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Lemmas.lean
/- Copyright (c) 2020 Frédéric Dupuis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Frédéric Dupuis -/ import Mathlib.Analysis.Normed.Module.FiniteDimension import Mathlib.Analysis.RCLike.Basic /-! # Further lemmas about `RCLike` -/ open scoped Finset variable {K ...
Basic.lean
/- Copyright (c) 2023 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.Algebra.Group.Submonoid.Operations import Mathlib.Algebra.GroupWithZero.Regular import Mathlib.Algebra.NoZeroSMulDivisors.Defs import Mathlib.Algebra.Order...
Comparable.lean
/- Copyright (c) 2025 Violeta Hernández Palacios. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Violeta Hernández Palacios -/ import Mathlib.Order.Antisymmetrization /-! # Comparability and incomparability relations Two values in a preorder are said to be comparable...
Size.lean
/- Copyright (c) 2014 Floris van Doorn (c) 2016 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro -/ import Mathlib.Algebra.Group.Nat.Defs import Mathlib.Algebra.Group.Basic import M...
Profinite.lean
/- Copyright (c) 2024 Nailin Guan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Nailin Guan, Yuyang Zhao, Jujian Zhang -/ import Mathlib.FieldTheory.KrullTopology import Mathlib.FieldTheory.Galois.GaloisClosure import Mathlib.Topology.Algebra.Category.ProfiniteGrp.B...
countalg.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 ss...
Nullstellensatz.lean
/- Copyright (c) 2021 Devon Tuma. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Devon Tuma -/ import Mathlib.RingTheory.Jacobson.Ring import Mathlib.FieldTheory.IsAlgClosed.Basic import Mathlib.RingTheory.Spectrum.Prime.Basic /-! # Nullstellensatz This file establish...
Products.lean
/- Copyright (c) 2025 Robin Carlier. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Robin Carlier -/ import Mathlib.CategoryTheory.Sums.Associator import Mathlib.CategoryTheory.Products.Associator /-! # Functors out of sums of categories. This file records the univer...
Constructions.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.Group.TypeTags.Basic import Mathlib.Topology.Bornology.Basic /-! # Bornology structure on products and subtypes In this file we define `Bor...
Hilbert90.lean
/- Copyright (c) 2023 Amelia Livingston. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Amelia Livingston -/ import Mathlib.RepresentationTheory.Homological.GroupCohomology.Hilbert90 deprecated_module (since := "2025-06-14")
Orientation.lean
/- Copyright (c) 2024 Rida Hamadani. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rida Hamadani -/ import Mathlib.Combinatorics.Digraph.Basic import Mathlib.Combinatorics.SimpleGraph.Basic /-! # Graph Orientation This module introduces conversion operations betwee...
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...
Part.lean
/- Copyright (c) 2017 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Jeremy Avigad, Simon Hudon -/ import Mathlib.Algebra.Notation.Defs import Mathlib.Data.Set.Subsingleton import Mathlib.Logic.Equiv.Defs /-! # Partial values of a type ...
Mul.lean
/- Copyright (c) 2018 Ellen Arlt. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Ellen Arlt, Blair Shi, Sean Leather, Mario Carneiro, Johan Commelin, Lu-Ming Zhang -/ import Mathlib.Algebra.BigOperators.GroupWithZero.Action import Mathlib.Algebra.BigOperators.Ring.Fins...
Basic.lean
/- Copyright (c) 2020 Adam Topaz. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Zhangir Azerbayev, Adam Topaz, Eric Wieser -/ import Mathlib.LinearAlgebra.CliffordAlgebra.Basic import Mathlib.LinearAlgebra.Alternating.Curry /-! # Exterior Algebras We construct the e...
Basic.lean
/- Copyright (c) 2023 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Dynamics.FixedPoints.Basic import Mathlib.Algebra.BigOperators.Group.Finset.Basic /-! # Birkhoff sums In this file we define `birkhoffSum f g n x` ...
PicardGroup.lean
/- Copyright (c) 2025 Junyan Xu. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Junyan Xu -/ import Mathlib.Algebra.Category.ModuleCat.Monoidal.Symmetric import Mathlib.Algebra.Module.FinitePresentation import Mathlib.Algebra.Module.LocalizedModule.Submodule import Mat...
Presentation.lean
import Mathlib.RingTheory.Extension.Presentation.Basic deprecated_module (since := "2025-05-11")
Powerset.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl -/ import Mathlib.Algebra.BigOperators.Group.Finset.Basic import Mathlib.Data.Finset.Powerset /-! # Big operators In this file we prove theorems about products and sum...
Ring_finiteness.lean
import Mathlib -- https://github.com/leanprover-community/mathlib4/pull/17557#issuecomment-2426920648 variable (R : Type*) [Ring R] [IsSemisimpleRing R] example : IsNoetherianRing R := inferInstance example : IsArtinianRing R := inferInstance
Basic.lean
/- Copyright (c) 2022 Mario Carneiro, Heather Macbeth. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Heather Macbeth, Yaël Dillies -/ import Mathlib.Algebra.Order.Group.PosPart import Mathlib.Algebra.Order.Ring.Basic import Mathlib.Algebra.Order.Hom.Ba...
fintype.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 ssrnotations eqtype. From mathcomp Require Import ssrnat seq choice pat...
BestFirst.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 Batteries.Data.MLList.Basic import Mathlib.Data.Prod.Lex import Mathlib.Data.Set.Finite.Range import Mathlib.Order.Estimator /-! # Best first search We perform b...
ModelsWithJ.lean
/- Copyright (c) 2021 Kevin Buzzard. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Buzzard, David Kurniadi Angdinata -/ import Mathlib.AlgebraicGeometry.EllipticCurve.Weierstrass /-! # Models of elliptic curves with prescribed j-invariant This file defines the...
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 -/ import Mathlib.Algebra.Field.Periodic import Mathlib.Algebra.Field.Subfield.Basic import Mathlib.Topology.Algebra.Order.Archimedean import Mathlib.Top...
prime.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 path. From mathcomp Require Import choice fintype div bigop. (*************************...
Monotone.lean
/- Copyright (c) 2021 Bolton Bailey. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bolton Bailey -/ import Mathlib.Analysis.SpecialFunctions.Pow.Real /-! # Logarithm Tonality In this file we describe the tonality of the logarithm function when multiplied by function...
Lift.lean
/- Copyright (c) 2019 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn -/ import Mathlib.Tactic.Basic import Batteries.Lean.Expr import Batteries.Lean.Meta.UnusedNames /-! # lift tactic This file defines the `lift` tactic, allowing th...
Semilat.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.Order.Category.PartOrd import Mathlib.Order.Hom.BoundedLattice /-! # The categories of semilattices This defines `SemilatSupCat` and `SemilatInfCat`, the...
ssralg.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 choice fintype finf...
monoid.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq. From mathcomp Require Import bigop fintype finfun. (******************************************************************************) (* Group-like structures ...
RightAngle.lean
/- Copyright (c) 2022 Joseph Myers. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joseph Myers -/ import Mathlib.Geometry.Euclidean.Angle.Oriented.Affine import Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle /-! # Oriented angles in right-angled triangles. T...
Pi.lean
/- Copyright (c) 2024 Yaël Dillies, Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Andrew Yang -/ import Mathlib.Algebra.Algebra.Pi import Mathlib.Algebra.Algebra.Subalgebra.Lattice import Mathlib.LinearAlgebra.Pi /-! # Products of subalgebr...
CC.lean
/- Copyright (c) 2016 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Leonardo de Moura, Miyahara Kō -/ import Mathlib.Tactic.CC.Addition /-! # Congruence closure The congruence closure tactic `cc` tries to solve the goal by chaining equalities ...
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...
zmodp.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 choice eqtype ssrnat seq. From mathcomp Require Import div fintype bigo...
TrivSqZeroExt.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.Analysis.Normed.Algebra.Exponential import Mathlib.Analysis.Normed.Lp.ProdLp import Mathlib.Topology.Instances.TrivSqZeroExt /-! # Results on `TrivSqZeroExt...
QuaternionExponential.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.Analysis.Quaternion import Mathlib.Analysis.Normed.Algebra.Exponential import Mathlib.Analysis.SpecialFunctions.Trigonometric.Series /-! # Lemmas about `Nor...
ssrfun.v
From mathcomp Require Import ssreflect. From Corelib Require Export ssrfun. From mathcomp Require Export ssrnotations. #[export] Set Warnings "-overwriting-delimiting-key". (* remove above line when requiring Rocq >= 9.0 *) Set Implicit Arguments. Unset Strict Implicit. Unset Printing Implicit Defensive. (***********...
Completion.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.Analysis.Normed.Group.Completion import Mathlib.Analysis.NormedSpace.OperatorNorm.NormedSpace import Mathlib.Topology.Algebra.UniformRing import Math...
Independence.lean
/- Copyright (c) 2022 Michael Blyth. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Blyth -/ import Mathlib.LinearAlgebra.Projectivization.Basic /-! # Independence in Projective Space In this file we define independence and dependence of families of elements ...
Defs.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.Defs /-! # Invertible elements This file defines a typeclass `Invertible a` for elements `a` with a two-sided multiplicative inverse. The in...
generic_quotient.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice. From mathcomp Require Import seq fintype. (*****...
pgroup.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 prime fingroup morphism. From mat...
ToDFinsupp.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.Module.Equiv.Defs import Mathlib.Data.DFinsupp.Module import Mathlib.Data.Finsupp.SMul /-! # Conversion between `Finsupp` and homogeneous `DFinsupp`...
Defs.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Tactic.Lemma import Mathlib.Tactic.TypeStar import Batteries.Tactic.Alias /-! # Extra definitions on `Option` This file defines more operations invol...
Convergence.lean
/- Copyright (c) 2022 Kexing Ying. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kexing Ying -/ import Mathlib.MeasureTheory.Constructions.Polish.Basic import Mathlib.MeasureTheory.Function.UniformIntegrable import Mathlib.Probability.Martingale.Upcrossing /-! # Mar...
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 ...
nmodule.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq. From mathcomp Require Import bigop fintype finfun monoid. (******************************************************************************) (* Additive group-like structures ...
Transport.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.Monoidal.NaturalTransformation /-! # Transport a monoidal structure along an equivalence. When `C` and `D` are equivalent as categories, w...
InfinitePi.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.Probability.Independence.Basic import Mathlib.Probability.ProductMeasure /-! # Random variables are independent iff their joint distribution is the pr...
ColimCoyoneda.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.Abelian.GrothendieckCategory.Subobject import Mathlib.CategoryTheory.Limits.FunctorCategory.EpiMono import Mathlib.CategoryTheory.MorphismProperty...
Lebesgue.lean
/- Copyright (c) 2021 Kexing Ying. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kexing Ying -/ import Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue import Mathlib.MeasureTheory.Measure.Complex import Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan imp...
GaloisConnection.lean
/- Copyright (c) 2017 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Stephen Morgan, Kim Morrison, Johannes Hölzl, Reid Barton -/ import Mathlib.CategoryTheory.Category.Preorder import Mathlib.CategoryTheory.Adjunction.Basic import Mathlib.Order.GaloisCon...
Basic.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Devon Tuma -/ import Mathlib.Topology.Instances.ENNReal.Lemmas import Mathlib.MeasureTheory.Measure.Dirac /-! # Probability mass functions This file is about probabil...
Finite.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 -/ import Mathlib.Combinatorics.SimpleGraph.Maps import Mathlib.Data.Finset.Max import Mathlib.Data.Sy...
Rat.lean
/- Copyright (c) 2018 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot, Johannes Hölzl, Yaël Dillies -/ import Mathlib.Analysis.Normed.Group.Int import Mathlib.Topology.Instances.Rat /-! # ℚ as a normed group -/ namespace Rat instance i...
SchwartzZippel.lean
/- Copyright (c) 2023 Bolton Bailey. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bolton Bailey, Yaël Dillies, Andrew Yang -/ import Mathlib.Algebra.BigOperators.Field import Mathlib.Algebra.MvPolynomial.Equiv import Mathlib.Algebra.MvPolynomial.Variables import Math...
Basic.lean
/- Copyright (c) 2014 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Amelia Livingston, Yury Kudryashov, Neil Strickland, Aaron Anderson -/ import Mathlib.Algebra.Group.Basic import Mathlib.Tactic.Commo...
polyXY.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq. From mathcomp Require Import fintype tuple fi...
HausdorffDistance.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.Analysis.SpecificLimits.Basic import Mathlib.Topology.MetricSpace.IsometricSMul import Mathlib.Tactic.Finiteness /-! # Hausdorff distance The H...
Integral.lean
/- Copyright (c) 2022 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.MeasureTheory.Integral.Bochner.Basic import Mathlib.Probability.Kernel.Basic /-! # Bochner integrals of kernels -/ open MeasureTheory namespace Probabi...
Option.lean
/- Copyright (c) 2021 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Mario Carneiro, Sean Leather -/ import Mathlib.Data.Finset.Card import Mathlib.Data.Finset.Union /-! # Finite sets in `Option α` In this file we define * `Option.t...
Defs.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, Floris van Doorn -/ import Mathlib.Data.ULift import Mathlib.Util.Delaborators import Mathlib.Util.AssertExists /-! # Cardinal Numbers We define cardi...
generic_quotient.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice. From mathcomp Require Import seq fintype. (*****...
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.
DualQuaternion.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.Algebra.Quaternion /-! # Dual quaternions Similar to the way that rotations in 3D space can be represented by quaternions...
galois.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div. From mathcomp Require Import choice fintype tupl...
FlexibleLinter.lean
import Batteries.Tactic.PermuteGoals import Mathlib.Tactic.Linter.FlexibleLinter import Mathlib.Tactic.Abel import Mathlib.Tactic.Ring import Mathlib.Tactic.LinearCombination set_option linter.flexible true set_option linter.unusedVariables false /-- warning: 'simp at h' is a flexible tactic modifying 'h'… Note: Thi...
Basic.lean
/- Copyright (c) 2024 Yakov Pechersky. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yakov Pechersky -/ import Mathlib.Topology.MetricSpace.Pseudo.Lemmas /-! ## Ultrametric spaces This file defines ultrametric spaces, implemented as a mixin on the `Dist`, so that it...
Constructions.lean
/- Copyright (c) 2025 Yakov Pechersky. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yakov Pechersky -/ import Mathlib.Topology.UniformSpace.DiscreteUniformity import Mathlib.Topology.UniformSpace.Pi import Mathlib.Topology.UniformSpace.Ultra.Basic /-! # Products of ...
Flat.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.Filtered.Connected import Mathlib.CategoryTheory.Limits.ConeCategory import Mathlib.CategoryTheory.Limits.FilteredColimitCommutesFiniteLimit i...
Count.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.FreeMonoid.Basic import Mathlib.Algebra.Group.TypeTags.Basic /-! # `List.count` as a bundled homomorphism In this file we define `FreeMonoi...
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 ...
Symmetrized.lean
/- Copyright (c) 2021 Christopher Hoskin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christopher Hoskin -/ import Mathlib.Algebra.Jordan.Basic import Mathlib.Algebra.Module.Defs /-! # Symmetrized algebra A commutative multiplication on a real or complex space can...
algebraics_fundamentals.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun ssrnat eqtype seq choice. From mathcomp Require Import div fintype path...
Lex.lean
/- Copyright (c) 2022 Damiano Testa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damiano Testa -/ import Mathlib.Data.Finsupp.Order import Mathlib.Data.DFinsupp.Lex import Mathlib.Data.Finsupp.ToDFinsupp /-! # Lexicographic order on finitely supported functions Th...
Submodule.lean
/- Copyright (c) 2024 Jz Pan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jz Pan -/ import Mathlib.Algebra.Algebra.Operations import Mathlib.Algebra.Algebra.Subalgebra.Lattice import Mathlib.LinearAlgebra.DirectSum.Finsupp /-! # Some results on tensor product of s...
Header.lean
/- Copyright (c) 2024 Damiano Testa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Rothgang, Damiano Testa -/ import Lean.Elab.Command import Lean.Elab.ParseImportsFast import Mathlib.Tactic.Linter.DirectoryDependency /-! # The "header" linter The "header" ...
Separation.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Patrick Massot, Yury Kudryashov -/ import Mathlib.Tactic.ApplyFun import Mathlib.Topology.Separation.Regular import Mathlib.Topology.UniformSpace.Basic /-! # Hausdorff...
Pow.lean
/- Copyright (c) 2021 Damiano Testa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damiano Testa -/ import Mathlib.Algebra.BigOperators.Group.Finset.Defs import Mathlib.Algebra.Regular.Basic /-! # Product of regular elements ## TODO Move to `Mathlib/Algebra/BigOper...
Boundary.lean
/- Copyright (c) 2021 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Kim Morrison, Adam Topaz -/ import Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex /-! # The boundary of the standard simplex We introduce the boundary `∂Δ[n]` of th...
UniqueGluing.lean
/- Copyright (c) 2021 Justus Springer. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Justus Springer -/ import Mathlib.Topology.Sheaves.Forget import Mathlib.Topology.Sheaves.SheafCondition.PairwiseIntersections import Mathlib.CategoryTheory.Limits.Types.Shapes /-! #...
Retract.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.ShortComplex.QuasiIso import Mathlib.CategoryTheory.MorphismProperty.Retract /-! # Quasi-isomorphisms of short complexes are stable under retr...
Defs.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.RingTheory.WittVector.StructurePolynomial /-! # Witt vectors In this file we define the type of `p`-typical Witt vectors and ring op...
Traversable.lean
/- Copyright (c) 2025 Edward van de Meent. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Edward van de Meent -/ import Mathlib.Data.Tree.Basic import Mathlib.Control.Applicative import Mathlib.Control.Traversable.Basic /-! # Traversable Binary Tree Provides a `Trav...
Basic.lean
/- Copyright (c) 2021 Aaron Anderson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Anderson -/ import Mathlib.Algebra.Notation.Support import Mathlib.Algebra.Order.Monoid.Unbundled.WithTop import Mathlib.Data.Finsupp.Defs import Mathlib.Order.WellFoundedSet /-...
Filtered.lean
/- Copyright (c) 2018 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Reid Barton -/ import Mathlib.CategoryTheory.Limits.Types.Colimits import Mathlib.CategoryTheory.Filtered.Basic /-! # Filtered colimits in the category of types. We give ...
ApproximateSubgroup.lean
/- Copyright (c) 2024 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.Group.Subgroup.Pointwise import Mathlib.Combinatorics.Additive.CovBySMul import Mathlib.Combinatorics.Additive.RuzsaCovering import M...
ContinuousOfBounded.lean
/- Copyright (c) 2022 Anatole Dedecker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Moritz Doll -/ import Mathlib.Analysis.LocallyConvex.Bounded import Mathlib.Analysis.RCLike.Basic /-! # Continuity and Von Neumann boundedness This files proves that for `E` and `F...
SimpRw.lean
/- Copyright (c) 2020 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen, Mario Carneiro -/ import Mathlib.Tactic.SimpRw private axiom test_sorry : ∀ {α}, α -- `simp_rw` can perform rewrites under binders: example : (fun (x y : Nat) ↦ x + y) = (...
Flat.lean
/- Copyright (c) 2025 Jakob von Raumer. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jakob von Raumer -/ import Mathlib.CategoryTheory.Filtered.CostructuredArrow import Mathlib.CategoryTheory.Functor.Flat /-! # Pulling back filteredness along representably flat func...
LocallyConnected.lean
/- Copyright (c) 2022 Anatole Dedecker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anatole Dedecker -/ import Mathlib.Topology.Connected.Basic /-! # Locally connected topological spaces A topological space is **locally connected** if each neighborhood filter admi...
Lemmas.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.Group.Units.Hom import Mathlib.Algebra.GroupWithZero.Commute import Mathlib.Algebra.GroupWithZero.Hom /-! # Further lemmas about units in a `M...
Ring.lean
/- Copyright (c) 2025. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: euprunin -/ import Mathlib.Tactic.Ring.Basic import Mathlib.Tactic.Ring.RingNF import Mathlib.Tactic.Ring.PNat /-! We register `ring` with the `hint` tactic. -/ register_hint ring
Euclidean.lean
/- Copyright (c) 2021 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen -/ import Mathlib.Algebra.Order.AbsoluteValue.Basic import Mathlib.Algebra.EuclideanDomain.Int /-! # Euclidean absolute values This file defines a predicate `AbsoluteValue.I...
Multiplicity.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.RingTheory.Multiplicity import Mathlib.RingTheory.UniqueFactorizationDomain.NormalizedFactors /-! # Unique factorizati...
Restrict.lean
/- Copyright (c) 2014 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Andrew Zipperer, Haitao Zhang, Minchao Wu, Yury Kudryashov -/ import Mathlib.Data.Set.Image /-! # Restrict the domain of a function to a set ## Main definitions * `Set...
Extension.lean
/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Heather Macbeth -/ import Mathlib.Analysis.Convex.Cone.Extension import Mathlib.Analysis.NormedSpace.RCLike import Mathlib.Analysis.NormedSpace.Extend import Mathlib....
StrictConvexSpace.lean
/- Copyright (c) 2022 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Yury Kudryashov -/ import Mathlib.Analysis.Normed.Module.Convex import Mathlib.Analysis.Normed.Module.Ray import Mathlib.Analysis.NormedSpace.Pointwise /-! # Strictly conv...