chars int64 40 24k | content_type stringclasses 9
values | id stringlengths 13 64 | source stringclasses 5
values | subset stringclasses 31
values | text stringlengths 40 24k |
|---|---|---|---|---|---|
23,994 | lean_file_chunk | e3e69bfbfbbe79dc0028a2533d8aa7d0ad711d5af773754297fb0e9dc34e089d | 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.MinMaxOn
import Init.Data.List.Nat.TakeDrop
import Init.ByCases
import Init.Data.Bool
import Init.Data.List.Sublist
import ... |
9,931 | lean_file_chunk | 2a26e6de13f326da6298a7df2ecd00946803789a1dddbdc5b89e96be87f1631c | lean_source_file | lean_toolchain_source_file_chunks | protected theorem maxIdxOn_replicate [LE β] [DecidableLE β] [Refl (α := β) (· ≤ ·)]
{n : Nat} {a : α} {f : α → β} (h : replicate n a ≠ []) :
(replicate n a).maxIdxOn f h = 0 :=
letI : LE β := (inferInstance : LE β).opposite
List.minIdxOn_replicate h
@[simp]
protected theorem minIdxOn?_nil [LE β] [Decidable... |
22,483 | lean_file_chunk | cc5128298761436860b05980418cd555eb9ee2f36e35af7a9891575e01596f42 | 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
-/
module
prelude
public import Init.Ext
import Init.Data.Array.Bootstrap
import Init.Data.Bool
import Init.Data.List.Lemmas
import Init.Data.Option.Lemmas
p... |
17,131 | lean_file_chunk | 4e576cb32f0018fade7398a9fc491e56b77f4eb336ccb9c43e7c42aaf0b28d8f | 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 all Init.Data.List.Basic
public import Init.BinderPredicates
public imp... |
10,878 | lean_file_chunk | 4efe36fcd7edcac9fef259e19b0ab98e324bc37bac9d22ed7e2ad082e8f711f9 | 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.BinderPredicates
public import Init.Ext
public import Init.... |
6,182 | lean_file_chunk | 691fb71787b7c721aae398e88f441c6dec34f526de768ed269f200809a5350a8 | 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: Mario Carneiro, Kim Morrison
-/
module
prelude
public import Init.Data.Fin.Fold
public import Init.NotationExtra
import Init.Data.Fin.Lemmas
import Init.Data.List.Lemmas
import Init.Data.Na... |
254 | lean_file_chunk | 27fec553d048084240ac3dede2f29d9879f9effb94e39a207d86324377f96611 | 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.List.SplitOn.Basic
public import Init.Data.List.SplitOn.Lemmas |
23,923 | lean_file_chunk | 1a44db66084068a12f00fa560fac81fe37a22510bd4965457e627e6bd63bb158 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2023 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.Lemmas -- for dsimping with `getElem?_cons_succ`
public import Init.Data.List.Lemmas
import Init.Data.List.Count
import Ini... |
10,685 | lean_file_chunk | b997d6986dd432d1c1645db098ffd9bdce614f5e52eb761d16457a902c139982 | lean_source_file | lean_toolchain_source_file_chunks | theorem countP_attachWith {p : α → Prop} {q : α → Bool} {l : List α} (H : ∀ a ∈ l, p a) :
(l.attachWith p H).countP (fun a : {x // p x} => q a) = l.countP q := by
simp only [← Function.comp_apply (g := Subtype.val), ← countP_map, attachWith_map_subtype_val]
@[simp, grind =]
theorem count_attach [BEq α] {l : List... |
20,293 | lean_file_chunk | 02b35ca1e300e240f7043599e636df1ff74de682f52ff1145e90517f58414a62 | 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, Mario Carneiro
-/
module
prelude
public import Init.Data.Option.Attach
public import Init.Data.List.OfFn
import Init.ByCases
import Init.Data.Array.Bootstrap
import Init.Data... |
23,941 | lean_file_chunk | 051fd62d6b3a58ca04136c92e5b15bb39964b07e72b7e69a76e62d040cdaccdb | 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,
Yury Kudryashov
-/
module
prelude
public import Init.BinderPredicates
public import Init.Ext
... |
629 | lean_file_chunk | d05913a8200acb3f2cd829a38d634d7149e233e628cd5601e17219378a797e4e | lean_source_file | lean_toolchain_source_file_chunks | -- See also `mem_eraseIdx_iff_getElem` and `mem_eraseIdx_iff_getElem?` in
-- `Init/Data/List/Nat/Basic.lean`.
theorem erase_eq_eraseIdx_of_idxOf [BEq α] [LawfulBEq α]
{l : List α} {a : α} {i : Nat} (w : l.idxOf a = i) :
l.erase a = l.eraseIdx i := by
subst w
rw [erase_eq_iff]
by_cases h : a ∈ l
· right... |
23,976 | lean_file_chunk | bd3dcb397ef8e76dc9c49a0ab685c3798a7bc08a301b6072d346f46fa504089d | 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, Jannis Limperg
-/
module
prelude
import all Init.Data.List.Attach
public import... |
23,975 | lean_file_chunk | 55743c74b2b100aa812fa9943393564628a6d2ba96d6401a2a300670cb8e5c87 | lean_source_file | lean_toolchain_source_file_chunks | exact absurd (@findIdx_getElem _ p xs (Nat.lt_trans f h)) (by simpa using h2 (xs.findIdx p) f)
/-- If `¬ p xs[j]` for all `j ≤ i`, then `i < xs.findIdx p`. -/
theorem lt_findIdx_of_not {p : α → Bool} {xs : List α} {i : Nat} (h : i < xs.length)
(h2 : ∀ j (hji : j ≤ i), ¬p (xs[j]'(Nat.lt_of_le_of_lt hji h))) : i < x... |
3,774 | lean_file_chunk | 070b121c863dd80373d93bc53f592c6a23428f9834b25b0ae22afce8c0293013 | lean_source_file | lean_toolchain_source_file_chunks | theorem lookup_eq_findSome? {l : List (α × β)} {k : α} :
l.lookup k = l.findSome? fun p => if k == p.1 then some p.2 else none := by
induction l with
| nil => rfl
| cons p l ih =>
match p with
| (k', v) =>
simp only [lookup_cons, findSome?_cons]
split <;> simp_all
@[simp, grind =] theorem... |
1,560 | lean_file_chunk | 57a73ee8bf7bde653d80535592c0a3b2cea398983c6845b0fb7a7a9484f0e12c | 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
import Init.Data.String.Search
public import Init.Data.ToString.Basic
import Init.Data.Iterators.Consumers.Collect
public section
open Std
... |
2,320 | lean_file_chunk | 9cd979c8332d86568bf0e0bf2748f33652e749180e39eb145c60326ebcb172d0 | 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.
Author: Leonardo de Moura
-/
module
prelude
import Init.Data.ToString.Name
public import Init.Data.ToString.Basic
import Init.Data.Format.Instances
import Init.Data.Format.Macro
public... |
15,979 | lean_file_chunk | cd9f9017f060aa7f0139a2f85dcd9334d098191f11087027c56f202375afddfb | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2018 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.Int.Basic
public import Init.Data.String.Bootstrap
import Init.Control.State
import Init.Data.Nat.Bitwise.Basic
publ... |
425 | lean_file_chunk | 920debaf7d8e0a986cc1e21c804719fcad9ae94fd78502d34943fd041bf1c31c | 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 meta import Init.Meta
public import Init.Notation
public section
namespace Std
syntax:max "f!" interpolatedStr(term) : term
macro_... |
3,929 | lean_file_chunk | ec3d3bad915418503bd88cfe1cd1c13bc8788a34d90465e223ed44b021d8a9e5 | 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.Repr
import Init.Data.Char.Basic
public section
open Sum Subtype Nat
open Std
/--
Types that can be converted int... |
399 | lean_file_chunk | b645464d2f91e42a2490c06462dd25cd7728598d98d2476f7b86cd4aed5fcc03 | 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 meta import Init.Meta
public import Init.Notation
public section
syntax:max "s!" interpolatedStr(term) : term
macro_rules
| `(s! ... |
5,474 | lean_file_chunk | a312c3e442de48f8b340cea26db59c54f4c76c2dc5c151f9729141b3a13bce06 | 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 and Sebastian Ullrich
-/
module
prelude
public import Init.Data.String.Substring
import Init.Data.String.TakeDrop
import Init.Data.String.Search
/-!
Here we ... |
1,231 | lean_file_chunk | 0ca0b7ca421a9a4b8ebaea1a39a8e36816c93708440255dfd3858ce6a69bc01c | 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.String.Defs
public import Init.Data.Int.Repr
public section
/--
Converts a list into a string, using `ToString.toSt... |
418 | lean_file_chunk | 0dc04f6979d09f54b95fd54ba949879afa8310585c4da98795af1b5c8fcab33e | 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.Hashable
public import Init.Data.String.Defs
public section
namespace String
deriving instance Hashable for String.Pos.Raw
der... |
8,404 | lean_file_chunk | 9c128740dc15fab24e2459b2cc2eecf2d0fffd6ba19de4203cfef219334d4f3d | 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.String.Basic
import Init.Data.String.Lemmas.IsEmpty
import Init.Data.String.Lemmas.Basic
set_option doc.verso true
public sect... |
16,905 | lean_file_chunk | e7616968fc417f969313922d75bc9064f9d87a8dae595b1d7cc555ed8ae79b98 | 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: Henrik Böving, Markus Himmel
-/
module
prelude
public import Init.Data.String.Basic
public import Init.Data.String.FindPos
public import Init.Data.Iterators.Combinators.FilterMap
publi... |
880 | lean_file_chunk | eb64b880991a3827ef571008680b6f0e69aff5336880162014f1e35e5c3819da | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2024 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.Data.String.Lemmas.Splits
public import Init.Data.String.Lemmas.Modify
public import Init.Data.String.Lemmas... |
4,137 | lean_file_chunk | 7deab69ff8e4d2b63e8ca0d49461096c8eab5c8d71e1c9e0a55ead7cfbd765aa | 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, Mario Carneiro
-/
module
prelude
public import Init.Data.String.Basic
/-!
# Legacy string functions
This file contains `String` functions which have since b... |
9,829 | lean_file_chunk | 03f88110ea0dfdffd85277be3a440de24f3a170df58718c49b2ae86990fcb799 | 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, Mario Carneiro
-/
module
prelude
public import Init.Data.String.Termination
import Init.Data.ByteArray.Lemmas
import Init.Data.Char.Lemmas
/-!
# Modification... |
346 | lean_file_chunk | b6bc26680405c3e540264393d031b826190e27da411d9b76237717155b3af4e7 | 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: Henrik Böving
-/
module
prelude
public import Init.Data.String.Pattern.Basic
public import Init.Data.String.Pattern.Char
public import Init.Data.String.Pattern.String
public import Ini... |
837 | lean_file_chunk | b4e01f561a29b2aa1a6e4d9ec216bed59f6f724fc4cfb6ef93f4f6be448b1a43 | 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
public import Init.Data.String.Defs
/-!
# The `ToSlice` typeclass
-/
public section
namespace String
/--
Typeclass for types that have a conversion ... |
23,989 | lean_file_chunk | 34479ff97b1781e4234fe7cff914c58f7f8f684c561460e1fb3cedfdf828cf06 | 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, Mario Carneiro, Markus Himmel
-/
module
prelude
public import Init.Data.String.Decode
public import Init.Data.String.Defs
import Init.Data.ByteArray.Lemmas
im... |
23,982 | lean_file_chunk | f52a9d1bc5162d472ba47dddab8a72ad7cf40e0b3302667b6e9316343b02f755 | lean_source_file | lean_toolchain_source_file_chunks | · exact Or.inl h
· omega
@[simp]
theorem utf8ByteSize_push {s : String} {c : Char} :
(s.push c).utf8ByteSize = s.utf8ByteSize + c.utf8Size := by
simp [← size_toByteArray, List.utf8Encode_singleton]
@[simp]
theorem rawEndPos_push {s : String} {c : Char} : (s.push c).rawEndPos = s.rawEndPos + c := by
simp [... |
23,935 | lean_file_chunk | b9f97878b7157d5431c765ad2a584862fc3ccb65e2e55fb22940ecb44bbc4184 | lean_source_file | lean_toolchain_source_file_chunks | theorem Pos.Raw.isValidForSlice_sliceTo {s : Slice} {p : s.Pos} {off : Pos.Raw} :
off.IsValidForSlice (s.sliceTo p) ↔ off ≤ p.offset ∧ off.IsValidForSlice s := by
refine ⟨fun ⟨h₁, h₂⟩ => ⟨?_, ?_, ?_⟩, fun ⟨h₁, ⟨h₂, h₃⟩⟩ => ⟨?_, ?_⟩⟩
· simpa using h₁
· simp only [Slice.rawEndPos_sliceTo] at h₁
exact Pos.Ra... |
23,959 | lean_file_chunk | 1ff776542fd67e078d80a02e983099475437d66a8df22cffd14336184be77745 | lean_source_file | lean_toolchain_source_file_chunks | theorem Slice.Pos.offset_cast {s t : Slice} {pos : s.Pos} {h : s.copy = t.copy} :
(pos.cast h).offset = pos.offset := (rfl)
@[simp]
theorem Slice.Pos.cast_rfl {s : Slice} {pos : s.Pos} : pos.cast rfl = pos :=
Slice.Pos.ext (by simp)
@[simp]
theorem Slice.Pos.cast_le_cast_iff {s t : Slice} {pos pos' : s.Pos} {h ... |
23,984 | lean_file_chunk | db955a1e4e9709561a19bb0406d933252d701b5152686cbc084bf6b0238f43d8 | lean_source_file | lean_toolchain_source_file_chunks | {q r : (s.sliceTo p).Pos} : Pos.ofSliceTo q < Pos.ofSliceTo r ↔ q < r := by
simp [Pos.lt_iff, Slice.Pos.lt_iff, Pos.Raw.lt_iff]
@[simp]
theorem Pos.ofSliceTo_le_ofSliceTo_iff {s : String} {p : s.Pos}
{q r : (s.sliceTo p).Pos} : Pos.ofSliceTo q ≤ Pos.ofSliceTo r ↔ q ≤ r := by
simp [Pos.le_iff, Slice.Pos.le_iff,... |
5,464 | lean_file_chunk | 7e04e4d6b48fca5d5e87d4d4ea26eee1b979d4ba2443940da324151ee0058b1e | lean_source_file | lean_toolchain_source_file_chunks | * `"L∃∀N".offsetOfPos ⟨2⟩ = 2`
* `"L∃∀N".offsetOfPos ⟨4⟩ = 2`
* `"L∃∀N".offsetOfPos ⟨5⟩ = 3`
* `"L∃∀N".offsetOfPos ⟨50⟩ = 4`
-/
@[inline] def Pos.Raw.offsetOfPos (s : String) (pos : Pos.Raw) : Nat :=
offsetOfPosAux s pos 0 0
@[deprecated String.Pos.Raw.offsetOfPos (since := "2025-11-17")]
def offsetOfPos (s : String... |
3,947 | lean_file_chunk | dbd412109c820ebf2134e970570670d6615c290e0fbbd7b80de884a6d465705b | 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.String.Defs
public import Init.Grind.ToInt
public import Init.Data.Order.Classes
import Init.Data.Order.PackageFactories
import I... |
6,487 | lean_file_chunk | 4eba2222b904cefc28338347bf5d54e18dd6fd721f02d5781e88c324e7739089 | 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, Mario Carneiro
-/
module
prelude
public import Init.Data.ByteArray.Bootstrap
import Init.Data.Char.Basic
public section
namespace String
instance : OfNat S... |
21,447 | lean_file_chunk | 15320fae3a0ca0e255dd83422c76130411eebf38ccd3866ae36e410312f534d1 | 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, Mario Carneiro
-/
module
prelude
public import Init.Data.String.Slice
import Init.Data.Option.BasicAux
/-!
# The `Substring` type
This file contains API for... |
22,630 | lean_file_chunk | 5d81fa180101d834220d12f605d067a370bf1dacd566f6b73b2cca952895797d | 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, Mario Carneiro
-/
module
prelude
public import Init.Data.String.PosRaw
import Init.Data.ByteArray.Lemmas
import Init.Omega
/-!
# Preliminary developments for... |
14,000 | lean_file_chunk | 6f7d2a945d23d98df477ca81efb92ad65cd83fbc13eb09645dc27da07a3b6bd6 | 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, Mario Carneiro
-/
module
prelude
public import Init.Data.ByteArray.Basic
import Init.Data.Nat.Simproc
import Init.Omega
/-!
# Arithmetic of `String.Pos.Raw`
... |
18,928 | lean_file_chunk | 8177d08e4e497f3e0a49e773c57cda251cc0b38c1b6b9d8e4c091bcf1911e41d | 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
public import Init.Data.String.Slice
import Init.Data.Iterators.Consumers.Collect -- shake: keep (used in verso)
set_option doc.verso true
/-!
# Stri... |
20,054 | lean_file_chunk | 63acc328e449a2397dddab10fe1d4e2b31bfa861d20351b0a38754a8e056bce6 | 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, Mario Carneiro, Markus Himmel
-/
module
prelude
public import Init.Data.String.Substring
set_option doc.verso true
/-!
# `String.take` and variants
This fi... |
5,257 | lean_file_chunk | abdca23a906e810c7c45b2e0a2fd05057682c084f60019579e1039c40e1e58e1 | 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
public import Init.Data.String.Basic
import Init.Omega
import Init.Data.String.OrderInstances
import Init.Data.String.Lemmas.Basic
set_option doc.verso... |
10,372 | lean_file_chunk | 0e2c97b8b03f5b88ba8ca1aa74d989639dc6b723cedcf8b6dc9640c5663884ba | 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.String.Lemmas.Splits
public import Init.Data.String.FindPos
import Init.Data.Option.Lemmas
import Init.Omega
import Init.ByCases
... |
257 | lean_file_chunk | 62241f736b76efd77628b4b756c36009897064c441bc0bc85e55a6341c518bf2 | 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.String.Iter.Basic
public import Init.Data.String.Iter.Intercalate |
11,209 | lean_file_chunk | 527931a2b4f765267042e57cd2423a5929f05a8667815b38b333ad7269c16650 | 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, Mario Carneiro
-/
module
prelude
public import Init.Data.String.Modify
/-!
# `String.Iterator`
This file contains `String.Iterator`, an outgoing API to be r... |
23,983 | lean_file_chunk | c083f7a0eeb5ef206a6520c583943e4b48dbed72c6daa720e6ab9102489242e5 | 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: Henrik Böving, Markus Himmel
-/
module
prelude
public import Init.Data.String.Pattern
public import Init.Data.Ord.Basic
public import Init.Data.Iterators.Combinators.FilterMap
public i... |
21,031 | lean_file_chunk | 736a35c09d96f50c34ae1a3fc4e55fe00bf8ff98849aef8a28673699d933422a | lean_source_file | lean_toolchain_source_file_chunks | | ⟨.operating _ s⟩, .yield ⟨.atEnd ..⟩ _ => True
| ⟨.operating _ s⟩, .skip ⟨.operating _ s'⟩ => s'.IsPlausibleSuccessorOf s
| ⟨.operating _ s⟩, .skip ⟨.atEnd ..⟩ => False
| ⟨.operating _ s⟩, .done => True
| ⟨.atEnd⟩, .yield .. => False
| ⟨.atEnd⟩, .skip _ => False
| ⟨.atEnd⟩, .done => True
ste... |
4,664 | lean_file_chunk | 538726bdd5c17d28f91713c89f62dfd6848a774211868491cdb6786c3cb7fff8 | 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
import all Init.Data.ByteArray.Basic
public import Init.Data.String.Basic
import all Init.Data.String.Basic
import Init.Data.String.Search
im... |
23,994 | lean_file_chunk | b242962fe987cb9cf183c463d924802d9f119563d4c3a63ae02a6b7d6d390d10 | 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
import Init.Data.Char.Lemmas
public import Init.Data.ByteArray.Basic
import Init.Data.ByteArray.Lemmas
public import Init.Data.UInt.Basic
import Init.Dat... |
23,951 | lean_file_chunk | 9d894c53f6bc0762efc36f18903ef3ba0adf26e0835b2939f2e593a862652c3b | lean_source_file | lean_toolchain_source_file_chunks | simp only [assemble₁, Option.some.injEq]
rintro rfl
rfl
theorem val_assemble₁_le {w : UInt8} {h} {c : Char} (h' : assemble₁ w h = some c) : c.val ≤ 127 := by
have := toBitVec_val_assemble₁ h'
have hx := helper₅ h
simp only [UInt8.lt_iff_toNat_lt, UInt8.reduceToNat] at hx
rw [UInt32.le_iff_toBitVec_le, this... |
23,926 | lean_file_chunk | 549a9b9f689b9111363e004a920f7702dcf360d0af05ef0e8035cc82d9749298 | lean_source_file | lean_toolchain_source_file_chunks | have hc : c.utf8Size = 4 := String.length_utf8EncodeChar _ ▸ h₀
obtain ⟨rfl, rfl, rfl, rfl⟩ :
w = (String.utf8EncodeChar c)[0] ∧ x = (String.utf8EncodeChar c)[1] ∧ y = (String.utf8EncodeChar c)[2]
∧ z = (String.utf8EncodeChar c)[3] := by simp [h]
refine ⟨parseFirstByte_utf8EncodeChar_eq_threeMore... |
1,924 | lean_file_chunk | 0079296c77ba1fc9aac483dbfef0173e2f0ef727bb66f6b7dea709fff1bf6293 | lean_source_file | lean_toolchain_source_file_chunks | public theorem ByteArray.isUTF8FirstByte_of_isSome_utf8DecodeChar? {b : ByteArray} {i : Nat}
(h : (utf8DecodeChar? b i).isSome) : (b[i]'(lt_size_of_isSome_utf8DecodeChar? h)).IsUTF8FirstByte := by
rw [utf8DecodeChar?_eq_utf8DecodeChar?_extract] at h
suffices ((b.extract i b.size)[0]'
(by simpa using lt_si... |
482 | lean_file_chunk | 53cfa93e46c90da2a22196c148b5ee4c5798033522a71053d69f3f3066d1f30f | 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: Sebastian Ullrich, Andrew Kent, Leonardo de Moura
-/
module
prelude
public import Init.Data.String.Basic
public import Init.Data.Stream
public instance : Std.Stream Substring.... |
1,153 | lean_file_chunk | a2a44baea207b63cca7b1e985d21341386a6c30b49ecd728f0019fb0111796fe | 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, Paul Reichert, Robin Arnez
-/
module
prelude
public import Init.Data.Order.Ord
public import Init.Data.String.Basic
import Init.Data.Char.Lemmas
import Init.Data.String.... |
734 | lean_file_chunk | dae11647e2782f231ecc76910ee14610fa18b2d09dca87e5910dba2ee8f99b29 | 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, Paul Reichert, Robin Arnez
-/
module
prelude
public import Init.Data.Order.Ord
import Init.Data.BitVec.Lemmas
public section
/-!
# Instances for strings.
-/
set_opti... |
3,580 | lean_file_chunk | 706894b3a23bb0dcd6ccbeffdcaa8c2e8ca1cacc64900955cf793fa277442877 | 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, Paul Reichert, Robin Arnez
-/
module
prelude
public import Init.Data.Order.Ord
public import Init.Data.Order.ClassesExtra
public import Init.Data.SInt.Basic
import Init.... |
23,952 | lean_file_chunk | d39e4faa6670383f4c42b1f11a1a7daecad910fc89aebe094eece6942364cfc6 | 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: Dany Fabian, Sebastian Ullrich
-/
module
prelude
import Init.ByCases
import Init.Ext
public import Init.PropLemmas
public import Init.Data.Char.Basic
import Init.Classical
pub... |
1,333 | lean_file_chunk | 78333f31614f1c5378baf81ca0aee4a725d7b0d125e7711580b25b724e30346d | lean_source_file | lean_toolchain_source_file_chunks | and that returns `Ordering.gt` when `ord` would return `Ordering.lt`.
-/
@[expose, implicit_reducible] protected def opposite (ord : Ord α) : Ord α where
compare x y := ord.compare y x
/--
Constructs an `Ord` instance that compares values according to the results of `f`.
In particular, `ord.on f` compares `x` and `... |
2,760 | lean_file_chunk | af1d348c73d0fefdbdd4b7aa18ca2194a63fffed9f0d13b9e279b9926ddc955f | 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, Paul Reichert, Robin Arnez
-/
module
prelude
public import Init.Data.Order.Ord
public import Init.Data.Vector.Basic
import Init.Data.Vector.Lemmas
public section
/-!
#... |
2,610 | lean_file_chunk | 24c75673b1e6b2c9d40daaa82bca5a35bb7af0d5100af06dbadda1dff63f5049 | 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, Paul Reichert, Robin Arnez
-/
module
prelude
public import Init.Data.Ord.Basic
import Init.Omega
import Init.ByCases
import Init.Data.Array.Basic
import Init.WFTactics
... |
3,630 | lean_file_chunk | b267cdff50a575293d2ad7b05c5bff168409b64fec48b33fb94b619b6f4b1a02 | 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, Paul Reichert, Robin Arnez
-/
module
prelude
public import Init.Data.Order.Ord
public import Init.Data.Order.ClassesExtra
public import Init.Data.UInt.Basic
import Init.... |
4,020 | lean_file_chunk | 01de438f1231391f659feb617309ba2116dddc0d57e5ce6f6530506a28fadf74 | 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.Data.Range.Basic
import all Init.Data.Range.Basic
public import Init.Data.List.Control
import Init.Data.List.Monadic
import Init.Data.... |
3,288 | lean_file_chunk | 69aa0e8d399b15c64bd410bd67ab4777b86c9ab56d1ec1257ed530afa762e93d | 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
-/
module
prelude
public import Init.Control.Basic
public import Init.Grind.Tactics
public meta import Init.Grind.Tactics
import Init.Omega
import Init.WFTact... |
1,663 | lean_file_chunk | 762f1dbdaaeb3afbcf9be3bbc127787afc92405e8fc1511ee648ba4f1cc91fcd | 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.Range.Polymorphic.Basic
public import Init.Data.Range.Polymorphic.Iterators
public import Init.Data.Range.Polymorphic.Stream
pub... |
23,966 | lean_file_chunk | b4d2987ba88261ae5272c10ac6f24abcc8a966df5374bbf8f8d07920e275e296 | 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.UInt.Basic
import all Init.Data.BitVec.Basic
import all Init.Data.BitVec.Lemmas
import all Init.Data.SInt.Basic
public import Init.... |
23,982 | lean_file_chunk | ed87b179ad0dc387f09fe65917d33770eb1f8837208a97f8b901666373ce17a3 | lean_source_file | lean_toolchain_source_file_chunks | instance : Std.IdempotentOp (α := Int32) (· ||| ·) := ⟨fun _ => Int32.or_self⟩
instance : Std.IdempotentOp (α := Int64) (· ||| ·) := ⟨fun _ => Int64.or_self⟩
instance : Std.IdempotentOp (α := ISize) (· ||| ·) := ⟨fun _ => ISize.or_self⟩
@[simp] protected theorem Int8.or_zero {a : Int8} : a ||| 0 = a := Int8.toBitVec_i... |
9,388 | lean_file_chunk | c46334eef2270511c6a5367dcff731c791965fdce8416b3a7ade5d8237b11298 | lean_source_file | lean_toolchain_source_file_chunks | @[simp] theorem Int64.not_ne_self {a : Int64} : ~~~a ≠ a := by simp [← Int64.toBitVec_inj]
@[simp] theorem ISize.not_ne_self {a : ISize} : ~~~a ≠ a := by simp [← ISize.toBitVec_inj]
theorem Int8.not_xor {a b : Int8} : ~~~a ^^^ b = ~~~(a ^^^ b) := by
simp [← Int8.toBitVec_inj, BitVec.not_xor_left]
theorem Int16.not_x... |
4,686 | lean_file_chunk | 2fd861f34854e85ce73bad3cb0d503cbc87c76a0a1cca132b95f4c6a89765294 | 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
public import Init.Data.Float32
public import Init.Data.SInt.Basic
public section
set_option linter.missingDocs true
/--
Truncates a floating-point n... |
4,343 | lean_file_chunk | 46d69646a191f4f8578265da694c98c5c29d188c5e7d2afd451f00ee30dc5ad5 | 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
public import Init.Data.Float
public import Init.Data.SInt.Basic
public section
set_option linter.missingDocs true
/--
Truncates a floating-point num... |
23,929 | lean_file_chunk | 1d3598e2b7a437e5771a523db4f440c09d3d721831ff1d6c58d16f2fd1385229 | 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.Nat.Bitwise.Basic
public import Init.Data.SInt.Basic
import all Init.Data.SInt.Basic
import all Init.Data.BitVec.Basic
import all I... |
23,975 | lean_file_chunk | 315d8ad50d1c5f739183703074d149bef0fc57b815bffd452274217ad8a116a3 | lean_source_file | lean_toolchain_source_file_chunks | rw [minValue, toInt_ofInt_of_two_pow_numBits_le] <;> cases System.Platform.numBits_eq
<;> simp_all
theorem ISize.le_toInt_maxValue : 2 ^ 31 - 1 ≤ ISize.maxValue.toInt := by
rw [maxValue, toInt_ofInt_of_two_pow_numBits_le] <;> cases System.Platform.numBits_eq
<;> simp_all
theorem Int8.iSizeMinValue_le_toInt ... |
23,966 | lean_file_chunk | 52e90a031fd66047f4c28a923d385198f66d02c5b9636ef0eeff9c2eab4eb4ae | lean_source_file | lean_toolchain_source_file_chunks | @[simp] theorem ISize.ofInt_int64ToInt (x : Int64) : ISize.ofInt x.toInt = x.toISize := (rfl)
@[simp] theorem Int8.toInt_ofIntLE {x : Int} {h₁ h₂} : (ofIntLE x h₁ h₂).toInt = x := by
rw [ofIntLE, toInt_ofInt_of_le h₁ (Int.lt_of_le_sub_one h₂)]
@[simp] theorem Int16.toInt_ofIntLE {x : Int} {h₁ h₂} : (ofIntLE x h₁ h₂)... |
23,924 | lean_file_chunk | b7952deb0c3c74d4dd089ac32e3ac760b13c11ccd86b87818aec45ac61b2dd06 | lean_source_file | lean_toolchain_source_file_chunks | @[simp] theorem Int64.toNatClampNeg_ofBitVec (b) : (Int64.ofBitVec b).toNatClampNeg = b.toInt.toNat := (rfl)
@[simp] theorem ISize.toNatClampNeg_ofBitVec (b) : (ISize.ofBitVec b).toNatClampNeg = b.toInt.toNat := (rfl)
theorem Int8.toNatClampNeg_ofInt_of_le {n : Int} (h₁ : -2 ^ 7 ≤ n) (h₂ : n < 2 ^ 7) :
(Int8.ofInt... |
23,919 | lean_file_chunk | 992f83d32f760a4359891f44b483cce3ba1f750e3cc07f7c6c9b0fde321c28eb | lean_source_file | lean_toolchain_source_file_chunks | @[simp] theorem Int16.toInt32_ofBitVec (b) : (Int16.ofBitVec b).toInt32 = Int32.ofBitVec (b.signExtend _) := (rfl)
@[simp] theorem Int16.toInt64_ofBitVec (b) : (Int16.ofBitVec b).toInt64 = Int64.ofBitVec (b.signExtend _) := (rfl)
@[simp] theorem Int16.toISize_ofBitVec (b) : (Int16.ofBitVec b).toISize = ISize.ofBitVec (... |
23,961 | lean_file_chunk | d9067180d602db67c8816044b27e991dffeea9d70ba09de3ff2eceb3586efd2b | lean_source_file | lean_toolchain_source_file_chunks | theorem Int8.toInt16_div_of_ne_right (a b : Int8) (hb : b ≠ -1) : (a / b).toInt16 = a.toInt16 / b.toInt16 :=
Int16.toInt_inj.1 (by rw [toInt_toInt16, toInt_div_of_ne_right _ _ hb,
Int16.toInt_div_of_ne_right _ _ (b.toInt16_ne_neg_one hb), toInt_toInt16, toInt_toInt16])
theorem Int8.toInt32_div_of_ne_right (a b : ... |
23,895 | lean_file_chunk | 0c8697d5033b7fd5f2c18fcc4c3a5f2d4ec49ee89273b4fa211150d4a70951f5 | lean_source_file | lean_toolchain_source_file_chunks | @[simp] theorem Int64.ofNat_mul (a b : Nat) : Int64.ofNat (a * b) = Int64.ofNat a * Int64.ofNat b := by
simp [← Int64.ofInt_eq_ofNat]
@[simp] theorem ISize.ofNat_mul (a b : Nat) : ISize.ofNat (a * b) = ISize.ofNat a * ISize.ofNat b := by
simp [← ISize.ofInt_eq_ofNat]
theorem Int8.ofIntLE_mul {a b : Int} {hab₁ hab₂... |
23,973 | lean_file_chunk | 5d35f15354deb15913d9d90751090e509cab51a14a65ed1d28a9a9472fed9e5b | lean_source_file | lean_toolchain_source_file_chunks | @[simp] protected theorem Int16.sub_zero (a : Int16) : a - 0 = a := Int16.toBitVec_inj.1 (BitVec.sub_zero _)
@[simp] protected theorem Int32.sub_zero (a : Int32) : a - 0 = a := Int32.toBitVec_inj.1 (BitVec.sub_zero _)
@[simp] protected theorem Int64.sub_zero (a : Int64) : a - 0 = a := Int64.toBitVec_inj.1 (BitVec.sub_z... |
23,985 | lean_file_chunk | 6bf1a5902561e730c0be02e4da8314f50382019b6156d0d4800b966488bd16b1 | lean_source_file | lean_toolchain_source_file_chunks | protected theorem Int16.neg_mul_comm (a b : Int16) : -a * b = a * -b := Int16.toBitVec_inj.1 (BitVec.neg_mul_comm _ _)
protected theorem Int32.neg_mul_comm (a b : Int32) : -a * b = a * -b := Int32.toBitVec_inj.1 (BitVec.neg_mul_comm _ _)
protected theorem Int64.neg_mul_comm (a b : Int64) : -a * b = a * -b := Int64.toBi... |
23,906 | lean_file_chunk | 44c4539e0ce9c2d87b0da4cca418d411476353da2ba1276ad8cd9410d653c4ff | lean_source_file | lean_toolchain_source_file_chunks | theorem Int8.neg_eq_neg_one_mul (a : Int8) : -a = -1 * a := Int8.toInt_inj.1 (by simp)
theorem Int16.neg_eq_neg_one_mul (a : Int16) : -a = -1 * a := Int16.toInt_inj.1 (by simp)
theorem Int32.neg_eq_neg_one_mul (a : Int32) : -a = -1 * a := Int32.toInt_inj.1 (by simp)
theorem Int64.neg_eq_neg_one_mul (a : Int64) : -a = -... |
3,952 | lean_file_chunk | db2e4028e656720d5207b84c390be355692df98e10dc8b044d487ddd87057839 | lean_source_file | lean_toolchain_source_file_chunks | (hb₁ : minValue.toInt ≤ b) (hb₂ : b ≤ maxValue.toInt) : ISize.ofInt (a.tmod b) = ISize.ofInt a % ISize.ofInt b := by
rw [ISize.ofInt_eq_iff_bmod_eq_toInt, ← toInt_bmod_size, toInt_mod, toInt_ofInt, toInt_ofInt,
Int.bmod_eq_of_le (n := a), Int.bmod_eq_of_le (n := b)]
· exact le_of_eq_of_le (by cases System.Platf... |
23,992 | lean_file_chunk | 718349e6a0619cb7da9bce6c4c727d2d04a34dfbd810fdfe6ca1b9369956552c | 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: Henrik Böving
-/
module
prelude
public import Init.Data.UInt.Basic
public import Init.Data.ToString.Extra
@[expose] public section
set_option linter.missingDocs true
/-!
This module... |
23,942 | lean_file_chunk | 63fe1bc7edf2b888b8eec013c7cb2daf23a5d68cbafce63f2ba56b0c64dbf810 | lean_source_file | lean_toolchain_source_file_chunks | Computes the absolute value of a 16-bit signed integer.
This function is equivalent to `if a < 0 then -a else a`, so in particular `Int16.minValue` will be
mapped to `Int16.minValue`.
This function is overridden at runtime with an efficient implementation.
-/
@[extern "lean_int16_abs"]
protected def Int16.abs (a : In... |
23,436 | lean_file_chunk | 15f2e9a9da8f4a00dbb34b2c0f30fe91ce5933850a11d9441169abdd211869d8 | lean_source_file | lean_toolchain_source_file_chunks | protected def Int64.add (a b : Int64) : Int64 := ⟨⟨a.toBitVec + b.toBitVec⟩⟩
/--
Subtracts one 64-bit signed integer from another, wrapping around on over- or underflow. Usually
accessed via the `-` operator.
This function is overridden at runtime with an efficient implementation.
-/
@[extern "lean_int64_sub"]
protect... |
10,968 | lean_file_chunk | b2a0192548fc9448e4627b3427679a423beb1d6ebd74e1e1f3af8f45df475591 | 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
import all Init.Data.Array.Basic
import all Init.Data.Vector.Basic
public import Init.Data.Function
public import Init.Data.Vector.Basic
import Init.Data... |
9,475 | lean_file_chunk | 805c936ea68532470437753ec4516b800ae113818fd48dd5ce359a596d1602cf | 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
import all Init.Data.Array.Count
import all Init.Data.Vector.Basic
public import Init.BinderPredicates
public import Init.Data.Vector.Basic
import Init.D... |
1,089 | lean_file_chunk | 56770a5fa27fde8968640922f91fc07954892e796eec7686bfb0c2f983a3a9ca | 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: Kim Morrison, Sebastian Graf, Paul Reichert
-/
module
prelude
public import Init.Data.Vector.Basic
import Init.Data.Array.Int
import Init.Data.Int.Lemmas
import Init.Data.Vector.Lemmas... |
23,993 | lean_file_chunk | 2656778d87a20daa7fd9bef8aede205942fa24e662edfb78c5e7c2457c9737d1 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2024 Shreyas Srinivas. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shreyas Srinivas, Francois Dorais, Kim Morrison
-/
module
prelude
import all Init.Data.Array.Basic
public import Init.Data.Vector.Basic
import all Init.Data.Vector.Basic
public impo... |
23,978 | lean_file_chunk | 5332286aed18b0ef6123ea1aae28d04d253fafad2394ecdaa62616d803a5e36f | lean_source_file | lean_toolchain_source_file_chunks | (xs.mapFinIdx f).toList =
xs.toList.mapFinIdx (fun i a h => f i a (by simpa [xs.size_toArray] using h)) := by
simp [toList]
theorem toList_ofFn {f : Fin n → α} : (Vector.ofFn f).toList = List.ofFn f := by simp [toList]
theorem toList_pop {xs : Vector α n} : xs.pop.toList = xs.toList.dropLast := by simp [toLis... |
23,993 | lean_file_chunk | 1071b66df08b235eeb6f2b56277e78383ae4d146de70a7965c9786ceda68a2ee | lean_source_file | lean_toolchain_source_file_chunks | rcases as with ⟨as, rfl⟩
simp
@[simp] theorem contains_push [BEq α] {xs : Vector α n} {a : α} {b : α} :
(xs.push a).contains b = (xs.contains b || b == a) := by
rcases xs with ⟨xs, rfl⟩
simp [Array.contains_push]
/-! ### set -/
@[grind =] theorem getElem_set {xs : Vector α n} {i : Nat} {x : α} (hi : i < n)... |
23,981 | lean_file_chunk | 69266f6663d4b5eddfa183eafbde457452c0334d99bd4852f599cbd674009f2e | lean_source_file | lean_toolchain_source_file_chunks | xss[i / m][i % m] := by
rcases xss with ⟨⟨l⟩, rfl⟩
simp only [flatten_mk, List.map_toArray, getElem_mk, List.getElem_toArray, Array.flatten_toArray]
induction l generalizing i with
| nil => simp at hi
| cons xs l ih =>
simp only [List.map_cons, List.map_map, List.flatten_cons, toList_toArray]
by_cases... |
22,531 | lean_file_chunk | 72c7fe1732959c310a574a0c5440c0058430d4ee402009d969cebdd62cc2dc1e | lean_source_file | lean_toolchain_source_file_chunks | xs.foldr op (op a₁ a₂) = op (xs.foldr op a₁) a₂ := by
rcases xs with ⟨xs, rfl⟩
simp [Array.foldr_assoc]
-- The argument `f : α₁ → α₂` is intentionally explicit, as it is sometimes not found by unification.
theorem foldl_hom (f : α₁ → α₂) {g₁ : α₁ → β → α₁} {g₂ : α₂ → β → α₂} {xs : Vector β n} {init : α₁}
(H : ... |
2,010 | lean_file_chunk | 11a3ebe3278756d26f375da2e5d3b2083936242b0f94e4fa013de32009dad85d | 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.Vector.Basic
import Init.Data.Vector.Lemmas
public section
set_option linter.listVariables true -- Enforce naming conventions f... |
4,611 | lean_file_chunk | 83cad0f146c9f63577ba6d3ec16cc61e8b6a41496548841bd36be9226eb1ec6d | 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.Vector.Basic
import Init.Data.Array.InsertIdx
import Init.Data.Vector.Lemmas
import Init.Omega
public section
/-!
# insertIdx
... |
11,009 | lean_file_chunk | d58fe7a831cde98711a8f6488c097e8673156ff7cb24cacee7e7550a5bb0f596 | 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 all Init.Data.Vector.Basic
import all Init.Data.Array.Lex.Basic
import Init.Data.Range.Polymorphic.Lemmas
public import Init.Data.Array.Lex.Basic
... |
6,578 | lean_file_chunk | 104d4ae413bd1934604eba692af3c613942055d18d01f67af6301077778cfd6a | 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.Vector.Basic
import Init.ByCases
import Init.Data.Array.Bootstrap
import Init.Data.Array.Extract
import Init.Data.Vector.Lemmas
i... |
1,427 | lean_file_chunk | 6f2f935241f4c00c6cf72653b966d6b4decb71b6973fb753e493dd090065f15c | 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: Kim Morrison, Sebastian Graf, Paul Reichert
-/
module
prelude
public import Init.Data.Vector.Basic
import Init.Data.Array.Nat
public import Init.BinderPredicates
import Init.Data.Vecto... |
1,474 | lean_file_chunk | be7e480c88818f517dea16ca084629bbfb5767592c036b1ccc9be9f4ae210433 | 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
public import Init.Data.Vector.Basic
import Init.Data.Fin.Lemmas
import Init.Data.Vector.Lemmas
import Init.Data.Vector.OfFn
import Init.Omega... |
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