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 |
|---|---|---|---|---|---|
1,094 | lean_file_chunk | 81db4104f88ab315219bee92cad949fdb492d9c1ab64dccc46e8f3a794c2ef38 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
module
public import Mathlib.Algebra.Module.Basic
public import Mathlib.Algebra.Order.AbsoluteValue.Basic
/-!
# Absolute values and the integers
This file contains some ... |
5,077 | lean_file_chunk | e0c30cd4e867459ae34aaf8bce2bba1f99f269e8f8d03a45b8b7439708a0d379 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Tom Kranz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tom Kranz
-/
module
public import Mathlib.Data.FinEnum
public import Mathlib.Logic.Equiv.Fin.Basic
/-!
# FinEnum instance for Option
Provides a recursor for FinEnum types like `Fintype.t... |
2,786 | lean_file_chunk | 9ab3198f584d035aee21201457c7a80207d83ae26690f0fa0a08ef5930af8192 | 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.Data.Set.Pairwise.Basic
public import Mathlib.Data.Rel
/-!
# Uniform separation
This file defines a notion of separation of a set relative... |
3,170 | lean_file_chunk | 78d32afeeba84b8e6cf8d302ffb308f363c6cfb9e8dcde2bf7dab85c13a55cb3 | 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.Data.Rel.Separated
/-!
# Covers in a uniform space
This file defines covers, aka nets, which are a quantitative notion of compactness give... |
16,348 | lean_file_chunk | bf2bcfbf3a0bb4da5dafc5e867a865e980138d2c8fb28eb809bd928022cfd695 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Data.Finset.Sum
public import Mathlib.Data.Sum.Order
public import Mathlib.Order.Interval.Finset.Defs
/-!
# Finite intervals in a disjoint ... |
23,942 | lean_file_chunk | a58a7accd60cb4f2cf2580a9c90559b5e49925eb9939f65168e9f5a0aa1d8311 | 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.Heyting.Basic
public import Mathlib.Order.Hom.Basic
public import Mathlib.Order.Lex
public import Mathlib.Order.WithBot
/-!
# Orders ... |
2,201 | lean_file_chunk | f92e19b2aa02b94fd6e56ea87c0b5846d17aa117da3d1fc1fc74abe518df7e3a | lean_source_file | pkg_mathlib_source_file_chunks | /-- `WithBot α` is order-isomorphic to `PUnit ⊕ₗ α`, by sending `⊥` to `Unit` and `↑a` to
`a`. -/
def orderIsoPUnitSumLex : WithBot α ≃o PUnit ⊕ₗ α :=
⟨(Equiv.optionEquivSumPUnit α).trans <| (Equiv.sumComm _ _).trans toLex, fun {a b} => by
simp only [Equiv.optionEquivSumPUnit, Option.elim, Equiv.trans_apply, Equi... |
10,640 | lean_file_chunk | edce73ad21a0af2f1e2f45fe6c9e16a8eb6701bc4ffddb70c19313c532d74aae | 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, Yury Kudryashov
-/
module
public import Mathlib.Logic.Function.Basic
public import Mathlib.Tactic.MkIffOfInductiveProp
/-!
# Additional lemmas about sum types
Most o... |
4,199 | lean_file_chunk | ec4045352da4c883131514dbc043d1f6df63f8e9ed71dda4a82ced477966e761 | 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.Data.Sum.Order
public import Mathlib.Order.Hom.Lattice
/-!
# Lexicographic sum of lattices
This file proves that we can combine two lattic... |
1,769 | lean_file_chunk | a47c5007eb9ba985b2002b910dca263418a63adb48acc674ea2f507cabe358c2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 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.Ordering.Basic
public import Mathlib.Order.Defs.Unbundled
/-!
# Some `Ordering` lemmas
-/
public section
universe u
n... |
1,547 | lean_file_chunk | 1a521a7d9b51bdd59d124f19ecbef49375e6e77d964336f62bf8eeae260a126c | 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.Init
/-!
# Helper definitions and instances for `Ordering`
-/
@[expose] public section
universe u
namespace Ordering
vari... |
14,598 | lean_file_chunk | e50075000e06785d7a1a44d7dc847960903fbbe6e67cdda61823e0ed8c1334cd | 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, Kenny Lau
-/
module
public import Mathlib.Data.List.Forall2
/-!
# Lists with no duplicates
`List.Nodup` is defined in `Data/List/Basic`. In this file we prove variou... |
5,401 | lean_file_chunk | 0c3975ef5853e50cabadca099c83b5424369922e150e9b4a1b093c1de51490b0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky, Anthony DeRossi
-/
module
public import Mathlib.Data.List.Basic
/-!
# Properties of `List.reduceOption`
In this file we prove basic lemmas about `List.reduceOption... |
5,020 | lean_file_chunk | 6eaf0875ac9d9fb8671edff56342b247b7a7a2bac8974865856963afbe46dbff | 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, Kenny Lau
-/
module
public import Mathlib.Data.List.Forall2
public import Mathlib.Data.Nat.Basic
/-!
# zip & unzip
This file provides results about `List.zipWith`, `... |
3,322 | lean_file_chunk | fc56e8db96c9fe203b695defc904db793f3566f96e4bed7636c2c9a05733ab44 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Daniel Weber. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Daniel Weber
-/
module
public import Mathlib.Algebra.Group.Nat.Defs
public import Mathlib.Order.MinMax
/-!
# Splitting a list to chunks of specified lengths
This file defines splittin... |
1,952 | lean_file_chunk | a4ae3f11b6cf5a15791688eee564499e346679e8a0198d8b4fb74084809f3d05 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
-/
module
public import Batteries.Data.List.Perm
public import Mathlib.Tactic.Common
public impo... |
22,461 | lean_file_chunk | b20db05022c4f4c4997bf82bddce06bad89427a11f15ca4fed9ad6db4279c7c7 | 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, Kenny Lau, Yury Kudryashov
-/
module
public import Mathlib.Data.List.Forall2
public import Mathlib.Data.List.Induction
public import Mathlib.Data.List.Lex
public impor... |
1,857 | lean_file_chunk | 7ff74eb8b39674edb24a4c8ef28414349ebe6b321f3bd200c76cb03e2f2cbe42 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Miyahara Kō. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Miyahara Kō
-/
module
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Data.List.Defs
/-!
# iterate
Proves various lemmas about `List.iterate`.
-/
public section
v... |
1,474 | lean_file_chunk | 900fca3c16ab0f7ba97b0ae18cf70b332cd539b1ff3f46aea92218673616432c | 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.List.Forall2
/-!
# List sections
This file proves some stuff about `List.sections` (definition in `Data.List.Defs`). A section of ... |
3,194 | lean_file_chunk | c36f2dd8b677664aa9d581eb29dc0e9219e6e964f73c9a61cf806add05181231 | 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: Sébastien Gouëzel, Floris van Doorn, Mario Carneiro, Martin Dvorak
-/
module
public import Mathlib.Tactic.GCongr.Core
/-!
# Join of a list of lists
This file proves basic properties... |
3,696 | lean_file_chunk | a9fa65704ab5c0ab23e1dd612ed39d118b4bd08fe4a73883b3a59eeaf594fd5c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky, Yury Kudryashov
-/
module
public import Mathlib.Data.Set.Image
public import Mathlib.Data.List.Basic
/-! # Some lemmas about lists involving sets
Split out from `D... |
4,875 | lean_file_chunk | 72b78c9c72ef0777e877af90888d3d82764ad916004f9897bcaeb66a0f31b024 | 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 Batteries.Data.List.Pairwise
public import Mathlib.Logic.Pairwise
public import Mathlib.Logic.Relation
public import Batteries.Data.List.Lemmas
... |
17,724 | lean_file_chunk | 97930118d19d6ff2ffae5c48450e2851e431516a5a050c0cdc5f8bb7d4efff3f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Minchao Wu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Minchao Wu, Chris Hughes, Mantas Bakšys
-/
module
public import Mathlib.Data.List.Basic
public import Mathlib.Order.BoundedOrder.Lattice
public import Mathlib.Data.List.Induction
public i... |
4,680 | lean_file_chunk | 055d95a1f1a027aa56e92ef25f0a8223609106dd24e1227d64deebadc3aa54e3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
-/
module
public import Mathlib.Tactic.Attr.Core
public import Mathlib.Tactic.Common
public impo... |
4,902 | lean_file_chunk | 9824a0506f38c43accecbde05eb4193f30b0504bdc1e5edc5cb12c83d4ed3787 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
import Mathlib.Data.List.Count
import Mathlib.Data.List.Enum
import Mathlib.Data.List.Nodup
import Mathlib.Data.List.Perm.Basic
public import Mathlib.Data.N... |
5,735 | lean_file_chunk | dab85091c0ef4336e504f69bf50187f5423df144ab06fb636342d986e486da9c | 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.List.Basic
public import Mathlib.Data.Nat.Basic
public import Mathlib.Order.RelClasses
/-!
# Lexicographic ordering of lists.
The... |
4,091 | lean_file_chunk | d17bd8994197add68f7ca6eedfa043847f01ffdc3340cc740b6a8be2429ee1ca | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Simon Hudon
-/
module
public import Batteries.Tactic.Alias
public import Batteries.Data.List.Basic
public import Mathlib.Init
/-!
# The Following Are Equivalent
This... |
22,634 | lean_file_chunk | c46f3463a60274aa5512be02c1445d3030477a5df0e7ca8b8cacd0ef458582f2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
-/
module
public import Mathlib.Data.Nat.Factorial.Basic
public import Mathlib.Data.List.Count
p... |
23,965 | lean_file_chunk | 15ad62fccaeead60b5c5e5e70a833aa6df0198a40869176988864e22df5e42f9 | 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, Sean Leather
-/
module
public import Batteries.Data.List.Perm
public import Mathlib.Data.List.Pairwise
public import Mathlib.Data.List.Nodup
public import Mathlib.Data... |
2,721 | lean_file_chunk | ca25e2e92240b5bcb8d844f81d3fdb26bb4add6b41bbb7a381e0035278537b55 | lean_source_file | pkg_mathlib_source_file_chunks | | s :: _, l => by by_cases h : a = s.1 <;> simp [h, kerase_comm a s.1 l, kunion_kerase]
theorem NodupKeys.kunion (nd₁ : l₁.NodupKeys) (nd₂ : l₂.NodupKeys) : (kunion l₁ l₂).NodupKeys := by
induction l₁ generalizing l₂ with
| nil => simp only [nil_kunion, nd₂]
| cons s l₁ ih =>
simp only [nodupKeys_cons] at nd... |
6,283 | lean_file_chunk | a5d07ce9f32f62c94b9187afae5a1befdf27241a88a7b8bd028ca4c14532b3f0 | 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.List.Nodup
public import Mathlib.Data.List.Lattice
public import Batteries.Data.List.Pairwise
/-!
# Erasure of duplicates in a lis... |
2,616 | lean_file_chunk | 8b9b8da130b17d1cba518e709e81cbe7d927443a68276a34db6c48f197577cb5 | 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, Kenny Lau, Kim Morrison, Alex Keizer
-/
module
public import Mathlib.Data.List.OfFn
public import Batteries.Data.List.Perm
public import Mathlib.Data.List.Nodup
/-!
#... |
13,492 | lean_file_chunk | 3bdf91977c5ea39495e2c0551efc3ec156508667f9a25dee37a6ae2ad3699c7c | 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, Johannes Hölzl
-/
module
public import Mathlib.Data.List.Basic
public import Mathlib.Logic.Relator
/-!
# Double universal quantification on a list
This file provides... |
7,999 | lean_file_chunk | 93f42cdbad26853641a735d768f1ce07f7b26c671ae27c9e8560da8dadbd89a5 | 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.Data.List.Duplicate
public import Mathlib.Data.List.Sort
/-!
# Equivalence between `Fin (length l)` and elements of a list
Given a l... |
2,333 | lean_file_chunk | 338c46d46c1b5900c4214e58dd5af789c3136da65aacf4b023e2167230b3ee83 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Jannis Limperg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jannis Limperg
-/
module
public import Mathlib.Data.List.Defs
/-!
# Lemmas about `List.*Idx` functions.
Some specification lemmas for `List.mapIdx`, `List.mapIdxM`, `List.foldlIdx` ... |
3,441 | lean_file_chunk | cf9418b6e88498523fb773919a65b073a331170184dd4d551f372b0af6f46a4d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yuyang Zhao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuyang Zhao
-/
module
public import Mathlib.Data.Multiset.Pi
/-!
# The Cartesian product of lists
## Main definitions
* `List.pi`: Cartesian product of lists indexed by a list.
-/
@[... |
1,159 | lean_file_chunk | 358c53ed1716008b721ec19d9a271c029198fbe938039dba5e59dcc7f0bcdbc8 | 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.Init
public import Batteries.Control.AlternativeMonad
/-!
# Monad instances for `List`
-/
@[expose] public section
universe ... |
4,243 | lean_file_chunk | ea92c572f9d9ddb0ef5f5285f301b6bd82641f528a5cd05b51c7f77e5231054e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky, Chris Hughes
-/
module
public import Mathlib.Data.List.Nodup
/-!
# List duplicates
## Main definitions
* `List.Duplicate x l : Prop` is an inductive property that... |
23,971 | lean_file_chunk | 1b1dddcaf1d175e49138a292be2eb466c922f15f213607679b4986856f187169 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
-/
module
public import Mathlib.Data.List.Defs
public import Mathlib.Data.List.Monad
public impo... |
16,981 | lean_file_chunk | 65949424fb1104005c2da09e42e8449c24d9570ff118223ebb1f26aa76a1da3c | lean_source_file | pkg_mathlib_source_file_chunks | -- TODO: Upstream the tagging to Core?
attribute [simp] map_const'
theorem flatMap_pure_eq_map (f : α → β) (l : List α) : l.flatMap (pure ∘ f) = map f l :=
.symm <| map_eq_flatMap ..
theorem flatMap_congr {l : List α} {f g : α → List β} (h : ∀ x ∈ l, f x = g x) :
l.flatMap f = l.flatMap g :=
(congr_arg List.f... |
5,994 | lean_file_chunk | b824257f48582f88d183d45d2ac9cfa82ad6d14f4b2380b056e5e435f5c635e6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Hannah Fechtner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Hannah Fechtner
-/
module
public import Mathlib.Data.List.Lex
public import Mathlib.Order.RelClasses
public import Mathlib.Tactic.NormNum
/-!
# Shortlex ordering of lists.
Given a ... |
23,969 | lean_file_chunk | 575751ece81770b1a71625c5548e05fffcb94d677bd5a776ca17a31f6a96e686 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Wrenna Robson
-/
module
public import Batteries.Data.List.Pairwise
public import Batteries.Data.List.Perm
public import Mathlib.Data.List.OfFn
public import Mathlib.Data... |
9,738 | lean_file_chunk | 10cb265252fbc793870db21dde46ac3b79bce4d64f8979bbc4b4d9b0dc1822f7 | lean_source_file | pkg_mathlib_source_file_chunks | @[simp] theorem sortedGE_map_ofDual :
(l.map OrderDual.ofDual).SortedGE ↔ l.SortedLE := by
grind [OrderDual.ofDual_le_ofDual]
@[simp] theorem sortedLT_map_ofDual {l : List αᵒᵈ} :
(l.map OrderDual.ofDual).SortedLT ↔ l.SortedGT := by
grind [OrderDual.ofDual_lt_ofDual]
@[simp] theorem sortedGT_map_ofDual {l : ... |
7,416 | lean_file_chunk | 39d1e09f274865dfd0c092fd6b709511ccd53ff7c27052597f39099c11c7856f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 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.List.Induction
public import Mathlib.Data.List.TakeWhile
public import Mathlib.Data.List.Basic
/-!
# Dropping or taking from li... |
3,068 | lean_file_chunk | 39f1273393fb19933359dc43ded8013a2d8bd95e074a1fb0681455b5b07ce910 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Myers, Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers, Yaël Dillies
-/
module
public import Mathlib.Tactic.MkIffOfInductiveProp
public import Batteries.Data.List.Lemmas
/-!
# Triplewise predicates on list.
## M... |
16,968 | lean_file_chunk | 7df0303bc7c4be0729c375eac14503eb857e995b96578403a057fae87392e20c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
-/
module
public import Mathlib.Data.Nat.Notation
public import Mathlib.Control.Functor
public i... |
4,162 | lean_file_chunk | 18e7be5c00e744f4e2c193300fa161f8984d343448e5af79dfeee9ae41a12b1b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Bolton Bailey. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bolton Bailey, Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn,
Mario Carneiro
-/
module
public import Mathlib.Data.List.Defs
public import Mathlib.Logic.Basic
/-... |
11,332 | lean_file_chunk | 961faf0a0f119d41ae5aa896e8bff9bac06aa440bea6e156b2584a3a736ebbb8 | 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.List.TakeDrop
public import Mathlib.Data.List.Induction
public import Mathlib.Data.Nat.Basic
public import Mathlib.Order.Basic
publ... |
769 | lean_file_chunk | 1f54c2c81621f9ac448a9a255b1558e8722a01a3416f8652f5e478d5f2fbe8d0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
module
public import Batteries.Data.List.Lemmas
public import Mathlib.Tactic.Common
public import Mathlib.Tactic.Finiteness.Attr
public import Mathlib.Tactic.ToDual
publ... |
2,187 | lean_file_chunk | 65d674b506e0811346cab9d2697a88a27dcfbf5b05f6b4ff786135364bc6c9ac | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
-/
module
public import Batteries.Data.List.Basic
public import Batteries.Tactic.Alias
public im... |
9,410 | lean_file_chunk | 550f87673f3ffb155577c270f4da3124994f46d5c3d971502049de85790647c3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Štěpán Holub. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Štěpán Holub
-/
module
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Data.Nat.Lattice
public import Mathlib.Tactic.TacticAnalysis.Declarations
/-! # Periods of wo... |
6,732 | lean_file_chunk | 10225e90d476642bdcf5a197cff87f84f7b3fdc60cefaa853de7e9df16663c1e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
-/
module
public import Mathlib.Data.List.Defs
public import Mathlib.Tactic.Common
/-!
# Map₂ L... |
5,095 | lean_file_chunk | 11e3f64bf6ad2eb741224b85407d92791d3660e77995a33cdd755a10cf11957a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
module
public import Mathlib.Algebra.Group.Embedding
public import Mathlib.Algebra.Group.Finsupp
public import Mathlib.Algebra.Group.Nat.Defs
public import Mathlib... |
3,762 | lean_file_chunk | 4630586d1c3dddc90168047f5b0b921eb7d85684194eeec5f8f8405d8ce8886c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Jeremy Tan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Tan
-/
module
public import Batteries.Tactic.Alias
public import Mathlib.Logic.OpClass
/-!
# Bird–Wadler duality of list folds
In their 1988 book _Introduction to Functional Prog... |
9,279 | lean_file_chunk | a0c608aff860fc3e6960c9429cd88d0b51610a877880029670958919f775aa27 | 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.Data.List.Chain
public import Mathlib.Data.List.Flatten
/-!
# Split a list into contiguous runs of elements whi... |
15,004 | lean_file_chunk | 12a029e9266589039abc3a43b7a583aaab3635c92fe2fca613e4c753f1d9c24c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Sean Leather. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sean Leather, Mario Carneiro
-/
module
public import Mathlib.Data.List.Sigma
/-!
# Association Lists
This file defines association lists. An association list is a list where every ele... |
11,221 | lean_file_chunk | 3651a24abb31ee266e056593c203e4c6c952ac89a1902fdab777428d7aa26031 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Eric Rodriguez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Rodriguez, Eric Wieser
-/
module
public import Mathlib.Data.List.Chain
public import Mathlib.Data.List.Dedup
/-!
# Destuttering of Lists
This file proves theorems about `List.d... |
5,621 | lean_file_chunk | 4fa0b3b08a35f3f4cc1262c08512301f445e25b1f578df6f5a85837751e974b3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
-/
module
public import Mathlib.Data.List.Defs
public import Mathlib.Tactic.Common
public import... |
2,929 | lean_file_chunk | cca3ef7ff4a160c3da6265d0fd587fff7fdef832e5bccbe52b4d17fc64043dd1 | 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, Jens Wagemaker, Anne Baanen
-/
module
public import Mathlib.Algebra.BigOperators.Group.List.Lemmas
public import Mathlib.Algebra.GroupWithZero.Associated
/-!
# Produc... |
3,075 | lean_file_chunk | 497305eab44e0286dfa8254a8aa719e8d7eab79eeb7b99ebf6f707709c791231 | 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, Kenny Lau, Kim Morrison
-/
module
public import Mathlib.Data.List.Chain
/-!
# Ranges of naturals as lists
This file shows basic results about `List.iota`, `List.rang... |
3,874 | lean_file_chunk | f985e759aff1243dcaaf9c8c794634a9acf61ec0081cd52ebc364cf84de4169f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
-/
module
public import Mathlib.Order.Basic
public import Mathlib.Data.Nat.Basic
public import M... |
7,325 | lean_file_chunk | 75926a395edbfa4bcb4e198436259d6f1a4826512db884990b07631d1dd7a75c | 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.Fin.Tuple.Basic
/-!
# Lists from functions
Theorems and lemmas for dealing with `List.ofFn`, which converts a function on `Fin n`... |
2,202 | lean_file_chunk | f1d0f0164c9cdab98aeb10cede57d34cbcb18f3e61f7f0bd03b990a46938f5d1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Google LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Wong
-/
module
public import Mathlib.Data.List.Induction
/-!
# Palindromes
This module defines *palindromes*, lists which are equal to their reverse.
The main result is the `Pali... |
3,640 | lean_file_chunk | 671dd1032a56ae05c94a1ca5ead7e24bb038e2e5bb97c2e5708df291152cd573 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
-/
module
public import Batteries.Logic
public import Batteries.Data.List.Basic
public import Ma... |
1,281 | lean_file_chunk | c0f348b1c544da2f30a9d9c3264a70469bb6012c8f5a6ef81ac24b305077082f | 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, Yakov Pechersky, Eric Wieser
-/
module
public import Mathlib.Data.List.Basic
/-!
# Properties of `List.enum`
-/
public section
namespace List
variable {α : Type*}
... |
7,935 | lean_file_chunk | 0281c7f56de2199060f81081e8b219c5ebe5d3fc4667408c5f1ee30896c590e3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
-/
module
public import Mathlib.Tactic.Attr.Core
public import Mathlib.Tactic.Common
public impo... |
369 | lean_file_chunk | e1498859dc406302f496c37fe0774c00e969e64c30e95a564ae3a5bc1a560a7a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
-/
module -- shake: keep-all
public import Mathlib.Tactic.Linter.DeprecatedModule
deprecated_mo... |
469 | lean_file_chunk | aa64893d62484f8ce5a2699e16661ed4cf3cec31f5ae7b292c21b9629f0790fc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Lean FRO. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.Tactic.Common
public import Mathlib.Util.CompileInductive
/-!
This is a stub file for importing `Mathlib/Data/List/InsertNth.lean`,
which has b... |
6,338 | lean_file_chunk | 212406ccb1c3a300ccad489914804fcb9a244e35cbf556bbef6a4774a0cf61bb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro,
Kim Morrison
-/
module
public import Mathlib.Data.List.Basic
/-!
# Lattice structure of lists
... |
2,379 | lean_file_chunk | a44bef8888d2dbd606b60e506610ac966be4470c45ea7ec1de957bbac58eff98 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2015 Leonardo de Moura. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Mario Carneiro
-/
module
public import Mathlib.Data.List.Defs
public import Mathlib.Tactic.Attr.Core
public import Mathlib.Tactic.Common
/-!
# Lists in product ... |
2,735 | lean_file_chunk | c709ed3f970811138db6e6c9bbccc92ee403699d4bb80205a7ccdfb027f7ba21 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
module
public import Mathlib.Data.List.Nodup
/-!
# Antidiagonals in ℕ × ℕ as lists
This file defines the antidiagonals of ℕ × ℕ as lists: the `n`-th antidiagonal i... |
17,118 | lean_file_chunk | ac66538f4f79bb7aafeb5c49b92983804ce15936860a5ec5322c76f393b90604 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 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.Nat.Choose.Basic
public import Mathlib.Data.List.Perm.Basic
public import Mathlib.Data.List.Perm.Subperm
public import Mathlib.Data... |
23,968 | lean_file_chunk | e8d4717ffcec1148a102c7662efc2961a49d34d27f1109195fd0ba905ebc4a5b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 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.Fintype.List
public import Mathlib.Data.Fintype.OfMap
public import Mathlib.Data.Fin.Basic
/-!
# Cycles of a list
Lists have an... |
9,340 | lean_file_chunk | 1b338c03fcbf4e1a59d1dd693442ddc30b44e814703a2d187e57f350cbcd13f7 | lean_source_file | pkg_mathlib_source_file_chunks | instance {s : Cycle α} : Decidable (Nontrivial s) :=
Quot.recOnSubsingleton s decidableNontrivialCoe
instance {s : Cycle α} : Decidable (Nodup s) :=
Quot.recOnSubsingleton s List.nodupDecidable
instance fintypeNodupCycle [Fintype α] : Fintype { s : Cycle α // s.Nodup } :=
Fintype.ofSurjective (fun l : { l : Lis... |
6,572 | lean_file_chunk | b6277b42c9b639ee9a74c662b7993fb8d704c4bd16628bb4885d0613e4228c3b | 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
-/
module
public import Mathlib.Data.List.Lattice
public import Mathlib.Data.Bool.Basic
public import Mathlib.Order.Lattice
/-!
# Intervals in ℕ
This file defines interva... |
10,361 | lean_file_chunk | 734955e3f9738d706c4daaeecfc79c45cb6662065affae097144c801308418e4 | 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.Data.Nat.Choose.Basic
public import Mathlib.Data.Sym.Sym2
/-! # Unordered tuples of elements of a list
Defines `List.sym` and the specialize... |
23,588 | lean_file_chunk | 066bce978d44800d58e582c3e94e76ab6072ed1a45a02eae2d1acabe794c31e8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Yakov Pechersky
-/
module
public import Mathlib.Data.List.Nodup
public import Mathlib.Data.List.Infix
public import Mathlib.Data.Quot
/-!
# List rotation
This file prove... |
3,828 | lean_file_chunk | ab2c8af61faf9ba77782f70ba148c3ac6d9f6c48c23abd1be4a50c5957f97eed | 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.Nat
public import Mathlib.Algebra.Order.Monoid.NatCast
public import Mathlib.Algebra.Ring.Parity
public import Mat... |
754 | lean_file_chunk | ff67bd993103e33da0e52e5d47634244379b8bad1f165a77a80a55453ed89a8d | 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.Init
/-!
# Boolean quantifiers
This proves a few properties about `List.all` and `List.any`, which are the `Bool` universal and
existe... |
6,779 | lean_file_chunk | 5604a2fe39f881b8f4191c121172d1477f3435dfcb1da7ffa97c5cb6e77bf3f3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad
-/
module
public import Mathlib.Logic.Basic
public import Mathlib.Order.Defs.LinearOrder
/-!
# Booleans
This file proves various trivial lemm... |
671 | lean_file_chunk | cf76a674bfd1232c4358326c5a932dd97218a78cc56db2128397ea03b5f32abe | 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.Insert
/-!
# Booleans and set operations
This file contains three trivial lemmas about `Bool`, `Set.univ`, and `Set.range`.... |
1,006 | lean_file_chunk | 5e96727d7f42a052715701cb1a1337f11c1c1da1096213acc86592b3b06b2a5d | 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
-/
module
public import Mathlib.Algebra.Group.Indicator
public import Mathlib.Data.ENNReal.Basic
public import Mathlib.Data.Finset.Lattice.Fold
/-!
# ... |
6,321 | lean_file_chunk | 0861865c319bd7faf518fd392511e7e79249d9f2a1a2b1f72658a99f4ecbfc1e | 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.Data.ENNReal.Inv
/-! # Hölder triples
This file defines a new class: `ENNReal.HolderTriple` which takes arguments `p q r : ℝ≥0∞`,
with `... |
23,984 | lean_file_chunk | a96a106acf006c5bd11124e33d0186d5947c080ee6f28eb9ccaf5ab464aa6f0d | 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
-/
module
public import Mathlib.Algebra.Order.Ring.WithTop
public import Mathlib.Algebra.Order.Sub.WithTop
public import Mathlib.Data.NNReal.Defs
publi... |
4,002 | lean_file_chunk | 8105df791fc6b30eeb4f4ca0fa4b48bc4d6ff8551949ba666bd64d513e580c6c | lean_source_file | pkg_mathlib_source_file_chunks | theorem iInter_Ioi_coe_nat : ⋂ n : ℕ, Ioi (n : ℝ≥0∞) = {∞} := by
simp only [← compl_Iic, ← compl_iUnion, iUnion_Iic_coe_nat, compl_compl]
@[simp, norm_cast]
theorem coe_min (r p : ℝ≥0) : ((min r p : ℝ≥0) : ℝ≥0∞) = min (r : ℝ≥0∞) p := rfl
@[simp, norm_cast]
theorem coe_max (r p : ℝ≥0) : ((max r p : ℝ≥0) : ℝ≥0∞) = ma... |
23,981 | lean_file_chunk | 659f071c00c26be7c60b79c259af2e61745dbeba3798e7ee3b8708f510c61ed5 | 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
-/
module
public import Mathlib.Data.ENNReal.Real
public import Mathlib.Tactic.Finiteness
/-!
# Properties of addition, multiplication and subtraction... |
5,424 | lean_file_chunk | 08e75860f594682ec093cbbf3ad0dc84825922e7a47772bfc14ca0fe3616cace | lean_source_file | pkg_mathlib_source_file_chunks | simpa using le_iInf₂_add_iInf₂ h
end iInf
section iSup
variable {ι κ : Sort*} {f g : ι → ℝ≥0∞} {s : Set ℝ≥0∞} {a : ℝ≥0∞}
theorem toNNReal_iSup (hf : ∀ i, f i ≠ ∞) : (iSup f).toNNReal = ⨆ i, (f i).toNNReal := by
lift f to ι → ℝ≥0 using hf
simp_rw [toNNReal_coe]
by_cases h : BddAbove (range f)
· rw [← coe_iSu... |
4,341 | lean_file_chunk | 13975c65141ed96c094dcd172caaed46e9cafdeb6dab465f632b1f484d0db95f | 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
-/
module
public import Mathlib.Algebra.Module.Torsion.Field
public import Mathlib.Data.ENNReal.Operations
/-!
# Scalar multiplication on `ℝ≥0∞`.
Thi... |
6,597 | lean_file_chunk | e4a173ba7e4754429dad967082181a8792901ee0b344fe066c2f110c23e78749 | 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
-/
module
public import Mathlib.Algebra.BigOperators.WithTop
public import Mathlib.Data.NNReal.Basic
public import Mathlib.Data.ENNReal.Inv
/-!
# Prop... |
23,949 | lean_file_chunk | 6f8394d69d1819983666c0fcca09737e25a6fae52438852adea632173b4bf35b | 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
-/
module
public import Mathlib.Data.ENNReal.Operations
/-!
# Results about division in extended non-negative reals
This file establishes basic prope... |
16,652 | lean_file_chunk | 8ea25820f4355759e966de1ead6bf5c9a4e52afca71c70bc850e84db82f92ab9 | lean_source_file | pkg_mathlib_source_file_chunks | (fun x y hxy => ?_) (fun x => (x.1⁻¹ - 1)⁻¹) fun x => Subtype.ext ?_
· simpa only [Subtype.mk_lt_mk, ENNReal.inv_lt_inv, ENNReal.add_lt_add_iff_right one_ne_top]
· have : (1 : ℝ≥0∞) ≤ x.1⁻¹ := ENNReal.one_le_inv.2 x.2
simp only [inv_inv, tsub_add_cancel_of_le this]
@[simp]
theorem orderIsoIicOneBirational_symm... |
15,127 | lean_file_chunk | ec6e5372abb4f0467618aef50a4ac4f70ab5f057178ed5891ca2feec538eb94e | 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
-/
module
public import Mathlib.Data.ENNReal.Basic
/-!
# Maps between real and extended non-negative real numbers
This file focuses on the functions ... |
940 | lean_file_chunk | 26dcf30ab58c1ce212820ed74332c76a0577e9a4256b19e5368c28f6baab6408 | 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.Data.SetLike.Basic
public import Mathlib.Data.Fintype.Powerset
/-!
# Set-like fintype
This file contains a fintype instance for set-like o... |
10,564 | lean_file_chunk | 97607bbfeda2a589c85dc8b9a618493a9131d9215c143c501c55c21ba15ba427 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
module
public import Mathlib.Tactic.Monotonicity.Attr
public import Mathlib.Tactic.SetLike
public import Mathlib.Data.Set.Basic
/-!
# Typeclass for types with a set-like ... |
1,230 | lean_file_chunk | 3b03aab4b2010e8b9b469055be9681e3320ca61cfe516347eb679242bba244df | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Chris Bailey. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Bailey
-/
module
public import Mathlib.Data.Nat.Notation
public import Mathlib.Data.String.Defs
/-!
# Miscellaneous lemmas about strings
-/
public section
namespace String
lem... |
7,454 | lean_file_chunk | bdf27eb598b5e6a0232abf84e1c51b1827af4702a2f6980143c04f12f20068d7 | 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 Batteries.Data.String.Lemmas
public import Mathlib.Data.List.Lex
public import Mathlib.Data.Char
public import Mathlib.Algebra.Order.Group.Nat
i... |
2,436 | lean_file_chunk | d34c34bc3199c422182370adf7c903f2bd7a9d38ce951d0a628e3bbfe4b958de | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Keeley Hoek, Floris van Doorn, Chris Bailey
-/
module
public import Mathlib.Init
/-!
# Definitions for `String`
This file defines a bunch of functions for the `String` data... |
4,046 | lean_file_chunk | acb270cbed869153be9a63865310833f24a5b3fc0a8b1e08ebce9a1bb91d24b3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 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.BigOperators.Group.Finset
public import Mathlib.Algebra.Order.Ring.Defs
/-!
# Equitable functions... |
2,883 | lean_file_chunk | 5d70ca00f658cb181f1193c9e091033ea473f3adbd6df9d370dddee01e26b827 | 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.Algebra.Group.Nat.Defs
public import Mathlib.Tactic.Common
public import Mathlib.Data.Set.Insert
/-!
# Set enumeration
This file allows... |
23,941 | lean_file_chunk | 39783e8f4e9fb56f1659f03850823c7156c25ed427e449fd12d7098a0e362eb2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Peter Nelson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Peter Nelson
-/
module
public import Mathlib.SetTheory.Cardinal.Finite
public import Mathlib.Data.Set.Finite.Powerset
/-!
# Noncomputable Set Cardinality
We define the cardinality of ... |
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