path stringlengths 11 71 | content stringlengths 75 124k |
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LinearAlgebra\QuadraticForm\TensorProduct.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.LinearAlgebra.BilinearForm.TensorProduct
import Mathlib.LinearAlgebra.QuadraticForm.Basic
/-!
# The quadratic form on a tensor product
## Main definitions
... |
LinearAlgebra\QuadraticForm\QuadraticModuleCat\Monoidal.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.CategoryTheory.Monoidal.Transport
import Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic
import Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat
impo... |
LinearAlgebra\QuadraticForm\QuadraticModuleCat\Symmetric.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.LinearAlgebra.QuadraticForm.QuadraticModuleCat.Monoidal
import Mathlib.Algebra.Category.ModuleCat.Monoidal.Symmetric
/-!
# The monoidal structure on `Quadra... |
LinearAlgebra\QuadraticForm\TensorProduct\Isometries.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.LinearAlgebra.QuadraticForm.TensorProduct
import Mathlib.LinearAlgebra.QuadraticForm.IsometryEquiv
/-!
# Linear equivalences of tensor products as isometrie... |
LinearAlgebra\RootSystem\Basic.lean | /-
Copyright (c) 2023 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash, Deepro Choudhury, Scott Carnahan
-/
import Mathlib.LinearAlgebra.RootSystem.Defs
/-!
# Root data and root systems
This file contains basic results for root systems and root... |
LinearAlgebra\RootSystem\Defs.lean | /-
Copyright (c) 2023 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash, Deepro Choudhury, Scott Carnahan
-/
import Mathlib.LinearAlgebra.PerfectPairing
import Mathlib.LinearAlgebra.Reflection
/-!
# Root data and root systems
This file contains ... |
LinearAlgebra\RootSystem\RootPositive.lean | /-
Copyright (c) 2024 Scott Carnahan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Carnahan
-/
import Mathlib.LinearAlgebra.RootSystem.Defs
/-!
# Root-positive bilinear forms on root pairings
This file contains basic results on Weyl-invariant inner products f... |
LinearAlgebra\TensorAlgebra\Basic.lean | /-
Copyright (c) 2020 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz
-/
import Mathlib.Algebra.FreeAlgebra
import Mathlib.Algebra.RingQuot
import Mathlib.Algebra.TrivSqZeroExt
import Mathlib.Algebra.Algebra.Operations
import Mathlib.LinearAlgebra... |
LinearAlgebra\TensorAlgebra\Basis.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.LinearAlgebra.TensorAlgebra.Basic
import Mathlib.LinearAlgebra.FreeAlgebra
/-!
# A basis for `TensorAlgebra R M`
## Main definitions
* `TensorAlgebra.equi... |
LinearAlgebra\TensorAlgebra\Grading.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.LinearAlgebra.TensorAlgebra.Basic
import Mathlib.RingTheory.GradedAlgebra.Basic
/-!
# Results about the grading structure of the tensor algebra
The main re... |
LinearAlgebra\TensorAlgebra\ToTensorPower.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.LinearAlgebra.TensorAlgebra.Basic
import Mathlib.LinearAlgebra.TensorPower
/-!
# Tensor algebras as direct sums of tensor powers
In this file we show that ... |
LinearAlgebra\TensorProduct\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, Mario Carneiro
-/
import Mathlib.Algebra.Module.Submodule.Bilinear
import Mathlib.Algebra.Module.Equiv.Basic
import Mathlib.GroupTheory.Congruence.Basic
import Mathlib.Tactic.Abe... |
LinearAlgebra\TensorProduct\Basis.lean | /-
Copyright (c) 2021 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer
-/
import Mathlib.LinearAlgebra.DirectSum.Finsupp
import Mathlib.LinearAlgebra.FinsuppVectorSpace
/-!
# Bases and dimensionality of tensor products of modules
Thes... |
LinearAlgebra\TensorProduct\DirectLimit.lean | /-
Copyright (c) 2023 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
import Mathlib.Algebra.DirectLimit
/-!
# Tensor product and direct limits commute with each other.
Given a family of `R`-modules `Gᵢ` with a family of compatible `R`-l... |
LinearAlgebra\TensorProduct\Finiteness.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.TensorProduct.Basic
import Mathlib.RingTheory.Finiteness
/-!
# Some finiteness results of tensor product
This file contains some finiteness results of... |
LinearAlgebra\TensorProduct\Matrix.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.Matrix.Kronecker
import Mathlib.LinearAlgebra.Matrix.ToLin
import Mathlib.LinearAlgebra.TensorProduct.Basis
/-!
# Connections between `TensorProduct` a... |
LinearAlgebra\TensorProduct\Opposite.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.RingTheory.TensorProduct.Basic
import Mathlib.Algebra.Algebra.Opposite
/-! # `MulOpposite` distributes over `⊗`
The main result in this file is:
* `Algebr... |
LinearAlgebra\TensorProduct\Pi.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.LinearAlgebra.TensorProduct.Tower
import Mathlib.LinearAlgebra.Pi
/-!
# Tensor product and products
In this file w... |
LinearAlgebra\TensorProduct\Prod.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.LinearAlgebra.TensorProduct.Basic
import Mathlib.LinearAlgebra.Prod
/-!
# Tensor products of products
This file shows that taking `TensorProduct`s commutes... |
LinearAlgebra\TensorProduct\RightExactness.lean | /-
Copyright (c) 2023 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
import Mathlib.Algebra.Exact
import Mathlib.RingTheory.TensorProduct.Basic
/-! # Right-exactness properties of tensor product
## Modules
* `LinearMa... |
LinearAlgebra\TensorProduct\Subalgebra.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.TensorProduct.Submodule
import Mathlib.RingTheory.TensorProduct.Basic
import Mathlib.LinearAlgebra.FreeModule.StrongRankCondition
/-!
# Some results on... |
LinearAlgebra\TensorProduct\Submodule.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.DirectSum.Finsupp
import Mathlib.Algebra.Algebra.Operations
import Mathlib.Algebra.Algebra.Subalgebra.Basic
/-!
# Some results on tensor product of sub... |
LinearAlgebra\TensorProduct\Tower.lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Johan Commelin, Eric Wieser
-/
import Mathlib.Algebra.Algebra.Tower
import Mathlib.LinearAlgebra.TensorProduct.Basic
/-!
# The `A`-module structure on `M ⊗[R] N`
When... |
LinearAlgebra\TensorProduct\Vanishing.lean | /-
Copyright (c) 2024 Mitchell Lee. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mitchell Lee
-/
import Mathlib.LinearAlgebra.TensorProduct.RightExactness
import Mathlib.LinearAlgebra.TensorProduct.Finiteness
/-! # Vanishing of elements in a tensor product of two mo... |
LinearAlgebra\TensorProduct\Graded\External.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.Int.Order.Units
import Mathlib.Data.ZMod.IntUnitsPower
import Mathlib.RingTheory.TensorProduct.Basic
import Mathlib.LinearAlgebra.DirectSum.TensorProduc... |
LinearAlgebra\TensorProduct\Graded\Internal.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.LinearAlgebra.TensorProduct.Graded.External
import Mathlib.RingTheory.GradedAlgebra.Basic
import Mathlib.GroupTheory.GroupAction.Ring
/-!
# Graded tensor pr... |
Logic\Basic.lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura
-/
import Mathlib.Init.Algebra.Classes
import Mathlib.Tactic.Attr.Register
import Mathlib.Tactic.Basic
import Batteries.Logic
import Batteries.Util.Libr... |
Logic\Denumerable.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Data.Fintype.Card
import Mathlib.Data.List.MinMax
import Mathlib.Data.Nat.Order.Lemmas
import Mathlib.Logic.Encodable.Basic
/-!
# Denumerable types
T... |
Logic\Hydra.lean | /-
Copyright (c) 2022 Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junyan Xu
-/
import Mathlib.Data.Finsupp.Lex
import Mathlib.Data.Finsupp.Multiset
import Mathlib.Order.GameAdd
/-!
# Termination of a hydra game
This file deals with the following version... |
Logic\IsEmpty.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.Logic.Function.Basic
/-!
# Types that are empty
In this file we define a typeclass `IsEmpty`, which expresses that a type has no elements.
## Ma... |
Logic\Lemmas.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.Logic.Basic
import Mathlib.Tactic.Convert
import Mathlib.Tactic.SplitIfs
import Mathlib.Tactic.Tauto
/-!
# More basic logic properties
A few more logic le... |
Logic\Nonempty.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.Group.ZeroOne
import Mathlib.Logic.Function.Defs
/-!
# Nonempty types
This file proves a few extra facts about `Nonempty`, which is defined i... |
Logic\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.Init.Set
import Mathlib.Tactic.Common
/-!
# Relations holding pairwise
This file defines pairwise relations.
## ... |
Logic\Relation.lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.Logic.Function.Basic
import Mathlib.Logic.Relator
import Mathlib.Init.Data.Quot
import Mathlib.Tactic.Cases
import Mathlib.Tactic.Use
import Mathlib.Ta... |
Logic\Relator.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
/-!
# Relator for functions, pairs, sums, and lists.
-/
namespace Relator
universe u₁ u₂ v₁ v₂
/- TODO(johoelzl):
* should we ... |
Logic\Unique.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.Logic.IsEmpty
import Mathlib.Init.Logic
import Mathlib.Tactic.Inhabit
/-!
# Types with a unique term
In this file we define a typeclass `Unique`,
whi... |
Logic\UnivLE.lean | /-
Copyright (c) 2023 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.Logic.Small.Defs
/-!
# UnivLE
A proposition expressing a universe inequality. `UnivLE.{u, v}` expresses that `u ≤ v`,
in the form `∀ α : Type u, Smal... |
Logic\Embedding\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, Mario Carneiro
-/
import Mathlib.Data.Option.Basic
import Mathlib.Data.Prod.PProd
import Mathlib.Logic.Equiv.Basic
/-!
# Injective functions
-/
universe u v w x
name... |
Logic\Embedding\Set.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.Data.Set.Notation
import Mathlib.Order.SetNotation
import Mathlib.Logic.Embedding.Basic
import Mathlib.Logic.Pairwise
import Mathlib.Da... |
Logic\Encodable\Basic.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, Mario Carneiro
-/
import Mathlib.Data.Countable.Defs
import Mathlib.Data.Fin.Basic
import Mathlib.Data.Nat.Find
import Mathlib.Data.PNat.Equiv
import Mathlib.... |
Logic\Encodable\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... |
Logic\Equiv\Array.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Data.Vector.Basic
import Mathlib.Logic.Equiv.List
/-!
# Equivalences involving `Array`
-/
/-
Porting note:
The following commented-out definitions ... |
Logic\Equiv\Basic.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, Mario Carneiro
-/
import Mathlib.Data.Bool.Basic
import Mathlib.Data.Option.Defs
import Mathlib.Data.Prod.Basic
import Mathlib.Data.Sigma.Basic
import Mathlib... |
Logic\Equiv\Defs.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, Mario Carneiro
-/
import Mathlib.Data.FunLike.Equiv
import Mathlib.Data.Quot
import Mathlib.Data.Bool.Basic
import Mathlib.Logic.Unique
import Mathlib.Tactic.... |
Logic\Equiv\Embedding.lean | /-
Copyright (c) 2021 Eric Rodriguez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Rodriguez
-/
import Mathlib.Logic.Embedding.Set
/-!
# Equivalences on embeddings
This file shows some advanced equivalences on embeddings, useful for constructing larger
embeddi... |
Logic\Equiv\Fin.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.Data.Int.Defs
import Mathlib.Data.Fin.VecNotation
import Mathlib.Logic.Embedding.Set
import Mathlib.Logic.Equiv.Option
/-!
# Equivalences for `Fin n`
-/
assert... |
Logic\Equiv\Fintype.lean | /-
Copyright (c) 2021 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
import Mathlib.Data.Fintype.Basic
import Mathlib.GroupTheory.Perm.Sign
import Mathlib.Logic.Equiv.Defs
/-! # Equivalence between fintypes
This file contains some ... |
Logic\Equiv\Functor.lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Simon Hudon, Scott Morrison
-/
import Mathlib.Control.Bifunctor
import Mathlib.Logic.Equiv.Defs
/-!
# Functor and bifunctors can be applied to `Equiv`s.
We define
```... |
Logic\Equiv\List.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Data.Finset.Sort
import Mathlib.Data.Vector.Basic
import Mathlib.Logic.Denumerable
/-!
# Equivalences involving `List`-like types
This file defines s... |
Logic\Equiv\Nat.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Data.Nat.Bits
import Mathlib.Data.Nat.Pairing
/-!
# Equivalences involving `ℕ`
This file defines some additional constructive equivalences using `Enc... |
Logic\Equiv\Option.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.Control.EquivFunctor
import Mathlib.Data.Option.Basic
import Mathlib.Data.Subtype
import Mathlib.Logic.Equiv.Defs
import Mathlib.Tactic.Cases
/-!
# Equivale... |
Logic\Equiv\Pairwise.lean | /-
Copyright (c) 2024 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import Mathlib.Data.FunLike.Equiv
import Mathlib.Logic.Pairwise
/-!
# Interaction of equivalences with `Pairwise`
-/
lemma EmbeddingLike.pairwise_comp {X : Type*} {Y : ... |
Logic\Equiv\PartialEquiv.lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Data.Set.Function
import Mathlib.Logic.Equiv.Defs
import Mathlib.Tactic.Core
import Mathlib.Tactic.Attr.Core
/-!
# Partial equivalences
This fi... |
Logic\Equiv\Set.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, Mario Carneiro
-/
import Mathlib.Data.Set.Function
import Mathlib.Logic.Equiv.Defs
import Mathlib.Tactic.Says
/-!
# Equivalences and sets
In this file we pr... |
Logic\Equiv\TransferInstance.lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.Algebra.Algebra.Equiv
import Mathlib.Algebra.Field.Basic
import Mathlib.Logic.Equiv.Defs
import Mathlib.Logic.Small.Defs
/-!
# Transfer algebraic stru... |
Logic\Function\Basic.lean | /-
Copyright (c) 2016 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import Mathlib.Logic.Nonempty
import Mathlib.Init.Set
import Mathlib.Logic.Basic
/-!
# Miscellaneous function constructions and lemmas
-/
open Funct... |
Logic\Function\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.Defs
/-!
# Propositional typeclasses on several maps
This file contains typeclasses that are used in the definition of
... |
Logic\Function\Conjugate.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.Logic.Function.Basic
/-!
# Semiconjugate and commuting maps
We define the following predicates:
* `Function.Semiconj`: `f : α → β` semiconjugates ... |
Logic\Function\Defs.lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad, Haitao Zhang
-/
import Mathlib.Tactic.AdaptationNote
import Mathlib.Tactic.Attr.Register
import Mathlib.Tactic.Basic
import Mathlib.Tactic.Eqns... |
Logic\Function\FromTypes.lean | /-
Copyright (c) 2024 Brendan Murphy. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Brendan Murphy
-/
import Mathlib.Data.Fin.VecNotation
/-! # Function types of a given heterogeneous arity
This provides `Function.FromTypes`, such that `FromTypes ![α, β] τ = α → β ... |
Logic\Function\Iterate.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.Logic.Function.Conjugate
/-!
# Iterations of a function
In this file we prove simple properties of `Nat.iterate f n` a.k.a. `f^[n]`:
* `iterate_ze... |
Logic\Function\OfArity.lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Logic.Function.FromTypes
/-! # Function types of a given arity
This provides `Function.OfArity`, such that `OfArity α β 2 = α → α → β`.
Note that it... |
Logic\Function\ULift.lean | /-
Copyright (c) 2016 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import Mathlib.Logic.Function.Defs
/-!
# `ULift` and `PLift`
-/
theorem ULift.down_injective {α : Sort _} : Function.Injective (@ULift.down α)
| ⟨... |
Logic\Godel\GodelBetaFunction.lean | /-
Copyright (c) 2023 Shogo Saito. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shogo Saito. Adapted for mathlib by Hunter Monroe
-/
import Mathlib.Data.Nat.ModEq
import Mathlib.Data.Nat.ChineseRemainder
import Mathlib.Data.Nat.Prime.Defs
import Mathlib.Data.Nat.Pai... |
Logic\Nontrivial\Basic.lean | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Data.Prod.Basic
import Mathlib.Logic.Function.Basic
import Mathlib.Logic.Nontrivial.Defs
import Mathlib.Logic.Unique
import Mathlib.Order.Defs
im... |
Logic\Nontrivial\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.Init.Logic
import Mathlib.Logic.Function.Defs
import Mathlib.Tactic.TypeStar
/-!
# Nontrivial types
A type is *nontrivial* if it contains at le... |
Logic\Small\Basic.lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.Logic.Small.Defs
import Mathlib.Logic.Equiv.Set
/-!
# Instances and theorems for `Small`.
In particular we prove `small_of_injective` and `small_of_s... |
Logic\Small\Defs.lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.Logic.Equiv.Defs
import Mathlib.Tactic.MkIffOfInductiveProp
import Mathlib.Tactic.PPWithUniv
/-!
# Small types
A type is `w`-small if there exists an... |
Logic\Small\Group.lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.Logic.Small.Defs
import Mathlib.Logic.Equiv.TransferInstance
/-!
# Transfer group structures from `α` to `Shrink α`.
-/
noncomputable section
variab... |
Logic\Small\List.lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.Logic.Small.Basic
import Mathlib.Data.Vector.Basic
/-!
# Instances for `Small (List α)` and `Small (Vector α)`.
These must not be in `Logic.Small.Bas... |
Logic\Small\Module.lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.Logic.Small.Group
import Mathlib.Logic.Small.Ring
/-!
# Transfer module and algebra structures from `α` to `Shrink α`.
-/
noncomputable section
vari... |
Logic\Small\Ring.lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.Logic.Small.Defs
import Mathlib.Logic.Equiv.TransferInstance
/-!
# Transfer ring structures from `α` to `Shrink α`.
-/
noncomputable section
variabl... |
Logic\Small\Set.lean | /-
Copyright (c) 2024 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import Mathlib.Data.Set.Lattice
import Mathlib.Logic.Small.Basic
/-!
# Results about `Small` on coerced sets
-/
universe u v w
theorem small_subset {α : Type v} {s t... |
Mathport\Notation.lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Kyle Miller
-/
import Mathlib.Lean.Elab.Term
import Mathlib.Lean.PrettyPrinter.Delaborator
import Mathlib.Tactic.ScopedNS
import Batteries.Linter.UnreachableTact... |
Mathport\Syntax.lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Lean.Elab.Command
import Lean.Elab.Quotation
import Batteries.Tactic.Where
import Mathlib.Data.Matrix.Notation
import Mathlib.Logic.Equiv.PartialEquiv
i... |
MeasureTheory\PiSystem.lean | /-
Copyright (c) 2021 Martin Zinkevich. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Martin Zinkevich, Rémy Degenne
-/
import Mathlib.Logic.Encodable.Lattice
import Mathlib.MeasureTheory.MeasurableSpace.Defs
/-!
# Induction principles for measurable ... |
MeasureTheory\SetAlgebra.lean | /-
Copyright (c) 2024 Etienne Marion. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Etienne Marion
-/
import Mathlib.MeasureTheory.SetSemiring
/-!
# Algebra of sets
In this file we define the notion of algebra of sets and give its basic properties. An algebra
of set... |
MeasureTheory\SetSemiring.lean | /-
Copyright (c) 2023 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Peter Pfaffelhuber
-/
import Mathlib.Data.Set.Pairwise.Lattice
import Mathlib.MeasureTheory.PiSystem
/-! # Semirings and rings of sets
A semi-ring of sets `C` (in the sen... |
MeasureTheory\Category\MeasCat.lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.MeasureTheory.Measure.GiryMonad
import Mathlib.CategoryTheory.ConcreteCategory.UnbundledHom
import Mathlib.CategoryTheory.Monad.Algebra
import Mathlib.... |
MeasureTheory\Constructions\Cylinders.lean | /-
Copyright (c) 2023 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Peter Pfaffelhuber
-/
import Mathlib.MeasureTheory.PiSystem
import Mathlib.Order.OmegaCompletePartialOrder
import Mathlib.Topology.Constructions
import Mathlib.MeasureTheor... |
MeasureTheory\Constructions\EventuallyMeasurable.lean | /-
Copyright (c) 2024 Felix Weilacher. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Felix Weilacher
-/
import Mathlib.MeasureTheory.MeasurableSpace.Defs
import Mathlib.Order.Filter.CountableInter
/-!
# Measurability modulo a filter
In this file we consider the gen... |
MeasureTheory\Constructions\HaarToSphere.lean | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Algebra.Order.Pointwise
import Mathlib.Analysis.NormedSpace.SphereNormEquiv
import Mathlib.Analysis.SpecialFunctions.Integrals
import Mathlib.Measure... |
MeasureTheory\Constructions\Pi.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.MeasureTheory.Constructions.Prod.Basic
import Mathlib.MeasureTheory.Group.Measure
import Mathlib.Topology.Constructions
/-!
# Product measures
In... |
MeasureTheory\Constructions\Projective.lean | /-
Copyright (c) 2023 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Peter Pfaffelhuber
-/
import Mathlib.MeasureTheory.Constructions.Cylinders
import Mathlib.MeasureTheory.Measure.Typeclasses
/-!
# Projective measure families and projectiv... |
MeasureTheory\Constructions\UnitInterval.lean | /-
Copyright (c) 2024 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Topology.UnitInterval
import Mathlib.MeasureTheory.Constructions.BorelSpace.Basic
import Mathlib.MeasureTheory.Measure.Haar.OfBasis
import Mathlib.MeasureThe... |
MeasureTheory\Constructions\BorelSpace\Basic.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yury Kudryashov
-/
import Mathlib.MeasureTheory.Group.Arithmetic
import Mathlib.Topology.GDelta
import Mathlib.Topology.Instances.EReal
import Mathlib.Topology.Instance... |
MeasureTheory\Constructions\BorelSpace\Complex.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.Analysis.Complex.Basic
import Mathlib.MeasureTheory.Constructions.BorelSpace.Basic
/-! # Equip `ℂ` with the Borel sigma-algebra -/
noncomputable s... |
MeasureTheory\Constructions\BorelSpace\ContinuousLinearMap.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.MeasureTheory.Constructions.BorelSpace.Basic
import Mathlib.Analysis.NormedSpace.OperatorNorm.NormedSpace
import Mathlib.Topology.Algebra.Module.Finite... |
MeasureTheory\Constructions\BorelSpace\Metric.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yury Kudryashov
-/
import Mathlib.Analysis.Normed.Group.Basic
import Mathlib.MeasureTheory.Constructions.BorelSpace.Real
import Mathlib.Topology.MetricSpace.Thickening
... |
MeasureTheory\Constructions\BorelSpace\Metrizable.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.MeasureTheory.Constructions.BorelSpace.Metric
import Mathlib.Topology.Metrizable.Basic
import Mathlib.Topology.IndicatorConstPointwise
/-!
# Measu... |
MeasureTheory\Constructions\BorelSpace\Order.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yury Kudryashov, Kexing Ying
-/
import Mathlib.Topology.Semicontinuous
import Mathlib.MeasureTheory.Function.AEMeasurableSequence
import Mathlib.MeasureTheory.Order.Lat... |
MeasureTheory\Constructions\BorelSpace\Real.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yury Kudryashov
-/
import Mathlib.MeasureTheory.Constructions.BorelSpace.Order
/-!
# Borel (measurable) spaces ℝ, ℝ≥0, ℝ≥0∞
## Main statements
* `borel_eq_generateFr... |
MeasureTheory\Constructions\Polish\Basic.lean | /-
Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Felix Weilacher
-/
import Mathlib.MeasureTheory.Constructions.BorelSpace.Metric
import Mathlib.Topology.CountableSeparatingOn
import Mathlib.Topology.MetricSpace.... |
MeasureTheory\Constructions\Polish\EmbeddingReal.lean | /-
Copyright (c) 2023 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
import Mathlib.Data.Real.Cardinality
import Mathlib.MeasureTheory.Constructions.Polish.Basic
/-!
# A Polish Borel space is measurably equivalent to a set of reals
-/
op... |
MeasureTheory\Constructions\Prod\Basic.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.MeasureTheory.Measure.GiryMonad
import Mathlib.Dynamics.Ergodic.MeasurePreserving
import Mathlib.MeasureTheory.Integral.Lebesgue
import Mathlib.Mea... |
MeasureTheory\Constructions\Prod\Integral.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.MeasureTheory.Constructions.Prod.Basic
import Mathlib.MeasureTheory.Integral.DominatedConvergence
import Mathlib.MeasureTheory.Integral.SetIntegral... |
MeasureTheory\Covering\Besicovitch.lean | /-
Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.MeasureTheory.Covering.Differentiation
import Mathlib.MeasureTheory.Covering.VitaliFamily
import Mathlib.MeasureTheory.Integral.Lebesgue
import M... |
MeasureTheory\Covering\BesicovitchVectorSpace.lean | /-
Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar
import Mathlib.MeasureTheory.Covering.Besicovitch
import Mathlib.Tactic.AdaptationNote
/-!
# Satellite con... |
MeasureTheory\Covering\DensityTheorem.lean | /-
Copyright (c) 2022 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.MeasureTheory.Measure.Doubling
import Mathlib.MeasureTheory.Covering.Vitali
import Mathlib.MeasureTheory.Covering.Differentiation
/-!
# Uniformly locally do... |
MeasureTheory\Covering\Differentiation.lean | /-
Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.MeasureTheory.Covering.VitaliFamily
import Mathlib.MeasureTheory.Measure.Regular
import Mathlib.MeasureTheory.Function.AEMeasurableOrder
import M... |
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