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preorder.v
(* (c) Copyright 2006-2019 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 path fintype tup...
Rat.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.Data.NNRat.Order import Mathlib.Topology.Algebra.Order.Archimedean import Mathlib.Topology.Algebra.Ring.Real import Mathlib.Topology.In...
Rat.lean
/- Copyright (c) 2019 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.GroupWithZero.Units.Basic import Mathlib.Algebra.Ring.Basic import Mathlib.Algebra.Ring.Int.Defs import Mathlib.Data.Rat.Defs i...
CommGrp_.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.Monoidal.CommGrp_ import Mathlib.CategoryTheory.Preadditive.Biproducts /-! # Commutative group objects in additive categories. We constr...
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...
NamePolyVars.lean
/- Copyright (c) 2025 Adam Topaz. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Adam Topaz -/ import Mathlib.Algebra.MvPolynomial.Basic /-! The command `name_poly_vars` names variables in `MvPolynomial (Fin n) R` for the appropriate value of `n`. The notation introdu...
Irreducible.lean
/- Copyright (c) 2023 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Data.Finset.Lattice.Fold /-! # Irreducible and prime elements in an order This file defines irreducible and prime elements in an order and shows that 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. (*****...
Basic.lean
/- Copyright (c) 2024 Daniel Weber. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Daniel Weber -/ import Mathlib.RingTheory.Derivation.MapCoeffs import Mathlib.FieldTheory.PrimitiveElement /-! # Differential Fields This file defines the logarithmic derivative `Diffe...
Taylor.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.Polynomial.AlgebraMap import Mathlib.Algebra.Polynomial.Degree.Lemmas import Mathlib.Algebra.Polynomial.Eval.SMul import Mathlib.Algebra.Polyno...
Monoid.lean
/- Copyright (c) 2019 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Algebra.Order.Monoid.OrderDual import Mathlib.Algebra.Order.Monoid.Unbundled.Pow import Mathlib.Order.Filter.AtTopBot.Tendsto /-! # Convergence to ±...
Basic.lean
/- Copyright (c) 2022 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.Analysis.CStarAlgebra.ContinuousLinearMap /-! # Von Neumann algebras We give the "abstract" and "concrete" definitions of a von Neumann algebra. We still...
Exp.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne -/ import Mathlib.Analysis.Complex.Asymptotics import Mathlib.Analysis.SpecificLimits.Normed import Mathlib.Data.Complex.Trig...
MayerVietorisSquare.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.Grp.Abelian import Mathlib.Algebra.Category.Grp.Adjunctions import Mathlib.Algebra.Homology.ShortComplex.ShortExact import Mathlib.Algebra.Homol...
CompleteLattice.lean
/- Copyright (c) 2022 Yaël Dillies, Sara Rousta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Sara Rousta -/ import Mathlib.Data.Set.Lattice.Image import Mathlib.Data.SetLike.Basic import Mathlib.Order.UpperLower.Basic /-! # The complete lattice struct...
WithBot.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes -/ import Mathlib.Algebra.Order.Group.Nat import Mathlib.Algebra.Order.GroupWithZero.Canonical import Mathlib.Data.Nat.Cast.WithTop import Mathlib.Order.Nat /-! # `WithBot ...
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...
Radical.lean
/- Copyright (c) 2024 Colva Roney-Dougal. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Colva Roney-Dougal, Inna Capdeboscq, Susanna Fishel, Kim Morrison -/ import Mathlib.Order.Atoms /-! # The radical of a lattice This file contains results on the order radical of ...
ToAdditive.lean
/- Copyright (c) 2024 Miyahara Kō. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Miyahara Kō -/ import Mathlib.Tactic.ToAdditive.Frontend /-! ## `@[to_additive]` attributes for basic types -/ attribute [to_additive self] Empty PEmpty Unit PUnit attribute [to_additi...
implications.lean
import Mathlib.Tactic.GCongr variable {a b c d : Prop} example (h : a → b) : (a ∧ ¬b) ∨ c → (b ∧ ¬a) ∨ c := by gcongr example (h : a → b) : (a ∧ ¬b) ∨ c → (b ∧ ¬a) ∨ c := by gcongr ?_ ∧ ¬?_ ∨ c example (h : d → b) : (a ∨ b ∧ c → d) → (a ∨ d ∧ c → b) := by gcongr example (h : d → b) : (a ∨ b ∧ c → d) → (a ∨ d ∧ c → b...
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.
PositiveVector.lean
/- Copyright (c) 2024 Vasily Nesterov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Vasily Nesterov -/ import Lean.Meta.Basic import Mathlib.Tactic.Linarith.Oracle.SimplexAlgorithm.SimplexAlgorithm import Mathlib.Tactic.Linarith.Oracle.SimplexAlgorithm.Gauss /-! # `...
Square.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.Comma.Arrow import Mathlib.CategoryTheory.CommSq /-! # The category of commutative squares In this file, we define a bundled version of `CommSq`...
FourierSchwartz.lean
/- Copyright (c) 2024 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Analysis.Distribution.SchwartzSpace import Mathlib.Analysis.Fourier.FourierTransformDeriv import Mathlib.Analysis.Fourier.Inversion /-! # Fourie...
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...
StrongTopology.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.Algebra.Module.StrongTopology import Mathlib.Topology.Algebra.Module.LocallyConvex /-! # Local convexity of the strong topology In this ...
Finite.lean
/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Johannes Hölzl, Mario Carneiro, Patrick Massot -/ import Mathlib.Order.Filter.Bases.Basic import Mathlib.Order.Filter.Finite /-! # Finiteness results on filter bases...
SmallSets.lean
/- Copyright (c) 2022 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot, Floris van Doorn, Yury Kudryashov -/ import Mathlib.Order.Filter.Lift import Mathlib.Order.Filter.AtTopBot.Basic /-! # The filter of small sets This file defines the ...
Opposites.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.Algebra.Polynomial.Degree.Support /-! # Interactions between `R[X]` and `Rᵐᵒᵖ[X]` This file contains the basic API for "pushing through" the isomorph...
Curry.lean
/- Copyright (c) 2025 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Eric Wieser -/ import Mathlib.LinearAlgebra.Alternating.Curry import Mathlib.Analysis.NormedSpace.Alternating.Basic import Mathlib.Analysis.NormedSpace.Multilinear.Cu...
Basic.lean
/- Copyright (c) 2022 Chris Birkbeck. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Birkbeck -/ import Mathlib.Algebra.DirectSum.Algebra import Mathlib.Analysis.Calculus.FDeriv.Star import Mathlib.Analysis.Complex.UpperHalfPlane.FunctionsBoundedAtInfty import Ma...
Prod.lean
/- Copyright (c) 2019 Gabriel Ebner. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Gabriel Ebner, Yury Kudryashov, Eric Wieser -/ import Mathlib.Analysis.Calculus.Deriv.Basic import Mathlib.Analysis.Calculus.FDeriv.Prod /-! # Derivatives of functions taking values in...
Notation.lean
/- Copyright (c) 2016 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad -/ import Mathlib.Init /-! # Notation `ℤ` for the integers. -/ @[inherit_doc] notation "ℤ" => Int
SheafOfTypes.lean
/- Copyright (c) 2020 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta -/ import Mathlib.CategoryTheory.Sites.Pretopology import Mathlib.CategoryTheory.Sites.IsSheafFor /-! # Sheaves of types on a Grothendieck topology Defines the notion of a...
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, Yury Kudryashov, Neil Strickland -/ import Mathlib.Algebra.Divisibility.Hom import Mathlib.Algebra.Group.Equiv.Basic import Mathlib.A...
TerminatesIffRat.lean
/- Copyright (c) 2020 Kevin Kappelmann. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Kappelmann -/ import Mathlib.Algebra.ContinuedFractions.Computation.Approximations import Mathlib.Algebra.ContinuedFractions.Computation.CorrectnessTerminating import Mathlib.D...
burnside_app.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...
Basic.lean
/- Copyright (c) 2017 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Ralf Stephan, Neil Strickland, Ruben Van de Velde -/ import Mathlib.Algebra.GroupWithZero.Divisibility import Mathlib.Algebra.Order.Positive.Ring import Mathlib....
SimpleFuncDense.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, Heather Macbeth -/ import Mathlib.MeasureTheory.Function.SimpleFunc import Mathlib.MeasureTheory.Constructions.BorelSpace.Metrizable /-! # Density of si...
Lifting.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.AlgebraicTopology.FundamentalGroupoid.SimplyConnected import Mathlib.Topology.Connected.LocPathConnected import Mathlib.Topology.Covering import Mathlib.Topology...
IsBaseChangePi.lean
/- Copyright (c) 2025 Christian Merten. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christian Merten -/ import Mathlib.LinearAlgebra.TensorProduct.Pi import Mathlib.LinearAlgebra.TensorProduct.Prod import Mathlib.RingTheory.Localization.BaseChange /-! # Base change...
Product.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.Topology.Category.Profinite.Basic /-! # Compact subsets of products as limits in `Profinite` This file exhibits a compact subset `C` of a product...
Basic.lean
/- Copyright (c) 2022 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.RingTheory.FinitePresentation import Mathlib.RingTheory.FiniteStability import Mathlib.RingTheory.Ideal.Cotangent import Mathlib.RingTheory.Ideal.Quotient.Ni...
gseries.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 path. From mathcomp Require Import fintype bigop finset fingroup morphism. From mathcomp...
Equitabilise.lean
/- Copyright (c) 2022 Yaël Dillies, Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Bhavik Mehta -/ import Mathlib.Algebra.Order.Ring.Canonical import Mathlib.Order.Partition.Equipartition /-! # Equitabilising a partition This file allows t...
ContinuousSqrt.lean
/- Copyright (c) 2024 Jireh Loreaux. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jireh Loreaux -/ import Mathlib.Analysis.Complex.Basic import Mathlib.Data.Real.StarOrdered import Mathlib.Topology.ContinuousMap.StarOrdered /-! # Instances of `ContinuousSqrt` This ...
Basic.lean
/- Copyright (c) 2018 Mitchell Rowett. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mitchell Rowett, Kim Morrison -/ import Mathlib.Algebra.Group.Action.Pointwise.Set.Basic import Mathlib.Algebra.Group.Subgroup.Basic import Mathlib.Data.Setoid.Basic import Mathlib.Gr...
GuardHypNums.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_hyp_nums` tactic. -/ open Lean Meta Elab Tactic /-- `guard_hyp_nums n` su...
Basic.lean
/- Copyright (c) 2024 Ali Ramsey. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Ali Ramsey -/ import Mathlib.RingTheory.Bialgebra.Basic /-! # Hopf algebras In this file we define `HopfAlgebra`, and provide instances for: * Commutative semirings: `CommSemiring.toHop...
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...
preorder.v
(* (c) Copyright 2006-2019 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 path fintype tup...
Reduced.lean
/- Copyright (c) 2018 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau, Joey van Langen, Casper Putz -/ import Mathlib.Algebra.CharP.Frobenius import Mathlib.RingTheory.Nilpotent.Defs /-! # Results about characteristic p reduced rings -/ open Fins...
CompleteLattice.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.Data.Set.Lattice.Image import Mathlib.Order.Hom.BoundedLattice /-! # Complete lattice homomorphisms This file defines frame homomorphisms and complete la...
all_ssreflect.v
Attributes deprecated(since="mathcomp 2.5.0", note="Use 'all_boot' and/or 'all_order' instead."). From mathcomp Require Export all_boot. From mathcomp Require Export preorder. From mathcomp Require Export order.
SurjectiveOnStalks.lean
/- Copyright (c) 2024 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.RingTheory.Localization.AtPrime.Basic import Mathlib.RingTheory.TensorProduct.Basic /-! # Ring Homomorphisms surjective on stalks In this file, we prove so...
Limits.lean
/- Copyright (c) 2024 Christian Merten. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christian Merten -/ import Mathlib.Algebra.Category.Ring.Under.Basic import Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers import Mathlib.CategoryTheory.Li...
Pi.lean
/- Copyright (c) 2021 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Alex Kontorovich -/ import Mathlib.Data.Set.Piecewise import Mathlib.Order.Filter.Tendsto import Mathlib.Order.Filter.Bases.Finite /-! # (Co)product of a family of f...
Gamma.lean
/- Copyright (c) 2023 Xavier Roblot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Xavier Roblot -/ import Mathlib.Analysis.SpecialFunctions.PolarCoord import Mathlib.Analysis.SpecialFunctions.Gamma.Basic /-! # Integrals involving the Gamma function In this file, we...
Periodic.lean
/- Copyright (c) 2024 David Loeffler. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Loeffler -/ import Mathlib.Analysis.Complex.RemovableSingularity import Mathlib.Analysis.Calculus.InverseFunctionTheorem.Deriv import Mathlib.Order.Filter.ZeroAndBoundedAtFilter ...
Mate.lean
/- Copyright (c) 2025 Yuma Mizuno. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yuma Mizuno, Joël Riou -/ import Mathlib.CategoryTheory.Bicategory.Adjunction.Basic import Mathlib.CategoryTheory.HomCongr /-! # Mates in bicategories This file establishes the bijectio...
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 ...
Small.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.Cover.Over import Mathlib.AlgebraicGeometry.Sites.MorphismProperty import Mathlib.CategoryTheory.Sites.DenseSubsite.InducedTopolo...
Monovary.lean
/- Copyright (c) 2023 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Algebra.Order.Module.OrderedSMul import Mathlib.Algebra.Order.Module.Synonym import Mathlib.Algebra.Order.Monoid.OrderDual import Mathlib.Order.Monotone.Mo...
IsLUB.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, Yury Kudryashov -/ import Mathlib.Topology.Order.LeftRightNhds /-! # Properties of LUB and GLB in an order topology -/ open Set Filter TopologicalSpa...
order.v
(* (c) Copyright 2006-2019 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 path fintype tup...
Linter.lean
/- This is the `Linter`s file: it imports files defining linters. Most syntax linters, in particular the ones enabled by default, are imported in `Mathlib.Init`; this file contains all linters not imported in that file. This file is ignored by `shake`: * it is in `ignoreAll`, meaning that all its imports are considere...
Aleph.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, Violeta Hernández Palacios -/ import Mathlib.SetTheory.Cardinal.ToNat import Mathlib.SetTheory.Cardinal.ENat import Mathlib.SetTheory....
GaussSum.lean
/- Copyright (c) 2024 David Loeffler. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Loeffler -/ import Mathlib.NumberTheory.DirichletCharacter.Basic import Mathlib.NumberTheory.GaussSum /-! # Gauss sums for Dirichlet characters -/ variable {N : ℕ} [NeZero N] {R...
Datatypes.lean
/- Copyright (c) 2024 Yuma Mizuno. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yuma Mizuno -/ import Lean.Meta.Basic import Mathlib.Init /-! # Datatypes for bicategory like structures This file defines the basic datatypes for bicategory like structures. We will us...
PID.lean
/- Copyright (c) 2022 Pierre-Alexandre Bazin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Pierre-Alexandre Bazin -/ import Mathlib.Algebra.Module.DedekindDomain import Mathlib.LinearAlgebra.FreeModule.PID import Mathlib.Algebra.Module.Projective import Mathlib.Algeb...
ZornAtoms.lean
/- Copyright (c) 2022 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Order.Zorn import Mathlib.Order.Atoms /-! # Zorn lemma for (co)atoms In this file we use Zorn's lemma to prove that a partial order is atomic if ev...
FromTypes.lean
/- Copyright (c) 2024 Brendan Murphy. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Brendan Murphy -/ import Mathlib.Data.Fin.VecNotation /-! # Function types of a given heterogeneous arity This provides `Function.FromTypes`, such that `FromTypes ![α, β] τ = α → β ...
Complement.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.Index /-! # Complements In this file we define the complement of a subgroup. ## Main definitions - `Subgroup.IsComplement S T` where ...
TotallyDisconnected.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, Yury Kudryashov -/ import Mathlib.Topology.Connected.Clopen /-! # Totally disconnected and totally separated topological spaces ## Main definitions We define th...
TVS.lean
/- Copyright (c) 2023 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Eric Wieser -/ import Mathlib.Analysis.Convex.EGauge import Mathlib.Analysis.LocallyConvex.BalancedCoreHull import Mathlib.Analysis.Seminorm import Mathlib.Tactic.Pee...
WedderburnArtin.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.RingTheory.FiniteLength import Mathlib.RingTheory.SimpleModule.Isotypic import Mathlib.RingTheory.SimpleRing.Congr /-! # Wedderburn–Artin Theorem ## Main resul...
ExactFunctor.lean
/- Copyright (c) 2022 Markus Himmel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Markus Himmel -/ import Mathlib.CategoryTheory.Limits.Preserves.Finite /-! # Bundled exact functors We say that a functor `F` is left exact if it preserves finite limits, it is right ...
MeasCat.lean
/- Copyright (c) 2018 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl -/ import Mathlib.MeasureTheory.Measure.GiryMonad import Mathlib.CategoryTheory.Monad.Algebra import Mathlib.Topology.Category.TopCat.Basic /-! # The category of measur...
Lattice.lean
/- Copyright (c) 2023 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Data.Sum.Order import Mathlib.Order.Hom.Lattice /-! # Lexicographic sum of lattices This file proves that we can combine two lattices `α` and `β` into a ...
tuple.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat. From mathcomp Require Import seq choice fintype path. S...
BifunctorAssociator.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.GradedObject.Associator import Mathlib.CategoryTheory.Linear.LinearFunctor import Mathlib.Algebra.Homology.Bifunctor /-! # The associator for act...
test_regular_conv.v
From mathcomp Require Import all_boot all_order all_algebra all_field. Section regular. Import GRing. Goal forall R : ringType, [the lalgType R of R^o] = R :> ringType. Proof. by move=> [? []]. Qed. Goal forall R : comRingType, [the algType R of R^o] = R :> ringType. Proof. by move=> [? []]. Qed. Goal forall R : c...
PowModTotient.lean
/- Copyright (c) 2025 Bolton Bailey. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bolton Bailey -/ import Mathlib.FieldTheory.Finite.Basic /-! # Modular exponentiation with the totient function This file contains lemmas about modular exponentiation. In particular, ...
Defs.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.Data.Finite.Defs import Mathlib.Data.Bool.Basic import Mathlib.Data.Subtype import Mathlib.Tactic.MkIffOfInductiveProp /-! # Countable and uncountab...
Whiskering.lean
/- Copyright (c) 2018 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.Tactic.CategoryTheory.IsoReassoc import Mathlib.CategoryTheory.Functor.Category import Mathlib.CategoryTheory.Functor.FullyFaithful /-! # Whiskering Give...
SumOfPrimeReciprocalsDiverges.lean
/- Copyright (c) 2021 Manuel Candales. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Manuel Candales -/ import Mathlib.Topology.Algebra.InfiniteSum.Real import Mathlib.Data.Nat.Cast.Order.Field import Mathlib.Data.Nat.Squarefree /-! # Divergence of the Prime Reciproc...
Basic.lean
/- Copyright (c) 2019 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo, Yury Kudryashov, Frédéric Dupuis, Heather Macbeth -/ import Mathlib.Algebra.Module.Opposite import Mathlib.Topology.Algebra.Group.Qu...
UniformOn.lean
/- Copyright (c) 2025 Chris Birkbeck. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Birkbeck, David Loeffler -/ import Mathlib.Topology.Algebra.InfiniteSum.Defs import Mathlib.Topology.Algebra.UniformConvergence import Mathlib.Order.Filter.AtTopBot.Finset /-! #...
Construction.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes -/ import Mathlib.Algebra.CharP.Algebra import Mathlib.FieldTheory.SplittingField.IsSplittingField import Mathlib.LinearAlgebra.Dual.Lemmas import Mathlib.RingTheory.Algebra...
Grothendieck.lean
/- Copyright (c) 2020 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Sina Hazratpour -/ import Mathlib.CategoryTheory.Category.Cat.AsSmall import Mathlib.CategoryTheory.Elements import Mathlib.CategoryTheory.Comma.Over.Basic /-! # The Groth...
Periodic.lean
/- Copyright (c) 2021 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Alex Kontorovich, Heather Macbeth -/ import Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic deprecated_module (since := "2025-04-13")
Basic.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.PropInstances import Mathlib.Order.GaloisConnection.Defs /-! # Heyting algebras This file defines Heyting, co-Heyting and bi-Heyting algebras. A H...
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 seq div. From mathcomp Require Import choice fintype prim...
Basic.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.Sites.ConstantSheaf import Mathlib.CategoryTheory.Sites.Equivalence import Mathlib.Condensed.Basic import Mathlib.Condensed.Light.Ba...
Base.lean
/- Copyright (c) 2022 Bolton Bailey. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bolton Bailey, Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne -/ import Mathlib.Algebra.BigOperators.Field import Mathlib.Analysis.SpecialFunctions.Pow.Real import Mathlib...
Units.lean
/- Copyright (c) 2023 Wrenna Robson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Wrenna Robson -/ import Mathlib.Algebra.Group.Submonoid.Operations import Mathlib.Algebra.Group.Submonoid.Pointwise import Mathlib.Algebra.Group.Subgroup.Lattice /-! # Submonoid of un...
Opposite.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.RingTheory.TensorProduct.Basic import Mathlib.Algebra.Algebra.Opposite /-! # `MulOpposite` distributes over `⊗` The main result in this file is: * `Algebr...
qfpoly.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import fintype tuple div bigop binomial finset finfun. From mathcomp Require Import ssralg countalg finalg poly polydiv qpoly perm. From mathcomp Require Import fingroup falgebra fiel...
QuadraticMap.lean
/- Copyright (c) 2024 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Analysis.Calculus.LineDeriv.Basic import Mathlib.Analysis.Calculus.Deriv.Mul import Mathlib.LinearAlgebra.QuadraticForm.Basic /-! # Quadratic forms ...
fingroup.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 fintype div path...