path stringlengths 11 71 | content stringlengths 75 124k |
|---|---|
NumberTheory\NumberField\House.lean | /-
Copyright (c) 2024 Michail Karatarakis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michail Karatarakis
-/
import Mathlib.NumberTheory.SiegelsLemma
import Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic
import Mathlib.NumberTheory.NumberField.EquivReind... |
NumberTheory\NumberField\Norm.lean | /-
Copyright (c) 2022 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca, Eric Rodriguez
-/
import Mathlib.NumberTheory.NumberField.Basic
import Mathlib.RingTheory.Localization.NormTrace
/-!
# Norm in number fields
Given a finite extension... |
NumberTheory\NumberField\CanonicalEmbedding\Basic.lean | /-
Copyright (c) 2022 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
-/
import Mathlib.Algebra.Module.Zlattice.Basic
import Mathlib.NumberTheory.NumberField.Embeddings
import Mathlib.NumberTheory.NumberField.FractionalIdeal
/-!
# Canonical... |
NumberTheory\NumberField\CanonicalEmbedding\ConvexBody.lean | /-
Copyright (c) 2022 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
-/
import Mathlib.MeasureTheory.Group.GeometryOfNumbers
import Mathlib.MeasureTheory.Measure.Lebesgue.VolumeOfBalls
import Mathlib.NumberTheory.NumberField.CanonicalEmbedd... |
NumberTheory\NumberField\Units\Basic.lean | /-
Copyright (c) 2023 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
-/
import Mathlib.NumberTheory.NumberField.Embeddings
/-!
# Units of a number field
We prove some basic results on the group `(𝓞 K)ˣ` of units of the ring of integers `... |
NumberTheory\NumberField\Units\DirichletTheorem.lean | /-
Copyright (c) 2023 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
-/
import Mathlib.LinearAlgebra.Matrix.Gershgorin
import Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody
import Mathlib.NumberTheory.NumberField.Units.Basic... |
NumberTheory\NumberField\Units\Regulator.lean | /-
Copyright (c) 2024 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
-/
import Mathlib.Algebra.Module.Zlattice.Covolume
import Mathlib.LinearAlgebra.Matrix.Determinant.Misc
import Mathlib.NumberTheory.NumberField.Units.DirichletTheorem
/-!... |
NumberTheory\Padics\Hensel.lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis
-/
import Mathlib.Algebra.Polynomial.Identities
import Mathlib.Analysis.SpecificLimits.Basic
import Mathlib.NumberTheory.Padics.PadicIntegers
import Mathlib.Topology.A... |
NumberTheory\Padics\PadicIntegers.lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Mario Carneiro, Johan Commelin
-/
import Mathlib.NumberTheory.Padics.PadicNumbers
import Mathlib.RingTheory.DiscreteValuationRing.Basic
/-!
# p-adic integers
This f... |
NumberTheory\Padics\PadicNorm.lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis
-/
import Mathlib.Algebra.Order.Field.Power
import Mathlib.NumberTheory.Padics.PadicVal
/-!
# p-adic norm
This file defines the `p`-adic norm on `ℚ`.
The `p`-adic v... |
NumberTheory\Padics\PadicNumbers.lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis
-/
import Mathlib.RingTheory.Valuation.Basic
import Mathlib.NumberTheory.Padics.PadicNorm
import Mathlib.Analysis.Normed.Field.Basic
import Mathlib.Tactic.Peel
import ... |
NumberTheory\Padics\PadicVal.lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Matthew Robert Ballard
-/
import Mathlib.NumberTheory.Divisors
import Mathlib.Data.Nat.Digits
import Mathlib.Data.Nat.MaxPowDiv
import Mathlib.Data.Nat.Multiplicity
i... |
NumberTheory\Padics\RingHoms.lean | /-
Copyright (c) 2020 Johan Commelin, Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Robert Y. Lewis
-/
import Mathlib.NumberTheory.Padics.PadicIntegers
import Mathlib.RingTheory.ZMod
/-!
# Relating `ℤ_[p]` to `ZMod (p ^ n)`
In this ... |
NumberTheory\Zsqrtd\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.Algebra.Associated.Basic
import Mathlib.Algebra.Star.Unitary
import Mathlib.RingTheory.Int.Basic
import Mathlib.RingTheory.PrincipalIdealDomain
import ... |
NumberTheory\Zsqrtd\GaussianInt.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.NumberTheory.Zsqrtd.Basic
import Mathlib.RingTheory.PrincipalIdealDomain
import Mathlib.Data.Complex.Basic
import Mathlib.Data.Real.Archimedean
/-!
# Gaus... |
NumberTheory\Zsqrtd\QuadraticReciprocity.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.NumberTheory.Zsqrtd.GaussianInt
import Mathlib.NumberTheory.LegendreSymbol.Basic
import Mathlib.Analysis.Normed.Field.Basic
/-!
# Facts about the gaussian... |
NumberTheory\Zsqrtd\ToReal.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.Real.Sqrt
import Mathlib.NumberTheory.Zsqrtd.Basic
/-!
# Image of `Zsqrtd` in `ℝ`
This file defines `Zsqrtd.toReal` and related lemmas.
It is in a sep... |
Order\Antichain.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.Set.Pairwise.Basic
import Mathlib.Order.Bounds.Basic
import Mathlib.Order.Directed
import Mathlib.Order.Hom.Set
/-!
# Antichains
This file defines a... |
Order\Antisymmetrization.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.Order.Hom.Basic
import Mathlib.Logic.Relation
/-!
# Turning a preorder into a partial order
This file allows to make a preorder into a partial order by q... |
Order\Atoms.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.Data.Set.Lattice
import Mathlib.Order.ModularLattice
import Mathlib.Order.SuccPred.Basic
import Mathlib.Order.WellFounded
import Mathlib.Tactic.Nontriv... |
Order\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, Mario Carneiro
-/
import Mathlib.Init.Order.LinearOrder
import Mathlib.Data.Prod.Basic
import Mathlib.Data.Subtype
import Mathlib.Tactic.Spread
import Mathlib.Tactic.Conv... |
Order\Birkhoff.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Filipo A. E. Nuccio, Sam van Gool
-/
import Mathlib.Order.Interval.Finset.Basic
import Mathlib.Data.Fintype.Order
import Mathlib.Order.Irreducible
import Mathlib.Order.Uppe... |
Order\BooleanAlgebra.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Bryan Gin-ge Chen
-/
import Mathlib.Order.Heyting.Basic
/-!
# (Generalized) Boolean algebras
A Boolean algebra is a bounded distributive lattice with a complement ope... |
Order\BooleanGenerators.lean | /-
Copyright (c) 2024 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.Order.CompleteLattice
import Mathlib.Order.CompactlyGenerated.Basic
/-!
# Generators for boolean algebras
In this file, we provide an alternative con... |
Order\Booleanisation.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.Order.Hom.Lattice
/-!
# Adding complements to a generalized Boolean algebra
This file embeds any generalized Boolean algebra into a Boolean algebra.
Thi... |
Order\Bounded.lean | /-
Copyright (c) 2022 Violeta Hernández Palacios. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Violeta Hernández Palacios
-/
import Mathlib.Order.RelClasses
import Mathlib.Order.Interval.Set.Basic
/-!
# Bounded and unbounded sets
We prove miscellaneous lemmas about ... |
Order\BoundedOrder.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.Order.Lattice
import Mathlib.Order.ULift
import Mathlib.Tactic.PushNeg
/-!
# ⊤ and ⊥, bounded lattices and variants
This file defines top and bottom ... |
Order\Chain.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.Pairwise.Basic
import Mathlib.Data.Set.Lattice
import Mathlib.Data.SetLike.Basic
/-!
# Chains and flags
This file defines chains for an arbi... |
Order\Circular.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.Set.Basic
/-!
# Circular order hierarchy
This file defines circular preorders, circular partial orders and circular orders.
## Hierarchy
* A terna... |
Order\Closure.lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Yaël Dillies
-/
import Mathlib.Data.Set.Lattice
import Mathlib.Data.SetLike.Basic
import Mathlib.Order.GaloisConnection
import Mathlib.Order.Hom.Basic
/-!
# Closure operat... |
Order\Compare.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.Ordering.Basic
import Mathlib.Order.Synonym
/-!
# Comparison
This file provides basic results about orderings and comparison in linear orders.
... |
Order\CompleteBooleanAlgebra.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yaël Dillies
-/
import Mathlib.Order.CompleteLattice
import Mathlib.Order.Directed
import Mathlib.Logic.Equiv.Set
/-!
# Frames, completely distributive lattices and co... |
Order\CompleteLattice.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.Bool.Set
import Mathlib.Data.Nat.Set
import Mathlib.Data.Set.Prod
import Mathlib.Data.ULift
import Mathlib.Order.Bounds.Basic
import Mathlib.Order... |
Order\CompleteLatticeIntervals.lean | /-
Copyright (c) 2022 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
import Mathlib.Order.ConditionallyCompleteLattice.Basic
import Mathlib.Order.LatticeIntervals
import Mathlib.Order.Interval.Set.OrdConnected
/-! # Subtypes of cond... |
Order\CompletePartialOrder.lean | /-
Copyright (c) 2023 Christopher Hoskin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Hoskin
-/
import Mathlib.Order.OmegaCompletePartialOrder
/-!
# Complete Partial Orders
This file considers complete partial orders (sometimes called directedly comple... |
Order\CompleteSublattice.lean | /-
Copyright (c) 2024 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.Order.Sublattice
import Mathlib.Order.Hom.CompleteLattice
/-!
# Complete Sublattices
This file defines complete sublattices. These are subsets of complete ... |
Order\Concept.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.Lattice
/-!
# Formal concept analysis
This file defines concept lattices. A concept of a relation `r : α → β → Prop` is a pair of sets
`s : Set ... |
Order\Copy.lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Yaël Dillies
-/
import Mathlib.Order.ConditionallyCompleteLattice.Basic
/-!
# Tooling to make copies of lattice structures
Sometimes it is useful to make a copy of a ... |
Order\CountableDenseLinearOrder.lean | /-
Copyright (c) 2020 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn
-/
import Mathlib.Order.Ideal
import Mathlib.Data.Finset.Lattice
/-!
# The back and forth method and countable dense linear orders
## Results
Suppose `α β` are linear orders,... |
Order\Cover.lean | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Violeta Hernández Palacios, Grayson Burton, Floris van Doorn
-/
import Mathlib.Order.Interval.Set.OrdConnected
import Mathlib.Order.Antisymmetrization
/-!
# The covering r... |
Order\Defs.lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Mathlib.Init.Algebra.Classes
import Mathlib.Data.Ordering.Basic
import Mathlib.Tactic.SplitIfs
import Mathlib.Tactic.TypeStar
import Batteries.Classe... |
Order\Directed.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yaël Dillies
-/
import Mathlib.Data.Set.Image
/-!
# Directed indexed families and sets
This file defines directed indexed families and directed sets. An indexed famil... |
Order\Disjoint.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 Aesop
import Mathlib.Order.BoundedOrder
/-!
# Disjointness and complements
This file defines `Disjoint`, `Codisjoint`, and the `IsCompl` predicate.
## Main ... |
Order\Disjointed.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yaël Dillies
-/
import Mathlib.Order.PartialSups
/-!
# Consecutive differences of sets
This file defines the way to make a sequence of elements into a sequence of dis... |
Order\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.Set.Defs
import Mathlib.Order.Heyting.Basic
import Mathlib.Order.RelClasses
import Mathlib.Order.Hom.Basic
import Mathlib.Lean.Thunk
/-!
# Improvab... |
Order\FixedPoints.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau, Yury Kudryashov
-/
import Mathlib.Dynamics.FixedPoints.Basic
import Mathlib.Order.Hom.Order
/-!
# Fixed point construction on complete lattices
This file s... |
Order\GaloisConnection.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.Order.CompleteLattice
import Mathlib.Order.Synonym
import Mathlib.Order.Hom.Set
import Mathlib.Order.Bounds.Basic
/-!
# Galois connections, insertions... |
Order\GameAdd.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.Sym.Sym2
import Mathlib.Logic.Relation
/-!
# Game addition relation
This file defines, given relations `rα : α → α → Prop` and `rβ : β → β → Prop`, a rela... |
Order\Grade.lean | /-
Copyright (c) 2022 Yaël Dillies, Violeta Hernández Palacios. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Violeta Hernández Palacios, Grayson Burton, Vladimir Ivanov
-/
import Mathlib.Data.Int.SuccPred
import Mathlib.Order.Fin.Basic
/-!
# Graded ord... |
Order\Height.lean | /-
Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.Data.ENat.Lattice
import Mathlib.Order.OrderIsoNat
import Mathlib.Tactic.TFAE
/-!
# Maximal length of chains
This file contains lemmas to work with the ma... |
Order\Ideal.lean | /-
Copyright (c) 2020 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn
-/
import Mathlib.Logic.Encodable.Basic
import Mathlib.Order.Atoms
import Mathlib.Order.Chain
import Mathlib.Order.UpperLower.Basic
import Mathlib.Data.Set.Subsingleton
/-!
# O... |
Order\InitialSeg.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Floris van Doorn
-/
import Mathlib.Logic.Equiv.Set
import Mathlib.Order.RelIso.Set
import Mathlib.Order.WellFounded
/-!
# Initial and principal segments
This file defi... |
Order\Irreducible.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.Lattice
/-!
# Irreducible and prime elements in an order
This file defines irreducible and prime elements in an order and shows that in a wel... |
Order\IsWellOrderLimitElement.lean | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.Algebra.Order.Group.Nat
import Mathlib.Order.WellFounded
/-!
# Limit elements in well-ordered types
This file introduces two main definitions:
- `wellOrderSucc... |
Order\Iterate.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.Logic.Function.Iterate
import Mathlib.Order.Monotone.Basic
/-!
# Inequalities on iterates
In this file we prove some inequalities comparing `... |
Order\JordanHolder.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.Order.Lattice
import Mathlib.Data.List.Sort
import Mathlib.Logic.Equiv.Fin
import Mathlib.Logic.Equiv.Functor
import Mathlib.Data.Fintype.Card
import Mathl... |
Order\KonigLemma.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.Order.Atoms.Finite
import Mathlib.Order.Grade
/-!
# Kőnig's infinity lemma
Kőnig's infinity lemma is most often stated as a graph theory result:
every in... |
Order\KrullDimension.lean | /-
Copyright (c) 2023 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang, Fangming Li
-/
import Mathlib.Order.RelSeries
import Mathlib.Order.WithBot
import Mathlib.Data.Nat.Lattice
/-!
# Krull dimension of a preordered set
If `α` is a preorder... |
Order\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.Bool.Basic
import Mathlib.Order.Defs
import Mathlib.Order.Monotone.Basic
import Mathlib.Order.ULift
import Mathlib.Tactic.GCongr.Core
/-!
# (Semi... |
Order\LatticeIntervals.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.Order.Bounds.Basic
/-!
# Intervals in Lattices
In this file, we provide instances of lattice structures on intervals within lattices.
Some of them de... |
Order\LiminfLimsup.lean | /-
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Johannes Hölzl, Rémy Degenne
-/
import Mathlib.Order.Filter.Cofinite
import Mathlib.Order.Hom.CompleteLattice
/-!
# liminfs and limsups of functions and filters
... |
Order\Max.lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Yury Kudryashov, Yaël Dillies
-/
import Mathlib.Order.Synonym
/-!
# Minimal/maximal and bottom/top elements
This file defines predicates for elements to be minimal/maxi... |
Order\Minimal.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Peter Nelson
-/
import Mathlib.Order.Antichain
import Mathlib.Order.UpperLower.Basic
import Mathlib.Order.Interval.Set.Basic
/-!
# Minimality and Maximality
This file def... |
Order\MinMax.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.Lattice
/-!
# `max` and `min`
This file proves basic properties about maxima and minima on a `LinearOrder`.
## Tags
min, max
-/
universe u ... |
Order\ModularLattice.lean | /-
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson, Yaël Dillies
-/
import Mathlib.Order.Cover
import Mathlib.Order.LatticeIntervals
import Mathlib.Order.GaloisConnection
/-!
# Modular Lattices
This file defines (semi)... |
Order\Nat.lean | /-
Copyright (c) 2014 Floris van Doorn (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-/
import Mathlib.Order.BoundedOrder
/-!
# The natural numbers form a linear order
... |
Order\Notation.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, Yaël Dillies
-/
import Mathlib.Tactic.Basic
import Mathlib.Tactic.Simps.NotationClass
/-!
# Notation classes for lattice operations
In this file we i... |
Order\OmegaCompletePartialOrder.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.Monad.Basic
import Mathlib.Order.Chain
import Mathlib.Order.Hom.Order
import Mathlib.Order.Part
/-!
# Omega Complete Partial Orders
An omega-comple... |
Order\OrdContinuous.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, Johannes Hölzl
-/
import Mathlib.Order.ConditionallyCompleteLattice.Basic
import Mathlib.Order.RelIso.Basic
/-!
# Order continuity
We say that a function is *... |
Order\OrderIsoNat.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.Lattice
import Mathlib.Logic.Denumerable
import Mathlib.Logic.Function.Iterate
import Mathlib.Order.Hom.Basic
import Mathlib.Data.Set.Subsing... |
Order\Part.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.Part
import Mathlib.Order.Hom.Basic
import Mathlib.Tactic.Common
/-!
# Monotonicity of monadic operations on `Part`
-/
open Part
variable {α β γ : ... |
Order\PartialSups.lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.Data.Finset.Lattice
import Mathlib.Order.Hom.Basic
import Mathlib.Data.Set.Finite
import Mathlib.Order.ConditionallyCompleteLattice.Basic
/-!
# The mo... |
Order\PFilter.lean | /-
Copyright (c) 2020 Mathieu Guay-Paquet. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mathieu Guay-Paquet
-/
import Mathlib.Order.Ideal
/-!
# Order filters
## Main definitions
Throughout this file, `P` is at least a preorder, but some sections require more struc... |
Order\PiLex.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.Order.WellFounded
import Mathlib.Tactic.Common
/-!
# Lexicographic order on Pi types
This file defines the lexicographic order for Pi types. `a` is less ... |
Order\PrimeIdeal.lean | /-
Copyright (c) 2021 Noam Atar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Noam Atar
-/
import Mathlib.Order.Ideal
import Mathlib.Order.PFilter
/-!
# Prime ideals
## Main definitions
Throughout this file, `P` is at least a preorder, but some sections require mo... |
Order\PrimeSeparator.lean | /-
Copyright (c) 2024 Sam van Gool. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sam van Gool
-/
import Mathlib.Order.PrimeIdeal
import Mathlib.Order.Zorn
/-!
# Separating prime filters and ideals
In a bounded distributive lattice, if $F$ is a filter, $I$ is an id... |
Order\PropInstances.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.Order.Disjoint
/-!
# The order on `Prop`
Instances on `Prop` such as `DistribLattice`, `BoundedOrder`, `LinearOrder`.
-/
/-- Propositions form a d... |
Order\Radical.lean | /-
Copyright (c) 2024 Colva Roney-Dougal. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Colva Roney-Dougal, Inna Capdeboscq, Susanna Fishel, Kim Morrison
-/
import Mathlib.Order.CompleteLattice
import Mathlib.Order.Atoms
/-!
# The radical of a lattice
This file cont... |
Order\RelClasses.lean | /-
Copyright (c) 2020 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Mario Carneiro, Yury G. Kudryashov
-/
import Mathlib.Data.Nat.Defs
import Mathlib.Logic.IsEmpty
import Mathlib.Order.Basic
import Mathlib.Tactic.MkIffOfInductiveProp
impo... |
Order\RelSeries.lean | /-
Copyright (c) 2023 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang, Fangming Li
-/
import Mathlib.Algebra.Ring.Int
import Mathlib.Data.List.Chain
import Mathlib.Data.List.OfFn
import Mathlib.Data.Rel
import Mathlib.Order.Fin.Basic
import Ma... |
Order\SemiconjSup.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.Algebra.Group.Units.Equiv
import Mathlib.Logic.Function.Conjugate
import Mathlib.Order.Bounds.OrderIso
import Mathlib.Order.ConditionallyComple... |
Order\SetNotation.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Yury Kudryashov
-/
import Mathlib.Data.Set.Defs
import Mathlib.Mathport.Notation
/-!
# Notation classes for set supremum and infimum
In this file we i... |
Order\Sublattice.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.Order.SupClosed
/-!
# Sublattices
This file defines sublattices.
## TODO
Subsemilattices, if people care about them.
## Tags
sublattice
-/
open Func... |
Order\SupClosed.lean | /-
Copyright (c) 2023 Yaël Dillies, Christopher Hoskin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Christopher Hoskin
-/
import Mathlib.Data.Finset.Lattice
import Mathlib.Data.Set.Finite
import Mathlib.Order.Closure
import Mathlib.Order.UpperLower.Bas... |
Order\SupIndep.lean | /-
Copyright (c) 2021 Aaron Anderson, Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson, Kevin Buzzard, Yaël Dillies, Eric Wieser
-/
import Mathlib.Data.Finset.Sigma
import Mathlib.Data.Finset.Pairwise
import Mathlib.Data.Finset.Powerset
impor... |
Order\SymmDiff.lean | /-
Copyright (c) 2021 Bryan Gin-ge Chen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz, Bryan Gin-ge Chen, Yaël Dillies
-/
import Mathlib.Order.BooleanAlgebra
import Mathlib.Logic.Equiv.Basic
/-!
# Symmetric difference and bi-implication
This file defines... |
Order\Synonym.lean | /-
Copyright (c) 2020 Johan Commelin, Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Damiano Testa, Yaël Dillies
-/
import Mathlib.Logic.Equiv.Defs
import Mathlib.Logic.Nontrivial.Defs
import Mathlib.Order.Basic
/-!
# Type synonyms
This... |
Order\ULift.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.Logic.Function.ULift
import Mathlib.Order.Basic
/-! # Ordered structures on `ULift.{v} α`
Once these basic instances are setup, the instances of more compl... |
Order\WellFounded.lean | /-
Copyright (c) 2020 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Mario Carneiro
-/
import Mathlib.Data.Set.Basic
/-!
# Well-founded relations
A relation is well-founded if it can be used for induction: for each `x`, `(∀ y, r y x → P ... |
Order\WellFoundedSet.lean | /-
Copyright (c) 2021 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import Mathlib.Init.Data.Sigma.Lex
import Mathlib.Data.Prod.Lex
import Mathlib.Data.Sigma.Lex
import Mathlib.Order.Antichain
import Mathlib.Order.OrderIsoNat
import M... |
Order\WithBot.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.Init.Algebra.Classes
import Mathlib.Logic.Nontrivial.Basic
import Mathlib.Order.BoundedOrder
import Mathlib.Data.Option.NAry
import Mathlib.Tactic.Lift... |
Order\Zorn.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.Order.Chain
/-!
# Zorn's lemmas
This file proves several formulations of Zorn's Lemma.
## Variants
The primary statement of Zorn's lemma is `exists... |
Order\ZornAtoms.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.Order.Zorn
import Mathlib.Order.Atoms
/-!
# Zorn lemma for (co)atoms
In this file we use Zorn's lemma to prove that a partial order is atomic if ev... |
Order\Atoms\Finite.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.Order.Interval.Finset.Defs
import Mathlib.Order.Atoms
/-!
# Atoms, Coatoms, Simple Lattices, and Finiteness
This module contains some results on atom... |
Order\Bounds\Basic.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yury Kudryashov
-/
import Mathlib.Order.Interval.Set.Basic
import Mathlib.Data.Set.NAry
import Mathlib.Order.Directed
/-!
# Upper / lower bounds
In this file we defin... |
Order\Bounds\OrderIso.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.Order.Bounds.Basic
import Mathlib.Order.Hom.Set
/-!
# Order isomorphisms and bounds.
-/
open Set
namespace OrderIso
variable {α β ... |
Order\Category\BddDistLat.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.Order.Category.BddLat
import Mathlib.Order.Category.DistLat
/-!
# The category of bounded distributive lattices
This defines `BddDistLat`, the category o... |
Order\Category\BddLat.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.CategoryTheory.Adjunction.Unique
import Mathlib.Order.Category.BddOrd
import Mathlib.Order.Category.Lat
import Mathlib.Order.Category.Semilat
/-!
# The ca... |
Order\Category\BddOrd.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.CategoryTheory.Category.Bipointed
import Mathlib.Order.Category.PartOrd
import Mathlib.Order.Hom.Bounded
/-!
# The category of bounded orders
This define... |
Order\Category\BoolAlg.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.Order.Category.HeytAlg
import Mathlib.Order.Hom.CompleteLattice
/-!
# The category of boolean algebras
This defines `BoolAlg`, the category of boolean al... |
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