chars int64 40 24k | content_type stringclasses 9
values | id stringlengths 13 64 | source stringclasses 5
values | subset stringclasses 31
values | text stringlengths 40 24k |
|---|---|---|---|---|---|
23,965 | lean_file_chunk | 3afadc430085e9bc3902fe5ee1193ce7070e65cce840128fe000e63259da8ef6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
module
public import Mathlib.Algebra.Group.Action.Pi
public import Mathlib.Data.Finset.Prod
public import Mathlib.Data.SetLike.Basic
public import Mathlib.Data.Sym.Basic
p... |
11,424 | lean_file_chunk | aace023efb828ada25438ac2f2d669328c2f4b137fbc2ff0b992453d80acd678 | lean_source_file | pkg_mathlib_source_file_chunks | Set.ext fun z => Sym2.ind (fun _ _ => Iff.rfl) z
theorem toRel_mono_iff (s₁ s₂ : Set (Sym2 α)) : ToRel s₁ ≤ ToRel s₂ ↔ s₁ ⊆ s₂ :=
⟨(Sym2.ind ·), (@· s(·, ·))⟩
@[gcongr]
alias ⟨_, toRel_mono⟩ := toRel_mono_iff
variable (α) in
/-- `ToRel` induces an order embedding from `Sym2` sets to relations -/
def toRelOrderEmbe... |
159 | lean_file_chunk | deb5a81161ad2013739390cbabd9deb84beb13b4f6c6c46a0fd3ac7dd4cb1b27 | lean_source_file | pkg_mathlib_source_file_chunks | module -- shake: keep-all
public import Mathlib.Util.CompileInductive
import Mathlib.Tactic.Linter.DeprecatedModule
deprecated_module (since := "2026-01-16") |
2,189 | lean_file_chunk | e9ebfa263670f7e4041823a52c8fe06fa093079a2f4cc773708baef928052267 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Edward van de Meent. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Edward van de Meent
-/
module
public import Mathlib.Data.Tree.Basic
public import Mathlib.Control.Applicative
public import Mathlib.Control.Traversable.Basic
/-!
# Traversable B... |
4,234 | lean_file_chunk | 6c670e6e34b0e1f9bf0f714105a06653d3e48186706275ede41897f704449aef | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 mathlib community. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Wojciech Nawrocki
-/
module
public import Mathlib.Data.Nat.Notation
public import Mathlib.Util.CompileInductive
/-!
# Binary tree
Provides binary tree storage for... |
1,834 | lean_file_chunk | cbebfc3bbcaecac27afb65a80908894e87a1c0a177ee3ef728925f877162c6be | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 mathlib community. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Wojciech Nawrocki
-/
module
public import Mathlib.Data.Num.Basic
public import Mathlib.Data.Ordering.Basic
public import Mathlib.Data.Tree.Basic
/-!
# Binary tree ... |
1,001 | lean_file_chunk | d664253b72b0bf3bd6ecc572e03873d44113ea021722d387cf05e29dac7c7055 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
module
public import Batteries.Data.DList.Lemmas
public import Mathlib.Control.Traversable.Equiv
public import Mathlib.Control.Traversable.Instances
/-!
# Traversable ins... |
6,516 | lean_file_chunk | 0982583c0c0794e48c140d0b00169aa58d00a54871a94b53c7e61c234e7884ec | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau
-/
module
public import Mathlib.Algebra.GroupWithZero.Action.Pi
public import Mathlib.Algebra.Module.LinearMap.Defs
public import Mathlib.Algebra.Module.Pi
public... |
2,003 | lean_file_chunk | 305daefa267c4bf931b82220d0a95f10c27dac6d2d7735a75c4024e9a6ef0cff | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau
-/
module
public import Mathlib.Data.DFinsupp.Defs
public import Mathlib.Data.Fintype.Pi
/-!
# Finiteness and infiniteness of the `DFinsupp` type
## Main result... |
6,896 | lean_file_chunk | 8476631a55ef04fcc250390d564f8f474d80a94ea9a28f6940c2f6b1db4b65f9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Data.Fintype.BigOperators
public import Mathlib.Data.DFinsupp.BigOperators
public import Mathlib.Data.DFinsupp.Order
public import Mathlib.O... |
11,482 | lean_file_chunk | fe9ddfa80a3064d3b060989182f70ad637b8a28f2de681e7d19dc671bf1faf36 | 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: Damiano Testa, Junyan Xu
-/
module
public import Mathlib.Algebra.Order.Group.PiLex
public import Mathlib.Data.DFinsupp.Order
public import Mathlib.Data.DFinsupp.NeLocus
public import Mathl... |
5,491 | lean_file_chunk | 9ad10c98d91305774c55b000e9fbcfcf05a6192b233f39ecb38cd62aed5abbab | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau
-/
module
public import Mathlib.Data.DFinsupp.Module
public import Mathlib.Data.Fintype.Quotient
/-!
# `DFinsupp` on `Sigma` types
## Main definitions
* `DFins... |
9,849 | lean_file_chunk | 77d97c49a8563ee43ed9fc90672f07a02920dfae80fcff0f39dcc17c5bde2494 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Algebra.Order.Module.Defs
public import Mathlib.Algebra.Order.Sub.Basic
public import Mathlib.Data.DFinsupp.Module
/-!
# Pointwise order on... |
4,304 | lean_file_chunk | 381e6623dcd2a5138217cf8dc9004eee4af8bd9616e75bab66b28f6eadb24142 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
module
public import Mathlib.Data.DFinsupp.BigOperators
public import Mathlib.Data.DFinsupp.Order
/-!
# Equivalence between `Multiset` and `ℕ`-valued finitely supported f... |
12,131 | lean_file_chunk | 3377fce41c2a58c4b9249e8c3c632be41325d0327066ca5915b8acaeb8cbf2d0 | 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.DFinsupp.Lex
public import Mathlib.Order.Antisymmetrization
public import Mathlib.Order.GameAdd
public import Mathlib.SetTheory.Cardinal.Orde... |
1,959 | lean_file_chunk | 430b7c18cd865f5aae21da49e8d45fa8aa87108d19a131842741f2c1bd7015af | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau
-/
module
public import Mathlib.Algebra.Group.Submonoid.Basic
public import Mathlib.Data.DFinsupp.Defs
/-!
# Extensionality principles for `DFinsupp`
## Main re... |
2,837 | lean_file_chunk | 745f350f01452b01225f8964cdae490b3a0447676f1c6f98456e832f7ba82362 | 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.Data.DFinsupp.Defs
public import Mathlib.Data.Finsupp.Notation
/-!
# Notation for `DFinsupp`
This file extends the existing `fun₀ | 3 => a |... |
23,984 | lean_file_chunk | 2631ae152ad10f65270ba00f007054a865f93d4eb20fad292bb3a0b6e5588ad9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau
-/
module
public import Mathlib.Data.Set.Finite.Basic
public import Mathlib.Algebra.Group.InjSurj
public import Mathlib.Algebra.Group.Equiv.Defs
public import Mat... |
21,995 | lean_file_chunk | c9239ce2d1219f8a87cc08c0dfc7da070495be3f96431b23e8c93ed5ea1202b2 | lean_source_file | pkg_mathlib_source_file_chunks | map_zero' := single_zero i
map_add' := single_add i
/-- `DFinsupp.erase` as an `AddMonoidHom`. -/
@[simps]
def eraseAddHom (i : ι) : (Π₀ i, β i) →+ Π₀ i, β i where
toFun := erase i
map_zero' := erase_zero i
map_add' := erase_add i
variable {β}
@[simp]
theorem single_neg {β : ι → Type v} [∀ i, AddGroup (β i)]... |
4,393 | lean_file_chunk | fa6c2e83b5fd6776227749e781b62a437ef6786bdd3cffbd9b2ae870442a9422 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau
-/
module
public import Mathlib.Algebra.Group.Submonoid.BigOperators
public import Mathlib.Algebra.Group.Submonoid.Membership
public import Mathlib.Data.DFinsupp.... |
1,028 | lean_file_chunk | 7cbec208510dfaecd106fbc423ed3c55958f1a647902a4c18e58d24c4f9b8c8b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Sophie. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sophie Morel, Antoine Chambert-Loir
-/
module
public import Mathlib.Data.Finsupp.ToDFinsupp
public import Mathlib.Data.DFinsupp.Defs
public import Mathlib.Logic.Small.Basic
/-!
# Smallness o... |
22,571 | lean_file_chunk | 4018cc0ff18e46b0bab9c5134d071ab1aee28c553fc34c7d6b1bff9c394f48f0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau
-/
module
public import Mathlib.Algebra.BigOperators.GroupWithZero.Action
public import Mathlib.Data.DFinsupp.Ext
public import Mathlib.Algebra.BigOperators.Group... |
5,633 | lean_file_chunk | b72d20c602e45050f828a8dfd40e4065521a3eadabd3ff329e18529371ec3ecf | 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: Damiano Testa, Junyan Xu
-/
module
public import Mathlib.Data.DFinsupp.Defs
/-!
# Locus of unequal values of finitely supported dependent functions
Let `N : α → Type*` be a type family, ... |
1,028 | lean_file_chunk | 675286515db56f1e65ff68da9d474a3e43b8932509c25e53b1d36001cadd92f4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Data.DFinsupp.Defs
public import Mathlib.Logic.Encodable.Pi
/-!
# `Encodable` and `Countable` instances for `Π₀ i, α i`
In this file ... |
23,985 | lean_file_chunk | 7833f9883ff7e00db5c60edcc8d28fdb14e37e5f7df098748416e027f6205b97 | 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
-/
module
public import Mathlib.Data.Fin.Basic
public import Mathlib.Logic.Equiv.Set
/-!
# Successors and predecessor operations of `Fin n`
This file contains a numbe... |
14,152 | lean_file_chunk | e36f80c8ce6085f14f8a635ca219bcce366f8d520c6c96cbe70bb3e99c0c8edf | lean_source_file | pkg_mathlib_source_file_chunks | /-- Embedding a positive `Fin n` results in a positive `Fin (n + 1)` -/
lemma succAbove_pos [NeZero n] (p : Fin (n + 1)) (i : Fin n) (h : 0 < i) : 0 < p.succAbove i := by
by_cases H : castSucc i < p
· simpa [succAbove_of_castSucc_lt _ _ H] using castSucc_pos' h
· simp [succAbove_of_le_castSucc _ _ (Fin.not_lt.1 H... |
17,296 | lean_file_chunk | c275a8a688ff5e79e7ce85f6aa47bfdf4e3e8fe561c23c5c3d4cd319492b228d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Eric Wieser
-/
module
public import Mathlib.Data.Fin.Tuple.Basic
/-!
# Matrix and vector notation
This file defines notation for vectors and matrices. Given `a b c d : α`,... |
2,359 | lean_file_chunk | 7e7439e005c4fcd93fd90af957891504d3ae4c5b85ef174f4fff51df01924ed5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Order.Fin.Basic
public import Mathlib.Order.Preorder.Chain
/-!
# Range of `f : Fin (n + 1) → α` as a `Flag`
Let `f : Fin (n + 1) → α... |
2,150 | lean_file_chunk | f0099f4828adc5dcb9b231a9048aff0201c6769e9ccc40f869deba6d32ef368c | 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
-/
module
public import Mathlib.Order.Fin.Basic
public import Mathlib.Order.SuccPred.Basic
/-!
# `SuccOrder` and `PredOrder` of `Fin n`
In this file, we show that `Fi... |
17,883 | lean_file_chunk | aaefaa3bf3ae466f04037bf5df4cb482e3df26255fb85a560d8d3a3207c3aaac | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Keeley Hoek
-/
module
public import Mathlib.Data.Int.DivMod
public import Mathlib.Order.Lattice
public import Mathlib.Tactic.Common
public import Batteries.Data.Fin.... |
2,004 | lean_file_chunk | d2637f2ad1bc67c9433dec5d7db0b7de0b8ba570e8863ec5cac09b4e5be91c1d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Martin Dvorak. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Martin Dvorak
-/
module
public import Mathlib.Data.Fintype.Card
/-!
# Pigeonhole-like results for Fin
This adapts Pigeonhole-like results from `Mathlib.Data.Fintype.Card` to the sett... |
5,116 | lean_file_chunk | 77b1461c9e9892096ae12068b0aedf7eaae9b52a6d0cd15b9552a9670eb02ce5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Keeley Hoek
-/
module
public import Mathlib.Data.Fin.SuccPred
public import Mathlib.Logic.Embedding.Basic
/-!
# Embeddings of `Fin n`
`Fin n` is the type whose ele... |
4,084 | lean_file_chunk | 3585976063221a977d9aee63b3983fb2791632a2b3d595d8aba8bcee7d685398 | 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, Joel Riou, Yury Kudryashov
-/
module
public import Mathlib.Data.Fin.SuccPred
/-!
# Reverse on `Fin n`
This file contains lemmas about `Fin.rev : Fin n → Fin n` which ... |
4,515 | lean_file_chunk | 901b82dca6d5e9e7dd409e101f2245650890df7d2863be982b23842b5c54d740 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Iván Renison
-/
module
public import Mathlib.Algebra.Ring.Parity
public import Mathlib.Data.Fin.Basic
public import Mathlib.Data.ZMod.Defs
/-!
# Parity in `Fin n`
... |
6,437 | lean_file_chunk | 0d5e8dbb378bb73bea6b44a8ebf5f778a3adf5c394daab41395f6bef48dd26da | 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.Finset.Image
public import Mathlib.Data.Fintype.Defs
public import Mathlib.Data.Nat.Notation
public import Mathlib.Logic.Function.B... |
1,133 | lean_file_chunk | 31c10173fd5f1c54ccdd5b75dfecbdc300da56b2362cc3af7b5d7bf010ffcb60 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Alex J. Best
-/
module
public import Mathlib.Data.Finsupp.Single
public import Mathlib.Data.Fintype.BigOperators
/-!
# Finiteness and infiniteness of `Finsupp`
Some lemma... |
7,336 | lean_file_chunk | b75298ad3acfdcaffb270ff98770c89dd7a7bfd9db0645aff08261cf53d41d11 | 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, Kim Morrison
-/
module
public import Mathlib.Algebra.Group.Action.Basic
public import Mathlib.Algebra.Module.Basic
public import Mathlib.Algebra.Module.Torsion.Free
pu... |
3,819 | lean_file_chunk | 4eedb3c82b7e9698efeb32d5aa0ddc4ae7588764a7d4856ad80852c30d50204e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Ivan Sadofschi Costa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ivan Sadofschi Costa
-/
module
public import Mathlib.Data.Finsupp.Single
/-!
# `cons` and `tail` for maps `Fin n →₀ M`
We interpret maps `Fin n →₀ M` as `n`-tuples of elements... |
6,625 | lean_file_chunk | 731712e7710a045c15dd9b9e044d26d58b1a6ae0b4d8897094b7d476cd9ed3b2 | 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.Finsupp.Basic
public import Mathlib.Algebra.Module.Defs
/-!
# Operations on `Finsupp`s with an `Option` domain
Similar to how `Finsup... |
2,796 | lean_file_chunk | 7bcb781cd349fdf6b2274b8ec99283c7bbcea6fc2b42894de084fd06304cd57e | 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.Finsupp.Single
/-!
# Building finitely supported functions off finsets
This file defines `Finsupp.indicator` to help create finsupps ... |
3,625 | lean_file_chunk | a48d237509df6030abbf10b285752396a913eb7f9574e63513a0649f7c6b9521 | 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, Kim Morrison
-/
module
public import Mathlib.Algebra.Group.Action.Pi
public import Mathlib.Algebra.Group.Finsupp
public import Mathlib.Algebra.GroupWithZero.Action.Def... |
4,223 | lean_file_chunk | 64018c025bd137a7229ba34c3582e4ff442fe04b68d05cf7702b573cd78b4322 | 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.Finsupp
public import Mathlib.Data.Finsupp.Order
public import Mathlib.Order.Interval.Finset.Basic
/-!
# Finite intervals of fi... |
8,826 | lean_file_chunk | 24dbf69ee607162eb3dd8498446adc1caa46250e7b50cc38af094be43973d751 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
module
public import Mathlib.Data.Finsupp.Order
public import Mathlib.Data.DFinsupp.Lex
public import Mathlib.Data.Finsupp.ToDFinsupp
/-!
# Lexicographic order on fin... |
4,516 | lean_file_chunk | d10c44b1cc8f55ad0d30c024c45c9ccef2f0e05b1e94f30a28eef273a9e6d877 | 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.Finset.NatAntidiagonal
public import Mathlib.Data.Finsupp.Multiset
public import Mathlib.Data.Multiset.Antidiagona... |
3,622 | lean_file_chunk | 8d756d8c7312a00bec0e5fc34027af55b9163ba7329bc8f653502e71e24552f6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 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.Finsupp.Basic
public import Mathlib.Logic.Embedding.Basic
/-!
# Embedding a finitely supported function into a sigma type summand
Thi... |
4,176 | lean_file_chunk | ca8ee3c2aa1a71a975459a28dee3ff908c71751c29f24f44b8e997dcc3aab1ee | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.Algebra.Ring.InjSurj
public import Mathlib.Algebra.Module.Pi
public import Mathlib.Data.Finsupp.SMulWithZero
/-!
# The pointwise product on... |
12,297 | lean_file_chunk | 65ca40335d3cd27c35986ba24dd80297df9a52c956ea3faaf1c782ce5dc8eaa7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Aaron Anderson
-/
module
public import Mathlib.Algebra.Order.BigOperators.Group.Finset
public import Mathlib.Algebra.Order.Module.Defs
public import Mathlib.Algebra.Or... |
3,634 | lean_file_chunk | a80f638d4ddcdec25b8648b44c93b2752a43a16ca359134559a80676814dc34d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Scott Carnahan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Carnahan
-/
module
public import Mathlib.Algebra.BigOperators.Group.Finset.Basic
public import Mathlib.Algebra.GroupWithZero.Action.Defs
public import Mathlib.Data.Finsupp.Defs
... |
14,671 | lean_file_chunk | e2e3236a94463afa39a04511b37c312a1bb166fb9a8e4b492cf96931b7789964 | 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, Kim Morrison
-/
module
public import Mathlib.Algebra.Notation.Indicator
public import Mathlib.Data.Finsupp.Defs
/-!
# Finitely supported functions on exactly one poin... |
23,967 | lean_file_chunk | bac6b91221caa06c6eda2deece1e303879be25c6d23f44b7e88c2be2abe77c08 | 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, Kim Morrison
-/
module
public import Mathlib.Algebra.BigOperators.Finsupp.Basic
public import Mathlib.Algebra.BigOperators.Group.Finset.Preimage
public import Mathlib.... |
23,997 | lean_file_chunk | 748cdfbdd6ca00804e16636ea9c3251420e2495c43794b67f6eb2e44eba0ece7 | lean_source_file | pkg_mathlib_source_file_chunks | refine Finset.prod_congr rfl fun x hx => ?_
rw [support_filter, Finset.mem_filter] at hx
rw [filter_apply_pos _ _ hx.2]
@[to_additive (attr := simp)]
theorem prod_filter_mul_prod_filter_not [CommMonoid N] (g : α → M → N) :
(f.filter p).prod g * (f.filter fun a => ¬p a).prod g = f.prod g := by
simp_rw [prod_f... |
2,558 | lean_file_chunk | ad2db0843568965d6f2bbe4b8405800195853cf1d7e0c64d24ff11650dbea6a1 | lean_source_file | pkg_mathlib_source_file_chunks | toFun := split
invFun f :=
onFinset (Finset.univ.sigma fun j => (f j).support) (fun ji => f ji.1 ji.2) fun _ hg =>
Finset.mem_sigma.mpr ⟨Finset.mem_univ _, mem_support_iff.mpr hg⟩
left_inv f := by
ext
simp [split]
right_inv f := by
ext
simp [split]
@[simp]
theorem sigmaFinsuppEquivPiFin... |
10,581 | lean_file_chunk | 20030fa533ee83b1194650a249ed5dc0090f9acd553b108efd452281f02bcfd7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
module
public import Mathlib.Algebra.Order.Group.Finset
public import Mathlib.Data.Finsupp.Basic
public import Mathlib.Data.Sym.Basic
public import Mathlib.Order.Pre... |
1,443 | lean_file_chunk | e0efc030f745237589feb5f128e81381ce88fbfe08d91f8bdffb97ff1cc5eec7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Alex J. Best. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex J. Best
-/
module
public import Mathlib.Order.Preorder.Finsupp
public import Mathlib.Order.WellFoundedSet
/-!
# Partial well ordering on finsupps
This file contains the fact that... |
3,757 | lean_file_chunk | 3cfc896a4be03096e43b84ac83b5ae51fa74ed97d5bba380ca287ebed0581a14 | 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.DFinsupp.WellFounded
public import Mathlib.Data.Finsupp.Lex
/-!
# Well-foundedness of the lexicographic and product orders on `Finsupp`
`Fi... |
2,665 | lean_file_chunk | 2d16c140a8223c367a6f64c5d1b005fe78e7a57e411042cef6b074ebf0382ee7 | 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, Kim Morrison
-/
module
public import Mathlib.Algebra.Group.Finsupp
public import Mathlib.Algebra.Group.Submonoid.Basic
public import Mathlib.Algebra.Group.TypeTags.Hom... |
3,830 | lean_file_chunk | 95400240f86f169c713e719c6af0cdea1e9884b1a39830a5496ebff8bf4a1b87 | 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.Data.Finsupp.Single
/-!
# Notation for `Finsupp`
This file provides `fun₀ | 3 => a | 7 => b` notation for `Finsupp`, which desugars to
`Fins... |
17,306 | lean_file_chunk | 86dd4f89fa2d157aa6eee64b4f27ad18ef00048ff39fece53f669f74397c3b0b | 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, Kim Morrison
-/
module
public import Mathlib.Algebra.FiniteSupport.Defs
/-!
# Type of functions with finite support
For any type `α` and any type `M` with zero, we d... |
12,897 | lean_file_chunk | 57302e966f604a130e0446e2264822331bcee4e916b42747d59d26a86a8f8d71 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Antoine Chambert-Loir, María Inés de Frutos-Fernández. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir, María Inés de Frutos-Fernández
-/
module
public import Mathlib.Data.Finsupp.Antidiagonal
public import Mathlib.Data.Finsu... |
3,901 | lean_file_chunk | 1efd0fdb06c78354787e60f20a1293977c6f616ed2a99b922682341d05c6d13b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Violeta Hernández Palacios. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Violeta Hernández Palacios
-/
module
public import Mathlib.Data.Finsupp.Basic
public import Mathlib.Data.List.AList
/-!
# Connections between `Finsupp` and `AList`
## Ma... |
5,013 | lean_file_chunk | 9eff6e6ea44f978216fe173a101a72edd8122fbf5e2d6a256a3be09a5b5b4e6a | 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.BigOperators.Group.Finset.Basic
public import Mathlib.Algebra.Group.Finsupp
public import Mathlib.Data.Finset.Pairwise
/-!
#... |
11,234 | lean_file_chunk | 717178ab37ce63766d81718846531ade726cd139d86a3daa2496a68348ad6166 | 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.Algebra.Module.Equiv.Defs
public import Mathlib.Data.DFinsupp.Module
public import Mathlib.Data.Finsupp.SMul
/-!
# Conversion between `Finsup... |
5,192 | lean_file_chunk | 5b7f39f4428715c17d758730ad94af3dbfdc68d5ee966105d196e2da2edaa5dc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 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.Group.Finsupp
/-!
# Locus of unequal values of finitely supported functions
Let `α N` be two Types, assume that `N` has a `0` an... |
6,110 | lean_file_chunk | 5f095ed4016ffc7fdc63c8d0ccfecc27d384473df5439e0422e239c987f3c15b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
module
public import Mathlib.Data.Finsupp.Lex
public import Mathlib.Data.Finsupp.WellFounded
public import Mathlib.Data.List.TFAE
/-! # Monomial order... |
784 | lean_file_chunk | ffb7a0f2a3abbb922c7a80dee7da2f9b0471ba3ec6aec2b6f9cae5c5f65e2484 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Data.Finsupp.ToDFinsupp
public import Mathlib.Data.DFinsupp.Encodable
/-!
# `Encodable` and `Countable` instances for `α →₀ β`
In thi... |
9,522 | lean_file_chunk | effd4c55a1bf35b11159ae1e851f42a3344d924963e0e9872c9df273702e6da0 | 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.Analysis.Filter
public import Mathlib.Topology.Bases
public import Mathlib.Topology.LocallyFinite
/-!
# Computational realization ... |
11,528 | lean_file_chunk | c7ef8e4835a39e704627861770d68fa6e51a0a1ff56ce6224601952ba95e39c7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
module
public import Mathlib.Order.Filter.Cofinite
/-!
# Computational realization of filters (experimental)
This file provides infrastructure to compute with filt... |
23,972 | lean_file_chunk | b128e670a42fc06806b2683d331ec9e2afd32dca7bdc12ab221a54053fba53dd | 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: Mario Carneiro
-/
module
public import Mathlib.Data.Seq.Basic
public import Mathlib.Util.CompileInductive
/-!
# Partially defined possibly infinite lists
This file provides a... |
3,593 | lean_file_chunk | a79b135c256224cc502a9bc4b88a718396fe3647e274b8121de8f74aa7ed9f87 | lean_source_file | pkg_mathlib_source_file_chunks | intro ej m <;> simp at ej <;> have := congr_arg Seq.destruct ej <;> simp at this <;>
subst ss
case cons s S =>
apply Or.inr
simp only [join_cons, nil_append, mem_think, mem_cons_iff, exists_eq_or_imp] at m ⊢
exact IH s S rfl m
case think S =>
apply Or.inr
replace m : a ∈ S.jo... |
22,707 | lean_file_chunk | 5b3e59c2dae6db5701b0453a2c940c02e9dd66b8c0577b777c9009f95e620ece | 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: Mario Carneiro
-/
module
public import Mathlib.Data.WSeq.Basic
public import Mathlib.Logic.Relation
/-!
# Relations between and equivalence of weak sequences
This file define... |
9,018 | lean_file_chunk | 49eaee4558123a5900e360f2f4ec5cc5b4ef09652f016aad2a3a1ffad97952e2 | 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: Mario Carneiro
-/
module
public import Batteries.Data.DList.Basic
public import Mathlib.Data.WSeq.Basic
/-!
# Miscellaneous definitions concerning weak sequences
These defini... |
2,422 | lean_file_chunk | 880e7d7b34d9c55ba9ac33464c98d6c081c6896924c024f3e260ab293b90d4ca | 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: Mario Carneiro
-/
module
public import Mathlib.Data.WSeq.Relation
/-!
# Productive weak sequences
This file defines the property of a weak sequence being productive as never ... |
817 | lean_file_chunk | 121a8119c961a2cb9a05a856025439b06ed0eee317908020a2ee8ab519dd8357 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jiecheng Zhao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jiecheng Zhao
-/
module
public import Mathlib.Init
public import Batteries.Data.Array.Lemmas
/-!
# Lemmas about `Array.extract`
Some useful lemmas about Array.extract
-/
public secti... |
1,468 | lean_file_chunk | 749a1adbc18d5ff356f0e62017a83a7bb9c65b0065c002d604025ceac936b6bb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Arthur Paulino, Floris van Doorn
-/
module
public import Mathlib.Init
public import Mathlib.Tactic.Linter.DeprecatedModule
/-!
# Definitions on Arrays
This file contains various d... |
3,626 | lean_file_chunk | 420dc950d6015bd8ad1f5a1fcde342175cdd6e609e80e73e87dd6fa8e436996e | 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.RingTheory.Ideal.Quotient.Operations
public import Mathlib.RingTheory.Int.Basic
public import Mathlib.RingTheory.ZMod
public import Mathlib.Da... |
1,007 | lean_file_chunk | a450a383c10b061cf1f40bf486c4e4b830471c6d91ea33b4db27c1aba5cfe40a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
module
public import Mathlib.Algebra.Ring.AddAut
public import Mathlib.Data.ZMod.Basic
/-!
# Automorphism Group of `ZMod`.
-/
@[expose] public section
assert_no... |
4,488 | lean_file_chunk | aa7beb79830f1dd89c7cf45be8dee76b490718abaa67f5f4eef1e9a023cdd108 | 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.Algebra.GroupWithZero.Divisibility
public import Mathlib.Data.Int.Order.Units
public import Mathlib.Data.ZMod.Basic
/-!
# The power operator ... |
7,425 | lean_file_chunk | 030ea4016917df7462b710e28d08244e4bf37fae32068630c950731618b478a9 | 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
-/
module
public import Mathlib.Data.ZMod.Basic
public import Mathlib.Tactic.Linarith
/-!
# Absolute value in `ZMod n`
-/
@[expose] public section
namespace ZMod
variabl... |
23,980 | lean_file_chunk | 809fd45148931ffaed9f6d5cec91f5e63b43d8edc671e85648d4dce0d08a54bf | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
module
public import Mathlib.Algebra.CharP.Basic
public import Mathlib.Algebra.Ring.Prod
public import Mathlib.Data.Fintype.Units
public import Mathlib.GroupTheory.Group... |
22,958 | lean_file_chunk | 19b1e4dedd18cd54abf12d8b6597bafc34846085164c6cf5e5c733537db93eb1 | lean_source_file | pkg_mathlib_source_file_chunks | | 0 => Int.sign_zero
| n + 1 =>
show (Nat.gcdA _ (n + 1) : ZMod (n + 1)) = 0 by
rw [val_zero]
unfold Nat.gcdA Nat.xgcd Nat.xgcdAux
rfl
theorem mul_inv_eq_gcd {n : ℕ} (a : ZMod n) : a * a⁻¹ = Nat.gcd a.val n := by
rcases n with - | n
· dsimp [ZMod] at a ⊢
calc
_ = a * Int.sign a :=... |
10,214 | lean_file_chunk | a2c286d0a3bb37e1c8245176e7fe33a3bb6c425beab3879d17737d874c72711d | 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
-/
module
public import Mathlib.Algebra.Group.Fin.Basic
public import Mathlib.Algebra.NeZero
public import Mathlib.Algebra.Ring.Int.Defs
public import Mathlib.Algebra.R... |
1,866 | lean_file_chunk | a5570682376916726bb548451aaa37a7638b811853fa5575e528b617b01f73e7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
module
public import Mathlib.Algebra.EuclideanDomain.Int
public import Mathlib.Data.Nat.Prime.Int
public import Mathlib.Data.ZMod.Basic
public import Mathlib.RingTheor... |
1,346 | lean_file_chunk | 14dcac6c97261f6355f4937e829c9cf3d5dff1f57961abc35b83fe9176805e7f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Moritz Firsching. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Firsching
-/
module
public import Mathlib.Data.Nat.Factorial.BigOperators
public import Mathlib.Data.ZMod.Basic
/-!
# Facts about factorials in ZMod
We collect facts about ... |
6,541 | lean_file_chunk | 6665b60afe1d5ad57019645b78d66093940a4b7c2646d16993f90542d584955d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Moritz Firsching. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Firsching, Ashvni Narayanan, Michael Stoll
-/
module
public import Mathlib.Algebra.BigOperators.Associated
public import Mathlib.Data.ZMod.Basic
public import Mathlib.RingThe... |
8,462 | lean_file_chunk | a023bcf62fac7574fc4cc9dc03de6808d3893ca86b8d71f17fd94fbfcd358544 | 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.Data.ZMod.Basic
/-!
# `ZMod n` and quotient groups / rings
This file relates `ZMod n` to the quotient group `ℤ / AddSubgroup.zmultiples (n :... |
730 | lean_file_chunk | 341c642bb19a52bd4b098bebaf6248198caa1e1ca2f13b7839e1d43cbbf64726 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 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.NNReal.Defs
public import Mathlib.Data.Real.Star
/-!
# The non-negative real numbers are a `*`-ring, with the trivial `*`-structure
... |
9,242 | lean_file_chunk | 7485b51894d29e84f55532b3224ae2c8fc9bf977e59ce26ebfac8e50d56fbf14 | 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
-/
module
public import Mathlib.Algebra.BigOperators.Expect
public import Mathlib.Algebra.Order.BigOperators.Group.Finset
public import Mathlib.Algebra.Order.BigOperato... |
23,933 | lean_file_chunk | e476dec99e9caaa9cc6a6c030366015f80f51ae51540dc351ee85ba64c77626b | 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
-/
module
public import Mathlib.Algebra.Algebra.Defs
public import Mathlib.Algebra.Order.Nonneg.Module
public import Mathlib.Data.Real.Archimedean
public import Mathlib... |
12,820 | lean_file_chunk | 990e2b289d9555da087dd14f099f06d9d187285cb6fcd4e1cc6c04c76dd6e6cf | lean_source_file | pkg_mathlib_source_file_chunks | simp only [(hp.trans_le r.coe_nonneg).not_ge, toNNReal_eq_zero.2 hp.le, hr.not_ge]
theorem toNNReal_lt_iff_lt_coe {r : ℝ} {p : ℝ≥0} (ha : 0 ≤ r) : Real.toNNReal r < p ↔ r < ↑p := by
rw [← NNReal.coe_lt_coe, Real.coe_toNNReal r ha]
theorem lt_toNNReal_iff_coe_lt {r : ℝ≥0} {p : ℝ} : r < Real.toNNReal p ↔ ↑r < p :=
... |
9,598 | lean_file_chunk | 4ddb6623530652d30bb826e9d8a5ef3135a38548307967ce77ad0d5766e11a89 | 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, Bhavik Mehta
-/
module
public import Mathlib.Data.Finset.Card
public import Mathlib.Data.Finset.Fold
public import Mathlib.Data.Multiset.Sum
/-!
# Disjoint sum of finsets... |
1,777 | lean_file_chunk | 94592adadc98fdf7ced4e862ba2b422ed9786412ccf7fe3c2a9252b17e75fa98 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
module
public import Mathlib.Data.Finset.Max
public import Mathlib.Data.Set.Finite.Basic
/-!
# Dense orders and finsets
We prove that in a dense order, there's always an ele... |
2,564 | lean_file_chunk | eb910411373e4d1a2942176040e3376391f3382b43bbc21418cc89cb55580e30 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Kim Morrison, Johan Commelin
-/
module
public import Mathlib.Data.Finset.Card
public import Mathlib.Data.Fin.Embedding
/-!
# Finsets in `Fin n`
A few constructions for F... |
23,974 | lean_file_chunk | f579515b3affc69ea000dec5732249d6fe42d7137807fa42bd432562e5f7924c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2015 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.Data.Finset.Basic
public import Mathlib.Data.Finset.Image
public import Mathlib.Data.Finset.Lattice.Lemmas
/-!... |
11,723 | lean_file_chunk | a28b71ce05714f6fe2e99b0dbfc9343aa4530ed766525decf8606edceafb4e1a | lean_source_file | pkg_mathlib_source_file_chunks | @[deprecated (since := "2025-12-12")]
alias filter_card_add_filter_neg_card_eq_card := card_filter_add_card_filter_not
/-- Given a subset `s` of a set `t`, of sizes at most and at least `n` respectively, there exists a
set `u` of size `n` which is both a superset of `s` and a subset of `t`. -/
lemma exists_subsuperset... |
17,456 | lean_file_chunk | be77c809ebc39ca5e72dc6e7cee97614b22167cfd6fd850183744ff4c4a31318 | 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.Algebra.BigOperators.Group.Finset.Basic
public import Mathlib.Algebra.Group.Commute.Hom
public import Mathlib.Algebra.Group.Pi.Lemmas
... |
5,416 | lean_file_chunk | d1b88c73a04e78b1159b850e8536816edb4aa477ce0cb2d4e962ed6975cca977 | 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, Mario Carneiro, Sean Leather
-/
module
public import Mathlib.Data.Finset.Card
public import Mathlib.Data.Finset.Union
/-!
# Finite sets in `Option α`
In this file ... |
3,647 | lean_file_chunk | 8b29925d8eca0441b3a1b74bbb5c93e523724446bc03afb3ed415c6e2bcb3b66 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Data.Finset.Lattice.Fold
public import Mathlib.Data.Set.Pairwise.List
/-!
# Relations holding pairwise on finite sets
In this file we prov... |
532 | lean_file_chunk | e7893ea194b2e3c11e20494f05047117d3e82c8c0758849779aa1b01c05c7c21 | 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.Init
public import Aesop.Frontend
/-!
# Aesop rule set for finsets
This file defines `finsetNonempty`, an aesop rule set to prove that a g... |
3,006 | lean_file_chunk | 4820cbef949369ea9cc2780585d210e7630bd2db73aa91ff859dd296c46ff0f2 | 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.Finset.Option
public import Mathlib.Data.PFun
public import Mathlib.Data.Part
/-!
# Image of a `Finset α` under a partially defi... |
22,703 | lean_file_chunk | 25a7c7669ed8a474ff814019e133f1418080a9c4d7c7deb79a498cc9147e630f | 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.NAry
public import Mathlib.Data.Finset.Slice
public import Mathlib.Data.Set.Sups
/-!
# Set family operations
This file defines... |
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