path stringlengths 11 71 | content stringlengths 75 124k |
|---|---|
Control\Bitraversable\Lemmas.lean | /-
Copyright (c) 2019 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import Mathlib.Control.Bitraversable.Basic
/-!
# Bitraversable Lemmas
## Main definitions
* tfst - traverse on first functor argument
* tsnd - traverse on second func... |
Control\EquivFunctor\Instances.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.Data.Fintype.Basic
import Mathlib.Control.EquivFunctor
/-!
# `EquivFunctor` instances
We derive some `EquivFunctor` instances, to enable `equiv_rw` t... |
Control\Functor\Multivariate.lean | /-
Copyright (c) 2018 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Mario Carneiro, Simon Hudon
-/
import Mathlib.Data.Fin.Fin2
import Mathlib.Data.TypeVec
import Mathlib.Logic.Equiv.Defs
/-!
# Functors between the category of tuples of... |
Control\Monad\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
-/
import Mathlib.Logic.Equiv.Defs
/-!
# Monad
## Attributes
* ext
* functor_norm
* monad_norm
## Implementation Details
Set of rewrite rules and automation for monads... |
Control\Monad\Cont.lean | /-
Copyright (c) 2019 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import Mathlib.Control.Monad.Basic
import Mathlib.Control.Monad.Writer
import Mathlib.Control.Lawful
import Batteries.Tactic.Congr
/-!
# Continuation Monad
Monad encapsul... |
Control\Monad\Writer.lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, E.W.Ayers
-/
import Mathlib.Algebra.Group.Defs
import Mathlib.Logic.Equiv.Defs
/-!
# Writer monads
This file introduces monads for managing immutable, appendable ... |
Control\Traversable\Basic.lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import Mathlib.Data.Option.Defs
import Mathlib.Control.Functor
import Batteries.Data.List.Basic
/-!
# Traversable type class
Type classes for traversing collections. The ... |
Control\Traversable\Equiv.lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import Mathlib.Control.Traversable.Lemmas
import Mathlib.Logic.Equiv.Defs
/-!
# Transferring `Traversable` instances along isomorphisms
This file allows to transfer `Trav... |
Control\Traversable\Instances.lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import Mathlib.Control.Applicative
import Mathlib.Control.Traversable.Basic
import Mathlib.Data.List.Forall2
import Mathlib.Data.Set.Functor
/-!
# LawfulTraversable instan... |
Control\Traversable\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
-/
import Mathlib.Control.Applicative
import Mathlib.Control.Traversable.Basic
/-!
# Traversing collections
This file proves basic properties of traversable and applicative ... |
Data\BitVec.lean | /-
Copyright (c) 2020 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Harun Khan, Alex Keizer
-/
import Mathlib.Algebra.Ring.InjSurj
import Mathlib.Data.ZMod.Defs
/-!
# Basic Theorems About Bitvectors
This file contains theorems about bitvect... |
Data\Bracket.lean | /-
Copyright (c) 2021 Patrick Lutz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Lutz, Oliver Nash
-/
import Mathlib.Tactic.TypeStar
/-!
# Bracket Notation
This file provides notation which can be used for the Lie bracket, for the commutator of two
subgroups... |
Data\Bundle.lean | /-
Copyright (c) 2021 Nicolò Cavalleri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolò Cavalleri
-/
import Mathlib.Data.Set.Basic
/-!
# Bundle
Basic data structure to implement fiber bundles, vector bundles (maybe fibrations?), etc. This file
should contain all... |
Data\ByteArray.lean | /-
Copyright (c) 2021 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
/-!
# Main result
Introduce main properties of `Up` (well-ordered relation for "upwards" induction on `ℕ`) and of
`ByteArray`
-/
namespace Nat
/-- A well-ordered ... |
Data\Char.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.Defs
import Mathlib.Order.Defs
/-!
# More `Char` instances
This file provides a `LinearOrder` instance on `Char`. `Char` is the type of Unic... |
Data\Erased.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.Logic.Equiv.Defs
/-!
# A type for VM-erased data
This file defines a type `Erased α` which is classically isomorphic to `α`,
but erased in the VM. Th... |
Data\FinEnum.lean | /-
Copyright (c) 2019 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import Mathlib.Data.Fintype.Basic
import Mathlib.Data.List.ProdSigma
import Mathlib.Data.List.Pi
/-!
Type class for finitely enumerable types. The property is stronger
tha... |
Data\Finmap.lean | /-
Copyright (c) 2018 Sean Leather. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sean Leather, Mario Carneiro
-/
import Mathlib.Data.List.AList
import Mathlib.Data.Finset.Sigma
import Mathlib.Data.Part
/-!
# Finite maps over `Multiset`
-/
universe u v w
open List
... |
Data\HashMap.lean | /-
Copyright (c) 2022 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
As `HashMap` has been completely reimplemented in `Batteries`,
nothing from the mathlib3 file `data.hash_map` is reflected here.
The porting header is just here to mark... |
Data\Holor.lean | /-
Copyright (c) 2018 Alexander Bentkamp. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp
-/
import Mathlib.Algebra.BigOperators.Group.Finset
import Mathlib.Algebra.Module.Pi
/-!
# Basic properties of holors
Holors are indexed collections of tensor ... |
Data\Opposite.lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Reid Barton, Simon Hudon, Kenny Lau
-/
import Mathlib.Logic.Equiv.Defs
/-!
# Opposites
In this file we define a structure `Opposite α` containing a single field of ty... |
Data\Part.lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Jeremy Avigad, Simon Hudon
-/
import Mathlib.Data.Set.Subsingleton
import Mathlib.Logic.Equiv.Defs
import Mathlib.Algebra.Group.Defs
/-!
# Partial values of a type
Thi... |
Data\PEquiv.lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.Data.Option.Basic
import Mathlib.Data.Set.Basic
import Batteries.Tactic.Congr
/-!
# Partial Equivalences
In this file, we define partial equivalences `P... |
Data\PFun.lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Jeremy Avigad, Simon Hudon
-/
import Mathlib.Data.Part
import Mathlib.Data.Rel
import Batteries.WF
/-!
# Partial functions
This file defines partial functions. Partia... |
Data\Quot.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.Init.Data.Quot
import Mathlib.Logic.Relator
import Mathlib.Logic.Unique
import Mathlib.Mathport.Notation
/-!
# Quotient types
This module extends the ... |
Data\Rel.lean | /-
Copyright (c) 2018 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
-/
import Mathlib.Order.CompleteLattice
import Mathlib.Order.GaloisConnection
import Mathlib.Data.Set.Lattice
import Mathlib.Tactic.AdaptationNote
/-!
# Relations
This f... |
Data\Semiquot.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.Set.Lattice
/-! # Semiquotients
A data type for semiquotients, which are classically equivalent to
nonempty sets, but are useful for programming... |
Data\Sign.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.GroupWithZero.Units.Lemmas
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Data.Fintype.BigOperators
/-!
# Sign function
... |
Data\SProd.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.FBinop
/-!
# Set Product Notation
This file provides notation for a product of sets, and other similar types.
## Main Definitions
* `SProd α β γ` ... |
Data\Subtype.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.Tactic.AdaptationNote
/-!
# Subtypes
This file provides basic API for subtypes, which are defined in core.
A sub... |
Data\TwoPointing.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.Nontrivial.Defs
import Mathlib.Logic.Nonempty
import Batteries.Data.Sum.Lemmas
/-!
# Two-pointings
This file defines `TwoPointing α`, the type of t... |
Data\TypeMax.lean | /-
Copyright (c) 2023 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Tactic.ToAdditive
/-!
# Workaround for changes in universe unification
Universe inequalities in Mathlib 3 are expressed through use of `max u v`. Unf... |
Data\TypeVec.lean | /-
Copyright (c) 2018 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Mario Carneiro, Simon Hudon
-/
import Mathlib.Data.Fin.Fin2
import Mathlib.Logic.Function.Basic
import Mathlib.Tactic.Common
/-!
# Tuples of types, and their categorica... |
Data\UInt.lean | /-
Copyright (c) 2021 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Data.ZMod.Defs
/-!
# Adds Mathlib specific instances to the `UIntX` data types.
The `CommRing` instances (and the `NatCast` and `IntCast` instances f... |
Data\ULift.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.Control.ULift
import Mathlib.Logic.Equiv.Basic
/-!
# Extra lemmas about `ULift` and `PLift`
In this file we provide `Subsingleton`, `Unique`, `Deci... |
Data\Vector3.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.Data.Fin.Fin2
import Mathlib.Init.Logic
import Mathlib.Mathport.Notation
import Mathlib.Tactic.TypeStar
/-!
# Alternate definition of `Vector` in term... |
Data\Analysis\Filter.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.Order.Filter.Cofinite
/-!
# Computational realization of filters (experimental)
This file provides infrastructure to compute with filters.
## Main d... |
Data\Analysis\Topology.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.Data.Analysis.Filter
import Mathlib.Topology.Bases
import Mathlib.Topology.LocallyFinite
/-!
# Computational realization of topological spaces (experi... |
Data\Array\Defs.lean | /-
Copyright (c) 2021 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Arthur Paulino, Floris van Doorn
-/
/-!
## Definitions on Arrays
This file contains various definitions on `Array`. It does not contain
proofs about these definitions, those are co... |
Data\Array\ExtractLemmas.lean | /-
Copyright (c) 2024 Jiecheng Zhao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jiecheng Zhao
-/
/-!
# Lemmas about `Array.extract`
Some useful lemmas about Array.extract
-/
universe u
variable {α : Type u} {i : Nat}
namespace Array
@[simp]
theorem extract_eq_n... |
Data\Array\Lemmas.lean | /-
Copyright (c) 2017 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.Algebra.Group.Fin.Basic
import Mathlib.Data.List.Basic
/-!
Porting note:
Following the discussion on [Zulip](https://leanpro... |
Data\Bool\AllAny.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.Data.List.Basic
/-!
# Boolean quantifiers
This proves a few properties about `List.all` and `List.any`, which are the `Bool` universal and
existentia... |
Data\Bool\Basic.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
-/
import Mathlib.Logic.Function.Defs
import Mathlib.Order.Defs
/-!
# Booleans
This file proves various trivial lemmas about booleans and thei... |
Data\Bool\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.Order.Ring.Nat
import Mathlib.Data.List.Chain
/-!
# List of booleans
In this file we prove lemmas about the number of `false`s and `true`s ... |
Data\Bool\Set.lean | /-
Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import Mathlib.Data.Set.Image
/-!
# Booleans and set operations
This file contains two trivial lemmas about `Bool`, `Set.univ`, and `Set.range`.
-/
open S... |
Data\Complex\Abs.lean | /-
Copyright (c) 2017 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Mario Carneiro
-/
import Mathlib.Data.Complex.Basic
import Mathlib.Data.Real.Sqrt
/-!
# Absolute values of complex numbers
-/
open Set ComplexConjugate
namespace Comp... |
Data\Complex\Basic.lean | /-
Copyright (c) 2017 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Mario Carneiro
-/
import Mathlib.Algebra.CharZero.Lemmas
import Mathlib.Algebra.GroupWithZero.Divisibility
import Mathlib.Algebra.Star.Basic
import Mathlib.Data.Real.Basi... |
Data\Complex\BigOperators.lean | /-
Copyright (c) 2017 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Mario Carneiro
-/
import Mathlib.Algebra.BigOperators.Group.Finset
import Mathlib.Data.Complex.Basic
/-!
# Finite sums and products of complex numbers
-/
namespace Com... |
Data\Complex\Cardinality.lean | /-
Copyright (c) 2022 Violeta Hernández Palacios. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Violeta Hernández Palacios
-/
import Mathlib.Data.Complex.Basic
import Mathlib.Data.Real.Cardinality
/-!
# The cardinality of the complex numbers
This file shows that the... |
Data\Complex\Determinant.lean | /-
Copyright (c) 2022 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import Mathlib.Data.Complex.Module
import Mathlib.LinearAlgebra.Determinant
/-!
# Determinants of maps in the complex numbers as a vector space over `ℝ`
This file provi... |
Data\Complex\Exponential.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir
-/
import Mathlib.Algebra.Order.CauSeq.BigOperators
import Mathlib.Algebra.Star.Order
import Mathlib.Data.Complex.Abs
import Mathlib.Data.Complex.B... |
Data\Complex\ExponentialBounds.lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Joseph Myers
-/
import Mathlib.Data.Complex.Exponential
import Mathlib.Analysis.SpecialFunctions.Log.Deriv
/-!
# Bounds on specific values of the exponential
-/
namesp... |
Data\Complex\FiniteDimensional.lean | /-
Copyright (c) 2020 Alexander Bentkamp, Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp, Sébastien Gouëzel, Eric Wieser
-/
import Mathlib.Algebra.Algebra.Rat
import Mathlib.Data.Complex.Cardinality
import Mathlib.Data.Complex.Modu... |
Data\Complex\Module.lean | /-
Copyright (c) 2020 Alexander Bentkamp, Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp, Sébastien Gouëzel, Eric Wieser
-/
import Mathlib.Algebra.Algebra.RestrictScalars
import Mathlib.Algebra.CharP.Invertible
import Mathlib.Data.... |
Data\Complex\Order.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.Data.Complex.Abs
/-!
# The partial order on the complex numbers
This order is defined by `z ≤ w ↔ z.re ≤ w.re ∧ z.im = w.im`.
This is a natural orde... |
Data\Complex\Orientation.lean | /-
Copyright (c) 2021 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
import Mathlib.Data.Complex.Module
import Mathlib.LinearAlgebra.Orientation
/-!
# The standard orientation on `ℂ`.
This had previously been in `LinearAlgebra.Orie... |
Data\Countable\Basic.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.Logic.Equiv.Nat
import Mathlib.Logic.Equiv.Fin
import Mathlib.Data.Countable.Defs
/-!
# Countable types
In this file we provide basic instances of ... |
Data\Countable\Defs.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.Data.Finite.Defs
import Mathlib.Data.Bool.Basic
import Mathlib.Data.Subtype
import Mathlib.Tactic.MkIffOfInductiveProp
/-!
# Countable and uncountab... |
Data\Countable\Small.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.Countable.Defs
/-!
# All countable types are small.
That is, any countable type is equivalent to a type in any ... |
Data\DFinsupp\Basic.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau
-/
import Mathlib.Algebra.BigOperators.GroupWithZero.Finset
import Mathlib.Algebra.Group.Submonoid.Membership
import Mathlib.Algebra.GroupWithZero.Action.Pi
import... |
Data\DFinsupp\Encodable.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.Data.DFinsupp.Basic
import Mathlib.Logic.Equiv.List
/-!
# `Encodable` and `Countable` instances for `Π₀ i, α i`
In this file we provide instances fo... |
Data\DFinsupp\Interval.lean | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Data.Finset.Pointwise
import Mathlib.Data.Fintype.BigOperators
import Mathlib.Data.DFinsupp.Order
import Mathlib.Order.Interval.Finset.Basic
/-!
# Finite ... |
Data\DFinsupp\Lex.lean | /-
Copyright (c) 2022 Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa, Junyan Xu
-/
import Mathlib.Algebra.Order.Group.PiLex
import Mathlib.Data.DFinsupp.Order
import Mathlib.Data.DFinsupp.NeLocus
import Mathlib.Order.WellFoundedSet
/-!
# Lexic... |
Data\DFinsupp\Multiset.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.Data.DFinsupp.Order
/-!
# Equivalence between `Multiset` and `ℕ`-valued finitely supported functions
This defines `DFinsupp.toMultiset` the equivalence bet... |
Data\DFinsupp\NeLocus.lean | /-
Copyright (c) 2022 Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa, Junyan Xu
-/
import Mathlib.Data.DFinsupp.Basic
/-!
# Locus of unequal values of finitely supported dependent functions
Let `N : α → Type*` be a type family, assume that `N... |
Data\DFinsupp\Notation.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.DFinsupp.Basic
import Mathlib.Data.Finsupp.Notation
/-!
# Notation for `DFinsupp`
This file extends the existing `fun₀ | 3 => a | 7 => b` notation to ... |
Data\DFinsupp\Order.lean | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Algebra.Order.Module.Defs
import Mathlib.Data.DFinsupp.Basic
/-!
# Pointwise order on finitely supported dependent functions
This file lifts order struct... |
Data\DFinsupp\WellFounded.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.DFinsupp.Lex
import Mathlib.Order.GameAdd
import Mathlib.Order.Antisymmetrization
import Mathlib.SetTheory.Ordinal.Basic
import Mathlib.Tactic.AdaptationNot... |
Data\DList\Basic.lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import Mathlib.Data.DList.Defs
import Mathlib.Tactic.TypeStar
/-!
# Difference list
This file provides a few results about `DList`, which is defined in `Batteries`.
A di... |
Data\DList\Defs.lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Batteries.Data.DList
import Mathlib.Tactic.Cases
/-!
# Difference list
This file provides a few results about `DList`, which is defined in `Batteri... |
Data\DList\Instances.lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import Mathlib.Data.DList.Defs
import Mathlib.Control.Traversable.Equiv
import Mathlib.Control.Traversable.Instances
/-!
# Traversable instance for DLists
This file provi... |
Data\ENat\Basic.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.Data.Nat.SuccPred
import Mathlib.Algebra.CharZero.Lemmas
import Mathlib.Algebra.Order.Sub.WithTop
import Mathlib.Algebra.Order.Ring.WithTop
import Ma... |
Data\ENat\Lattice.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.Data.Nat.Lattice
import Mathlib.Data.ENat.Basic
/-!
# Extended natural numbers form a complete linear order
This instance is not in `Data.ENat.Basi... |
Data\ENNReal\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.Algebra.Order.Ring.WithTop
import Mathlib.Algebra.Order.Sub.WithTop
import Mathlib.Data.NNReal.Basic
import Mathlib.Order.Interval.Set... |
Data\ENNReal\Inv.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.Data.ENNReal.Operations
/-!
# Results about division in extended non-negative reals
This file establishes basic properties related t... |
Data\ENNReal\Operations.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.Algebra.BigOperators.WithTop
import Mathlib.Algebra.GroupWithZero.Divisibility
import Mathlib.Data.ENNReal.Basic
/-!
# Properties of ... |
Data\ENNReal\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.Data.ENNReal.Inv
import Mathlib.Tactic.Bound.Attribute
/-!
# Maps between real and extended non-negative real numbers
This file focu... |
Data\Fin\Basic.lean | /-
Copyright (c) 2017 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Keeley Hoek
-/
import Mathlib.Algebra.NeZero
import Mathlib.Data.Nat.Defs
import Mathlib.Init.Data.Nat.Lemmas
import Mathlib.Logic.Embedding.Basic
import Mathlib.Logi... |
Data\Fin\Fin2.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.Data.Nat.Notation
import Mathlib.Data.Fintype.Basic
import Mathlib.Logic.Function.Basic
/-!
# Inductive type variant of `Fin`
`Fin` is defined as a s... |
Data\Fin\FlagRange.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.Data.Fin.Basic
import Mathlib.Order.Chain
import Mathlib.Order.Cover
import Mathlib.Order.Fin.Basic
/-!
# Range of `f : Fin (n + 1) → α` as a `Flag`... |
Data\Fin\SuccPred.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.Fin.Basic
import Mathlib.Order.Fin.Basic
import Mathlib.Order.SuccPred.Basic
/-!
# Successors and predecessors of `Fin n`
In this file,... |
Data\Fin\VecNotation.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.Data.Fin.Tuple.Basic
import Mathlib.Data.List.Range
/-!
# Matrix and vector notation
This file defines notation for vectors and matrices. Given `a b c d : ... |
Data\Fin\Tuple\Basic.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.Data.Fin.Basic
import Mathlib.Data.Nat.Find
import Batteries.Data.Fin.Lemmas
/-!
# Operation on ... |
Data\Fin\Tuple\BubbleSortInduction.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.Data.Fin.Tuple.Sort
import Mathlib.Order.WellFounded
import Mathlib.Order.PiLex
/-!
# "Bubble sort" induction
We implement the following induction prin... |
Data\Fin\Tuple\Curry.lean | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Brendan Murphy
-/
import Mathlib.Data.Fin.Tuple.Basic
import Mathlib.Logic.Equiv.Fin
import Mathlib.Logic.Function.OfArity
/-!
# Currying and uncurrying of n-ary functions
... |
Data\Fin\Tuple\Finset.lean | /-
Copyright (c) 2023 Bolton Bailey. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bolton Bailey
-/
import Mathlib.Data.Fin.Tuple.Basic
import Mathlib.Data.Fintype.Pi
/-!
# Fin-indexed tuples of finsets
-/
open Fintype
namespace Fin
variable {n : ℕ} {α : Fin (n + 1... |
Data\Fin\Tuple\NatAntidiagonal.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.BigOperators.Fin
import Mathlib.Algebra.Group.Fin.Tuple
import Mathlib.Data.Finset.NatAntidiagonal
import Mathlib.Order.Fin.Tuple
/-!
# Collections ... |
Data\Fin\Tuple\Reflection.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.Data.Fin.VecNotation
import Mathlib.Algebra.BigOperators.Fin
/-!
# Lemmas for tuples `Fin m → α`
This file contains alternative definitions of common opera... |
Data\Fin\Tuple\Sort.lean | /-
Copyright (c) 2021 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
import Mathlib.Data.Finset.Sort
import Mathlib.Data.List.FinRange
import Mathlib.Data.Prod.Lex
import Mathlib.GroupTheory.Perm.Basic
import Mathlib.Order.Interval.Finset.Fi... |
Data\Finite\Basic.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.Powerset
import Mathlib.Data.Fintype.Prod
import Mathlib.Data.Fintype.Sigma
import Mathlib.Data.Fintype.Sum
import Mathlib.Data.Fintype.Vector
... |
Data\Finite\Card.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.SetTheory.Cardinal.Finite
/-!
# Cardinality of finite types
The cardinality of a finite type `α` is given by `Nat.card α`. This function has
the "junk val... |
Data\Finite\Defs.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.Logic.Equiv.Defs
/-!
# Definition of the `Finite` typeclass
This file defines a typeclass `Finite` saying that `α : Sort*` is finite. A type is `Finite` if... |
Data\Finite\Set.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.Card
/-!
# Lemmas about `Finite` and `Set`s
In this file we prove two lemmas about `Finite` and `Set`s.
## Tags
finiteness, finite sets
-/
... |
Data\Finset\Attr.lean | /-
Copyright (c) 2024 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Aesop
import Qq
/-!
# Aesop rule set for finsets
This file defines `finsetNonempty`, an aesop rule set to prove that a given finset is nonempty.
-/
-- `finsetNo... |
Data\Finset\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, Jeremy Avigad, Minchao Wu, Mario Carneiro
-/
import Mathlib.Data.Finset.Attr
import Mathlib.Data.Multiset.FinsetOps
import Mathlib.Logic.Equiv.Set
import Math... |
Data\Finset\Card.lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad
-/
import Mathlib.Data.Finset.Image
/-!
# Cardinality of a finite set
This defines the cardinality of a `Finset` and provides induction princi... |
Data\Finset\Density.lean | /-
Copyright (c) 2023 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Algebra.Order.Field.Basic
import Mathlib.Algebra.Order.Field.Rat
import Mathlib.Data.Fintype.Card
/-!
# Density of a finite set
This defines the density ... |
Data\Finset\Fin.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Scott Morrison, Johan Commelin
-/
import Mathlib.Data.Finset.Card
/-!
# Finsets in `Fin n`
A few constructions for Finsets in `Fin n`.
## Main declarations
* `Finset.at... |
Data\Finset\Finsupp.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.BigOperators.Finsupp
import Mathlib.Data.Finset.Pointwise
import Mathlib.Data.Finsupp.Indicator
import Mathlib.Data.Fintype.BigOperators
/-!
# Fin... |
Data\Finset\Fold.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.Algebra.Order.Monoid.Unbundled.MinMax
import Mathlib.Data.Finset.Image
import Mathlib.Data.Multiset.Fold
import Mathlib.Algebra.Order.Monoid.Unbundled.... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.