path stringlengths 11 71 | content stringlengths 75 124k |
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Order\Category\CompleteLat.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.Hom.CompleteLattice
/-!
# The category of complete lattices
This file defines `CompleteLat`, the category of c... |
Order\Category\DistLat.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.Lat
/-!
# The category of distributive lattices
This file defines `DistLat`, the category of distributive lattices.
Note that [`DistLat`]... |
Order\Category\FinBddDistLat.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.Fintype.Order
import Mathlib.Order.Category.BddDistLat
import Mathlib.Order.Category.FinPartOrd
/-!
# The category of finite bounded distributive lat... |
Order\Category\FinBoolAlg.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.Fintype.Powerset
import Mathlib.Order.Category.BoolAlg
import Mathlib.Order.Category.FinBddDistLat
import Mathlib.Order.Hom.CompleteLattice
import Mat... |
Order\Category\FinPartOrd.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.FintypeCat
import Mathlib.Order.Category.PartOrd
/-!
# The category of finite partial orders
This defines `FinPartOrd`, the category of fi... |
Order\Category\Frm.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.Lat
import Mathlib.Order.Hom.CompleteLattice
import Mathlib.Topology.Category.CompHaus.Basic
import Mathlib.Topology.Sets.Opens
/-!
# The c... |
Order\Category\HeytAlg.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.BddDistLat
import Mathlib.Order.Heyting.Hom
/-!
# The category of Heyting algebras
This file defines `HeytAlg`, the category of Heyting al... |
Order\Category\Lat.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.PartOrd
import Mathlib.Order.Hom.Lattice
/-!
# The category of lattices
This defines `Lat`, the category of lattices.
Note that `Lat` doe... |
Order\Category\LinOrd.lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.Order.Category.Lat
/-!
# Category of linear orders
This defines `LinOrd`, the category of linear orders with monotone maps.
-/
open CategoryTheory
... |
Order\Category\NonemptyFinLinOrd.lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.Data.Fintype.Order
import Mathlib.Data.Set.Finite
import Mathlib.Order.Category.FinPartOrd
import Mathlib.Order.Category.LinOrd
import Mathlib.Category... |
Order\Category\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.Order.OmegaCompletePartialOrder
import Mathlib.CategoryTheory.Limits.Shapes.Products
import Mathlib.CategoryTheory.Limits.Shapes.Equalizers
import Mathlib.Ca... |
Order\Category\PartOrd.lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.Order.Antisymmetrization
import Mathlib.Order.Category.Preord
import Mathlib.CategoryTheory.Adjunction.Basic
/-!
# Category of partial orders
This de... |
Order\Category\Preord.lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.CategoryTheory.Category.Cat
import Mathlib.CategoryTheory.Category.Preorder
import Mathlib.CategoryTheory.ConcreteCategory.BundledHom
import Mathlib.Or... |
Order\Category\Semilat.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.PartOrd
import Mathlib.Order.Hom.Lattice
/-!
# The categories of semilattices
This defines `SemilatSupCat` and `SemilatInfCat`, the catego... |
Order\CompactlyGenerated\Basic.lean | /-
Copyright (c) 2021 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.Order.Atoms
import Mathlib.Order.OrderIsoNat
import Mathlib.Order.RelIso.Set
import Mathlib.Order.SupClosed
import Mathlib.Order.SupIndep
import Mathlib.Orde... |
Order\CompactlyGenerated\Intervals.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.CompleteLatticeIntervals
import Mathlib.Order.CompactlyGenerated.Basic
/-!
# Results about compactness properties for intervals in complete lattices
... |
Order\ConditionallyCompleteLattice\Basic.lean | /-
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Order.Bounds.Basic
import Mathlib.Order.WellFounded
import Mathlib.Data.Set.Image
import Mathlib.Order.Interval.Set.Basic
import Mathlib.Data.Set... |
Order\ConditionallyCompleteLattice\Finset.lean | /-
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Order.ConditionallyCompleteLattice.Basic
import Mathlib.Data.Set.Finite
/-!
# Conditionally complete lattices and finite sets.
-/
open Set
v... |
Order\ConditionallyCompleteLattice\Group.lean | /-
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Order.ConditionallyCompleteLattice.Basic
import Mathlib.Algebra.Order.Group.Unbundled.Basic
import Mathlib.Algebra.Order.Monoid.Unbundled.OrderDu... |
Order\Extension\Linear.lean | /-
Copyright (c) 2021 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import Mathlib.Order.Zorn
/-!
# Extend a partial order to a linear order
This file constructs a linear order which is an extension of the given partial order, using Zor... |
Order\Extension\Well.lean | /-
Copyright (c) 2022 Yaël Dillies, Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Junyan Xu
-/
import Mathlib.Data.Prod.Lex
import Mathlib.SetTheory.Ordinal.Arithmetic
/-!
# Extend a well-founded order to a well-order
This file constructs a ... |
Order\Filter\Archimedean.lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yury Kudryashov
-/
import Mathlib.Algebra.Order.Archimedean.Basic
import Mathlib.Order.Filter.AtTopBot
import Mathlib.Tactic.GCongr
/-!
# `Filter.atTop` filter and arc... |
Order\Filter\AtTopBot.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jeremy Avigad, Yury Kudryashov, Patrick Massot
-/
import Mathlib.Algebra.BigOperators.Group.Finset
import Mathlib.Algebra.Order.Field.Defs
import Mathlib.Algebra.Order.... |
Order\Filter\Bases.lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Johannes Hölzl, Mario Carneiro, Patrick Massot
-/
import Mathlib.Data.Prod.PProd
import Mathlib.Data.Set.Countable
import Mathlib.Order.Filter.Prod
import Mathlib.Ord... |
Order\Filter\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, Jeremy Avigad
-/
import Mathlib.Data.Set.Finite
/-!
# Theory of filters on sets
## Main definitions
* `Filter` : filters on a set;
* `Filter.principal` : filter of a... |
Order\Filter\CardinalInter.lean | /-
Copyright (c) 2024 Josha Dekker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Josha Dekker
-/
import Mathlib.Order.Filter.Basic
import Mathlib.Order.Filter.CountableInter
import Mathlib.SetTheory.Cardinal.Ordinal
import Mathlib.SetTheory.Cardinal.Cofinality
/-!
#... |
Order\Filter\Cocardinal.lean | /-
Copyright (c) 2024 Josha Dekker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Josha Dekker
-/
import Mathlib.Order.Filter.Cofinite
import Mathlib.Order.Filter.CountableInter
import Mathlib.Order.Filter.CardinalInter
import Mathlib.SetTheory.Cardinal.Ordinal
import... |
Order\Filter\Cofinite.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jeremy Avigad, Yury Kudryashov
-/
import Mathlib.Order.Filter.AtTopBot
import Mathlib.Order.Filter.Pi
/-!
# The cofinite filter
In this file we define
`Filter.cofini... |
Order\Filter\CountableInter.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.Order.Filter.Curry
import Mathlib.Data.Set.Countable
/-!
# Filters with countable intersection property
In this file we define `CountableInte... |
Order\Filter\CountableSeparatingOn.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.Order.Filter.CountableInter
/-!
# Filters with countable intersections and countable separating families
In this file we prove some facts about a f... |
Order\Filter\Curry.lean | /-
Copyright (c) 2022 Kevin H. Wilson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin H. Wilson
-/
import Mathlib.Order.Filter.Prod
/-!
# Curried Filters
This file provides an operation (`Filter.curry`) on filters which provides the equivalence
`∀ᶠ a in l, ∀ᶠ b... |
Order\Filter\ENNReal.lean | /-
Copyright (c) 2021 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
import Mathlib.Topology.Instances.ENNReal
/-!
# Order properties of extended non-negative reals
This file compiles filter-related results about `ℝ≥0∞` (see Data/Real/EN... |
Order\Filter\EventuallyConst.lean | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Floris van Doorn
-/
import Mathlib.Order.Filter.AtTopBot
import Mathlib.Order.Filter.Subsingleton
/-!
# Functions that are eventually constant along a filter
In this... |
Order\Filter\Extr.lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Order.Filter.Basic
import Mathlib.Order.ConditionallyCompleteLattice.Basic
import Mathlib.Algebra.Order.Group.Defs
/-!
# Minimum and maximum w.r.t. ... |
Order\Filter\FilterProduct.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, Yury Kudryashov
-/
import Mathlib.Order.Filter.Ultrafilter
import Mathlib.Order.Filter.Ring
/-!
# Ultraproducts
If `φ` is an ultrafilter, then the... |
Order\Filter\IndicatorFunction.lean | /-
Copyright (c) 2020 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Yury Kudryashov
-/
import Mathlib.Order.Filter.AtTopBot
/-!
# Indicator function and filters
Properties of additive and multiplicative indicator functions involving `=ᶠ... |
Order\Filter\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
-/
import Mathlib.Order.Interval.Set.OrdConnected
import Mathlib.Order.Filter.SmallSets
import Mathlib.Order.Filter.AtTopBot
/-!
# Convergence of intervals
## ... |
Order\Filter\Ker.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.Filter.Basic
/-!
# Kernel of a filter
In this file we define the *kernel* `Filter.ker f` of a filter `f`
to be the intersection of all its sets.
W... |
Order\Filter\Lift.lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.Order.Filter.Bases
import Mathlib.Order.ConditionallyCompleteLattice.Basic
/-!
# Lift filters along filter and set functions
-/
open Set Filter Funct... |
Order\Filter\ListTraverse.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.Control.Traversable.Instances
import Mathlib.Order.Filter.Basic
/-!
# Properties of `Traversable.traverse` on `List`s and `Filter`s
In this file we pr... |
Order\Filter\ModEq.lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Algebra.Order.Ring.Abs
import Mathlib.Data.Nat.ModEq
import Mathlib.Order.Filter.AtTopBot
/-!
# Numbers are frequently ModEq to fixed numbers
In th... |
Order\Filter\NAry.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Order.Filter.Prod
/-!
# N-ary maps of filter
This file defines the binary and ternary maps of filters. This is mostly useful to define pointwise
operatio... |
Order\Filter\Partial.lean | /-
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
-/
import Mathlib.Order.Filter.Basic
import Mathlib.Data.PFun
/-!
# `Tendsto` for relations and partial functions
This file generalizes `Filter` definitions from functio... |
Order\Filter\Pi.lean | /-
Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov, Alex Kontorovich
-/
import Mathlib.Order.Filter.Bases
/-!
# (Co)product of a family of filters
In this file we define two filters on `Π i, α i` and prove some... |
Order\Filter\Pointwise.lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Yaël Dillies
-/
import Mathlib.Data.Set.Pointwise.SMul
import Mathlib.Order.Filter.NAry
import Mathlib.Order.Filter.Ultrafilter
/-!
# Pointwise operations on filters
Th... |
Order\Filter\Prod.lean | /-
Copyright (c) 2022 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johanes Hölzl, Patrick Massot, Yury Kudryashov, Kevin Wilson, Heather Macbeth
-/
import Mathlib.Order.Filter.Basic
/-!
# Product and coproduct filters
In this file we define `Filter.... |
Order\Filter\Ring.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jeremy Avigad
-/
import Mathlib.Order.Filter.Germ.OrderedMonoid
import Mathlib.Algebra.Order.Ring.Defs
/-!
# Lemmas about filters and ordered rings.
-/
namespace Filte... |
Order\Filter\SmallSets.lean | /-
Copyright (c) 2022 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Floris van Doorn, Yury Kudryashov
-/
import Mathlib.Order.Filter.Lift
import Mathlib.Order.Filter.AtTopBot
/-!
# The filter of small sets
This file defines the filter... |
Order\Filter\Subsingleton.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.Order.Filter.Bases
import Mathlib.Order.Filter.Ultrafilter
/-!
# Subsingleton filters
We say that a filter `l` is a *subsingleton* if there exists a... |
Order\Filter\Ultrafilter.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jeremy Avigad, Yury Kudryashov
-/
import Mathlib.Order.Filter.Cofinite
import Mathlib.Order.ZornAtoms
/-!
# Ultrafilters
An ultrafilter is a minimal (maximal in the s... |
Order\Filter\ZeroAndBoundedAtFilter.lean | /-
Copyright (c) 2022 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck, David Loeffler
-/
import Mathlib.Algebra.Module.Submodule.Basic
import Mathlib.Topology.Algebra.Monoid
import Mathlib.Analysis.Asymptotics.Asymptotics
import Mathlib.Al... |
Order\Filter\Germ\Basic.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, Abhimanyu Pallavi Sudhir
-/
import Mathlib.Order.Filter.Basic
import Mathlib.Algebra.Module.Pi
/-!
# Germ of a function at a filter
The germ of a function `f ... |
Order\Filter\Germ\OrderedMonoid.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, Abhimanyu Pallavi Sudhir
-/
import Mathlib.Algebra.Module.Pi
import Mathlib.Algebra.Order.Monoid.Canonical.Defs
import Mathlib.Order.Filter.Germ.Basic
/-!
# Or... |
Order\Fin\Basic.lean | /-
Copyright (c) 2017 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Keeley Hoek
-/
import Mathlib.Data.Fin.Basic
import Mathlib.Order.Hom.Set
/-!
# `Fin n` forms a bounded linear order
This file contains the linear ordered instance ... |
Order\Fin\Tuple.lean | /-
Copyright (c) 2019 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Yury Kudryashov, Sébastien Gouëzel, Chris Hughes
-/
import Mathlib.Data.Fin.VecNotation
import Mathlib.Logic.Equiv.Fin
import Mathlib.Order.Fin.Basic
import Mathlib... |
Order\Heyting\Basic.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.PropInstances
/-!
# Heyting algebras
This file defines Heyting, co-Heyting and bi-Heyting algebras.
A Heyting algebra is a bounded distributive la... |
Order\Heyting\Boundary.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.BooleanAlgebra
import Mathlib.Tactic.Common
/-!
# Co-Heyting boundary
The boundary of an element of a co-Heyting algebra is the intersection of its... |
Order\Heyting\Hom.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.Lattice
/-!
# Heyting algebra morphisms
A Heyting homomorphism between two Heyting algebras is a bounded lattice homomorphism that preserves
He... |
Order\Heyting\Regular.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.GaloisConnection
/-!
# Heyting regular elements
This file defines Heyting regular elements, elements of a Heyting algebra that are their own double... |
Order\Hom\Basic.lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.Logic.Equiv.Option
import Mathlib.Order.RelIso.Basic
import Mathlib.Order.Disjoint
import Mathlib.Order.WithBot
import Mathlib.Tactic.Monotonicity.Attr... |
Order\Hom\Bounded.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.Order.BoundedOrder
/-!
# Bounded order homomorphisms
This file defines (bounded) order homomorphisms.
We use the `DFunLik... |
Order\Hom\CompleteLattice.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
import Mathlib.Order.Hom.Lattice
/-!
# Complete lattice homomorphisms
This file defines frame homomorphisms and complete lattice homomor... |
Order\Hom\Lattice.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.Bounded
import Mathlib.Order.SymmDiff
/-!
# Lattice homomorphisms
This file defines (bounded) lattice homomorphisms.
We use the `DFunLike` des... |
Order\Hom\Order.lean | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Anne Baanen
-/
import Mathlib.Logic.Function.Iterate
import Mathlib.Order.GaloisConnection
import Mathlib.Order.Hom.Basic
/-!
# Lattice structure on order homomorphisms
... |
Order\Hom\Set.lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.Order.Hom.Basic
import Mathlib.Logic.Equiv.Set
import Mathlib.Data.Set.Image
/-!
# Order homomorphisms and sets
-/
open OrderDual
variable {F α β γ... |
Order\Interval\Basic.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.Interval.Set.Basic
import Mathlib.Data.Set.Lattice
import Mathlib.Data.SetLike.Basic
/-!
# Order intervals
This file defines (nonempty) closed inte... |
Order\Interval\Multiset.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.Basic
/-!
# Intervals as multisets
This file defines intervals as multisets.
## Main declarations
In a `LocallyFiniteOrder`,
* `M... |
Order\Interval\Finset\Basic.lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Yaël Dillies
-/
import Mathlib.Order.Cover
import Mathlib.Order.Interval.Finset.Defs
/-!
# Intervals as finsets
This file provides basic results about all the `Finset... |
Order\Interval\Finset\Box.lean | /-
Copyright (c) 2024 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Algebra.Order.Ring.Prod
import Mathlib.Data.Int.Interval
import Mathlib.Order.Disjointed
import Mathlib.Tactic.AdaptationNote
import Mathlib.Tactic.Ring
im... |
Order\Interval\Finset\Defs.lean | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Data.Finset.Preimage
import Mathlib.Order.Interval.Set.Image
import Mathlib.Order.Interval.Set.UnorderedInterval
/-!
# Locally finite orders
This file de... |
Order\Interval\Finset\Fin.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
/-!
# Finite intervals in `Fin n`
This file proves that `Fin n` is a `LocallyFiniteOrder` and calculates the cardinality of its... |
Order\Interval\Finset\Nat.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.Multiset
/-!
# Finite intervals of naturals
This file proves that `ℕ` is a `LocallyFiniteOrder` and calculates the cardinality of its
inte... |
Order\Interval\Set\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, Mario Carneiro, Patrick Massot, Yury Kudryashov, Rémy Degenne
-/
import Mathlib.Order.MinMax
import Mathlib.Data.Set.Subsingleton
import Mathlib.Tactic.Says
/-!
# Inte... |
Order\Interval\Set\Disjoint.lean | /-
Copyright (c) 2019 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Yury Kudryashov
-/
import Mathlib.Data.Set.Lattice
/-!
# Extra lemmas about intervals
This file contains lemmas about intervals that cannot be included into `Orde... |
Order\Interval\Set\Image.lean | /-
Copyright (c) 2023 Kim Liesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Liesinger, Yaël Dillies
-/
import Mathlib.Order.Interval.Set.Basic
import Mathlib.Data.Set.Function
import Mathlib.Order.Directed
/-!
# Monotone functions on intervals
This file s... |
Order\Interval\Set\Infinite.lean | /-
Copyright (c) 2020 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton
-/
import Mathlib.Data.Set.Finite
/-!
# Infinitude of intervals
Bounded intervals in dense orders are infinite, as are unbounded intervals
in orders that are unbounded on th... |
Order\Interval\Set\IsoIoo.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.Monotone.Odd
import Mathlib.Algebra.Order.Field.Basic
import Mathlib.Tactic.FieldSimp
/-!
# Order isomorphism between a linear ordered field a... |
Order\Interval\Set\Monotone.lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Order.Interval.Set.Disjoint
import Mathlib.Order.SuccPred.Basic
/-!
# Monotonicity on intervals
In this file we prove that `Set.Ici` etc are monoto... |
Order\Interval\Set\OrdConnected.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.Order.Interval.Set.OrderEmbedding
import Mathlib.Order.Antichain
import Mathlib.Order.SetNotation
/-!
# Order-connected sets
We say that a se... |
Order\Interval\Set\OrdConnectedComponent.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.Interval.Set.OrdConnected
import Mathlib.Data.Set.Lattice
/-!
# Order connected components of a set
In this file we define `Set.ordConnectedC... |
Order\Interval\Set\OrderEmbedding.lean | /-
Copyright (c) 2024 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Order.Interval.Set.UnorderedInterval
import Mathlib.Order.Hom.Basic
/-!
# Preimages of intervals under order embeddings
In this file we prove that ... |
Order\Interval\Set\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, Mario Carneiro, Patrick Massot, Yury Kudryashov, Rémy Degenne
-/
import Mathlib.Order.Interval.Set.Basic
import Mathlib.Order.Hom.Set
/-!
# Lemmas about images of inte... |
Order\Interval\Set\Pi.lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Algebra.Group.Pi.Basic
import Mathlib.Order.Interval.Set.Basic
import Mathlib.Order.Interval.Set.UnorderedInterval
import Mathlib.Data.Set.Lattice
/... |
Order\Interval\Set\ProjIcc.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.Data.Set.Function
import Mathlib.Order.Interval.Set.OrdConnected
/-!
# Projection of a line onto a closed interval
Given a li... |
Order\Interval\Set\SurjOn.lean | /-
Copyright (c) 2020 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
import Mathlib.Order.Interval.Set.Basic
import Mathlib.Data.Set.Function
/-!
# Monotone surjective functions are surjective on intervals
A monotone surjective fun... |
Order\Interval\Set\UnorderedInterval.lean | /-
Copyright (c) 2020 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou
-/
import Mathlib.Order.Interval.Set.Image
import Mathlib.Order.Bounds.Basic
import Mathlib.Tactic.Common
/-!
# Intervals without endpoints ordering
In any lattice `α`, ... |
Order\Interval\Set\WithBotTop.lean | /-
Copyright (c) 2022 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import Mathlib.Data.Set.Image
import Mathlib.Order.Interval.Set.Basic
/-!
# Intervals in `WithTop α` and `WithBot α`
In this file we prove various lemmas ab... |
Order\Monotone\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, Yaël Dillies
-/
import Mathlib.Logic.Function.Iterate
import Mathlib.Init.Data.Int.Order
import Mathlib.Order.Compare
import Mathlib.Order.Max
import Math... |
Order\Monotone\Extension.lean | /-
Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Yury Kudryashov
-/
import Mathlib.Order.ConditionallyCompleteLattice.Basic
/-!
# Extension of a monotone function from a set to the whole space
In this file we ... |
Order\Monotone\Monovary.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.Defs
import Mathlib.Order.Lattice
/-!
# Monovariance of functions
Two functions *vary together* if a strict change in the first implies a change... |
Order\Monotone\Odd.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.Monotone.Union
import Mathlib.Algebra.Order.Group.Instances
/-!
# Monotonicity of odd functions
An odd function on a linear ordered additive ... |
Order\Monotone\Union.lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Sébastien Gouëzel
-/
import Mathlib.Order.Bounds.Basic
/-!
# Monotonicity on intervals
In this file we prove that a function is (strictly) monotone (or antitone) on... |
Order\Partition\Equipartition.lean | /-
Copyright (c) 2022 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.Equitable
import Mathlib.Logic.Equiv.Fin
import Mathlib.Order.Partition.Finpartition
/-!
# Finite equipartitions
Thi... |
Order\Partition\Finpartition.lean | /-
Copyright (c) 2022 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.Algebra.BigOperators.Group.Finset
import Mathlib.Order.SupIndep
import Mathlib.Order.Atoms
/-!
# Finite partitions
In this fi... |
Order\Rel\GaloisConnection.lean | /-
Copyright (c) 2024 Lagrange Mathematics and Computing Research Center. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anthony Bordg
-/
import Mathlib.Data.Rel
import Mathlib.Order.GaloisConnection
/-!
# The Galois Connection Induced by a Relation
In this file, we ... |
Order\RelIso\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.Init.Algebra.Classes
import Mathlib.Data.FunLike.Basic
import Mathlib.Logic.Embedding.Basic
import Mathlib.Order.RelClasses
/-!
# Relation homomorphis... |
Order\RelIso\Group.lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Algebra.Group.Defs
import Mathlib.Order.RelIso.Basic
/-!
# Relation isomorphisms form a group
-/
variable {α : Type*} {r : α → α → Prop}
namespace ... |
Order\RelIso\Set.lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Order.RelIso.Basic
import Mathlib.Logic.Embedding.Set
import Mathlib.Logic.Equiv.Set
/-!
# Interactions between relation homomorphisms and sets
It is... |
Order\SuccPred\Basic.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.CompleteLattice
import Mathlib.Order.Cover
import Mathlib.Order.GaloisConnection
import Mathlib.Order.Iterate
import Mathlib.Order.WellFounded
/-!
#... |
Order\SuccPred\CompleteLinearOrder.lean | /-
Copyright (c) 2023 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.Order.SuccPred.Limit
import Mathlib.Order.ConditionallyCompleteLattice.Basic
/-!
# Relation between `IsSuccLimit` and `iSup` in (conditionally) complete li... |
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