filename stringlengths 5 42 | content stringlengths 15 319k |
|---|---|
Semiring.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.Algebra.Order.Kleene
import Mathlib.Algebra.Order.Ring.Canonical
import Mathlib.Data.Set.BooleanAlgebra
import Mathlib.Algebra.Group.Pointwise.Set.... |
Centralizer.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.GroupTheory.Perm.Centralizer
import Mathlib.GroupTheory.SpecificGroups.Alternating
/-! # Centralizer of an element in the alternating gr... |
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.
|
AscendingDescendingSequences.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.Data.Finset.Max
import Mathlib.Data.Finset.Prod
import Mathlib.Data.Fintype.Powerset
/-!
# Erdős–Szekeres theorem
This file proves Theorem 73 from the [1... |
Piecewise.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.Group.Finset.Basic
import Mathlib.Data.Finset.Piecewise
/-!
# Interaction of big operators with piecewise functions
This file pr... |
Embeddings.lean | /-
Copyright (c) 2024 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca
-/
import Mathlib.NumberTheory.Cyclotomic.PrimitiveRoots
import Mathlib.NumberTheory.NumberField.InfinitePlace.Basic
/-!
# Cyclotomic extensions of `ℚ` are totally c... |
Defs.lean | /-
Copyright (c) 2023 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Algebra.Group.Subgroup.Defs
import Mathlib.RingTheory.NonUnitalSubsemiring.Defs
import Mathlib.Tactic.FastInstance
/-!
# `NonUnitalSubring`s
Let `R` be... |
Manifold.lean | /-
Copyright (c) 2023 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
import Mathlib.Analysis.Complex.UpperHalfPlane.Manifold
import Mathlib.Geometry.Manifold.MFDeriv.FDeriv
import Mathlib.NumberTheory.ModularForms.JacobiTheta.OneVariab... |
cyclotomic.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path.
From mathcomp Require Import div choice fintype tuple finfun bigop prime.
From mat... |
RealSqrt.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.Data.Real.Sqrt
/-! # `norm_num` extension for `Real.sqrt`
This module defines a `norm_num` extension for `Real.sqrt` and `NNReal.sqrt`.
-/
namespa... |
Derivative.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.Polynomial.Degree.Domain
import Mathlib.Algebra.Polynomial.Degree.Support
import Mathlib.Algebra.Poly... |
LaurentSeries.lean | /-
Copyright (c) 2021 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson, María Inés de Frutos-Fernández, Filippo A. E. Nuccio
-/
import Mathlib.Data.Int.Interval
import Mathlib.FieldTheory.RatFunc.AsPolynomial
import Mathlib.RingTheory.Binom... |
morphism.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq choice.
From mathcomp Require Import fintype finfun bigop finset fingroup.
(***********... |
Pairwise.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.Logic.Function.Basic
import Mathlib.Data.Set.Defs
/-!
# Relations holding pairwise
This file defines pairwise relations.
## Main declarations
* `Pa... |
ChosenFiniteProducts.lean | import Mathlib.Algebra.Category.Grp.CartesianMonoidal
deprecated_module (since := "2025-05-15")
|
ScopedNS.lean | /-
Copyright (c) 2021 Gabriel Ebner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner, Mario Carneiro
-/
import Mathlib.Util.WithWeakNamespace
/-! # `scoped[NS]` syntax
This is a replacement for the `localized` command in mathlib. It is similar to `scoped... |
MapFold.lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Data.List.Perm.Basic
import Mathlib.Data.Multiset.Replicate
import Mathlib.Data.Set.List
/-!
# Mapping and folding multisets
## Main definitio... |
Elab.lean | /-
Copyright (c) 2024 Tomáš Skřivan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tomáš Skřivan
-/
import Mathlib.Tactic.FunProp.Core
/-!
## `funProp` tactic syntax
-/
namespace Mathlib
open Lean Meta Elab Tactic
namespace Meta.FunProp
open Lean.Parser.Tactic
/-... |
ExactFunctor.lean | /-
Copyright (c) 2023 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou, Jujian Zhang
-/
import Mathlib.Algebra.Homology.ShortComplex.PreservesHomology
import Mathlib.Algebra.Homology.ShortComplex.ShortExact
import Mathlib.Algebra.Homology.ShortComple... |
LimitsOfProductsAndEqualizers.lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Kim Morrison
-/
import Mathlib.CategoryTheory.Limits.Constructions.BinaryProducts
import Mathlib.CategoryTheory.Limits.Constructions.Equalizers
import Mathlib.CategoryTheor... |
Lemmas.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.Algebra.Field.Rat
import Mathlib.Algebra.Group.Indicator
import Mathlib.Algebra.GroupWithZero.Action.End
import Mathlib.Algebra... |
Linear.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.Analytic.Basic
import Mathlib.Analysis.Analytic.CPolynomialDef
/-!
# Linear functions are analytic
In this file we prove that a `Continuou... |
StandardSmooth.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.RingTheory.LocalProperties.Basic
import Mathlib.RingTheory.Smooth.StandardSmooth
import Mathlib.Tactic.Algebraize
/-!
# Standard smooth ring homom... |
Asymptotics.lean | /-
Copyright (c) 2024 Lawrence Wu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lawrence Wu
-/
import Mathlib.MeasureTheory.Group.Measure
import Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap
/-!
# Bounding of integrals by asymptotics
We establish integ... |
Add.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johannes Hölzl
-/
import Mathlib.MeasureTheory.Constructions.BorelSpace.Real
import Mathlib.MeasureTheory.Integral.Lebesgue.Basic
/-!
# Monotone convergence theorem an... |
Floor.lean | /-
Copyright (c) 2022 Yuyang Zhao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuyang Zhao
-/
import Mathlib.Algebra.Order.Floor.Semiring
import Mathlib.Order.Filter.AtTopBot.Finite
/-!
# `a * c ^ n < (n - d)!` holds true for sufficiently large `n`.
-/
open Filter... |
Convolution.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.Analysis.Convolution
import Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension
import Mathlib.Analysis.Calculus.BumpFunction.Normed
import Math... |
Basic.lean | /-
Copyright (c) 2024 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
import Mathlib.Tactic.Abel
import Mathlib.Algebra.Ring.Opposite
import Mathlib.GroupTheory.GroupAction.SubMulAction
import Mathlib.RingTheory.Congruence.Opposite
/-!
# ... |
ClosureSwap.lean | /-
Copyright (c) 2024 Thomas Browning, Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning, Junyan Xu
-/
import Mathlib.Algebra.Group.Subgroup.Ker
import Mathlib.GroupTheory.GroupAction.Basic
import Mathlib.GroupTheory.GroupAction.FixedPoints
impo... |
IsIntegrallyClosed.lean | /-
Copyright (c) 2019 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca, Paul Lezeau, Junyan Xu
-/
import Mathlib.RingTheory.AdjoinRoot
import Mathlib.FieldTheory.Minpoly.Field
import Mathlib.RingTheory.Polynomial.GaussLemma
/-!
# Minimal... |
AlexandrovDiscrete.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.Data.Set.Image
import Mathlib.Topology.Bases
import Mathlib.Topology.Inseparable
import Mathlib.Topology.Compactness.NhdsKer
/-!
# Alexandrov-discrete top... |
IsCoprime.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.RingTheory.Coprime.Lemmas
import Mathlib.Tactic.NormNum.GCD
/-! # `norm_num` extension for `IsCoprime`
This module defines a `norm_num` extension for `IsCo... |
div.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.
(******************************************************************************)
(* Th... |
Definitions.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.MonoidAlgebra.Degree
import Mathlib.Algebra.Order.Ring.WithTop
import Mathlib.Algebra.Polynomial.Basi... |
Basic.lean | /-
Copyright (c) 2018 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Johan Commelin, Bhavik Mehta
-/
import Mathlib.CategoryTheory.Iso
import Mathlib.CategoryTheory.Functor.Category
import Mathlib.CategoryTheory.EqToHom
import Mathlib.Catego... |
Monoidal.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.BigOperators.Fin
import Mathlib.CategoryTheory.Monoidal.Linear
import Mathlib.CategoryTheory.Monoidal.Rigid.FunctorCategory
import Mathlib.Category... |
AsTensorProduct.lean | /-
Copyright (c) 2024 Judith Ludwig, Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Judith Ludwig, Christian Merten
-/
import Mathlib.Algebra.Homology.ShortComplex.ModuleCat
import Mathlib.CategoryTheory.Abelian.DiagramLemmas.Four
import Mathlib.Linea... |
character.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 choice ssrnat seq.
From mathcomp Require Import path div fintype... |
Stability.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.RingTheory.Flat.Basic
import Mathlib.RingTheory.IsTensorProduct
import Mathlib.LinearAlgebra.TensorProduct.Tower
import Mathlib.RingTheory.Localiza... |
Basic.lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import Mathlib.Algebra.CharP.Defs
import Mathlib.Algebra.MvPolynomial.CommRing
import Mathlib.Algebra.MvPolynomial.Equiv
import Mathlib.Algebra.Polynomial.BigOperators
import M... |
Polynomial.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.Kaehler.Basic
import Mathlib.Algebra.MvPolynomial.PDeriv
import Mathlib.Algebra.Polynomial.Derivation
/-!
# The Kaehler differential module of po... |
HomEquiv.lean | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.Algebra.Homology.Embedding.Restriction
import Mathlib.Algebra.Homology.Embedding.Extend
import Mathlib.Algebra.Homology.Embedding.Boundary
import Mathlib.Categor... |
Yoneda.lean | /-
Copyright (c) 2018 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.Limits.Types.Limits
/-!
# Cones and limits
In this file, we give the natural isomorphism between cones on `F` with cone point... |
OfFixingSubgroup.lean | /-
Copyright (c) 2025 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
import Mathlib.Data.Finite.Card
import Mathlib.Data.Set.Card
import Mathlib.GroupTheory.GroupAction.FixingSubgroup
import Mathlib.GroupTheory.GroupActi... |
NormLeOne.lean | /-
Copyright (c) 2025 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
-/
import Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone
import Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord
import Mathlib.NumberTh... |
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
-/
import Mathlib.Logic.Function.Defs
import Mathlib.Logic.Function.Iterate
import Aesop
import Mathlib.Tactic.Inhabit
/-!
# Extra facts about `Prod`
This file proves ... |
ENNReal.lean | /-
Copyright (c) 2024 Edward van de Meent. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Edward van de Meent
-/
import Mathlib.Data.Real.ENatENNReal
import Mathlib.Data.Set.Card
import Mathlib.Topology.Instances.ENNReal.Lemmas
/-!
# Infinite sums of ENNReal and Set.e... |
Exact.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.Exact
import Mathlib.LinearAlgebra.Basis.Basic
/-!
# Basis from a split exact sequence
Let `0 → K → M → P → 0` be a split exact sequence ... |
derive_encodable.lean | import Mathlib.Tactic.DeriveEncodable
/-!
# Tests for the `Encodable` deriving handler
-/
/-!
Structures
-/
structure Struct where
x : Nat
y : Bool
deriving Encodable
example : Encodable Struct := inferInstance
/-!
Inductive types with parameters
-/
inductive T (α : Type) where
| a (x : α) (y : Bool) (z :... |
Construction.lean | import Mathlib.Algebra.Algebra.Rat
import Mathlib.FieldTheory.SplittingField.Construction
universe u v w
open Polynomial
variable {F : Type u} {K : Type v} {L : Type w}
variable [Field K] [Field L] [Field F]
variable (f : K[X])
-- The algebra instance deriving from `K` should be definitionally equal to that
-- de... |
eqtype.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool.
(********************************************************************... |
IndicatorFunction.lean | /-
Copyright (c) 2020 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Yury Kudryashov
-/
import Mathlib.Algebra.Group.Indicator
import Mathlib.Order.CompleteLattice.Finset
import Mathlib.Order.ConditionallyCompleteLattice.Basic
import Mathl... |
ContDiff.lean | /-
Copyright (c) 2024 Tomáš Skřivan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tomáš Skřivan
-/
import Mathlib.Analysis.Calculus.IteratedDeriv.Lemmas
import Mathlib.Analysis.SpecialFunctions.ExpDeriv
import Mathlib.Analysis.SpecialFunctions.Log.Deriv
import Mathli... |
eqtype.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool.
(********************************************************************... |
BigOperators.lean | /-
Copyright (c) 2019 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
import Mathlib.Algebra.BigOperators.Group.Multiset.Basic
import Mathlib.Algebra.BigOperators.Group.List.Lemmas
import Mathlib.GroupTheory.Congruence.Defs
impor... |
FiniteMeasureExt.lean | /-
Copyright (c) 2024 Jakob Stiefel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob Stiefel
-/
import Mathlib.Analysis.RCLike.BoundedContinuous
import Mathlib.Analysis.SpecialFunctions.MulExpNegMulSqIntegral
import Mathlib.MeasureTheory.Measure.HasOuterApproxClos... |
StdSimplex.lean | /-
Copyright (c) 2021 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Kim Morrison, Adam Topaz, Joël Riou
-/
import Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex
import Mathlib.CategoryTheory.Subpresheaf.OfSection
import Mathlib.Catego... |
Basic.lean | import Mathlib.CategoryTheory.Monoidal.Cartesian.Basic
deprecated_module (since := "2025-05-08")
|
Conv.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.Tactic.Conv.Basic
import Lean.Elab.Command
/-!
Additional `conv` tactics.
-/
namespace Mathlib.Tactic.Conv
open Lean Parser.Tacti... |
Unitary.lean | /-
Copyright (c) 2025 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Algebra.Star.Unitary
import Mathlib.Topology.Algebra.Group.Defs
import Mathlib.Topology.Algebra.Star
import Mathlib.Topology.Algebra.Monoid
/-! # `unita... |
Limits.lean | /-
Copyright (c) 2024 Jack McKoen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jack McKoen
-/
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
/-!
# Lifting properties and (co)limits
In this file, we show some consequences of lifting properties in the p... |
Saturated.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.Group.Subgroup.Ker
import Mathlib.Algebra.NoZeroSMulDivisors.Defs
/-!
# Saturated subgroups
## Tags
subgroup, subgroups
-/
namespace Subgr... |
Sigma.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.Data.Fintype.EquivFin
import Mathlib.Data.Fintype.Sigma
/-!
# Finiteness of sigma types
-/
variable {α : Type*}
namespace Finite
instance {β : α → Type*}... |
Measurability.lean | /-
Copyright (c) 2023 Miyahara Kō. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Miyahara Kō
-/
import Mathlib.Tactic.Measurability.Init
import Mathlib.Algebra.Group.Defs
/-!
# Measurability
We define the `measurability` tactic using `aesop`. -/
open Lean.Parser.T... |
Combinators.lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura
-/
import Mathlib.Init
/-!
# Monad combinators, as in Haskell's Control.Monad.
-/
universe u v w
/-- Collapses two layers of monadic structur... |
finalg.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 finset f... |
Skolem.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.ModelTheory.ElementarySubstructures
/-!
# Skolem Functions and Downward Löwenheim–Skolem
## Main Definitions
- `FirstOrder.Language.skolem₁` is a la... |
morphism.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq choice.
From mathcomp Require Import fintype finfun bigop finset fingroup.
(***********... |
Int.lean | /-
Copyright (c) 2025 María Inés de Frutos-Fernández, Filippo A. E. Nuccio. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: María Inés de Frutos-Fernández, Filippo A. E. Nuccio
-/
import Mathlib.Algebra.Group.Int.Defs
import Mathlib.Algebra.GroupWithZero.WithZero
/-!
#... |
PID.lean | /-
Copyright (c) 2024 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca
-/
import Mathlib.NumberTheory.NumberField.ClassNumber
import Mathlib.NumberTheory.Cyclotomic.Rat
import Mathlib.NumberTheory.Cyclotomic.Embeddings
/-!
# Cyclotomic ... |
Defs.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.Logic.Function.Defs
import Mathlib.Tactic.TypeStar
/-!
# Nontrivial types
A type is *nontrivial* if it contains at least two elements. This is ... |
Mat.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.BigOperators.Group.Finset.Pi
import Mathlib.Algebra.BigOperators.Pi
import Mathlib.Algebra.Opposites
import Mathlib.Algebra.Ring.Opposite
import Ma... |
ULift.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.Logic.Function.ULift
import Mathlib.Order.Basic
/-! # Ordered structures on `ULift.{v} α`
Once these basic instances are setup, the instances of more compl... |
HopkinsLevitzki.lean | /-
Copyright (c) 2025 Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junyan Xu
-/
import Mathlib.Algebra.Module.Torsion
import Mathlib.RingTheory.FiniteLength
import Mathlib.RingTheory.Noetherian.Nilpotent
import Mathlib.RingTheory.Spectrum.Prime.Noetherian
... |
Algebra.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.Algebra.Defs
import Mathlib.Algebra.Polynomial.Eval.Defs
/-!
# Evaluation of polynomials in an algeb... |
Pullback.lean | /-
Copyright (c) 2024 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Analysis.Calculus.VectorField
import Mathlib.Geometry.Manifold.ContMDiffMFDeriv
import Mathlib.Geometry.Manifold.MFDeriv.NormedSpace
import Mathl... |
Prod.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.Algebra.Ring.Prod
import Mathlib.Algebra.Star.Basic
/-!
# Basic Results about Star on Product Type
This file provides basic results about the star on produ... |
Rat.lean | /-
Copyright (c) 2019 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Kim Morrison
-/
import Mathlib.Init
import Batteries.Data.Rat.Basic
import Batteries.Tactic.Alias
/-!
# Additional operations on Expr and rational numbers
This file ... |
IsConjRoot.lean | /-
Copyright (c) 2024 Jiedong Jiang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jiedong Jiang
-/
import Mathlib.FieldTheory.Extension
import Mathlib.FieldTheory.IntermediateField.Adjoin.Basic
import Mathlib.FieldTheory.Minpoly.Basic
import Mathlib.FieldTheory.Norma... |
frobenius.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat div.
From mathcomp Require Import fintype bigop prime finset fingroup morphism.
From mathcom... |
Defs.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Yury Kudryashov
-/
import Mathlib.Algebra.Group.Action.Opposite
import Mathlib.Algebra.GroupWithZero.Hom
import Mathlib.Algebra.GroupWithZero.Opposite
import Mathlib.Algebr... |
Union.lean | /-
Copyright (c) 2025 Oliver Butterley. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Butterley
-/
import Mathlib.Data.Finset.Range
import Mathlib.Data.Set.Lattice
import Mathlib.Order.Interval.Set.LinearOrder
/-!
# Extra lemmas about unions of intervals
This... |
quotient.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq div.
From mathcomp Require Import choice fintype prim... |
Basic.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.Hom
import Mathlib.RingTheory.LocalRing.MaximalIdeal.Basic
import Mathlib.RingTheory.Ideal.Maps
/-!
# Local r... |
Ideal.lean | /-
Copyright (c) 2021 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang, Eric Wieser
-/
import Mathlib.LinearAlgebra.Finsupp.SumProd
import Mathlib.RingTheory.GradedAlgebra.Basic
import Mathlib.RingTheory.Ideal.Basic
import Mathlib.RingTheory.Id... |
IntegralNormalization.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, Andrew Yang, Yuyang Zhao
-/
import Mathlib.Algebra.Polynomial.Monic
import Mathlib.RingTheory.Polynomial.ScaleRoots
/-!
# The... |
Separation.lean | /-
Copyright (c) 2022 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Yaël Dillies
-/
import Mathlib.Analysis.Convex.Cone.Extension
import Mathlib.Analysis.Convex.Gauge
import Mathlib.Topology.Algebra.Module.FiniteDimension
import Mathlib.Top... |
Lemmas.lean | /-
Copyright (c) 2021 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Sébastien Gouëzel
-/
import Mathlib.Analysis.Normed.Operator.BoundedLinearMaps
import Mathlib.Dynamics.Ergodic.MeasurePreserving
import Mathlib.MeasureTheory.Function.Stron... |
ComposableArrows.lean | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou, Andrew Yang
-/
import Mathlib.CategoryTheory.ComposableArrows
import Mathlib.CategoryTheory.Localization.CalculusOfFractions
/-! # Essential surjectivity of the functor induced ... |
Path.lean | /-
Copyright (c) 2021 David Wärn,. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn, Kim Morrison, Matteo Cipollina
-/
import Mathlib.Combinatorics.Quiver.Prefunctor
import Mathlib.Logic.Lemmas
import Batteries.Data.List.Basic
/-!
# Paths in quivers
Given a... |
Closure.lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Yaël Dillies
-/
import Mathlib.GroupTheory.Perm.Cycle.Basic
/-!
# Closure results for permutation groups
* This file contains several closure results:
* `closure_isCycle... |
Colimits.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.Algebra.Category.MonCat.Basic
import Mathlib.CategoryTheory.Limits.HasLimits
import Mathlib.CategoryTheory.ConcreteCategory.Elementwise
/-!
# The category... |
character.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 choice ssrnat seq.
From mathcomp Require Import path div fintype... |
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: ... |
Defs.lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import Mathlib.Algebra.Polynomial.Degree.Definitions
import Mathlib.Algebra.Polynomial.Eval.Defs
import Mathlib.Tactic.Algebraize
/-!
# Integral closure of a subring.
If A is... |
MulOppositeLemmas.lean | /-
Copyright (c) 2022 Alex Kontorovich. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Kontorovich, Eric Wieser
-/
import Mathlib.Algebra.Group.Subgroup.Basic
import Mathlib.Algebra.Group.Subgroup.MulOpposite
import Mathlib.Algebra.Group.Submonoid.MulOpposite
impo... |
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.
(******************************************... |
Presheaf.lean | /-
Copyright (c) 2023 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Joël Riou
-/
import Mathlib.Algebra.Category.ModuleCat.ChangeOfRings
import Mathlib.Algebra.Category.Ring.Basic
/-!
# Presheaves of modules over a presheaf of rings.
Give... |
all_order.v | Require Export order.
|
Defs.lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Simon Hudon, Mario Carneiro
-/
import Batteries.Logic
import Mathlib.Algebra.Regular.Defs
import Mathlib.Data.Int.Notation
import Mathlib.Data.Nat.Bina... |
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