheory.DiscreteValuationRing.Basic import Mathlib.RingTheory.HopkinsLevitzki import Mathlib.RingTh...
Cocartesian.lean
/- Copyright (c) 2024 Calle Sönne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Calle Sönne -/ import Mathlib.CategoryTheory.FiberedCategory.HomLift /-! # Cocartesian morphisms This file defines cocartesian resp. strongly cocartesian morphisms with respect to a fu...
Basic.lean
/- Copyright (c) 2024 Jujian Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jujian Zhang, Nailin Guan, Yuyang Zhao -/ import Mathlib.Algebra.Category.Grp.FiniteGrp import Mathlib.Topology.Algebra.Group.ClosedSubgroup import Mathlib.Topology.Algebra.ContinuousMon...
MorphismProperty.lean
/- Copyright (c) 2024 Christian Merten. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christian Merten, Joël Riou, Adam Topaz -/ import Mathlib.AlgebraicGeometry.Pullbacks import Mathlib.CategoryTheory.Sites.MorphismProperty /-! # Site defined by a morphism property...
LongNames.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.Lean.Name import Mathlib.Lean.Expr.Basic import Lean.Elab.Command /-! # Commands `#long_names` and `#long_instances` For finding declarations with excess...
coe.lean
import Mathlib.Tactic.Coe example : { n : Nat // n > 3 } → Nat := (↑)
NAry.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 Batteries.Tactic.Init import Mathlib.Logic.Function.Defs /-! # Binary map of options This file defines the binary map of `Option`. This is mostly useful to defin...
RewriteSearch.lean
/- Copyright (c) 2023 Lean FRO, LLC. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Lean.Meta.Tactic.Rewrites import Mathlib.Algebra.Order.Group.Nat import Mathlib.Data.List.EditDistance.Estimator import Mathlib.Data.MLList.BestFirst import Mathl...
Multiplicity.lean
/- Copyright (c) 2022 Tian Chen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Tian Chen, Mantas Bakšys -/ import Mathlib.Algebra.Order.Ring.Basic import Mathlib.Algebra.Ring.GeomSum import Mathlib.Algebra.Ring.Int.Parity import Mathlib.Data.Nat.Choose.Sum import Math...
Basic.lean
/- Copyright (c) 2023 Kevin Buzzard. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Buzzard, Yaël Dillies, Jineon Baek -/ import Mathlib.Algebra.EuclideanDomain.Int import Mathlib.Algebra.GCDMonoid.Finset import Mathlib.Algebra.GCDMonoid.Nat import Mathlib.Algebr...
Cylinder.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.AlgebraicTopology.ModelCategory.Basic import Mathlib.AlgebraicTopology.ModelCategory.IsCofibrant /-! # Cylinders We introduce a notion of cylinder for an objec...
FixedPointApproximants.lean
/- Copyright (c) 2024 Ira Fesefeldt. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Ira Fesefeldt -/ import Mathlib.SetTheory.Ordinal.Arithmetic /-! # Ordinal Approximants for the Fixed points on complete lattices This file sets up the ordinal-indexed approximation t...
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...
Set.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.Data.Set.FunctorToTypes import Mathlib.CategoryTheory.Limits.Lattice import Mathlib.CategoryTheory.Limits.Preserves.Basic import Mathlib.CategoryTheory.Limits.Ty...
FiniteDimensional.lean
/- Copyright (c) 2019 Zhouhang Zhou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Zhouhang Zhou, Frédéric Dupuis, Heather Macbeth -/ import Mathlib.Analysis.InnerProductSpace.Projection.Basic import Mathlib.Analysis.InnerProductSpace.Projection.Reflection import Math...
OfFn.lean
/- Copyright (c) 2025 Fabrizio Barroero. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Fabrizio Barroero -/ import Mathlib.Algebra.BigOperators.Fin import Mathlib.Algebra.Polynomial.Degree.Lemmas import Mathlib.Data.List.ToFinsupp import Mathlib.LinearAlgebra.Pi /-! #...
Invertible.lean
/- Copyright (c) 2020 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen -/ import Mathlib.Algebra.Group.Invertible.Basic import Mathlib.Algebra.GroupWithZero.Units.Basic /-! # Theorems about invertible elements in a `GroupWithZero` We intentiona...
Limits.lean
/- Copyright (c) 2020 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Bhavik Mehta -/ import Mathlib.CategoryTheory.Limits.Preserves.Basic /-! # Isomorphisms about functors which preserve (co)limits If `G` preserves limits, and `C` and `D` ...
Functors.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.Limits.Preserves.Ulift import Mathlib.CategoryTheory.Sites.Coherent.CoherentSheaves import Mathlib.CategoryTheory.Sites.Whiskering i...
Units.lean
/- Copyright (c) 2019 Neil Strickland. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Neil Strickland, Yury Kudryashov -/ import Mathlib.Algebra.Group.Commute.Defs import Mathlib.Algebra.Group.Semiconj.Units /-! # Lemmas about commuting pairs of elements involving uni...
DualNumber.lean
/- Copyright (c) 2023 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.Algebra.DualNumber import Mathlib.Data.Matrix.Basic /-! # Matrices of dual numbers are isomorphic to dual numbers over matrices Showing this for the more g...
Bicones.lean
/- Copyright (c) 2021 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.CategoryTheory.Limits.Cones import Mathlib.CategoryTheory.FinCategory.Basic /-! # Bicones Given a category `J`, a walking `Bicone J` is a category whose ob...
Basis.lean
/- Copyright (c) 2025 Raphael Douglas Giles. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Raphael Douglas Giles, Zhixuan Dai, Zhenyan Fu, Yiming Fu, Jingting Wang, Eric Wieser -/ import Mathlib.LinearAlgebra.SymmetricAlgebra.Basic import Mathlib.LinearAlgebra.Dimensi...
QuasiMeasurePreserving.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 -/ import Mathlib.MeasureTheory.Measure.AbsolutelyContinuous import Mathlib.MeasureTheory.OuterMeasure.BorelCantelli /-! # Quasi Measure Preserving Func...
Coyoneda.lean
/- Copyright (c) 2018 Michael Jendrusch. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Jendrusch, Kim Morrison -/ import Mathlib.CategoryTheory.Monoidal.Types.Basic import Mathlib.CategoryTheory.Monoidal.CoherenceLemmas /-! # `(𝟙_ C ⟶ -)` is a lax monoidal f...
Basic.lean
/- Copyright (c) 2023 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes -/ import Mathlib.ModelTheory.Syntax import Mathlib.ModelTheory.Semantics import Mathlib.ModelTheory.Algebra.Ring.Basic import Mathlib.Algebra.Field.MinimalAxioms import Ma...
Induction.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.Algebra.Category.ModuleCat.Free import Mathlib.Topology.Category.Profinite.Nobeling.Span import Mathlib.Topology.Category.Profinite.Nobeling.Succes...
Gluing.lean
/- Copyright (c) 2021 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.Topology.Gluing import Mathlib.Geometry.RingedSpace.OpenImmersion import Mathlib.Geometry.RingedSpace.LocallyRingedSpace.HasColimits /-! # Gluing Structured...
gfunctor.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 fintype. From mathcomp Require Import bigop finset fingroup morphism automorphism. From math...
Field.lean
/- Copyright (c) 2024 Violeta Hernández Palacios. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Violeta Hernández Palacios -/ import Mathlib.Algebra.CharP.Two import Mathlib.SetTheory.Nimber.Basic import Mathlib.Tactic.Abel import Mathlib.Tactic.Linter.DeprecatedModul...
ExpLog.lean
/- Copyright (c) 2024 Frédéric Dupuis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Frédéric Dupuis -/ import Mathlib.Analysis.Normed.Algebra.Spectrum import Mathlib.Analysis.SpecialFunctions.Exponential import Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalcu...
ToLin.lean
/- Copyright (c) 2019 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen -/ import Mathlib.Algebra.Algebra.Subalgebra.Tower import Mathlib.Data.Finite.Sum import Mathlib.Data.Matrix.Block import Mathl...
PossibleTypes.lean
/- Copyright (c) 2023 Antoine Chambert-Loir. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Antoine Chambert-Loir -/ import Mathlib.GroupTheory.Perm.Cycle.Concrete /-! # Possible cycle types of permutations * For `m : Multiset ℕ`, `Equiv.Perm.exists_with_cycleType_i...
SchurZassenhaus.lean
/- Copyright (c) 2021 Thomas Browning. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Thomas Browning -/ import Mathlib.GroupTheory.Transfer /-! # The Schur-Zassenhaus Theorem In this file we prove the Schur-Zassenhaus theorem. ## Main results - `Subgroup.exists_ri...
Indization.lean
/- Copyright (c) 2025 Markus Himmel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Markus Himmel -/ import Mathlib.CategoryTheory.Limits.Indization.Category import Mathlib.CategoryTheory.Preadditive.Transfer import Mathlib.CategoryTheory.Preadditive.Opposite import Ma...
Zip.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Kenny Lau -/ import Mathlib.Data.List.Forall2 /-! # zip & unzip This file provides results about `List.zipWith`, `List.zip` and `List.unzip` (definitions are in core ...
GameMultiplication.lean
/- Copyright (c) 2024 Violeta Hernández Palacios. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Violeta Hernández Palacios -/ import Mathlib.SetTheory.Game.Basic import Mathlib.Tactic.FinCases import Mathlib.Tactic.Linter.DeprecatedModule deprecated_module "This m...
Basic.lean
/- Copyright (c) 2019 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Floris van Doorn, Yaël Dillies -/ import Mathlib.Algebra.Group.Action.Basic import Mathlib.Algebra.Group.Action.Opposite import Mathlib.Algebra.Group.Pointwise.Set.Scal...
Defs.lean
/- Copyright (c) 2020 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Analysis.Calculus.Deriv.Basic import Mathlib.Analysis.Calculus.ContDiff.Defs /-! # One-dimensional iterated derivatives We define the `n`-th de...
Hensel.lean
/- Copyright (c) 2018 Robert Y. Lewis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Robert Y. Lewis -/ import Mathlib.Algebra.Polynomial.Identities import Mathlib.Analysis.SpecificLimits.Basic import Mathlib.NumberTheory.Padics.PadicIntegers import Mathlib.Topology.A...
HNNExtension.lean
/- Copyright (c) 2023 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes -/ import Mathlib.Algebra.Ring.CharZero import Mathlib.Algebra.Ring.Int.Units import Mathlib.GroupTheory.Coprod.Basic import Mathlib.GroupTheory.Complement /-! ## HNN Exte...
Counit.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.Algebra.MvPolynomial.Eval /-! ## Counit morphisms for multivariate polynomials One may consider the ring of multivariate polynomials `MvPolynomial A ...
Dart.lean
/- Copyright (c) 2020 Kyle Miller. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kyle Miller -/ import Mathlib.Combinatorics.SimpleGraph.Basic import Mathlib.Data.Fintype.Sigma /-! # Darts in graphs A `Dart` or half-edge or bond in a graph is an ordered pair of adja...
Centralizer.lean
/- Copyright (c) 2021 Thomas Browning. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Thomas Browning, Jireh Loreaux -/ import Mathlib.Algebra.Group.Center import Mathlib.Algebra.Group.Subsemigroup.Basic import Mathlib.GroupTheory.Subsemigroup.Center /-! # Centralizer...
SMulAntidiagonal.lean
/- Copyright (c) 2024 Scott Carnahan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Scott Carnahan -/ import Mathlib.Algebra.Order.AddTorsor import Mathlib.Order.WellFoundedSet /-! # Antidiagonal for scalar multiplication Given partially ordered sets `G` and `P`, wi...
Forall2.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Johannes Hölzl -/ import Mathlib.Data.List.Basic /-! # Double universal quantification on a list This file provides an API for `List.Forall₂` (definition in `Data.Lis...
Lemmas.lean
/- Copyright (c) 2019 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Fabian Glöckle, Kyle Miller -/ import Mathlib.LinearAlgebra.Basis.Basic import Mathlib.LinearAlgebra.Dimension.ErdosKaplansky import Mathlib.LinearAlgebra.Dual.Basis im...
Spec.lean
/- Copyright (c) 2020 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Justus Springer -/ import Mathlib.Geometry.RingedSpace.LocallyRingedSpace import Mathlib.AlgebraicGeometry.StructureSheaf import Mathlib.RingTheory.Localization.Localizatio...
Adjunction.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.Functor.Derived.LeftDerived import Mathlib.CategoryTheory.Functor.Derived.RightDerived /-! # Derived adjunction Assume that functors `G : C₁ ⥤ C...
separable.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...
imset2_finset.v
From mathcomp Require Import all_boot. Set Implicit Arguments. Unset Strict Implicit. Unset Printing Implicit Defensive. Check @imset2_pair.
CPolynomial.lean
/- Copyright (c) 2023 Sophie Morel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sophie Morel -/ import Mathlib.Analysis.Analytic.Constructions import Mathlib.Analysis.Analytic.CPolynomialDef /-! # Properties of continuously polynomial functions We expand the API a...
Monotone.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.Data.Set.Monotone import Mathlib.Order.Interval.Set.Disjoint import Mathlib.Order.SuccPred.Archimedean /-! # Monotonicity on intervals In this file...
CheckCompositions.lean
import Mathlib.CategoryTheory.Limits.Preserves.Limits import Mathlib.Tactic.Recall universe v₁ v₂ v₃ v u₁ u₂ u₃ u open CategoryTheory Limits variable {J : Type u} [Category.{v} J] {C : Type u₁} [Category.{v₁} C] {D : Type u₂} [Category.{v₂} D] {E : Type u₃} [Category.{v₃} E] (F : J ⥤ C) (G : C ⥤ D) (H : D ⥤ E) ...
ConvergenceInMeasure.lean
/- Copyright (c) 2022 Rémy Degenne, Kexing Ying. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne, Kexing Ying -/ import Mathlib.MeasureTheory.Function.Egorov import Mathlib.MeasureTheory.Function.LpSpace.Complete /-! # Convergence in measure We define con...
finfun.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 tuple. ...
Invertible.lean
/- Copyright (c) 2023 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser, Ahmad Alkhalawi -/ import Mathlib.Data.Matrix.ConjTranspose import Mathlib.Tactic.Abel /-! # Extra lemmas about invertible matrices A few of the `Invertible` lemmas general...
vector.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 fi...
Module.lean
import Mathlib.Algebra.Algebra.Rat import Mathlib.Data.Complex.Module -- Test that the `SMul ℚ ℂ` instance is correct. example : (Complex.SMul.instSMulRealComplex : SMul ℚ ℂ) = (Algebra.toSMul : SMul ℚ ℂ) := by with_reducible_and_instances rfl
mxrepresentation.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path. From mathcomp Require Import div choice fintype...
Spectrum.lean
/- Copyright (c) 2022 Alexander Bentkamp. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Alexander Bentkamp -/ import Mathlib.Analysis.InnerProductSpace.Spectrum import Mathlib.Data.Matrix.Rank import Mathlib.LinearAlgebra.Matrix.Diagonal import Mathlib.LinearAlgebra.M...
UpstreamableDecl.lean
/- Copyright (c) 2024 Damiano Testa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damiano Testa, Anne Baanen -/ import ImportGraph.Imports import Mathlib.Init /-! # The `upstreamableDecl` linter The `upstreamableDecl` linter detects declarations that could be moved...
Congruence.lean
/- Copyright (c) 2023 Jovan Gerbscheid. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jovan Gerbscheid, Chu Zheng -/ import Mathlib.Topology.MetricSpace.Congruence import Mathlib.Analysis.InnerProductSpace.Basic import Mathlib.Analysis.Normed.Group.AddTorsor import M...
Irreducible.lean
/- Copyright (c) 2025 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.LinearAlgebra.RootSystem.RootPositive import Mathlib.LinearAlgebra.RootSystem.WeylGroup import Mathlib.RepresentationTheory.Submodule /-! # Irreducible root...
Limits.lean
/- Copyright (c) 2024 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.Algebra.Category.ModuleCat.Presheaf import Mathlib.Algebra.Category.ModuleCat.ChangeOfRings import Mathlib.CategoryTheory.Limits.Preserves.Limits import Mathlib....
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...
NatAbs.lean
/- Copyright (c) 2021 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen, Jeremy Tan -/ import Mathlib.Algebra.GroupWithZero.Hom import Mathlib.Algebra.GroupWithZero.Nat import Mathlib.Algebra.Ring.Int.Defs /-! # Lemmas about `Int.natAbs` This fi...
ExistsAndEq.lean
/- Copyright (c) 2025 Vasilii Nesterov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Vasilii Nesterov -/ import Mathlib.Init /-! # simproc for `∃ a', ... ∧ a' = a ∧ ...` This module implements the `existsAndEq` simproc that triggers on goals of the form `∃ a, body`...
Basic.lean
/- Copyright (c) 2024 María Inés de Frutos Fernández. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: María Inés de Frutos Fernández, Xavier Généreux -/ import Mathlib.LinearAlgebra.FreeModule.Basic /-! # Skew Monoid Algebras Given a monoid `G` acting on a ring `k`, t...
WithZeroMulInt.lean
/- Copyright (c) 2025 Salvatore Mercuri. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Salvatore Mercuri -/ import Mathlib.GroupTheory.ArchimedeanDensely import Mathlib.Topology.Algebra.Valued.ValuationTopology /-! # Topological results for integer-valued rings This...
Pointwise.lean
/- Copyright (c) 2024 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.Algebra.Ring.Action.End import Mathlib.RingTheory.Ideal.Maps /-! # Pointwise instances on `Ideal`s This file provides the action `Ideal.pointwiseMulAction`...
SeparationQuotient.lean
/- Copyright (c) 2024 Yoh Tanimoto. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yoh Tanimoto -/ import Mathlib.Analysis.Normed.Group.Hom import Mathlib.Topology.Algebra.SeparationQuotient.Hom /-! # Lifts of maps to separation quotients of seminormed groups For any...
DeleteEdges.lean
/- Copyright (c) 2020 Aaron Anderson, Jalex Stark, Kyle Miller. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Anderson, Jalex Stark, Kyle Miller, Alena Gusakov, Hunter Monroe -/ import Mathlib.Algebra.Ring.Defs import Mathlib.Combinatorics.SimpleGraph.Finite imp...
BigOperators.lean
/- Copyright (c) 2022 Yakov Pechersky. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yakov Pechersky -/ import Mathlib.Algebra.BigOperators.Group.Finset.Basic import Mathlib.Algebra.Group.Finsupp import Mathlib.Data.Finset.Pairwise /-! # Sums of collections of Finsu...
jacobiSym.lean
import Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol import Mathlib.Tactic.NormNum.Prime -- TODO(kmill): remove once the mathlib ToExpr Int instance is removed set_option eval.pp false section Csimp /-! We test that `@[csimp]` replaces `jacobiSym` (i.e. `J(· | ·)`) and `legendreSym` with `jacobiSym.fastJacobiSym`...