path stringlengths 11 71 | content stringlengths 75 124k |
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Algebra\DirectSum\Algebra.lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.Algebra.Defs
import Mathlib.Algebra.DirectSum.Module
import Mathlib.Algebra.DirectSum.Ring
/-! # Additively-graded algebra structures on `⨁ i, A i`
... |
Algebra\DirectSum\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.Group.Submonoid.Operations
import Mathlib.Data.DFinsupp.Basic
/-!
# Direct sum
This file defines the direct sum of abelian groups, indexed by a discret... |
Algebra\DirectSum\Decomposition.lean | /-
Copyright (c) 2022 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Jujian Zhang
-/
import Mathlib.Algebra.DirectSum.Module
import Mathlib.Algebra.Module.Submodule.Basic
/-!
# Decompositions of additive monoids, groups, and modules into dire... |
Algebra\DirectSum\Finsupp.lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.Algebra.DirectSum.Module
import Mathlib.Data.Finsupp.ToDFinsupp
/-!
# Results on direct sums and finitely supported functions.
1. The linear equivale... |
Algebra\DirectSum\Internal.lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Kevin Buzzard, Jujian Zhang, Fangming Li
-/
import Mathlib.Algebra.Algebra.Operations
import Mathlib.Algebra.Algebra.Subalgebra.Basic
import Mathlib.Algebra.DirectSum.Algebra... |
Algebra\DirectSum\LinearMap.lean | /-
Copyright (c) 2023 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.LinearAlgebra.FreeModule.Finite.Basic
import Mathlib.LinearAlgebra.FreeModule.PID
import Mathlib.LinearAlgebra.Eigenspace.Basic
import Mathlib.LinearAlgebra.... |
Algebra\DirectSum\Module.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import Mathlib.Algebra.DirectSum.Basic
import Mathlib.LinearAlgebra.DFinsupp
import Mathlib.LinearAlgebra.Basis
/-!
# Direct sum of modules
The first part of the file provide... |
Algebra\DirectSum\Ring.lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.GradedMonoid
import Mathlib.Algebra.DirectSum.Basic
/-!
# Additively-graded multiplicative structures on `⨁ i, A i`
This module provides a set of h... |
Algebra\Divisibility\Basic.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, Floris van Doorn, Amelia Livingston, Yury Kudryashov,
Neil Strickland, Aaron Anderson
-/
import Mathlib.Algebra.Group.Basic
import Mathlib.Algebra.Grou... |
Algebra\Divisibility\Prod.lean | /-
Copyright (c) 2023 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.Algebra.Divisibility.Basic
import Mathlib.Algebra.Group.Prod
import Mathlib.Tactic.Common
/-!
# Lemmas about the divisibility relation in product (sem... |
Algebra\Divisibility\Units.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, Floris van Doorn, Amelia Livingston, Yury Kudryashov,
Neil Strickland, Aaron Anderson
-/
import Mathlib.Algebra.Divisibility.Basic
import Mathlib.Algeb... |
Algebra\EuclideanDomain\Basic.lean | /-
Copyright (c) 2018 Louis Carlin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Louis Carlin, Mario Carneiro
-/
import Mathlib.Algebra.EuclideanDomain.Defs
import Mathlib.Algebra.Ring.Divisibility.Basic
import Mathlib.Algebra.Ring.Regular
import Mathlib.Algebra.Grou... |
Algebra\EuclideanDomain\Defs.lean | /-
Copyright (c) 2018 Louis Carlin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Louis Carlin, Mario Carneiro
-/
import Mathlib.Algebra.Divisibility.Basic
import Mathlib.Algebra.Group.Basic
import Mathlib.Algebra.Ring.Defs
/-!
# Euclidean domains
This file introduc... |
Algebra\EuclideanDomain\Field.lean | /-
Copyright (c) 2018 Louis Carlin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Louis Carlin, Mario Carneiro
-/
import Mathlib.Algebra.EuclideanDomain.Defs
import Mathlib.Algebra.Field.Defs
import Mathlib.Algebra.GroupWithZero.Units.Basic
/-!
# Instances for Euclid... |
Algebra\EuclideanDomain\Int.lean | /-
Copyright (c) 2018 Louis Carlin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Louis Carlin, Mario Carneiro
-/
import Mathlib.Algebra.EuclideanDomain.Defs
import Mathlib.Algebra.Order.Group.Int
import Mathlib.Algebra.Ring.Int
/-!
# Instances for Euclidean domains
... |
Algebra\Field\Basic.lean | /-
Copyright (c) 2014 Robert Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Lewis, Leonardo de Moura, Johannes Hölzl, Mario Carneiro
-/
import Mathlib.Algebra.Field.Defs
import Mathlib.Algebra.GroupWithZero.Units.Lemmas
import Mathlib.Algebra.Ring.Commute... |
Algebra\Field\Defs.lean | /-
Copyright (c) 2014 Robert Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Lewis, Leonardo de Moura, Johannes Hölzl, Mario Carneiro, Yaël Dillies
-/
import Mathlib.Algebra.Ring.Defs
import Mathlib.Data.Rat.Init
/-!
# Division (semi)rings and (semi)field... |
Algebra\Field\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.GroupWithZero.Hom
/-!
# If a semiring is a field, any isomorphic semiring is also a field.
This is in a separate f... |
Algebra\Field\IsField.lean | /-
Copyright (c) 2014 Robert Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Lewis, Leonardo de Moura, Johannes Hölzl, Mario Carneiro
-/
import Mathlib.Algebra.Field.Defs
import Mathlib.Tactic.Common
/-!
# `IsField` predicate
Predicate on a (semi)ring th... |
Algebra\Field\MinimalAxioms.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.Algebra.Field.Defs
import Mathlib.Algebra.Ring.MinimalAxioms
/-!
# Minimal Axioms for a Field
This file defines constructors to define a `Field` structu... |
Algebra\Field\Opposite.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import Mathlib.Algebra.Field.Defs
import Mathlib.Algebra.Ring.Opposite
import Mathlib.Data.Int.Cast.Lemmas
/-!
# Field structure on the multiplicative/additive opposite
-/
va... |
Algebra\Field\Power.lean | /-
Copyright (c) 2014 Robert Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Lewis, Leonardo de Moura, Johannes Hölzl, Mario Carneiro
-/
import Mathlib.Algebra.Field.Defs
import Mathlib.Algebra.Ring.Int
/-!
# Results about powers in fields or division rin... |
Algebra\Field\Rat.lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import Mathlib.Algebra.Field.Defs
import Mathlib.Data.NNRat.Defs
/-!
# The rational numbers form a field
This file contains the field instance on th... |
Algebra\Field\Subfield.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.Algebra.Ring.Subring.Basic
import Mathlib.Algebra.Algebra.Defs
import Mathlib.Data.Rat.Cast.Defs
/-!
# Subfields
Let `K` be a division ring, for example a ... |
Algebra\Field\ULift.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.Field.Defs
import Mathlib.Algebra.GroupWithZero.ULift
import Mathlib.Algebra.Ring.ULift
/-!
# Field instances for `ULift`
This file defines insta... |
Algebra\FreeMonoid\Basic.lean | /-
Copyright (c) 2019 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Yury Kudryashov
-/
import Mathlib.Algebra.BigOperators.Group.List
import Mathlib.Algebra.Group.Action.Defs
import Mathlib.Algebra.Group.Units
/-!
# Free monoid over a given ... |
Algebra\FreeMonoid\Count.lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Algebra.FreeMonoid.Basic
/-!
# `List.count` as a bundled homomorphism
In this file we define `FreeMonoid.countP`, `FreeMonoid.count`, `FreeAddMonoi... |
Algebra\GCDMonoid\Basic.lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jens Wagemaker
-/
import Mathlib.Algebra.Associated.Basic
import Mathlib.Algebra.Ring.Regular
/-!
# Monoids with normalization functions, `gcd`, and `lcm`
This file d... |
Algebra\GCDMonoid\Finset.lean | /-
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import Mathlib.Data.Finset.Fold
import Mathlib.Algebra.GCDMonoid.Multiset
/-!
# GCD and LCM operations on finsets
## Main definitions
- `Finset.gcd` - the greatest... |
Algebra\GCDMonoid\IntegrallyClosed.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.GCDMonoid.Basic
import Mathlib.RingTheory.IntegralClosure.IntegrallyClosed
import Mathlib.RingTheory.Polynomial.Eisenstein.Basic
/-!
# GCD domains ... |
Algebra\GCDMonoid\Multiset.lean | /-
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import Mathlib.Algebra.GCDMonoid.Basic
import Mathlib.Data.Multiset.FinsetOps
import Mathlib.Data.Multiset.Fold
/-!
# GCD and LCM operations on multisets
## Main de... |
Algebra\GCDMonoid\Nat.lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jens Wagemaker, Aaron Anderson
-/
import Mathlib.Algebra.GCDMonoid.Basic
import Mathlib.Algebra.Order.Ring.Int
import Mathlib.Data.Int.GCD
/-!
# ℕ and ℤ are normalized... |
Algebra\Group\AddChar.lean | /-
Copyright (c) 2022 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
import Mathlib.Logic.Equiv.TransferInstance
/-!
# Characters from additive to multiplicative monoids
Let `A` be an additive monoid, and `M` a multiplicative one. An *... |
Algebra\Group\Aut.lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Callum Sutton, Yury Kudryashov
-/
import Mathlib.Algebra.GroupWithZero.Action.Defs
import Mathlib.GroupTheory.Perm.Basic
/-!
# Multiplicative and additive group automo... |
Algebra\Group\Basic.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 Aesop
import Mathlib.Algebra.Group.Defs
import Mathlib.Data.Nat.Defs
import Mathlib.Data.Int.Defs
import Mathlib.... |
Algebra\Group\Center.lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Jireh Loreaux
-/
import Mathlib.Algebra.Group.Commute.Units
import Mathlib.Algebra.Group.Invertible.Basic
import Mathlib.Data.Set.Basic
import Mathlib.Logic.Basic
/-!
# Cent... |
Algebra\Group\Commutator.lean | /-
Copyright (c) 2022 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import Mathlib.Algebra.Group.Defs
import Mathlib.Data.Bracket
/-!
# The bracket on a group given by commutator.
-/
assert_not_exists MonoidWithZero
assert_not_exi... |
Algebra\Group\Conj.lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Chris Hughes, Michael Howes
-/
import Mathlib.Algebra.Group.Aut
import Mathlib.Algebra.Group.Semiconj.Units
/-!
# Conjugacy of group elements
See also `MulAut.conj` a... |
Algebra\Group\ConjFinite.lean | /-
Copyright (c) 2022 Eric Rodriguez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Rodriguez
-/
import Mathlib.Algebra.Group.Conj
import Mathlib.Data.Finite.Basic
import Mathlib.Data.Fintype.Units
/-!
# Conjugacy of elements of finite groups
-/
-- TODO: After ... |
Algebra\Group\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 Mathlib.Data.Int.Notation
import Mathlib.Algebra.Group.ZeroOne
import Mathlib.Tactic.Lemma
import Mathlib.Tactic.... |
Algebra\Group\Embedding.lean | /-
Copyright (c) 2021 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
import Mathlib.Algebra.Group.Basic
import Mathlib.Logic.Embedding.Basic
/-!
# The embedding of a cancellative semigroup into itself by multiplication by a fixed elemen... |
Algebra\Group\Even.lean | /-
Copyright (c) 2022 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
import Mathlib.Algebra.Group.Opposite
import Mathlib.Algebra.Group.TypeTags
/-!
# Squares and even elements
This file defines square and even elements in a monoid.
#... |
Algebra\Group\Ext.lean | /-
Copyright (c) 2021 Bryan Gin-ge Chen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bryan Gin-ge Chen, Yury Kudryashov
-/
import Mathlib.Algebra.Group.Hom.Defs
/-!
# Extensionality lemmas for monoid and group structures
In this file we prove extensionality lemmas... |
Algebra\Group\FiniteSupport.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.Group.Support
import Mathlib.Data.Set.Finite
/-!
# Finiteness of support
-/
namespace Function
variable {α β γ : Type*} [One γ]
@[to_additive (att... |
Algebra\Group\Indicator.lean | /-
Copyright (c) 2020 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou
-/
import Mathlib.Algebra.Group.Pi.Lemmas
import Mathlib.Algebra.Group.Support
/-!
# Indicator function
- `Set.indicator (s : Set α) (f : α → β) (a : α)` is `f a` if `a ... |
Algebra\Group\InjSurj.lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.Algebra.Group.Defs
import Mathlib.Logic.Function.Basic
import Mathlib.Data.Int.Cast.Basic
import Mathlib.Tactic.Spread
/-!
# Lifting algebraic data cl... |
Algebra\Group\Int.lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
-/
import Mathlib.Algebra.Group.Nat
import Mathlib.Data.Int.Sqrt
/-!
# The integers form a group
This file contains the additive group and multiplicative monoid instance... |
Algebra\Group\MinimalAxioms.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.Algebra.Group.Defs
/-!
# Minimal Axioms for a Group
This file defines constructors to define a group structure on a Type, while proving only three
equal... |
Algebra\Group\Nat.lean | /-
Copyright (c) 2014 Floris van Doorn (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-/
import Mathlib.Algebra.Group.Even
import Mathlib.Algebra.Group.Units
/-!
# The n... |
Algebra\Group\NatPowAssoc.lean | /-
Copyright (c) 2023 Scott Carnahan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Carnahan
-/
import Mathlib.Algebra.Group.Action.Prod
import Mathlib.Algebra.Ring.Int
import Mathlib.Data.Nat.Cast.Basic
/-!
# Typeclasses for power-associative structures
In th... |
Algebra\Group\Opposite.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import Mathlib.Algebra.Group.Commute.Defs
import Mathlib.Algebra.Group.Equiv.Basic
import Mathlib.Algebra.Group.InjSurj
import Mathlib.Algebra.Group.Units
import Mathlib.Algebr... |
Algebra\Group\PNatPowAssoc.lean | /-
Copyright (c) 2023 Scott Carnahan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Carnahan
-/
import Mathlib.Algebra.Group.Action.Prod
import Mathlib.Data.PNat.Basic
/-!
# Typeclasses for power-associative structures
In this file we define power-associativi... |
Algebra\Group\Prod.lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Patrick Massot, Yury Kudryashov
-/
import Mathlib.Algebra.Group.Opposite
import Mathlib.Algebra.Group.Units.Hom
/-!
# Monoid, group etc structures on `M × N`
In this fi... |
Algebra\Group\Support.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.Prod
import Mathlib.Order.Cover
/-!
# Support of a function
In this file we define `Function.support f = {x | f x ≠ 0}` and prove its... |
Algebra\Group\TypeTags.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.Hom.Defs
import Mathlib.Data.Finite.Defs
import Mathlib.Logic.Nontrivial.Basic
/-!
# Type tags that turn additive structures into multip... |
Algebra\Group\ULift.lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.Algebra.Group.Equiv.Basic
import Mathlib.Algebra.Group.InjSurj
import Mathlib.Logic.Nontrivial.Basic
/-!
# `ULift` instances for groups and monoids
T... |
Algebra\Group\UniqueProds.lean | /-
Copyright (c) 2022 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
import Mathlib.Data.DFinsupp.Basic
import Mathlib.Data.Finset.Pointwise
import Mathlib.LinearAlgebra.Basis.VectorSpace
/-!
# Unique products and related notions
A gro... |
Algebra\Group\Units.lean | /-
Copyright (c) 2017 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Mario Carneiro, Johannes Hölzl, Chris Hughes, Jens Wagemaker, Jon Eugster
-/
import Mathlib.Algebra.Group.Basic
import Mathlib.Algebra.Group.Commute.Defs
import Mathlib.Logic.Uni... |
Algebra\Group\ZeroOne.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.Tactic.ToAdditive
/-!
## Classes for `Zero` and `One`
-/
class Zero.{u} (α : Type u) where
zero : α
instance (priority := 300) Zero.... |
Algebra\Group\Action\Basic.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.Action.Units
import Mathlib.Algebra.Group.Invertible.Basic
import Mathlib.GroupTheory.Perm.Basic
/-!
# More lemmas about group actions
This... |
Algebra\Group\Action\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.Commute.Defs
import Mathlib.Algebra.Group.TypeTags
import Mathlib.Algebra.Opposites
import Mathlib.Logic.Embedding.Basic
/-... |
Algebra\Group\Action\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.Defs
import Mathlib.Algebra.Group.Opposite
/-!
# Scalar actions on and by `Mᵐᵒᵖ`
This file defines the actions on the opposite type `S... |
Algebra\Group\Action\Option.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Algebra.Group.Action.Defs
/-!
# Option instances for additive and multiplicative actions
This file defines instances for additive and multiplicative acti... |
Algebra\Group\Action\Pi.lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Patrick Massot
-/
import Mathlib.Algebra.Group.Action.Defs
import Mathlib.Data.Set.Function
/-!
# Pi instances for multiplicative actions
This file defines instances for `M... |
Algebra\Group\Action\Prod.lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Patrick Massot, Eric Wieser
-/
import Mathlib.Algebra.Group.Action.Defs
import Mathlib.Algebra.Group.Prod
/-!
# Prod instances for additive and multiplicative actions
This ... |
Algebra\Group\Action\Sigma.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Algebra.Group.Action.Defs
/-!
# Sigma instances for additive and multiplicative actions
This file defines instances for arbitrary sum of additive and mul... |
Algebra\Group\Action\Sum.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Algebra.Group.Action.Defs
/-!
# Sum instances for additive and multiplicative actions
This file defines instances for additive and multiplicative actions... |
Algebra\Group\Action\Units.lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.Group.Action.Defs
import Mathlib.Algebra.Group.Units
/-! # Group actions on and by `Mˣ`
This file provides the action of a unit on a type `α`, `SMu... |
Algebra\Group\Commute\Basic.lean | /-
Copyright (c) 2019 Neil Strickland. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Neil Strickland, Yury Kudryashov
-/
import Mathlib.Algebra.Group.Commute.Defs
import Mathlib.Algebra.Group.Semiconj.Basic
/-!
# Additional lemmas about commuting pairs of elements in... |
Algebra\Group\Commute\Defs.lean | /-
Copyright (c) 2019 Neil Strickland. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Neil Strickland, Yury Kudryashov
-/
import Mathlib.Algebra.Group.Semiconj.Defs
import Mathlib.Init.Algebra.Classes
/-!
# Commuting pairs of elements in monoids
We define the predica... |
Algebra\Group\Commute\Hom.lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Kevin Buzzard, Scott Morrison, Johan Commelin, Chris Hughes,
Johannes Hölzl, Yury Kudryashov
-/
import Mathlib.Algebra.Group.Commute.Defs
import Mathlib.Algebra.Group... |
Algebra\Group\Commute\Units.lean | /-
Copyright (c) 2019 Neil Strickland. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Neil Strickland, Yury Kudryashov
-/
import Mathlib.Algebra.Group.Commute.Defs
import Mathlib.Algebra.Group.Semiconj.Units
/-!
# Lemmas about commuting pairs of elements involving uni... |
Algebra\Group\Equiv\Basic.lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Callum Sutton, Yury Kudryashov
-/
import Mathlib.Algebra.Group.Hom.Basic
import Mathlib.Data.FunLike.Equiv
import Mathlib.Logic.Equiv.Basic
/-!
# Multiplicative and ad... |
Algebra\Group\Equiv\TypeTags.lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Callum Sutton, Yury Kudryashov
-/
import Mathlib.Algebra.Group.Equiv.Basic
import Mathlib.Algebra.Group.TypeTags
/-!
# Additive and multiplicative equivalences associa... |
Algebra\Group\Fin\Basic.lean | /-
Copyright (c) 2021 Yakov Peckersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Peckersky
-/
import Mathlib.Algebra.Group.Basic
import Mathlib.Algebra.NeZero
import Mathlib.Data.Nat.Cast.Defs
import Mathlib.Data.Nat.Defs
import Mathlib.Data.Fin.Basic
/-!
#... |
Algebra\Group\Fin\Tuple.lean | /-
Copyright (c) 2019 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Yury Kudryashov, Sébastien Gouëzel, Chris Hughes
-/
import Mathlib.Algebra.Group.Basic
import Mathlib.Algebra.Group.Pi.Basic
import Mathlib.Data.Fin.VecNotation
/-... |
Algebra\Group\Hom\Basic.lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Kevin Buzzard, Scott Morrison, Johan Commelin, Chris Hughes,
Johannes Hölzl, Yury Kudryashov
-/
import Mathlib.Algebra.Group.Basic
import Mathlib.Algebra.Group.Hom.De... |
Algebra\Group\Hom\CompTypeclasses.lean | /-
Copyright (c) 2024 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
import Mathlib.Logic.Function.CompTypeclasses
import Mathlib.Algebra.Group.Hom.Defs
/-!
# Propositional typeclasses on several monoid homs
This file... |
Algebra\Group\Hom\Defs.lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Kevin Buzzard, Scott Morrison, Johan Commelin, Chris Hughes,
Johannes Hölzl, Yury Kudryashov
-/
import Mathlib.Algebra.Group.Pi.Basic
import Mathlib.Data.FunLike.Basi... |
Algebra\Group\Hom\End.lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Kevin Buzzard, Scott Morrison, Johan Commelin, Chris Hughes,
Johannes Hölzl, Yury Kudryashov
-/
import Mathlib.Algebra.Group.Commute.Defs
import Mathlib.Algebra.Group... |
Algebra\Group\Hom\Instances.lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Kevin Buzzard, Scott Morrison, Johan Commelin, Chris Hughes,
Johannes Hölzl, Yury Kudryashov
-/
import Mathlib.Algebra.Group.Hom.Basic
/-!
# Instances on spaces of m... |
Algebra\Group\Invertible\Basic.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.Algebra.Group.Commute.Units
import Mathlib.Algebra.Group.Invertible.Defs
import Mathlib.Algebra.Group.Hom.Defs
import Mathlib.Logic.Equiv.Defs
/-!
# Theorems... |
Algebra\Group\Invertible\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.Algebra.Group.Defs
/-!
# Invertible elements
This file defines a typeclass `Invertible a` for elements `a` with a two-sided
multiplicative inverse.
The in... |
Algebra\Group\Pi\Basic.lean | /-
Copyright (c) 2020 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Patrick Massot, Eric Wieser
-/
import Mathlib.Algebra.Group.Defs
import Mathlib.Data.Prod.Basic
import Mathlib.Data.Sum.Basic
import Mathlib.Logic.Unique
import Mathlib.Tacti... |
Algebra\Group\Pi\Lemmas.lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Patrick Massot
-/
import Mathlib.Algebra.Group.Commute.Defs
import Mathlib.Algebra.Group.Hom.Instances
import Mathlib.Data.Set.Function
import Mathlib.Logic.Pairwise
/-!
# E... |
Algebra\Group\Semiconj\Basic.lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Algebra.Group.Semiconj.Defs
import Mathlib.Algebra.Group.Basic
/-!
# Lemmas about semiconjugate elements of a group
-/
assert_not_exists MonoidWit... |
Algebra\Group\Semiconj\Defs.lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
Some proofs and docs came from `Algebra/Commute` (c) Neil Strickland
-/
import Mathlib.Algebra.Group.Defs
import Mathlib.Init.Logic
import Mathlib.Tactic.Cases
/-!
#... |
Algebra\Group\Semiconj\Units.lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
Some proofs and docs came from `Algebra/Commute` (c) Neil Strickland
-/
import Mathlib.Algebra.Group.Semiconj.Defs
import Mathlib.Algebra.Group.Units
/-!
# Semiconju... |
Algebra\Group\Subgroup\Actions.lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.Group.Submonoid.DistribMulAction
import Mathlib.GroupTheory.Subgroup.Center
/-!
# Actions by `Subgroup`s
These are just copies of the definitions a... |
Algebra\Group\Subgroup\Basic.lean | /-
Copyright (c) 2020 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
import Mathlib.Algebra.Group.Conj
import Mathlib.Algebra.Group.Pi.Lemmas
import Mathlib.Algebra.Group.Subsemigroup.Operations
import Mathlib.Algebra.Group.Submonoid.Operati... |
Algebra\Group\Subgroup\Finite.lean | /-
Copyright (c) 2020 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
import Mathlib.Algebra.Group.Subgroup.Basic
import Mathlib.Algebra.Group.Submonoid.Membership
import Mathlib.Data.Finite.Card
/-!
# Subgroups
This file provides some resu... |
Algebra\Group\Subgroup\MulOpposite.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.Submonoid.MulOpposite
import Mathlib.Logic.Encodable.Basic
/-!
# Mul-opposi... |
Algebra\Group\Subgroup\Order.lean | /-
Copyright (c) 2021 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa, Ruben Van de Velde
-/
import Mathlib.Order.Atoms
import Mathlib.Algebra.Group.Subgroup.Basic
import Mathlib.Algebra.Order.Group.InjSurj
import Mathlib.Algebra.Order.Group... |
Algebra\Group\Subgroup\Pointwise.lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.Group.Subgroup.MulOpposite
import Mathlib.Algebra.Group.Submonoid.Pointwise
import Mathlib.GroupTheory.GroupAction.ConjAct
/-! # Pointwise instances... |
Algebra\Group\Subgroup\ZPowers.lean | /-
Copyright (c) 2020 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.Algebra.Group.Subgroup.Basic
import Mathlib.Data.Countable.Basic
import Mathlib.Data.Set.Image
import Mathlib.Data.Set.Subsingleton
import Mathlib.Data.Int... |
Algebra\Group\Submonoid\Basic.lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau, Johan Commelin, Mario Carneiro, Kevin Buzzard,
Amelia Livingston, Yury Kudryashov
-/
import Mathlib.Algebra.Group.Hom.Defs
import Mathlib.Algebra.Group.Subse... |
Algebra\Group\Submonoid\DistribMulAction.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Algebra.Group.Submonoid.Operations
import Mathlib.Algebra.GroupWithZero.Action.Defs
/-!
# Distributive actions by submonoids
-/
namespace Submonoid
varia... |
Algebra\Group\Submonoid\Membership.lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau, Johan Commelin, Mario Carneiro, Kevin Buzzard,
Amelia Livingston, Yury Kudryashov
-/
import Mathlib.Algebra.FreeMonoid.Basic
import Mathlib.Algebra.Group.Sub... |
Algebra\Group\Submonoid\MulOpposite.lean | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Jujian Zhang
-/
import Mathlib.Algebra.Group.Opposite
import Mathlib.Algebra.Group.Submonoid.Basic
/-!
# Submonoid of opposite monoids
For every monoid `M`, we construct an... |
Algebra\Group\Submonoid\Operations.lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau, Johan Commelin, Mario Carneiro, Kevin Buzzard,
Amelia Livingston, Yury Kudryashov
-/
import Mathlib.Algebra.Group.Action.Defs
import Mathlib.Algebra.Group.Na... |
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