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 |
|---|---|---|---|---|---|
6,704 | lean_file_chunk | 5fc4e88bd08adf3c440c54878f24e2130fb27980f3cac64dc2a6de5e57fc4568 | 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, Floris van Doorn
-/
module
public import Mathlib.Algebra.Notation.Indicator
public import Mathlib.Order.Filter.AtTopBot.Basic
public import Mathlib.Order.Filter.Subs... |
23,923 | lean_file_chunk | 78b6585e6957857f6650ce0af259c43e5d077824b72feb5c88ffe3b08829e50a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Yury Kudryashov, Kevin H. Wilson, Heather Macbeth
-/
module
public import Mathlib.Order.Filter.Tendsto
/-!
# Product and coproduct filters
In this fi... |
329 | lean_file_chunk | 12678e2c99c4196759b74e06d699aa324162fac62f76896329c5e5902c2ec334 | lean_source_file | pkg_mathlib_source_file_chunks | lemma Tendsto.coprod_of_prod_top_left {f : α × β → γ} {la : Filter α} {lb : Filter β}
{lc : Filter γ} (h₁ : ∀ s : Set β, s ∈ lb → Tendsto f (la ×ˢ 𝓟 sᶜ) lc)
(h₂ : Tendsto f (⊤ ×ˢ lb) lc) :
Tendsto f (la.coprod lb) lc := by
simp_all [tendsto_prod_iff, coprod_eq_prod_top_sup_top_prod]
grind
end Coprod
... |
10,304 | lean_file_chunk | aa25123543609a87b0f08d900a9a5a420d6dc60c75a73c424f683629c331f57f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
-/
module
public import Mathlib.Order.Filter.Tendsto
public import Mathlib.Data.PFun
/-!
# `Tendsto` for relations and partial functions
This file generalizes `Filter` ... |
23,957 | lean_file_chunk | e7e1ebf68ab13fa16444ce26a161ceedd18c84bd4bb2628f4ba8dd47ed3f8c0a | lean_source_file | pkg_mathlib_source_file_chunks | /-
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
-/
module
public import Mathlib.Algebra.Group.Action.Pointwise.Set.Basic
public import Mathlib.Algebra.GroupWithZero.Action.Defs
public import Mathlib.Algeb... |
15,009 | lean_file_chunk | 43f92c324b7eb4bdb9040a489025bb9f51c94cde6b106eaccaadfd5538db4284 | lean_source_file | pkg_mathlib_source_file_chunks | theorem NeBot.zero_mul_nonneg (hg : g.NeBot) : 0 ≤ 0 * g :=
le_mul_iff.2 fun _ h₁ _ h₂ =>
let ⟨_, hb⟩ := hg.nonempty_of_mem h₂
⟨_, h₁, _, hb, zero_mul _⟩
end MulZeroClass
section Group
variable [Group α] [DivisionMonoid β] [FunLike F α β] [MonoidHomClass F α β]
(m : F) {f g f₁ g₁ : Filter α} {f₂ g₂ : Fil... |
23,943 | lean_file_chunk | f3e8593a3c3e186960cd2f2ae2d2dd60c733f007c472474f121dbabe63588d37 | 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.Control.Basic
public import Mathlib.Data.Set.Lattice.Image
public import Mathlib.Order.Filter.Basic
/-!
# Theorems about... |
14,183 | lean_file_chunk | cfb2070f7b6e7f7b8d0d60764f3e8457ec1c2c076f899f9c98bf2072610fb813 | lean_source_file | pkg_mathlib_source_file_chunks | theorem map_neBot_iff (f : α → β) {F : Filter α} : NeBot (map f F) ↔ NeBot F := by
simp only [neBot_iff, Ne, map_eq_bot_iff]
theorem NeBot.map (hf : NeBot f) (m : α → β) : NeBot (map m f) :=
(map_neBot_iff m).2 hf
theorem NeBot.of_map : NeBot (f.map m) → NeBot f :=
(map_neBot_iff m).1
instance map_neBot [hf : ... |
13,307 | lean_file_chunk | 3f59ddc5be0020c67224c71e49b0fe34118122c565d83473f1c419640971515a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Alex Kontorovich
-/
module
public import Mathlib.Data.Set.Piecewise
public import Mathlib.Order.Filter.Tendsto
public import Mathlib.Order.Filter.Bases.Finite
/-!
#... |
23,970 | lean_file_chunk | 7a9e316e68483c7874836452b2107f1d31b78b4fe8d17bea3e95e80823356b76 | 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.Algebra.Group.Pi.Basic
public import Mathlib.Data.Set.Lattice
public import Mathlib.Order.Filter.Defs
public import Mathl... |
23,965 | lean_file_chunk | b2c9906f688fe7828ae95e11c785f13d015653fd32589676bd552f99aeb6fbe8 | lean_source_file | pkg_mathlib_source_file_chunks | Filter.ext fun x => by simp only [mem_iSup, mem_principal, iUnion_subset_iff]
@[simp]
theorem principal_sdiff_principal {s t : Set α} : 𝓟 s \ 𝓟 t = 𝓟 (s \ t) :=
Filter.ext fun _ => by simp [← le_principal_iff, principal_mono]
@[simp]
theorem hnot_principal {s : Set α} : ￢𝓟 s = 𝓟 sᶜ := by
simpa [← compl_eq_un... |
2,751 | lean_file_chunk | b0e96270c4ad2b2c9651eb59da66fb732444738aca4c8f67e38fd27a795def68 | lean_source_file | pkg_mathlib_source_file_chunks | (s ∩ s' : Set α) ≤ᶠ[l] (t ∩ t' : Set α) :=
h'.mp <| h.mono fun _ => And.imp
@[mono]
theorem EventuallyLE.union {s t s' t' : Set α} {l : Filter α} (h : s ≤ᶠ[l] t) (h' : s' ≤ᶠ[l] t') :
(s ∪ s' : Set α) ≤ᶠ[l] (t ∪ t' : Set α) :=
h'.mp <| h.mono fun _ => Or.imp
@[mono]
theorem EventuallyLE.compl {s t : Set α} {l ... |
23,947 | lean_file_chunk | 82e36e3b7abfff52e3c243969917c776fc13f3a59526f832cefc9e7fb075101f | 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, Johannes Hölzl, Rémy Degenne
-/
module
public import Mathlib.Algebra.BigOperators.Group.Finset.Basic
public import Mathlib.Algebra.Order.Group.Unbundled.Abs
publ... |
5,592 | lean_file_chunk | 4eb91cb3dd80a6537652fa93c33f71da06e1dc01a24c3be94f1e68f759f1ebea | lean_source_file | pkg_mathlib_source_file_chunks | {g : β → γ} {f : α → β} {l : Filter α} (hg : Antitone g) (hg' : Tendsto g atBot atTop) :
IsBoundedUnder (· ≤ ·) l (g ∘ f) ↔ IsBoundedUnder (· ≥ ·) l f :=
hg.dual_right.isBoundedUnder_ge_comp_iff hg'
theorem Antitone.isBoundedUnder_ge_comp_iff [Nonempty β] [LinearOrder β] [Preorder γ] [NoMinOrder γ]
{g : β → ... |
5,156 | lean_file_chunk | 63b51a4cf26c4a5caf864cea0f26ed3838da495f5d0504b6d462624a391421cb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Bingyu Xia. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca, Bingyu Xia
-/
module
public import Mathlib.Order.Filter.Cofinite
public import Mathlib.Data.Finsupp.Weight
/-!
# Functions tending to the cofinite filter
This file intr... |
18,953 | lean_file_chunk | 91d6f250cf226b321a458c8be0bc59ff367da4d68b98367b6a693c2b375c75e1 | 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.Insert
public import Mathlib.Order.SetNotation
public import Mathlib.Order.BooleanAlgebra.Set
public import Math... |
13,660 | lean_file_chunk | 7273e50518d89ccadb5beae588d7732294e1fe3fdae0cf3a684fb219470936c5 | 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.Filter.Curry
public import Mathlib.Data.Set.Countable
/-!
# Filters with countable intersection property
In this file we defin... |
5,272 | lean_file_chunk | 9670e92e631d60dfddb19cd6b4a0ee518bc65527c64f7008ce7fcd95d7234345 | lean_source_file | pkg_mathlib_source_file_chunks | /-
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
-/
module
public import Mathlib.Algebra.Group.Indicator
public import Mathlib.Order.CompleteLattice.Finset
public import Mathlib.Order.ConditionallyCompl... |
15,607 | lean_file_chunk | ba1cee88e2edffc94539438a90a1740dffb37a4bf65304bbf8fa79877b1c2830 | 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.Tendsto
public import Mathlib.Order.Filter.Finite
public import Mathlib.Order.Filter.CountableInter
public import Mathlib.SetTh... |
3,227 | lean_file_chunk | 143dfc5a279fb22c0e94518fed1affb51db355af10795a9dd5a22e08cf81ba9c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 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.Map
/-!
# Kernel of a filter
In this file we define the *kernel* `Filter.ker f` of a filter `f`
to be the intersection of all... |
1,879 | lean_file_chunk | a7fa7a44015e50cef3611cafd20b9f1f36b18a6781bb838ffd79a6a92d2a0cab | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
module
public import Mathlib.Control.Traversable.Instances
public import Mathlib.Order.Filter.Map
/-!
# Properties of `Traversable.traverse` on `List`s and `Filter`s... |
3,382 | lean_file_chunk | a232e7940e1e44330292572ab535847cddd8a56ff99db6072252700fd322f8d1 | 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.CountablyGenerated
public import Mathlib.Order.Filter.Prod
public import Mathlib.Order.Filter.Ultrafilter.Defs
/-!
# Subs... |
17,347 | lean_file_chunk | ddb6ac065b1743d881e5227d80bf20ee0fbbe8d9b5998d188505243b9c6d284c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 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.Filter.Prod
public import Mathlib.Order.ConditionallyCompleteLattice.Basic
public import Mathlib.Order.Filter.Bases.Basic
/-!
# L... |
8,647 | lean_file_chunk | a86d80b36982eb52d47d07ddeffe0d850244fbdcc5b7de18358e1c9aeecfde4d | lean_source_file | pkg_mathlib_source_file_chunks | /-
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
-/
module
public import Mathlib.Order.Filter.Lift
public import Mathlib.Order.Filter.AtTopBot.Basic
/-!
# The filter of small sets
... |
23,993 | lean_file_chunk | 6084f89083a6817b22e1cf96f1f8d3464173df26ae16b8806e2db3231b771a0b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 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.Tendsto
public import Mathlib.Order.ConditionallyCompleteLattice.Indexed
public import Mathlib.Algebra.Order.Group.Defs
p... |
6,318 | lean_file_chunk | 7a04f543ca43f944aa779c18130eefbb46df62e033745ced6491d8cfc2f4a65a | lean_source_file | pkg_mathlib_source_file_chunks | IsMinOn f (Ioi a) b :=
isMaxOn_Ioi_of_mono_anti (β := βᵒᵈ) h₀ h₁
/-- If `f` is monotone on `Icc a b` and antitone on `Ici b`, then the maximum of `f` on `Ici a` is
attained at `b`. -/
lemma isMaxOn_Ici_of_mono_anti (h₀ : MonotoneOn f (Icc a b)) (h₁ : AntitoneOn f (Ici b)) :
IsMaxOn f (Ici a) b := by
intro x hx... |
23,971 | lean_file_chunk | dfe405a1b5fc75f53e81d7bf737ca968dd33999ce643e640cfd988b536b51f34 | lean_source_file | pkg_mathlib_source_file_chunks | /-
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
-/
module
public import Mathlib.Algebra.BigOperators.Group.Finset.Basic
public import Mathlib.Data.Finset.Pairwise
public import Mathlib.Data.Fi... |
11,630 | lean_file_chunk | 0e5174ebc2ff7f1bb5445f60bacb52501e729084594647cadf26e57993af8189 | lean_source_file | pkg_mathlib_source_file_chunks | /-! ### Finite partitions of finsets -/
namespace Finpartition
variable [DecidableEq α] {s t u : Finset α} (P : Finpartition s) {a : α}
lemma subset {a : Finset α} (ha : a ∈ P.parts) : a ⊆ s := P.le ha
theorem nonempty_of_mem_parts {a : Finset α} (ha : a ∈ P.parts) : a.Nonempty :=
nonempty_iff_ne_empty.2 <| P.ne... |
21,885 | lean_file_chunk | 2f0e1396e0e97aa6e6976e2b62e190b62dd3da358bca78ac384384a614fd9d71 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Peter Nelson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Peter Nelson
-/
module
public import Mathlib.Data.SetLike.Basic
public import Mathlib.Order.SupIndep
/-!
# Partitions
A `Partition` of an element `a` in a complete lattice is an indep... |
7,611 | lean_file_chunk | 5fd427a339e50e4549b0b29b819c3c8e755c6a9cd0aa6af76b24d6520a06a257 | lean_source_file | pkg_mathlib_source_file_chunks | /-
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
-/
module
public import Mathlib.Algebra.Order.Ring.Nat
public import Mathlib.Data.Set.Equitable
public import Mathlib.Logic.Equiv.Fin.Basic
publ... |
1,106 | lean_file_chunk | ee79161293b800c629040b9ea5760e71d6a056ee47e5511481d9033c74fec1ea | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Paul Lezeau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Paul Lezeau, Oliver Nash, Yaël Dillies
-/
module
public import Mathlib.Order.Circular
public import Mathlib.Order.Fin.Basic
public import Mathlib.Data.ZMod.Defs
/-!
# The circular order... |
4,324 | lean_file_chunk | 125ba7647c7231eede226b130812296a619ca755524a29a1f2915d3b0b486d37 | 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.Data.Set.Lattice
public import Mathlib.Order.Preorder.Chain
/-!
# Hausdorff's maximality principle
This file proves Hausdorff's maxima... |
9,143 | lean_file_chunk | 60320c840e76b56504ac91114020f74340995b8aea4e7ecda6e7dcd09beebf38 | 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.Data.Bool.Set
public import Mathlib.Data.Nat.Set
public import Mathlib.Order.CompleteLattice.Basic
/-!
# Theory of complete lattices
T... |
1,147 | lean_file_chunk | fe134ddcc58efca98c70a0ad93d16d79415dae5e8d730f99285c5992f77568b0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
module
public import Mathlib.Algebra.Order.Monoid.Unbundled.Basic
public import Mathlib.Algebra.Order.Monoid.Unbundled.OrderDual
public import Mathlib.Order.CompleteLa... |
10,178 | lean_file_chunk | 756beece282b1933dc769ab2ffdbe2acbb0893fdb4e448e58fca7804643545e9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
module
public import Mathlib.Data.Finset.Option
public import Mathlib.Data.Set.Lattice.Image
/-!
# Lattice operations on finsets
This file is concerned with how bi... |
23,950 | lean_file_chunk | b9fc99e1da6fcc91d31904a208f2039c76624b3aa962230923360d2436f6dc34 | 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.Data.Set.NAry
public import Mathlib.Data.ULift
public import Mathlib.Order.Bounds.Image
public import Mathlib.Order.CompleteLattice.Defs... |
11,589 | lean_file_chunk | d3931205252bdbf42316a3b36de5f439ed4b7ac15133884fb9508f9e63893ba9 | lean_source_file | pkg_mathlib_source_file_chunks | rw [← sSup_image, ← sSup_image, ← image_comp, comp_def]
@[to_dual]
theorem iSup_extend_bot {e : ι → β} (he : Injective e) (f : ι → α) :
⨆ j, extend e f ⊥ j = ⨆ i, f i := by
rw [iSup_split _ fun j => ∃ i, e i = j]
simp +contextual [he.extend_apply, extend_apply', @iSup_comm _ β ι]
@[to_dual]
theorem Set.BijOn.... |
11,635 | lean_file_chunk | cecc39046e036cf47e4a3e47170515476b19fb268e93009dc354792deca392c1 | 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.Bounds.Basic
public import Mathlib.Order.SetNotation
/-!
# Definition of complete lattices
This file contains the definition of ... |
4,405 | lean_file_chunk | 105cdf3d6722bdd81044ecaafe3052e9901dcbb4c27797134ed14646b069fe06 | 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.CompleteLattice.Lemmas
public import Mathlib.CategoryTheory.Category.Preorder
public import Mathlib.CategoryTheory.Limits.Shapes.Multiequali... |
1,836 | lean_file_chunk | 80885c8c5ab4775482640923dde39290965b86516053b96c7aed67a670442776 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Sven Manthe. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sven Manthe
-/
module
public import Mathlib.Order.CompleteSublattice
/-!
# `SetLike` instance for elements of `CompleteSublattice (Set X)`
This file provides lemmas for the `SetLike` i... |
5,097 | lean_file_chunk | 4e8cdbac2f1478e28f587d18e46295c634885f0b6ca26742f67e4d1f08ada4de | 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.Order.CompleteLattice.Basic
public import Mathlib.Order.PiLex
public import Mathlib.Order.ConditionallyCompleteL... |
17,045 | lean_file_chunk | c329f64f3e2ebdb03a4baf4c801b5936a18aca8b39ec36bffcd9d53493889f19 | 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.Bounds.Image
public import Mathlib.Order.CompleteLattice.Basic
public import Mathlib.Order.WithBot
/-!
# Galois connections, inse... |
12,292 | lean_file_chunk | 4782e654deaa46d9e4655da0b89990a9bd2759d5bf58bbec0e916e9b98fbdca7 | 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
/-!
# Galois connections, insertions and coinsertions
Galois conne... |
23,984 | lean_file_chunk | 4be099af40e7c40211b6f04ff9d7f01c2fec3d180dd730070f3d95fba45aab73 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
module
public import Mathlib.Order.Atoms
public import Mathlib.Order.OrderIsoNat
public import Mathlib.Order.RelIso.Set
public import Mathlib.Order.SupClosed
public import... |
7,021 | lean_file_chunk | 0f3f04826c802c28b58ab644ce2961bb633929fadc9d9225fda0c639a7b4717f | lean_source_file | pkg_mathlib_source_file_chunks | variable [IsModularLattice α] [IsCompactlyGenerated α]
/--
If each family `f i` is `iSupIndep`, then the family of pointwise infima
`k ↦ ⨅ i, f i (k i)` is also `iSupIndep`.
-/
theorem iSupIndep.iInf {ι : Type*} {κ : ι → Type*} (f : (i : ι) → κ i → α)
(h_indep : ∀ i : ι, iSupIndep (f i)) : iSupIndep (fun k : (i : ... |
2,412 | lean_file_chunk | e7ae2d58a87317f028e64bbe62f1208a57150e0d5133d2dc349437c06dc0b077 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
module
public import Mathlib.Order.CompleteLatticeIntervals
public import Mathlib.Order.CompactlyGenerated.Basic
/-!
# Results about compactness properties for intervals ... |
2,388 | lean_file_chunk | 4e831c0f9dfca5eb5c45225edffc515ab20d9e47ef479c4032207f1978b5a45e | 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.Algebra.Order.Group.Defs
public import Mathlib.Algebra.Order.Monoid.OrderDual
public import Mathlib.Order.Monotone.Union
/-!
# Monoto... |
13,433 | lean_file_chunk | 5b37e5cc3e4ac55c5e5a1202eb7aa99cf7850396c8621e5cca1b06a0e30ae64e | 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.Data.Set.Operations
public import Mathlib.Order.Lattice
/-!
# Monovariance of functions
Two functions *vary together* if a strict change i... |
5,155 | lean_file_chunk | 6b4f7e31c34571cfb62508472acff317facb5d410559f683217c8bba927ea009 | 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, Sébastien Gouëzel
-/
module
public import Mathlib.Order.Bounds.Basic
public import Mathlib.Order.Interval.Set.LinearOrder
/-!
# Monotonicity on intervals
In this f... |
2,366 | lean_file_chunk | b048f404993e3b0eef087aae49e6f255224aa760e366d1c5c7d677ae7edb02ca | lean_source_file | pkg_mathlib_source_file_chunks | /-
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
-/
module
public import Mathlib.Data.Set.Monotone
public import Mathlib.Order.ConditionallyCompleteLattice.Basic
/-!
# Extension of a monotone f... |
23,959 | lean_file_chunk | 4c75afe17c9ce3ad9b12419e4d5297232fcc5ef1a5c30f34b41236de22657a74 | 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, Mario Carneiro, Yaël Dillies
-/
module
public import Mathlib.Data.Nat.Basic
public import Mathlib.Data.Int.Order.Basic
public import Mathlib.Logic.Function.Iterate
publi... |
5,499 | lean_file_chunk | ba15eaee409cb3e6ce2016f5a37ebafc5f0690dd6398d00080429a82c1b38bcc | lean_source_file | pkg_mathlib_source_file_chunks | theorem antitone_int_of_succ_le {f : ℤ → α} (hf : ∀ n, f (n + 1) ≤ f n) : Antitone f :=
Int.rel_of_forall_rel_succ_of_le (· ≥ ·) hf
theorem strictMono_int_of_lt_succ {f : ℤ → α} (hf : ∀ n, f n < f (n + 1)) : StrictMono f :=
Int.rel_of_forall_rel_succ_of_lt (· < ·) hf
theorem strictAnti_int_of_succ_lt {f : ℤ → α} ... |
4,147 | lean_file_chunk | 35f055e20de3adf3a54755a40f00b63b2add7fb522c046978f390b4afee2255c | 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.Monotone.Monovary
public import Mathlib.SetTheory.Cardinal.Order
/-!
# Interpreting monovarying functions as monotone functions
This... |
20,630 | lean_file_chunk | 87bc70b4c5a63fdd27ac6d22fa858928d203abfe4b2929893e97f7e720f4dd08 | 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, Mario Carneiro, Yaël Dillies
-/
module
public import Mathlib.Data.Set.Operations
public import Mathlib.Logic.Function.Iterate
public import Mathlib.Order.Basic
public im... |
17,814 | lean_file_chunk | 15e8132be56e11f9baa5218b8efca7b14d7f1bc9d118958ab890a2140cc82b0f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
module
public import Mathlib.Data.Set.Defs
public import Batteries.Tactic.Alias
public import Mathlib.Tactic.ExtendDoc
import Mathlib.Tactic.ToDual
/-!
#... |
10,546 | lean_file_chunk | 523263d543527b2ba611964d4f1ce197a011a547aa716155b796ef25dbf19bf0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
module
public import Batteries.Classes.Order
public import Batteries.Tactic.Trans
public import Mathlib.Data.Ordering.Basic
public import Mathlib.Tactic.Ex... |
7,573 | lean_file_chunk | 5f6ca711ab8b75d269c2a6026904a61a66ee0a351182ff15df20626348a1a1ee | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
module
public import Batteries.Tactic.Alias
public import Batteries.Tactic.Trans
public import Mathlib.Tactic.ExtendDoc
public import Mathlib.Tactic.ToDual... |
501 | lean_file_chunk | 680d2e9434719c1347f204ad195bb94ec744270be12fbeae2703f8825a3f40e6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
module
public import Mathlib.Data.Prod.Lex
public import Mathlib.Order.Hom.Basic
/-!
# Order homomorphism for `Prod.Lex`
-/
@[expose] public section
/-- `toLex`... |
8,546 | lean_file_chunk | ff1076932ddc88a78424595e568091b7f0e808901d9660c5c4a00770bbf0ba53 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yizheng Zhu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yizheng Zhu
-/
module
public import Mathlib.Data.Finset.Sort
public import Mathlib.Data.Prod.Lex
/-!
# Gaps of disjoint closed intervals
This file defines `Finset.intervalGapsWithin` t... |
2,572 | lean_file_chunk | 9c736e04fd389c2ab17f799aae61c3c73dab4e67e70208a1eead461b5c0cbbd0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
module
public import Mathlib.Order.Interval.Finset.Basic
/-!
# Linear locally finite orders are densely ordered iff they are trivial
## Main results
* `LocallyFi... |
23,988 | lean_file_chunk | 3d618d4fba1175593f8508ffe8549173f52a49e21190a552111dd9dcdeedddac | 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, Yury Kudryashov
-/
module
public import Mathlib.Data.Finset.Fin
public import Mathlib.Order.Interval.Finset.Nat
public import Mathlib.Order.Interval.Set.Fin
/-!
# Finite ... |
3,077 | lean_file_chunk | a5fa983a0bc4e5093e17800f7c2c22a1305099e38791a6856384f9d47da2a281 | lean_source_file | pkg_mathlib_source_file_chunks | theorem card_uIcc : #(uIcc a b) = (b - a : ℤ).natAbs + 1 := by
rw [← Nat.card_uIcc, ← map_valEmbedding_uIcc, card_map]
@[simp]
theorem card_Ici : #(Ici a) = n - a := by
rw [← attachFin_Ico_eq_Ici, card_attachFin, Nat.card_Ico]
@[simp]
theorem card_Ioi : #(Ioi a) = n - 1 - a := by
rw [← card_map, map_valEmbeddin... |
8,578 | lean_file_chunk | c5edb637801ae627212cadb1f806775ab87101afcb70c8be749ef18482159ed8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 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.Defs
public import Mathlib.Order.Interval.Set.SuccPred
/-!
# Finset intervals in a successor-predecessor order
This ... |
10,625 | lean_file_chunk | 2ba1fdc79eb275859b3a9d879a24321ccafd27133104e14120c31fbe7c61ed15 | 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.Algebra.Group.Embedding
public import Mathlib.Order.Interval.Multiset
/-!
# Finite intervals of naturals
This file proves that `ℕ` is a `L... |
23,986 | lean_file_chunk | b0f729b8b72a89de142cbc536c97c5eb2e23dfe997b0870ffb00dd57c1b7ffcf | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Yaël Dillies
-/
module
public import Mathlib.Order.Cover
public import Mathlib.Order.Interval.Finset.Defs
public import Mathlib.Order.Preorder.Finite
/-!
# Intervals as f... |
17,132 | lean_file_chunk | 8ef817b0bd97dc0f821c31b121ad0768d2815a7698b4aefedcb998856cd960b0 | lean_source_file | pkg_mathlib_source_file_chunks | aesop (add safe forward [le_antisymm, le_of_lt])
lemma Ioo_map_sectR : (Ioo a b).map (.sectR c _) = Ioo (c, a) (c, b) := by
aesop (add safe forward [le_antisymm, le_of_lt])
end sectR
end Prod
section BoundedPartialOrder
variable [PartialOrder α]
section OrderTop
variable [LocallyFiniteOrderTop α]
@[simp]
theo... |
23,944 | lean_file_chunk | d4fe739581ee6f7af3e00dd4edd7a8007d014b73e6fd5b0bc503151c657bab4e | 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.Data.Finset.Preimage
public import Mathlib.Data.Finset.Prod
public import Mathlib.Order.Hom.WithTopBot
public import Mathlib.Order.Interval.... |
18,189 | lean_file_chunk | eba1c2ddc89dbd8d28f318dcb263e6d837f69ea6da8d4901125df0ee7761a623 | lean_source_file | pkg_mathlib_source_file_chunks | finsetIcc a b := (Icc (f a) (f b)).preimage f f.toEmbedding.injective.injOn
finsetIco a b := (Ico (f a) (f b)).preimage f f.toEmbedding.injective.injOn
finsetIoc a b := (Ioc (f a) (f b)).preimage f f.toEmbedding.injective.injOn
finsetIoo a b := (Ioo (f a) (f b)).preimage f f.toEmbedding.injective.injOn
finset_m... |
3,731 | lean_file_chunk | 60c40a1f36227cf0e2e5068a07bc5d1f79f13a121d007cc4cdba655de4dac6bd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Algebra.Order.Disjointed
public import Mathlib.Algebra.Order.Ring.Int
public import Mathlib.Algebra.Order.Ring.Prod
public import Mathlib.Da... |
1,647 | lean_file_chunk | 2ae7a67aeb93a0039172a45ceaefbc29358abfd0d58d34fe28c04b848e47638f | 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.Order.Monotone.Odd
public import Mathlib.Algebra.Order.Field.Basic
public import Mathlib.Tactic.FieldSimp
/-!
# Order isomorphism bet... |
1,025 | lean_file_chunk | 193e8de4265af2ca6ac432bcf1e7adb391fa798fff0d26ad2b9dc15bb78b35aa | 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.SetIsMax
public import Mathlib.Order.SuccPred.Limit
/-!
# Limit elements in Set.Ici
If `J` is a linearly ordered type, `j : J`,
and `m : S... |
14,812 | lean_file_chunk | 7273481863464083481ca21dad523f11fd56c2222163f0b36202666f42f03bfa | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou
-/
module
public import Mathlib.Data.Set.Order
public import Mathlib.Order.Bounds.Basic
public import Mathlib.Order.Interval.Set.Image
public import Mathlib.Order.Interva... |
2,463 | lean_file_chunk | 28591c1dedefb571d871adc14e5bc7a3f326c71b6ba20749e3601f8e7a51b4c8 | 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, Mario Carneiro, Patrick Massot, Yury Kudryashov, Rémy Degenne
-/
module
public import Mathlib.Order.Interval.Set.Basic
public import Mathlib.Order.Hom.Set
/-!
# Lemma... |
23,955 | lean_file_chunk | 3f5ad2f15849b2adb5757997d4cd9194c4cc0ce7641e436c45c3f59094476c35 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 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.Fin.Basic
public import Mathlib.Order.Interval.Set.UnorderedInterval
/-!
# (Pre)images of set intervals under `Fin` operations
... |
3,387 | lean_file_chunk | 7598eb515bf45e71114c32f9f51e8678fe79cd8628d9767f1e59865426bae830 | lean_source_file | pkg_mathlib_source_file_chunks | theorem preimage_succ_uIoc_succ (i j : Fin n) : succ ⁻¹' uIoc i.succ j.succ = uIoc i j :=
preimage_addNat_uIoc_addNat ..
@[simp]
theorem preimage_succ_uIoo_succ (i j : Fin n) : succ ⁻¹' uIoo i.succ j.succ = uIoo i j :=
preimage_addNat_uIoo_addNat ..
@[simp] theorem image_succ_Ici (i : Fin n) : succ '' Ici i = Ici... |
8,804 | lean_file_chunk | 53656a262a40d3e4232c1d1115386bfea50a13ac1a90d3aba5f8ac53110a04bf | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 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.Order.SuccPred.Basic
/-!
# Set intervals in a successor-predecessor order
This file proves ... |
1,568 | lean_file_chunk | fad721f1de993ed09c8caf3ddadb9bcb84cc26bcc144b5593af53f6be674f282 | 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.LatticeIntervals
public import Mathlib.Order.SuccPred.Basic
/-!
# Successors in intervals
If `j` is an element of a partially ordered set ... |
3,301 | lean_file_chunk | c7fc17613f139ffda72d765a8495e5b88600d861e510cc72a11bb75b13eff45a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
module
public import Mathlib.Data.Set.Function
public import Mathlib.Order.Interval.Set.LinearOrder
/-!
# Monotone surjective functions are surjective on interval... |
1,294 | lean_file_chunk | 12b9921ab551ae8851d28ee695e933bdcb8dbe1709ce7c15aae10503233c1d56 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Yael Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yael Dillies
-/
module
public import Mathlib.Data.Set.Card
import Mathlib.Order.Interval.Finset.Nat
/-!
# Finite intervals of naturals
This file calculates the cardinality of interva... |
522 | lean_file_chunk | 45a3aee6058ba823a389f876a0e666c4c778992b4a09cb56fb7f55865aab72bc | 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.CategoryTheory.Filtered.Final
/-!
# Final functors between intervals
-/
@[expose] public section
universe u
instance Set.Ici.subtype_functor_... |
1,596 | lean_file_chunk | e0720179e6574b4782b485117ea2e3a4e883c32ac7f416806206298c1b3265f4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Oliver Butterley. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Butterley
-/
module
public import Mathlib.Data.Finset.Range
public import Mathlib.Data.Set.Lattice
public import Mathlib.Order.Interval.Set.LinearOrder
/-!
# Extra lemmas ab... |
8,650 | lean_file_chunk | 08fab50616cf93d44409df180d5beac137b07bb3550f38d0b40b33535eb4a1e8 | 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.Image
public import Mathlib.Order.Interval.Set.Basic
public import Mathlib.Order.WithBot
/-!
# Intervals in `WithTop α` and ... |
12,383 | lean_file_chunk | 4599dbbccf8b4064a093f7ef7df48d58906a67b7fe2d0feaa35506f114b449f7 | 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.Algebra.Notation.Pi.Basic
public import Mathlib.Data.Set.BooleanAlgebra
public import Mathlib.Data.Set.Piecewise
public import Mathlib... |
18,157 | lean_file_chunk | be822746783ca74f59378bd411af067077e9a0b2e005f47968ce0b0bb7aafe63 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Yaël Dillies
-/
module
public import Mathlib.Order.Interval.Set.Basic
public import Mathlib.Data.Set.Function
public import Mathlib.Order.Directed
/-!
# Monotone function... |
4,242 | lean_file_chunk | eb7126b0d4bbd932dd61242d3a9f530916304f066013668e17dc1bf0050fd695 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Bhavik Mehta, Oliver Nash
-/
module
public import Mathlib.Data.Nat.Lattice
public import Mathlib.Data.Int.ConditionallyCompleteOrder
public import Mathlib.Data.Int.Interva... |
23,991 | lean_file_chunk | 38a3f57974494637041888d783c46a2ba786bef627838d76a5228cddef75447c | 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, Mario Carneiro, Patrick Massot, Yury Kudryashov, Rémy Degenne
-/
module
public import Mathlib.Data.Set.Subsingleton
public import Mathlib.Order.BooleanAlgebra.Set
publ... |
2,447 | lean_file_chunk | 9ec287a5ad2ac86b0bc4986b019e4c65d043e94c101d396ed657f72d21ec5080 | lean_source_file | pkg_mathlib_source_file_chunks | section Inf
variable [SemilatticeInf α]
@[to_dual (attr := simp)]
theorem Iic_inter_Iic {a b : α} : Iic a ∩ Iic b = Iic (a ⊓ b) := by
ext x
simp [Iic]
@[to_dual (reorder := a b) (attr := simp)]
theorem Ioc_inter_Iic (a b c : α) : Ioc a b ∩ Iic c = Ioc a (b ⊓ c) := by
rw [← Ioi_inter_Iic, ← Ioi_inter_Iic, inter... |
10,534 | lean_file_chunk | 14df58c34409300ac542bc4da0e3353d1210a771341319eaa68eb31ca9521bb2 | 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, Patrick Massot
-/
module
public import Mathlib.Data.Set.Function
public import Mathlib.Order.Interval.Set.OrdConnected
/-!
# Projection of a line onto a closed inte... |
9,028 | lean_file_chunk | 9a51d6a521bbe90ffea8e78b934deb23e155a112adce4618e7d0eccf3635e91f | 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
-/
module
public import Mathlib.Data.Set.Lattice.Image
public import Mathlib.Order.Interval.Set.LinearOrder
public import Mathlib.Order.MinMax
/-!... |
3,583 | lean_file_chunk | 8236e2204d288976a9f740fab1615aa36be78012c240b05a49e4c498be0ea6e1 | 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.Data.Set.Defs
public import Mathlib.Order.Defs.PartialOrder
public import Mathlib.Tactic.Push.Attr
/-!
# Intervals
In any preorder `α`... |
2,459 | lean_file_chunk | 8c1107cb92e94c1aaab75d46185444a3fd71ae4ff6e202567ab7364619dc2af1 | 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.InitialSeg
/-!
# Intervals as initial segments
We show that `Set.Iic` and `Set.Iio` are respectively initial and
principal segments, and t... |
19,880 | lean_file_chunk | 7c85a250d0eff3ade916c88a07427e51ce8d4d2ed0bc15ae02b6cd9ba3cd9cc2 | 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, Mario Carneiro, Patrick Massot, Yury Kudryashov, Rémy Degenne
-/
module
public import Mathlib.Order.Interval.Set.Basic
/-!
# Interval properties in linear orders
Sin... |
8,900 | lean_file_chunk | 8d222048170a36b727c4d402481aaaf8bbbd783ec50461865b0d8a00ed344116 | 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.Order.Interval.Set.OrdConnected
public import Mathlib.Data.Set.Lattice.Image
/-!
# Order connected components of a set
In this file ... |
13,171 | lean_file_chunk | 50d420a041911dd75efd886ca2366613730b3a306d6ac3d90848fbc5c60c3886 | 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.OrderEmbedding
public import Mathlib.Order.Antichain
public import Mathlib.Order.SetNotation
/-!
# Order-connected... |
1,559 | lean_file_chunk | 11e5db7b5d0bd147fd4f6a89e5fa1d5ff76980686dc0b6ca98417b49a71a973f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 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.UnorderedInterval
public import Mathlib.Order.Hom.Basic
/-!
# Preimages of intervals under order embeddings
In th... |
7,915 | lean_file_chunk | 2347e259851dd3a5b7dda95d4c6e759ccac8bd41f066f4a04be8bac0e80b4ee8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 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.Monotone
public import Mathlib.Order.Interval.Set.Disjoint
public import Mathlib.Order.SuccPred.Archimedean
/-!
# Monotonici... |
2,478 | lean_file_chunk | c13869615bd745b054964154baec43017904f37505fa502802ed8c5914098470 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton
-/
module
public import Mathlib.Data.Set.Finite.Basic
public import Mathlib.Order.Interval.Set.Basic
/-!
# Infinitude of intervals
Bounded intervals in dense orders are inf... |
23,974 | lean_file_chunk | e03b1044f957440cfc01484972d76c9a2dac878dd52d5554a6736c2c00778907 | 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, Abhimanyu Pallavi Sudhir
-/
module
public import Mathlib.Algebra.Module.Pi
public import Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE
public import Mathlib.Data... |
3,964 | lean_file_chunk | de4718817aa02d45c869da5dbb90130b73d5b9a1ccb845e913865aba80a09b3a | lean_source_file | pkg_mathlib_source_file_chunks | instance instModule [Semiring R] [AddCommMonoid M] [Module R M] : Module R (Germ l M) where
add_smul c₁ c₂ f :=
inductionOn f fun f => by
norm_cast
simp [add_smul]
zero_smul f :=
inductionOn f fun f => by
norm_cast
simp [zero_smul]
instance instModule' [Semiring R] [AddCommMonoid M]... |
1,542 | lean_file_chunk | 74d01100f160c95220d4792c4d377638dff5ae4bca2e2c16b4137ba2f9a559fa | 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, Abhimanyu Pallavi Sudhir
-/
module
public import Mathlib.Algebra.Module.Pi
public import Mathlib.Algebra.Order.Monoid.Canonical.Defs
public import Mathlib.Order.Filt... |
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