path stringlengths 11 71 | content stringlengths 75 124k |
|---|---|
Data\Int\Cast\Lemmas.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.Ring.Hom.Basic
import Mathlib.Algebra.Ring.Int
/-!
# Cast of integers (additional theorems)
This file proves additional properties about the ... |
Data\Int\Cast\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.Nat.Cast.Prod
/-!
# The product of two `AddGroupWithOne`s.
-/
namespace Prod
variable {α β : Type*} [AddGroupWithOne α] [AddGroupWithOne β]
i... |
Data\Int\Order\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.Algebra.Order.Ring.Abs
/-!
# Further lemmas about the integers
The distinction between this file and `Data.Int.Order.Basic` is not particularly clear.
... |
Data\Int\Order\Units.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.Order.Ring.Abs
/-!
# Lemmas about units in `ℤ`, which interact with the order structure.
-/
namespace Int
theorem isUnit_iff_abs_eq {x : ℤ} :... |
Data\LazyList\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.Control.Traversable.Equiv
import Mathlib.Control.Traversable.Instances
import Batteries.Data.LazyList
import Mathlib.Lean.Thunk
/-!
## Definitions on lazy l... |
Data\List\AList.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.Sigma
/-!
# Association Lists
This file defines association lists. An association list is a list where every element consists o... |
Data\List\Basic.lean | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
-/
import Mathlib.Data.Nat.Defs
import Mathlib.Data.Option.Basic
import Mathlib.Data.List.Defs
im... |
Data\List\Chain.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, Yury Kudryashov
-/
import Mathlib.Logic.Relation
import Mathlib.Data.List.Forall2
import Mathlib.Data.List.Lex
import Mathlib.Data.List.Infix
/-!
# Relation... |
Data\List\Count.lean | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
-/
import Mathlib.Data.Nat.Defs
/-!
# Counting in lists
This file proves basic properties of `L... |
Data\List\Cycle.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.List
/-!
# Cycles of a list
Lists have an equivalence relation of whether they are rotational permutations of one another.
This relati... |
Data\List\Dedup.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.List.Nodup
import Mathlib.Data.List.Lattice
/-!
# Erasure of duplicates in a list
This file proves basic results about `List.dedup` (definition ... |
Data\List\Defs.lean | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
-/
import Mathlib.Data.Nat.Notation
import Mathlib.Control.Functor
import Mathlib.Data.SProd
impo... |
Data\List\Destutter.lean | /-
Copyright (c) 2022 Eric Rodriguez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Rodriguez, Eric Wieser
-/
import Mathlib.Data.List.Chain
/-!
# Destuttering of Lists
This file proves theorems about `List.destutter` (in `Data.List.Defs`), which greedily remov... |
Data\List\DropRight.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.Data.List.Infix
/-!
# Dropping or taking from lists on the right
Taking or removing element from the tail end of a list
## Main definitions
- `rd... |
Data\List\Duplicate.lean | /-
Copyright (c) 2021 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky, Chris Hughes
-/
import Mathlib.Data.List.Nodup
/-!
# List duplicates
## Main definitions
* `List.Duplicate x l : Prop` is an inductive property that holds when `x`... |
Data\List\Enum.lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Yakov Pechersky, Eric Wieser
-/
import Batteries.Tactic.Alias
import Mathlib.Tactic.TypeStar
import Mathlib.Data.Nat.Notation
/-!
# Properties of `List.enum`
-/
names... |
Data\List\FinRange.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, Scott Morrison, Alex Keizer
-/
import Mathlib.Data.List.OfFn
import Mathlib.Data.List.Range
/-!
# Lists of elements of `Fin n`
This file develops some resu... |
Data\List\Forall2.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johannes Hölzl
-/
import Mathlib.Data.List.Basic
/-!
# Double universal quantification on a list
This file provides an API for `List.Forall₂` (definition in `Data.Lis... |
Data\List\GetD.lean | /-
Copyright (c) 2024 Bolton Bailey. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bolton Bailey, Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn,
Mario Carneiro
-/
import Mathlib.Data.List.Defs
import Mathlib.Data.Option.Basic
import Mathlib.Init... |
Data\List\Indexes.lean | /-
Copyright (c) 2020 Jannis Limperg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jannis Limperg
-/
import Mathlib.Data.List.OfFn
import Mathlib.Data.List.Range
import Mathlib.Data.List.Zip
/-!
# Lemmas about List.*Idx functions.
Some specification lemmas for `Lis... |
Data\List\Infix.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
/-!
# Prefixes, suffixes, infixes
This file proves properties about
* `List.isPrefix`: `l₁` is a prefix of `l₂` if `l₂` starts with `... |
Data\List\InsertNth.lean | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
-/
import Mathlib.Data.List.Basic
/-!
# insertNth
Proves various lemmas about `List.insertNth`.... |
Data\List\Intervals.lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.Data.List.Lattice
import Mathlib.Data.Bool.Basic
import Mathlib.Init.Data.Nat.Lemmas
import Mathlib.Order.Lattice
/-!
# Intervals in ℕ
This file defin... |
Data\List\Iterate.lean | /-
Copyright (c) 2024 Miyahara Kō. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Miyahara Kō
-/
import Mathlib.Algebra.Order.Ring.Nat
import Mathlib.Data.List.Defs
import Mathlib.Data.Set.Function
/-!
# iterate
Proves various lemmas about `List.iterate`.
-/
variab... |
Data\List\Join.lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Floris van Doorn, Mario Carneiro, Martin Dvorak
-/
import Mathlib.Data.List.Basic
/-!
# Join of a list of lists
This file proves basic properties of `List.join`, w... |
Data\List\Lattice.lean | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro,
Scott Morrison
-/
import Mathlib.Data.List.Basic
/-!
# Lattice structure of lists
This files p... |
Data\List\Lemmas.lean | /-
Copyright (c) 2021 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky, Yury Kudryashov
-/
import Mathlib.Data.Set.Image
import Mathlib.Data.List.InsertNth
import Mathlib.Init.Data.List.Lemmas
/-! # Some lemmas about lists involving sets... |
Data\List\Lex.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.Order.RelClasses
import Mathlib.Data.List.Basic
/-!
# Lexicographic ordering of lists.
The lexicographic order on `List α` is defined by `L < M` iff
... |
Data\List\MinMax.lean | /-
Copyright (c) 2019 Minchao Wu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Minchao Wu, Chris Hughes, Mantas Bakšys
-/
import Mathlib.Data.List.Basic
import Mathlib.Order.MinMax
import Mathlib.Order.WithBot
/-!
# Minimum and maximum of lists
## Main definitions
... |
Data\List\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.Data.List.Nodup
/-!
# Antidiagonals in ℕ × ℕ as lists
This file defines the antidiagonals of ℕ × ℕ as lists: the `n`-th antidiagonal is the list of
p... |
Data\List\Nodup.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.List.Forall2
import Mathlib.Data.Set.Pairwise.Basic
import Mathlib.Init.Data.Fin.Basic
/-!
# Lists with no duplicates
`List.Nodup` is... |
Data\List\NodupEquivFin.lean | /-
Copyright (c) 2020 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.List.Duplicate
import Mathlib.Data.List.Sort
/-!
# Equivalence between `Fin (length l)` and elements of a list
Given a list `l`,
* if `... |
Data\List\OfFn.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.Fin.Tuple.Basic
import Mathlib.Data.List.Basic
/-!
# Lists from functions
Theorems and lemmas for dealing with `List.ofFn`, which converts a fun... |
Data\List\Pairwise.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.Pairwise
import Mathlib.Logic.Relation
import Mathlib.Data.List.Basic
/-!
# Pairwise relations on a list
This file provides basic results about... |
Data\List\Palindrome.lean | /-
Copyright (c) 2020 Google LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Wong
-/
import Mathlib.Data.List.Basic
/-!
# Palindromes
This module defines *palindromes*, lists which are equal to their reverse.
The main result is the `Palindrome` inductive t... |
Data\List\Perm.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, Mario Carneiro
-/
import Mathlib.Data.List.Count
import Mathlib.Data.List.Dedup
import Mathlib.Data.List.Duplicate
import Mathlib.Data.List.Ins... |
Data\List\Permutation.lean | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
-/
import Mathlib.Data.List.Join
/-!
# Permutations of a list
In this file we prove properties ... |
Data\List\Pi.lean | /-
Copyright (c) 2023 Yuyang Zhao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuyang Zhao
-/
import Mathlib.Data.Multiset.Pi
/-!
# The cartesian product of lists
## Main definitions
* `List.pi`: Cartesian product of lists indexed by a list.
-/
namespace List
n... |
Data\List\Prime.lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jens Wagemaker, Anne Baanen
-/
import Mathlib.Algebra.Associated.Basic
import Mathlib.Algebra.BigOperators.Group.List
import Mathlib.Data.List.Perm
/-!
# Products of l... |
Data\List\ProdSigma.lean | /-
Copyright (c) 2015 Leonardo de Moura. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Mario Carneiro
-/
import Mathlib.Data.List.Basic
import Mathlib.Data.Sigma.Basic
import Batteries.Data.Nat.Lemmas
/-!
# Lists in product and sigma types
This fi... |
Data\List\Range.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, Scott Morrison
-/
import Mathlib.Data.List.Chain
import Mathlib.Data.List.Nodup
import Mathlib.Data.List.Pairwise
import Batteries.Data.Nat.Lemmas
/-!
# Ran... |
Data\List\ReduceOption.lean | /-
Copyright (c) 2020 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
import Mathlib.Data.List.Basic
/-!
# Properties of `List.reduceOption`
In this file we prove basic lemmas about `List.reduceOption`.
-/
namespace List
variable ... |
Data\List\Rotate.lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Yakov Pechersky
-/
import Mathlib.Data.List.Nodup
import Mathlib.Data.Nat.Defs
import Mathlib.Data.List.Infix
/-!
# List rotation
This file proves basic results about `Li... |
Data\List\Sections.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.List.Forall2
/-!
# List sections
This file proves some stuff about `List.sections` (definition in `Data.List.Defs`). A section of a
list of lists... |
Data\List\Sigma.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Sean Leather
-/
import Mathlib.Data.List.Perm
import Mathlib.Data.List.Pairwise
/-!
# Utilities for lists of sigmas
This file includes several ways of interacting wit... |
Data\List\Sort.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.List.OfFn
import Mathlib.Data.List.Nodup
import Mathlib.Data.List.Infix
import Mathlib.Order.Fin.Basic
/-!
# Sorting algorithms on lists
In this f... |
Data\List\Sublists.lean | /-
Copyright (c) 2019 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Data.Nat.Choose.Basic
import Mathlib.Data.List.Perm
import Mathlib.Data.List.Range
/-! # sublists
`List.Sublists` gives a list of all (not necessaril... |
Data\List\Sym.lean | /-
Copyright (c) 2023 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
import Mathlib.Data.Nat.Choose.Basic
import Mathlib.Data.Sym.Sym2
/-! # Unordered tuples of elements of a list
Defines `List.sym` and the specialized `List.sym2` for comp... |
Data\List\TFAE.lean | /-
Copyright (c) 2018 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Simon Hudon
-/
import Batteries.Data.List.Lemmas
import Batteries.Tactic.Classical
import Mathlib.Tactic.TypeStar
/-!
# The Following Are Equivalent
This file allows ... |
Data\List\ToFinsupp.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.Data.Finsupp.Defs
import Mathlib.Data.List.GetD
/-!
# Lists as finsupp
## Main definitions
- `List.toFinsupp`: Interpret a list as a finitely sup... |
Data\List\Zip.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.List.Forall2
/-!
# zip & unzip
This file provides results about `List.zipWith`, `List.zip` and `List.unzip` (definitions are in
core ... |
Data\List\EditDistance\Bounds.lean | /-
Copyright (c) 2023 Kim Liesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Liesinger
-/
import Mathlib.Algebra.Order.Monoid.Canonical.Defs
import Mathlib.Data.List.Infix
import Mathlib.Data.List.MinMax
import Mathlib.Data.List.EditDistance.Defs
/-!
# Lowe... |
Data\List\EditDistance\Defs.lean | /-
Copyright (c) 2023 Kim Liesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Liesinger
-/
import Mathlib.Algebra.Group.Defs
/-!
# Levenshtein distances
We define the Levenshtein edit distance `levenshtein C xy ys` between two `List α`,
with a customizable ... |
Data\List\EditDistance\Estimator.lean | /-
Copyright (c) 2023 Kim Liesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Liesinger
-/
import Mathlib.Data.List.EditDistance.Bounds
import Mathlib.Order.Estimator
/-!
# `Estimator` for Levenshtein distance.
The usual algorithm for computing Levenshtein ... |
Data\Matrix\Auto.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.Expr
import Mathlib.Data.Matrix.Reflection
/-! # Automatically generated lemmas for working with concrete matrices
In Mathlib3, this file contained... |
Data\Matrix\Basic.lean | /-
Copyright (c) 2018 Ellen Arlt. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ellen Arlt, Blair Shi, Sean Leather, Mario Carneiro, Johan Commelin, Lu-Ming Zhang
-/
import Mathlib.Algebra.Algebra.Opposite
import Mathlib.Algebra.Algebra.Pi
import Mathlib.Algebra.BigOp... |
Data\Matrix\Basis.lean | /-
Copyright (c) 2020 Jalex Stark. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jalex Stark, Scott Morrison, Eric Wieser, Oliver Nash, Wen Yang
-/
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.Matrix.Trace
/-!
# Matrices with a single non-zero elemen... |
Data\Matrix\Block.lean | /-
Copyright (c) 2018 Ellen Arlt. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ellen Arlt, Blair Shi, Sean Leather, Mario Carneiro, Johan Commelin
-/
import Mathlib.Data.Matrix.Basic
/-!
# Block Matrices
## Main definitions
* `Matrix.fromBlocks`: build a block mat... |
Data\Matrix\CharP.lean | /-
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import Mathlib.Algebra.CharP.Defs
import Mathlib.Data.Matrix.Basic
/-!
# Matrices in prime characteristic
In this file we prove that matrices over a ring of charact... |
Data\Matrix\ColumnRowPartitioned.lean | /-
Copyright (c) 2023 Mohanad ahmed. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mohanad Ahmed
-/
import Mathlib.Data.Matrix.Basic
import Mathlib.Data.Matrix.Block
import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
/-! # Block Matrices from Rows and Columns
T... |
Data\Matrix\Composition.lean | /-
Copyright (c) 2024 Yunzhou Xie. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Yunzhou Xie
-/
import Mathlib.Data.Matrix.Basic
/-!
# Composition of matrices
This file shows that Mₙ(Mₘ(R)) ≃ Mₙₘ(R), Mₙ(Rᵒᵖ) ≃ₐ[K] Mₙ(R)ᵒᵖ
and also different levels of... |
Data\Matrix\DMatrix.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.Algebra.Group.Hom.Defs
/-!
# Dependent-typed matrices
-/
universe u u' v w z
/-- `DMatrix m n` is the type of dependently typed matrices
whose rows... |
Data\Matrix\DualNumber.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.Algebra.DualNumber
import Mathlib.Data.Matrix.Basic
/-!
# Matrices of dual numbers are isomorphic to dual numbers over matrices
Showing this for the more g... |
Data\Matrix\Hadamard.lean | /-
Copyright (c) 2021 Lu-Ming Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lu-Ming Zhang
-/
import Mathlib.LinearAlgebra.Matrix.Trace
/-!
# Hadamard product of matrices
This file defines the Hadamard product `Matrix.hadamard`
and contains basic properties ab... |
Data\Matrix\Invertible.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.Basic
/-! # Extra lemmas about invertible matrices
A few of the `Invertible` lemmas generalize to multiplication of rectangular matrices.
For ... |
Data\Matrix\Kronecker.lean | /-
Copyright (c) 2021 Filippo A. E. Nuccio. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Filippo A. E. Nuccio, Eric Wieser
-/
import Mathlib.Data.Matrix.Basic
import Mathlib.Data.Matrix.Block
import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
import Mathlib.Linear... |
Data\Matrix\Notation.lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Eric Wieser
-/
import Mathlib.Algebra.Group.Fin.Tuple
import Mathlib.Data.Matrix.Basic
import Mathlib.Data.Matrix.RowCol
import Mathlib.Data.Fin.VecNotation
import Mathlib.Ta... |
Data\Matrix\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.Matrix.Basic
import Mathlib.Data.PEquiv
/-!
# partial equivalences for matrices
Using partial equivalences to represent matrices.
This file introduc... |
Data\Matrix\Rank.lean | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Eric Wieser
-/
import Mathlib.LinearAlgebra.Determinant
import Mathlib.LinearAlgebra.FiniteDimensional
import Mathlib.LinearAlgebra.Matrix.Diagonal
import Mathlib.Linea... |
Data\Matrix\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.Matrix.Notation
import Mathlib.Data.Matrix.Basic
import Mathlib.Data.Fin.Tuple.Reflection
/-!
# Lemmas for concrete matrices `Matrix (Fin m) (Fin n) α`... |
Data\Matrix\RowCol.lean | /-
Copyright (c) 2019 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Eric Wieser
-/
import Mathlib.Data.Matrix.Basic
/-!
# Row and column matrices
This file provides results about row and column matrices
## Main definitions
* `Matrix.row r... |
Data\Matroid\Basic.lean | /-
Copyright (c) 2023 Peter Nelson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Peter Nelson
-/
import Mathlib.Data.Set.Card
import Mathlib.Order.Minimal
import Mathlib.Data.Matroid.Init
/-!
# Matroids
A `Matroid` is a structure that combinatorially abstracts
the ... |
Data\Matroid\Closure.lean | /-
Copyright (c) 2024 Peter Nelson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Peter Nelson
-/
import Mathlib.Data.Matroid.Restrict
import Mathlib.Order.Closure
/-!
# Matroid Closure
A `Flat` of a matroid `M` is a combinatorial analogue of a subspace of a vector ... |
Data\Matroid\Constructions.lean | /-
Copyright (c) 2024 Peter Nelson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Peter Nelson
-/
import Mathlib.Data.Matroid.Restrict
/-!
# Some constructions of matroids
This file defines some very elementary examples of matroids, namely those with at most one bas... |
Data\Matroid\Dual.lean | /-
Copyright (c) 2023 Peter Nelson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Peter Nelson
-/
import Mathlib.Data.Matroid.IndepAxioms
/-!
# Matroid Duality
For a matroid `M` on ground set `E`, the collection of complements of the bases of `M` is the
collection o... |
Data\Matroid\IndepAxioms.lean | /-
Copyright (c) 2023 Peter Nelson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Peter Nelson
-/
import Mathlib.Data.Matroid.Basic
/-!
# Matroid Independence and Basis axioms
Matroids in mathlib are defined axiomatically in terms of bases,
but can be described just... |
Data\Matroid\Init.lean | /-
Copyright (c) 2023 Peter Nelson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Peter Nelson
-/
import Aesop
/-!
# Matroid Rule Set
This module defines the `Matroid` Aesop rule set which is used by the
`aesop_mat` tactic. Aesop rule sets only become visible once t... |
Data\Matroid\Map.lean | /-
Copyright (c) 2024 Peter Nelson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Peter Nelson
-/
import Mathlib.Data.Matroid.Constructions
import Mathlib.Data.Set.Notation
/-!
# Maps between matroids
This file defines maps and comaps, which move a matroid on one ty... |
Data\Matroid\Restrict.lean | /-
Copyright (c) 2023 Peter Nelson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Peter Nelson
-/
import Mathlib.Data.Matroid.Dual
/-!
# Matroid Restriction
Given `M : Matroid α` and `R : Set α`, the independent sets of `M` that are contained in `R`
are the independ... |
Data\Matroid\Sum.lean | /-
Copyright (c) 2024 Peter Nelson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Peter Nelson
-/
import Mathlib.Data.Matroid.Map
import Mathlib.Logic.Embedding.Set
/-!
# Sums of matroids
The *sum* `M` of a collection `M₁, M₂, ..` of matroids is a matroid on the dis... |
Data\MLList\BestFirst.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 Batteries.Data.MLList.Basic
import Mathlib.Data.Prod.Lex
import Mathlib.Order.Estimator
import Mathlib.Data.Set.Finite
/-!
# Best first search
We perform bes... |
Data\MLList\Dedup.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 Batteries.Data.MLList.Basic
import Batteries.Data.HashMap.Basic
/-!
# Lazy deduplication of lazy lists
-/
open Batteries
namespace MLList
variable {α β : T... |
Data\MLList\DepthFirst.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 Lean.Data.HashSet
import Batteries.Data.MLList.Basic
import Mathlib.Control.Combinators
/-!
# Depth first search
We perform depth first search of a tree or g... |
Data\MLList\IO.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 Batteries.Data.MLList.Basic
/-!
# Reading from handles, files, and processes as lazy lists.
-/
open System IO.FS
namespace MLList
/-- Read lines of text fr... |
Data\MLList\Split.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 Batteries.Data.MLList.Basic
import Mathlib.Data.ULift
/-!
# Functions for splitting monadic lazy lists.
-/
namespace MLList
universe u
variable {α β : Type ... |
Data\Multiset\Antidiagonal.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.Multiset.Powerset
/-!
# The antidiagonal on a multiset.
The antidiagonal of a multiset `s` consists of all pairs `(t₁, t₂)`
such that `t₁ + t₂ =... |
Data\Multiset\Basic.lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Algebra.Group.Nat
import Mathlib.Algebra.Order.Sub.Canonical
import Mathlib.Data.List.Perm
import Mathlib.Data.Set.List
import Mathlib.Init.Quot... |
Data\Multiset\Bind.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.BigOperators.Group.Multiset
import Mathlib.Data.Multiset.Dedup
/-!
# Bind operation for multisets
This file defines a few basic operations on... |
Data\Multiset\Dedup.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.Multiset.Nodup
/-!
# Erasing duplicates in a multiset.
-/
namespace Multiset
open List
variable {α β : Type*} [DecidableEq α]
/-! ### dedup ... |
Data\Multiset\FinsetOps.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.Multiset.Dedup
import Mathlib.Data.List.Infix
/-!
# Preparations for defining operations on `Finset`.
The operations here ignore multiplicities,... |
Data\Multiset\Fintype.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.Algebra.BigOperators.Group.Finset
import Mathlib.Data.Fintype.Card
/-!
# Multiset coercion to type
This module defines a `CoeSort` instance for multisets a... |
Data\Multiset\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.Data.Multiset.Bind
/-!
# The fold operation for a commutative associative operation over a multiset.
-/
namespace Multiset
variable {α β : Type*}
... |
Data\Multiset\Functor.lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johannes Hölzl, Simon Hudon, Kenny Lau
-/
import Mathlib.Data.Multiset.Bind
import Mathlib.Control.Traversable.Lemmas
import Mathlib.Control.Traversable.Instances
/-!
# F... |
Data\Multiset\Interval.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.Interval
import Mathlib.Data.DFinsupp.Multiset
import Mathlib.Order.Interval.Finset.Nat
/-!
# Finite intervals of multisets
This file provide... |
Data\Multiset\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.Data.Multiset.FinsetOps
import Mathlib.Data.Multiset.Fold
/-!
# Lattice operations on multisets
-/
namespace Multiset
variable {α : Type*}
/-! ###... |
Data\Multiset\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.Data.Multiset.Nodup
import Mathlib.Data.List.NatAntidiagonal
/-!
# Antidiagonals in ℕ × ℕ as multisets
This file defines the antidiagonals of ℕ × ℕ a... |
Data\Multiset\Nodup.lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Data.Multiset.Range
import Mathlib.Data.List.Pairwise
/-!
# The `Nodup` predicate for multisets without duplicate elements.
-/
namespace Mult... |
Data\Multiset\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.Multiset.Bind
/-!
# The cartesian product of multisets
## Main definitions
* `Multiset.pi`: Cartesian product of multisets indexed by a multise... |
Data\Multiset\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.List.Sublists
import Mathlib.Data.List.Zip
import Mathlib.Data.Multiset.Bind
/-!
# The powerset of a multiset
-/
namespace Multiset
open List
... |
Data\Multiset\Range.lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Data.Multiset.Basic
/-! # `Multiset.range n` gives `{0, 1, ..., n-1}` as a multiset. -/
open List Nat
namespace Multiset
-- range
/-- `rang... |
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