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 |
|---|---|---|---|---|---|
3,760 | lean_file_chunk | 11bbf38711230119390dc4cfaee70b75912140bb404c80dd65493d305f7d2b8b | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2023 Lean FRO. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joe Hendrix
-/
module
prelude
public import Init.Grind.Tactics
import Init.Data.Bool
import Init.Data.Nat.Lemmas
public section
/-!
This contains lemmas used by the Nat simprocs for simpl... |
23,989 | lean_file_chunk | 062476f221a29427275081f43dc7f13322d6267134a7f2c675ba31e2088e2f46 | lean_source_file | lean_toolchain_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: Leonardo de Moura, Jeremy Avigad, Mario Carneiro, Floris van Doorn
-/
module
prelude
import all Init.Data.Nat.Bitwise.Basic
public import Init.Data.Na... |
23,932 | lean_file_chunk | 2c20987a508504662667daf33a998467ecf220ff70ff87bdc3a33a253e4e7777 | lean_source_file | lean_toolchain_source_file_chunks | protected theorem mul_ne_zero : n ≠ 0 → m ≠ 0 → n * m ≠ 0 := (Nat.mul_ne_zero_iff.2 ⟨·,·⟩)
protected theorem ne_zero_of_mul_ne_zero_left (h : n * m ≠ 0) : n ≠ 0 :=
(Nat.mul_ne_zero_iff.1 h).1
protected theorem mul_left_cancel {n m k : Nat} (np : 0 < n) (h : n * m = n * k) : m = k := by
match Nat.lt_trichotomy m k... |
23,993 | lean_file_chunk | 478c631f65d7302ecb429921b224d244491a404050fd7168508028a232562309 | lean_source_file | lean_toolchain_source_file_chunks | exact Nat.mul_lt_mul_of_le_of_lt (Nat.le_refl _) h (Nat.pow_pos (Nat.lt_trans Nat.zero_lt_one h))
protected theorem pow_lt_pow_of_lt {a n m : Nat} (h : 1 < a) (w : n < m) : a ^ n < a ^ m := by
have := Nat.exists_eq_add_of_lt w
cases this with | intro k p
rw [Nat.add_right_comm] at p
subst p
rw [Nat.pow_add, ... |
2,862 | lean_file_chunk | 7a612df4004c6bc861680ea2d62599fc869901eeb2101e5089d1e42e07169606 | lean_source_file | lean_toolchain_source_file_chunks | /-! ### Decidability of predicates -/
instance decidableBallLT :
∀ (n : Nat) (P : ∀ k, k < n → Prop) [∀ n h, Decidable (P n h)], Decidable (∀ n h, P n h)
| 0, _, _ => isTrue fun _ => (by cases ·)
| n + 1, P, H =>
match decidableBallLT n (P · <| lt_succ_of_lt ·) with
| isFalse h => isFalse (h fun _ _ => · _ _)
... |
5,161 | lean_file_chunk | 8337e84ccc018941980bc1d9cc681e7904807d8b82aa7d892e57f59b02e1bee2 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-/
module
prelude
public import Init.Data.Nat.Basic
import Init.ByCases
import Init.PropLemmas
public section
namespace Nat
... |
2,369 | lean_file_chunk | b8c89618d0d1a222cc6001557e0c031baca730691517071c948f1b2c3ac2270b | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner, Robin Arnez
-/
module
prelude
public import Init.Grind.Tactics
import Init.Data.Nat.Div.Basic
import Init.NotationExtra
import Init.WFTactics
public section
na... |
6,642 | lean_file_chunk | a7d4676679a10ebcc5789fbeffd76d249ddf76649ebb8d23fb117712a32afec6 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2022 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
module
prelude
public import Init.Data.Nat.Linear
import Init.ByCases
import Init.Data.List.BasicAux
import Init.Data.Prod
import Init.Meta
public section
n... |
3,306 | lean_file_chunk | 6aaa5cf0e9df9ef6ae5d2d935ace205a8b4ab2aed9a7fc14ca56d9515c491610 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
module
prelude
public import Init.Notation
import Init.Omega
public section
set_option linter.missingDocs true
namespace Nat
universe u v
/--
Executes a... |
6,530 | lean_file_chunk | 1d0bbc67be02485245caa9a34ccacae1f3d4a49c2327b67746f3d45fa81a4a5d | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-/
module
prelude
public import Init.Data.Nat.Div.Basic
public import Init.SimpLemmas
import Init.Data.List.Notation
import Ini... |
21,536 | lean_file_chunk | 7209c5367dc7616cb900500376a333b3501a5a0e3f97cda7c47071526af9c9b7 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2022 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
module
prelude
public import Init.Data.RArray
import Init.LawfulBEqTactics
import Init.ByCases
import Init.Data.Prod
public section
@[expose] section
na... |
10,579 | lean_file_chunk | 82ec18793f6113b825e50b98b0fb4daf6ff53889c4fc6767af616037aa69a410 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro, Markus Himmel
-/
module
prelude
public import Init.Data.Nat.Gcd
import Init.Data.Nat.Dvd
import Init.Data.Nat.Lemmas
import In... |
987 | lean_file_chunk | e1d013213761997a0281d695ee5d7b5941f581b2c70d3bd19a923ceee7ec15b7 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Paul Reichert
-/
module
prelude
public import Init.Data.Nat.Basic
import Init.Data.Nat.MinMax
public import Init.Data.Order.Classes
import Init.Data.Order.Factories
import Init.Notatio... |
23,990 | lean_file_chunk | 18df77e67cf1a23fd84b1b595fedaf9be41dbae9a47eca7e0f05e7f000d8cc48 | lean_source_file | lean_toolchain_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
prelude
public import Init.SimpLemmas
public import Init.Data.NeZero
public import Init.Grind.Tactics
public section
set_option ... |
21,623 | lean_file_chunk | 6a66cf53d6ac024a5e18df9466f118839d1928cd2106393921693d92a250b695 | lean_source_file | lean_toolchain_source_file_chunks | theorem succ_inj : succ a = succ b ↔ a = b := (Nat.succ.injEq a b).to_iff
theorem succ_le_succ_iff : succ a ≤ succ b ↔ a ≤ b := ⟨le_of_succ_le_succ, succ_le_succ⟩
theorem succ_lt_succ_iff : succ a < succ b ↔ a < b := ⟨lt_of_succ_lt_succ, succ_lt_succ⟩
theorem succ_ne_succ_iff : succ a ≠ succ b ↔ a ≠ b := by simp [Na... |
262 | lean_file_chunk | 513cc234a05208128010933392798857887d3d7a5e62abf861389ad086e7a1b0 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2022 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
module
prelude
public import Init.Data.Nat.Power2.Basic
public import Init.Data.Nat.Power2.Lemmas |
2,616 | lean_file_chunk | 30c39771a72a5b5607aba495994e1d3ba2b0e258f61bc800d9ae70d8e7ca1f9f | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-/
module
prelude
public import Init.Data.Order.ClassesExtra
import all Init.Data.Ord.Basic
public section
/-! # Basic lemmas... |
18,349 | lean_file_chunk | bf7981c05bfdbf58f41c35120f34c898a951da58f6da650bcf9af96125e33069 | lean_source_file | lean_toolchain_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, Kim Morrison
-/
module
prelude
public import Init.Data.List.FinRange
import Init.Data.Fin.Lemmas
import Init.Data.List.Lemmas
import Init.O... |
2,936 | lean_file_chunk | 58a73c9157b313e1199850606cbf6fe217a825b9058bf4e0f65c7b8aa9829782 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
prelude
public import Init.Grind.Tactics
import Init.Data.Nat.Dvd
import Init.Omega
import Init.RCases
public section
/-!
# Further results about `mod`.
This ... |
14,804 | lean_file_chunk | 0665cd2816e7f5ba0986fba2f7a1870e01ba7b4af2d2952a8c13ec50ebf9fede | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2026 Lean FRO, LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Marcus Rossel, Paul Reichert
-/
module
prelude
public import Init.Data.Repr
public import Init.Data.Char.Basic
public import Init.Data.ToString.Basic
public import Init.Data.String.Bas... |
7,600 | lean_file_chunk | 433b3f4d0d0a9ea837c8ed229ad72bb13a0e4ab8b23eabbe03867a26f74007a9 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro
-/
module
prelude
public import Init.Data.Nat.Gcd
import Init.Data.Nat.Dvd
public section
/-!
# Definitions and properties of `coprim... |
5,880 | lean_file_chunk | 2330e5ab75a56dc12f36979f7a995c8002bf28b93a45ca0524d3d87c0c3d1502 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
module
prelude
public import Init.Data.Float
import Init.Ext
public import Init.GetElem
public import Init.Data.ToString.Extra
public section
universe u
s... |
23,994 | lean_file_chunk | 8c526dc38f52568832205f1c9cae3ea0fc1949b07fc9355c242e14b1bea2b207 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2022 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johannes Hölzl, Robin Arnez
-/
module
prelude
public import Init.Data.Rat.Basic
public import Init.Data.Int.Gcd
import Init.ByCases
import Init.Data.Bool
import Init.D... |
23,976 | lean_file_chunk | 370440ff0fa3a86e34c6706c3bf10d55a7e478943ec0a0efded318c2cf68dafe | lean_source_file | lean_toolchain_source_file_chunks | protected theorem inv_mul_cancel (a : Rat) (h : a ≠ 0) : a⁻¹ * a = 1 :=
Eq.trans (Rat.mul_comm _ _) (Rat.mul_inv_cancel _ h)
protected theorem inv_eq_of_mul_eq_one {a b : Rat} (h : a * b = 1) : a⁻¹ = b := by
have : a ≠ 0 := by intro h; simp_all +decide
simpa [← Rat.mul_assoc, Rat.inv_mul_cancel _ this, eq_comm] ... |
6,288 | lean_file_chunk | b81fbba0d8e16bb8e26dac8fc12a288093a33fed069fec988ea3dba97afb9536 | lean_source_file | lean_toolchain_source_file_chunks | theorem lt_floor_add_one (a : Rat) : a < ((a.floor + 1 : Int): Rat) := by
rw [floor_def, Rat.lt_iff]
have : a.num / ↑a.den + 1 = (a.num + ↑a.den) / ↑a.den := by
rw [Int.add_ediv_of_dvd_right] <;> simp [a.den_nz]
simp [this]
simpa using Int.lt_ediv_mul (a.num + a.den) (b := a.den) (by have := a.den_nz; omega... |
13,250 | lean_file_chunk | d323339ab289fdd71076b9dcd6aee1d1b949ae848fed31cf6b21ca5d2ad9cd9c | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2022 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
module
prelude
public import Init.Data.Nat.Coprime
public import Init.Data.OfScientific
public import Init.Data.Int.DivMod.Basic
public import Init.Data.String.Defs
... |
5,280 | lean_file_chunk | 3d6cc64d5d0a0f75f31e85c12c47dd3f604cdb2bebab687cf3df87f1e8080333 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
module
prelude
public import Init.Data.Option.Basic
public section
universe u v
namespace Option
theorem eq_of_eq_some {α : Type u} : ∀ {x y : Option α... |
23,943 | lean_file_chunk | 518a0ae2e2538b60796a50a14db5fb92fdd66ff447854ee8be9ea3062584e39f | lean_source_file | lean_toolchain_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
prelude
import all Init.Data.Option.BasicAux
public import Init.Data.Option.Instances
import all Init.Data.Option.Instances
public import Init.Ext
public impo... |
23,919 | lean_file_chunk | c65ee429324832d8bee8bb2abbb62414835f269c3c13c912916be0f688f07813 | lean_source_file | lean_toolchain_source_file_chunks | ⟨fun a b c ↦ by cases a <;> cases b <;> cases c <;> simp [merge, Std.Associative.assoc]⟩
instance idempotentOp_merge (f : α → α → α) [Std.IdempotentOp f] :
Std.IdempotentOp (merge f) :=
⟨fun a ↦ by cases a <;> simp [merge, Std.IdempotentOp.idempotent]⟩
instance lawfulIdentity_merge (f : α → α → α) : Std.LawfulI... |
20,140 | lean_file_chunk | 9bd67cce6a6c4eaf8f57b08d5d30edea6d584a0a02666bfaa75879ceb87e2168 | lean_source_file | lean_toolchain_source_file_chunks | o.pfilter p = none ↔ o = none ∨ ∃ (a : α) (ha : o = some a), p a ha = false := by
cases o <;> simp
theorem pfilter_eq_some_iff {α : Type _} {o : Option α} {p : (a : α) → o = some a → Bool}
{a : α} : o.pfilter p = some a ↔ ∃ ha, p a ha = true := by
simp only [eq_some_iff_get_eq, get_pfilter, isSome_pfilter_iff]... |
449 | lean_file_chunk | ff0b9db4369e74555d9d7c35a4abd342f22eb2252b3816fc121cf87553ed6f98 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
module
prelude
public import Init.Util
public section
universe u
namespace Option
/--
Extracts the value from an `Option`, panicking on `none`.
-/
@[in... |
3,374 | lean_file_chunk | 2c98f25dcb7392c18ed67db41ce54bdf46f32fa99c0d69e6dd3dac0ee6c04207 | lean_source_file | lean_toolchain_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
prelude
import all Init.Data.List.Control
import all Init.Data.Option.Instances
public import Init.Data.List.Control
public import Init.Data.Option.Lemmas
import Init... |
7,400 | lean_file_chunk | 43a4cdf7e7d051816c4f8d0a2915e9251bcf864a46880dccfe72706a79475a0f | lean_source_file | lean_toolchain_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
prelude
import all Init.Data.Option.Instances
public import Init.Control.Lawful
public import Init.Data.Option.Lemmas
public section
namespace Option
@[simp, grin... |
21,091 | lean_file_chunk | 495300ba1a319f7e24e43d0c361f5c1e7d24ea0925863ea700d4e0a0d617a484 | lean_source_file | lean_toolchain_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
prelude
public import Init.Control.Basic
public import Init.Grind.Tactics
public section
@[expose] section
namespace Option
inst... |
528 | lean_file_chunk | 673995118d0e3fac8c63b156315dda6aeae9178733b41834568ba41ba9c08dfc | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2026 Lean FRO, LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
module
prelude
public import Init.Data.Function
import Init.NotationExtra
public section
namespace Option
theorem map_injective {f : α → β} (hf : Function.Injective... |
612 | lean_file_chunk | fe64c853296324c102b4c13f84e16a86ad35b1a7ca97f9229206f2111bc62d80 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Mario Carneiro
-/
module
prelude
public import Init.Coe
public section
/-!
In this file, we define the coercion `α → Option α`.
The use of this coercion i... |
3,408 | lean_file_chunk | 59ecc0ede7a50cd55dc413bf1ae47495c276be5b8fed6b74831b5cce0ba99f66 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
module
prelude
import all Init.Data.Option.Instances
public import Init.Control.Lawful
public import Init.Data.Option.Lemmas
import Init.Data.Array.Bootstrap
import In... |
18,998 | lean_file_chunk | ea338e2f0893c476592b143cf2c2aba1230840ead2c9a422af01c52949b49662 | lean_source_file | lean_toolchain_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
prelude
public import Init.Data.Array.Attach
public import Init.Data.Option.Lemmas
import Init.Data.Bool
import Init.Data.Option.Array
import Init.Data.Option.List
im... |
11,835 | lean_file_chunk | 8fa905651ab1b66bd412754794b262ef2952bb3db382e02a4b7bc22ae5094d47 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Markus Himmel
-/
module
prelude
public import Init.Data.ByteArray.Basic
import Init.ByCases
import Init.Data.Array.Bootstrap
import Init.Data.Array.Extract
import Init.Data.Array.Lemmas... |
15,226 | lean_file_chunk | 277b709a6a1648d735826ab09cb28abccc1ef091a6948ba6c37f76141f49dda0 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
module
prelude
import all Init.Data.UInt.BasicAux
public import Init.Data.Array.DecidableEq
public import Init.Data.List.Attach
import Init.Data.Array.Boots... |
1,660 | lean_file_chunk | c29f4df9323dd9b5d3b4611fef98aef05b0c4da0fe26fb9b98efa6624c407bf1 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Markus Himmel
-/
module
prelude
public import Init.Data.List.Basic
public section
set_option doc.verso true
namespace ByteArray
@[simp]
theorem data_push {a : ByteArray} {b : UInt8} ... |
1,263 | lean_file_chunk | 34a2af9cccd97746636ff60313e490eee554836570de31001369d00fd636c9be | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
module
prelude
public import Init.Data.ByteArray.Basic
import Init.Data.String.Defs
import Init.Data.UInt.Basic
set_option doc.verso true
/--
Interprets a... |
333 | lean_file_chunk | 058682c42b9172233403d9e123e738a06a57963e33b59efc704dc8748c1fe447 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
prelude
public import Init.Data.Int.DivMod.Basic
public import Init.Data.Int.DivMod.Bootstrap
public import Init.Data.Int.DivMod.Lemmas
public import Init.Data.I... |
251 | lean_file_chunk | 2e5516f60460df4ee5a0be102a2b5fc9992a09fa392488cfad9aa44396fba5e7 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
prelude
public import Init.Data.Int.Bitwise.Basic
public import Init.Data.Int.Bitwise.Lemmas |
4,831 | lean_file_chunk | 7ac93cdf7157c9c99eb9f2ae49f886e1b92f95113c959f542e62b5266d5f4509 | lean_source_file | lean_toolchain_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, Deniz Aydin, Floris van Doorn, Mario Carneiro
-/
module
prelude
public import Init.Data.Int.Basic
import Init.ByCases
import Init.Data.Nat.Lemmas
import Init.Omega
impor... |
23,979 | lean_file_chunk | fc8aed851d0359406463505a74a2698a9f9e0807f9bbeb9085a79b79a83633e3 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2022 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Markus Himmel
-/
module
prelude
public import Init.Data.Nat.Lcm
public import Init.Data.Int.DivMod.Basic
import Init.Data.Int.DivMod.Lemmas
import Init.Data.Int.Pow
im... |
5,738 | lean_file_chunk | 72c2b839a528e4d7c74aacff942d5cdb94684dce952555c76a42c0dca77e160c | lean_source_file | lean_toolchain_source_file_chunks | theorem lcm_ne_zero (hm : m ≠ 0) (hn : n ≠ 0) : lcm m n ≠ 0 := by
apply Nat.lcm_ne_zero <;> simpa
theorem lcm_pos : m ≠ 0 → n ≠ 0 → 0 < lcm m n := by
simpa [← Nat.pos_iff_ne_zero] using lcm_ne_zero
theorem eq_zero_of_lcm_eq_zero (h : lcm m n = 0) : m = 0 ∨ n = 0 := by
have := lcm_ne_zero (m := m) (n := n); omeg... |
23,957 | lean_file_chunk | 1a94b297c6508ad51c8789a7ed604ac4d10e492163d29197c4e371bf4de523c4 | lean_source_file | lean_toolchain_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, Deniz Aydin, Floris van Doorn, Mario Carneiro
-/
module
prelude
public import Init.Data.Int.Basic
import Init.PropLemmas
public section
namespace Int
open Nat
/-! ##... |
1,414 | lean_file_chunk | f566454df8026b9c80f2eb0e1292797323ee286b05c76ad851c7d42e188a2809 | lean_source_file | lean_toolchain_source_file_chunks | protected theorem eq_of_mul_eq_mul_left {a b c : Int} (ha : a ≠ 0) (h : a * b = a * c) : b = c :=
have : a * b - a * c = 0 := Int.sub_eq_zero_of_eq h
have : a * (b - c) = 0 := by rw [Int.mul_sub, this]
have : b - c = 0 := (Int.mul_eq_zero.1 this).resolve_left ha
Int.eq_of_sub_eq_zero this
theorem mul_eq_mul_le... |
9,149 | lean_file_chunk | 61c4fef7bb15715f3333d6cd39544d753e40b2f9754ed5a860db28ccaf025a89 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2023 Lean FRO, LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
prelude
public import Init.Data.Int.Gcd
import Init.Data.Int.DivMod.Lemmas
import Init.Omega
import Init.RCases
public section
/-!
## Cooper resolution: small ... |
557 | lean_file_chunk | b86ff13b01627e791288baaac67bab233eeddf2382da8c7b14b022b1f610f82b | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
module
prelude
public import Init.Data.Repr
public import Init.Data.String.Defs
namespace Int
/--
Returns the decimal string representation of an integer.... |
23,996 | lean_file_chunk | 74def23731989baeb9bdefb481a9f7ab86ec94773cbfe2e0d8d8bdbf04413009 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2025 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
module
prelude
import all Init.Data.Int.Gcd
import all Init.Data.AC
import Init.LawfulBEqTactics
public import Init.Data.Bool
public import Ini... |
23,952 | lean_file_chunk | 6c559fff27c5d7e45333f1eb9174895fa820f4a7c8e3a049a6b5ef9cf91753ea | lean_source_file | lean_toolchain_source_file_chunks | rw [Int.add_le_add_iff_right] at h
replace h := Int.lt_of_lt_of_le h' h
contradiction
theorem le_eq_true (ctx : Context) (lhs rhs : Expr) : (lhs.sub rhs).norm.isValidLe → (lhs.denote ctx ≤ rhs.denote ctx) = True := by
simp [Poly.isValidLe] <;> split <;> simp
next p k h =>
intro h'
replace h := cong... |
23,961 | lean_file_chunk | 820c980e6b785fb681665c66e7089e00731c7b5581af75adb2931d319396051f | lean_source_file | lean_toolchain_source_file_chunks | next n ih => intro h₁ h₂; exact ih (orOver_resolve h₁ h₂)
private theorem orOver_of_p {i n p} (h₁ : i < n) (h₂ : p i) : OrOver n p := by
induction n
next => simp at h₁
next n ih =>
simp [OrOver]
cases Nat.eq_or_lt_of_le <| Nat.le_of_lt_add_one h₁
next h => subst i; exact Or.inl h₂
next h => exact... |
11,111 | lean_file_chunk | f6aa7bd7f0c205aa3d4e4092cf06a7fa3a31e92d3125dee660b29b3ee9ba63cd | lean_source_file | lean_toolchain_source_file_chunks | Int.blt' 0 d |>.and' (p₂.beq' (p.addConst_k b₂) |>.and' (p₃.beq' (p.addConst_k (b₁ - d*((b₁ - b₂)/d)))))
theorem Poly.mul_minus_one_getConst_eq (p : Poly) : (p.mul (-1)).getConst = -p.getConst := by
simp [Poly.mul]
induction p <;> simp [Poly.mul', Poly.getConst, *]
theorem dvd_neg_le_tight (ctx : Context) (d : In... |
4,827 | lean_file_chunk | 4664186085241cdee1263f868f563ebe71ab2bafdb3581bf1fa9d0c2b08ebe91 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2025 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
module
prelude
public import Init.GrindInstances.ToInt
public import Init.Data.Nat.Div.Basic
import Init.ByCases
import Init.Data.Int.DivMod.L... |
23,995 | lean_file_chunk | bba96f9de3fc613a84f76f25ee29ea4bc39217513f7b88ac181cf83e8dab1741 | lean_source_file | lean_toolchain_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, Deniz Aydin, Floris van Doorn, Mario Carneiro
-/
module
prelude
import Init.Data.Order.Lemmas
public import Init.Data.Order.Classes
public import Init.NotationExtra
impo... |
23,924 | lean_file_chunk | ef4a006fbefa44a2adb0651b42aa20e40f6b51fe1cc90cd397752101cdd98fb1 | lean_source_file | lean_toolchain_source_file_chunks | | 0 => rfl
| succ _ => rfl
| -[_+1] => rfl
theorem natAbs_eq : ∀ (a : Int), a = natAbs a ∨ a = -↑(natAbs a)
| ofNat _ => Or.inl rfl
| -[_+1] => Or.inr rfl
theorem natAbs_negOfNat (n : Nat) : natAbs (negOfNat n) = n := by
cases n <;> rfl
theorem natAbs_mul (a b : Int) : natAbs (a * b) = natAbs a * nat... |
10,992 | lean_file_chunk | e272d0609ba243f167b1e4ab0e1e950c0cc1517b4ed2720c5154f4eb09411749 | lean_source_file | lean_toolchain_source_file_chunks | protected theorem mul_lt_mul_of_neg_left {a b c : Int} (h : b < a) (hc : c < 0) : c * a < c * b :=
have : -c > 0 := Int.neg_pos_of_neg hc
have : -c * b < -c * a := Int.mul_lt_mul_of_pos_left h this
have : -(c * b) < -(c * a) := by
rwa [← Int.neg_mul_eq_neg_mul, ← Int.neg_mul_eq_neg_mul] at this
Int.lt_of_ne... |
12,707 | lean_file_chunk | 1519c7d33395c42cbba7718dbbe9f10d50858b41c1135ef10e7e02d2c0d2a82c | lean_source_file | lean_toolchain_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, Leonardo de Moura
The integers, with addition, multiplication, and subtraction.
-/
module
prelude
public import Init.Data.Cast
public import Init.Data.Nat.Basic
public... |
2,752 | lean_file_chunk | 25adfe3a019227dac8cfd0520eb12ead913c388dff460f9771be256bdd5862b0 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad, Mario Carneiro, Paul Reichert
-/
module
prelude
public import Init.Data.Ord.Basic
public import Init.Data.Order.ClassesExtra
import all Init.Data.Ord.... |
8,688 | lean_file_chunk | 38a566ecaebaa422db172cf409b2a45fdfddef34259dc6329a80b7a5b60ece1b | lean_source_file | lean_toolchain_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
prelude
public import Init.Data.Int.Lemmas
import Init.ByCases
import Init.Data.Int.Pow
import Init.Omega
public section
/-!
# Further lemmas about `Int` relying o... |
549 | lean_file_chunk | e5b99e389d4607dec132fabadf89d59a15472aa4fc6e9d34cd1ec0c11ef71341 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2026 Lean FRO, LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julia Markus Himmel
-/
module
prelude
public import Init.Data.ToString.Extra
import all Init.Data.Int.Repr
import Init.Data.Int.Order
import Init.Data.Int.LemmasAux
namespace Int
pub... |
8,852 | lean_file_chunk | 9707f07c1fa0e956c19ac6276016b5cec2b83d11ce6a0b87372aa347a4497925 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Yury G. Kudryashov
-/
module
prelude
public import Init.Data.Sum.Basic
import all Init.Data.Sum.Basic
public import Init.Ext
public section
/-!
# Disjoint union of t... |
7,443 | lean_file_chunk | 3843563f8e68d0bddf70e08ca77711b4859eecb305e2f9c64cf4956bf6a5381b | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Yury G. Kudryashov
-/
module
prelude
public import Init.PropLemmas
public section
/-!
# Disjoint union of types
This file defines basic operations on the sum type `... |
17,422 | lean_file_chunk | 7349080de04aa042e6534cc99fd693fed74f95031f8472942a626deea9c63a5b | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
-/
module
prelude
public import Init.Data.Function
public import Init.Ext
public import Init.Not... |
16,124 | lean_file_chunk | a2f56c3188218f603a0549c97f87b4363cf2188b337106fb598ab6ed7dc66cd7 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
-/
module
prelude
import Init.Grind.Util -- shake: keep (`@[grind]` dependency)
public import I... |
199 | lean_file_chunk | 09c16a0c6d9a5e290a3ccc0a09e5b54f02c94b6fe43626a2723ff7da91c64699 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2026 Lean FRO. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Paul Reichert
-/
module
prelude
public import Init.Data.List.Int.Sum |
927 | lean_file_chunk | 68e869d086068a5468a2cad2e7b6048dd4f11b6121d3389fd97a4bc2ea98fedd | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2026 Lean FRO, LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Markus Himmel
-/
module
prelude
public import Init.Data.List.Control
public import Init.Data.List.Impl
public section
namespace List
/--
Applies a monadic function that returns a lis... |
23,969 | lean_file_chunk | 81b6977b8eed79c244ac5e2e57ba3dbdc0ae456cb9b5a37211778dd0825a9a2c | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro,
Kim Morrison
-/
module
prelude
public import Init.Data.List.BasicAux
import all Init.Data.Lis... |
23,940 | lean_file_chunk | 1944ea657b1c13431aced356237ba5de91b1add8986ac7dd136ea3c09babceeb | lean_source_file | lean_toolchain_source_file_chunks | @[simp] theorem getElem?_set_self {l : List α} {i : Nat} {a : α} (h : i < l.length) :
(l.set i a)[i]? = some a := by
simp_all
/-- This differs from `getElem?_set_self` by monadically mapping `Function.const _ a` over the `Option`
returned by `l[i]?`. -/
theorem getElem?_set_self' {l : List α} {i : Nat} {a : α} :... |
23,988 | lean_file_chunk | 300a0a376bf6caf075709784dccf80a86d0acc281d75dbef55dcbb46a44eb047 | lean_source_file | lean_toolchain_source_file_chunks | @[simp, grind =] theorem mem_filter : x ∈ filter p as ↔ x ∈ as ∧ p x := by
induction as with
| nil => simp
| cons a as ih =>
by_cases h : p a
· simp_all [or_and_left]
· simp_all [or_and_right]
@[simp] theorem filter_eq_nil_iff {l} : filter p l = [] ↔ ∀ a, a ∈ l → ¬p a := by
simp only [eq_nil_iff_fo... |
23,993 | lean_file_chunk | 16c6020061319105a0289492a120e38a877f5c9a1d180cb039e981cf622e6ab3 | lean_source_file | lean_toolchain_source_file_chunks | theorem eq_nil_or_concat : ∀ l : List α, l = [] ∨ ∃ l' b, l = concat l' b
| [] => .inl rfl
| a::l => match l, eq_nil_or_concat l with
| _, .inl rfl => .inr ⟨[], a, rfl⟩
| _, .inr ⟨l', b, rfl⟩ => .inr ⟨a::l', b, rfl⟩
/-! ### flatten -/
@[simp, grind _=_] theorem length_flatten {L : List (List α)} : L.flatt... |
23,978 | lean_file_chunk | f4f518f15cd91cd72b0b0dcb083e6a8e2e11d6e2851a0d0655cfd9bfcd8fe600 | lean_source_file | lean_toolchain_source_file_chunks | @[simp] theorem reverse_append {as bs : List α} : (as ++ bs).reverse = bs.reverse ++ as.reverse := by
induction as <;> simp_all
grind_pattern reverse_append => (as ++ bs).reverse where
as =/= []
bs =/= []
grind_pattern reverse_append => bs.reverse ++ as.reverse where
as =/= []
bs =/= []
@[simp] theorem reve... |
23,974 | lean_file_chunk | a69903939a625dac80dd380b912e4d63b2ce4f1f2bcdc31e27f97ad15c1e9178 | lean_source_file | lean_toolchain_source_file_chunks | by_cases p a <;> simp_all
grind_pattern mem_partition => a ∈ (partition p l).1
grind_pattern mem_partition => a ∈ (partition p l).2
/-! ### dropLast
`dropLast` is the specification for `Array.pop`, so theorems about `List.dropLast`
are often used for theorems about `Array.pop`.
-/
@[simp, grind =] theorem length_dr... |
1,159 | lean_file_chunk | c7a8250f11ec0155323a0ccfbbbaebdad580291d1dd968213831327658c16f49 | lean_source_file | lean_toolchain_source_file_chunks | theorem get_of_mem {a} {l : List α} (h : a ∈ l) : ∃ n, get l n = a := by
obtain ⟨n, h, e⟩ := getElem_of_mem h
exact ⟨⟨n, h⟩, e⟩
theorem get_mem : ∀ (l : List α) n, get l n ∈ l
| _ :: _, ⟨0, _⟩ => .head ..
| _ :: l, ⟨_+1, _⟩ => .tail _ (get_mem l ..)
theorem mem_iff_get {a} {l : List α} : a ∈ l ↔ ∃ n, get l n ... |
14,657 | lean_file_chunk | 1f7605297c00795ff4ba245a87587d137fadc39596ef5628213f605418357432 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
-/
module
prelude
public import Init.Data.List.Attach
import Init.ByCases
import Init.Data.List.... |
16,313 | lean_file_chunk | 234e31512d2746b41c4dae1f9cfd0a60b666634d04664953d356973ba34cf937 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
-/
module
prelude
public import Init.Data.Subtype.Order
import Init.Data.Order.Lemmas
public imp... |
23,986 | lean_file_chunk | 076d3cfbafcaa6635f9f05575640619179a2264fa542ca29aa2e25250ccb9ec9 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2026 Lean FRO, LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Paul Reichert
-/
module
prelude
public import Init.Data.Order.MinMaxOn
public import Init.Data.List.Lemmas
public import Init.Data.List.TakeDrop
import Init.Data.Order.Lemmas
import In... |
3,916 | lean_file_chunk | db9903cabd8c883bb63cbc086ab7dfb31074a29528e2a595ffee8ee15ff07bf7 | lean_source_file | lean_toolchain_source_file_chunks | ext; simp only [maxOn_eq_minOn]
simp only [List.maxOn?_eq_minOn?, this]
letI : LE β := (inferInstance : LE β).opposite
exact List.minOn?_cons
@[simp]
protected theorem maxOn?_singleton [LE β] [DecidableLE β] {x : α} {f : α → β} :
[x].maxOn? f = some x :=
List.minOn?_singleton (f := f)
@[simp]
protected th... |
10,906 | lean_file_chunk | 14bdcee6de5f932b105c70e816d76b504e5c93afe70a7c690500dcf1ba26ccea | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
module
prelude
public import Init.GetElem
public import Init.WFTactics
import Init.ByCases
import Init.Classical
import Init.Data.Array.Basic
import Init.Da... |
20,247 | lean_file_chunk | 389dcf8c471c5a2f52c14b5ec15081758d1b1b0c62a1a0a42a5058e5295ebb01 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
prelude
import Init.Data.Order.Lemmas
public import Init.Data.BEq
public import Init.Data.Order.Classes
public import Init.Ext
public import Init.NotationExtra
i... |
675 | lean_file_chunk | b19e5221b99ad4677c76b2fe9af08a6501b5ad9d3cf670ffac9242fe7dd87d50 | lean_source_file | lean_toolchain_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
prelude
public import Init.Data.List.Nat.Basic
public import Init.Data.List.Nat.Pairwise
public import Init.Data.List.Nat.Range
public import Init.Data.List.Nat.Subli... |
23,985 | lean_file_chunk | 27e82d9129b64dc353dbe7d5f514fad30b09697c9d511c25c6d8185a1e3d6fe4 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2022 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
module
prelude
import all Init.Data.List.Control
public import Init.Data.List.Monadic
import all Init.Data.Array.Basic
import all Init.Data.Array.Set
import Init.ByC... |
3,386 | lean_file_chunk | 282fd5548007952422d689318b75e2827a866c79c3a9fee2efc586ef0367cfdd | lean_source_file | lean_toolchain_source_file_chunks | simp only [append_assoc, cons_append]
rw [insertIdx_loop_toArray _ _ _ _ (by omega)]
simp only [swap_toArray, w, append_assoc, cons_append, mk.injEq]
rw [take_set_of_le (by omega), drop_eq_getElem_cons (i := j) (by simpa), getElem_set_self,
drop_set_of_lt (by omega), drop_set_of_lt (by omega), getElem... |
248 | lean_file_chunk | c5ab88c024a4bb212969e0a351b1ece5056576457ec144f92780d84d37515498 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2026 Lean FRO, LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Paul Reichert
-/
module
prelude
public import Init.Data.List.Scan.Basic
public import Init.Data.List.Scan.Lemmas |
15,038 | lean_file_chunk | 9a1f3636264c26e728ec8905dbf45b6b27a70b947d85eef34a33bdefd3168209 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
module
prelude
public import Init.Control.Lawful
public section
set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vec... |
3,623 | lean_file_chunk | 211ec62a058a4fe8a80542c14a409dffe65f98ce7d8c517f6d533576a25cb9e4 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2024 François G. Dorais. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: François G. Dorais
-/
module
prelude
import all Init.Data.List.OfFn
public import Init.Data.List.Control
public import Init.Data.List.OfFn
import Init.Data.List.Monadic
public se... |
23,641 | lean_file_chunk | e2349fc80d7fc1ee28f21a52aebb09ab7941d5fa7f57d37db6753ed5c192bef1 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
-/
module
prelude
public import Init.Data.List.Attach
import all Init.Data.List.Control
import I... |
23,718 | lean_file_chunk | 8a6bae655b916dbe8b9250ff90013dbd51c4014958bc9213a187e0f29597b0b5 | lean_source_file | lean_toolchain_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
prelude
import all Init.Data.List.Attach
public import Init.Data.List.Attach
import Init.Data.List.Erase
import Init.... |
23,960 | lean_file_chunk | aced6aeb646f614dddfba4fecf8ba62c022eb7aaabd0a4de76dd7b28f1127a94 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro,
Kim Morrison
-/
module
prelude
public import Init.BinderPredicates
public import Init.Ext
pub... |
23,960 | lean_file_chunk | f0c7dd14c3a466f294f2cdee183ef29d72ff06a5f8a00aeaa210592e206914f5 | lean_source_file | lean_toolchain_source_file_chunks | theorem infix_append_right : l₂ <:+: l₁ ++ l₂ := ⟨l₁, [], by simp⟩
theorem IsPrefix.isInfix : l₁ <+: l₂ → l₁ <:+: l₂ := fun ⟨t, h⟩ => ⟨[], t, h⟩
grind_pattern IsPrefix.isInfix => l₁ <+: l₂, IsInfix
theorem IsSuffix.isInfix : l₁ <:+ l₂ → l₁ <:+: l₂ := fun ⟨t, h⟩ => ⟨t, [], by rw [h, append_nil]⟩
grind_pattern IsSuff... |
5,302 | lean_file_chunk | eb1c766e858ddc52879750624d46177cfebbda66d6133608752fdbf536c19cef | lean_source_file | lean_toolchain_source_file_chunks | right; exact ih.mpr ⟨s', t, List.cons.inj h |>.2⟩
/-
Used internally by the `cbv` tactic.
-/
instance [DecidableEq α] (l₁ l₂ : List α) : Decidable (l₁ <:+: l₂) :=
decidable_of_iff (l₁.isInfixOf_internal l₂) isInfixOf_internal_iff_isInfix
theorem prefix_iff_eq_append : l₁ <+: l₂ ↔ l₁ ++ drop (length l₁) l₂ = l₂ :=... |
23,951 | lean_file_chunk | 734118e5f90e4019fff82deea9bf56a8334d18ea281fbb3881f20e4f672bc2dd | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
module
prelude
public import Init.Data.List.Notation
public import Init.Data.Zero
public import Init.Grind.Tactics
public import Init.SimpLemmas
import Init... |
23,956 | lean_file_chunk | e0ff6258b5983e42c8016b3babb04c0253b22038cede7720dd04241c86106a19 | lean_source_file | lean_toolchain_source_file_chunks | * `List.replicate 5 "five" = ["five", "five", "five", "five", "five"]`
* `List.replicate 0 "zero" = []`
* `List.replicate 2 ' ' = [' ', ' ']`
-/
def replicate : (n : Nat) → (a : α) → List α
| 0, _ => []
| n+1, a => a :: replicate n a
@[simp, grind =] theorem replicate_zero {a : α} : replicate 0 a = [] := rfl
@[g... |
23,988 | lean_file_chunk | 8cf6a69eea68edd2f83d3cecbec2d2640cf67a70b14d60e094609735387757df | lean_source_file | lean_toolchain_source_file_chunks | ["circle", "square", "triangle"].modifyTailIdx 1 (fun xs => xs ++ xs)
```
```output
["circle", "square", "triangle", "square", "triangle"]
```
```lean example
["circle", "square", "triangle"].modifyTailIdx 2 (fun xs => xs ++ xs)
```
```output
["circle", "square", "triangle", "triangle"]
```
```lean example
["circle", "... |
12,201 | lean_file_chunk | 02e3926c9a2fdc7a0eae865f8266aca3749f767db8e784f89f0e00a35be4f27d | lean_source_file | lean_toolchain_source_file_chunks | `List.intersperse` is a similar function that alternates a separator element with the elements of a
list.
Examples:
* `List.intercalate sep [] = []`
* `List.intercalate sep [a] = a`
* `List.intercalate sep [a, b] = a ++ sep ++ b`
* `List.intercalate sep [a, b, c] = a ++ sep ++ b ++ sep ++ c`
-/
noncomputable def inter... |
281 | lean_file_chunk | 9148bd25a603c4741cc2f002b6ed6ccece42e5af98f2cf10d2f85e764a090cb5 | lean_source_file | lean_toolchain_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
prelude
public import Init.Data.List.Sort.Basic
public import Init.Data.List.Sort.Impl
public import Init.Data.List.Sort.Lemmas |
2,275 | lean_file_chunk | f3353114a542893e821fae955ea7e5e5b790b3f2ad9d5bbca770f6082c36e46b | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
module
prelude
public meta import Init.Grind.Tactics
public import Init.Notation
public section
/-!
# Notation for `List` literals.
-/
set_option linter.... |
1,201 | lean_file_chunk | e9cefe733253467f5d054a06332c999233d8763b2eb3426f5f77ee1cea3a1a8d | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2024 Lean FRO. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Henrik Böving
-/
module
prelude
public import Init.Prelude
import Init.Data.List.Basic
public section
set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`... |
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