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alt.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq choice. From mathcomp Require Import div fintype tupl...
Expand.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.Algebra.MvPolynomial.Monad /-! ## Expand multivariate polynomials Given a multivariate polynomial `φ`, one may replace every occurre...
fieldext.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 div. From mathcomp Require Import choice fintype tupl...
ModEq.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.Algebra.Order.Group.Unbundled.Int import Mathlib.Algebra.Ring.Nat import Mathlib.Data.Int.GCD import Mathlib.Data.Nat.GCD.Basic /-! # Congruences modu...
Subcomplex.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.SimplicialSet.Basic import Mathlib.CategoryTheory.Subpresheaf.Basic /-! # Subcomplexes of a simplicial set Given a simplicial set `X`, this f...
Interval.lean
/- Copyright (c) 2021 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Order.Interval.Finset.Nat import Mathlib.Data.PNat.Defs /-! # Finite intervals of positive naturals This file proves that `ℕ+` is a `LocallyFiniteOrder` ...
Star.lean
/- Copyright (c) 2019 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Nicolò Cavalleri -/ import Mathlib.Topology.Algebra.Star import Mathlib.Algebra.Star.StarAlgHom import Mathlib.Topology.ContinuousMap.Algebra /-! # Star structures on cont...
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 ...
Equitable.lean
/- Copyright (c) 2021 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.Algebra.Order.BigOperators.Group.Finset import Mathlib.Algebra.Order.Ring.Defs /-! # Equitable functions This file defines eq...
Subfield.lean
/- Copyright (c) 2023 Junyan Xu. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Junyan Xu -/ import Mathlib.Algebra.Field.Subfield.Basic import Mathlib.Data.W.Cardinal import Mathlib.Tactic.FinCases /-! # Cardinality of the division ring generated by a set `Subfield....
Orthogonal.lean
/- Copyright (c) 2018 Andreas Swerdlow. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andreas Swerdlow, Kexing Ying -/ import Mathlib.Algebra.GroupWithZero.NonZeroDivisors import Mathlib.LinearAlgebra.BilinearForm.Properties /-! # Bilinear form This file defines ort...
Union.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.Algebra.Module.Submodule.Lattice import Mathlib.Data.Set.Card import Mathlib.LinearAlgebra.Dual.Defs import Mathlib.Tactic.Module /-! # Unions of `Submodule...
ssrnat.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From Corelib Require Import PosDef. From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype. #[export] Set Warnings "-ov...
closed_field.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq. From mathcomp Require Import fintype generic_...
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...
Group.lean
/- Copyright (c) 2018 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Order.ConditionallyCompleteLattice.Indexed import Mathlib.Algebra.Order.Group.Unbundled.Basic import Mathlib.Algebra.Order.Monoid.Unbundled.Order...
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...
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. (*****...
CommSq.lean
/- Copyright (c) 2022 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Joël Riou -/ import Mathlib.CategoryTheory.Comma.Arrow /-! # Commutative squares This file provide an API for commutative squares in categories. If `top`, `left`, `right`...
Over.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.AlgebraicGeometry.Morphisms.UnderlyingMap import Mathlib.CategoryTheory.Limits.MorphismProperty /-! # Covers of schemes over a base In this file...
MellinInversion.lean
/- Copyright (c) 2024 Lawrence Wu. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Lawrence Wu -/ import Mathlib.Analysis.Fourier.Inversion import Mathlib.Analysis.MellinTransform /-! # Mellin inversion formula We derive the Mellin inversion formula as a consequence o...
Basic.lean
/- Copyright (c) 2024 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.CategoryTheory.ObjectProperty.Shift import Mathlib.CategoryTheory.Triangulated.Pretriangulated /-! # t-structures on triangulated categories This files introdu...
Unitization.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.Algebra.Algebra.Unitization import Mathlib.Analysis.NormedSpace.OperatorNorm.Mul /-! # Unitization norms Given a not-necessarily-unital normed `𝕜`-al...
GuardGoalNums.lean
/- Copyright (c) 2022 Robert Y. Lewis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Robert Y. Lewis -/ import Mathlib.Init import Lean.Elab.Tactic.Basic /-! A tactic stub file for the `guard_goal_nums` tactic. -/ open Lean Meta Elab Tactic /-- `guard_goal_nums n...
GrpWithZero.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.Algebra.Category.MonCat.Basic import Mathlib.Algebra.GroupWithZero.WithZero import Mathlib.CategoryTheory.Category.Bipointed /-! # The category of groups ...
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, Mario Carneiro, Patrick Massot -/ import Mathlib.Data.Rel import Mathlib.Order.Filter.SmallSets import Mathlib.Topology.UniformSpace.Defs import Mathlib.Topology.Contin...
Contract.lean
/- Copyright (c) 2025 Peter Nelson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Peter Nelson -/ import Mathlib.Data.Matroid.Minor.Delete import Mathlib.Tactic.TautoSet /-! # Matroid Contraction Instead of deleting the the elements of `X : Set α` from `M : Matroid ...
Set.lean
/- Copyright (c) 2022 Kyle Miller. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kyle Miller -/ import Mathlib.Data.Fintype.EquivFin /-! # Lemmas about `Finite` and `Set`s In this file we prove two lemmas about `Finite` and `Set`s. ## Tags finiteness, finite sets ...
AEMeasurable.lean
/- Copyright (c) 2021 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.MeasureTheory.Function.LpSeminorm.Trim import Mathlib.MeasureTheory.Function.StronglyMeasurable.Lp /-! # Functions a.e. measurable with respect to a sub-σ...
Module.lean
/- Copyright (c) 2018 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau -/ import Mathlib.Algebra.DirectSum.Basic import Mathlib.LinearAlgebra.DFinsupp import Mathlib.LinearAlgebra.Basis.Defs /-! # Direct sum of modules The first part of the file pr...
VectorSpace.lean
/- Copyright (c) 2019 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl -/ import Mathlib.Algebra.FreeAbelianGroup.Finsupp import Mathlib.Algebra.MonoidAlgebra.Defs import Mathlib.Algebra.Polynomial.Basic import Mathlib.LinearAlgebra.Basis.D...
Star.lean
/- Copyright (c) 2021 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set import Mathlib.Algebra.Module.LinearMap.Prod import Mathlib.Algebra.Order.Module.Synonym import Mathlib.Analysis...
MutuallySingular.lean
/- Copyright (c) 2021 Kexing Ying. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kexing Ying, Yury Kudryashov -/ import Mathlib.MeasureTheory.Measure.Restrict /-! # Mutually singular measures Two measures `μ`, `ν` are said to be mutually singular (`MeasureTheory.Mea...
RegularWreathProduct.lean
/- Copyright (c) 2025 Francisco Silva. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Francisco Silva -/ import Mathlib.GroupTheory.Sylow import Mathlib.Algebra.Group.PUnit import Mathlib.Data.Finite.Perm import Mathlib.Algebra.Group.End /-! # Regular wreath product ...
AsLimit.lean
/- Copyright (c) 2021 Adam Topaz. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Calle Sönne, Adam Topaz -/ import Mathlib.Topology.Category.Profinite.Basic import Mathlib.Topology.DiscreteQuotient /-! # Profinite sets as limits of finite sets. We show that any profi...
Defs.lean
/- Copyright (c) 2022 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.Algebra.Order.ToIntervalMod import Mathlib.Algebra.Ring.AddAut import Mathlib.Data.Nat.Totient import Mathlib.GroupTheory.Divisible import Mathlib.Topology.A...
LinearLocallyFinite.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.Algebra.Order.Group.Nat import Mathlib.Data.Countable.Basic import Mathlib.Data.Finset.Max import Mathlib.Data.Fintype.Pigeonhole import Mathlib.Logic.Enco...
Coeff.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.Coeff import Mathlib.Algebra.Polynomial.Eval.Defs /-! # Evaluation of polynomials This f...
Basic.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.Discrete import Mathlib.CategoryTheory.Monoidal.NaturalTransformation import Mathlib.CategoryTheory.Monoidal.Opposite import Mathli...
finfield.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 div tupl...
Instances.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.MeasurableSpace.Defs import Mathlib.GroupTheory.GroupAction.IterateAct import Mathlib.Data.Rat.Init import Mathlib.Data.Z...
GaussSum.lean
/- Copyright (c) 2022 Michael Stoll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Stoll -/ import Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.Basic import Mathlib.NumberTheory.GaussSum /-! # Quadratic characters of finite fields Further facts relying ...
maximal.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq choice. From mathcomp Require Import div fintype finfun bigop finset prime binomial. Fro...
mxpoly.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq. From mathcomp Require Import div fintype tupl...
Cones.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, Floris van Doorn -/ import Mathlib.CategoryTheory.Functor.Const import Mathlib.CategoryTheory.Discrete.Basic import Mathlib.CategoryTheory.Yoneda import Mat...
Factors.lean
/- Copyright (c) 2019 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Yaël Dillies -/ import Mathlib.Data.List.Iterate import Mathlib.GroupTheory.Perm.Cycle.Basic import Mathlib.GroupTheory.NoncommPiCoprod import Mathlib.Tactic.Group /-! # ...
Basic.lean
/- Copyright (c) 2024 Kyle Miller, Jack Cheverton. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kyle Miller, Jack Cheverton, Jeremy Tan -/ import Mathlib.Order.CompleteBooleanAlgebra import Mathlib.Data.Fintype.Pi /-! # Digraphs This module defines directed graphs ...
SubDPIdeal.lean
/- Copyright (c) 2025 Antoine Chambert-Loir, María Inés de Frutos-Fernández. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Antoine Chambert-Loir, María Inés de Frutos-Fernández -/ import Mathlib.RingTheory.DividedPowers.DPMorphism import Mathlib.RingTheory.Ideal.Quot...
Pi.lean
/- Copyright (c) 2023 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn, Heather Macbeth -/ import Mathlib.Analysis.Calculus.FDeriv.Pi import Mathlib.Analysis.Calculus.Deriv.Basic /-! # One-dimensional derivatives on pi-types. -/ varia...
CompleteMultipartite.lean
/- Copyright (c) 2024 John Talbot and Lian Bremner Tattersall. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: John Talbot, Lian Bremner Tattersall -/ import Mathlib.Combinatorics.SimpleGraph.Coloring import Mathlib.Combinatorics.SimpleGraph.Hasse /-! # Complete Multip...
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...
Sub.lean
/- Copyright (c) 2022 Martin Zinkevich. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Martin Zinkevich -/ import Mathlib.MeasureTheory.Measure.Typeclasses.Finite /-! # Subtraction of measures In this file we define `μ - ν` to be the least measure `τ` such that `μ ≤ ...
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.SmallObject.IsCardinalForSmallObjectArgument /-! # The small object argument Let `C` be a category. A class of morphisms `I : MorphismProperty C...
PushoutI.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.GroupTheory.CoprodI import Mathlib.GroupTheory.Coprod.Basic import Mathlib.GroupTheory.Complement /-! ## Pushouts of Monoids and Groups This file defin...
MulExpNegMulSqIntegral.lean
/- Copyright (c) 2025 Jakob Stiefel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jakob Stiefel -/ import Mathlib.Analysis.SpecialFunctions.MulExpNegMulSq import Mathlib.Analysis.SpecialFunctions.Complex.LogBounds import Mathlib.MeasureTheory.Integral.BoundedContinuo...
Basic.lean
/- Copyright (c) 2018 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad -/ import Mathlib.Data.W.Basic /-! # Polynomial Functors This file defines polynomial functors and the W-type construction as a polynomial functor. (For the M-type const...
L1.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.SetToL1 /-! # Bochner integral The Bochner integral extends the definition of ...
MkProof.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.Datatypes import Mathlib.Tactic.CC.Lemmas import Mathlib.Tactic.Relation.Rfl import Mathlib.Tactic.Relation.Symm /-! ...
Multinomial.lean
/- Copyright (c) 2022 Pim Otte. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kyle Miller, Pim Otte -/ import Mathlib.Algebra.Order.Antidiag.Pi import Mathlib.Data.Finsupp.Multiset import Mathlib.Data.Nat.Choose.Sum import Mathlib.Data.Nat.Factorial.BigOperators impor...
Operations.lean
/- Copyright (c) 2018 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau, Patrick Massot -/ import Mathlib.Algebra.Algebra.Subalgebra.Operations import Mathlib.Algebra.Ring.Fin import Mathlib.LinearAlgebra.Quotient.Basic import Mathlib.RingTheory.Ideal...
Riemannian.lean
/- Copyright (c) 2025 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Analysis.InnerProductSpace.LinearMap import Mathlib.Topology.VectorBundle.Constructions import Mathlib.Topology.VectorBundle.Hom /-! # Riemannia...
External.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.Data.Int.Order.Units import Mathlib.Data.ZMod.IntUnitsPower import Mathlib.RingTheory.TensorProduct.Basic import Mathlib.LinearAlgebra.DirectSum.TensorProduc...
UpperLower.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.Algebra.Group.Action.Pointwise.Set.Basic import Mathlib.Algebra.Group.Pointwise.Set.Lattice import Mathlib.Algebra.Order.Group.Defs import Mathlib.Algebra....
FiniteDimensional.lean
/- Copyright (c) 2022 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.LinearAlgebra.Multilinear.Curry import Mathlib.LinearAlgebra.FreeModule.Finite.Matrix /-! # Multilinear maps over finite dimensional spaces The main result...
MinimalAxioms.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.Field.Defs import Mathlib.Algebra.Ring.MinimalAxioms /-! # Minimal Axioms for a Field This file defines constructors to define a `Field` structu...
UpperLowerSetTopology.lean
/- Copyright (c) 2023 Christopher Hoskin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christopher Hoskin -/ import Mathlib.Topology.AlexandrovDiscrete import Mathlib.Topology.ContinuousMap.Basic import Mathlib.Topology.Order.LowerUpperTopology /-! # Upper and lower...
Isometric.lean
/- Copyright (c) 2025 Jireh Loreaux. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jireh Loreaux -/ import Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic import Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Isometric /-! # ...
Defs.lean
/- Copyright (c) 2019 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau -/ import Mathlib.RingTheory.IntegralClosure.IsIntegral.Defs /-! # Integral algebras ## Main definitions Let `R` be a `CommRing` and let `A` be an R-algebra. * `Algebra.IsInte...
FiniteType.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.FreeAlgebra import Mathlib.RingTheory.Adjoin.Polynomial import Mathlib.RingTheory.Adjoin.Tower import Mathlib.RingTheory.Ideal.Quotient.Operati...
commutator.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 fintype. From mathcomp Require Import bigop finset binomial fingroup morphism. From mathcomp...
Extensions.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.Algebra.Homology.ShortComplex.ShortExact import Mathlib.CategoryTheory.ObjectProperty.Basic /-! # Properties of objects that are closed under extensions Given ...
SnakeLemma.lean
/- Copyright (c) 2023 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.Algebra.Homology.ExactSequence import Mathlib.Algebra.Homology.ShortComplex.Limits import Mathlib.CategoryTheory.Abelian.Refinements /-! # The snake lemma The ...
ContinuousMonoidHom.lean
/- Copyright (c) 2022 Thomas Browning. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Thomas Browning, Nailin Guan -/ import Mathlib.Algebra.Group.Equiv.Basic import Mathlib.Topology.Algebra.Group.Defs /-! # Continuous Monoid Homs This file defines the space of cont...
EpiMono.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.Colimits import Mathlib.Algebra.Category.ModuleCat.Presheaf.Limits /-! # Epimorphisms and monomorphisms in the category of ...
Function.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.Prod import Mathlib.Data.Set.Restrict /-! # Functions over sets This file contains...
Cauchy.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.Topology.Algebra.Constructions import Mathlib.Topology.Bases import Mathlib.Algebra.Order.Group.Nat import Mathlib.Topology.UniformSpac...
Piecewise.lean
/- Copyright (c) 2025 Mitchell Horner. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mitchell Horner -/ import Mathlib.Analysis.Convex.Function /-! # Convex and concave piecewise functions This file proves convex and concave theorems for piecewise functions. ## Mai...
ParallelPair.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.Comma.Final import Mathlib.CategoryTheory.Limits.Indization.IndObject /-! # Parallel pairs of natural transformations between ind-objects...
Arg.lean
/- Copyright (c) 2022 Eric Rodriguez. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Rodriguez -/ import Mathlib.Analysis.InnerProductSpace.Convex import Mathlib.Analysis.SpecialFunctions.Complex.Arg /-! # Rays in the complex numbers This file links the definiti...
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...
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...
CondexpL1.lean
/- Copyright (c) 2021 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2 import Mathlib.MeasureTheory.Measure.Real /-! # Conditional expectation in L1 This file contains ...
Equiv.lean
/- Copyright (c) 2018 Simon Hudon. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Simon Hudon -/ import Mathlib.Control.Traversable.Lemmas import Mathlib.Logic.Equiv.Defs import Batteries.Tactic.SeqFocus /-! # Transferring `Traversable` instances along isomorphisms T...
Cardinal.lean
/- Copyright (c) 2025 Peter Nelson and Junyan Xu. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Peter Nelson, Junyan Xu -/ import Mathlib.Data.Matroid.Map import Mathlib.Data.Matroid.Rank.ENat import Mathlib.Data.Matroid.Rank.Finite import Mathlib.SetTheory.Cardinal.A...
HasConicalPullbacks.lean
/- Copyright (c) 2025 Jon Eugster. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Dagur Asgeirsson, Jon Eugster, Emily Riehl -/ import Mathlib.CategoryTheory.Enriched.Limits.HasConicalLimits /-! # Existence of conical pullbacks -/ universe w v' v u u' namespace Cate...
ChevalleyWarning.lean
/- Copyright (c) 2019 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.FieldTheory.Finite.Basic /-! # The Chevalley–Warning theorem This file contains a proof of the Chevalley–Warning theorem. Throughout most of this fil...
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...
cc.lean
import Mathlib.Algebra.Group.Basic import Mathlib.Algebra.Ring.Defs import Mathlib.Data.Set.Insert import Mathlib.Data.Vector.Defs import Mathlib.Tactic.CC set_option linter.unusedVariables false /-- warning: The tactic `cc` is deprecated since 2025-07-31, please use `grind` instead. Please report any regressions at...
Finsupp.lean
/- Copyright (c) 2024 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.Algebra.BigOperators.Finsupp.Basic import Mathlib.Algebra.Group.Subgroup.Lattice /-! # Connection between `Subgroup.closure` and `Finsupp.prod` -/ assert...
Bundled.lean
/- Copyright (c) 2022 Aaron Anderson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Anderson -/ import Mathlib.ModelTheory.ElementarySubstructures import Mathlib.CategoryTheory.ConcreteCategory.Bundled /-! # Bundled First-Order Structures This file bundles typ...
Log.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.Order.Floor.Semiring import Mathlib.Data.Nat.Log /-! # Integer logarithms in a field with respect to a natural base This file defines two `ℤ`-value...
test_ssrAC.v
From mathcomp Require Import all_boot ssralg. Section Tests. Lemma test_orb (a b c d : bool) : (a || b) || (c || d) = (a || c) || (b || d). Proof. time by rewrite orbACA. Abort. Lemma test_orb (a b c d : bool) : (a || b) || (c || d) = (a || c) || (b || d). Proof. time by rewrite (AC (2*2) ((1*3)*(2*4))). Abort. Lemma ...
import_all.lean
import Lean import Std import Qq import Batteries import Aesop import ProofWidgets import Mathlib import Plausible /-! Verify that Mathlib and all its upstream dependencies can be simultaneously imported. We don't `import Cli` or `import ImportGraph` here as these are only used by scripts, and may not have been built...
Subgroup.lean
/- Copyright (c) 2020 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.Algebra.Group.Action.End import Mathlib.Algebra.Group.Subgroup.Finite import Mathlib.Data.Fintype.Perm /-! # Lemmas about subgroups within the permutations ...
AdjointFunctorTheorems.lean
/- Copyright (c) 2021 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta -/ import Mathlib.CategoryTheory.Comma.StructuredArrow.Small import Mathlib.CategoryTheory.Generator.Basic import Mathlib.CategoryTheory.Limits.ConeCategory import Mathlib.C...
Finsupp.lean
/- Copyright (c) 2019 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Antoine Chambert-Loir -/ import Mathlib.Algebra.DirectSum.Finsupp import Mathlib.LinearAlgebra.DirectSum.TensorProduct import Mathlib.LinearAlgebra.Finsupp.SumProd /-!...
Functor.lean
/- Copyright (c) 2018 Simon Hudon. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Johannes Hölzl, Simon Hudon, Kenny Lau -/ import Mathlib.Data.Multiset.Bind import Mathlib.Control.Traversable.Lemmas import Mathlib.Control.Traversable.Instances /-! # F...
ContinuousAffineMap.lean
/- Copyright (c) 2021 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.Analysis.Normed.Affine.Isometry import Mathlib.Topology.Algebra.ContinuousAffineMap import Mathlib.Analysis.NormedSpace.OperatorNorm.NormedSpace /-! # Conti...
Basic.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.MeasureTheory.Function.SimpleFunc /-! # Lower Lebesgue integral for `ℝ≥0∞`-valued functions We define the lower Lebesgue integral of ...
Basic.lean
/- Copyright (c) 2018 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau, Chris Hughes, Mario Carneiro -/ import Mathlib.Algebra.Ring.Action.End import Mathlib.RingTheory.Finiteness.Cardinality import Mathlib.RingTheory.LocalRing.ResidueField.Defs impo...