chars int64 40 24k | content_type stringclasses 9
values | id stringlengths 13 64 | source stringclasses 5
values | subset stringclasses 31
values | text stringlengths 40 24k |
|---|---|---|---|---|---|
23,939 | lean_file_chunk | a0e5074de9ee287833eeb7d5f108d907f560cc3130c9565c0374938a4ac3b873 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Order.PropInstances
public import Mathlib.Order.GaloisConnection.Defs
/-!
# Heyting algebras
This file defines Heyting, co-Heyting and bi-... |
16,714 | lean_file_chunk | 95d73d383e1924ddfb67f534cbe2cd368fe216feacc2324e1cbf6f1eee7bca28 | lean_source_file | pkg_mathlib_source_file_chunks | theorem compl_bot : (⊥ : α)ᶜ = ⊤ := by rw [← himp_bot, himp_self]
@[simp] theorem le_compl_self : a ≤ aᶜ ↔ a = ⊥ := by
rw [le_compl_iff_disjoint_left, disjoint_self]
@[simp] theorem ne_compl_self [Nontrivial α] : a ≠ aᶜ := by
intro h
cases le_compl_self.1 (le_of_eq h)
simp at h
@[simp] theorem compl_ne_self ... |
18,305 | lean_file_chunk | 2cb0ecbf680013df5044676f367b10f41c356dfaf50cdffd3387d38d1054e120 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Order.Hom.BoundedLattice
/-!
# Heyting algebra morphisms
A Heyting homomorphism between two Heyting algebras is a bounded lattice homomorp... |
3,584 | lean_file_chunk | 2058bec8a44d9e58d65226688fcae8574e8028678bc67d4676d4e9319b17214c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
module
public 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 o... |
3,666 | lean_file_chunk | 21ec013be90ccb20da98aad3f895b8ed82530c1473c3d53964f1973ef8f2f6df | lean_source_file | pkg_mathlib_source_file_chunks | /-
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
-/
module
public import Mathlib.Data.Prod.Lex
public import Mathlib.SetTheory.Ordinal.Rank
/-!
# Extend a well-founded order to a well-order
This fi... |
7,707 | lean_file_chunk | c5007857bebb2f7a4d0b679dfbb65a23741317a6c7ef7d60c2e9cb6e14c6a3ed | lean_source_file | pkg_mathlib_source_file_chunks | /-
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
-/
module
public import Mathlib.Data.Fin.VecNotation
public import Mathlib.Logic.Equiv.Fin.Basic
public import Mat... |
2,535 | lean_file_chunk | 083afbcddaeb4fb781441c956468d58f23f50cf05cfe39c8a4fcaaf10c4e35a6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.Order.Fin.Tuple
public import Mathlib.Order.Hom.Set
public import Mathlib.Data.Finset.Insert
/-!
# Order isomorphisms from Fin to finsets
We def... |
15,405 | lean_file_chunk | 9b4522d595be7f8d31ac7148292dba8b7fc3a909636f85d2a15ac5d072c75657 | lean_source_file | pkg_mathlib_source_file_chunks | /-
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
-/
module
public import Mathlib.Data.Fin.Embedding
public import Mathlib.Data.Fin.Rev
public import Mathlib.Order.Hom.Basic
/-!
# `Fin n` forms a bounde... |
563 | lean_file_chunk | 55a880e3ddd85d9fac2bf3fb92d5e536eb35a3c3b460d4f862bf5eb71903e81e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Batteries.Data.Fin.Lemmas
public import Mathlib.Order.Fin.Basic
public import Mathlib.Order.MinMax
/-!
# Lemmas about `Fin.clamp`
-/
namespace Fin
pub... |
1,220 | lean_file_chunk | 70719b2d1d16dfbffa6240f75cdb1667fe28a35c858b90f427e8dd278cd7b481 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.Order.Fin.Basic
public import Mathlib.Data.Fintype.Basic
/-!
# The order isomorphism `Fin (n + 1) ≃o {i}ᶜ`
Given `i : Fin (n + 2)`, we show that... |
19,220 | lean_file_chunk | 8dfa5cfcbc4c4e68084d9f16938c4cf7e0eb4c119c5610329722dab5461114ba | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Order.Hom.Bounded
public import Mathlib.Order.Hom.Lattice
public import Mathlib.Order.SymmDiff
/-!
# Bounded lattice homomorphisms
This fi... |
7,332 | lean_file_chunk | f9a14f8238487e74787269bb9a6fa86fec19b55a574dbc90e87329d465eaddea | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Violeta Hernández Palacios. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Violeta Hernández Palacios
-/
module
public import Mathlib.Data.Prod.Lex
public import Mathlib.Data.Sum.Order
public import Mathlib.Order.Hom.Set
public import Mathlib.Ord... |
4,673 | lean_file_chunk | 645c08d536f419bda7b14a7264ce388eaa964d505457778e0272a602b42dedf5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
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
-/
module
public import Mathlib.Logic.Function.Iterate
public import Mathlib.Order.GaloisConnection.Basic
public import Mathlib.Order.Hom.Basic
/-!
# Lattice... |
23,995 | lean_file_chunk | 9284873c2ff6f47729e22b004db352687bfe85f9c73c56ea64579067e790df1f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
module
public import Mathlib.Order.Disjoint
public import Mathlib.Order.RelIso.Basic
public import Mathlib.Tactic.Monotonicity.Attr
public import Mathlib.Tactic.PPWi... |
17,835 | lean_file_chunk | b49f73036c7e854ad1f591d7640fb1a9ab33ec3848fdb015d4be2743406f7e63 | lean_source_file | pkg_mathlib_source_file_chunks | lemma IsCompl.of_orderEmbedding [BoundedOrder α] [BoundedOrder β] {a₁ a₂ : α} :
IsCompl (f a₁) (f a₂) → IsCompl a₁ a₂ := fun ⟨hd, hcd⟩ ↦
⟨Disjoint.of_orderEmbedding f hd, Codisjoint.of_orderEmbedding f hcd⟩
end Disjoint
section RelHom
variable [PartialOrder α] [Preorder β]
namespace RelHom
variable (f : ((· ... |
8,237 | lean_file_chunk | b2c145dd30361c83c71ec1fb906d0e88f292bb9e1c28d4d6ec58b106b287843d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
module
public import Mathlib.Logic.Equiv.Set
public import Mathlib.Order.Hom.Basic
public import Mathlib.Order.Interval.Set.Defs
public import Mathlib.Order.WellFoun... |
16,289 | lean_file_chunk | fdc675a73ae33fed4a58746528a099e9f0aceafa215536596ca71b5237afb0eb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Order.Hom.Basic
/-!
# Bounded order homomorphisms
This file defines (bounded) order homomorphisms.
We use the `DFunLike` design, so each ... |
11,313 | lean_file_chunk | 7879fa465ec1b88b73fb7097d64390ddef731d94223c04618bff7b2cbe830395 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Order.Hom.BoundedLattice
public import Mathlib.Order.WithBot
/-!
# Adjoining `⊤` and `⊥` to order maps and lattice homomorphisms
This file... |
22,121 | lean_file_chunk | a3b98f03041738e6d9f8ffd4cb8040f8b2e36aad17c2ad3c152b5edc6b818c7e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Data.Set.Lattice.Image
public import Mathlib.Order.Hom.BoundedLattice
/-!
# Complete lattice homomorphisms
This file defines frame homomor... |
18,459 | lean_file_chunk | 1a4d6dfb34fd0457ffc7cfba877f27ece5391472e42b18a33fa8151d014e5d61 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Order.Hom.Basic
/-!
# Unbounded lattice homomorphisms
This file defines unbounded lattice homomorphisms. _Bounded_ lattice homomorphisms a... |
2,706 | lean_file_chunk | dc1ecb78a3a4bfda4dffd0b3bc318449eeece27e6d725d6d5a13c482b6894397 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Daniel Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Daniel Morrison
-/
module
public import Mathlib.Data.Set.PowersetCard
public import Mathlib.Data.Finset.Sort
public import Mathlib.Logic.Equiv.Fin.Basic
/-!
# Finite sets of an orde... |
5,248 | lean_file_chunk | 946d2f6b77567192ca0e7b0c30e66c52869c22db093f05edca1aca20ed31cb3c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Order.Category.Lat
/-!
# The category of distributive lattices
This file defines `DistLat`, the category of distributive lattices.
Note t... |
7,656 | lean_file_chunk | 9a382f68f19b084164694e6f469be7e5a187c40453241bf67e0f0f513b3f6f03 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.CategoryTheory.Adjunction.Unique
public import Mathlib.Order.Category.BddOrd
public import Mathlib.Order.Category.Lat
public import Mathlib.... |
5,149 | lean_file_chunk | 4a29f1d7cae999678acf89469378db3ca371315a1c8dbdb05c1c54c92555c43a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
module
public import Mathlib.CategoryTheory.Category.Cat
public import Mathlib.CategoryTheory.Category.Preorder
public import Mathlib.CategoryTheory.ConcreteCategory... |
12,009 | lean_file_chunk | 0211d5a031d5296b6fd99cad557dbcf30ea5b3bd382baa2a3f7d536767160673 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou, Johan Commelin
-/
module
public import Mathlib.Order.Category.PartOrd
public import Mathlib.CategoryTheory.Limits.Filtered
public import Mathlib.CategoryTheory.Limits.Preserves.... |
6,346 | lean_file_chunk | 6697798969803b5912fd9a3bc6c53e32b1aaa4b7162a9d3fd88b8ee5a7c7da35 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Order.Category.BddLat
public import Mathlib.Order.Category.DistLat
/-!
# The category of bounded distributive lattices
This defines `BddDi... |
6,404 | lean_file_chunk | 07fb0d6ba4d56918c173358a73952e9a3c6de5bf9ef2d15323c1a6fe96305c0e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Data.Fintype.Order
public import Mathlib.Order.Category.BddDistLat
public import Mathlib.Order.Category.FinPartOrd
/-!
# The category of fi... |
4,416 | lean_file_chunk | d4a95415be572a9e5ee9ff3fb002d1e6fe24651b5ded05392d606e6462f653a9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
module
public import Mathlib.Order.Category.Lat
/-!
# Category of linear orders
This defines `LinOrd`, the category of linear orders with monotone maps.
-/
@[expo... |
7,269 | lean_file_chunk | 4dc7006e24a60516e96f66610607c887a80cd8afc6e55d8dae6be4a00b83257b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
module
public import Mathlib.Order.Antisymmetrization
public import Mathlib.Order.Category.Preord
public import Mathlib.CategoryTheory.Adjunction.Basic
/-!
# Catego... |
3,868 | lean_file_chunk | ec65c39790e2ee0c93d3a4a22a6fdd3d08023ef856fa033b99a2f6902df8a780 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.CategoryTheory.FintypeCat
public import Mathlib.Order.Category.PartOrd
/-!
# The category of finite partial orders
This defines `FinPartOr... |
4,986 | lean_file_chunk | 23e07f3a151a9895fb52114892c8bb1ab4420c5b0bfab048332f46ef2fb3aa51 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Order.Category.PartOrd
public import Mathlib.Order.Hom.Lattice
/-!
# The category of lattices
This defines `Lat`, the category of lattices... |
4,615 | lean_file_chunk | 657c5155a0c88e457652b3cc5ebb63ae240229d4920b19943e410a12b6b41e82 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Order.Category.BddDistLat
public import Mathlib.Order.Heyting.Hom
/-!
# The category of Heyting algebras
This file defines `HeytAlg`, the ... |
8,010 | lean_file_chunk | c3b3bd48af255c6cf788a6d5592488443f28b3f45ac25a5126e59336dcfd9d25 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
module
public import Mathlib.CategoryTheory.ConcreteCategory.EpiMono
public import Mathlib.CategoryTheory.Limits.Shapes.Images
public import Mathlib.CategoryTheory.L... |
4,222 | lean_file_chunk | dc95f064ee425d779626bd2f8b18a0ebc88e54883c5671d48a17766d5eda480d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
module
public import Mathlib.Order.OmegaCompletePartialOrder
public import Mathlib.CategoryTheory.Limits.Shapes.Products
public import Mathlib.CategoryTheory.Limits.Shapes... |
2,436 | lean_file_chunk | b583253da3bfece5114d85815feda2a6ff53994c4e3509d785dbe2cdeefae0fe | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Order.Category.BddLat
public import Mathlib.Order.Hom.CompleteLattice
/-!
# The category of complete lattices
This file defines `CompleteL... |
4,923 | lean_file_chunk | 422d7490563cd7e951c8258da7fcd1291b2678a1a7478f3ca74645c492356b41 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Order.Category.PartOrd
public import Mathlib.Order.Hom.BoundedLattice
/-!
# The categories of semilattices
This defines `SemilatSupCat` an... |
5,899 | lean_file_chunk | a6fed73ef06597ea557f50d0280f93c0f971d2d329134eddae98098e9a8fb86b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.CategoryTheory.Category.Bipointed
public import Mathlib.Order.Category.PartOrd
public import Mathlib.Order.Hom.Bounded
/-!
# The category o... |
5,869 | lean_file_chunk | ab58bab11beddbfa157503c2a0af0074cdacdd35dca03b2be7e2b144c3cd9676 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Order.Category.HeytAlg
public import Mathlib.Order.Hom.CompleteLattice
/-!
# The category of Boolean algebras
This defines `BoolAlg`, the ... |
4,218 | lean_file_chunk | b05cbfdacc1721a98291e2a4a0cf44f1e852df9fccc956f220e65053ba85b8f6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Order.Category.Lat
public import Mathlib.Order.Hom.CompleteLattice
public import Mathlib.CategoryTheory.ConcreteCategory.Bundled
/-!
# The ... |
3,884 | lean_file_chunk | bba52daa4bd0dadb18fa21a309fc2bed80a9b59a6de569e118dbaeff9f22131d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Data.Fintype.Powerset
public import Mathlib.Order.Category.BoolAlg
public import Mathlib.Order.Category.FinBddDistLat
public import Mathlib.... |
22,111 | lean_file_chunk | 2aed1941b4a2e8caddc55006d9bd2ec038a52c7b768e199f94cd640a66415c1d | lean_source_file | pkg_mathlib_source_file_chunks | /-
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
-/
module
public import Mathlib.Order.SuccPred.Archimedean
public import Mathlib.Order.BoundedOrder.Lattice
/-!
# Successor and predecessor lim... |
16,558 | lean_file_chunk | 9c1f845ca6e19e2726428d02fa5e36edc4a4ed9b8d178c0090b42e4d83d72cc4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Order.SuccPred.Basic
/-!
# Archimedean successor and predecessor
* `IsSuccArchimedean`: `SuccOrder` where `succ` iterated to an element gi... |
6,460 | lean_file_chunk | bb161039be0076a5446cb70de6a351a2fbbdee1eb0e65c939f05b2f30365ca59 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.Order.ConditionallyCompleteLattice.Indexed
public import Mathlib.Order.SuccPred.Limit
/-!
# Relation between `IsSuccPrelimit` and `iSup` in ... |
17,697 | lean_file_chunk | be22b5c0992ddc75744efc3ad9f16398feec6f261647844febca759061afaad4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
module
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Data.Countable.Basic
public import Mathlib.Data.Finset.Max
public import Mathlib.Data.Fintype.... |
23,982 | lean_file_chunk | c6ad59260f3c77e24d89c81181048352633d6e68ceeba05075df3a6822c1dbe0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Order.ConditionallyCompleteLattice.Basic
public import Mathlib.Order.Cover
public import Mathlib.Order.Iterate
/-!
# Successor and predeces... |
12,660 | lean_file_chunk | 0f241bc21ab23e5e320ebdedff20160626e14283a9c99c23f88f9bd5ffe664ab | lean_source_file | pkg_mathlib_source_file_chunks | simp_rw [← Ioi_inter_Iio, Ioi_pred_eq_insert, insert_inter_of_mem (mem_Iio.2 h)]
@[simp]
theorem Ioo_eq_empty_iff_pred_le : Ioo a b = ∅ ↔ pred b ≤ a := by
refine ⟨fun h ↦ ?_, fun h ↦ ?_⟩
· contrapose! h
exact ⟨pred b, h, pred_lt_iff_not_isMin.mpr (not_isMin b)⟩
· ext x
suffices a < x → b ≤ x by simpa
... |
7,082 | lean_file_chunk | 0a562e145cd666db3d6bd879fa797daf06601ec6c2595737f7b06f4f47a4ba34 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Daniel Weber. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Daniel Weber
-/
module
public import Mathlib.Order.SuccPred.Archimedean
public import Mathlib.Data.Nat.Find
public import Mathlib.Order.Atoms
public import Mathlib.Data.SetLike.Basic
/... |
6,559 | lean_file_chunk | fc81e3f13935020028c75a3702074e812ebb69c2a9ad3f0e832431d4de669268 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
module
public import Mathlib.Order.SuccPred.Archimedean
/-!
# Relations on types with a `SuccOrder`
This file contains properties about relations on types with... |
2,602 | lean_file_chunk | 090c6dab734cdf91937917f65fa29e6c0e1317b9c2cddd6fd98867ad0bb94ba7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Violeta Hernández Palacios. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Violeta Hernández Palacios
-/
module
public import Mathlib.Order.InitialSeg
public import Mathlib.Order.SuccPred.Limit
/-!
# Initial segments and successors
We establish... |
3,355 | lean_file_chunk | 900ff3bfda72493f989927d3a226c6fd5a62d98ca101ac800ee641303579aa5a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yaël Dillies, Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Andrew Yang
-/
module
public import Mathlib.Order.SuccPred.Basic
/-!
# Successor function on `WithBot`
This file defines the successor of `a : WithBot α` as... |
8,987 | lean_file_chunk | 8951dbffd2293f2048271ba3cb5d264604bdeee26e9cb7841dd4f83aee4340cb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Data.Set.Pairwise.Basic
public import Mathlib.Data.Set.Lattice
public import Mathlib.Order.SuccPred.Archimedean
/-!
# Intervals `Ixx ... |
5,836 | lean_file_chunk | d13ca8802a425993a1f9c171a432beae4f249b025211942648aef90fb71445c2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies, Sara Rousta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Sara Rousta
-/
module
public import Mathlib.Order.UpperLower.Closure
/-!
# Upper and lower set product
The Cartesian product of sets carries over to upper a... |
11,286 | lean_file_chunk | 35b918f92167af19e3ae7d23a1786a587adea3d2c82acc54def6d20b61ae398d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies, Sara Rousta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Sara Rousta
-/
module
public import Mathlib.Order.Interval.Set.OrdConnected
public import Mathlib.Order.Minimal
public import Mathlib.Order.UpperLower.Princip... |
8,140 | lean_file_chunk | ceb4c0e0901091f9dd00ac02fcad8994d0c688043cf9a92ca9bc242b5603543b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies, Sara Rousta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Sara Rousta
-/
module
public import Mathlib.Logic.Equiv.Set
public import Mathlib.Order.Interval.Set.OrderEmbedding
public import Mathlib.Order.SetNotation
pu... |
2,312 | lean_file_chunk | 7ffc97ff65e2bad0050c4c3a673d6e373bf5d73373f5980b6740bccf077a381f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies, Sara Rousta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Sara Rousta
-/
module
public import Mathlib.Order.UpperLower.Basic
/-!
# Upper/lower sets and fibrations
-/
public section
open Set
namespace Relation
va... |
4,019 | lean_file_chunk | 52e8f1503a79ceb0f9eba83b40c467f9d53600044d29dcb516557fae96d2a674 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies, Sara Rousta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Sara Rousta
-/
module
public import Mathlib.Order.Interval.Set.OrderIso
public import Mathlib.Order.UpperLower.CompleteLattice
/-!
# Principal upper/lower se... |
11,653 | lean_file_chunk | 1d988aebee000e97c057062c85ea124a744a34f46a6e464938f76e4bef0fef06 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies, Sara Rousta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Sara Rousta
-/
module
public import Mathlib.Data.Set.Lattice.Image
public import Mathlib.Data.SetLike.Basic
public import Mathlib.Order.UpperLower.Basic
/-!
... |
7,574 | lean_file_chunk | f437b70023b1e99de2fb7ae64fa7ae92c100662b695b5b58981aaf17b23ff06d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Jeremy Tan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Tan
-/
module
public import Mathlib.Data.Set.Image
public import Mathlib.Data.SetLike.Basic
public import Mathlib.Order.Interval.Set.Defs
public import Mathlib.Order.SetNotation
/... |
1,911 | lean_file_chunk | ef9d245c7a140c2e142a320e99d2bd86b7f6102389e10114ecd552061192b36d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies, Sara Rousta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Order.Hom.CompleteLattice
public import Mathlib.Order.UpperLower.Principal
/-!
# `UpperSet.Ici` etc. as `Sup`/`sSup`/`Inf`/`sI... |
938 | lean_file_chunk | 732a502a6bbfd81e54b1f6592ffe24c82653f2131d43c3fc234e6d0640467157 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yaël Dillies, Sara Rousta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Data.Set.Finite.Lattice
public import Mathlib.Order.Interval.Finset.Defs
public import Mathlib.Order.UpperLower.Closure
/-!
# ... |
7,047 | lean_file_chunk | 3df8c419175874a2924f40ec70dbb9ac308776cc86ac68cc360ee9aeb123e848 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
module
public import Mathlib.Order.CompleteLattice.Defs
public import Mathlib.Order.ConditionallyCompletePartialOrder.Defs
import Mathlib.Data.Set.Lattice
/-! # Basi... |
4,839 | lean_file_chunk | f9e59cbeb24ee5c2089ecfcd4537a64e2e764beaae60be7c08c658a55c7f7483 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
module
public import Mathlib.Order.Bounds.Defs
public import Mathlib.Order.Directed
public import Mathlib.Order.SetNotation
/-! # Conditionally complete partial order... |
12,208 | lean_file_chunk | 3d4316e99b779de6592b8d6ded7739cf415c452a686259b728e40da7d9e33c89 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
module
public import Mathlib.Order.ConditionallyCompletePartialOrder.Basic
public import Mathlib.Order.GaloisConnection.Basic
/-!
# Indexed sup / inf in conditionally... |
2,943 | lean_file_chunk | 0cb68117def8b2d0ff9c69e8aa35af3af1b2dc44186702f8ef9363d6d8419499 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
module
public import Mathlib.Order.Interval.Basic
public import Mathlib.Data.Prod.Lex
public import Mathlib.Tactic.FastInstance
meta import Mathlib.Order.Interval.Basic -... |
20,868 | lean_file_chunk | 73ca120cecf48924f439bcd955539e2fa0f8113fd70fcc34a43a6f56e141eff4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Order.Interval.Set.Basic
public import Mathlib.Data.Set.Lattice.Image
public import Mathlib.Data.SetLike.Basic
/-!
# Order intervals
This ... |
9,660 | lean_file_chunk | 96ab518836445467fc674ce7657b37ebb62979e0f62e7af9ad1d35cef5cd238a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Order.Interval.Finset.Basic
/-!
# Intervals as multisets
This file defines intervals as multisets.
## Main declarations
In a `LocallyFin... |
5,042 | lean_file_chunk | b84c4038d6f8d1302b750f34a0d4815071c43ce8daaf767d00c2e844103ab0c4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Christopher Hoskin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Hoskin
-/
module
public import Mathlib.Data.Setoid.Basic
public import Mathlib.Order.Lattice
public import Mathlib.Order.Hom.Lattice
/-!
# Lattice Congruences
## Mai... |
4,203 | lean_file_chunk | 4d1114984ce9f5048054f250b2f4ff2f29812249337e24e2cb08871f5c16cfca | lean_source_file | pkg_mathlib_source_file_chunks | /-
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
-/
module
public import Mathlib.Data.Rel
/-!
# The Galois Connection Induced by a Relation
In this file, we show that an arbitrary ... |
1,777 | lean_file_chunk | 036ad800b842365ffd388fbb88a60a681af190afde4fb47670a86a7692dca9dd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Christopher Hoskin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Hoskin
-/
module
public import Mathlib.Order.ScottContinuity.Prod
/-!
# Scott continuity on complete lattices
## Main results
- `scottContinuous_iff_map_sSup`: A f... |
2,971 | lean_file_chunk | a407fc3ca9644d1b33b66625ca3c82b83d681afc117e558c21430596fe7041c9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Christopher Hoskin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Hoskin
-/
module
public import Mathlib.Order.ScottContinuity
public import Mathlib.Order.Bounds.Lattice
/-!
# Scott continuity on product spaces
## Main result
- `S... |
23,967 | lean_file_chunk | d8f80654c52a514c252697d17b6937aa8f125f2edf92bae164600c024017cdf7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
module
public import Mathlib.Logic.Embedding.Basic
public import Mathlib.Order.RelClasses
/-!
# Relation homomorphisms, embeddings, isomorphisms
This file defines ... |
6,041 | lean_file_chunk | e70d09883bbb1979ffad316ae26514237b589087b6fe245fb43e37c25e30ce55 | lean_source_file | pkg_mathlib_source_file_chunks | protected def cast {α β : Type u} {r : α → α → Prop} {s : β → β → Prop} (h₁ : α = β)
(h₂ : r ≍ s) : r ≃r s :=
⟨Equiv.cast h₁, @fun a b => by
subst h₁
rw [eq_of_heq h₂]
rfl⟩
protected theorem cast_symm {α β : Type u} {r : α → α → Prop} {s : β → β → Prop} (h₁ : α = β)
(h₂ : r ≍ s) : (RelIso.cast h₁... |
5,378 | lean_file_chunk | eb0490003163d284b6046f802d8522e1b8bfb6899810c00e0347a20379580865 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
module
public import Mathlib.Order.Directed
public import Mathlib.Order.RelIso.Basic
public import Mathlib.Logic.Embedding.Set
public import Mathlib.Logic.Equiv.Set
... |
13,380 | lean_file_chunk | fb534745795cbd52c997aa2ee3c903e227c2412bdfe2eb1c7705090654eea8f3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
module
public import Mathlib.Order.Max
public import Mathlib.Order.ULift
public import Mathlib.Tactic.ByCases
public import Mathlib.Tactic.Finiteness.Attr
/-!
# ⊤ a... |
3,728 | lean_file_chunk | 42e710ca1b20d3f7fe05dd7329f9baf25e2ab825daf0420e8d7e93a753aa59a1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
module
public import Mathlib.Order.BoundedOrder.Basic
public import Mathlib.Order.Monotone.Basic
/-!
# Monotone functions on bounded orders
-/
public section
ass... |
2,776 | lean_file_chunk | 56eee905606e6b63cdcaf76c2f635667e7c9d30c41b46f2c011347d7e76f7c02 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
module
public import Mathlib.Order.BoundedOrder.Basic
public import Mathlib.Order.Lattice
/-!
# Bounded lattices
This file contains miscellaneous lemmas about latt... |
23,965 | lean_file_chunk | c281c7f70a5ae20bea5c98407949a05e17dff843d833ebdded4915d82c311549 | lean_source_file | pkg_mathlib_source_file_chunks | /-
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
-/
module
public import Mathlib.Order.BooleanAlgebra.Defs
public import Mathlib.Tactic.GRewrite
/-!
# Basic properties of Boolean algebras
This fil... |
2,142 | lean_file_chunk | 32b3edea82a0e2c5e6864aaf631407fc9ba3ac321200cb4a59faedcab10398d0 | lean_source_file | pkg_mathlib_source_file_chunks | sup_inf_sdiff a b := hf <| by rw [map_sup, map_sdiff, map_inf, sup_inf_sdiff]
inf_inf_sdiff a b := hf <| by rw [map_inf, map_sdiff, map_inf, inf_inf_sdiff, map_bot]
-- See note [reducible non-instances]
/-- Pullback a `BooleanAlgebra` along an injection. -/
protected abbrev Function.Injective.booleanAlgebra [Max α] ... |
6,510 | lean_file_chunk | 4ed4ec2be01a6ecb24b165617c2dcc20c2d1c9a8a8fca7c5bf3a3c9c8a63f892 | lean_source_file | pkg_mathlib_source_file_chunks | /-
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
-/
module
public import Aesop
public import Mathlib.Order.Heyting.Basic
/-!
# (Generalized) Boolean algebras
This file sets up the theory of (gener... |
17,611 | lean_file_chunk | 9bd6e4190749414bf19fe56a89181b50fb8d2aa8a5222960c1a040be3413d83f | lean_source_file | pkg_mathlib_source_file_chunks | /-
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
-/
module
public import Mathlib.Data.Set.Insert
public import Mathlib.Order.BooleanAlgebra.Basic
public import Mathlib.Tactic.Tauto
public import Mathl... |
2,369 | lean_file_chunk | 0ae4a3d44169e345e63fac93f33a21a5310445143f0b942d90e024056ded04c2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
module
public import Mathlib.Order.ConditionallyCompleteLattice.Indexed
public import Mathlib.Algebra.Order.Group.Unbundled.Basic
public import Mathlib.Algebra... |
9,130 | lean_file_chunk | 3bdb161bf4a3d33f4399e35582c83e41c8540ba8af100b412456c71fc0f02009 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
module
public import Mathlib.Data.Finset.Max
public import Mathlib.Data.Set.Finite.Lattice
public import Mathlib.Order.ConditionallyCompleteLattice.Indexed
/-... |
23,990 | lean_file_chunk | f494b4e2b752a235d159c8b498101fbd7a68d69be50944960096e7cdc765104f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
module
public import Mathlib.Data.Set.Lattice
public import Mathlib.Order.ConditionallyCompleteLattice.Defs
public import Mathlib.Order.ConditionallyCompletePa... |
14,875 | lean_file_chunk | faf318d36517bc290239f9c24a782268ab6fc1dbd6c09bb9d8f8fb9a214c91c4 | lean_source_file | pkg_mathlib_source_file_chunks | theorem lt_csSup_iff' (hb : BddAbove s) : a < sSup s ↔ ∃ b ∈ s, a < b := by
simpa only [not_le, not_forall₂, exists_prop] using (csSup_le_iff' hb).not
theorem le_csSup_iff' {s : Set α} {a : α} (h : BddAbove s) :
a ≤ sSup s ↔ ∀ b, b ∈ upperBounds s → a ≤ b :=
⟨fun h _ hb => le_trans h (csSup_le' hb), fun hb => ... |
9,038 | lean_file_chunk | e392cfe71020e4b25c22065ca8ebd2f72f8942284be791afe4ef1ca51db8db10 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
module
public import Mathlib.Order.Bounds.Basic
public import Mathlib.Order.SetNotation
public import Mathlib.Order.WellFounded
/-!
# Definitions of condition... |
23,939 | lean_file_chunk | 553fe19b2e69a396be2e33053f86d16a728aae75b8e718c6148248048ce845ec | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Sébastian Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastian Gouëzel
-/
module
public import Mathlib.Order.ConditionallyCompleteLattice.Basic
public import Mathlib.Order.ConditionallyCompletePartialOrder.Indexed
/-!
# Indexed sup ... |
1,558 | lean_file_chunk | 39bfe3bcc4c0b8dc56956e8d1fab2488331e48fe2e11eafa37303fedca143c7a | lean_source_file | pkg_mathlib_source_file_chunks | (hne : s.Nonempty) : e (⨅ i : s, f i) = ⨅ i : s, e (f i) :=
e.dual.map_ciSup_set hf hne
end ConditionallyCompleteLattice
section ConditionallyCompleteLinearOrderBot
variable [ConditionallyCompleteLinearOrderBot α] [ConditionallyCompleteLinearOrderBot β]
@[simp]
lemma map_ciSup' (e : α ≃o β) (f : ι → α) : e (⨆ i, f... |
14,113 | lean_file_chunk | 1373b0756e46f43a33c826dfe2d45d6e8c8cc501d116f5c7f5c480f21c47ddce | lean_source_file | pkg_mathlib_source_file_chunks | /-
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
-/
module
public import Mathlib.Data.Set.Finite.Lattice
public import Mathlib.Order.CompleteLattice.Finset
public import Mathlib.Order.Filter.Basic
/-!
... |
12,686 | lean_file_chunk | ad2d0516d29131e42283ac8bb443624dad939d274b5181c2862c1ed6770bc8ae | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Order.Filter.CountableInter
/-!
# Filters with countable intersections and countable separating families
In this file we prove some ... |
14,513 | lean_file_chunk | 7b3816d1da32bcb4064fde8b8dcb7f39b3de1b4ae81bcb7490f39773cde6f2dd | lean_source_file | pkg_mathlib_source_file_chunks | /-
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
-/
module
public import Mathlib.Data.Finite.Prod
public import Mathlib.Data.Fintype.Pi
public import Mathlib.Data.Set.Finite.Lemmas
publ... |
4,599 | lean_file_chunk | b5d3eb6dbc041cd586f0bc8dd3d674f555f6159b9007e2f30b5ba916873ecfff | lean_source_file | pkg_mathlib_source_file_chunks | /-
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
-/
module
public import Mathlib.Algebra.Field.Defs
public import Mathlib.Algebra.Order.Group.Unbundled.Abs
public import Mathlib.Or... |
4,135 | lean_file_chunk | a872029bfdcc012a9cf839dc2c08ad4139562c807aa04f388335b3e4ac8b6acc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Josha Dekker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Josha Dekker
-/
module
public import Mathlib.Order.Filter.Cofinite
public import Mathlib.Order.Filter.CountableInter
public import Mathlib.Order.Filter.CardinalInter
public import Mathl... |
10,936 | lean_file_chunk | 40862e0a55d46647fdab25ac85c2a92fbd9ce66b9c9e0a3d41a2c400af0f1cd3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
module
public import Mathlib.Topology.Order.LiminfLimsup
public import Mathlib.Topology.Metrizable.Real
/-!
# Limsup and liminf of reals
This file compiles filter-rela... |
2,028 | lean_file_chunk | 48edb82532596fd4793cdec457af374f6a6b9d6dee2f45f8cc9775c6b5dd1f9f | lean_source_file | pkg_mathlib_source_file_chunks | /-
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
-/
module
public import Mathlib.Order.Filter.Germ.OrderedMonoid
public import Mathlib.Algebra.Order.Ring.Defs
/-!
# Lemmas about filters and ordered rin... |
3,407 | lean_file_chunk | 35cbfe34f871100d6d5449f2aef240af3cfba04827d9b907e5f31eb9545fb774 | lean_source_file | pkg_mathlib_source_file_chunks | /-
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
-/
module
public import Mathlib.Order.Filter.Prod
/-!
# Curried Filters
This file provides an operation (`Filter.curry`) on filters which provides the equivalence
`... |
10,504 | lean_file_chunk | 940d508e52780f87e83e171cd60aeddf7b234a3085d3f38a65952c2499b92909 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Gabriel Ebner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner, Yury Kudryashov, Patrick Massot
-/
module
public import Mathlib.Data.Set.Countable
public import Mathlib.Order.Filter.Bases.Finite
/-!
# Countably generated filters
In... |
12,894 | lean_file_chunk | ff10576b1518d07bf8f39b977e99c43b79b2b164a3bf10993f1bb5967ae26f2f | lean_source_file | pkg_mathlib_source_file_chunks | /-
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
-/
module
public import Mathlib.Order.Filter.Basic
public import Mathlib.Order.Filter.Map
/-!
# Convergence in terms of filters
The general notion of l... |
5,201 | lean_file_chunk | 196a7dbe9c6bd6a49165a93120ed52c5e7c47ca2c5c4851b06c3de97c1bb70e9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
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
-/
module
public import Mathlib.Algebra.Module.Submodule.Basic
public import Mathlib.Analysis.Asymptotics.Lemmas
public import Mathlib.Algebra.Algebra.P... |
13,578 | lean_file_chunk | e42645647f4a1c50d934f8988ee19755156e8b092a15fcd1bc2537d670490fc4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Order.Interval.Set.OrdConnected
public import Mathlib.Order.Filter.SmallSets
public import Mathlib.Order.Filter.AtTopBot.Basic
public ... |
12,492 | lean_file_chunk | cac908dc5a61f30358cf69d53d16a9d5230ab18b6126e236b63e7b2be0cbb90a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Order.Filter.Bases.Basic
public import Mathlib.Order.Filter.Prod
/-!
# N-ary maps of filter
This file defines the binary and ternary maps ... |
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