path stringlengths 11 71 | content stringlengths 75 124k |
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Data\Finset\Functor.lean | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Scott Morrison
-/
import Mathlib.Data.Finset.Lattice
import Mathlib.Data.Finset.NAry
import Mathlib.Data.Multiset.Functor
/-!
# Functoriality of `Finset`
This file define... |
Data\Finset\Grade.lean | /-
Copyright (c) 2023 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Data.Finset.Card
import Mathlib.Data.Set.Finite
import Mathlib.Order.Atoms
import Mathlib.Order.Grade
/-!
# Finsets and multisets form a graded order
Thi... |
Data\Finset\Image.lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad, Minchao Wu, Mario Carneiro
-/
import Mathlib.Algebra.Group.Embedding
import Mathlib.Data.Fin.Basic
import Mathlib.Data.Finset.Union
/-! # Imag... |
Data\Finset\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.Grade
import Mathlib.Order.Interval.Finset.Basic
/-!
# Intervals of finsets as finsets
This file provides the `LocallyFiniteOrder` instance f... |
Data\Finset\Lattice.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.Order.Monoid.Unbundled.Pow
import Mathlib.Data.Finset.Fold
import Mathlib.Data.Finset.Option
import Mathlib.Data.Finset.Pi
import Mathlib.Data.... |
Data\Finset\MulAntidiagonal.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, Yaël Dillies
-/
import Mathlib.Data.Set.Pointwise.Basic
import Mathlib.Data.Set.MulAntidiagonal
/-! # Multiplication antidiagonal as a `Finset`.
We construct the ... |
Data\Finset\NAry.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.Data.Finset.Prod
import Mathlib.Data.Set.Finite
/-!
# N-ary images of finsets
This file defines `Finset.image₂`, the binary image of finsets. This is the... |
Data\Finset\NatAntidiagonal.lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.Algebra.Order.Antidiag.Prod
import Mathlib.Algebra.Order.Group.Nat
import Mathlib.Data.Finset.Card
import Mathlib.Data.Multiset.NatAntidiagonal
/-!
# ... |
Data\Finset\NatDivisors.lean | /-
Copyright (c) 2023 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa, Yury Kudryashov
-/
import Mathlib.NumberTheory.Divisors
import Mathlib.Data.Nat.Order.Lemmas
import Mathlib.Data.Finset.Pointwise
/-!
# `Nat.divisors` as a multiplicati... |
Data\Finset\NoncommProd.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.Algebra.BigOperators.Group.Finset
import Mathlib.Algebra.Group.Commute.Hom
import Mathlib.Data.Fintype.Card
/-!
# Products (respectively, sums) over... |
Data\Finset\Option.lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Mario Carneiro, Sean Leather
-/
import Mathlib.Data.Finset.Card
/-!
# Finite sets in `Option α`
In this file we define
* `Option.toFinset`: construct an empty or s... |
Data\Finset\Order.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Kenny Lau
-/
import Mathlib.Data.Finset.Basic
/-!
# Finsets of ordered types
-/
universe u v w
variable {α : Type u}
theorem Directed.finset_le {r : α → α → Prop} ... |
Data\Finset\Pairwise.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.Lattice
/-!
# Relations holding pairwise on finite sets
In this file we prove a few results about the interaction of `Set.PairwiseDisjoint` a... |
Data\Finset\Pi.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.Data.Finset.Card
import Mathlib.Data.Multiset.Pi
/-!
# The cartesian product of finsets
## Main definitions
* `Finset.pi`: Cartesian product of fins... |
Data\Finset\Piecewise.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.Fintype.Basic
import Mathlib.Order.Interval.Set.Basic
/-!
# Functions defined piecewise on a finset
This file defines `Finset.piecewise`: ... |
Data\Finset\PiInduction.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.Data.Finset.Sigma
import Mathlib.Data.Fintype.Card
/-!
# Induction principles for `∀ i, Finset (α i)`
In this file we prove a few induction princip... |
Data\Finset\PImage.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.Data.Finset.Option
import Mathlib.Data.PFun
import Mathlib.Data.Part
/-!
# Image of a `Finset α` under a partially defined function
In this file we... |
Data\Finset\Pointwise.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, Yaël Dillies
-/
import Mathlib.Algebra.Group.Action.Pi
import Mathlib.Data.Finset.NAry
import Mathlib.Data.Finset.Preimage
import Mathlib.Data.Set.Pointwise.Finite
... |
Data\Finset\Powerset.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.Lattice
import Mathlib.Data.Multiset.Powerset
/-!
# The powerset of a finset
-/
namespace Finset
open Function Multiset
variable {α : ... |
Data\Finset\Preimage.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.Finite
/-!
# Preimage of a `Finset` under an injective map.
-/
assert_not_exists Finset.sum
open Set Function
universe u v... |
Data\Finset\Prod.lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Oliver Nash
-/
import Mathlib.Data.Finset.Card
/-!
# Finsets in product types
This file defines finset constructions on the product type `α × β... |
Data\Finset\Sigma.lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Yaël Dillies, Bhavik Mehta
-/
import Mathlib.Data.Finset.Lattice
import Mathlib.Data.Set.Sigma
/-!
# Finite sets in a sigma type
This file defines a few `Finset` cons... |
Data\Finset\Slice.lean | /-
Copyright (c) 2021 Bhavik Mehta, Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Alena Gusakov, Yaël Dillies
-/
import Mathlib.Algebra.BigOperators.Group.Finset
import Mathlib.Order.Antichain
import Mathlib.Order.Interval.Finset.Nat
/-!
#... |
Data\Finset\SMulAntidiagonal.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.Data.Set.Pointwise.SMul
import Mathlib.Data.Set.SMulAntidiagonal
/-!
# Antidiagonal for scalar multiplication as a `Finset`.
Given partially ordered ... |
Data\Finset\Sort.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.RelIso.Set
import Mathlib.Data.Multiset.Sort
import Mathlib.Data.List.NodupEquivFin
import Mathlib.Data.Finset.Lattice
import Mathlib.Data.Fintyp... |
Data\Finset\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.Data.Multiset.Sum
import Mathlib.Data.Finset.Card
/-!
# Disjoint sum of finsets
This file defines the disjoint sum of two finsets as `Finset (α ⊕ β)`. Be... |
Data\Finset\Sups.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.Data.Finset.NAry
import Mathlib.Data.Finset.Slice
import Mathlib.Data.Set.Sups
/-!
# Set family operations
This file defines a few binary operations on `... |
Data\Finset\Sym.lean | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
[`data.finset.sym`@`98e83c3d541c77cdb7da20d79611a780ff8e7d90`..`02ba8949f486ebecf93fe7460f1ed0564b5e442c`](https://leanprover-community.github.io/mathlib-port-status/file/d... |
Data\Finset\Union.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.Finset.Basic
import Mathlib.Data.Multiset.Bind
import Mathlib.Order.SetNotation
/-!
# Unions of finite sets
This file defines the union of a fam... |
Data\Finset\Update.lean | /-
Copyright (c) 2023 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import Mathlib.Data.Finset.Basic
/-!
# Update a function on a set of values
This file defines `Function.updateFinset`, the operation that updates a function on ... |
Data\Finset\Pointwise\Interval.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.Finset.Pointwise
import Mathlib.Data.Set.Pointwise.Interval
/-! # Pointwise operations on intervals
This should be kept in sync with `Mathlib/Data/Set... |
Data\Finsupp\AList.lean | /-
Copyright (c) 2022 Violeta Hernández. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Violeta Hernández
-/
import Mathlib.Data.Finsupp.Basic
import Mathlib.Data.List.AList
/-!
# Connections between `Finsupp` and `AList`
## Main definitions
* `Finsupp.toAList`
* `A... |
Data\Finsupp\Antidiagonal.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.Finset.NatAntidiagonal
import Mathlib.Data.Finsupp.Multiset
import Mathlib.Data.Multiset.Antidiagonal
/-!
# The `Finsupp` counte... |
Data\Finsupp\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, Scott Morrison
-/
import Mathlib.Algebra.BigOperators.Finsupp
import Mathlib.Algebra.Module.Basic
import Mathlib.Algebra.Regular.SMul
import Mathlib.Data.Rat.BigOperato... |
Data\Finsupp\BigOperators.lean | /-
Copyright (c) 2022 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
import Mathlib.Algebra.BigOperators.Group.Finset
import Mathlib.Data.Finsupp.Defs
import Mathlib.Data.Finset.Pairwise
/-!
# Sums of collections of Finsupp, and th... |
Data\Finsupp\Defs.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Scott Morrison
-/
import Mathlib.Algebra.Group.Indicator
import Mathlib.Algebra.Group.Submonoid.Basic
import Mathlib.Data.Set.Finite
/-!
# Type of functions with finit... |
Data\Finsupp\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.Finsupp.ToDFinsupp
import Mathlib.Data.DFinsupp.Encodable
/-!
# `Encodable` and `Countable` instances for `α →₀ β`
In this file we provide inst... |
Data\Finsupp\Fin.lean | /-
Copyright (c) 2021 Ivan Sadofschi Costa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ivan Sadofschi Costa
-/
import Mathlib.Data.Finsupp.Defs
/-!
# `cons` and `tail` for maps `Fin n →₀ M`
We interpret maps `Fin n →₀ M` as `n`-tuples of elements of `M`,
We defin... |
Data\Finsupp\Fintype.lean | /-
Copyright (c) 2022 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Alex J. Best
-/
import Mathlib.Data.Finsupp.Defs
import Mathlib.Data.Fintype.Basic
/-!
# Finiteness and infiniteness of `Finsupp`
Some lemmas on the combination of `Finsup... |
Data\Finsupp\Indicator.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.Data.Finsupp.Defs
/-!
# Building finitely supported functions off finsets
This file defines `Finsupp.indicator` to help create finsupps from finsets.
##... |
Data\Finsupp\Interval.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.Data.Finset.Finsupp
import Mathlib.Data.Finsupp.Order
import Mathlib.Order.Interval.Finset.Basic
/-!
# Finite intervals of finitely supported functions
T... |
Data\Finsupp\Lex.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.Finsupp.Order
import Mathlib.Data.DFinsupp.Lex
import Mathlib.Data.Finsupp.ToDFinsupp
/-!
# Lexicographic order on finitely supported functions
Th... |
Data\Finsupp\Multiset.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.Data.Finsupp.Basic
import Mathlib.Data.Finsupp.Order
/-!
# Equivalence between `Multiset` and `ℕ`-valued finitely supported functions
This defines `F... |
Data\Finsupp\NeLocus.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.Finsupp.Defs
/-!
# Locus of unequal values of finitely supported functions
Let `α N` be two Types, assume that `N` has a `0` and let `f g : α →₀ N... |
Data\Finsupp\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.Finsupp.Defs
/-!
# Notation for `Finsupp`
This file provides `fun₀ | 3 => a | 7 => b` notation for `Finsupp`, which desugars to
`Finsupp.update` and `... |
Data\Finsupp\Order.lean | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Aaron Anderson
-/
import Mathlib.Algebra.Order.Module.Defs
import Mathlib.Data.Finsupp.Basic
/-!
# Pointwise order on finitely supported functions
This file lifts ord... |
Data\Finsupp\Pointwise.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.Module.Defs
import Mathlib.Algebra.Ring.Pi
import Mathlib.Data.Finsupp.Defs
/-!
# The pointwise product on `Finsupp`.
For the convolution pro... |
Data\Finsupp\PWO.lean | /-
Copyright (c) 2022 Alex J. Best. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex J. Best
-/
import Mathlib.Data.Finsupp.Order
import Mathlib.Order.WellFoundedSet
/-!
# Partial well ordering on finsupps
This file contains the fact that finitely supported functi... |
Data\Finsupp\ToDFinsupp.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.Module.Equiv.Defs
import Mathlib.Data.DFinsupp.Basic
import Mathlib.Data.Finsupp.Basic
/-!
# Conversion between `Finsupp` and homogenous `DFinsupp`
... |
Data\Finsupp\Weight.lean | /-
Copyright (c) 2024 Antoine Chambert-Loir, María Inés de Frutos Fernández. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir, María Inés de Frutos Fernández
-/
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Algebra.Order.Mod... |
Data\Finsupp\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.WellFounded
import Mathlib.Data.Finsupp.Lex
/-!
# Well-foundedness of the lexicographic and product orders on `Finsupp`
`Finsupp.Lex.wellFounded`... |
Data\Fintype\Basic.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.Finset.Image
import Mathlib.Data.List.FinRange
/-!
# Finite types
This file defines a typeclass to state that a type is finite.
## Main declara... |
Data\Fintype\BigOperators.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.Fintype.Option
import Mathlib.Data.Fintype.Sigma
import Mathlib.Data.Fintype.Sum
import Mathlib.Data.Fintype.Prod
import Mathlib.Data.Fintype.Vect... |
Data\Fintype\Card.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.Fintype.Basic
import Mathlib.Data.Finset.Card
import Mathlib.Data.List.NodupEquivFin
import Mathlib.Data.Set.Image
import Mathlib.Order.WellFounde... |
Data\Fintype\CardEmbedding.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.Data.Fintype.BigOperators
import Mathlib.Logic.Equiv.Embedding
/-!
# Number of embeddings
This file establishes the cardinality of `α ↪ β` in full ge... |
Data\Fintype\Fin.lean | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import Mathlib.Order.Interval.Finset.Fin
/-!
# The structure of `Fintype (Fin n)`
This file contains some basic results about the `Fintype` instance for `Fin`,
especially... |
Data\Fintype\Lattice.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.Fintype.Card
import Mathlib.Data.Finset.Lattice
/-!
# Lemmas relating fintypes and order/lattice structure.
-/
open Function
open Nat
univers... |
Data\Fintype\List.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.Data.Finset.Powerset
/-!
# Fintype instance for nodup lists
The subtype of `{l : List α // l.nodup}` over a `[Fi... |
Data\Fintype\Option.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.Fintype.Card
import Mathlib.Data.Finset.Option
/-!
# fintype instances for option
-/
assert_not_exists MonoidWithZero
assert_not_exists MulActio... |
Data\Fintype\Order.lean | /-
Copyright (c) 2021 Peter Nelson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Peter Nelson, Yaël Dillies
-/
import Mathlib.Data.Finset.Order
import Mathlib.Order.Atoms
import Mathlib.Data.Set.Finite
/-!
# Order structures on finite types
This file provides order... |
Data\Fintype\Parity.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.Fintype.Card
/-!
# The cardinality of `Fin 2` is even.
-/
variable {α : Type*}
namespace Fintype
instance IsSquare.decidablePred [Mul α] [Fin... |
Data\Fintype\Perm.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.Fintype.Card
import Mathlib.GroupTheory.Perm.Basic
import Mathlib.Tactic.Ring
/-!
# `Fintype` instances for `Equiv` and `Perm`
Main declarations... |
Data\Fintype\Pi.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.Finset.Card
import Mathlib.Data.Finset.Pi
import Mathlib.Data.Fintype.Basic
/-!
# Fintype instances for pi types
-/
open Finset Function
variab... |
Data\Fintype\Powerset.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.Fintype.Card
import Mathlib.Data.Finset.Powerset
/-!
# fintype instance for `Set α`, when `α` is a fintype
-/
variable {α : Type*}
open Finset... |
Data\Fintype\Prod.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.Fintype.Card
import Mathlib.Data.Finset.Prod
/-!
# fintype instance for the product of two fintypes.
-/
open Function
open Nat
universe u v
... |
Data\Fintype\Quotient.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.Basic
/-!
# Quotients of families indexed by a finite type
This file provides `Quotient.finChoice`, a mechanism to go from a finite fami... |
Data\Fintype\Shrink.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 Mathlib.Data.Countable.Small
import Mathlib.Data.Fintype.Card
/-!
# Fintype instance for `Shrink`
-/
universe u v
variable {α : Type u} [Fintype α]
noncomputabl... |
Data\Fintype\Sigma.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.Fintype.Basic
import Mathlib.Data.Finset.Sigma
/-!
# fintype instances for sigma types
-/
open Function
open Nat
universe u v
variable {ι α ... |
Data\Fintype\Sort.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.Finset.Sort
import Mathlib.Data.Fintype.Basic
/-!
# Sorting a finite type
This file provides two equivalences for linearly ordered fintypes:
* `... |
Data\Fintype\Sum.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.Fintype.Card
import Mathlib.Data.Finset.Sum
import Mathlib.Logic.Embedding.Set
/-!
## Instances
We provide the `Fintype` instance for the sum of... |
Data\Fintype\Units.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.Fintype.Prod
import Mathlib.Data.Fintype.Sum
import Mathlib.SetTheory.Cardinal.Finite
/-!
# fintype instances relating to units
-/
variable {α ... |
Data\Fintype\Vector.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.Fintype.Pi
import Mathlib.Data.Sym.Basic
/-!
# `Vector α n` and `Sym α n` are fintypes when `α` is.
-/
open Mathlib (Vector)
variable {α : Type... |
Data\FP\Basic.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.Semiquot
import Mathlib.Data.Nat.Size
import Mathlib.Tactic.Ring.RingNF
/-!
# Implementation of floating-point numbers (experimental).
-/
-- Por... |
Data\FunLike\Basic.lean | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import Mathlib.Logic.Function.Basic
import Mathlib.Util.CompileInductive
/-!
# Typeclass for a type `F` with an injective map to `A → B`
This typeclass is primarily for u... |
Data\FunLike\Embedding.lean | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import Mathlib.Data.FunLike.Basic
/-!
# Typeclass for a type `F` with an injective map to `A ↪ B`
This typeclass is primarily for use by embeddings such as `RelEmbedding`... |
Data\FunLike\Equiv.lean | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import Mathlib.Data.FunLike.Embedding
/-!
# Typeclass for a type `F` with an injective map to `A ≃ B`
This typeclass is primarily for use by isomorphisms like `MonoidEqui... |
Data\FunLike\Fintype.lean | /-
Copyright (c) 2022 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import Mathlib.Data.Finite.Basic
import Mathlib.Data.Fintype.Basic
import Mathlib.Data.FunLike.Basic
/-!
# Finiteness of `DFunLike` types
We show a type `F` with a `DFunL... |
Data\Int\AbsoluteValue.lean | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import Mathlib.Algebra.GroupWithZero.Action.Units
import Mathlib.Algebra.Module.Defs
import Mathlib.Algebra.Order.AbsoluteValue
import Mathlib.Data.Int.Cast.Lemmas
/-!
# A... |
Data\Int\Align.lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
-/
/-!
# Align statements for results about the integers
-/
|
Data\Int\Associated.lean | /-
Copyright (c) 2022 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import Mathlib.Algebra.Associated.Basic
import Mathlib.Algebra.Ring.Int
/-!
# Associated elements and the integers
This file contains some results on equality up to units ... |
Data\Int\Bitwise.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.Ring.Int
import Mathlib.Data.Nat.Bitwise
import Mathlib.Data.Nat.Size
/-!
# Bitwise operations on integers
Possibly only of archaeological sign... |
Data\Int\CardIntervalMod.lean | /-
Copyright (c) 2024 Jeremy Tan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Tan
-/
import Mathlib.Data.Int.Interval
import Mathlib.Data.Int.ModEq
import Mathlib.Data.Nat.Count
import Mathlib.Data.Rat.Floor
import Mathlib.Order.Interval.Finset.Nat
/-!
# Cou... |
Data\Int\CharZero.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.Group.Support
import Mathlib.Data.Int.Cast.Field
import Mathlib.Data.Int.Cast.Lemmas
/-!
# Injectivity of `Int.Cast` into characteristic zero ... |
Data\Int\ConditionallyCompleteOrder.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.Order.ConditionallyCompleteLattice.Basic
import Mathlib.Data.Int.LeastGreatest
/-!
## `ℤ` forms a conditionally complete linear order
The integer... |
Data\Int\Defs.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.Data.Int.Notation
import Mathlib.Data.Nat.Defs
import Mathlib.Algebra.Group.ZeroOne
import Mathlib.Logic.Nontrivial.Defs
import Mathlib.Tactic.Convert
im... |
Data\Int\GCD.lean | /-
Copyright (c) 2018 Guy Leroy. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sangwoo Jo (aka Jason), Guy Leroy, Johannes Hölzl, Mario Carneiro
-/
import Mathlib.Algebra.Group.Int
import Mathlib.Algebra.GroupWithZero.Semiconj
import Mathlib.Order.Bounds.Basic
import ... |
Data\Int\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.Algebra.CharZero.Lemmas
import Mathlib.Algebra.Order.Group.Int
import Mathlib.Algebra.Ring.Int
import Mathlib.Order.Interval.Finset.Basic
/-!
# Finite int... |
Data\Int\LeastGreatest.lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Mario Carneiro
-/
import Mathlib.Algebra.Order.Ring.Int
import Mathlib.Data.Nat.Find
/-! # Least upper bound and greatest lower bound properties for integers
In this fi... |
Data\Int\Lemmas.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.Data.Int.Bitwise
import Mathlib.Data.Int.Order.Lemmas
import Mathlib.Data.Set.Function
import Mathlib.Order.Interval.Set.Basic
/-!
# Miscellaneous lemma... |
Data\Int\Log.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.Order.Floor
import Mathlib.Algebra.Order.Field.Power
import Mathlib.Data.Nat.Log
/-!
# Integer logarithms in a field with respect to a natural base
... |
Data\Int\ModEq.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.Data.Nat.ModEq
import Mathlib.Tactic.Abel
import Mathlib.Tactic.GCongr.Core
/-!
# Congruences modulo an integer
This file defines the equivalence relati... |
Data\Int\NatPrime.lean | /-
Copyright (c) 2020 Bryan Gin-ge Chen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Lacker, Bryan Gin-ge Chen
-/
import Mathlib.Data.Nat.Prime.Basic
/-!
# Lemmas about `Nat.Prime` using `Int`s
-/
open Nat
namespace Int
theorem not_prime_of_int_mul {a b :... |
Data\Int\Notation.lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
-/
/-!
# Notation `ℤ` for the integers.
-/
@[inherit_doc] notation "ℤ" => Int
|
Data\Int\Range.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Kenny Lau
-/
import Mathlib.Algebra.Order.Ring.Int
/-!
# Intervals in ℤ
This file defines integer ranges. `range m n` is the set of integers greater than `m` and strictly
... |
Data\Int\Sqrt.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.Nat.Defs
import Mathlib.Tactic.Common
/-!
# Square root of integers
This file defines the square root function on integers. `... |
Data\Int\Star.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 Mathlib.Algebra.Star.Order
import Mathlib.Algebra.Order.Monoid.Submonoid
import Mathlib.Algebra.Order.Ring.Basic
/-!
# Star ordered ring structure on `ℤ`
This fi... |
Data\Int\SuccPred.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.Ring.Int
import Mathlib.Data.Nat.SuccPred
/-!
# Successors and predecessors of integers
In this file, we show that `ℤ` is both an archimede... |
Data\Int\Cast\Basic.lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Gabriel Ebner
-/
import Mathlib.Data.Int.Cast.Defs
import Mathlib.Algebra.Group.Basic
/-!
# Cast of integers (additional theorems)
This file proves additional propert... |
Data\Int\Cast\Defs.lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Gabriel Ebner
-/
import Mathlib.Data.Nat.Cast.Defs
/-!
# Cast of integers
This file defines the *canonical* homomorphism from the integers into an
additive group with... |
Data\Int\Cast\Field.lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import Mathlib.Algebra.Field.Defs
import Mathlib.Algebra.Ring.Int
/-!
# Cast of integers into fields
This file concerns the canonical homomorphism `ℤ → F`, where `F` ... |
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