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 |
|---|---|---|---|---|---|
2,608 | lean_file_chunk | b92602f20a6d167ad62d31c8476d429c39e243388d452a0dc38438c4199357f1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
module
public import Mathlib.Algebra.Field.Rat
public import Mathlib.Algebra.Group.Indicator
public import Mathlib.Algebra.Order.Field.Rat
pu... |
733 | lean_file_chunk | 1837255d81e2c749847988d69d3398e7a39c8cf021fc3f278994c1fb50d162e9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
module
public import Mathlib.Data.NNRat.Defs
public import Mathlib.Algebra.Order.Ring.Rat
public import Mathlib.Algebra.Order.Nonneg.Ring
/-... |
14,312 | lean_file_chunk | 1e94a6ee4ee6c7dcfeb7e0e6fa1ad3aa5d74159499ff66dd41d4136df0583658 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
module
public import Mathlib.Algebra.Order.Group.Unbundled.Int
public import Mathlib.Algebra.Order.Nonneg.Basic
public import Mathlib.Algebra... |
5,462 | lean_file_chunk | 3d833527d5ea2c756a121611d12117a6ea32fcd19edecf82c65e44d1ce7e2f55 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 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.Order.Floor.Semiring
public import Mathlib.Data.NNRat.Order
public import Mathlib.Data.Rat.Floor
public meta import Mathlib.Data.Rat.F... |
2,049 | lean_file_chunk | 349b246822ac45539962fb02f0531e329c6a95696ec3c8a10bd907fedf967060 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
module
public import Mathlib.Algebra.Order.BigOperators.GroupWithZero.Finset
public import Mathlib.Algebra.Order.BigOperators.Group.Finset
pu... |
769 | lean_file_chunk | 622541cbc6fe4877f3e0d72a237674ea3694717fd960c3a80d74e6cbd69039a7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Aaron Liu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Liu
-/
module
public import Mathlib.Logic.Encodable.Basic
public import Mathlib.Data.NNRat.Defs
/-! # The nonnegative rationals are `Encodable`.
As a consequence we also get the in... |
23,334 | lean_file_chunk | fa14a09d69bd6cf667f05cc58c3c966a23b9c53e4f7dffb12a8df98931fbe447 | 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.Algebra.Order.Group.Unbundled.Int
public import Mathlib.Algebra.Group.ModEq
public import Mathlib.Data.Int.GCD
public import Mathlib.Dat... |
22,241 | lean_file_chunk | df4b56af2283c424a1f63d99f999d51ce27a0f148280322077b5b16508fc4661 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Vladimir Goryachev. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Vladimir Goryachev, Kyle Miller, Kim Morrison, Eric Rodriguez
-/
module
public import Mathlib.Data.List.GetD
public import Mathlib.Data.Nat.Count
public import Mathl... |
14,487 | lean_file_chunk | 536ae4d3ecb037fc39d2b91c1913ecd43851224f76736e2710dbe028c6a2ea82 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Alex Keizer
-/
module
public import Mathlib.Algebra.NeZero
public import Mathlib.Algebra.Ring.Nat
public import Mathlib.Algebra.Ring.Parity
public import Mathlib.Data.Bo... |
5,464 | lean_file_chunk | ec8f596e3ac08c7ecf5c38719a33e4fa5b6db468e433c217b4a25948071aefa6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Vladimir Goryachev. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Vladimir Goryachev, Kyle Miller, Kim Morrison, Eric Rodriguez
-/
module
public import Mathlib.Algebra.Group.Nat.Range
public import Mathlib.Data.Set.Finite.Basic
/-... |
5,072 | lean_file_chunk | adce60e05e2674934184ca7c14d7651efe8c8c6d9768ccd340d4e58cd397702b | 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, Mario Carneiro
-/
module
public import Mathlib.Data.Countable.Defs
public import Mathlib.Data.Nat.Factors
public import Mathlib.Data.Nat.Prime... |
2,572 | lean_file_chunk | 90d12959bc8a005fcd65e2453e0aba60f7f6b59114d86952a75dfc6f20166ac6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Jeremy Avigad
-/
module
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order.Ring.Canonical
/-!
# Distance function on ℕ
This file d... |
3,102 | lean_file_chunk | f5d1c1ee2a4ffcc7572704691e49ce0e6145b3c4c563cbd0ab25101f9b426d8e | 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.Group.Nat
public import Mathlib.Algebra.Ring.Nat
public import Mathlib.Algebra.Order.Monoid.Unbundled.WithTop
public import Ma... |
8,034 | lean_file_chunk | e1a6d78704357f0824eaf6c3baa3295b719447c7f54814c8ad9f6deaa6310ed4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 Floris van Doorn (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-/
module
public import Mathlib.Data.Nat.Basic
public import Batteries.Data.Nat.Bas... |
8,026 | lean_file_chunk | 906317ff1147b1aa59be25d65960188eeeb75a0c0ca883b3c74f941e69770983 | 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, Praneeth Kolichala, Yuyang Zhao
-/
module
public import Mathlib.Init
/-!
# Binary recursion on `Nat`
This file defines binary recursion on `Nat`.
## Main res... |
5,047 | lean_file_chunk | d3ea275d2f2e207cf140b44148f46cc87dbcfba9c1f62e1422305553b9c04346 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Peter Nelson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Peter Nelson
-/
module
public import Mathlib.Algebra.BigOperators.Ring.List
public import Mathlib.Algebra.Order.BigOperators.Group.List
public import Mathlib.Algebra.Order.Group.Nat
pub... |
2,344 | lean_file_chunk | 85c0b71a2208291c045b1f588a9d83b01e1cbd9ab78c34c259704258a1b8811b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Stuart Presnell. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stuart Presnell
-/
module
public import Mathlib.Algebra.Ring.Parity
public import Mathlib.Data.Nat.BinaryRec
/-! # A recursion principle based on even and odd numbers. -/
@[expose]... |
19,827 | lean_file_chunk | a9690694f61db1fd9b69c45c6cb45845d7dba98f9cf19aae2244141daaf7e243 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 Floris van Doorn (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-/
module
public import Batteries.Tactic.Alias
public import Batteries.Util.Library... |
12,873 | lean_file_chunk | 663c7524708ccd24300d3d560aca4f1fe9baadd8fa7a0707cd133170a4e2c199 | 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, Mario Carneiro
-/
module
public import Mathlib.Algebra.BigOperators.Ring.List
public import Mathlib.Data.Nat.GCD.Basic
public import Mathlib.D... |
13,748 | lean_file_chunk | 07a09f67ace8f64e6be5160ce7e93ddd1b51c84cc1acd71bea5c2a304cbbbdc8 | 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.Nat.Choose.Factorization
/-!
# Natural number multiplicity
This file contains lemmas about the multiplicity function (the maximum pri... |
9,729 | lean_file_chunk | 48966685a341a120f3c27f53fb0b332572d4316e7b0710c6eb30918bc76dc2e0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Matthew Robert Ballard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Matthew Robert Ballard, Yury Kudryashov
-/
module
public import Mathlib.Logic.Basic
import Mathlib.Data.Nat.Notation
/-!
# The maximal power of one natural number dividing an... |
4,546 | lean_file_chunk | 93668041753d6ae852eeb7209a8ea2c5b8e0659d96284e070f9c48e3d0c0970c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 Floris van Doorn (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-/
module
public import Mathlib.Data.Nat.Init
public import Mathlib.Logic.Basic
pub... |
3,807 | lean_file_chunk | 75d2e31cb47690c6252df8234a4c2f7198f7eabd1b33d33a3e854f6efc1ae562 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 Floris van Doorn (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-/
module
public import Mathlib.Data.Nat.Bits
/-! Lemmas about `size`. -/
public ... |
2,404 | lean_file_chunk | ca1a23c476e4054a60e27b17bcd70c26a0760bcacc93c62f6634b77296fa7fda | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Mark Andrew Gerads. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mark Andrew Gerads, Junyan Xu, Eric Wieser
-/
module
public import Mathlib.Tactic.NormNum.Inv
public import Mathlib.Tactic.NormNum.Pow
/-!
# Hyperoperation sequence
This file de... |
316 | lean_file_chunk | 53a7def5cbdfa4f3c0ecd0bf40bfd6d3390e2e30887b99b9ed1d4203d6692fbb | 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: Floris van Doorn, Leonardo de Moura
-/
module
public import Mathlib.Init
/-!
# Notation `ℕ` for the natural numbers.
-/
public section
@[inherit_doc] notation "ℕ" => Nat |
1,206 | lean_file_chunk | b9564e53edfd75db70bad737eb06e912bf5159456ea6135aaa39dde35c487f79 | 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.Set.Image
/-!
### Recursion on the natural numbers and `Set.range`
-/
public section
namespace Nat
section Set
open Set
th... |
7,629 | lean_file_chunk | 465ca8382e5895ef5324b246c9378030ae29c60799dbde99d8b51331187e5a60 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Shogo Saito. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shogo Saito. Adapted for mathlib by Hunter Monroe
-/
module
public import Mathlib.Algebra.BigOperators.Ring.List
public import Mathlib.Data.Nat.ModEq
public import Mathlib.Data.Nat.GCD.B... |
23,955 | lean_file_chunk | 4aa026e9deabe4b12cc904cbcfe14b39ef7de2a067d2247e63f8b1d0459a1480 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
module
public import Mathlib.Algebra.Order.BigOperators.GroupWithZero.Finset
public import Mathlib.Algebra.Squarefree.Basic
public import Mathlib.Data.Nat.Factorizat... |
593 | lean_file_chunk | ece0b16d97a0166f4ff4504fdeae0d83492cee3a2e00d2b8f14ffd59c2edbf74 | lean_source_file | pkg_mathlib_source_file_chunks | pure <| q(squarefree_bit1).mk_app [en', p]
| _ => failed
/-- Evaluates the `Squarefree` predicate on naturals. -/
@[norm_num]
unsafe def eval_squarefree : expr → tactic (expr × expr)
| q(@Squarefree ℕ $(inst) $(e)) => do
is_def_eq inst q(Nat.monoid)
let n ← e.toNat
match n with
| 0 => false_intro... |
2,260 | lean_file_chunk | 8e24c0eba097eaf511b041dfb72250d419f965e6054d2eb5db4ab75024e5d605 | 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.Data.Nat.Cast.WithTop
public import Mathlib.Order.Nat
/-!
# `WithBot ℕ`
Lemmas about the type of natural numbers with a bottom element adj... |
9,173 | lean_file_chunk | 6c9c3ddddc2dfc3b4953419fb94870e9e1c3e837d8cb85532ce124edb8be358f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Praneeth Kolichala. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Praneeth Kolichala
-/
module
public import Mathlib.Data.Nat.BinaryRec
public import Mathlib.Data.List.Defs
/-!
# Additional properties of binary recursion on `Nat`
This file doc... |
2,072 | lean_file_chunk | edfe06e57cf2788d8eaeb64efc37a331a4d732abf554b0f52c77e485a8e5b0bb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Bolton Bailey. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bolton Bailey
-/
module
public import Mathlib.Algebra.Ring.Periodic
public import Mathlib.Data.Nat.Count
/-!
# Periodic Functions on ℕ
This file identifies a few functions on `ℕ` whi... |
19,177 | lean_file_chunk | be6981d7a98a021164a9b79ce1f33aca57da1e4c5494686aa4df790165bb3f6a | 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.BigOperators.Ring.Finset
public import Mathlib.Algebra.CharP.Two
public import Mathlib.Algebra.Order.AbsoluteValue.Basic
public impo... |
3,215 | lean_file_chunk | 23af8366e206eab3de6fefe0c28afe07f9f70ea22ff3a1efd528bb1ce2b305fa | 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.Algebra.Group.Basic
public import Mathlib.Algebra.Group.Nat.Defs
public import Mathlib.Data.Nat.Basic
/-!
# Partial predecessor and par... |
6,283 | lean_file_chunk | bb2d54ba41eb6b719d2aa452dc44b9f642b426d54ded0485ed41858c8c539b10 | 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, Mario Carneiro
-/
module
public import Mathlib.Algebra.Notation.Prod
public import Mathlib.Data.Nat.Sqrt
public import Mathlib.Data.Set.Lattice.Image
/-!
# ... |
8,447 | lean_file_chunk | 8f3f9ff7778f1e3b4195dfb63014581177ede5018f03f0ccbda0c26d07fefa05 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Floris van Doorn, Gabriel Ebner, Yury Kudryashov
-/
module
public import Mathlib.Order.ConditionallyCompleteLattice.Finset
public import Mathlib.Order.Interval.Finset.... |
19,950 | lean_file_chunk | f9d05321a8b3e3e8547927cc8c761297a3b2c79d000fa7f8eccb19151d78540f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Yaël Dillies, Yury Kudryashov
-/
module
public import Mathlib.Data.Nat.BinaryRec
public import Mathlib.Order.Interval.Set.Defs
public import Mathlib.Order.Monotone.Basic
pub... |
2,444 | lean_file_chunk | c051747325f71fcae345ed7cef497e9e62330ed893759ce70dfeb8199c69b960 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
module
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order.Sub.Basic
/-!
# `Nat.Upto`
`Nat.Upto p`, with `p` a predicate on `ℕ`, is a subty... |
9,803 | lean_file_chunk | adede8eeae86293d127790ccc551d946afa4ebec9203b7a3bdb78d4b4f0687bf | 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, Johannes Hölzl, Mario Carneiro
-/
module
public import Mathlib.Data.Nat.Basic
public import Mathlib.Tactic.Push
public import Batteries.Tactic.Init
/-!
# `N... |
23,735 | lean_file_chunk | fa3a716587c035026d0f02c495b56be87e0055993ac883346a70b7f78d7b62ff | 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
-/
module
public import Mathlib.Data.Stream.Defs
public import Mathlib.Logic.Function.Basic
public import Mathlib.Data.Nat.Basic
public import Mathlib.Tactic.... |
6,212 | lean_file_chunk | fb2cf082de0a3010658064757006468866e41663c6798caebfdc11c4127f601a | 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
-/
module
public import Mathlib.Data.Nat.Notation
/-!
# Definition of `Stream'` and functions on streams
A stream `Stream' α` is an infinite sequence of ele... |
6,964 | lean_file_chunk | c29ea5b8bfdce4a7ad268709d6b559867516376af3aafd580fc5165f110fd57d | 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.Semiquot
public import Mathlib.Data.Nat.Size
public import Mathlib.Data.PNat.Defs
public import Mathlib.Data.Rat.Init
public import... |
20,544 | lean_file_chunk | 5b3631ef9f2e7bfa0e7ab5a5f84661ff967099fb2e4af582566a0233ce6f6ab5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston, Bryan Gin-ge Chen
-/
module
public import Mathlib.Logic.Relation
public import Mathlib.Order.CompleteLattice.Basic
public import Mathlib.Order.GaloisConnection.D... |
22,183 | lean_file_chunk | ae53ac2e3aa541858b791b9c8ede7d12cf4f61f1cede9819da7b96ca185ac775 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston, Bryan Gin-ge Chen, Patrick Massot, Wen Yang, Johan Commelin
-/
module
public import Mathlib.Data.Set.Finite.Range
public import Mathlib.Order.Partition.Finpartit... |
5,850 | lean_file_chunk | 98729b67fcf4e5c49645a96bbf94b60918ebbdba2b0ea84e48854d2a6574bd9e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Damien Thomine. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damien Thomine
-/
module
public import Mathlib.Algebra.Order.Monoid.Unbundled.Pow
public import Mathlib.Data.ENat.Basic
/-!
# Powers of extended natural numbers
We define the power ... |
23,802 | lean_file_chunk | 4ebd56e323765ee7bbac4cb6e13de977602875bc9da3543d9e9e9da873740cbf | 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.Group.Nat.Units
public import Mathlib.Algebra.Order.AddGroupWithTop
public import Mathlib.Algebra.Order.Ring.Nat
public import... |
1,066 | lean_file_chunk | e25c3945fcf2bbe7b226bdb0d0c6d3d1c75aefc51ce2ffa94308392525d87d54 | 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, Simon Hudon, Yury Kudryashov
-/
module
public import Mathlib.Data.Nat.Notation
public import Mathlib.Order.TypeTags
/-! # Definition and notation for extended natural... |
3,878 | lean_file_chunk | 8f9b0843bc1df32d4b9cc154d0084f9ecde3d744e87612b85be10ac4dd4558a2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Joachim Breitner, Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joachim Breitner, Yaël Dillies, Bhavik Mehta
-/
module
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Algebra.BigOperators.WithTop
public... |
12,108 | lean_file_chunk | d10b81dc7b4c63d9e10f5e8049fa9f6d09fa34b17769649c94c56ebb156eb477 | 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, Bhavik Mehta
-/
module
public import Mathlib.Algebra.Group.Action.Defs
public import Mathlib.Data.Nat.Lattice
public import Mathlib.Data.ENat.Basic
/-!
# Extended n... |
1,870 | lean_file_chunk | 942d5e1832c6654c317f6dad3c0d8c17b96b492d74e0254a893426209d0f4f44 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
module
public import Mathlib.Algebra.Order.Ring.Abs
public import Mathlib.Algebra.Order.Ring.Unbundled.Rat
public import Mathlib.Data.Rat.Lemmas
publ... |
13,830 | lean_file_chunk | c9c56d4b0191a395fd2ba9a2fd4d41750171d962edc38b208b4d96be511dcf70 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
module
public import Mathlib.Algebra.GroupWithZero.Divisibility
public import Mathlib.Algebra.Ring.Rat
public import Mathlib.Algebra.Ring.Int.Parity
... |
2,276 | lean_file_chunk | 8a0cb9d4438f9ef975782e08d770519db1f6e8efe651a49d1b1790d6467ed172 | 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, Yaël Dillies
-/
module
public import Mathlib.Algebra.GroupWithZero.Commute
public import Mathlib.Algebra.Order.Monoid.Submonoid
public import Mathlib.Algebra.Order.Ring.... |
2,428 | lean_file_chunk | 4b02abc17bb28d2942ecbcebf8501de8900dc8908fa9600321a5cf503df49508 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Yaël Dillies
-/
module
public import Mathlib.Data.Nat.Notation
public import Batteries.Classes.RatCast
/-!
# Basic definitions around the rational num... |
697 | lean_file_chunk | 4493586ca0fd793938664ae1ae97d0230be0a7202d3b55ae1e94d33f91614d8d | 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.Algebra.Ring.Rat
public import Mathlib.Data.Rat.Encodable
public import Mathlib.Algebra.CharZero.Infinite
public import Mathlib.Logic.Denume... |
9,941 | lean_file_chunk | 56a60a31ddbb8b3ac13ab84cc377bd29a68ebf21c7f6ee4b5eeb61a2e5178ba1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
module
public import Mathlib.Algebra.Group.Defs
public import Mathlib.Data.Nat.Basic
public import Mathlib.Data.Rat.Init
public import Mathlib.Order.... |
17,318 | lean_file_chunk | c41088e2fc38121fa358e826b233e5cd9916d0c897d65fda1d70001f77503c7d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Kevin Kappelmann
-/
module
public import Mathlib.Algebra.Order.Round
public import Mathlib.Data.Rat.Cast.Order
public import Mathlib.Tactic.FieldSimp
p... |
1,354 | lean_file_chunk | f1fc528bad6d8a8741d557a1357648da852a257c2602af5e1c25722a84f7b60a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
module
public import Mathlib.Data.Rat.Cast.CharZero
public import Mathlib.Algebra.BigOperators.Group.Finset.Defs
/-! # Casting lemmas for rational n... |
542 | lean_file_chunk | 5ee030d6e5e28912957e9e2591e89e73308235a768c7c2778575c85fa350aadb | 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, Floris Van Doorn
-/
module
public import Mathlib.Algebra.CharZero.Infinite
public import Mathlib.Algebra.Ring.Rat
public import Mathlib.Data.Rat.Encodable
public import Ma... |
745 | lean_file_chunk | 61e35e93d18c9fb2788281a0d0eb4e6947fd86c4a24c016d55d0b8f4d371db04 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
module
public import Mathlib.Logic.Encodable.Basic
public import Mathlib.Data.Rat.Init
/-! # The rationals are `Encodable`.
As a consequence we als... |
12,286 | lean_file_chunk | 1ca43c6c6de5e349518cc2dab38604afad7f4da3ded870d114025723c0096607 | 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: Mario Carneiro
-/
module
public import Mathlib.Data.Num.Basic
public import Mathlib.Data.Vector.Basic
/-!
# Bitwise operations using binary representation of integers
## Defi... |
23,946 | lean_file_chunk | c2c17b3f07ab01525ea97c0fd521ec25c6947378c8a75a13a3686dec9fff7d05 | 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: Mario Carneiro
-/
module
public import Mathlib.Algebra.Order.Ring.Nat
public import Mathlib.Algebra.Ring.Int.Defs
public import Mathlib.Data.Nat.Bitwise
public import Mathlib.D... |
6,256 | lean_file_chunk | 6b52c15455faefcd07ab96352d81a0422d15794473eda70200c0b44e2be3dac0 | lean_source_file | pkg_mathlib_source_file_chunks | revert this; cases cmp m n <;> simp_all [LT.lt.ne, LT.lt.ne']
@[simp, norm_cast]
theorem cast_lt [Semiring α] [PartialOrder α] [IsStrictOrderedRing α] {m n : Num} :
(m : α) < n ↔ m < n := by
rw [← cast_to_nat m, ← cast_to_nat n, Nat.cast_lt (α := α), lt_to_nat]
@[simp, norm_cast]
theorem cast_le [Semiring α] [L... |
14,727 | lean_file_chunk | 816c8a3f0d13f5c2b7706ce6450e6a0506928eab3a6d8fac8aff12ac96006b71 | 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, Mario Carneiro
-/
module
public import Lean.Linter.Deprecated
public import Mathlib.Data.Nat.Notation
public import Mathlib.Data.Int.Notation
public import M... |
23,988 | lean_file_chunk | ee1f988750c85c2f22bfcfa3c8492f7ee0f922306173af399c6b6e3619633cf5 | 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: Mario Carneiro
-/
module
public import Mathlib.Algebra.Order.Ring.Cast
public import Mathlib.Data.Int.Cast.Lemmas
public import Mathlib.Data.Num.Lemmas
/-!
# Properties of the... |
131 | lean_file_chunk | 070f34891e360c60851522989c07b46a670cc3bb172f923373f845d96482e024 | lean_source_file | pkg_mathlib_source_file_chunks | instance decidableDvd : DecidableRel ((· ∣ ·) : ZNum → ZNum → Prop)
| _a, _b => decidable_of_iff' _ dvd_iff_mod_eq_zero
end ZNum |
4,461 | lean_file_chunk | 239ee9f41dbc8d01f30af0fc97ddd23349b089dd64e34403423d5484a68fe6cd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 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.Prime.Defs
public import Mathlib.Data.Num.ZNum
public import Mathlib.Tactic.NormNum.Inv
public import Mathlib.Tactic.NormNum.Po... |
7,711 | lean_file_chunk | 6942af76edcad7e4e5527d38bbea4cb9d5d51dc55b395abe956f0599ef5466e9 | 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.Init
/-!
# Binary map of options
This file defines the binary map of `Option`. This is mostly useful to define pointwise operations
on int... |
8,781 | lean_file_chunk | e1fa9c6ce7386dc76bbfcbe79e69a63318a4d8c60ce7401724789596afb87f8a | 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.Control.Combinators
public import Mathlib.Data.Option.Defs
public import Mathlib.Logic.IsEmpty.Basic
public import Mathlib.Logic.Relator... |
1,898 | lean_file_chunk | 49299198cef5e59232fdb26f69e3212f29e789aac11657699fc27a995d0b507a | 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.Init
/-!
# Extra definitions on `Option`
This file defines more operations involving `Option α`. Lemmas about them are located in othe... |
2,955 | lean_file_chunk | 98fe56af255069d53b3d7687a73dcdc8f7849b298ca0997a83c5eb5abc98138b | 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
-/
module
public import Mathlib.Data.Fintype.Basic
public import Mathlib.Data.FunLike.Basic
public import Mathlib.Data.Finite.Prod
/-!
# Finiteness of `DFunLike` types
We s... |
3,086 | lean_file_chunk | c2f4457101879864f2481fa40e38f132cd7e457263ea988ab9a7d3a28befdbe4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 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.SetLike.Basic
/-! # Class of grading-preserving functions and isomorphisms
We define `GradedFunLike F 𝒜 ℬ` where `𝒜` and `ℬ` represent so... |
8,592 | lean_file_chunk | 9aaa7f01677fda20f49ac450b9deaefb99bc5bd6b7a55a8273a6e0b27a42deea | 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 meta import Lean.Meta.CoeAttr
public import Mathlib.Logic.Function.Basic
public import Mathlib.Logic.Unique
public import Mathlib.Util.CompileInductive
publi... |
5,281 | lean_file_chunk | 2f22868f5a77c09902e378a532b4b709650e6812e154d0d79be40db6b0a9eca5 | 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.FunLike.Basic
/-!
# Typeclass for a type `F` with an injective map to `A ↪ B`
This typeclass is primarily for use by embeddings such as... |
8,284 | lean_file_chunk | 842cb34372c6d9b80c8eeabd6e376080baa7bac7944d91108bdc7a815b2e6f9a | 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.FunLike.Embedding
/-!
# Typeclass for a type `F` with an injective map to `A ≃ B`
This typeclass is primarily for use by isomorphisms l... |
4,576 | lean_file_chunk | 86f9203b38b63158d92e51cadea93ea2bfae46e32afc67cf734e170ee9cef4cb | 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.Sigma.Order
public import Mathlib.Order.Interval.Finset.Defs
/-!
# Finite intervals in a sigma type
This file provides the `LocallyFi... |
6,394 | lean_file_chunk | f858f7a8538b8a46d58dc1c0df274a267cc2ba0092fcf188f5617bb3aaed9483 | 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.Logic.Function.Defs
public import Mathlib.Order.Defs.Unbundled
public import Batteries.Logic
/-!
# Lexicographic order on a sigma type
Thi... |
9,410 | lean_file_chunk | 25abab3c93298a704784abe74208109ab19855c6ceaa9eccfc840c013d602adc | 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.Sigma.Lex
public import Mathlib.Util.Notation3
public import Mathlib.Data.Sigma.Basic
public import Mathlib.Order.BoundedOrder.Basic
pu... |
10,139 | lean_file_chunk | 84a1de9629bd0b0f79594939792ff68304059d8abb921226fb41dd9914e3faed | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
module
public import Mathlib.Logic.Function.Defs
public import Mathlib.Logic.Function.Basic
/-!
# Sigma types
This file proves basic results about sigma types.
A ... |
2,726 | lean_file_chunk | d7f23fbc1f7273b97ba08c5abffee7bec33802f58ec860a96ee5f67cf7ed877b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Order.Interval.Finset.Basic
public import Mathlib.Data.Fintype.BigOperators
/-!
# Intervals in a pi type
This file shows that (dependent) ... |
13,978 | lean_file_chunk | df9d3e471b2b8d63ba860a9ba83cbb7a16614b78dfd745c4f92d51a59ab100cd | 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.Data.Nat.ModEq
import Mathlib.Data.Int.Cast.Lemmas
/-!
# Congruences modulo an integer
This file defines the equivalence relation `a ≡ b ... |
1,067 | lean_file_chunk | bf0bce45acd9f5b3ebe1fd61da47c7b55c3afe449964d50138e254e7ee62883e | 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 Batteries.Tactic.Alias
public import Mathlib.Init
/-!
# Basic lemmas about division and modulo for integers
-/
public section
namespace Int
/-! ###... |
14,725 | lean_file_chunk | 31b14e1753db8c77cd0b938e4ef5b514ecd4efad4b0d75d88d1bb30c2c7c57d8 | 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
-/
module
public import Mathlib.Algebra.Ring.Int.Defs
public import Mathlib.Data.Nat.Bitwise
public import Mathlib.Data.Nat.Size
public import Batteries.Data.Int
import a... |
12,101 | lean_file_chunk | 423ddccf12e2b28977d104e4f6407d237d0ad2da53f4424e5bd779ec2c1f8920 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Guy Leroy. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sangwoo Jo (aka Jason), Guy Leroy, Johannes Hölzl, Mario Carneiro
-/
module
public import Mathlib.Algebra.GroupWithZero.Semiconj
public import Mathlib.Algebra.Group.Commute.Units
public im... |
1,814 | lean_file_chunk | 762a120c02abffc7618242a9b104bb608f9ebd63ec30497629438740f09873d1 | 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.Ring.Int
public import Mathlib.Data.Nat.SuccPred
/-!
# Successors and predecessors of integers
In this file, we show that `ℤ... |
1,315 | lean_file_chunk | 18e5c301aa5c9d7aefb4d1066ef578aff20b8c706bcb87be190895232d3c353f | 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: Kenny Lau
-/
module
public import Mathlib.Data.Nat.Sqrt
public import Mathlib.Tactic.Common
/-!
# Square root of integers
This file defines the square root function on integers. `Int.sqr... |
3,788 | lean_file_chunk | 32431fef96a82c1f50af56eb82148406be399098bd8bac5b38b3f612d503a313 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 María Inés de Frutos-Fernández, Filippo A. E. Nuccio. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: María Inés de Frutos-Fernández, Filippo A. E. Nuccio
-/
module
public import Mathlib.Data.NNReal.Defs
/-!
# WithZero
In this file we provide so... |
6,755 | lean_file_chunk | 590e2e6703fba9ccb5d51a2006594f46ab005292b91aa5c4234efb867a7be89e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jeremy Tan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Tan
-/
module
public import Mathlib.Data.Int.Interval
public import Mathlib.Data.Int.ModEq
public import Mathlib.Data.Nat.Count
public import Mathlib.Data.Rat.Floor
public import M... |
4,134 | lean_file_chunk | 1602629f4f8eede8c50869179dcad8d4f424af1c4fedbf704a789ca28d5b31e2 | 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
-/
module
public import Mathlib.Data.Int.Bitwise
public import Mathlib.Data.Int.Order.Lemmas
public import Mathlib.Order.Interval.Set.Defs
/-!
# Miscellaneous lemmas abo... |
1,206 | lean_file_chunk | 6398e04b4300d697b3fc2b2a8c0d7a4f6de24e1e9be4fc77a123d37c904478cf | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Algebra.Order.Group.Abs
public import Mathlib.Algebra.Order.Monoid.Submonoid
public import Mathlib.Algebra.Order.Ring.Basic
public import Ma... |
6,425 | lean_file_chunk | f2566fe0cab3ecd62748f88df509a117febd207420240a36f1c0964fab46f650 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Algebra.Group.Embedding
public import Mathlib.Algebra.Ring.CharZero
public import Mathlib.Algebra.Ring.Int.Defs
public import Mathlib.Algebr... |
1,612 | lean_file_chunk | 9679fa16af3d5edcf0026fd67fe3c857c863b9fdffa46dcfe384b6b39642ae26 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Bryan Gin-ge Chen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Lacker, Bryan Gin-ge Chen
-/
module
public import Mathlib.Data.Nat.Prime.Basic
public import Mathlib.Algebra.Group.Int.Defs
public import Mathlib.Data.Int.Basic
/-!
# Lemmas... |
12,296 | lean_file_chunk | 18822a3861475cd151d72eb2031d37b62da29a7ea232fa30b1e44a3e4b574e4d | 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
-/
module
public import Batteries.Logic
public import Mathlib.Data.Int.Notation
public import Mathlib.Data.Nat.Notation
/-!
# Basic operations on the integers
This file... |
3,809 | lean_file_chunk | 8cc0df0d5683c562335a54e1ccfd5bcc1bc217b8c28730e980dc75358e19c50c | 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
-/
module
public import Mathlib.Data.Int.Init
public import Mathlib.Data.Nat.Basic
public import Mathlib.Logic.Function.Basic
public import Mathlib.Tactic.Conv
public imp... |
3,150 | lean_file_chunk | f9799655bc5d544bbccb224cf94a51bcf9c4a54cc66d992e8ce3f44d3e2afe0a | 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: Floris van Doorn
-/
module
public import Mathlib.Data.Int.LeastGreatest
public import Mathlib.Order.ConditionallyCompleteLattice.Defs
/-!
## `ℤ` forms a conditionally complete line... |
278 | lean_file_chunk | 6f0020a8a9281ee201d0ac00be2341d7ee50cc7d4ec9a7f13c03fcaf8fa120a1 | 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
-/
module
public import Mathlib.Init
/-!
# Notation `ℤ` for the integers.
-/
public section
@[inherit_doc] notation "ℤ" => Int |
1,562 | lean_file_chunk | 89914b000b430fc0a7a0cb9a6044accdb73078b17b98bc938e36c5ad55766a24 | 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.Algebra.Notation.Support
public import Mathlib.Data.Int.Cast.Field
public import Mathlib.Data.Int.Cast.Lemmas
public import Mathlib.Data... |
1,835 | lean_file_chunk | 3ded3d1111a78e1df5a4832cff362215083d9a1e3d7fcde7832bd12a58a8b322 | 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: Mario Carneiro, Kenny Lau
-/
module
public import Mathlib.Algebra.Group.Int.Defs
public import Mathlib.Algebra.Order.Group.Unbundled.Basic
/-!
# Intervals in ℤ
This file defines integer ... |
996 | lean_file_chunk | 8b84b774282e5290b1862d2b0c467613c739f1b0ed2b57317ecbc0d37a63d257 | 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, Jeremy Tan
-/
module
public import Mathlib.Algebra.GroupWithZero.Hom
public import Mathlib.Algebra.GroupWithZero.Nat
public import Mathlib.Algebra.Ring.Int.Defs
/-!
# Lemma... |
12,982 | lean_file_chunk | bda99ebb865259474c2f5dcb8fe4241de7f305b3cb423151f9b34e37d32ea49c | 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.Algebra.Field.Defs
public import Mathlib.Algebra.Order.Floor.Semiring
public import Mathlib.Data.Nat.Log
/-!
# Integer logarithms in a field ... |
833 | lean_file_chunk | c3311bb59f4436195cd589e068114183672d8c0407ac5077fe3335098361f9b2 | 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
-/
module
public import Mathlib.Algebra.GroupWithZero.Associated
public import Mathlib.Algebra.Ring.Int.Units
/-!
# Associated elements and the integers
This file contains s... |
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