filename stringlengths 5 42 | content stringlengths 15 319k |
|---|---|
Lemmas.lean | /-
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Topology.Order.Compact
import Mathlib.Topology.MetricSpace.ProperSpace
import Mathlib.Topology.Order.IntermediateValue
import Mathlib.Topology.O... |
Basic.lean | /-
Copyright (c) 2021 Shing Tak Lam. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shing Tak Lam
-/
import Mathlib.Topology.Order.ProjIcc
import Mathlib.Topology.ContinuousMap.Ordered
import Mathlib.Topology.CompactOpen
import Mathlib.Topology.UnitInterval
/-!
# Homo... |
Range.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, Minchao Wu, Mario Carneiro
-/
import Mathlib.Algebra.Group.Embedding
import Mathlib.Algebra.Group.Nat.Defs
import Mathlib.Data.Finset.Image
/-... |
LocallyIntegrable.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
-/
import Mathlib.MeasureTheory.Integral.IntegrableOn
/-!
# Locally integrable functions
A function is called *locally integrable* (`MeasureTheory.LocallyIntegrabl... |
Coherence.lean | /-
Copyright (c) 2022 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno, Junyan Xu
-/
import Mathlib.CategoryTheory.PathCategory.Basic
import Mathlib.CategoryTheory.Functor.FullyFaithful
import Mathlib.CategoryTheory.Bicategory.Free
import Mathlib... |
ContinuousAffineMap.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.LinearAlgebra.AffineSpace.AffineMap
import Mathlib.Topology.Algebra.Module.LinearMap
/-!
# Continuous affine maps.
This file defines a type of bundled cont... |
Basic.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.Algebra.Group.End
import Mathlib.Data.Set.Function
/-!
# Fixed points of a self-map
In this file we define
* the predicate `IsFixedPt f x := f x =... |
Thin.lean | /-
Copyright (c) 2019 Kim Morrison, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Bhavik Mehta
-/
import Mathlib.CategoryTheory.Functor.Category
import Mathlib.CategoryTheory.Iso
/-!
# Thin categories
A thin category (also known as a spars... |
FullSubcategory.lean | /-
Copyright (c) 2017 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Reid Barton
-/
import Mathlib.CategoryTheory.Functor.FullyFaithful
deprecated_module "Auto-generated deprecation" (since := "2025-04-23")
|
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 ... |
FreeCommRing.lean | /-
Copyright (c) 2023 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.RingTheory.FreeCommRing
/-!
# Constructing Ring terms from MvPolynomial
This file provides tools for constructing ring terms that can be evaluated to p... |
Opposite.lean | /-
Copyright (c) 2020 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.Group.Action.Faithful
import Mathlib.Algebra.Group.Action.Opposite
import Mathlib.Algebra.GroupWithZero.Action.Defs
import Mathlib.Algebra.GroupWithZ... |
Projection.lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.LinearAlgebra.Quotient.Basic
import Mathlib.LinearAlgebra.Prod
import Mathlib.Algebra.Module.Submodule.Invariant
import Mathlib.LinearAlgebra.General... |
Basic.lean | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Anne Baanen
-/
import Mathlib.Algebra.GroupWithZero.Regular
import Mathlib.Algebra.GroupWithZero.Units.Lemmas
import Mathlib.Algebra.Order.Hom.Basic
import Mathlib.Algebra... |
QuasiCompact.lean | /-
Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap
import Mathlib.Topology.Spectral.Hom
import Mathlib.AlgebraicGeometry.Limits
/-!
# Quasi-compact morphisms
A morp... |
EpiMono.lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton
-/
import Mathlib.Topology.Category.TopCat.Adjunctions
import Mathlib.CategoryTheory.Functor.EpiMono
/-!
# Epi- and monomorphisms in `Top`
This file shows that a continuous ... |
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... |
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... |
Star.lean | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Analysis.Calculus.Deriv.Basic
import Mathlib.Analysis.Calculus.FDeriv.Star
/-!
# Star operations on derivatives
This file contains the usual formulas (and ... |
List.lean | /-
Copyright (c) 2021 Stuart Presnell. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stuart Presnell, Daniel Weber
-/
import Mathlib.Algebra.BigOperators.Group.List.Defs
import Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic
/-!
# Big operators on a list in order... |
NhdsKer.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.Tactic.Peel
import Mathlib.Topology.Compactness.Compact
import Mathlib.Topology.NhdsKer
/-!
# Compactness of the neighborhoods kernel of a set
In t... |
BaseChange.lean | /-
Copyright (c) 2024 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
import Mathlib.Algebra.Field.Subfield.Defs
/-!
# Matrices and base change
This file is a home for results about bas... |
Core.lean | /-
Copyright (c) 2023 Sebastian Zimmer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Zimmer, Mario Carneiro, Heather Macbeth, Jovan Gerbscheid
-/
import Mathlib.Tactic.GCongr.Core
/-!
# The generalized rewriting tactic
This module defines the core of the... |
Pseudo.lean | /-
Copyright (c) 2024 Calle Sönne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Calle Sönne
-/
import Mathlib.CategoryTheory.Bicategory.Functor.Pseudofunctor
import Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Oplax
/-!
# Strong transformations of pseud... |
Intervals.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.Order.BigOperators.Group.LocallyFinite
import Mathlib.Algebra.Order.Interval.Finset.Basic
import Mathlib.Algebra.Order.Sub.Basic
import Mathlib... |
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... |
Quotient.lean | /-
Copyright (c) 2025 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Xavier Roblot
-/
import Mathlib.Data.ZMod.QuotientRing
import Mathlib.LinearAlgebra.Dimension.Constructions
import Mathlib.LinearAlgebra.FreeModule.PID
import Mathlib.Linea... |
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... |
NatAntidiagonal.lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.Data.List.NatAntidiagonal
import Mathlib.Data.Multiset.MapFold
/-!
# Antidiagonals in ℕ × ℕ as multisets
This file defines the antidiagonals of ℕ × ℕ... |
Angle.lean | /-
Copyright (c) 2019 Calle Sönne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Calle Sönne
-/
import Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic
import Mathlib.Analysis.Normed.Group.AddCircle
import Mathlib.Algebra.CharZero.Quotient
import Mathlib.Topology... |
Fintype.lean | /-
Copyright (c) 2022 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import Mathlib.Data.Fintype.Basic
import Mathlib.Data.FunLike.Basic
import Mathlib.Data.Finite.Prod
/-!
# Finiteness of `DFunLike` types
We show a type `F` with a `DFunLi... |
numdomain.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... |
Defs.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Chris Hughes, Mario Carneiro
-/
import Mathlib.Algebra.Group.Units.Defs
import Mathlib.Algebra.Ring.Defs
/-!
# Local rings
Define local rings as commutative rings having a uni... |
Basic.lean | /-
Copyright (c) 2017 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stephen Morgan, Kim Morrison, Johannes Hölzl, Reid Barton
-/
import Mathlib.CategoryTheory.Category.Init
import Mathlib.Combinatorics.Quiver.Basic
import Mathlib.Tactic.PPWithUniv
import... |
MulOpposite.lean | /-
Copyright (c) 2024 Jz Pan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jz Pan
-/
import Mathlib.Algebra.Group.Submonoid.MulOpposite
import Mathlib.Algebra.Ring.Subsemiring.Basic
import Mathlib.Algebra.Ring.Opposite
/-!
# Subsemiring of opposite semirings
For e... |
Int.lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-/
import Mathlib.Algebra.Ring.Int.Defs
import Mathlib.Data.Nat.Prime.Basic
import Mathlib.Algebra.Group.Int.Units
import Mathli... |
Filtration.lean | /-
Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.Algebra.Polynomial.Module.Basic
import Mathlib.RingTheory.Finiteness.Nakayama
import Mathlib.RingTheory.LocalRing.MaximalIdeal.Basic
import Mathlib.RingTheor... |
CommSq.lean | /-
Copyright (c) 2022 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Joël Riou, Calle Sönne
-/
import Mathlib.CategoryTheory.Limits.Constructions.ZeroObjects
import Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts
import Mathlib.Catego... |
Characterization.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.Colimit
import Mathlib.Condensed.Discrete.Module
/-!
# Characterizing discrete condensed sets and `R`-modules.
This file prove... |
Restrict.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import Mathlib.MeasureTheory.Measure.Comap
import Mathlib.MeasureTheory.Measure.QuasiMeasurePreserving
/-!
# Restricting a measure to a subset or a s... |
IncMatrix.lean | /-
Copyright (c) 2021 Gabriel Moise. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Moise, Yaël Dillies, Kyle Miller
-/
import Mathlib.Combinatorics.SimpleGraph.Finite
import Mathlib.Data.Finset.Sym
import Mathlib.Data.Matrix.Mul
/-!
# Incidence matrix of a si... |
Nontrivial.lean | /-
Copyright (c) 2024 Jz Pan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jz Pan
-/
import Mathlib.LinearAlgebra.Basis.VectorSpace
import Mathlib.RingTheory.Flat.FaithfullyFlat.Basic
import Mathlib.RingTheory.Localization.FractionRing
/-!
# Nontriviality of tensor... |
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.
(**********************... |
Basic.lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Floris van Doorn, Yaël Dillies
-/
import Mathlib.Algebra.Group.Equiv.Basic
import Mathlib.Algebra.Group.Prod
import Mathlib.Algebra.Order.Monoid.Unbundled.Pow
import Ma... |
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.Order.GameAdd
import Mathlib.Order.RelIso.Set
import Mathlib.SetTheory.ZFC.Basic
/-!
# Von Neumann ordinals
This file works t... |
Path.lean | /-
Copyright (c) 2020 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import Mathlib.Topology.Order.ProjIcc
import Mathlib.Topology.CompactOpen
import Mathlib.Topology.UnitInterval
/-!
# Paths in topological spaces
This file introduce... |
SubGaussian.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.Probability.Kernel.Condexp
import Mathlib.Probability.Moments.MGFAnalytic
import Mathlib.Probability.Moments.Tilted
/-!
# Sub-Gaussian random variables
T... |
Abelian.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.Algebra.Category.Grp.Colimits
import Mathlib.Algebra.Category.Grp.Limits
import Mathlib.Algebra.Category.Grp.ZModuleEquivalence
import Mathlib.Algebra.Ca... |
Defs.lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Thomas Browning, Patrick Lutz
-/
import Mathlib.Algebra.Polynomial.Splits
import Mathlib.FieldTheory.IntermediateField.Basic
import Mathlib.FieldTheory.Minpoly.Field
/-!
# Norma... |
Opposite.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.Algebra.Group.Equiv.Basic
import Mathlib.Algebra.Group.Opposite
/-!
# Group isomorphism between a group and its opposite
-/
variable {α : Type*}
n... |
Analytic.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.FDeriv.Symmetric
import Mathlib.Analysis.Complex.CauchyIntegral
import Mathlib.Analysis.Complex.Conformal
import Mathlib.Analysis.Inn... |
Cast.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.RingTheory.Polynomial.Pochhammer
/-!
# Cast of factorials
This file allows calculating factorials (including ascending and descending ones) as elements o... |
Init.lean | /-
Copyright (c) 2023 Jannis Limperg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jannis Limperg
-/
import Mathlib.Init
import Aesop
/-!
# Sym2 Rule Set
This module defines the `Sym2` Aesop rule set. Aesop rule sets only become
visible once the file in which they... |
Basic.lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.Algebra.Polynomial.Expand
import Mathlib.Algebra.Polynomial.Roots
import Mathlib.RingTheory.Adjoin.Polynomial
import Mathlib.RingTheory.Algebraic.Defs
... |
NatInt.lean | /-
Copyright (c) 2015 Nathaniel Thomas. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nathaniel Thomas, Jeremy Avigad, Johannes Hölzl, Mario Carneiro
-/
import Mathlib.Algebra.Module.Defs
import Mathlib.Data.Int.Cast.Lemmas
/-!
# Modules over `ℕ` and `ℤ`
This file c... |
FinitelyGenerated.lean | /-
Copyright (c) 2022 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import Mathlib.Data.Set.Finite.Lemmas
import Mathlib.ModelTheory.Substructures
/-!
# Finitely Generated First-Order Structures
This file defines what it means for a... |
Basic.lean | /-
Copyright (c) 2021 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import Mathlib.Algebra.Order.Sub.Defs
import Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE
/-!
# Lemmas about subtraction in an unbundled canonically ordered... |
QuasiSeparated.lean | /-
Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.Topology.Compactness.Bases
import Mathlib.Topology.NoetherianSpace
/-!
# Quasi-separated spaces
A topological space is quasi-separated if the intersections... |
Basic.lean | /-
Copyright (c) 2019 Gabriel Ebner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner, Sébastien Gouëzel
-/
import Mathlib.Analysis.Calculus.FDeriv.Const
import Mathlib.Analysis.NormedSpace.OperatorNorm.NormedSpace
/-!
# One-dimensional derivatives
This ... |
ERealExp.lean | /-
Copyright (c) 2024 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Pietro Monticone, Rémy Degenne, Lorenzo Luccioli
-/
import Mathlib.Data.Complex.Exponential
import Mathlib.Data.EReal.Basic
/-!
# Extended Nonnegative Real Exponential
We define `exp` ... |
Frobenius.lean | /-
Copyright (c) 2021 Jakob Scholbach. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob Scholbach
-/
import Mathlib.Algebra.Algebra.Defs
import Mathlib.Algebra.CharP.Lemmas
/-!
### The Frobenius endomorphism
## Tags
Frobenius endomorphism
## Implementation note... |
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_... |
Basic.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.CategoryTheory.Sites.Sheaf
import Mathlib.CategoryTheory.Sites.CoverLifting
import Mathlib.CategoryTheory.Sites.CoverPreserving
import Mathlib.CategoryTheory... |
ExtraRecognizers.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 Mathlib.Data.Set.Operations
/-!
# Additional Expr recognizers needing theory imports
-/
namespace Lean.Expr
/-- If `e` is a coercion of a set to a type, return t... |
CartanSubalgebra.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.Lie.Nilpotent
import Mathlib.Algebra.Lie.Normalizer
/-!
# Cartan subalgebras
Cartan subalgebras are one of the most important concepts in Lie theor... |
NegOnePow.lean | /-
Copyright (c) 2023 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou, Johan Commelin
-/
import Mathlib.Algebra.Field.Defs
import Mathlib.Algebra.Ring.NegOnePow
import Mathlib.Tactic.NormNum
/-! # Integer powers of `-1` in a field -/
namespace Int... |
Fin.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Kim Morrison, Johan Commelin
-/
import Mathlib.Data.Finset.Card
import Mathlib.Data.Fin.Embedding
/-!
# Finsets in `Fin n`
A few constructions for Finsets in `Fin n`.
##... |
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.
|
FiniteIndex.lean | /-
Copyright (c) 2025 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
import Mathlib.GroupTheory.Index
import Mathlib.RepresentationTheory.Coinduced
import Mathlib.RepresentationTheory.Induced
/-!
# (Co)induced representations of... |
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.AlgCat.Monoidal
import Mathlib.Algebra.Category.BialgCat.Basic
import Mathlib.Algebra.Category.CoalgCat.Monoidal
import Mathlib.... |
Div.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Kim Morrison, Jens Wagemaker
-/
import Mathlib.Algebra.Field.IsField
import Mathlib.Algebra.Polynomial.Inductions
import Mathlib.Algebra.Polynomial.Monic
im... |
Mon_.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.Monoidal.Opposite
import Mathlib.CategoryTheory.Monoidal.Mon_
/-!
# Monoid objects internal to monoidal opposites
In this file, we recor... |
Lemmas.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.LinearAlgebra.Matrix.ToLin
import Mathlib.LinearAlgebra.Quotient.Basic
import Mathlib.RingTheory.Ideal.Maps
import Mathlib.RingTheory.Nilpotent.Defs
/-!
# N... |
Coe.lean | /-
Copyright (c) 2021 Gabriel Ebner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner
-/
import Mathlib.Init
import Lean.Elab.ElabRules
/-!
# Additional coercion notation
Defines notation for coercions.
1. `↑ t` is defined in core.
2. `(↑)` is equivalent ... |
Linearity.lean | /-
Copyright (c) 2024 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
import Mathlib.Algebra.BigOperators.Field
import Mathlib.NumberTheory.LSeries.Basic
/-!
# Linearity of the L-series of `f` as a function of `f`
We show that the `LSer... |
RegularEpi.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.RegularMono
import Mathlib.CategoryTheory.EffectiveEpi.Basic
/-!
# The relationship between effective and regular epi... |
OverAdjunction.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.CategoryTheory.MorphismProperty.Comma
import Mathlib.CategoryTheory.Comma.Over.Pullback
import Mathlib.CategoryTheory.MorphismProperty.Limits
/-!
... |
Resolution.lean | /-
Copyright (c) 2022 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang, Kim Morrison
-/
import Mathlib.CategoryTheory.Preadditive.Injective.Resolution
import Mathlib.Algebra.Homology.HomotopyCategory
import Mathlib.Data.Set.Subsingleton
import ... |
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... |
IntegralCompProd.lean | /-
Copyright (c) 2023 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Etienne Marion
-/
import Mathlib.Probability.Kernel.Composition.MeasureComp
import Mathlib.Probability.Kernel.MeasurableIntegral
/-!
# Bochner integral of a function again... |
Limits.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.Category.Grp.ForgetCorepresentable
import Mathlib.Algebra.Category.Grp.Preadditive
import Mathlib.Algebra.Category.MonCat.ForgetCorepresentable
imp... |
Laurent.lean | /-
Copyright (c) 2022 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
import Mathlib.Algebra.Polynomial.Taylor
import Mathlib.FieldTheory.RatFunc.AsPolynomial
/-!
# Laurent expansions of rational functions
## Main declarations
* `R... |
FBinop.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.App
import Lean.Elab.BuiltinNotation
import Mathlib.Tactic.ToExpr
/-! # Elaborator for functorial binary operators
`fbinop% f x y` elaborates `f x y` for... |
Infinite.lean | /-
Copyright (c) 2024 Nailin Guan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nailin Guan
-/
import Mathlib.FieldTheory.KrullTopology
import Mathlib.FieldTheory.Galois.GaloisClosure
import Mathlib.Topology.Algebra.Group.ClosedSubgroup
/-!
# The Fundamental Theorem... |
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... |
Surjective.lean | /-
Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.RingTheory.LocalProperties.Basic
/-!
# The meta properties of surjective ring homomorphisms.
## Main results
Let `R` be a commutative ring, `M` be a subm... |
Complex.lean | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Data.Complex.Module
import Mathlib.RingTheory.Norm.Defs
import Mathlib.RingTheory.Trace.Defs
/-! # Lemmas about `Algebra.trace` and `Algebra.norm` on `ℂ` -/... |
Simp.lean | import Mathlib.Algebra.Algebra.Pi
import Mathlib.Algebra.Algebra.Defs
/-!
Tests for the behavior of `simp`.
-/
/- Taken from [Zulip](https://leanprover.zulipchat.com/#narrow/stream/270676-lean4/
topic/simp.20.5BX.5D.20fails.2C.20rw.20.5BX.5D.20works) -/
-- Example 1: succeeds
example {α R : Type*} [CommRing R] (f :... |
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... |
CoprodI.lean | /-
Copyright (c) 2021 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn, Joachim Breitner
-/
import Mathlib.Algebra.Group.Action.End
import Mathlib.Algebra.Group.Action.Pointwise.Set.Basic
import Mathlib.Algebra.Group.Submonoid.Membership
import Mat... |
Lattice.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.Logic.Encodable.Basic
import Mathlib.Logic.Pairwise
import Mathlib.Data.Set.Subsingleton
/-!
# Lattice operations on encodable types
Lemmas about... |
VerySmallDoubling.lean | /-
Copyright (c) 2024 Yaël Dillies, Patrick Luo, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Patrick Luo, Bhavik Mehta
-/
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Group.Action.Pointwise.Finset
import Mathlib.... |
StandardBorel.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.Probability.Kernel.Composition.MeasureCompProd
import Mathlib.Probability.Kernel.Disintegration.Basic
import Mathlib.Probability.Kernel.Disintegration.Cond... |
HausdorffDimension.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.Calculus.ContDiff.RCLike
import Mathlib.MeasureTheory.Measure.Hausdorff
/-!
# Hausdorff dimension
The Hausdorff dimension of a set `X` in ... |
ParametricIntervalIntegral.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.Calculus.ParametricIntegral
import Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic
/-!
# Derivatives of interval integrals depending ... |
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... |
NormedSpace.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, Sébastien Gouëzel
-/
import Mathlib.MeasureTheory.Measure.Haar.InnerProductSpace
import Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar
import Mathlib.MeasureTheory.I... |
RationalRoot.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.RingTheory.IntegralClosure.IntegrallyClosed
import Mathlib.RingTheory.Localization.NumDen
import Mathlib.RingTheory.Polynomial.ScaleRoots
/-!
# Rational roo... |
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... |
PProd.lean | /-
Copyright (c) 2020 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Logic.Function.Defs
/-!
# Extra facts about `PProd`
-/
open Function
variable {α β γ δ : Sort*}
namespace PProd
def mk.injArrow {α : Type*} {β : Type*}... |
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