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Basic.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.LocalInvariantProperties import Mathlib.Topology.Sheaves.LocalPredicate /-! # Generic construction of a sheaf from a `LocalInvaria...
BigOps.lean
import Mathlib.Algebra.BigOperators.Group.Finset.Basic section variable {ι M : Type*} [CommMonoid M] [AddCommMonoid M] [Fintype ι] {s : Finset ι} {p : ι → Prop} [DecidablePred p] {f : ι → M} /-! ### Big operators over a finset -/ /-- info: ∑ i ∈ s, f i : M -/ #guard_msgs in #check Finset.sum s fun i ↦ f i /-- inf...
interval_cases.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.Tactic.IntervalCases import Mathlib.Tactic.Set set_option linter.unusedVariables false in example (n : ℕ) : True := by fail_if_success interval_cases n...
Basic.lean
/- Copyright (c) 2019 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Bhavik Mehta, Adam Topaz -/ import Mathlib.CategoryTheory.Functor.Category import Mathlib.CategoryTheory.Functor.FullyFaithful import Mathlib.CategoryTheory.Functor.Reflect...
Basic.lean
/- Copyright (c) 2017 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot, Kim Morrison, Mario Carneiro -/ import Mathlib.CategoryTheory.Elementwise import Mathlib.Topology.ContinuousMap.Basic /-! # Category instance for topological spaces We ...
Equiv.lean
/- Copyright (c) 2025 Weiyi Wang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Weiyi Wang -/ import Mathlib.Algebra.Module.Equiv.Basic import Mathlib.Algebra.Order.Group.Equiv import Mathlib.Algebra.Order.Module.Synonym /-! # Linear equivalence for order type synony...
all_algebra.v
(* N.B. interval_inference is not exported here. To enjoys the automation it provides, you need to explictly "Import interval_inference". *) From mathcomp Require Export ssralg. From mathcomp Require Export ssrnum. From mathcomp Require Export finalg. From mathcomp Require Export countalg. From mathcomp Require Export...
DocString.lean
/- Copyright (c) 2025 Damiano Testa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Rothgang, Damiano Testa -/ import Mathlib.Tactic.Linter.Header /-! # The "DocString" style linter The "DocString" linter validates style conventions regarding doc-string for...
ConcreteCategory.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.Ab import Mathlib.Algebra.Homology.ShortComplex.ExactFunctor import Mathlib.Algebra.Homology.ShortComplex.SnakeLemma import Mathlib...
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...
Determinant.lean
/- Copyright (c) 2019 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen -/ import Mathlib.LinearAlgebra.FreeModule.StrongRankCondition import Mathlib.LinearAlgebra.GeneralLinearGroup import Mathlib.L...
Basic.lean
/- Copyright (c) 2023 Luke Mantle. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Luke Mantle -/ import Mathlib.Algebra.Polynomial.Derivative import Mathlib.Data.Nat.Factorial.DoubleFactorial /-! # Hermite polynomials This file defines `Polynomial.hermite n`, the `n`...
fingraph.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 seq path fintype. (******************************************...
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.BialgCat.Monoidal import Mathlib.Algebra.Category.HopfAlgCat.Basic import Mathlib.RingTheory.HopfAlgebra.TensorProduct /-! # Th...
CompletelyPositiveMap.lean
/- Copyright (c) 2025 Frédéric Dupuis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Frédéric Dupuis -/ import Mathlib.Analysis.CStarAlgebra.PositiveLinearMap import Mathlib.Analysis.CStarAlgebra.CStarMatrix /-! # Completely positive maps A linear map `φ : A₁ →ₗ[ℂ]...
Defs.lean
/- Copyright (c) 2024 Florent Schaffhauser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Florent Schaffhauser, Artie Khovanov -/ import Mathlib.Algebra.Ring.SumsOfSquares /-! # Semireal rings A semireal ring is a commutative ring (with unit) in which `-1` is *not* ...
RestrictScalars.lean
/- Copyright (c) 2025 Stefan Kebekus. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Stefan Kebekus -/ import Mathlib.Analysis.Calculus.ContDiff.Defs import Mathlib.Analysis.Calculus.FDeriv.RestrictScalars /-! ### Restricting Scalars in Iterated Fréchet Derivatives T...
Mul.lean
/- Copyright (c) 2023 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Algebra.Order.Monovary import Mathlib.Algebra.Order.Ring.Basic import Mathlib.Analysis.Convex.Function import Mathlib.Tactic.FieldSimp /-! # Product of co...
HasConicalProducts.lean
/- Copyright (c) 2025 Jon Eugster. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Dagur Asgeirsson, Jon Eugster, Emily Riehl -/ import Mathlib.CategoryTheory.Enriched.Limits.HasConicalLimits /-! # Existence of conical products -/ universe w v' v u u' namespace Categ...
dummy_label_attr.lean
import Lean.LabelAttribute register_label_attr dummy_label_attr
Wilson.lean
/- Copyright (c) 2022 John Nicol. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: John Nicol -/ import Mathlib.FieldTheory.Finite.Basic /-! # Wilson's theorem. This file contains a proof of Wilson's theorem. The heavy lifting is mostly done by the previous `wilsons_l...
Basic.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, Scott Carnahan -/ import Mathlib.LinearAlgebra.RootSystem.Defs import Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate /-! # Root data and root system...
Konigsberg.lean
/- Copyright (c) 2022 Kyle Miller. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kyle Miller -/ import Mathlib.Combinatorics.SimpleGraph.Trails import Mathlib.Tactic.DeriveFintype import Mathlib.Tactic.NormNum /-! # The Königsberg bridges problem We show that a grap...
Booleanisation.lean
/- Copyright (c) 2023 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Order.BooleanAlgebra.Basic import Mathlib.Order.Hom.Lattice /-! # Adding complements to a generalized Boolean algebra This file embeds any generalized Bo...
LineDeriv.lean
/- Copyright (c) 2024 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Analysis.Calculus.LocalExtr.Basic import Mathlib.Analysis.Calculus.LineDeriv.Basic /-! # Local extremum and line derivatives If `f` has a local ext...
CartesianMonoidal.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.Algebra.Category.Grp.Biproducts import Mathlib.Algebra.Category.Grp.Zero import Mathlib.Algebra.Ring.PUnit import Mathlib.CategoryTheory.Monoidal.Types.B...
set_like.lean
import Mathlib.Algebra.Field.Subfield.Basic import Mathlib.Algebra.Star.Subalgebra import Mathlib.Algebra.Star.SelfAdjoint import Mathlib.Algebra.Star.NonUnitalSubalgebra set_option autoImplicit true section Delab variable {M : Type u} [Monoid M] (S S' : Submonoid M) set_option linter.style.commandStart false /-- i...
Submodule.lean
/- Copyright (c) 2024 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang, David Swinarski -/ import Mathlib.Algebra.Module.LocalizedModule.Submodule import Mathlib.RingTheory.Localization.AtPrime.Basic import Mathlib.RingTheory.Localization.Away.Ba...
Basic.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.Algebra.BigOperators.Option import Mathlib.Analysis.BoxIntegral.Box.Basic import Mathlib.Data.Set.Pairwise.Lattice /-! # Partitions of rectangular b...
qfpoly.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import fintype tuple div bigop binomial finset finfun. From mathcomp Require Import ssralg countalg finalg poly polydiv qpoly perm. From mathcomp Require Import fingroup falgebra fiel...
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. (*************************...
SeparatedNhds.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Mario Carneiro -/ import Mathlib.Topology.Continuous import Mathlib.Topology.NhdsSet /-! # Separated neighbourhoods This file defines the predicates `SeparatedNhds` a...
ProdSigma.lean
/- Copyright (c) 2015 Leonardo de Moura. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Leonardo de Moura, Mario Carneiro -/ import Mathlib.Data.List.Basic /-! # Lists in product and sigma types This file proves basic properties of `List.product` and `List.sigma`, wh...
SetNotation.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Patrick Massot, Yury Kudryashov -/ import Mathlib.Data.Set.Operations import Mathlib.Util.Notation3 /-! # Notation classes for set supremum and infimum In this file w...
PointwiseRightDerived.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.Functor.Derived.RightDerived import Mathlib.CategoryTheory.Functor.KanExtension.Pointwise import Mathlib.CategoryTheory.Localization.StructuredArr...
Closed.lean
/- Copyright (c) 2020 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta -/ import Mathlib.CategoryTheory.Sites.SheafOfTypes import Mathlib.Order.Closure /-! # Closed sieves A natural closure operator on sieves is a closure operator on `Sieve X...
Limits.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.Constructions.EpiMono import Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits import Ma...
Prod.lean
/- Copyright (c) 2022 George Peter Banyard, Yaël Dillies, Kyle Miller. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: George Peter Banyard, Yaël Dillies, Kyle Miller -/ import Mathlib.Combinatorics.SimpleGraph.Paths import Mathlib.Combinatorics.SimpleGraph.Metric /-! ...
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: ...
CountableSeparating.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.Topology.Order.Basic import Mathlib.Order.Filter.CountableSeparatingOn /-! # Countably many infinite intervals separate points In this file we prov...
List.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 -/ import Mathlib.Data.List.Nodup import Mathlib.Data.Set.Pairwise.Basic /-! # Translating pairwise relations on sets to lists On a list with no duplicates,...
Minpoly.lean
/- Copyright (c) 2020 Aaron Anderson, Jalex Stark. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Anderson, Jalex Stark, Eric Wieser -/ import Mathlib.LinearAlgebra.Matrix.Charpoly.Coeff import Mathlib.LinearAlgebra.Matrix.ToLin import Mathlib.RingTheory.PowerBas...
Binomial.lean
/- Copyright (c) 2024 Scott Carnahan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Scott Carnahan -/ import Mathlib.RingTheory.Binomial import Mathlib.RingTheory.PowerSeries.WellKnown /-! # Binomial Power Series We introduce formal power series of the form `(1 + X) ...
Ordinal.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.SetTheory.Game.Basic import Mathlib.SetTheory.Ordinal.NaturalOps import Mathlib.Tactic.Linter.DeprecatedModule deprecated_modu...
test_regular_conv.v
From mathcomp Require Import all_boot all_order all_algebra all_field. Section regular. Import GRing. Goal forall R : ringType, [the lalgType R of R^o] = R :> ringType. Proof. by move=> [? []]. Qed. Goal forall R : comRingType, [the algType R of R^o] = R :> ringType. Proof. by move=> [? []]. Qed. Goal forall R : c...
Sign.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes -/ import Mathlib.Algebra.Group.Conj import Mathlib.Algebra.Group.Subgroup.Lattice import Mathlib.Algebra.Group.Submonoid.BigOperators import Mathlib.Data.Finset.Fin import ...
ConditionalExpectation.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.Probability.Notation import Mathlib.Probability.Independence.Basic import Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic /-! # Probabilistic p...
CommSq.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.Abelian.Refinements import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq import Mathlib.Algebra.Homology.CommSq /-! # The exact sequence a...
DeriveFintype.lean
import Mathlib.Tactic.DeriveFintype import Mathlib.Data.Fintype.Prod import Mathlib.Data.Fintype.Pi set_option autoImplicit true namespace tests /- Tests that the enumerable types succeed, even with universe levels. -/ inductive A | x | y | z deriving Fintype /-- info: tests.A.enumList : List A -/ #guard_msgs in ...
spectral.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat. From mathcomp Require Import seq div fintype bigop ssralg finset fingroup zmodp. From mathcomp Require Import poly polydiv order ssrnum matrix mxalgebra vector. From mathcomp Require Import mxpoly mxred sesqui...
Real.lean
/- Copyright (c) 2022 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne, Kexing Ying -/ import Mathlib.MeasureTheory.Function.ConditionalExpectation.Indicator import Mathlib.MeasureTheory.Function.UniformIntegrable import Mathlib.MeasureTheory.V...
Basic.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Algebra.Group.Action.Pi import Mathlib.Algebra.Order.AbsoluteValue.Basic import Mathlib.Algebra.Order.Field.Basic import Mathlib.Algebra.Order.Group.Mi...
Filter.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.SubboxInduction import Mathlib.Analysis.BoxIntegral.Partition.Split /-! # Filters used in box-based integrals First ...
MeasurableStieltjes.lean
/- Copyright (c) 2024 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.MeasureTheory.Measure.GiryMonad import Mathlib.MeasureTheory.Measure.Stieltjes import Mathlib.Analysis.Normed.Order.Lattice import Mathlib.MeasureTheory.Fu...
CauchyBound.lean
/- Copyright (c) 2024 Daniel Weber. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Daniel Weber -/ import Mathlib.Algebra.Order.Field.GeomSum import Mathlib.Algebra.Polynomial.Monic import Mathlib.Analysis.Normed.Field.Basic /-! # Cauchy's bound on polynomial roots. ...
BddDistLat.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.Category.BddLat import Mathlib.Order.Category.DistLat /-! # The category of bounded distributive lattices This defines `BddDistLat`, the category o...
UniformApproximation.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.Topology.UniformSpace.LocallyUniformConvergence /-! # Uniform approximation In this file, we give lemmas ensuring that a function is continuous...
qpoly.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import fintype tuple bigop binomial finset finfun ssralg. From mathcomp Require Import countalg finalg poly polydiv perm fingroup matrix. From mathcomp Require Import mxalgebra mxpoly...
Synonym.lean
/- Copyright (c) 2021 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Algebra.Group.Action.Defs import Mathlib.Algebra.Order.Group.Synonym /-! # Actions by and on order synonyms This PR transfers group action instances from...
Recover.lean
/- Copyright (c) 2022 Siddhartha Gadgil. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Gabriel Ebner, Siddhartha Gadgil, Jannis Limperg -/ import Mathlib.Init /-! # The `recover` tactic modifier This defines the `recover` tactic modifier, which can be used to debug ...
Paths.lean
/- Copyright (c) 2021 Kyle Miller. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kyle Miller -/ import Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkDecomp import Mathlib.Combinatorics.SimpleGraph.Walk /-! # Trail, Path, and Cycle In a simple graph, * A *trai...
DerivationBundle.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.Geometry.Manifold.Algebra.SmoothFunctions import Mathlib.RingTheory.Derivation.Basic /-! # Derivation bundle In this file we define the derivati...
Rotate.lean
/- Copyright (c) 2019 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Yakov Pechersky -/ import Mathlib.Data.List.Nodup import Mathlib.Data.List.Infix import Mathlib.Data.Quot /-! # List rotation This file proves basic results about `List.r...
Pell.lean
/- Copyright (c) 2023 Michael Stoll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Geißer, Michael Stoll -/ import Mathlib.Data.ZMod.Basic import Mathlib.NumberTheory.DiophantineApproximation.Basic import Mathlib.NumberTheory.Zsqrtd.Basic import Mathlib.Tactic...
Finite.lean
/- Copyright (c) 2020 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Johan Commelin -/ import Mathlib.LinearAlgebra.Isomorphisms import Mathlib.RingTheory.Finiteness.Basic import Mathlib.RingTheory.Finiteness.Bilinear import Mathlib.RingTheo...
Yoneda.lean
/- Copyright (c) 2017 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.CategoryTheory.Functor.Hom import Mathlib.CategoryTheory.Products.Basic import Mathlib.Data.ULift import Mathlib.Logic.Function.ULift /-! # The Yoneda emb...
ResidueField.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.AlgebraicGeometry.Stalk import Mathlib.Geometry.RingedSpace.LocallyRingedSpace.ResidueField /-! # Residue fields of points ## Main definitions The follow...
IsInvertedBy.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.Functor.ReflectsIso.Basic import Mathlib.CategoryTheory.MorphismProperty.Basic /-! # Morphism properties that are inverted by a functor In this ...
pgroup.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 bigop finset prime fingroup morphism. From mat...
Field.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.Etale.Pi import Mathlib.RingTheory.Unramified.Field /-! # Etale algebras over fields ## Main results Let `K` be a field, `A` be a `K`-algebra a...
GeomSum.lean
/- Copyright (c) 2019 Neil Strickland. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Neil Strickland -/ import Mathlib.Algebra.Order.BigOperators.Group.Finset import Mathlib.Algebra.Order.Ring.Defs import Mathlib.Algebra.Ring.GeomSum /-! # Partial sums of geometric s...
Basic.lean
/- Copyright (c) 2020 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.Geometry.Manifold.MFDeriv.Defs import Mathlib.Geometry.Manifold.ContMDiff.Defs /-! # Basic properties of the manifold Fréchet ...
ring.lean
import Mathlib.Algebra.Ring.GrindInstances import Mathlib.Algebra.Order.Field.Defs /-! # Preliminary tests for `grind` using Mathlib typeclasses. These are far from exhaustive tests, for now just testing the minimal functionality for `grind` using Mathlib's `CommRing` typeclass. -/ -- We mock ℝ here so that we don't...
Basic.lean
/- Copyright (c) 2021 Adam Topaz. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joseph Tooby-Smith, Adam Topaz -/ import Mathlib.CategoryTheory.Limits.Shapes.IsTerminal import Mathlib.CategoryTheory.Limits.Shapes.Terminal import Mathlib.CategoryTheory.Bicategory.Funct...
ListTraverse.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.Control.Traversable.Instances import Mathlib.Order.Filter.Map /-! # Properties of `Traversable.traverse` on `List`s and `Filter`s In this file we prov...
Equiv.lean
/- Copyright (c) 2023 Junyan Xu. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Junyan Xu -/ import Mathlib.Algebra.Field.IsField import Mathlib.Algebra.Group.Units.Equiv import Mathlib.Algebra.GroupWithZero.Equiv /-! # If a semiring is a field, any isomorphic semirin...
ForbiddenWindows.lean
import Mathlib.Tactic.Linter.TextBased /-! # Unit tests for the module name Windows-compatibility check in the text-based linters -/ open Lean.Linter Mathlib.Linter.TextBased /-- Some unit tests for `modulesForbiddenWindows` -/ def testModulesForbiddenWindows : IO Unit := do -- Explicitly enable the linter, althou...
MapCoeffs.lean
/- Copyright (c) 2024 Daniel Weber. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Daniel Weber -/ import Mathlib.RingTheory.Derivation.DifferentialRing import Mathlib.Algebra.Polynomial.Module.Basic import Mathlib.Algebra.Polynomial.Derivation import Mathlib.FieldTheo...
BifunctorShift.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.Bifunctor import Mathlib.Algebra.Homology.TotalComplexShift /-! # Behavior of the action of a bifunctor on cochain complexes with respect to sh...
Defs.lean
/- Copyright (c) 2020 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen -/ import Mathlib.LinearAlgebra.FiniteDimensional.Lemmas import Mathlib.LinearAlgebra.Matrix.BilinearForm import Mathlib.LinearAlgebra.Trace /-! # Trace for (finite) ring ext...
LawfulFix.lean
/- Copyright (c) 2020 Simon Hudon. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Simon Hudon -/ import Mathlib.Data.Stream.Init import Mathlib.Tactic.ApplyFun import Mathlib.Control.Fix import Mathlib.Order.OmegaCompletePartialOrder /-! # Lawful fixed point operators...
ClosedImmersion.lean
/- Copyright (c) 2023 Jonas van der Schaaf. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Amelia Livingston, Christian Merten, Jonas van der Schaaf -/ import Mathlib.AlgebraicGeometry.Morphisms.Affine import Mathlib.AlgebraicGeometry.IdealSheaf.Subscheme import Mathli...
ssralg.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat div seq. From mathcomp Require Import choice fintype finf...
GeneratorEquiv.lean
/- Copyright (c) 2021 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.Algebra.FreeAbelianGroup.Finsupp import Mathlib.GroupTheory.FreeGroup.IsFreeGroup import Mathlib.LinearAlgebra.Dimension.StrongRankCondition /-! # Iso...
vector.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import fintype bigop fi...
Lie.lean
/- Copyright (c) 2020 Nicolò Cavalleri. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Nicolò Cavalleri, Andrew Yang -/ import Mathlib.Algebra.Lie.OfAssociative import Mathlib.RingTheory.Derivation.Basic /-! # Results - `Derivation.instLieAlgebra`: The `R`-derivation...
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 -/ import Mathlib.MeasureTheory.Group.Arithmetic import Mathlib.Topology.GDelta.MetrizableSpace import Mathlib.Topology.Instances.EReal.Lemmas import Ma...
EuclideanSpace.lean
import Mathlib.Analysis.InnerProductSpace.PiL2 set_option linter.style.commandStart false #guard_expr !₂[] = WithLp.toLp 2 (V := ∀ _ : Fin 0, _) ![] #guard_expr !₂[1, 2, 3] = WithLp.toLp 2 (V := ∀ _ : Fin 3, ℕ) ![1, 2, 3] #guard_expr !₁[1, 2, (3 : ℝ)] = WithLp.toLp 1 (V := ∀ _ : Fin 3, ℝ) ![1, 2, 3] section delabora...
FiberwiseLinear.lean
/- Copyright (c) 2022 Floris van Doorn, Heather Macbeth. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn, Heather Macbeth -/ import Mathlib.Geometry.Manifold.ContMDiff.NormedSpace /-! # The groupoid of `C^n`, fiberwise-linear maps This file contains p...
spectral.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat. From mathcomp Require Import seq div fintype bigop ssralg finset fingroup zmodp. From mathcomp Require Import poly polydiv order ssrnum matrix mxalgebra vector. From mathcomp Require Import mxpoly mxred sesqui...
gproduct.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...
TorusIntegral.lean
/- Copyright (c) 2022 Cuma Kökmen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Cuma Kökmen, Yury Kudryashov -/ import Mathlib.MeasureTheory.Integral.CircleIntegral import Mathlib.MeasureTheory.Integral.Prod import Mathlib.Order.Fin.Tuple import Mathlib.Util.Superscr...
IntegrableOn.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 -/ import Mathlib.MeasureTheory.Function.L1Space.Integrable import Mathlib.MeasureTheory.Function.LpSpace.Indicator /-! # Functions integrable on a set an...
Tagged.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.Basic /-! # Tagged partitions A tagged (pre)partition is a (pre)partition `π` enriched with a tagged point for each ...
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.
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...
Imo2024Q5.lean
/- Copyright (c) 2024 Joseph Myers. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joseph Myers -/ import Mathlib.Data.Fin.VecNotation import Mathlib.Data.List.ChainOfFn import Mathlib.Data.List.TakeWhile import Mathlib.Data.Nat.Dist import Mathlib.Order.Fin.Basic impo...
poly.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 bigop fi...
Nat.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Mario Carneiro -/ import Mathlib.Topology.Instances.Int /-! # Topology on the natural numbers The structure of a metric space on `ℕ` is introduced in this file, induc...
PiTopology.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.RingTheory.MvPowerSeries.Basic import Mathlib.RingTheory.MvPowerSeries.Tr...