path stringlengths 11 71 | content stringlengths 75 124k |
|---|---|
Data\PNat\Find.lean | /-
Copyright (c) 2022 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky, Floris van Doorn
-/
import Mathlib.Data.Nat.Find
import Mathlib.Data.PNat.Basic
/-!
# Explicit least witnesses to existentials on positive natural numbers
Implement... |
Data\PNat\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.Order.Interval.Finset.Nat
import Mathlib.Data.PNat.Defs
/-!
# Finite intervals of positive naturals
This file proves that `ℕ+` is a `LocallyFiniteOrder` ... |
Data\PNat\Prime.lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Neil Strickland
-/
import Mathlib.Data.Nat.Prime.Defs
import Mathlib.Data.PNat.Basic
/-!
# Primality and GCD on pnat
This file extends the theory of `ℕ+` with ... |
Data\PNat\Xgcd.lean | /-
Copyright (c) 2019 Neil Strickland. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Neil Strickland
-/
import Mathlib.Tactic.Ring
import Mathlib.Data.PNat.Prime
/-!
# Euclidean algorithm for ℕ
This file sets up a version of the Euclidean algorithm that only works w... |
Data\Prod\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
-/
import Mathlib.Logic.Function.Defs
import Mathlib.Logic.Function.Iterate
import Mathlib.Tactic.Inhabit
/-!
# Extra facts about `Prod`
This file defines `Prod.swap :... |
Data\Prod\Lex.lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Minchao Wu
-/
import Mathlib.Order.BoundedOrder
/-!
# Lexicographic order
This file defines the lexicographic relation for pairs of orders, partial orders and linear ... |
Data\Prod\PProd.lean | /-
Copyright (c) 2020 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Logic.Function.Defs
/-!
# Extra facts about `PProd`
-/
open Function
variable {α β γ δ : Sort*}
namespace PProd
@[simp]
theorem mk.eta {p : PProd α β} ... |
Data\Prod\TProd.lean | /-
Copyright (c) 2020 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import Mathlib.Data.List.Nodup
/-!
# Finite products of types
This file defines the product of types over a list. For `l : List ι` and `α : ι → Type v` we define... |
Data\PSigma\Order.lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Minchao Wu
-/
import Mathlib.Data.Sigma.Lex
import Mathlib.Order.BoundedOrder
import Mathlib.Mathport.Notation
import Init.NotationExtra
import Mathlib.Data.Sigma.Basic... |
Data\QPF\Multivariate\Basic.lean | /-
Copyright (c) 2018 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Simon Hudon
-/
import Mathlib.Data.PFunctor.Multivariate.Basic
/-!
# Multivariate quotients of polynomial functors.
Basic definition of multivariate QPF. QPFs form a co... |
Data\QPF\Multivariate\Constructions\Cofix.lean | /-
Copyright (c) 2018 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Simon Hudon
-/
import Mathlib.Control.Functor.Multivariate
import Mathlib.Data.PFunctor.Multivariate.Basic
import Mathlib.Data.PFunctor.Multivariate.M
import Mathlib.Data... |
Data\QPF\Multivariate\Constructions\Comp.lean | /-
Copyright (c) 2018 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Simon Hudon
-/
import Mathlib.Data.PFunctor.Multivariate.Basic
import Mathlib.Data.QPF.Multivariate.Basic
/-!
# The composition of QPFs is itself a QPF
We define compos... |
Data\QPF\Multivariate\Constructions\Const.lean | /-
Copyright (c) 2020 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import Mathlib.Control.Functor.Multivariate
import Mathlib.Data.QPF.Multivariate.Basic
/-!
# Constant functors are QPFs
Constant functors map every type vectors to the sa... |
Data\QPF\Multivariate\Constructions\Fix.lean | /-
Copyright (c) 2018 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Simon Hudon
-/
import Mathlib.Data.PFunctor.Multivariate.W
import Mathlib.Data.QPF.Multivariate.Basic
/-!
# The initial algebra of a multivariate qpf is again a qpf.
Fo... |
Data\QPF\Multivariate\Constructions\Prj.lean | /-
Copyright (c) 2020 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import Mathlib.Control.Functor.Multivariate
import Mathlib.Data.QPF.Multivariate.Basic
/-!
Projection functors are QPFs. The `n`-ary projection functors on `i` is an `n`-a... |
Data\QPF\Multivariate\Constructions\Quot.lean | /-
Copyright (c) 2018 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Simon Hudon
-/
import Mathlib.Data.QPF.Multivariate.Basic
/-!
# The quotient of QPF is itself a QPF
The quotients are here defined using a surjective function and
its r... |
Data\QPF\Multivariate\Constructions\Sigma.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.PFunctor.Multivariate.Basic
import Mathlib.Data.QPF.Multivariate.Basic
/-!
# Dependent product and sum of QPFs are QPFs
-/
universe u
namespace MvQP... |
Data\QPF\Univariate\Basic.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.Data.PFunctor.Univariate.M
/-!
# Quotients of Polynomial Functors
We assume the following:
* `P`: a polynomial functor
* `W`: its W-type
* `M`: its M... |
Data\Rat\BigOperators.lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import Mathlib.Algebra.BigOperators.Group.Finset
import Mathlib.Data.Rat.Cast.CharZero
/-! # Casting lemmas for rational numbers involving sums and p... |
Data\Rat\Defs.lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import Mathlib.Algebra.Group.Defs
import Mathlib.Data.Int.Defs
import Mathlib.Data.Rat.Init
import Mathlib.Order.Basic
import Mathlib.Tactic.Common
im... |
Data\Rat\Denumerable.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.Algebra.Order.Ring.Rat
import Mathlib.SetTheory.Cardinal.Basic
/-!
# Denumerability of ℚ
This file proves that ℚ is infinite, denumerable, and deduces th... |
Data\Rat\Encodable.lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import Mathlib.Logic.Encodable.Basic
import Mathlib.Data.Nat.GCD.Basic
import Mathlib.Data.Rat.Init
/-! # The rationals are `Encodable`.
As a conseq... |
Data\Rat\Floor.lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Kevin Kappelmann
-/
import Mathlib.Algebra.Order.Floor
import Mathlib.Data.Rat.Cast.Order
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.Ring
/-... |
Data\Rat\Init.lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Yaël Dillies
-/
import Mathlib.Data.Nat.Notation
import Mathlib.Tactic.Lemma
import Mathlib.Tactic.ProjectionNotation
import Mathlib.Tactic.TypeStar
imp... |
Data\Rat\Lemmas.lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import Mathlib.Algebra.GroupWithZero.Divisibility
import Mathlib.Algebra.Ring.Rat
import Mathlib.Data.PNat.Defs
/-!
# Further lemmas for the Rational... |
Data\Rat\Sqrt.lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import Mathlib.Algebra.Order.Ring.Abs
import Mathlib.Algebra.Order.Ring.Rat
import Mathlib.Data.Rat.Lemmas
import Mathlib.Data.Int.Sqrt
/-!
# Square ... |
Data\Rat\Star.lean | /-
Copyright (c) 2023 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux, Yaël Dillies
-/
import Mathlib.Algebra.GroupWithZero.Commute
import Mathlib.Algebra.Order.Ring.Abs
import Mathlib.Algebra.Star.Order
import Mathlib.Data.NNRat.Lemmas
impo... |
Data\Rat\Cast\CharZero.lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import Mathlib.Algebra.GroupWithZero.Units.Lemmas
import Mathlib.Data.Rat.Cast.Defs
/-!
# Casts of rational numbers into characteristic zero fields (... |
Data\Rat\Cast\Defs.lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import Mathlib.Algebra.Field.Rat
import Mathlib.Algebra.Group.Commute.Basic
import Mathlib.Algebra.GroupWithZero.Units.Lemmas
import Mathlib.Algebra.O... |
Data\Rat\Cast\Lemmas.lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import Mathlib.Data.Rat.Cast.Defs
import Mathlib.Algebra.Field.Basic
/-!
# Some exiled lemmas about casting
These lemmas have been removed from `Mat... |
Data\Rat\Cast\Order.lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import Mathlib.Algebra.Order.Ring.Rat
import Mathlib.Data.Rat.Cast.CharZero
import Mathlib.Tactic.Positivity.Core
import Mathlib.Algebra.Order.Field.B... |
Data\Real\Archimedean.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Floris van Doorn
-/
import Mathlib.Algebra.Bounds
import Mathlib.Algebra.Order.Archimedean.Basic
import Mathlib.Data.Real.Basic
import Mathlib.Order.Interval.Set.Disjoi... |
Data\Real\Basic.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Floris van Doorn
-/
import Mathlib.Algebra.Order.CauSeq.Completion
/-!
# Real numbers from Cauchy sequences
This file defines `ℝ` as the type of equivalence classes o... |
Data\Real\Cardinality.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
-/
import Mathlib.Analysis.SpecificLimits.Basic
import Mathlib.Data.Rat.Denumerable
import Mathlib.Data.Set.Pointwise.Interval
import Mathlib.SetTheory.Cardinal.Cont... |
Data\Real\ConjExponents.lean | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Yury Kudryashov
-/
import Mathlib.Data.ENNReal.Real
/-!
# Real conjugate exponents
This file defines conjugate exponents in `ℝ` and `ℝ≥0`. Real numbers `p` and ... |
Data\Real\ENatENNReal.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.ENat.Basic
import Mathlib.Data.ENNReal.Basic
/-!
# Coercion from `ℕ∞` to `ℝ≥0∞`
In this file we define a coercion from `ℕ∞` to `ℝ≥0∞` and prov... |
Data\Real\EReal.lean | /-
Copyright (c) 2019 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard
-/
import Mathlib.Data.Real.Basic
import Mathlib.Data.ENNReal.Real
import Mathlib.Data.Sign
/-!
# The extended reals [-∞, ∞].
This file defines `EReal`, the real numbers... |
Data\Real\GoldenRatio.lean | /-
Copyright (c) 2020 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker, Alexey Soloyev, Junyan Xu, Kamila Szewczyk
-/
import Mathlib.Data.Real.Irrational
import Mathlib.Data.Nat.Fib.Basic
import Mathlib.Data.Fin.VecNotation
import Mathl... |
Data\Real\Hyperreal.lean | /-
Copyright (c) 2019 Abhimanyu Pallavi Sudhir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Abhimanyu Pallavi Sudhir
-/
import Mathlib.Order.Filter.FilterProduct
import Mathlib.Analysis.SpecificLimits.Basic
/-!
# Construction of the hyperreal numbers as an ultrapro... |
Data\Real\Irrational.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Yury Kudryashov
-/
import Mathlib.Algebra.Algebra.Rat
import Mathlib.Data.Rat.Sqrt
import Mathlib.Data.Real.Sqrt
import ... |
Data\Real\Pointwise.lean | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Eric Wieser
-/
import Mathlib.Algebra.Order.Module.OrderedSMul
import Mathlib.Algebra.Order.Module.Pointwise
import Mathlib.Data.Real.Archimedean
/-!
# Pointwise operation... |
Data\Real\Sign.lean | /-
Copyright (c) 2021 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying, Eric Wieser
-/
import Mathlib.Data.Real.Basic
import Mathlib.Tactic.NormNum.Inv
/-!
# Real sign function
This file introduces and contains some results about `Real.sign` wh... |
Data\Real\Sqrt.lean | /-
Copyright (c) 2020 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Floris van Doorn, Yury Kudryashov
-/
import Mathlib.Topology.Instances.NNReal
import Mathlib.Topology.Order.MonotoneContinuity
/-!
# Square root of a real number
In t... |
Data\Real\Star.lean | /-
Copyright (c) 2020 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Floris van Doorn, Yury Kudryashov
-/
import Mathlib.Algebra.Star.Basic
import Mathlib.Data.Real.Basic
/-!
# The real numbers are a `*`-ring, with the trivial `*`-struc... |
Data\Real\StarOrdered.lean | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
import Mathlib.Algebra.Star.Order
import Mathlib.Data.Real.Sqrt
/-! # `ℝ` and `ℝ≥0` are *-ordered rings. -/
open scoped NNReal
/-- Although the instance `RCLike.toStar... |
Data\Real\Pi\Bounds.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, Mario Carneiro
-/
import Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds
/-!
# Pi
This file contains lemmas which establish bounds on `Real.pi`.
Notably, t... |
Data\Real\Pi\Leibniz.lean | /-
Copyright (c) 2020 Benjamin Davidson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Benjamin Davidson, Jeremy Tan
-/
import Mathlib.Analysis.Complex.AbelLimit
import Mathlib.Analysis.SpecialFunctions.Complex.Arctan
/-! ### Leibniz's series for `π` -/
namespace Re... |
Data\Real\Pi\Wallis.lean | /-
Copyright (c) 2021 Hanting Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Hanting Zhang
-/
import Mathlib.Analysis.SpecialFunctions.Integrals
/-! # The Wallis formula for Pi
This file establishes the Wallis product for `π` (`Real.tendsto_prod_pi_div_two`). ... |
Data\Seq\Computation.lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
Coinductive formalization of unbounded computations.
-/
import Mathlib.Data.Nat.Find
import Mathlib.Data.Stream.Init
import Mathlib.Tactic.Common
/-!
# Coinduct... |
Data\Seq\Parallel.lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Data.Seq.WSeq
/-!
# Parallel computation
Parallel computation of a computable sequence of computations by
a diagonal enumeration.
The importan... |
Data\Seq\Seq.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.Option.NAry
import Mathlib.Data.Seq.Computation
/-!
# Possibly infinite lists
This file provides a `Seq α` type representing possibly infinite l... |
Data\Seq\WSeq.lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Logic.Relation
import Mathlib.Data.Option.Basic
import Mathlib.Data.Seq.Seq
import Batteries.Data.DList
/-!
# Partially defined possibly infini... |
Data\Set\Accumulate.lean | /-
Copyright (c) 2020 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import Mathlib.Data.Set.Lattice
/-!
# Accumulate
The function `Accumulate` takes a set `s` and returns `⋃ y ≤ x, s y`.
-/
variable {α β γ : Type*} {s : α → Se... |
Data\Set\Basic.lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura
-/
import Mathlib.Algebra.Group.ZeroOne
import Mathlib.Data.Set.Defs
import Mathlib.Order.Basic
import Mathlib.Order.SymmDiff
import Mathlib.Tactic.Taut... |
Data\Set\BoolIndicator.lean | /-
Copyright (c) 2022 Dagur Tómas Ásgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Tómas Ásgeirsson, Leonardo de Moura
-/
import Mathlib.Data.Set.Basic
/-!
# Indicator function valued in bool
See also `Set.indicator` and `Set.piecewise`.
-/
open Bool... |
Data\Set\Card.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.SetTheory.Cardinal.Finite
/-!
# Noncomputable Set Cardinality
We define the cardinality of set `s` as a term `Set.encard s : ℕ∞` and a term `Set.ncard s ... |
Data\Set\Constructions.lean | /-
Copyright (c) 2020 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz
-/
import Mathlib.Data.Finset.Basic
import Mathlib.Data.Set.Lattice
/-!
# Constructions involving sets of sets.
## Finite Intersections
We define a structure `FiniteInter` wh... |
Data\Set\Countable.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.Data.Set.Finite
import Mathlib.Data.Countable.Basic
import Mathlib.Logic.Equiv.List
import Mathlib.Data.Set.Subsingleton
/-!
# Countable sets
In this... |
Data\Set\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, Johannes Hölzl, Reid Barton, Scott Morrison, Patrick Massot, Kyle Miller,
Minchao Wu, Yury Kudryashov, Floris van Doorn
-/
import Mathlib.Data.SProd
import Mathlib.Data.S... |
Data\Set\Enumerate.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.Algebra.Group.Basic
import Mathlib.Algebra.Group.Nat
import Mathlib.Data.Set.Basic
import Mathlib.Tactic.Common
/-!
# Set enumeration
This file allows... |
Data\Set\Equitable.lean | /-
Copyright (c) 2021 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
import Mathlib.Data.Set.Subsingleton
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Algebra.Group.Nat
import Mathlib.Da... |
Data\Set\Finite.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, Kyle Miller
-/
import Mathlib.Data.Finset.Basic
import Mathlib.Data.Finite.Basic
import Mathlib.Data.Set.Functor
import Mathlib.Data.Set.Lattice
/-!
# ... |
Data\Set\Function.lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Andrew Zipperer, Haitao Zhang, Minchao Wu, Yury Kudryashov
-/
import Mathlib.Data.Set.Prod
import Mathlib.Logic.Function.Conjugate
/-!
# Functions over sets
## Main def... |
Data\Set\Functor.lean | /-
Copyright (c) 2016 Leonardo de Moura. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Mathlib.Data.Set.Lattice
import Mathlib.Init.Set
import Mathlib.Control.Basic
import Mathlib.Data.Set.Notation
/-!
# Functoriality of `Set`
This file d... |
Data\Set\Image.lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura
-/
import Mathlib.Data.Set.Subsingleton
import Mathlib.Order.WithBot
import Mathlib.Tactic.Use
import Batteries.Tactic.Congr
/-!
# Images and preimages... |
Data\Set\Lattice.lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Johannes Hölzl, Mario Carneiro
-/
import Mathlib.Logic.Pairwise
import Mathlib.Order.CompleteBooleanAlgebra
import Mathlib.Order.Directed
import Mathli... |
Data\Set\List.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.Set.Image
import Mathlib.Data.List.Defs
/-!
# Lemmas about `List`s and `Set.range`
In this file we prove lemmas about range of some operations... |
Data\Set\MemPartition.lean | /-
Copyright (c) 2024 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
import Mathlib.Data.Set.Finite
/-!
# Partitions based on membership of a sequence of sets
Let `f : ℕ → Set α` be a sequence of sets. For `n : ℕ`, we can form the set of... |
Data\Set\MulAntidiagonal.lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Floris van Doorn
-/
import Mathlib.Order.WellFoundedSet
/-! # Multiplication antidiagonal -/
namespace Set
variable {α : Type*}
section Mul
variable [Mul α] {s s₁... |
Data\Set\NAry.lean | /-
Copyright (c) 2020 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import Mathlib.Data.Set.Prod
/-!
# N-ary images of sets
This file defines `Set.image2`, the binary image of sets.
This is mostly useful to define pointwise oper... |
Data\Set\Notation.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.Mathport.Notation
import Mathlib.Lean.Expr.ExtraRecognizers
/-!
# Set Notation
This file defines two pieces of scoped notation related to sets and subtyp... |
Data\Set\Opposite.lean | /-
Copyright (c) 2022 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import Mathlib.Data.Opposite
import Mathlib.Data.Set.Defs
/-!
# The opposite of a set
The opposite of a set `s` is simply the set obtained by taking the opposite of e... |
Data\Set\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, Johannes Hölzl, Patrick Massot
-/
import Mathlib.Data.Set.Image
import Mathlib.Data.SProd
/-!
# Sets in product and pi types
This file defines the product of sets in ... |
Data\Set\Semiring.lean | /-
Copyright (c) 2020 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import Mathlib.Algebra.Order.Kleene
import Mathlib.Algebra.Order.Ring.Canonical
import Mathlib.Data.Set.Pointwise.Basic
/-!
# Sets as a semiring under union
Thi... |
Data\Set\Sigma.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Data.Set.Image
import Mathlib.Data.Set.Lattice
/-!
# Sets in sigma types
This file defines `Set.sigma`, the indexed sum of sets.
-/
namespace Set
varia... |
Data\Set\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.Algebra.Order.AddTorsor
import Mathlib.Order.WellFoundedSet
/-!
# Antidiagonal for scalar multiplication
Given partially ordered sets `G` and `P`, wi... |
Data\Set\Subset.lean | /-
Copyright (c) 2024 Miguel Marco. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Miguel Marco
-/
import Mathlib.Data.Set.Function
import Mathlib.Data.Set.Functor
/-!
# Sets in subtypes
This file is about sets in `Set A` when `A` is a set.
It defines notation `↓∩` ... |
Data\Set\Subsingleton.lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura
-/
import Mathlib.Data.Set.Basic
/-!
# Subsingleton
Defines the predicate `Subsingleton s : Prop`, saying that `s` has at most one element.
Also defi... |
Data\Set\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.Set.NAry
import Mathlib.Order.UpperLower.Basic
import Mathlib.Order.SupClosed
/-!
# Set family operations
This file defines a few binary operations ... |
Data\Set\UnionLift.lean | /-
Copyright (c) 2021 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.Data.Set.Lattice
import Mathlib.Order.Directed
/-!
# Union lift
This file defines `Set.iUnionLift` to glue together functions defined on each of a collect... |
Data\Set\Pairwise\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
-/
import Mathlib.Data.Set.Function
import Mathlib.Logic.Pairwise
import Mathlib.Logic.Relation
/-!
# Relations holding pairwise
This file develops pairwise relations ... |
Data\Set\Pairwise\Lattice.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.Data.Set.Lattice
import Mathlib.Data.Set.Pairwise.Basic
/-!
# Relations holding pairwise
In this file we prove many facts about `Pairwise` and the se... |
Data\Set\Pointwise\Basic.lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Floris van Doorn
-/
import Mathlib.Algebra.Group.Equiv.Basic
import Mathlib.Algebra.Group.Units.Hom
import Mathlib.Algebra.Opposites
import Mathlib.Algebra.Ring.Defs
im... |
Data\Set\Pointwise\BigOperators.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.BigOperators.Group.Finset
import Mathlib.Data.Set.Pointwise.Basic
/-!
# Results about pointwise operations on sets and big operators.
-/
namespace... |
Data\Set\Pointwise\BoundedMul.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. KudryashovJ
-/
import Mathlib.Algebra.Order.Monoid.Defs
import Mathlib.Data.Set.Pointwise.Basic
/-!
# Pointwise multiplication of sets preserves boundedness above.
TODO:... |
Data\Set\Pointwise\Finite.lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Floris van Doorn
-/
import Mathlib.Data.Set.Finite
import Mathlib.Data.Set.Pointwise.SMul
/-! # Finiteness lemmas for pointwise operations on sets -/
open Pointwise
... |
Data\Set\Pointwise\Interval.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, Patrick Massot
-/
import Mathlib.Order.Interval.Set.UnorderedInterval
import Mathlib.Algebra.Order.Interval.Set.Monoid
import Mathlib.Data.Set.Pointwise.Basic
i... |
Data\Set\Pointwise\Iterate.lean | /-
Copyright (c) 2022 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.Algebra.GroupPower.IterateHom
import Mathlib.Data.Set.Pointwise.SMul
import Mathlib.Dynamics.FixedPoints.Basic
/-!
# Results about pointwise operations on s... |
Data\Set\Pointwise\ListOfFn.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.Group.List
import Mathlib.Data.List.OfFn
import Mathlib.Data.Set.Pointwise.Basic
/-!
# Pointwise operations with lists of sets
This fi... |
Data\Set\Pointwise\SMul.lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Floris van Doorn
-/
import Mathlib.Algebra.Group.Pi.Basic
import Mathlib.Algebra.Module.Defs
import Mathlib.Data.Set.Pairwise.Basic
import Mathlib.Data.Set.Pointwise.Ba... |
Data\Set\Pointwise\Support.lean | /-
Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Algebra.Group.Support
import Mathlib.Data.Set.Pointwise.SMul
/-!
# Support of a function composed with a scalar action
We show that the support... |
Data\SetLike\Basic.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.Data.Set.Basic
import Mathlib.Tactic.Monotonicity.Attr
import Mathlib.Tactic.SetLike
/-!
# Typeclass for types with a set-like extensionality property
The ... |
Data\SetLike\Fintype.lean | /-
Copyright (c) 2021 . All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.Data.SetLike.Basic
import Mathlib.Data.Fintype.Powerset
/-!
# Set-like fintype
This file contains a fintype instance for set-like objects such as subgroups. If `SetL... |
Data\Setoid\Basic.lean | /-
Copyright (c) 2019 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston, Bryan Gin-ge Chen
-/
import Mathlib.Logic.Relation
import Mathlib.Order.GaloisConnection
/-!
# Equivalence relations
This file defines the complete lattice of e... |
Data\Setoid\Partition.lean | /-
Copyright (c) 2019 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston, Bryan Gin-ge Chen, Patrick Massot, Wen Yang, Johan Commelin
-/
import Mathlib.Data.Set.Finite
import Mathlib.Order.Partition.Finpartition
/-!
# Equivalence relat... |
Data\Sigma\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
-/
import Mathlib.Logic.Function.Defs
import Mathlib.Logic.Function.Basic
/-!
# Sigma types
This file proves basic results about sigma types.
A sigma type is a depend... |
Data\Sigma\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.Sigma.Order
import Mathlib.Order.Interval.Finset.Defs
/-!
# Finite intervals in a sigma type
This file provides the `LocallyFiniteOrder` instance fo... |
Data\Sigma\Lex.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.Order.RelClasses
/-!
# Lexicographic order on a sigma type
This defines the lexicographical order of two arbitrary relations on a sigma type and proves s... |
Data\Sigma\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.Data.Sigma.Lex
import Mathlib.Order.BoundedOrder
import Mathlib.Mathport.Notation
import Mathlib.Data.Sigma.Basic
/-!
# Orders on a sigma type
This file ... |
Data\Stream\Defs.lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Mathlib.Data.Nat.Notation
/-!
# Definition of `Stream'` and functions on streams
A stream `Stream' α` is an infinite sequence of elements of `α`. O... |
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