filename
stringlengths
5
42
content
stringlengths
15
319k
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...
ApproximateUnit.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.CStarAlgebra.ContinuousFunctionalCalculus.Order import Mathlib.Analysis.CStarAlgebra.SpecialFunctions.PosPart import Mathlib.Analysis.SpecialFun...
CartesianClosed.lean
/- Copyright (c) 2024 Dagur Asgeirsson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Dagur Asgeirsson -/ import Mathlib.CategoryTheory.Closed.Ideal import Mathlib.CategoryTheory.Monoidal.Cartesian.FunctorCategory import Mathlib.CategoryTheory.Sites.CartesianMonoidal ...
Bitwise.lean
/- Copyright (c) 2020 Markus Himmel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Markus Himmel, Alex Keizer -/ import Mathlib.Algebra.Group.Nat.Even import Mathlib.Algebra.NeZero import Mathlib.Algebra.Ring.Nat import Mathlib.Data.Bool.Basic import Mathlib.Data.List...
Refinements.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.Abelian.Refinements import Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex /-! # Refinements This file contains lemmas about "refineme...
UniqueSums.lean
/- Copyright (c) 2025 Yaël Dillies, Paul Lezeau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Paul Lezeau -/ import Mathlib.Algebra.FreeAbelianGroup.Finsupp import Mathlib.Algebra.Group.UniqueProds.Basic /-! # Free abelian groups have unique sums -/ a...
LocPathConnected.lean
/- Copyright (c) 2020 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot, Ben Eltschig -/ import Mathlib.Topology.Connected.PathConnected import Mathlib.Topology.AlexandrovDiscrete /-! # Locally path-connected spaces This file defines `LocP...
Zify.lean
/- Copyright (c) 2022 Moritz Doll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Moritz Doll, Mario Carneiro, Robert Y. Lewis -/ import Mathlib.Tactic.Basic import Mathlib.Tactic.Attr.Register import Mathlib.Data.Int.Cast.Basic import Mathlib.Order.Basic /-! # `zify`...
Lemmas.lean
/- Copyright (c) 2025 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne, Lorenzo Luccioli -/ import Mathlib.Probability.Kernel.Composition.MeasureComp import Mathlib.Probability.Kernel.Composition.ParallelComp /-! # Lemmas relating different wa...
Isometric.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.CStarAlgebra.ContinuousFunctionalCalculus.Instances /-! # Isometric continuous functional calculus This file adds a class for an *isometric* c...
Nonempty.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.Logic.Function.Defs /-! # Nonempty types This file proves a few extra facts about `Nonempty`, which is defined in core Lean. ## Main declarations *...
Connected.lean
/- Copyright (c) 2018 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Reid Barton, Bhavik Mehta -/ import Mathlib.CategoryTheory.Limits.Creates import Mathlib.CategoryTheory.Comma.Over.Basic import Mathlib.CategoryTheory.IsConnected /-! ...
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.
falgebra.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq path. From mathcomp Require Import choice fintype div...
Span.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.Data.Finset.Sort import Mathlib.Topology.Category.Profinite.CofilteredLimit import Mathlib.Topology.Category.Profinite.Nobeling.Basic /-! # The go...
ComplexShape.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 -/ import Mathlib.Algebra.Group.Defs import Mathlib.Logic.Relation import Mathlib.Logic.Function.Basic /-! # Shapes of homological complexes We define a st...
Pi.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.Unramified.Basic /-! # Formal-unramification of finite products of rings ## Main result - `Algebra.FormallyUnramified.pi_iff`: If `I` is finit...
Defs.lean
/- Copyright (c) 2018 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Kenny Lau, Johan Commelin, Mario Carneiro, Kevin Buzzard, Amelia Livingston, Yury Kudryashov, Yakov Pechersky -/ import Mathlib.Algebra.Group.Hom.Defs import Mathlib.Al...
PImage.lean
/- Copyright (c) 2021 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Data.Finset.Option import Mathlib.Data.PFun import Mathlib.Data.Part /-! # Image of a `Finset α` under a partially defined function In this file we...
Zip.lean
/- Copyright (c) 2021 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.Data.Vector.Basic /-! # The `zipWith` operation on vectors. -/ namespace List namespace Vector section ZipWith variable {α β γ : Type*} {n : ℕ} (f : α...
imset2_gproduct.v
From mathcomp Require Import all_boot all_fingroup. Set Implicit Arguments. Unset Strict Implicit. Unset Printing Implicit Defensive. Import GroupScope. Open Scope group_scope. Check @ker_sdprodm.
Slope.lean
/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.LinearAlgebra.AffineSpace.AffineMap import Mathlib.Tactic.FieldSimp /-! # Slope of a function In this file we define the slope of a function `f : k...
NFA.lean
/- Copyright (c) 2020 Fox Thomson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Fox Thomson, Maja Kądziołka -/ import Mathlib.Computability.DFA import Mathlib.Data.Fintype.Powerset /-! # Nondeterministic Finite Automata A Nondeterministic Finite Automaton (NFA) is ...
Rat.lean
/- Copyright (c) 2018 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau, Yury Kudryashov -/ import Mathlib.Algebra.Algebra.Hom import Mathlib.Algebra.Algebra.Rat /-! # Homomorphisms of `ℚ`-algebras -/ namespace RingHom variable {R S : Type*} /--...
Basic.lean
/- Copyright (c) 2021 Shing Tak Lam. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Shing Tak Lam -/ import Mathlib.CategoryTheory.Category.Grpd import Mathlib.CategoryTheory.Groupoid import Mathlib.Topology.Category.TopCat.Basic import Mathlib.Topology.Homotopy.Path i...
Embeddings.lean
/- Copyright (c) 2022 Xavier Roblot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Alex J. Best, Xavier Roblot -/ import Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification import Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex deprecated_mo...
Kernel.lean
/- Copyright (c) 2023 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Probability.ConditionalProbability import Mathlib.Probability.Kernel.Basic import Mathlib.Probability.Kernel.Composition.MeasureComp import Mathlib.Tactic....
Submonoid.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.Group.Submonoid.Defs import Mathlib.Algebra.Order.Monoid.Basic import Mathlib.Order.Interval.Set.Defs /-! # Ordered instances on submonoids -/ ...
Module.lean
/- Copyright (c) 2020 Alexander Bentkamp, Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Alexander Bentkamp, Sébastien Gouëzel, Eric Wieser -/ import Mathlib.Algebra.Algebra.RestrictScalars import Mathlib.Algebra.CharP.Invertible import Mathlib.Data....
UInt.lean
/- Copyright (c) 2021 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Init import Mathlib.Algebra.Ring.InjSurj import Mathlib.Data.ZMod.Defs import Mathlib.Data.BitVec /-! # Adds Mathlib specific instances to the `UIntX...
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...
Dimension.lean
/- Copyright (c) 2024 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.Algebra.Homology.DerivedCategory.Ext.EnoughProjectives /-! # Projective dimension In an abelian category `C`, we shall say that `X : C` has projective dimensio...
LinearCombination.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.Module.Submodule.Equiv import Mathlib.Data.Finsupp.Option import Mathlib.LinearAlgebra.Finsupp.Supported /-! # `Finsupp.linearCombination` ##...
Nat.lean
/- Copyright (c) 2024 Pim Otte. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Pim Otte -/ import Mathlib.Algebra.BigOperators.Group.Finset.Lemmas import Mathlib.Data.Set.Finite.Lattice import Mathlib.SetTheory.Cardinal.Finite /-! # Big operators on a finset in the na...
CartanMatrix.lean
/- Copyright (c) 2025 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.LinearAlgebra.Matrix.BilinearForm import Mathlib.LinearAlgebra.RootSystem.Base import Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas import Mathlib.LinearAlg...
Count.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.Dirac import Mathlib.Topology.Algebra.InfiniteSum.ENNReal /-! # Counting measure In this file we define the counting measure `M...
Basic.lean
/- Copyright (c) 2015 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Leonardo de Moura, Jeremy Avigad, Mario Carneiro -/ import Mathlib.Algebra.GroupWithZero.Associated import Mathlib.Algebra.Ring.Parity import Mathlib.Data.Nat.Prime.Defs /-! # ...
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...
action.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun ssrnotations eqtype. From mathcomp Require Import ssrnat div seq prime fintype bigop finset. From mathcomp...
Completion.lean
/- Copyright (c) 2025 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Analysis.Asymptotics.Theta import Mathlib.Analysis.Normed.Group.Completion /-! # Asymptotics in the completion of a normed space In this file we pr...
all.v
From mathcomp Require Export all_boot. From mathcomp Require Export all_order. From mathcomp Require Export all_fingroup. From mathcomp Require Export all_algebra. From mathcomp Require Export all_solvable. From mathcomp Require Export all_field. From mathcomp Require Export all_character.
FinMeasAdditive.lean
/- Copyright (c) 2021 Rémy Degenne. 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.Function.SimpleFuncDenseLp /-! # Additivity on measurable sets with finite measure Let `...
Lax.lean
/- Copyright (c) 2024 Calle Sönne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Calle Sönne -/ import Mathlib.CategoryTheory.Bicategory.Functor.Prelax import Mathlib.Tactic.CategoryTheory.Slice import Mathlib.Tactic.CategoryTheory.ToApp /-! # Lax functors A lax fu...
Multiplicative.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.UniqueFactorizationDomain.NormalizedFactors /-! # Multiplicative maps on unique factorization domains ## M...
BigOperators.lean
/- Copyright (c) 2017 Kevin Buzzard. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Buzzard, Mario Carneiro -/ import Mathlib.Algebra.BigOperators.Balance import Mathlib.Data.Complex.Basic /-! # Finite sums and products of complex numbers -/ open Fintype open s...
StandardSmooth.lean
/- Copyright (c) 2024 Christian Merten. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jung Tao Cheng, Christian Merten, Andrew Yang -/ import Mathlib.Algebra.MvPolynomial.PDeriv import Mathlib.LinearAlgebra.Determinant import Mathlib.RingTheory.Extension.Presentation....
random.lean
import Mathlib.Control.Random import Mathlib.Tactic.NormNum import Batteries.Lean.LawfulMonad open Random -- TODO(kmill): remove once the mathlib ToExpr Int instance is removed set_option eval.pp false section Rand /-- info: 33 -/ #guard_msgs in #eval do IO.runRandWith 257 (show Rand _ from do let i ← randBou...
Well.lean
/- Copyright (c) 2022 Yaël Dillies, Junyan Xu. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Junyan Xu -/ import Mathlib.Data.Prod.Lex import Mathlib.SetTheory.Ordinal.Rank /-! # Extend a well-founded order to a well-order This file constructs a well-o...
ModEq.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.Data.Nat.ModEq /-! # Congruences modulo an integer This file defines the equivalence relation `a ≡ b [ZMOD n]` on the integers, similarly to how `Data.N...
Basic.lean
/- Copyright (c) 2022 David Loeffler. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Loeffler -/ import Mathlib.Analysis.SpecialFunctions.ImproperIntegrals import Mathlib.MeasureTheory.Integral.ExpDecay /-! # The Gamma function This file defines the `Γ` functio...
TypeTags.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.Order.SuccPred.Archimedean import Mathlib.Algebra.Order.Monoid.Unbundled.TypeTags /-! # Successor and predecessor on type tags This file declates s...
ModN.lean
/- Copyright (c) 2024 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Algebra.EuclideanDomain.Int import Mathlib.Algebra.Module.ZMod import Mathlib.LinearAlgebra.Dimension.Free /-! # Quotienting out a free `ℤ`-module If `G`...
Basic.lean
/- Copyright (c) 2025 Dexin Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Dexin Zhang -/ import Mathlib.Algebra.Group.Basic import Mathlib.ModelTheory.Semantics /-! # Presburger arithmetic This file defines the first-order language of Presburger arithmetic as...
CondVar.lean
/- Copyright (c) 2025 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.MeasureTheory.Function.ConditionalExpectation.Real import Mathlib.MeasureTheory.Integral.Average import Mathlib.Probability.Moments.Variance /-! # Conditi...
DeltaGenerated.lean
/- Copyright (c) 2024 Ben Eltschig. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Ben Eltschig -/ import Mathlib.CategoryTheory.Monad.Limits import Mathlib.Topology.Category.TopCat.Limits.Basic import Mathlib.Topology.Compactness.DeltaGeneratedSpace /-! # Delta-gener...
Units.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.Algebra.Group.Equiv.Defs import Mathlib.Algebra.Group.Pi.Basic import Mathlib.Algebra.Group.Units.Defs import Mathlib.Util.Delaborators /-! # Units in pi ty...
Preserves.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.Preadditive.Injective.Basic /-! # Preservation of injective objects We define a typeclass `Functor.PreservesInjectiveObjects`. We resta...
Monoidal.lean
/- Copyright (c) 2024 Amelia Livingston. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Amelia Livingston -/ import Mathlib.Algebra.Category.CoalgCat.Basic import Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic import Mathlib.CategoryTheory.Monoidal.Transport import...
Skeletal.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.Adjunction.Basic import Mathlib.CategoryTheory.Category.Preorder import Mathlib.CategoryTheory.IsomorphismClasses import Mathlib.CategoryThe...
SmoothSection.lean
/- Copyright (c) 2023 Heather Macbeth. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Heather Macbeth, Floris van Doorn, Michael Rothgang -/ import Mathlib.Geometry.Manifold.Algebra.LieGroup import Mathlib.Geometry.Manifold.MFDeriv.Basic import Mathlib.Topology.Continu...
Norm.lean
/- Copyright (c) 2024 Etienne Marion. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Etienne Marion -/ import Mathlib.Analysis.Calculus.Deriv.Abs import Mathlib.Analysis.Calculus.LineDeriv.Basic /-! # Differentiability of the norm in a real normed vector space This f...
LiftingProperties.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.Preadditive.Injective.Basic import Mathlib.CategoryTheory.MorphismProperty.LiftingProperty /-! # Characterization of injective objects in terms o...
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 ...
Powerset.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.Data.List.Sublists import Mathlib.Data.List.Zip import Mathlib.Data.Multiset.Bind import Mathlib.Data.Multiset.Range /-! # The powerset of a multiset ...
IsNonarchimedean.lean
/- Copyright (c) 2025 María Inés de Frutos-Fernández. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: María Inés de Frutos-Fernández, Fabrizio Barroero -/ import Mathlib.Algebra.Order.Hom.Basic import Mathlib.Data.Nat.Choose.Sum /-! # Nonarchimedean functions A functi...
CatCommSq.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.CategoryTheory.Equivalence /-! # 2-commutative squares of functors Similarly as `CommSq.lean` defines the notion of commutative squares, this file introduces t...
IndicatorConstPointwise.lean
/- Copyright (c) 2023 Kalle Kytölä. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kalle Kytölä -/ import Mathlib.Algebra.Notation.Indicator import Mathlib.Topology.Separation.Basic /-! # Pointwise convergence of indicator functions In this file, we prove the equival...
AsType.lean
/- Copyright (c) 2019 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.CategoryTheory.FinCategory.Basic import Mathlib.Data.Fintype.EquivFin /-! # Finite categories are equivalent to category in `Type 0`. -/ universe w v u ...
Basic.lean
/- Copyright (c) 2020 Thomas Browning, Patrick Lutz. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Thomas Browning, Patrick Lutz, Yongle Hu, Jingting Wang -/ import Mathlib.FieldTheory.Fixed import Mathlib.FieldTheory.Normal.Closure import Mathlib.FieldTheory.Primitiv...
AllAny.lean
/- Copyright (c) 2017 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Batteries.Tactic.Alias import Mathlib.Tactic.TypeStar /-! # Boolean quantifiers This proves a few properties about `List.all` and `List.any`, which are the `...
Path.lean
/- Copyright (c) 2021 Shing Tak Lam. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Shing Tak Lam -/ import Mathlib.Topology.Homotopy.Basic import Mathlib.Topology.Connected.PathConnected import Mathlib.Analysis.Convex.Basic /-! # Homotopy between paths In this file,...
Sum.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Patrick Stevens -/ import Mathlib.Algebra.BigOperators.Intervals import Mathlib.Algebra.BigOperators.NatAntidiagonal import Mathlib.Algebra.BigOperators.Ring.Finset import ...
Conv.lean
/- Copyright (c) 2024 Lean FRO LLC. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.CategoryTheory.Monoidal.Comon_ /-! # The convolution monoid. When `M : Comon_ C` and `N : Mon_ C`, the morphisms `M.X ⟶ N.X` form a monoid (in Type). -/ ...
Finiteness.lean
/- Copyright (c) 2024 Junyan Xu. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Junyan Xu -/ import Mathlib.Algebra.Colimit.Module import Mathlib.RingTheory.Finiteness.Basic /-! # Modules as direct limits of finitely generated submodules We show that every module is ...
ssrnum.v
From mathcomp Require Export orderedzmod. From mathcomp Require Export numdomain. From mathcomp Require Export numfield. Module Num. Export orderedzmod.Num. Export numdomain.Num. Export numfield.Num. Module Theory. Export orderedzmod.Num.Theory. Export numdomain.Num.Theory. Export numfield.Num.Theory. End Theory. Mo...
Kleisli.lean
/- Copyright (c) 2020 Wojciech Nawrocki. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Wojciech Nawrocki, Bhavik Mehta -/ import Mathlib.CategoryTheory.Adjunction.Basic import Mathlib.CategoryTheory.Monad.Basic /-! # Kleisli category on a (co)monad This file defines...
polydiv.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 choice. From mathcomp Require Import fintype bigop ssralg poly. (**********************...
Conv.lean
/- Copyright (c) 2023 Robin Böhne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Robin Böhne, Wojciech Nawrocki, Patrick Massot -/ import Mathlib.Tactic.Widget.SelectPanelUtils import Mathlib.Data.String.Defs import Batteries.Tactic.Lint import Batteries.Lean.Position...
ContinuousMap.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.CStarAlgebra.Classes import Mathlib.Topology.ContinuousMap.Compact import Mathlib.Topology.ContinuousMap.ZeroAtInfty /-! # C⋆-algebras of conti...
nilpotent.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 div bigop prime finset fingroup morphism. Fro...
WidePullbacks.lean
/- Copyright (c) 2020 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta, Jakob von Raumer -/ import Mathlib.CategoryTheory.Limits.HasLimits import Mathlib.CategoryTheory.Thin /-! # Wide pullbacks We define the category `WidePullbackShape`, (re...
Conformal.lean
/- Copyright (c) 2021 Yourong Zang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yourong Zang -/ import Mathlib.Analysis.Calculus.Conformal.NormedSpace import Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic /-! # Angles and conformal maps This file proves that co...
Differentiable.lean
/- Copyright (c) 2024 Tomáš Skřivan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Tomáš Skřivan -/ import Mathlib.Analysis.Calculus.FDeriv.Basic import Mathlib.Analysis.Calculus.FDeriv.Comp import Mathlib.Analysis.Calculus.FDeriv.Prod import Mathlib.Analysis.Calculus...
Applicative.lean
/- Copyright (c) 2017 Simon Hudon. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Simon Hudon -/ import Mathlib.Algebra.Group.Defs import Mathlib.Control.Functor import Mathlib.Control.Basic /-! # `applicative` instances This file provides `Applicative` instances for...
path.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. (******************************************************************************) (* ...
OfSequence.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.Category.Preorder import Mathlib.CategoryTheory.EqToHom /-! # Functors from the category of the ordered set `ℕ` In this file, we provide a const...
Prod.lean
/- Copyright (c) 2023 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.MeasureTheory.Measure.Prod import Mathlib.Probability.Kernel.Composition.CompProd import Mathlib.Probability.Kernel.Composition.CompMap /-! # Product and ...
Adjunctions.lean
/- Copyright (c) 2019 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Johannes Hölzl -/ import Mathlib.Algebra.Category.Grp.Preadditive import Mathlib.GroupTheory.FreeAbelianGroup import Mathlib.CategoryTheory.Limits.Types.Shapes /-! # Adjun...
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...
NormNum.lean
/- Copyright (c) 2025. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: euprunin -/ import Mathlib.Tactic.NormNum.Basic import Mathlib.Tactic.NormNum.OfScientific import Mathlib.Tactic.NormNum.Eq import Mathlib.Tactic.NormNum.Ineq import Mathlib.Tactic.NormNum.Pow impor...
SplitSimplicialObject.lean
/- Copyright (c) 2022 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.AlgebraicTopology.SimplicialObject.Split import Mathlib.AlgebraicTopology.DoldKan.Degeneracies import Mathlib.AlgebraicTopology.DoldKan.FunctorN /-! # Split si...
Basic.lean
/- Copyright (c) 2024 Michael Stoll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Stoll -/ import Mathlib.NumberTheory.GaussSum import Mathlib.NumberTheory.MulChar.Lemmas import Mathlib.RingTheory.RootsOfUnity.Lemmas /-! # Jacobi Sums This file defines the ...
AmpleSet.lean
/- Copyright (c) 2021 Anatole Dedecker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anatole Dedecker, Floris van Doorn -/ import Mathlib.Algebra.CharP.Invertible import Mathlib.Analysis.Normed.Module.Convex import Mathlib.Analysis.NormedSpace.Connected import Mathli...
Typeclasses.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Mario Carneiro -/ import Mathlib.MeasureTheory.Measure.Typeclasses.Finite import Mathlib.MeasureTheory.Measure.Typeclasses.NoAtoms import Mathlib.MeasureTheory.Measure....
IsCofibrant.lean
/- Copyright (c) 2025 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.AlgebraicTopology.ModelCategory.Instances import Mathlib.CategoryTheory.Limits.Shapes.Terminal /-! # Fibrant and cofibrant objects in a model category Once a c...
ClusterPt.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, Jeremy Avigad -/ import Mathlib.Topology.Neighborhoods /-! # Lemmas on cluster and accumulation points In this file we prove various lemmas on [cluste...
Instances.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 Batteries.Data.DList.Lemmas import Mathlib.Control.Traversable.Equiv import Mathlib.Control.Traversable.Instances /-! # Traversable instance for DLists This file p...
Completion.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.Analysis.Normed.Group.Uniform import Mathlib.Topology.Algebra.GroupCompletion import Mathlib.Topology.MetricSpace.Completion /-! # Completion of a nor...
Subadditive.lean
/- Copyright (c) 2021 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Order.Filter.AtTopBot.Archimedean import Mathlib.Order.Filter.AtTopBot.Finite import Mathlib.Order.Filter.AtTopBot.Prod import Mathlib.Topology.A...
Holor.lean
/- Copyright (c) 2018 Alexander Bentkamp. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Alexander Bentkamp -/ import Mathlib.Data.Nat.Find import Mathlib.Algebra.Module.Pi import Mathlib.Algebra.BigOperators.Group.Finset.Basic /-! # Basic properties of holors Holors...