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Defs.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.Equiv.Defs import Mathlib.Algebra.Module.Pi import Mathlib.Data.Finsupp.SMul /-! # Properties of the module `α →₀ M` Given an `R`-modu...
LeftHomology.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.ShortComplex.Basic import Mathlib.CategoryTheory.Limits.Shapes.Kernels /-! # Left Homology of short complexes Given a short complex `S : Shor...
BitIndices.lean
/- Copyright (c) 2024 Peter Nelson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Peter Nelson -/ import Mathlib.Algebra.BigOperators.Ring.List import Mathlib.Algebra.Order.BigOperators.Group.List import Mathlib.Algebra.Order.Group.Nat import Mathlib.Algebra.Order.Sub...
Functors.lean
/- Copyright (c) 2021 Junyan Xu. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Junyan Xu, Andrew Yang -/ import Mathlib.Topology.Sheaves.SheafCondition.Sites import Mathlib.CategoryTheory.Sites.Pullback /-! # functors between categories of sheaves Show that the push...
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...
PiTensorProduct.lean
/- Copyright (c) 2020 Frédéric Dupuis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Frédéric Dupuis, Eric Wieser -/ import Mathlib.LinearAlgebra.Multilinear.TensorProduct import Mathlib.Tactic.AdaptationNote import Mathlib.LinearAlgebra.Multilinear.Curry /-! # Tenso...
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_...
W.lean
/- Copyright (c) 2018 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Simon Hudon -/ import Mathlib.Data.PFunctor.Multivariate.Basic /-! # The W construction as a multivariate polynomial functor. W types are well-founded tree-like structu...
Circulant.lean
/- Copyright (c) 2021 Lu-Ming Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Lu-Ming Zhang -/ import Mathlib.Algebra.Group.Fin.Basic import Mathlib.LinearAlgebra.Matrix.Symmetric import Mathlib.Tactic.Abel /-! # Circulant matrices This file contains the defini...
SimpleFunc.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.Algebra.Order.Pi import Mathlib.Algebra.Algebra.Pi import Mathlib.MeasureTheory.Constructions.BorelSpace.Order /-! # Simple functions ...
Turan.lean
/- Copyright (c) 2024 Jeremy Tan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Tan -/ import Mathlib.Combinatorics.SimpleGraph.Clique import Mathlib.Order.Partition.Equipartition /-! # Turán's theorem In this file we prove Turán's theorem, the first importan...
TMComputable.lean
/- Copyright (c) 2020 Pim Spelier, Daan van Gent. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Pim Spelier, Daan van Gent -/ import Mathlib.Algebra.Polynomial.Eval.Defs import Mathlib.Computability.Encoding import Mathlib.Computability.TuringMachine /-! # Computable...
DistribMulAction.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.Submonoid.MulAction import Mathlib.Algebra.GroupWithZero.Action.Defs /-! # Distributive actions by submonoids -/ assert_not_exists RelIso R...
CochainComplex.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.Embedding.TruncLEHomology import Mathlib.Algebra.Homology.HomotopyCategory.SingleFunctors import Mathlib.Algebra.Homology.HomotopyCategory.Shift...
BanachSteinhaus.lean
/- Copyright (c) 2021 Jireh Loreaux. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jireh Loreaux -/ import Mathlib.Analysis.NormedSpace.OperatorNorm.NormedSpace import Mathlib.Analysis.LocallyConvex.Barrelled import Mathlib.Topology.Baire.CompleteMetrizable /-! # The...
Equiv.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro -/ import Mathlib.Algebra.BigOperators.Finsupp.Fin import Mathlib.Algebra.MvPolynomial.Degrees import Mathlib.Algebra.MvPolynomial.Rename...
GuardHypNums.lean
import Mathlib.Tactic.GuardHypNums set_option linter.unusedTactic false example (a b c : Nat) (_ : a = b) (_ : c = 3) : true := by guard_hyp_nums 6 trivial example : true := by guard_hyp_nums 1 trivial
Group.lean
/- Copyright (c) 2023 David Kurniadi Angdinata. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Kurniadi Angdinata -/ import Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Basic import Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula import Mathlib.Algebrai...
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.
Join.lean
/- Copyright (c) 2022 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Analysis.Convex.Hull /-! # Convex join This file defines the convex join of two sets. The convex join of `s` and `t` is the union of the segments with on...
ShiftedHomOpposite.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.Triangulated.Opposite.Basic import Mathlib.CategoryTheory.Shift.ShiftedHom /-! Shifted morphisms in the opposite category If `C` is a category ...
MvPolynomial.lean
/- Copyright (c) 2021 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.Algebra.MvPolynomial.Eval import Mathlib.Algebra.MvPolynomial.CommRing import Mathlib.LinearAlgebra.Matrix.Determinant.Basic /-! # Matrices of multivariate ...
Radon.lean
/- Copyright (c) 2023 Vasily Nesterov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Vasily Nesterov -/ import Mathlib.Analysis.Convex.Combination import Mathlib.Data.Set.Card import Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional import Mathlib.Topology.Separatio...
prime.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq path. From mathcomp Require Import choice fintype div bigop. (*************************...
ssrbool.v
From mathcomp Require Import ssreflect ssrfun. From Corelib Require Export ssrbool. Set Implicit Arguments. Unset Strict Implicit. Unset Printing Implicit Defensive. (**********************) (* not yet backported *) (**********************) Lemma homo_mono1 [aT rT : Type] [f : aT -> rT] [g : rT -> aT] [aP : pred ...
LinearGrowth.lean
/- Copyright (c) 2025 Damien Thomine. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damien Thomine -/ import Mathlib.Analysis.SpecificLimits.Basic /-! # Linear growth This file defines the linear growth of a sequence `u : ℕ → R`. This notion comes in two versions, u...
fintype.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool ssrnotations eqtype. From mathcomp Require Import ssrnat seq choice pat...
DirichletLSeries.lean
/- Copyright (c) 2023 Michael Stoll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Stoll -/ import Mathlib.NumberTheory.EulerProduct.ExpLog import Mathlib.NumberTheory.LSeries.Dirichlet /-! # The Euler Product for the Riemann Zeta Function and Dirichlet L-Ser...
morphism.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 fintype finfun bigop finset fingroup. (***********...
Factorial.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.Data.Nat.Factorial.Basic import Mathlib.Data.Nat.Prime.Basic /-! # Prime natural numbers and the factorial ope...
Basic.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.Counit import Mathlib.Algebra.MvPolynomial.Invertible import Mathlib.RingTheory.WittVector.Defs /-! # Witt vecto...
rat.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 prime fintype fi...
InjSurj.lean
/- Copyright (c) 2020 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.Algebra.Group.InjSurj import Mathlib.Algebra.GroupWithZero.NeZero /-! # Lifting groups with zero along injective/surjective maps -/ assert_not_exist...
HomologicalComplexBiprod.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.HomologicalComplexLimits import Mathlib.Algebra.Homology.Additive /-! Binary biproducts of homological complexes In this file, it is shown tha...
Induced.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.Data.Set.Lattice.Image import Mathlib.Topology.Basic /-! # Induced and coinduced topologies In this file we define the ...
nmodule.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq. From mathcomp Require Import bigop fintype finfun monoid. (******************************************************************************) (* Additive group-like structures ...
orderedzmod.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import ssrAC div fintyp...
LeftInvariantDerivation.lean
/- Copyright (c) 2020 Nicolò Cavalleri. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Nicolò Cavalleri -/ import Mathlib.RingTheory.Derivation.Lie import Mathlib.Geometry.Manifold.DerivationBundle /-! # Left invariant derivations In this file we define the concept ...
Finite.lean
/- Copyright (c) 2021 Alena Gusakov, Bhavik Mehta, Kyle Miller. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Alena Gusakov, Bhavik Mehta, Kyle Miller -/ import Mathlib.Data.Fintype.Basic import Mathlib.Data.Fintype.Powerset import Mathlib.Data.Set.Finite.Basic /-! #...
Attr.lean
/- Copyright (c) 2023 Heather Macbeth. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Heather Macbeth -/ import Mathlib.Init import Lean.LabelAttribute /-! # The @[mono] attribute -/ namespace Mathlib.Tactic.Monotonicity syntax mono.side := &"left" <|> &"right" <|> ...
PartialSups.lean
/- Copyright (c) 2023 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Topology.Order.Lattice import Mathlib.Order.PartialSups /-! # Continuity of `partialSups` In this file we prove that `partialSups` of a sequence of...
Egorov.lean
/- Copyright (c) 2022 Kexing Ying. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kexing Ying -/ import Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic /-! # Egorov theorem This file contains the Egorov theorem which states that an almost everywhere convergen...
Sifted.lean
/- Copyright (c) 2024 Robin Carlier. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Robin Carlier -/ import Mathlib.CategoryTheory.Limits.Final /-! # Sifted categories A category `C` is sifted if `C` is nonempty and the diagonal functor `C ⥤ C × C` is final. Sifted ca...
imset2_finset.v
From mathcomp Require Import all_boot. Set Implicit Arguments. Unset Strict Implicit. Unset Printing Implicit Defensive. Check @imset2_pair.
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. (*****...
BorelCantelli.lean
/- Copyright (c) 2022 Kexing Ying. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kexing Ying -/ import Mathlib.Algebra.Order.Archimedean.IndicatorCard import Mathlib.Probability.Martingale.Centering import Mathlib.Probability.Martingale.Convergence import Mathlib.Prob...
Extract.lean
/- Copyright (c) 2024 Jiecheng Zhao. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jiecheng Zhao -/ import Mathlib.Init /-! # Lemmas about `Array.extract` Some useful lemmas about Array.extract -/ universe u variable {α : Type u} {i : Nat} namespace Array @[simp] ...
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.AddCharacter import Mathlib.NumberTheory.LegendreSymbol.ZModChar import Mathlib.Algebra.CharP.CharAndCard /-! # Gauss sums ...
Nerve.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.SimplicialSet.Basic import Mathlib.CategoryTheory.ComposableArrows /-! # The nerve of a category This file provides the definition of the ne...
log.lean
import Mathlib.Data.Nat.Log /-! This used to fail (ran out of heartbeats) but with a new faster `Nat.logC` tagged `csimp`, it succeeds. -/ /-- info: 10000000 -/ #guard_msgs in #eval Nat.log 2 (2 ^ 10000000)
Synonym.lean
/- Copyright (c) 2021 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Yaël Dillies -/ import Mathlib.Algebra.Order.Group.Synonym import Mathlib.Algebra.Ring.Defs /-! # Ring structure on the order type synonyms Transfer algebraic insta...
InfSemilattice.lean
import Mathlib.CategoryTheory.Monoidal.Cartesian.InfSemilattice deprecated_module (since := "2025-05-15")
Lebesgue.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.Integral.Lebesgue.Basic import Mathlib.MeasureTheory.Integral.Lebesgue.Countable import Mathlib.MeasureTheory.Integral.Le...
NoncommCoprod.lean
/- Copyright (c) 2023 Antoine Chambert-Loir. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Antoine Chambert-Loir -/ import Mathlib.Algebra.Group.Commute.Hom import Mathlib.Algebra.Group.Prod import Mathlib.Algebra.Group.Subgroup.Ker import Mathlib.Algebra.Group.Subgro...
Small.lean
/- Copyright (c) 2025 Sophie. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sophie Morel, Antoine Chambert-Loir -/ import Mathlib.Data.Finsupp.ToDFinsupp import Mathlib.Data.DFinsupp.Defs import Mathlib.Logic.Small.Basic /-! # Smallness of the `DFinsupp` type Let `π...
cyclotomic.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 div choice fintype tuple finfun bigop prime. From mat...
FunctorN.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.DoldKan.PInfty /-! # Construction of functors N for the Dold-Kan correspondence In this file, we construct functors `N₁ : SimplicialObject C...
zmodp.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool choice eqtype ssrnat seq. From mathcomp Require Import div fintype bigo...
TopologicalAbelianization.lean
/- Copyright (c) 2023 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 -/ import Mathlib.GroupTheory.Commutator.Basic import Mathlib.Tactic.Group import Mathlib.Topology.Algebra.Group.Basic /-! # The topolog...
Iterate.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.Logic.Function.Conjugate /-! # Iterations of a function In this file we prove simple properties of `Nat.iterate f n` a.k.a. `f^[n]`: * `iterate_ze...
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...
GaloisField.lean
/- Copyright (c) 2021 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Anderson, Alex J. Best, Johan Commelin, Eric Rodriguez, Ruben Van de Velde -/ import Mathlib.Algebra.Algebra.ZMod import Mathlib.FieldTheory.Finite.Basic import Mathlib.FieldTheo...
primitive_action.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. From mathcomp Require Import div seq fintype tuple finset. From mathcomp Require Import fin...
Colimit.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.Condensed.Discrete.LocallyConstant import Mathlib.Condensed.Equivalence import Mathlib.Topology.Category.LightProfinite.Extend /-! # The condensed...
Round.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Kevin Kappelmann -/ import Mathlib.Algebra.Order.Floor.Ring import Mathlib.Algebra.Order.Interval.Set.Group /-! # Rounding This file defines the `round` function, whi...
NAry.lean
/- Copyright (c) 2020 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn -/ import Mathlib.Data.Set.Prod /-! # N-ary images of sets This file defines `Set.image2`, the binary image of sets. This is mostly useful to define pointwise oper...
intdiv.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 choice fintype...
Preserves.lean
/- Copyright (c) 2025 Robin Carlier. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Robin Carlier -/ import Mathlib.CategoryTheory.Functor.KanExtension.Adjunction import Mathlib.CategoryTheory.Limits.Preserves.Basic /-! # Preservation of Kan extensions Given functors...
GameAdd.lean
/- Copyright (c) 2022 Junyan Xu. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Junyan Xu -/ import Mathlib.Data.Sym.Sym2 import Mathlib.Logic.Relation /-! # Game addition relation This file defines, given relations `rα : α → α → Prop` and `rβ : β → β → Prop`, a rela...
Extend.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.Topology.Category.Profinite.AsLimit import Mathlib.Topology.Category.Profinite.CofilteredLimit import Mathlib.CategoryTheory.Filtered.Final /-! # ...
Localization.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.RingTheory.Flat.Stability import Mathlib.RingTheory.LocalProperties.Exactness /-! # Flatness and localization In this file we show that localizations are flat,...
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. (**********************...
Notation.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Yury Kudryashov, Yaël Dillies -/ import Qq import Mathlib.Lean.PrettyPrinter.Delaborator import Mathlib.Tactic.TypeStar import Mathlib.Tactic.Simps.NotationClass /-! #...
Lattice.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.Data.List.Forall2 import Mathlib.Data.List.TakeDrop import Mathlib.Data.List.Lattice import Mathlib.Data.List....
CongrExclamation.lean
/- Copyright (c) 2023 Kyle Miller. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kyle Miller -/ import Lean.Elab.Tactic.Config import Lean.Elab.Tactic.RCases import Lean.Meta.Tactic.Assumption import Lean.Meta.Tactic.Rfl import Mathlib.Lean.Meta.CongrTheorems import M...
Prod.lean
/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Simon Hudon, Patrick Massot, Yury Kudryashov -/ import Mathlib.Algebra.Group.Equiv.Defs import Mathlib.Algebra.Group.Hom.Basic import Mathlib.Algebra.Group.Opposite import Mathlib.Alg...
Depth.lean
/- Copyright (c) 2025 Nailin Guan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Nailin Guan, Yi Song -/ import Mathlib.Algebra.Module.FinitePresentation import Mathlib.LinearAlgebra.Dual.Lemmas import Mathlib.RingTheory.Ideal.AssociatedPrime.Finiteness import Mathlib...
Bounded.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.Hom.Basic /-! # Bounded order homomorphisms This file defines (bounded) order homomorphisms. We use the `DFunLike` design, so each type of morphis...
eqtype.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. (********************************************************************...
Pairing.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, Mario Carneiro -/ import Mathlib.Algebra.Notation.Prod import Mathlib.Data.Nat.Sqrt import Mathlib.Data.Set.Lattice.Image /-! # Naturals pairing function Th...
Notation3.lean
/- Copyright (c) 2021 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Kyle Miller -/ import Lean.Elab.BuiltinCommand import Lean.Elab.MacroArgUtil import Mathlib.Lean.Elab.Term import Mathlib.Lean.PrettyPrinter.Delaborator import M...
Basic.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.Algebra.Algebra.Subalgebra.Prod import Mathlib.Algebra.Algebra.Subalgebra.Tower import Mathlib.LinearAlgebra.Basis.Basic import Mathlib.LinearAlgebra.Prod /-! # ...
FundThmCalculus.lean
/- Copyright (c) 2020 Zhouhang Zhou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Zhouhang Zhou, Yury Kudryashov -/ import Mathlib.MeasureTheory.Integral.Bochner.Set /-! # Fundamental theorem of calculus for set integrals This file proves a version of the [Fundamen...
ssrnotations.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) (******************************************************************************) (* - Reserved notation for various arithmetic and algebraic operations: ...
CompletePartialOrder.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.Order.OmegaCompletePartialOrder /-! # Complete Partial Orders This file considers complete partial orders (sometimes called directedly comple...
Center.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.Star.Basic import Mathlib.Algebra.Star.Pointwise import Mathlib.Algebra.Group.Center /-! # `Set.center`, `Set.centralizer` and the `star` operat...
Weight.lean
/- Copyright (c) 2024 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.Data.Finsupp.Antidiagonal import Mathlib.Data.Finsupp.Order import Mathli...
Add.lean
/- Copyright (c) 2019 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Sébastien Gouëzel, Yury Kudryashov -/ import Mathlib.Analysis.Calculus.FDeriv.Linear import Mathlib.Analysis.Calculus.FDeriv.Comp import Mathlib.Analysis.Calculus.FDeriv....
all_order.v
Require Export order.
frobenius.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 div. From mathcomp Require Import fintype bigop prime finset fingroup morphism. From mathcom...
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...
ChosenFiniteProducts.lean
import Mathlib.CategoryTheory.Sites.Limits import Mathlib.CategoryTheory.Monoidal.Cartesian.FunctorCategory deprecated_module (since := "2025-05-11")
sylow.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div. From mathcomp Require Import fintype prime bigop finset fingroup morphism. From mat...
Lipschitz.lean
/- Copyright (c) 2018 Rohan Mitta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rohan Mitta, Kevin Buzzard, Alistair Tucker, Johannes Hölzl, Yury Kudryashov, Winston Yin -/ import Mathlib.Algebra.Group.End import Mathlib.Tactic.Finiteness import Mathlib.Topology.EMet...
VecNotation.lean
/- Copyright (c) 2020 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen, Eric Wieser -/ import Mathlib.Data.Fin.Tuple.Basic /-! # Matrix and vector notation This file defines notation for vectors and matrices. Given `a b c d : α`, the notation a...
Tilted.lean
/- Copyright (c) 2025 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.MeasureTheory.Measure.Tilted import Mathlib.Probability.Moments.MGFAnalytic /-! # Results relating `Measure.tilted` to `mgf` and `cgf` For a random varia...
Trim.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.Basic /-! # Lp seminorm with respect to trimmed measure In this file we prove basic properties of the Lp-seminorm of a ...
frobenius.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 div. From mathcomp Require Import fintype bigop prime finset fingroup morphism. From mathcom...
NonUnitalNonAssocAlgebra.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.Algebra.Algebra.NonUnitalHom import Mathlib.Algebra.Lie.Basic /-! # Lie algebras as non-unital, non-associative algebras The definition of Lie algebras use...
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...