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LocallyRingedSpace.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.Geometry.Manifold.Sheaf.Smooth import Mathlib.Geometry.RingedSpace.LocallyRingedSpace /-! # Smooth manifolds as locally ringed spaces This file equ...
Finset.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.Finset.Sort import Mathlib.Logic.Equiv.Multiset /-! # `Encodable` and `Denumerable` instances for `Finset` -/ variable {α} open Encodable /-- ...
Basic.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.CharP.Defs import Mathlib.Algebra.MvPolynomial.Degrees import Mathlib.Data.DFinsupp.Small import Mathlib.Data.Fintype.Pi import Mathlib.LinearA...
extremal.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 bigo...
Jordan.lean
/- Copyright (c) 2021 Kexing Ying. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kexing Ying -/ import Mathlib.MeasureTheory.VectorMeasure.Decomposition.Hahn import Mathlib.MeasureTheory.Measure.MutuallySingular import Mathlib.Topology.Algebra.UniformMulAction /-! # ...
SpeedCenterJson.lean
/- Copyright (c) 2023 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Lean.Data.Json open Lean /-! # `structure`s for the https://speed.lean-lang.org/ API -/ namespace SpeedCenterAPI structure CommitSource where repo_id : String...
Instances.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.Divisibility.Prod import Mathlib.Algebra.Polynomial.FieldDivision import Mathlib.RingTheory.Artinian.Module /-! # Instances related to Artinian rings W...
Discrete.lean
/- Copyright (c) 2020 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.Algebra.Group.Hom.Defs import Mathlib.CategoryTheory.Discrete.Basic import Mathlib.CategoryTheory.Monoidal.NaturalTransformation /-! # Monoids as discrete...
Sum.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.Order.Group.Multiset /-! # Disjoint sum of multisets This file defines the disjoint sum of two multisets as `Multiset (α ⊕ β)`. Beware not to con...
CommaMap.lean
/- Copyright (c) 2024 Jakob von Raumer. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jakob von Raumer -/ import Mathlib.CategoryTheory.Comma.StructuredArrow.Basic /-! # Structured arrow categories on `Comma.map` We characterize structured arrow categories on arbitr...
OmegaLimit.lean
/- Copyright (c) 2020 Jean Lo. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jean Lo -/ import Mathlib.Dynamics.Flow import Mathlib.Tactic.Monotonicity /-! # ω-limits For a function `ϕ : τ → α → β` where `β` is a topological space, we define the ω-limit under `ϕ` of...
Substitution.lean
/- Copyright (c) 2025 Antoine Chambert-Loir, María Inés de Frutos Fernández. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Antoine Chambert-Loir, María Inés de Frutos Fernández -/ import Mathlib.RingTheory.MvPowerSeries.Substitution import Mathlib.RingTheory.PowerSer...
TryThis.lean
/- Copyright (c) 2024 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Init import Lean.Meta.Tactic.TryThis /-! # 'Try this' tactic macro This is a convenient shorthand intended for macro authors to be able to generate "...
Operations.lean
/- Copyright (c) 2019 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, Floris van Doorn -/ import Mathlib.Analysis.Calculus.ContDiff.Basic import Mathlib.Analysis.Calculus.Deriv.Inverse /-! # Higher differentiability of usual operat...
Basic.lean
/- Copyright (c) 2018 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot, Johannes Hölzl, Yaël Dillies -/ import Mathlib.Analysis.Normed.Group.Seminorm import Mathlib.Data.NNReal.Basic import Mathlib.Topology.Algebra.Support import Mathlib.To...
AB.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, Moritz Firsching, Nikolas Kuhn, Amelia Livingston -/ import Mathlib.Algebra.Category.Grp.Biproducts import Mathlib.Algebra.Category.Grp.FilteredColi...
TwoDim.lean
/- Copyright (c) 2022 Heather Macbeth. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Heather Macbeth -/ import Mathlib.Analysis.InnerProductSpace.Dual import Mathlib.Analysis.InnerProductSpace.Orientation import Mathlib.Data.Complex.FiniteDimensional import Mathlib.Da...
AEEqOfIntegralContDiff.lean
/- Copyright (c) 2023 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Geometry.Manifold.PartitionOfUnity import Mathlib.Geometry.Manifold.Metrizable import Mathlib.MeasureTheory.Function.AEEqOfIntegral /-! # Functi...
Pi.lean
/- Copyright (c) 2020 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.CategoryTheory.Pi.Basic import Mathlib.CategoryTheory.Limits.HasLimits /-! # Limits in the category of indexed families of objects. Given a functor `F : ...
Pi.lean
/- Copyright (c) 2017 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Data.Finset.Pi import Mathlib.Data.Fintype.Basic import Mathlib.Data.Set.Finite.Basic /-! # Fintype instances for pi types -/ assert_not_exists Order...
LatticeIntervals.lean
/- Copyright (c) 2020 Aaron Anderson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Anderson -/ import Mathlib.Order.Bounds.Basic /-! # Intervals in Lattices In this file, we provide instances of lattice structures on intervals within lattices. Some of them de...
Bounded.lean
/- Copyright (c) 2022 Violeta Hernández Palacios. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Violeta Hernández Palacios -/ import Mathlib.Order.RelClasses import Mathlib.Order.Interval.Set.Basic /-! # Bounded and unbounded sets We prove miscellaneous lemmas about ...
InfSemilattice.lean
/- Copyright (c) 2025 Sina Hazratpour. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sina Hazratpour -/ import Mathlib.CategoryTheory.Limits.Preorder import Mathlib.CategoryTheory.Monoidal.Cartesian.Basic /-! # The preorder category of a meet-semilattice with a great...
RieszLemma.lean
/- Copyright (c) 2019 Jean Lo. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jean Lo, Yury Kudryashov -/ import Mathlib.Analysis.NormedSpace.Real import Mathlib.Analysis.Seminorm import Mathlib.Topology.MetricSpace.HausdorffDistance /-! # Applications of the Hausdorf...
all_solvable.v
From mathcomp Require Export abelian. From mathcomp Require Export alt. From mathcomp Require Export burnside_app. From mathcomp Require Export center. From mathcomp Require Export commutator. From mathcomp Require Export cyclic. From mathcomp Require Export extraspecial. From mathcomp Require Export extremal. From mat...
Chain.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Kenny Lau, Yury Kudryashov -/ import Mathlib.Data.List.Forall2 import Mathlib.Data.List.Lex import Mathlib.Logic.Function.Iterate import Mathlib.Logic.Relation /-! # R...
SelfAdjoint.lean
/- Copyright (c) 2021 Frédéric Dupuis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Frédéric Dupuis -/ import Mathlib.Algebra.Group.Subgroup.Defs import Mathlib.Algebra.Module.Defs import Mathlib.Algebra.Star.Rat /-! # Self-adjoint, skew-adjoint and normal elements ...
LinearAlgebra.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.Constructions import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq import Mathlib.LinearAlgebra.Basis.VectorSpace impo...
Support.lean
/- Copyright (c) 2022 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn, Patrick Massot -/ import Mathlib.Algebra.GroupWithZero.Indicator import Mathlib.Algebra.Module.Basic import Mathlib.Algebra.Order.Group.Unbundled.Abs import Mathlib...
Basic.lean
/- Copyright (c) 2024 Yakov Pechersky. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yakov Pechersky -/ import Mathlib.Algebra.Order.Hom.Basic import Mathlib.Analysis.Normed.Group.Basic /-! # Constructing (semi)normed groups from (semi)normed homs This file defines ...
BaseChange.lean
/- Copyright (c) 2025 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.Algebra.Algebra.Rat import Mathlib.LinearAlgebra.PerfectPairing.Restrict import Mathlib.LinearAlgebra.RootSystem.IsValuedIn /-! # Base change for root pairi...
Basic.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Yury Kudryashov, Kim Morrison -/ import Mathlib.Algebra.Algebra.Equiv import Mathlib.Algebra.Algebra.NonUnitalHom import Mathlib.Algebra.Module.BigOperators import Math...
NoncommRing.lean
import Mathlib.GroupTheory.GroupAction.Ring import Mathlib.Tactic.NoncommRing local infix:70 " ⚬ " => fun a b => a * b + b * a variable {R : Type _} [Ring R] variable (a b c : R) example : 0 = 0 := by noncomm_ring example : a = a := by noncomm_ring example : (a + b) * c = a * c + b * c := by noncomm_ring example : ...
NonPreadditive.lean
/- Copyright (c) 2020 Markus Himmel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Markus Himmel -/ import Mathlib.CategoryTheory.Limits.Shapes.FiniteProducts import Mathlib.CategoryTheory.Limits.Shapes.Kernels import Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Eq...
Arg.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, Benjamin Davidson -/ import Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle import Mathlib.Analysis.SpecialFunctions.T...
FiniteSpan.lean
/- Copyright (c) 2023 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash, Deepro Choudhury -/ import Mathlib.GroupTheory.OrderOfElement import Mathlib.LinearAlgebra.Span.Defs import Mathlib.Algebra.Module.Equiv.Basic /-! # Additional results abou...
QuotSMulTop.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.LinearAlgebra.DFinsupp import Mathlib.LinearAlgebra.TensorProduct.Quotient import Mathlib.LinearAlgebra.TensorProduct.RightExactness /-! # Reducing a ...
extremal.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 bigo...
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.Limits.Shapes.Countable import Mathlib.Topology.Category.Profinite.AsLimit import Mathlib.Topology.Category.Profinite.CofilteredLimi...
all_solvable.v
From mathcomp Require Export abelian. From mathcomp Require Export alt. From mathcomp Require Export burnside_app. From mathcomp Require Export center. From mathcomp Require Export commutator. From mathcomp Require Export cyclic. From mathcomp Require Export extraspecial. From mathcomp Require Export extremal. From mat...
all_character.v
From mathcomp Require Export character. From mathcomp Require Export classfun. From mathcomp Require Export inertia. From mathcomp Require Export integral_char. From mathcomp Require Export mxabelem. From mathcomp Require Export mxrepresentation. From mathcomp Require Export vcharacter.
LocallySurjective.lean
/- Copyright (c) 2022 Sam van Gool and Jake Levinson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sam van Gool, Jake Levinson -/ import Mathlib.Topology.Sheaves.Presheaf import Mathlib.Topology.Sheaves.Stalks import Mathlib.CategoryTheory.Limits.Preserves.Filtered i...
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.
Basic.lean
/- Copyright (c) 2021 Christopher Hoskin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christopher Hoskin -/ import Mathlib.Algebra.Lie.OfAssociative /-! # Jordan rings Let `A` be a non-unital, non-associative ring. Then `A` is said to be a (commutative, linear) Jo...
Embedding.lean
/- Copyright (c) 2021 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen -/ import Mathlib.Data.FunLike.Basic /-! # Typeclass for a type `F` with an injective map to `A ↪ B` This typeclass is primarily for use by embeddings such as `RelEmbedding`...
Lemmas.lean
/- Copyright (c) 2022 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot -/ import Mathlib.Analysis.Normed.Group.Uniform /-! # Further lemmas about normed groups This file contains further lemmas about normed groups, requiring heavier impor...
Increment.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.Combinatorics.SimpleGraph.Regularity.Chunk import Mathlib.Combinatorics.SimpleGraph.Regularity.Energy /-! # Increment partitio...
Map.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.Data.Matroid.Constructions import Mathlib.Data.Set.Notation /-! # Maps between matroids This file defines maps and comaps, which move a matroid on one ty...
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.Topology.Continuous import Mathlib.Topology.ContinuousMap.Defs /-! # Continuous order homomorphisms This file defines continuous order homomorphisms, tha...
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_...
Exact.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.Module.Submodule.Range import Mathlib.LinearAlgebra.Prod import Mathlib.LinearAlgebra.Quotient.Basic /-! # Exactness of a pair ...
ssreflect.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From Corelib Require Export ssreflect. Global Set SsrOldRewriteGoalsOrder. Global Set Asymmetric Patterns. Global Set Bullet Behavior "None". #[deprecated(sinc...
Lemmas.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.Data.Int.Bitwise import Mathlib.Data.Int.Order.Lemmas import Mathlib.Order.Interval.Set.Defs /-! # Miscellaneous lemmas about the integers This file co...
IntegrationByParts.lean
/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Patrick Massot, Sébastien Gouëzel -/ import Mathlib.MeasureTheory.Integral.IntervalIntegral.IntegrationByParts deprecated_module (since := "2025-04-06")
Properties.lean
/- Copyright (c) 2021 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.AlgebraicGeometry.AffineScheme import Mathlib.RingTheory.LocalProperties.Reduced /-! # Basic properties of schemes We provide some basic properties of sche...
Ultra.lean
/- Copyright (c) 2024 Yakov Pechersky. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yakov Pechersky, David Loeffler -/ import Mathlib.Analysis.Normed.Group.Uniform import Mathlib.Topology.Algebra.Nonarchimedean.Basic import Mathlib.Topology.MetricSpace.Ultra.Basic im...
MeasureComp.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.CompNotation import Mathlib.Probability.Kernel.Composition.MeasureCompProd import Mathlib.Probability.Kern...
Sum.lean
/- Copyright (c) 2022 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Bhavik Mehta -/ import Mathlib.Data.Finset.Card import Mathlib.Data.Finset.Fold import Mathlib.Data.Multiset.Sum /-! # Disjoint sum of finsets This file defines the disjo...
ReflectsPreregular.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.EffectiveEpi.Enough import Mathlib.CategoryTheory.EffectiveEpi.Preserves import Mathlib.CategoryTheory.Sites.Coherent.RegularTopolog...
DensityTheorem.lean
/- Copyright (c) 2022 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.MeasureTheory.Measure.Doubling import Mathlib.MeasureTheory.Covering.Vitali import Mathlib.MeasureTheory.Covering.Differentiation /-! # Uniformly locally do...
Composition.lean
/- Copyright (c) 2020 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Algebra.BigOperators.Fin import Mathlib.Algebra.Order.BigOperators.Group.Finset import Mathlib.Data.Finset.Sort /-! # Compositions A compositio...
finmodule.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path. From mathcomp Require Import div choice fintype...
OfBiproducts.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.Shapes.BinaryBiproducts import Mathlib.GroupTheory.EckmannHilton import Mathlib.Tactic.CategoryTheory.Reassoc /-! # Constructing a ...
Lemmas.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl -/ import Mathlib.Algebra.BigOperators.Intervals import Mathlib.Data.ENNReal.BigOperators import Mathlib.Tactic.Bound import Mathlib.Topology.Order.LiminfLimsup import M...
Order.lean
/- Copyright (c) 2024 Frédéric Dupuis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Frédéric Dupuis -/ import Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Basic import Mathlib.Analysis.CStarAlgebra.Unitization import Mathlib.Analysis.SpecialFunctions.C...
finfun.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 tuple. ...
Sites.lean
/- Copyright (c) 2021 Justus Springer. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Justus Springer -/ import Mathlib.CategoryTheory.Sites.Spaces import Mathlib.Topology.Sheaves.Sheaf import Mathlib.CategoryTheory.Sites.DenseSubsite.Basic /-! # Coverings and sieves...
Measure.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.Analysis.BoxIntegral.Partition.Additive import Mathlib.MeasureTheory.Measure.Lebesgue.Basic /-! # Box-additive functions defined by measures In thi...
Simple.lean
/- Copyright (c) 2020 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Markus Himmel, Kim Morrison -/ import Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms import Mathlib.CategoryTheory.Limits.Shapes.Kernels import Mathlib.CategoryTheory.Abelian.Basic i...
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...
Basic.lean
/- Copyright (c) 2020 Aaron Anderson, Jalex Stark, Kyle Miller. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Anderson, Jalex Stark, Kyle Miller, Alena Gusakov, Hunter Monroe -/ import Mathlib.Combinatorics.SimpleGraph.Init import Mathlib.Data.Finite.Prod import...
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...
algnum.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path. From mathcomp Require Import div choice fintype...
BooleanGenerators.lean
/- Copyright (c) 2024 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.Order.CompactlyGenerated.Basic /-! # Generators for boolean algebras In this file, we provide an alternative constructor for boolean algebras. A set...
SetSemiring.lean
/- Copyright (c) 2023 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne, Peter Pfaffelhuber -/ import Mathlib.Data.Nat.Lattice import Mathlib.Data.Set.Accumulate import Mathlib.Data.Set.Pairwise.Lattice import Mathlib.MeasureTheory.PiSystem /-!...
ring_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 choice ssrnat. From mathcomp Require Import seq ssralg generic_q...
WeakDual.lean
/- Copyright (c) 2022 Moritz Doll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Moritz Doll -/ import Mathlib.Analysis.Normed.Field.Lemmas import Mathlib.Analysis.LocallyConvex.WithSeminorms import Mathlib.Topology.Algebra.Module.WeakBilin /-! # Weak Dual in Topolog...
mxabelem.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path. From mathcomp Require Import div choice fintype...
ProdAssoc.lean
/- Copyright (c) 2023 Adam Topaz. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Adam Topaz -/ import Mathlib.Lean.Expr.Basic import Mathlib.Logic.Equiv.Defs /-! # Associativity of products This file constructs a term elaborator for "obvious" equivalences between ite...
BigOperators.lean
/- Copyright (c) 2022 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.GroupTheory.Congruence.BigOperators import Mathlib.RingTheory.Congruence.Defs /-! # Interactions between `∑, ∏` and `RingCon` -/ namespace RingCon /-- Co...
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: ...
Single.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.Algebra.Homology.HomologicalComplex /-! # Homological complexes supported in a single degree We define `single V j c : V ⥤ HomologicalComplex V c`, which...
Conjneg.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.BigOperators.Pi import Mathlib.Algebra.Star.Pi import Mathlib.Algebra.Group.Pointwise.Set.Basic /-! # Conjugation-negation operator This file def...
Misc.lean
/- Copyright (c) 2024 Xavier Roblot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Xavier Roblot -/ import Mathlib.LinearAlgebra.Matrix.Determinant.Basic import Mathlib.Algebra.Ring.NegOnePow /-! # Miscellaneous results about determinant In this file, we collect var...
Lint.lean
import Mathlib.Tactic.Linter.Lint import Mathlib.Tactic.ToAdditive /-- warning: The namespace 'add' is duplicated in the declaration 'add.add' Note: This linter can be disabled with `set_option linter.dupNamespace false` -/ #guard_msgs in def add.add := True namespace Foo /-- warning: The namespace 'Foo' is duplicat...
SimplicialNerve.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.AlgebraicTopology.SimplicialCategory.Basic import Mathlib.AlgebraicTopology.SimplicialSet.Nerve /-! # The simplicial nerve of a simplicial categor...
Yoneda.lean
/- Copyright (c) 2024 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.Algebra.Homology.ShortComplex.Ab import Mathlib.CategoryTheory.Preadditive.Yoneda.Basic import Mathlib.CategoryTheory.Shift.ShiftedHomOpposite import Mathlib.Cat...
WellQuasiOrder.lean
/- Copyright (c) 2025 Violeta Hernández Palacios. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Violeta Hernández Palacios, Aaron Anderson -/ import Mathlib.Data.Fintype.Card import Mathlib.Data.Set.Finite.Basic import Mathlib.Order.Antichain import Mathlib.Order.Orde...
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.
Calc.lean
/- Copyright (c) 2023 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot -/ import Lean.Elab.Tactic.Calc import Lean.Meta.Tactic.TryThis import Mathlib.Data.String.Defs import Mathlib.Tactic.Widget.SelectPanelUtils import Batteries.CodeActio...
matrix.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 finfun f...
ArctanDeriv.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, Benjamin Davidson -/ import Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan import Mathlib.Analysis.SpecialFunctions....
test_guard.v
From mathcomp Require Import all_boot. Set Implicit Arguments. Unset Strict Implicit. Unset Printing Implicit Defensive. Inductive tree := Node { children : seq tree }. Inductive ptree (T : Type) := singleton of T | branch of list (ptree T). (* has *) Fixpoint tree_has (T : Type) (p : pred T) (t : ptree T) : bool :...
Types.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.Limits.FilteredColimitCommutesFiniteLimit import Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic /-! # The category of types sati...
hall.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div choice. From mathcomp Require Import fintype finset prime fingroup morphism. From ma...
Biproducts.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.CategoryTheory.Idempotents.Karoubi /-! # Biproducts in the idempotent completion of a preadditive category In this file, we define an instance expressing that...
CasesM.lean
/- Copyright (c) 2022 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Init import Lean.Elab.Tactic.Conv.Pattern /-! # `casesm`, `cases_type`, `constructorm` tactics These tactics implement repeated `cases` / `constructo...
ProdL2.lean
/- Copyright (c) 2023 Moritz Doll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Moritz Doll -/ import Mathlib.Analysis.InnerProductSpace.PiL2 import Mathlib.Analysis.Normed.Lp.ProdLp /-! # `L²` inner product space structure on products of inner product spaces The `...
Aliases.lean
/- Copyright (c) 2024 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.Init /-! Deprecated aliases can be dumped here if they are no longer used in Mathlib, to avoid needing their imports if they are otherwise unnecessary. -/...
Defs.lean
/- Copyright (c) 2021 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes -/ import Mathlib.Algebra.MvPolynomial.CommRing /-! # Algebraic Independence This file defines algebraic independence of a family of elements of an `R` algebra. ## Main d...