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 |
|---|---|---|---|---|---|
1,107 | lean_file_chunk | ee637dac0d88559c872ed6e8dca58b9694dca239e6c712e16b53911035923456 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Kyle Miller
-/
module
public import Mathlib.Tactic.Linter.Header --shake: keep
/-!
# Support for `lemma` as a synonym for `theorem`.
-/
public meta section
open Le... |
13,994 | lean_file_chunk | 190136d2a0dd0f437e9d77d6d29615a369581677b5d921ec62d0b82e45206f18 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
module
public meta import Lean.Meta.Transform
public meta import Lean.Elab.Deriving.Basic
public meta import Lean.Elab.Deriving.Util -- shake: keep (???)
import Mathlib.L... |
8,571 | lean_file_chunk | 9e3e853077b6aa4009d2e694e2a7930f010a37218296aa751650b5d291ec2705 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
module
public meta import Lean.Meta.Tactic.Refl
public import Mathlib.Logic.Basic
/-!
# `subsingleton` tactic
The `subsingleton` tactic closes `Eq` or `HEq` goals using ... |
9,245 | lean_file_chunk | b744b40fbd7c53fd7b644a41e4b91dc851ec5ea05243a977fcec04b4b618bbd3 | 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
-/
module
public meta import Batteries.Lean.Expr
public meta import Batteries.Lean.Meta.UnusedNames
public meta import Lean.Elab.Tactic.RCases
public import Mathlib... |
10,819 | lean_file_chunk | ec34813eb9d6eafcf16e83004d4853a8e5bef109189e17af0d302ffffef577d7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
module
public meta import Lean.Meta.Transform
public meta import Lean.Meta.Inductive
public meta import Lean.Elab.Deriving.Basic
public meta import Lean.Elab.Deriving.Util... |
1,190 | lean_file_chunk | 3fff0d167a9f9288ab4cf9676ba590e793a80205852c9cf183a23c28094ba030 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
module
public import Mathlib.Init
public meta import Lean.Meta.Tactic.TryThis
/-!
# 'Try this' tactic macro
This is a convenient shorthand intended for macro autho... |
13,668 | lean_file_chunk | 2d2e91dba0525529db1d3b614508aa3bf6a954aae3bbe4aaf6cd3f443a64c8f8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
module
public meta import Mathlib.Util.AtLocation
public import Mathlib.Data.ZMod.Basic -- shake: keep (Qq dependency)
public import Mathlib.RingTheory.Polynomial.Basic ... |
17,942 | lean_file_chunk | 7dc9929b4b34610d06b4711ac5a81f6a021f60f5051d9fc729aaaa45f6c91d35 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jovan Gerbscheid, Patrick Massot, Simon Hudon, Alice Laroche, Frédéric Dupuis,
Jireh Loreaux
-/
module
public meta import Lean.Elab.Tactic.Conv.Simp
public import Mathlib.Logic.Basic
... |
23,980 | lean_file_chunk | a5c4ba817cc0d6451d3a878ea79090d88013dff1187076332b6b75b84db57894 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
module
public import Mathlib.Lean.Meta.CongrTheorems
/-! # `congr(...)` congruence quotations
This module defines a term elaborator for generating congruence lemmas
from... |
10,741 | lean_file_chunk | bcac18331ed5c7fc6dd4ea7abc227658648e18f2942da88925e5a77a5225e9c0 | lean_source_file | pkg_mathlib_source_file_chunks | let lhs := Expr.forallE lhs.bindingName! resDom.lhs resBody.lhs lhs.bindingInfo!
let rhs := Expr.forallE rhs.bindingName! resDom.rhs resBody.rhs rhs.bindingInfo!
if resDom.isRfl && resBody.isRfl then
return {lhs, rhs, pf? := none}
else
return CongrResult.mk' lhs rhs (← mkImpC... |
22,633 | lean_file_chunk | 4d29734b4efb7551c3652de6964ed4d81efe7154eb4fd4f2ea7958a5d2d5c47c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
module
public import Mathlib.Algebra.Polynomial.Degree.Lemmas
/-!
# `compute_degree` and `monicity`: tactics for explicit polynomials
This file defines two related ... |
8,676 | lean_file_chunk | 8ce1d1ae2df41a5c678659e045064d182ec51a40c5d37f901c45da4170977b90 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
module
public meta import Lean.Elab.Command
public import Mathlib.Init
/-!
# The `stacks` and `kerodon` attributes
This allows tagging of mathlib results with the co... |
5,910 | lean_file_chunk | 4e97971596dc53c3499f593f54306ce7cc15d9d090c3f1a1384ba46097cd881b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
module
public import Mathlib.Tactic.Push
/-! # Contrapose
The `contrapose` tactic transforms the goal into its contrapositive when that goal is an
implication or an ... |
4,898 | lean_file_chunk | d5799aa87de8e5aab70026406bf2baef03f5667eda6d0df84d4085601b0d83c2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
module
public import Mathlib.Tactic.Positivity.Core
/-!
# Finiteness tactic
This file implements a basic `finiteness` tactic, designed to solve goals of the form... |
12,225 | lean_file_chunk | 992247891d9a7da0fb3ee7703e20e5d97e7074450b0062463a4a67c9486730ba | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
module
public meta import Lean.Elab.DefView
public meta import Lean.Util.CollectAxioms
public meta import ImportGraph.Imports.Redundant
public meta import ImportGraph.... |
14,321 | lean_file_chunk | fbcb00fbf24f3b64c4f85bb5c4b43b4a9b35216897bba8a73fee509ab32cef96 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Abby J. Goldberg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Abby J. Goldberg, Mario Carneiro, Heather Macbeth
-/
module
public import Mathlib.Tactic.LinearCombination.Lemmas
public import Mathlib.Tactic.Positivity.Core
public import Mathlib.... |
10,403 | lean_file_chunk | 46e8a1af6c135a59e7c726b8d02d72767e67166dd8c9496447790d3b1252f75d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Arthur Paulino. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Arthur Paulino, Gabriel Ebner, Kyle Miller
-/
module
public meta import Lean.Meta.Tactic.Util
public meta import Lean.Elab.Tactic.Basic
public import Mathlib.Init
/-!
# The `use` tac... |
15,888 | lean_file_chunk | 376298a77d4fbbcbf8e91676b7eb6ea96bc481b12a75231e47155fb75bf6f292 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
module
public import Mathlib.Init
public meta import Lean.Meta.Tactic.TryThis
public meta import Lean.Linter.UnusedVariables
/-!
# The `variable?` command
This defines a... |
5,255 | lean_file_chunk | 6023cfa78d436dfbba92fbe6594407abbde11096b5803816f0b0db8397aad327 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Sebastian Ullrich. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Ullrich
-/
module
public import Mathlib.Init
public meta import Batteries.Util.Cache
public meta import Lean.HeadIndex
public meta import Lean.Elab.Command
public import ... |
3,399 | lean_file_chunk | d04850237b7de8af1c868c558be2ef092951dd40cd77d8de53594923f166e4eb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
module
public meta import Lean.Elab.Tactic.Simp
public import Mathlib.Init
public import Lean.Elab.Tactic.Simp
/-! # `simp_intro` tactic -/
public meta section
na... |
21,864 | lean_file_chunk | 0698a7ad4df9e2bc87f74dfbd7dfd99a066488caab80cff43674604c69758d40 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Arthur Paulino, Damiano Testa
-/
module
public meta import Mathlib.Lean.Meta
public import Mathlib.Algebra.Group.Basic
public import Mathlib.Order.Defs.LinearOrder
public meta import M... |
390 | lean_file_chunk | a35dd46b11a432256be7b333b1ed9c6260537554980c9828e253125319b17f1d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis
-/
module
public meta import Mathlib.Tactic.Hint
public import Mathlib.Tactic.Linarith.Frontend
public import Mathlib.Tactic.NormNum
/-!
We register `linarith` with ... |
12,486 | lean_file_chunk | 1ba3ed7ba7d30b716a3331a88aab031d39d257403b8e5471b96eafdfffce66f9 | 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, Floris van Doorn, Mario Carneiro, Reid Barton, Johan Commelin
-/
module
public import Mathlib.Logic.Function.Basic
/-!
# `choose` tactic
Performs Skolemization, that ... |
23,983 | lean_file_chunk | 4118794e02334e1451a66feaae987a5165962f19b60747d9c31181d136d68106 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
module
public import Mathlib.Data.Prod.Lex
public import Mathlib.Data.Sigma.Lex
public import Mathlib.Order.RelIso.Set
public import Mathlib.Order.WellQuasiOrder
pub... |
15,044 | lean_file_chunk | 159bced66c084694f3475210a46a8cff1243d10d5067b7ba02940a3df11730e3 | lean_source_file | pkg_mathlib_source_file_chunks | theorem isWF_bUnion [Preorder α] (s : Finset ι) {f : ι → Set α} :
(⋃ i ∈ s, f i).IsWF ↔ ∀ i ∈ s, (f i).IsWF :=
s.wellFoundedOn_bUnion
@[simp]
theorem isPWO_bUnion [Preorder α] (s : Finset ι) {f : ι → Set α} :
(⋃ i ∈ s, f i).IsPWO ↔ ∀ i ∈ s, (f i).IsPWO :=
s.partiallyWellOrderedOn_bUnion
end Finset
namesp... |
10,419 | lean_file_chunk | a5b45da86c501d86efab126c51d61f28933f472ef0cbdc545482f781efabfe15 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
module
public import Mathlib.Order.ConditionallyCompleteLattice.Basic
public import Mathlib.Order.LatticeIntervals
public import Mathlib.Order.Interval.Set.OrdConn... |
11,124 | lean_file_chunk | 4fbf0a3fab0414bcc3c9a8ca34d0882e6d23b295acccd37d21bc450c3c5d1b3d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn
-/
module
public import Mathlib.Order.Ideal
public import Mathlib.Data.Finset.Max
/-!
# The back and forth method and countable dense linear orders
## Results
Suppose `α β` ... |
7,694 | lean_file_chunk | 2abc3b855c33c60f16c850d0c7cba347504c8dbc5b7426b68fd667179fef9048 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 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.Fintype.Pigeonhole
public import Mathlib.Order.Atoms.Finite
public import Mathlib.Order.Grade
/-!
# Kőnig's infinity lemma
Kőnig's in... |
1,952 | lean_file_chunk | 32646c33ad485d167fc2a0b5ca3220181ba2e28f746f300285ed4da6133fd5c8 | 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.Data.Part
public import Mathlib.Order.Hom.Basic
public import Mathlib.Tactic.Common
/-!
# Monotonicity of monadic operations on `Part`
-/
... |
466 | lean_file_chunk | cc1f5d405f45160783129169b0d3efd889c5181635b33057527c873e75bab024 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Johan Commelin, Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Damiano Testa, Yaël Dillies
-/
module
public import Mathlib.Logic.Equiv.Defs
public import Mathlib.Order.Basic
public import Mathlib.Tactic.Linter.Depre... |
13,002 | lean_file_chunk | 3153c40a629754538dc8699bba2ab67fd2330e6d1e4e0e597510ad7f1ba92dcd | 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.Antisymmetrization
/-!
# Comparability and incomparability relations
Two values in a preorder are said t... |
11,001 | lean_file_chunk | 9d95bc787ec80cacfab5418abc74c9081a40dc422df21113bca9a3606e6bd51a | 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, Filippo A. E. Nuccio, Sam van Gool
-/
module
public import Mathlib.Data.Fintype.Order
public import Mathlib.Order.Interval.Finset.Basic
public import Mathlib.Order.Irreduc... |
16,406 | lean_file_chunk | 819493a6b243c3e91bb58845c145b9db63362187eed81f9f764e6494f8a1dd3d | 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.SupClosed
/-!
# Sublattices
This file defines sublattices.
## TODO
Subsemilattices, if people care about them.
## Tags
sublattic... |
5,909 | lean_file_chunk | 1a3b404c1fa82b91c442d20168b0f991d20b781ba7403e21e489d09838e37770 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Noam Atar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Noam Atar
-/
module
public import Mathlib.Order.Ideal
public import Mathlib.Order.PFilter
/-!
# Prime ideals
## Main definitions
Throughout this file, `P` is at least a preorder, but so... |
8,732 | lean_file_chunk | 80e1278b7872dd23ac75a813323e0fd7eed36bb9dbca830a7acde187cfb32455 | 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 Aesop
public import Mathlib.Logic.Function.Iterate
public import Mathlib.Order.Monotone.Basic
/-!
# Inequalities on iterates
In this file we... |
7,721 | lean_file_chunk | 1e1a7d7c671597932feae20bb790ae4bad9647a5b78ea58697aec55e434e62f0 | 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
-/
module
public import Mathlib.Logic.Equiv.Defs
public import Mathlib.Order.Basic
/-!
# Order dual
This file defines `OrderDual α`, a type synonym reve... |
4,354 | lean_file_chunk | d71d9f7b4af8d4c78094013bac63743fd596f248877f9e9c9ef51a4291f79488 | 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, Violeta Hernández Palacios
-/
module
public import Mathlib.Order.SuccPred.Limit
/-!
# Transfinite iteration of a function `I → I`
Given `φ : I → I` where `[SupSet I]`, we defi... |
23,943 | lean_file_chunk | 80412037910798df1f28538c7be11133d166e1d996e10738fd2462c613a18882 | 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, Yaël Dillies
-/
module
public import Mathlib.Logic.Equiv.Set
public import Mathlib.Logic.Pairwise
public import Mathlib.Order.CompleteLattice.Lemmas
public import Math... |
17,336 | lean_file_chunk | f21f70b1efade0b5b4a827a8735ea3f9ee1c30fe2cd6fff3a47148823807c91b | lean_source_file | pkg_mathlib_source_file_chunks | iInf_iSup_eq f := by ext <;> simp [fst_iSup, fst_iInf, snd_iSup, snd_iInf, iInf_iSup_eq]
instance Pi.instCompletelyDistribLattice {ι : Type*} {π : ι → Type*}
[∀ i, CompletelyDistribLattice (π i)] : CompletelyDistribLattice (∀ i, π i) where
__ := instFrame
__ := instCoframe
iInf_iSup_eq f := by ext i; simp on... |
4,961 | lean_file_chunk | c42087f08a1b932daf95bc6535928de22ac1a1ab6e596bc61e79b223130bb1e5 | 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.OpClass
public import Mathlib.Order.Lattice
/-!
# `max` and `min`
This file proves basic properties about maxima and minima on a... |
5,687 | lean_file_chunk | 14b313555462c305021a822affb1ebee444b82f71ebf81396f7eacd5e9e5351f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Sam van Gool. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sam van Gool
-/
module
public import Mathlib.Order.PrimeIdeal
public import Mathlib.Order.Zorn
/-!
# Separating prime filters and ideals
In a bounded distributive lattice, if $F$ is a... |
23,973 | lean_file_chunk | 2f45b85ba228a3900250e38f80d7ac440d28df6f40048c29ec6bb9b035f98592 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
module
public import Mathlib.Data.Set.Lattice
public import Mathlib.Data.SetLike.Basic
public import Mathlib.Order.ModularLattice
public import Mathlib.Order.SuccPre... |
23,941 | lean_file_chunk | ffa0eae1fa0ea39fb86fa5a1bfb61674d257365efb81a075e62ac2ec600ff5fd | lean_source_file | pkg_mathlib_source_file_chunks | CompleteLattice.isAtomistic_iff.2 fun b ↦ by
inhabit α
refine ⟨{ a | IsAtom a ∧ a ≤ b }, ?_, fun a ha => ha.1⟩
refine le_antisymm ?_ (sSup_le fun c hc => hc.2)
have : (⨅ c : α, ⨆ x, b ⊓ cond x c (cᶜ)) = b := by simp [iSup_bool_eq]
rw [← this]; clear this
simp_rw [iInf_iSup_eq, iSup_le_iff]; intr... |
870 | lean_file_chunk | af9408245c37c5f69e2ceab1484104cae76ca9bece302b03ea67f29b79af3f4c | lean_source_file | pkg_mathlib_source_file_chunks | theorem isAtom_singleton (x : α) : IsAtom ({x} : Set α) :=
⟨singleton_ne_empty _, fun _ hs => ssubset_singleton_iff.mp hs⟩
theorem isAtom_iff {s : Set α} : IsAtom s ↔ ∃ x, s = {x} := by
refine
⟨?_, by
rintro ⟨x, rfl⟩
exact isAtom_singleton x⟩
rw [isAtom_iff_le_of_ge, bot_eq_empty, ← nonempty_iff_... |
14,290 | lean_file_chunk | 0333f3b5a088fb27e5c980d2e996d2c8952c6fd935f8ef74566b26d6441afc2a | 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, Yaël Dillies, David Loeffler
-/
module
public import Mathlib.Order.PartialSups
public import Mathlib.Order.Interval.Finset.Fin
public import Mathlib.Order.SuccPred.Lin... |
1,964 | lean_file_chunk | f601177781240f6b4e3b4f46651cdc981bead3b5297deb5ee55ffe187360c3ee | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Ansar Azhdarov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ansar Azhdarov
-/
module
public import Mathlib.Data.Set.Finite.Range
public import Mathlib.Data.Set.Finite.Lattice
public import Mathlib.Order.Zorn
/-!
# Teichmuller-Tukey
This file... |
23,528 | lean_file_chunk | cc04d96f58eb20f844d4949911f7b7911c7fbecb8bd5c79e1373c7451fe12cc9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junyan Xu
-/
module
public import Mathlib.Order.SuccPred.Limit
public import Mathlib.Order.UpperLower.Basic
/-!
# Definition of direct systems, inverse systems, and cardinalities in speci... |
23,941 | lean_file_chunk | 6162f16a7d1ad4d87de6168a59c9ba0381e5bf0eaa28848304b56c2d53b49471 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang, Fangming Li
-/
module
public import Mathlib.Algebra.GroupWithZero.Nat
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order.Monoid.NatCast
publ... |
18,652 | lean_file_chunk | ae3e10284c5da027cfb8ef6de11da7b60a1d02e265b147814411ecb05fd2fb6a | lean_source_file | pkg_mathlib_source_file_chunks | step i := p.step ⟨i, lt_of_lt_of_le i.2 (Nat.sub_le _ _)⟩
@[simp] lemma head_eraseLast (p : RelSeries r) : p.eraseLast.head = p.head := rfl
@[simp] lemma last_eraseLast (p : RelSeries r) :
p.eraseLast.last = p ⟨p.length.pred, Nat.lt_succ_iff.2 (Nat.pred_le _)⟩ := rfl
/-- In a non-trivial series `p`, the last ele... |
4,826 | lean_file_chunk | f888492c8ac8760bd834c79d49440cc98bcb8aebbf415cd44c0074fd286ee1ba | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Johan Commelin, Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Damiano Testa, Yaël Dillies
-/
module
public import Mathlib.Logic.Equiv.Defs
public import Mathlib.Order.Basic
/-!
# Type synonyms
This file provides ... |
19,752 | lean_file_chunk | 39771f47774fc4951a520844884d3b21939c447011d967d19963e840b1c443d6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
module
public import Mathlib.Order.Lattice
public import Mathlib.Data.List.Sort
public import Mathlib.Logic.Equiv.Fin.Basic
public import Mathlib.Logic.Equiv.Functor
pub... |
23,056 | lean_file_chunk | 91e29db61b7b191e1427fa50823e27f0175a1bee7513716032e375d77087092b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Aaron Anderson, Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson, Kevin Buzzard, Yaël Dillies, Eric Wieser
-/
module
public import Mathlib.Data.Finset.Lattice.Union
public import Mathlib.Data.Finset.Lattice.Prod
public ... |
5,804 | lean_file_chunk | 3cbcef07cd53a96031c10023cbfdf33050c8373012055ea882e72b64905d6984 | 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, Johannes Hölzl
-/
module
public import Mathlib.Order.ConditionallyCompleteLattice.Basic
public import Mathlib.Order.RelIso.Basic
/-!
# Order continuity
We say that... |
1,405 | lean_file_chunk | 8be930f53871c1307c6650388be25ef638a45d432460d1134cacb9d54a51d503 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 Floris van Doorn (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-/
module
public import Mathlib.Data.Nat.Find
public import Mathlib.Order.BoundedOr... |
23,970 | lean_file_chunk | 945cc68bf4aa3b6945d0073afe8e1aa256af53857f5ce321e480bc4717b84f06 | 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.Order.ConditionallyCompleteLattice.Indexed
public import Mathlib.Order.Filter.IsBounded
public impor... |
23,996 | lean_file_chunk | d595d5eaf4dae82750bf41414b94b7f62f1fe686ef22fac94780fb326460a2ed | lean_source_file | pkg_mathlib_source_file_chunks | theorem mono_blimsup (h : ∀ x, p x → u x ≤ v x) : blimsup u f p ≤ blimsup v f p :=
mono_blimsup' <| Eventually.of_forall h
theorem mono_bliminf' (h : ∀ᶠ x in f, p x → u x ≤ v x) : bliminf u f p ≤ bliminf v f p :=
sSup_le_sSup fun _ ha => (ha.and h).mono fun _ hx hx' => (hx.1 hx').trans (hx.2 hx')
theorem mono_bli... |
8,133 | lean_file_chunk | 8bfc23b91f1773f7eb41509db59f46c979d26a7b6e97d6bcdbeb6654c73e39ee | lean_source_file | pkg_mathlib_source_file_chunks | above on `s k` (if there exists one). To ensure good measurability behavior, this index `k` is
chosen as the minimal suitable index. This function is used to write down a limsup in a measurable
way, in `Filter.HasBasis.limsup_eq_ciInf_ciSup` and `Filter.HasBasis.limsup_eq_ite`. -/
noncomputable def limsup_reparam
(... |
17,483 | lean_file_chunk | 626d11883c152a1b6f77996686f56413c747a8473025cd7cf5c4e571326301f3 | 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.Bounds.Basic
public import Mathlib.Order.Preorder.Chain
/-!
# Antichains
This file defines antichains. An antichain is a set where a... |
5,514 | lean_file_chunk | e2e21df36dec3baccff7a9c13a0422683a538400220c2ac8239655d52eafbd91 | 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.GaloisConnection.Basic
public import Mathlib.Order.Interval.Set.Basic
public import Mathlib.Order.WellFoun... |
18,833 | lean_file_chunk | 7c682a22e2a06a71083edf4a5b0b889a08f846c3bb317439f3a8506130d151ac | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Yaël Dillies
-/
module
public import Mathlib.Data.Set.BooleanAlgebra
public import Mathlib.Data.SetLike.Basic
public import Mathlib.Order.Hom.Basic
/-!
# Closure operator... |
7,604 | lean_file_chunk | a130da9643405e38fb9d5a005ced7a96d52d0f1a7f3b87cff90ddde28c827722 | 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.Concept
import Mathlib.Order.UpperLower.CompleteLattice
/-!
# Dedekind-MacNeille completion
The Dedekin... |
8,115 | lean_file_chunk | 889eee4d64c18b1c60347d62130f5d4f6e234aac2a4a543055c7f0fcacff2ae0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Christopher Hoskin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Hoskin
-/
module
public import Mathlib.Tactic.FunProp.Attr
public import Mathlib.Tactic.ToFun
import Mathlib.Order.Bounds.Image
public import Mathlib.Order.Bounds.Defs... |
4,231 | lean_file_chunk | 559467005b066e80b20fbe4d8b16ded71fa9bba68473a4ceacb890b99db0346f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Etienne Marion. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Etienne Marion
-/
module
public import Mathlib.Data.Finset.Update
public import Mathlib.Order.Interval.Finset.Basic
/-!
# Restriction of a function indexed by a preorder
Given a pre... |
656 | lean_file_chunk | 102879ce5908ea2cf6ece0ef5114f0cc4bee87dc66c2da7df653e336442cac84 | 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.Max
public import Mathlib.Data.Set.CoeSort
/-!
# Maximal elements of subsets
Let `S : Set J` and `m : S`. If `m` is not a maximal element ... |
23,998 | lean_file_chunk | 2391403b7a22dce84c631bfec1d9cbd41796ec09e90f70d007bcf4a888bfae13 | 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, Violeta Hernández Palacios, Grayson Burton, Floris van Doorn, Bhavik Mehta
-/
module
public import Mathlib.Order.Antisymmetrization
public import Mathlib.Order.Hom.WithTop... |
2,959 | lean_file_chunk | facc427ee9749cd4dbab5a5c2e4bdca8f865bd5825924dfd853b84b5a411bcb5 | lean_source_file | pkg_mathlib_source_file_chunks | · rintro ⟨i, hi, h⟩
exact ⟨i, b i, hi, by simpa [Function.eq_update_iff, eq_comm] using h⟩
· rintro ⟨i, x, h, rfl⟩
exact ⟨i, by simpa +contextual⟩
lemma covBy_iff_exists_right_eq [DecidableEq ι] :
a ⋖ b ↔ ∃ i x, a i ⋖ x ∧ b = Function.update a i x := by
rw [covBy_iff]
constructor
· rintro ⟨i, hi, h... |
2,375 | lean_file_chunk | 247b7a9ef24ff94233b6b9daf168b4416a9cc75de749d172f86f24e1a6ad1809 | 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, Kevin Buzzard
-/
module
public import Mathlib.Order.WithBot
/-!
# Adding both `⊥` and `⊤` to a type
This files defines an abbreviation `WithBotTop ι` for `WithBot (WithTop ι)`... |
9,314 | lean_file_chunk | a3f05b76cc0637bcb8e4d289a2482b565e334c03f9cf231af771ddb404e256c0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Christian Krause. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chriara Cimino, Christian Krause
-/
module
public import Mathlib.Order.Nucleus
public import Mathlib.Order.SupClosed
/-!
# Sublocale
Locales are the dual concept to frames. Locale... |
23,983 | lean_file_chunk | 9837b43de202f1ce51bd33f771ab40f01c59921e9d8d8bb46cfe77cddc45fd3b | 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
-/
module
public import Mathlib.Data.Subtype
public import Mathlib.Order.Defs.LinearOrder
public import Mathlib.Order.Notation
public import Mathlib.Tacti... |
16,713 | lean_file_chunk | 12fbddc0d94c72f9630d7c918f395c45a1da11460914fe4bddc7663116f6b6db | lean_source_file | pkg_mathlib_source_file_chunks | toDecidableEq := ‹_›
toDecidableLT := ‹_›
le_total _ _ := by simp only [← le, le_total]
min_def _ _ := by simp_rw [← hf.eq_iff, ← le, apply_ite f, ← min_def, min]
max_def _ _ := by simp_rw [← hf.eq_iff, ← le, apply_ite f, ← max_def, max]
compare_eq_compareOfLessAndEq _ _ := by
simp_rw [← compare, LinearOr... |
7,167 | lean_file_chunk | 9cc2a8cdb4630d6006d950f152b256737aab28ec455fb5733783b1785aab002b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 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.CompactlyGenerated.Basic
/-!
# Generators for Boolean algebras
In this file, we provide an alternative constructor for Boolean a... |
20,689 | lean_file_chunk | 4c7808a11bd3d01536b6b16f1cf4f8c12abfbd7c38bba371cad858f06e4a2f48 | 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.Lattice
/-!
# Disjointness and complements
This file defines `Disjoint`, `Codisjoint`, and the `IsCompl` predicate.... |
11,301 | lean_file_chunk | 49e3a6a7317fe9528c81121a61d6e00f78e916156d897a355730ab020ff58dbf | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.Data.Set.Finite.Lattice
public import Mathlib.Order.ConditionallyCompleteLattice.Indexed
public import Mathlib.Order.Interval.Finset.Nat
pub... |
3,286 | lean_file_chunk | c66adca6d322feca78146f6debafb545e6579e19ac266ac7e4562c74df7ed297 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
module
public import Mathlib.Logic.Function.ULift
public import Mathlib.Order.Basic
/-! # Ordered structures on `ULift.{v} α`
Once these basic instances are setup, the i... |
7,642 | lean_file_chunk | fa89e77b38cd008b9a5a9b82f8560a2976d0f5954e898fd42d4efdd9a1bcaead | 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.Data.Ordering.Basic
public import Mathlib.Order.OrderDual
/-!
# Comparison
This file provides basic results about orderings and compar... |
4,315 | lean_file_chunk | ec2e4c33181c0a812859f319f6933fe02b17d3f48da331885366163c5270e39e | 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.Interval.Set.OrdConnected
/-!
### Order instances on quotients
We define a `Preorder` instance on a gene... |
17,419 | lean_file_chunk | 279050074806c3aa24da0b297c58d54aeab2e3400e33fccc9852427ba795dcc5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn
-/
module
public import Mathlib.Data.Finset.Lattice.Fold
public import Mathlib.Logic.Encodable.Basic
public import Mathlib.Order.Atoms
public import Mathlib.Order.Cofinal
publi... |
13,720 | lean_file_chunk | c9fe64607d9186bf81bd1b5b1dd86cfcd7f37791406eb4f4e1a26bc3605bd79e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Mario Carneiro
-/
module
public import Mathlib.Data.Set.Function
public import Mathlib.Order.Bounds.Defs
/-!
# Well-founded relations
A relation is well-founded if it ... |
8,842 | lean_file_chunk | 55479f57a6dfe816b74000a002e1aed860f6de3385f8846bbc48602fe6aa29c6 | 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.SuccPred.CompleteLinearOrder
public import Mathlib.Order.SuccPred.InitialSeg
/-!
# Normal functions
A no... |
23,971 | lean_file_chunk | e1f03013e7dcc0c30bf36f6a609d030c401b551c36ab4baf46d85c1d97933e19 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Mario Carneiro, Yury Kudryashov
-/
module
public import Mathlib.Logic.IsEmpty.Basic
public import Mathlib.Order.OrderDual
public import Mathlib.Tactic.MkIffOfInductivePr... |
3,475 | lean_file_chunk | 440d1897b141e96838acbe223453c4ffe9759128c0cda391d30fcbf21d5ec53a | lean_source_file | pkg_mathlib_source_file_chunks | fun h => (h₁.trans_ssubset h).trans_subset h₂
@[gcongr]
theorem ssuperset_imp_ssuperset (h₁ : a ⊆ c) (h₂ : d ⊆ b) : a ⊃ b → c ⊃ d :=
ssubset_imp_ssubset h₂ h₁
/-- See if the term is `a ⊂ b` and the goal is `a ⊆ b`. -/
@[gcongr_forward] meta def exactSubsetOfSSubset : Mathlib.Tactic.GCongr.ForwardExt where
eval h ... |
21,210 | lean_file_chunk | c8ec0009bfea083f540a960eec6c13a3d648052dd9c68995d501f55a84a04c5e | 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, Peter Nelson
-/
module
public import Mathlib.Order.Hom.Basic
public import Mathlib.Order.Interval.Set.Defs
public import Mathlib.Order.WellFounded
/-!
# Minimality and Ma... |
20,912 | lean_file_chunk | 51a9792cd9bf7eac701a724491ff03f4e2e523cfe8d9a68b8e98154109927c13 | 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, Wrenna Robson, Violeta Hernández Palacios
-/
module
public import Mathlib.Data.Set.Lattice
public import Mathlib.Order.Closure
/-!
# Formal concept analysis
This file de... |
6,802 | lean_file_chunk | cddb7204762b4492e959f5df0a3247e860cc2adf696bd554ad48cfdbbb28ad2c | 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, Yury Kudryashov, Yaël Dillies
-/
module
public import Qq
public meta import Mathlib.Lean.PrettyPrinter.Delaborator
public import Mathlib.Tactic.Simps.NotationClass
pub... |
7,766 | lean_file_chunk | 5e408707087a274806608e77f3adfb1f5c6c05912dcb3153a0de5b693eb421a4 | 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.CompleteLattice.Chain
public import Mathlib.Order.Minimal
/-!
# Zorn's lemmas
This file proves several formulations of Zorn's Le... |
11,473 | lean_file_chunk | cb9c930853ea51d5609f6712727ec26a5708d7c6e94ac54759ea66cf052aac0f | 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.BooleanAlgebra.Basic
public import Mathlib.Order.Hom.Lattice
/-!
# Adding complements to a generalized Boolean algebra
This file emb... |
23,977 | lean_file_chunk | 34b5ce86e96f2d3d82e76557b25634ba4bba758b088d1d19231c7cbc3b08a13f | 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: Mario Carneiro, Floris van Doorn, Violeta Hernández Palacios
-/
module
public import Mathlib.Data.Sum.Order
public import Mathlib.Order.Hom.Lex
public import Mathlib.Order.RelIso.Set
... |
1,407 | lean_file_chunk | 3b81588de7e14aab278fcb7f20bed9609c8cb93a1182bf5dfaf4a2af1cfdf988 | lean_source_file | pkg_mathlib_source_file_chunks | (f : α ≤i β).mem_range_of_le h
theorem range_eq_Iio [LT α] (f : α <i β) : Set.range f = Set.Iio f.top :=
f.range_eq
theorem isLowerSet_range [LT α] (f : α <i β) : IsLowerSet (Set.range f) :=
(f : α ≤i β).isLowerSet_range
-- TODO: this would follow immediately if we had a `RelEmbeddingClass`
@[simp]
theorem le_if... |
2,446 | lean_file_chunk | 1a465179e008e8b96cf16555fa98fb16357cb26258b65e8b646fecbaf844b129 | 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.SuccPred.Basic
public import Mathlib.Logic.Small.Defs
/-!
# Order instances on Shrink
If `α : Type v` is `u`-small, we transport various o... |
602 | lean_file_chunk | 6d9889a68e2219c53ae675d55efbddfdbcda2f16e2b58e478eda15361fb27528 | 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.TypeTags
/-! # `Set.range` on `WithBot` and `WithTop` -/
public section
open Set
variab... |
8,111 | lean_file_chunk | dea0ffb369459e4c73529f5e19aa6ffb4c39aeb5abb44f6d70d2a6fd1facd186 | 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.Data.Set.Functor
public import Mathlib.Order.Sublattice
public import Mathlib.Order.Hom.CompleteLattice
/-!
# Complete Sublattices
This file... |
9,249 | lean_file_chunk | 8f3434fc1cc555b32647769d18f11bf275033de3ca0a14ccb28886757fce39f7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junyan Xu
-/
module
public import Mathlib.Data.Sym.Sym2
public import Mathlib.Logic.Relation
/-!
# Game addition relation
This file defines, given relations `rα : α → α → Prop` and `rβ :... |
3,031 | lean_file_chunk | 6d9d5e5f07a74b92c50f093a3ebb4011f9e5ea8126930cf33f921fe97f1bb6df | 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.Disjoint
/-!
# The order on `Prop`
Instances on `Prop` such as `DistribLattice`, `BoundedOrder`, `LinearOrder`.
-/
@[expose] ... |
21,896 | lean_file_chunk | a0a03a036c4aabeae8dd2e673c9da341f9cbf17815a051df91d309521b30db53 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Bryan Gin-ge Chen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz, Bryan Gin-ge Chen, Yaël Dillies
-/
module
public import Mathlib.Order.BooleanAlgebra.Basic
public import Mathlib.Logic.Equiv.Basic
/-!
# Symmetric difference and bi-im... |
1,706 | lean_file_chunk | efe048daeadcd80d76cf057d154756f9ba4382f6cc4b5c75c690aaf19d49ab6f | 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.Zorn
public import Mathlib.Order.Atoms
/-!
# Zorn lemma for (co)atoms
In this file we use Zorn's lemma to prove that a partial... |
14,090 | lean_file_chunk | b40eefbe82a6f579099dbd6942954e3df551b8dae1a9c8cd20522d64a22d60a3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies, Violeta Hernández Palacios. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Violeta Hernández Palacios, Grayson Burton, Vladimir Ivanov
-/
module
public import Mathlib.Data.Int.SuccPred
public import Mathlib.Order.Fin.B... |
23,943 | lean_file_chunk | dcbee9946697fe11052157877447becabdc1433926ad61a7157bc3bcbb48d352 | 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.Logic.Nontrivial.Basic
public import Mathlib.Order.TypeTags
public import Mathlib.Data.Option.NAry
public import Mathlib.Tactic.Contrapo... |
12,009 | lean_file_chunk | 75d1957a6486cbe69374b8094897525a061f0c96da1197818d737c0c5bee2015 | lean_source_file | pkg_mathlib_source_file_chunks | sup_le x y z := by cases x <;> cases y <;> cases z <;> simp; simpa using sup_le
@[to_dual (attr := simp, norm_cast)]
theorem coe_sup [SemilatticeSup α] (a b : α) :
((a ⊔ b : α) : WithBot α) = (a : WithBot α) ⊔ b := rfl
@[to_dual (attr := simp, norm_cast)]
theorem coe_inf [SemilatticeInf α] (a b : α) :
((a ⊓ b... |
8,463 | lean_file_chunk | da28d5adea942c55a3a11971753268103037efb978a528d767dfcaf90bc93305 | 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, Aaron Anderson
-/
module
public import Mathlib.Data.Fintype.Card
public import Mathlib.Data.Set.Finite.Basic
public import Mathlib.Order.Antich... |
3,836 | lean_file_chunk | caa3dd967cbac56664b99ec15e4b6cc64cdac40a6204184379f47381ffdfdc3a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir, Anatole Dedecker
-/
module
public import Mathlib.Order.ConditionallyCompleteLattice.Basic
public import Mathlib.Order.OmegaCompletePartialOrder
/-!
# Sa... |
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