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 |
|---|---|---|---|---|---|
18,131 | lean_file_chunk | 4b02b92bcb3d6f0d9cd49f19284af5c05699e85c94e8dd224dd080bdea8710df | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2025 Robin Arnez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robin Arnez
-/
module
prelude
public import Std.Data.DHashMap.Lemmas
import all Std.Data.DHashMap.Lemmas
public section
/-!
# Extensional dependent hash maps
This file develops the ty... |
23,975 | lean_file_chunk | 01be1fb17c0abd37cad71bd87219a16dba0ab0b92e64c189c3d2496d1e67f06c | 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: Markus Himmel
-/
module
prelude
public import Std.Data.ExtHashMap.Lemmas
public import Std.Data.ExtHashSet.Basic
@[expose] public section
/-!
# Extensional hash set lemmas
This modu... |
17,369 | lean_file_chunk | 2976bd9283a1c5b8491bda4d22483511d089e6131734d8d25c194e6ee8aa8415 | lean_source_file | lean_toolchain_source_file_chunks | ExtHashMap.getKey_unitOfList_of_mem k_beq distinct mem
theorem get!_ofList_of_contains_eq_false [EquivBEq α] [LawfulHashable α]
[Inhabited α] {l : List α} {k : α}
(contains_eq_false : l.contains k = false) :
get! (ofList l) k = default :=
ExtHashMap.getKey!_unitOfList_of_contains_eq_false contains_eq_fal... |
9,938 | lean_file_chunk | e7fc56c77426c4ace54ab00c70b5d284746c89a28bacc21ebec82820e916e981 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2025 Robin Arnez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robin Arnez
-/
module
prelude
public import Std.Data.ExtHashMap.Basic
@[expose] public section
/-!
# Extensional hash sets
This module develops the type `Std.ExtHashSet` of extensiona... |
510 | lean_file_chunk | ff1d7eeff0d14feecdb6535bf6af48fe41ec1c267d9013cc86d713fa181eb94c | 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: Wojciech Różowski
-/
module
prelude
public import Std.Data.HashMap.DecidableEquiv
public import Std.Data.HashSet.Basic
public section
/-!
# Decidable equivalence for `HashSet`
-/
na... |
23,956 | lean_file_chunk | d4bae6e2f2cb254008866420f22806c1da281f47ae466ad5d2b64c002caed5a1 | 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: Markus Himmel
-/
module
prelude
public import Std.Data.HashMap.Lemmas
public import Std.Data.HashSet.Basic
@[expose] public section
/-!
# Hash set lemmas
This module contains lemmas... |
23,989 | lean_file_chunk | 0108b4629f77a4dfbe67fab187b4c58378bc3af8f5248ac4a6dddd3aea9c8036 | lean_source_file | lean_toolchain_source_file_chunks | k ∈ insertMany m l ↔ k ∈ m ∨ l.contains k :=
HashMap.mem_insertManyIfNewUnit_list
theorem mem_of_mem_insertMany_list [EquivBEq α] [LawfulHashable α]
{l : List α} {k : α} (contains_eq_false : l.contains k = false) :
k ∈ insertMany m l → k ∈ m :=
HashMap.mem_of_mem_insertManyIfNewUnit_list contains_eq_false
... |
8,850 | lean_file_chunk | 60fa256d8e8090c2ef3f3fe012e17c39c9b5ab68848a4d18a85691660861efbe | lean_source_file | lean_toolchain_source_file_chunks | HashMap.getKey?_unitOfList_of_mem k_beq distinct mem
theorem get_ofList_of_mem [EquivBEq α] [LawfulHashable α]
{l : List α}
{k k' : α} (k_beq : k == k')
(distinct : l.Pairwise (fun a b => (a == b) = false))
(mem : k ∈ l) {h} :
get (ofList l) k' h = k :=
HashMap.getKey_unitOfList_of_mem k_beq dist... |
11,811 | lean_file_chunk | 57804b8e7764e70b988bd355c5057b35c47552db66924a475b4c4885cf701bef | 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: Markus Himmel
-/
module
prelude
public import Std.Data.HashMap.Basic
@[expose] public section
/-!
# Hash sets
This module develops the type `Std.HashSet` of hash sets.
Lemmas about... |
23,976 | lean_file_chunk | 53efec44981e5629a3565b7dab1a7fdd460fbe00bd90829412b6292c813a75cf | 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: Markus Himmel
-/
module
prelude
public import Std.Data.HashMap.RawLemmas
public import Std.Data.HashSet.Raw
@[expose] public section
/-!
# Hash set lemmas
This module contains lemma... |
23,949 | lean_file_chunk | 7f74f25efe4e294d95ef10c68325f3e9f7ab08bf17b2eb29da870a8129f9eace | lean_source_file | lean_toolchain_source_file_chunks | theorem any_eq_false_iff_forall_mem [LawfulBEq α] {p : α → Bool} (h : m.WF) :
m.any p = false ↔
∀ (a : α), a ∈ m → p a = false := by
simpa using @HashMap.Raw.any_eq_false_iff_forall_mem_getElem _ _ _ _ _ _ (fun a b => p a) h.out
@[simp]
theorem all_toList [LawfulHashable α] [EquivBEq α] {p : α → Bool} (h :... |
17,207 | lean_file_chunk | 63d72811850d0b02687d3c7f0b4b2f2231178f712e356caae8bcb03932de898d | lean_source_file | lean_toolchain_source_file_chunks | theorem mem_diff_iff [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF)
(h₂ : m₂.WF) {k : α} :
k ∈ m₁ \ m₂ ↔ k ∈ m₁ ∧ k ∉ m₂ :=
@HashMap.Raw.mem_diff_iff _ _ _ _ m₁.inner m₂.inner _ _ h₁.out h₂.out k
theorem not_mem_diff_of_not_mem_left [EquivBEq α] [LawfulHashable α]
(h₁ : m₁.WF) (h₂ : m₂.WF) {k : α}
(not... |
13,777 | lean_file_chunk | 2c183a46ed1c2b717acd7c060838dafba4eeba5f87b5f218f8bddc50383ab485 | 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: Markus Himmel
-/
module
prelude
public import Std.Data.HashMap.Raw
@[expose] public section
/-!
# Hash sets with unbundled well-formedness invariant
This module develops the type `S... |
1,808 | lean_file_chunk | 2d3cd8ecd1321cc9abb617d666b336d531f94d567f3e8b7d9a2c01a92e538234 | 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
import Std.Data.DHashMap.IteratorLemmas
import all Std.Data.HashMap.IteratorLemmas
public import Std.Data.HashSet.Iterator
import all Std.Data.HashSet.... |
668 | lean_file_chunk | d5064e07035040f73dd6cb0a7552476f7b9079c82eac987a783c7653939a748e | 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: Wojciech Różowski
-/
module
prelude
public import Std.Data.HashMap.RawDecidableEquiv
public import Std.Data.HashSet.Raw
public section
/-!
# Decidable equivalence for `HashSet.Raw`
-... |
952 | lean_file_chunk | 01732e53ffd44212d72eabe4ede6366f0e4dfedd58ae9dcb653354c5c382cdb3 | 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 Std.Data.HashMap.Iterator
public import Std.Data.HashSet.Basic
public import Std.Data.HashSet.Raw
import Init.Data.Iterators.Combinators.F... |
1,518 | lean_file_chunk | 733ffb75a8e0f99078d2bca75b5715d5861a42c88da62ad43c83590edda062ee | 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: Markus Himmel
-/
module
prelude
public import Std.Data.DHashMap.Internal.Raw
public import Std.Data.DHashMap.Internal.WF
public section
/-!
# Additional dependent hash map operations... |
699 | lean_file_chunk | 0cab538a0152d64e67c078ccaa13757eeb0efcdabcf68999577191a05c943db4 | 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: Wojciech Różowski
-/
module
prelude
public import Std.Data.DHashMap.Internal.RawLemmas
public section
/-!
# Decidable equivalence for `DHashMap`
-/
open Std.DHashMap.Internal
names... |
23,979 | lean_file_chunk | 27bf27845dd57dbd9a36d0f2add6ea872e627e7d9cfafd871d6065f5d936ed95 | 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: Markus Himmel
-/
module
prelude
public import Std.Data.DHashMap.Internal.RawLemmas
import all Std.Data.DHashMap.Basic
public import Std.Data.DHashMap.AdditionalOperations
import all St... |
23,974 | lean_file_chunk | 6389fc14d681593695b4026b67e9178dc38a2612739dc845b35e9ad112d4154a | lean_source_file | lean_toolchain_source_file_chunks | m.getD a fallback = (m.get? a).getD fallback :=
Raw₀.getD_eq_getD_get? ⟨m.1, _⟩ m.2
theorem get_eq_getD [LawfulBEq α] {a : α} {fallback : β a} {h} :
m.get a h = m.getD a fallback :=
Raw₀.get_eq_getD ⟨m.1, _⟩ m.2
theorem get!_eq_getD_default [LawfulBEq α] {a : α} [Inhabited (β a)] :
m.get! a = m.getD a def... |
23,973 | lean_file_chunk | 0c2c662670c9f45c5218d90d1447a8e42d5aefaa912cd409f7dfe251b4d78c4d | lean_source_file | lean_toolchain_source_file_chunks | m.toList.length = m.size :=
Raw₀.length_toList ⟨m.1, m.2.size_buckets_pos⟩ m.2
@[simp, grind =]
theorem isEmpty_toList [EquivBEq α] [LawfulHashable α] :
m.toList.isEmpty = m.isEmpty :=
Raw₀.isEmpty_toList ⟨m.1, m.2.size_buckets_pos⟩ m.2
@[simp, grind =]
theorem mem_toList_iff_get?_eq_some [LawfulBEq α]
{k... |
23,997 | lean_file_chunk | b8317acb26b92533eba2448d6355f53078fd7c61def0c7c26ef18645ad2cacd9 | lean_source_file | lean_toolchain_source_file_chunks | theorem getKey_insertMany_list_of_mem [EquivBEq α] [LawfulHashable α]
{l : List ((a : α) × β a)}
{k k' : α} (k_beq : k == k')
(distinct : l.Pairwise (fun a b => (a.1 == b.1) = false))
(mem : k ∈ l.map Sigma.fst)
{h} :
(m.insertMany l).getKey k' h = k :=
Raw₀.getKey_insertMany_list_of_mem ⟨m.1,... |
23,910 | lean_file_chunk | 4e9b2648af35c7215d233a249dde095c3899b2931431de4cde3cb502ceb06fae | lean_source_file | lean_toolchain_source_file_chunks | exact @Raw₀.get_inter _ _ _ _ ⟨m₁.1, _⟩ ⟨m₂.1, _⟩ _ m₁.2 m₂.2 k h_mem
/- getD -/
theorem getD_inter [LawfulBEq α] {k : α} {fallback : β k} :
(m₁ ∩ m₂).getD k fallback =
if k ∈ m₂ then m₁.getD k fallback else fallback :=
@Raw₀.getD_inter _ _ _ _ ⟨m₁.1, m₁.2.size_buckets_pos⟩ ⟨m₂.1, m₂.2.size_buckets_pos⟩ _ m₁... |
23,938 | lean_file_chunk | 7876e5985ab426ede1337eb9a24cfbb90d62f84a25f608cd3e9a8b1aeae8fe7a | lean_source_file | lean_toolchain_source_file_chunks | @Raw₀.size_diff_add_size_inter_eq_size_left _ _ _ _ ⟨m₁.1, m₁.2.size_buckets_pos⟩ ⟨m₂.1, m₂.2.size_buckets_pos⟩ _ _ m₁.2 m₂.2
/- isEmpty -/
@[simp]
theorem isEmpty_diff_left [EquivBEq α] [LawfulHashable α] (h : m₁.isEmpty) :
(m₁ \ m₂).isEmpty = true :=
@Raw₀.isEmpty_diff_left _ _ _ _ ⟨m₁.1, m₁.2.size_buckets_pos... |
23,965 | lean_file_chunk | 25da41598798bd7c2af63e272c979f63d5c49b950ebfc660cd92468de2adfce4 | lean_source_file | lean_toolchain_source_file_chunks | theorem ofList_eq_insertMany_empty {l : List ((a : α) × β a)} :
ofList l = insertMany (∅ : DHashMap α β) l := (rfl)
@[simp, grind =]
theorem contains_ofList [EquivBEq α] [LawfulHashable α]
{l : List ((a : α) × β a)} {k : α} :
(ofList l).contains k = (l.map Sigma.fst).contains k :=
Raw₀.contains_insertMan... |
23,941 | lean_file_chunk | 36b662da21698e1db4917267c308d994550bcae1a03015468c1a701564d82b88 | lean_source_file | lean_toolchain_source_file_chunks | simp only [getKey?_alter, beq_self_eq_true, ↓reduceIte]
@[grind =]
theorem getKey!_alter [LawfulBEq α] [Inhabited α] {k k' : α} {f : Option (β k) → Option (β k)} :
(m.alter k f).getKey! k' =
if k == k' then
if (f (m.get? k)).isSome then k else default
else
m.getKey! k' := by
simp only... |
23,995 | lean_file_chunk | ac3ca50373c0d86096b3e175e261977cda85a6c53e390ba6ce49620e8b50fe56 | lean_source_file | lean_toolchain_source_file_chunks | ⟨Raw₀.filterMap_equiv_congr ⟨m₁.1, m₁.2.size_buckets_pos⟩ ⟨m₂.1, m₂.2.size_buckets_pos⟩ h.1⟩
theorem of_forall_get?_eq [LawfulBEq α] (h : ∀ k, m₁.get? k = m₂.get? k) : m₁ ~m m₂ :=
⟨Raw₀.equiv_of_forall_get?_eq ⟨m₁.1, _⟩ ⟨m₂.1, _⟩ m₁.2 m₂.2 h⟩
section Const
variable {β : Type v} {m₁ m₂ : DHashMap α fun _ => β}
the... |
12,596 | lean_file_chunk | a195374cbbd4be337831ded72b6a367a83328194456969e264bf0caf33327753 | lean_source_file | lean_toolchain_source_file_chunks | {f : α → β → Bool} :
(m.filter f).isEmpty = true ↔
∀ (k : α) (h : k ∈ m), f (m.getKey k h) (Const.get m k h) = false :=
Raw₀.Const.isEmpty_filter_iff ⟨m.1, _⟩ m.2
theorem isEmpty_filter_eq_false_iff [EquivBEq α] [LawfulHashable α]
{f : α → β → Bool} :
(m.filter f).isEmpty = false ↔
∃ (k : α) ... |
16,976 | lean_file_chunk | 27a446110426813b38ddf7388177061b47232557f97ac46b3db87357a5c82529 | 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: Markus Himmel
-/
module
prelude
public import Std.Data.DHashMap.Raw
import all Std.Data.DHashMap.Raw
public section
/-!
# Dependent hash maps
This file develops the type `Std.DHashM... |
23,954 | lean_file_chunk | c3be9a7df009f84c1fc13f917f4dc821cc886ba2bfecc75f7cad33fc7ef82679 | 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: Markus Himmel
-/
module
prelude
public import Std.Data.DHashMap.Internal.Raw
public import Std.Data.DHashMap.Internal.RawLemmas
import all Std.Data.DHashMap.Raw
import Init.ByCases
imp... |
23,921 | lean_file_chunk | dc9844a5c5c3526569eabf237704d58961a2dc5f8d2363bb40f00eba55401fb1 | lean_source_file | lean_toolchain_source_file_chunks | simpa [← contains_iff_mem] using get!_eq_default_of_contains_eq_false h
@[grind =] theorem get!_erase [EquivBEq α] [LawfulHashable α] [Inhabited β] (h : m.WF) {k a : α} :
get! (m.erase k) a = if k == a then default else get! m a := by
simp_to_raw using Raw₀.Const.get!_erase
@[simp]
theorem get!_erase_self [Equi... |
23,935 | lean_file_chunk | 4f9367e5160899bdd1ef4deda7e93ad57811e80de47932c8cd3c199beb6689e5 | lean_source_file | lean_toolchain_source_file_chunks | get? (m.insertIfNew k v) a = if k == a ∧ ¬k ∈ m then some v else get? m a := by
simp only [mem_iff_contains, Bool.not_eq_true]
simp_to_raw using Raw₀.Const.get?_insertIfNew
@[grind =] theorem get_insertIfNew [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a : α} {v : β} {h₁} :
get (m.insertIfNew k v) a h₁ =
... |
23,951 | lean_file_chunk | 7a5ae3600ad8ced3388e9bd0feebe0695baae25754db7ed44ecb4f384eac4496 | lean_source_file | lean_toolchain_source_file_chunks | m.any p = true ↔ ∃ (a : α) (h : m.contains a), p (m.getKey a h) (Const.get m a h) := by
simp_to_raw using Raw₀.Const.any_eq_true ⟨m, h.size_buckets_pos⟩
theorem any_eq_true_iff_exists_mem_getKey_get [LawfulHashable α] [EquivBEq α]
{p : (_ : α) → β → Bool} (h : m.WF) :
m.any p = true ↔ ∃ (a : α) (h : a ∈ m), ... |
23,962 | lean_file_chunk | 4f94c506286fd1db3f491f907a45c07a37332a7ae287050fee9c99f2c92be881 | lean_source_file | lean_toolchain_source_file_chunks | theorem getKeyD_union_of_not_mem_right [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF)
(h₂ : m₂.WF) {k fallback : α} (mem : ¬k ∈ m₂) :
(m₁ ∪ m₂).getKeyD k fallback = m₁.getKeyD k fallback := by
rw [← contains_eq_false_iff_not_mem] at mem
revert mem
simp only [Union.union]
simp_to_raw
intro mem
apply Ra... |
23,973 | lean_file_chunk | 3181cb3693ba367c1238934a3726775f4d2643e2006c04f41d5000025dde0101 | lean_source_file | lean_toolchain_source_file_chunks | simp_to_raw using Raw₀.contains_diff
/- mem -/
@[simp]
theorem mem_diff_iff [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF) (h₂ : m₂.WF) {k : α} :
k ∈ m₁ \ m₂ ↔ k ∈ m₁ ∧ k ∉ m₂ := by
simp only [SDiff.sdiff, Membership.mem]
simp_to_raw using @Raw₀.contains_diff_iff _ _ _ _ ⟨m₁, _⟩ ⟨m₂, _⟩ _ _
theorem not_mem_diff... |
23,966 | lean_file_chunk | 66712f0155faf8db0c9394386e3740de936dd74ec561f2cb67199071ac7a95eb | lean_source_file | lean_toolchain_source_file_chunks | [Inhabited β] (h : m.WF) {l : List (α × β)} {k : α}
(contains_eq_false : (l.map Prod.fst).contains k = false) :
get! (insertMany m l) k = get! m k := by
simp_to_raw using Raw₀.Const.get!_insertMany_list_of_contains_eq_false
theorem get!_insertMany_list_of_mem [EquivBEq α] [LawfulHashable α] [Inhabited β] (h ... |
23,947 | lean_file_chunk | 593cddea04d6ade6b3f4488b3a0080935e83e36ed7b72faa3b02a0343682eb9e | lean_source_file | lean_toolchain_source_file_chunks | simp_to_raw using Raw₀.Const.getKeyD_insertMany_emptyWithCapacity_list_of_mem
theorem size_ofList [EquivBEq α] [LawfulHashable α]
{l : List (α × β)} (distinct : l.Pairwise (fun a b => (a.1 == b.1) = false)) :
(ofList l).size = l.length := by
simp_to_raw using Raw₀.Const.size_insertMany_emptyWithCapacity_list... |
23,993 | lean_file_chunk | 2c7b093c1b10c53c100aeeb6bba6640c3a15aa0f16f74d8d6a4f246f4d64e6b9 | lean_source_file | lean_toolchain_source_file_chunks | theorem isEmpty_modify [LawfulBEq α] {k : α} {f : β k → β k} (h : m.WF) :
(m.modify k f).isEmpty = m.isEmpty := by
simp_to_raw using Raw₀.isEmpty_modify
@[simp, grind =]
theorem contains_modify [LawfulBEq α] {k k': α} {f : β k → β k} (h : m.WF) :
(m.modify k f).contains k' = m.contains k' := by
simp_to_raw... |
23,968 | lean_file_chunk | 59534e171c255b7c7b9c0b4fe71560cc0045fdf25a66b40f79a94ec1991b1f2a | lean_source_file | lean_toolchain_source_file_chunks | ← contains_eq_isSome_get?, get_get?, h]
theorem contains_of_contains_filterMap [EquivBEq α] [LawfulHashable α]
{f : (a : α) → β a → Option (γ a)} {k : α} (h : m.WF) :
(m.filterMap f).contains k = true → m.contains k = true := by
simp_to_raw using Raw₀.contains_of_contains_filterMap
theorem mem_of_mem_filter... |
6,619 | lean_file_chunk | 50a764e679111686a62af0e666e29c6deb60f7c65db57cfbefdc2fe7d26b39f1 | lean_source_file | lean_toolchain_source_file_chunks | theorem isEmpty_map [EquivBEq α] [LawfulHashable α]
{f : (a : α) → β a → γ a} (h : m.WF) :
(m.map f).isEmpty = m.isEmpty := by
simp_to_raw using Raw₀.isEmpty_map
@[grind =]
theorem contains_map [EquivBEq α] [LawfulHashable α]
{f : (a : α) → β a → γ a} {k : α} (h : m.WF) :
(m.map f).contains k = m.con... |
3,831 | lean_file_chunk | a4852fefce75393874cb0ad16654488f1b88e9460f21a25d06aed0fa07541517 | 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.
Authors: Leonardo de Moura, Mario Carneiro, Markus Himmel
-/
module
prelude
public import Std.Data.DHashMap.Internal.AssocList.Basic
public import Init.Data.Array.Basic
public section
... |
23,999 | lean_file_chunk | 1b7c11ce03459a163029ffa8eae80ed5c00fea014b82f63f417724eac74e41ff | 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: Markus Himmel
-/
module
prelude
public import Init.Data.LawfulHashable
public import Std.Data.DHashMap.Internal.Defs
import all Std.Data.DHashMap.Internal.Defs
public section
/-!
# D... |
11,554 | lean_file_chunk | 50f91879126f9122d19c10103589117215edb4be8fa917db7b9fa3ef5b098479 | lean_source_file | lean_toolchain_source_file_chunks | @[inline, inherit_doc Raw.toList] def Const.toList {β : Type v} (m : Raw α (fun _ => β)) :
List (α × β) :=
Internal.foldRev (fun acc k v => ⟨k, v⟩ :: acc) [] m
instance [Repr α] [(a : α) → Repr (β a)] : Repr (Raw α β) where
reprPrec m prec := Repr.addAppParen ("Std.DHashMap.Raw.ofList " ++ reprArg m.toList) pr... |
5,132 | lean_file_chunk | 707019b068783df74043166fc6554cd17adf6af0e46a4484127d959a4469506e | 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 Std.Data.Iterators
public import Std.Data.DHashMap.Iterator
import all Std.Data.DHashMap.Basic
import all Std.Data.DHashMap.Raw
import all... |
651 | lean_file_chunk | fcaba177403d5f69a7c423e85f38cd8e57d19ca77887b37f80ec9579bedba1d7 | 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: Wojciech Różowski
-/
module
prelude
public import Std.Data.DHashMap.Internal.RawLemmas
public section
/-!
# Decidable equivalence for `DHashMap.Raw`
-/
open Std.DHashMap.Internal
n... |
2,226 | lean_file_chunk | 213606e6330a1f7e4b41215f0eaec0c8de87093790c15273f14e2cc01c99f2f7 | 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 Std.Data.Iterators.Producers.Array
public import Init.Data.Iterators.Combinators.FlatMap
public import Std.Data.DHashMap.Basic
public impo... |
2,097 | lean_file_chunk | b7ab90ba0407cdd69ea95a4aed43b01312828945e24f8f3d3ae48b2af513e97a | 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: Markus Himmel
-/
module
prelude
public import Init.Data.Order.Ord
import Init.RCases
@[expose] public section
set_option autoImplicit false
universe u
namespace Std.Internal
class... |
23,960 | lean_file_chunk | d28ae12e23090bc66d5301850c481dcb8b26d6d1c6bdd2e706000350e2df6490 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2025 Robin Arnez, LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robin Arnez
-/
module
prelude
public import Std.Data.ExtHashMap.Basic
import all Std.Data.ExtDHashMap.Basic
public import Std.Data.ExtDHashMap.Lemmas
@[expose] public section
/-!
... |
23,969 | lean_file_chunk | 2bd5fadb1b3a02b3b7b302b193afff387ec5b46009dcb55f824020b760bcfea6 | lean_source_file | lean_toolchain_source_file_chunks | (h : k == k') : m.getKeyD k fallback = m.getKeyD k' fallback :=
ExtDHashMap.getKeyD_congr h
theorem getKeyD_eq_of_contains [LawfulBEq α] {k fallback : α} (h : m.contains k) :
m.getKeyD k fallback = k :=
ExtDHashMap.getKeyD_eq_of_contains h
theorem getKeyD_eq_of_mem [LawfulBEq α] {k fallback : α} (h : k ∈ m) :... |
23,993 | lean_file_chunk | ebc1212d0a5941bc5448e56396c095924d3cf33194d35af4cc1988c642a97154 | lean_source_file | lean_toolchain_source_file_chunks | ExtDHashMap.Const.contains_ofList
@[simp, grind =]
theorem mem_ofList [EquivBEq α] [LawfulHashable α]
{l : List (α × β)} {k : α} :
k ∈ ofList l ↔ (l.map Prod.fst).contains k :=
ExtDHashMap.Const.mem_ofList
theorem getElem?_ofList_of_contains_eq_false [EquivBEq α] [LawfulHashable α]
{l : List (α × β)} {k... |
23,956 | lean_file_chunk | a3e2b00c3559a1939525c0bb3a750fa6ff55b9141f71f4d47c60f95e596ee6dd | lean_source_file | lean_toolchain_source_file_chunks | theorem get!_inter_of_not_mem_right [EquivBEq α] [LawfulHashable α]
{k : α} [Inhabited β] (not_mem : k ∉ m₂) :
(m₁ ∩ m₂).get! k = default :=
ExtDHashMap.Const.get!_inter_of_not_mem_right not_mem
@[deprecated getElem!_inter_of_not_mem_left (since := "2025-12-10")]
theorem get!_inter_of_not_mem_left [EquivBEq ... |
16,964 | lean_file_chunk | af5fbb5bf5d88d5f9ae6b8c843d8c76e1f91374607d14cd24ec0ff0f88160f20 | lean_source_file | lean_toolchain_source_file_chunks | (h : ∀ k : α, m₁[k]? = m₂[k]?) : m₁ = m₂ :=
ext (ExtDHashMap.Const.ext_get? h)
theorem ext_getKey?_unit [EquivBEq α] [LawfulHashable α]
{m₁ m₂ : ExtHashMap α Unit} (h : ∀ k, m₁.getKey? k = m₂.getKey? k) : m₁ = m₂ :=
ext (ExtDHashMap.Const.ext_getKey?_unit h)
theorem ext_contains_unit [LawfulBEq α]
{m₁ m₂ ... |
10,860 | lean_file_chunk | 8f157ab533ead11e7b6eb06cea30928791f008c78d4468d831adfbf65dd8be1f | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2025 Robin Arnez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robin Arnez
-/
module
prelude
public import Std.Data.ExtDHashMap.Basic
@[expose] public section
set_option linter.missingDocs true
set_option autoImplicit false
/-!
# Extensional hash... |
1,324 | lean_file_chunk | fcc19a13fc5dbe1bd10f1e16f60daa807aa37ce48f1e614dacba5ae3eca189c4 | 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: Markus Himmel
-/
module
prelude
public import Std.Data.DHashMap.AdditionalOperations
public import Std.Data.HashMap.Basic
public import Std.Data.HashMap.Raw
@[expose] public section
... |
548 | lean_file_chunk | 1adbde939a1f30b3e1d955c3387afbf78a3e123eb416a8031f459d2a793bd06a | 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: Wojciech Różowski
-/
module
prelude
public import Std.Data.DHashMap.DecidableEquiv
public import Std.Data.HashMap.Basic
public section
/-!
# Decidable equivalence for `HashMap`
-/
n... |
23,963 | lean_file_chunk | eb032e6b637abd732e8dfcc9176b8350d0d94006ff9ba56b5ea5966999f60723 | 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: Markus Himmel
-/
module
prelude
public import Std.Data.DHashMap.Lemmas
public import Std.Data.HashMap.AdditionalOperations
import all Std.Data.DHashMap.Basic
import Init.Data.List.Pair... |
23,993 | lean_file_chunk | 93e78d67cf9f41cf739f158a344d3a7ae495671437cdb1c965777ca9545d41fe | lean_source_file | lean_toolchain_source_file_chunks | {a : α} : m.contains a = false → m.getKey! a = default :=
DHashMap.getKey!_eq_default_of_contains_eq_false
theorem getKey!_eq_default [EquivBEq α] [LawfulHashable α] [Inhabited α] {a : α} :
¬a ∈ m → m.getKey! a = default :=
DHashMap.getKey!_eq_default
@[grind =] theorem getKey!_erase [EquivBEq α] [LawfulHasha... |
23,972 | lean_file_chunk | 4b55d5b949b6548f182c21b1ce4492b0daf41e1016a9af6f84317a44cec8cfff | lean_source_file | lean_toolchain_source_file_chunks | {l : List (α × β)} {k : α}
(contains_eq_false : (l.map Prod.fst).contains k = false) :
(insertMany m l)[k]? = m[k]? :=
DHashMap.Const.get?_insertMany_list_of_contains_eq_false contains_eq_false
theorem getElem?_insertMany_list_of_mem [EquivBEq α] [LawfulHashable α]
{l : List (α × β)} {k k' : α} (k_beq : ... |
23,995 | lean_file_chunk | e55bb53d18da6fed274420d7cb5ae7412c848521ef142ff97635ffef55dcda48 | lean_source_file | lean_toolchain_source_file_chunks | theorem getD_inter_of_not_mem_left [EquivBEq α] [LawfulHashable α]
{k : α} {fallback : β} (not_mem : k ∉ m₁) :
(m₁ ∩ m₂).getD k fallback = fallback :=
@DHashMap.Const.getD_inter_of_not_mem_left _ _ _ _ m₁.inner m₂.inner _ _ k fallback not_mem
/- getElem! -/
theorem getElem!_inter [EquivBEq α] [LawfulHashable... |
23,932 | lean_file_chunk | 4a873ad58715ed3d06242477194998e0fa220851f8b9f881097a21a7ba773ef3 | lean_source_file | lean_toolchain_source_file_chunks | theorem getKeyD_insertManyIfNewUnit_list_of_mem [EquivBEq α] [LawfulHashable α]
{l : List α} {k fallback : α} (mem : k ∈ m) :
getKeyD (insertManyIfNewUnit m l) k fallback = getKeyD m k fallback :=
DHashMap.Const.getKeyD_insertManyIfNewUnit_list_of_mem mem
theorem size_insertManyIfNewUnit_list [EquivBEq α] [L... |
23,980 | lean_file_chunk | 484e21017cede120f0251863b1cdccfc3d10524dc623c6dc02c35ebd1154e177 | lean_source_file | lean_toolchain_source_file_chunks | {f : β → β} : (modify m k f).getKeyD k fallback = if k ∈ m then k else fallback :=
DHashMap.Const.getKeyD_modify_self
end Modify
namespace Equiv
variable {m m₁ m₂ m₃ : HashMap α β}
@[refl, simp] theorem refl (m : HashMap α β) : m ~m m := ⟨.rfl⟩
theorem rfl : m ~m m := ⟨.rfl⟩
@[symm] theorem symm : m₁ ~m m₂ → m₂ ~... |
1,507 | lean_file_chunk | 7860dd70570937134a9f71e273bbaf258ec66ece03246aa154073d4dcfaf93af | lean_source_file | lean_toolchain_source_file_chunks | DHashMap.Const.getD_map
/-- Variant of `getD_map` that holds with `EquivBEq` (i.e. without `LawfulBEq`). -/
theorem getD_map' [EquivBEq α] [LawfulHashable α]
{f : α → β → γ} {k : α} {fallback : γ} :
(m.map f).getD k fallback =
(m[k]?.pmap (fun v h => f (m.getKey k h) v)
(fun _ h' => mem_iff_isSom... |
12,950 | lean_file_chunk | f760af98a44c280d64d94233e8d58cb039098c21cad59adc70628bc8da4b25ae | 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: Markus Himmel
-/
module
prelude
public import Std.Data.DHashMap.Basic
public import Init.Data.List.Impl
@[expose] public section
set_option linter.missingDocs true
set_option autoImp... |
23,998 | lean_file_chunk | 5713c248d84a46adac21482d6aed7c6d3c2c9fb49f1ca0c0adffa8d199535f92 | 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: Markus Himmel
-/
module
prelude
public import Std.Data.DHashMap.RawLemmas
public import Std.Data.HashMap.Raw
import all Std.Data.DHashMap.Raw
import Init.Data.List.Pairwise
@[expose] ... |
23,988 | lean_file_chunk | 84266466b6247b94341bdf83a6e692eea00603d5d0b6aca3c612b067e44a900b | lean_source_file | lean_toolchain_source_file_chunks | theorem getKey!_emptyWithCapacity [Inhabited α] {a : α} {c} : (emptyWithCapacity c : Raw α β).getKey! a = default :=
DHashMap.Raw.getKey!_emptyWithCapacity
@[simp, grind =]
theorem getKey!_empty [Inhabited α] {a : α} : (∅ : Raw α β).getKey! a = default :=
DHashMap.Raw.getKey!_empty
theorem getKey!_of_isEmpty [Equ... |
23,911 | lean_file_chunk | 875b5c4d14b8af43b38940594d8c34216bc12d9817e540df73465005245ee270 | lean_source_file | lean_toolchain_source_file_chunks | m.all p = true ↔ ∀ (a : α) (h : a ∈ m), p a (m[a]'h) :=
DHashMap.Raw.Const.all_eq_true_iff_forall_contains_get h.out
theorem all_eq_false_iff_exists_mem_getKey_getElem [EquivBEq α] [LawfulHashable α]
{p : α → β → Bool} (h : m.WF) :
m.all p = false ↔ ∃ (a : α) (h : a ∈ m), p (m.getKey a h) (m[a]'h) = false :=... |
23,987 | lean_file_chunk | 615f31cf8f269f774eb9515615d0d6c1c84a9b8b138a183c88e1b01948f703ef | lean_source_file | lean_toolchain_source_file_chunks | ⟨@DHashMap.Raw.Equiv.inter_left _ _ _ _ m₁.inner m₂.inner m₃.inner _ _ h₁.out h₂.out h₃.out equiv.1⟩
theorem Equiv.inter_right {m₃ : Raw α β} [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF) (h₂ : m₂.WF) (h₃ : m₃.WF)
(equiv : m₂ ~m m₃) :
(m₁ ∩ m₂) ~m (m₁ ∩ m₃) :=
⟨@DHashMap.Raw.Equiv.inter_right _ _ _ _ m₁.inner... |
23,976 | lean_file_chunk | bbd4f9ab22182a9a137ebaee02e5728f557a003353907f1f3fa00e45dc646081 | lean_source_file | lean_toolchain_source_file_chunks | @DHashMap.Raw.getKey!_diff _ _ _ _ m₁.inner m₂.inner _ _ _ h₁.out h₂.out k
theorem getKey!_diff_of_not_mem_right [EquivBEq α] [LawfulHashable α] [Inhabited α] (h₁ : m₁.WF)
(h₂ : m₂.WF) {k : α} (not_mem : k ∉ m₂) :
(m₁ \ m₂).getKey! k = m₁.getKey! k :=
@DHashMap.Raw.getKey!_diff_of_not_mem_right _ _ _ _ m₁.in... |
23,983 | lean_file_chunk | de791bbccf0db68d32c7df63fc5ba7ca5c6ef740427d76d93dbf01c26cc1edb3 | lean_source_file | lean_toolchain_source_file_chunks | DHashMap.Raw.Const.isEmpty_alter_eq_isEmpty_erase h.out
@[simp, grind =]
theorem isEmpty_alter [EquivBEq α] [LawfulHashable α] {k : α} {f : Option β → Option β} (h : m.WF) :
(alter m k f).isEmpty = ((m.isEmpty || (m.size == 1 && m.contains k)) && (f m[k]?).isNone) :=
DHashMap.Raw.Const.isEmpty_alter h.out
@[gri... |
16,762 | lean_file_chunk | 5079a4fb5fc0ee80726a50a6b3ffa76b772fd259cc23624d730aad2d0a9d6279 | lean_source_file | lean_toolchain_source_file_chunks | (m[k]'(mem_of_mem_filterMap h h'))).isSome :=
DHashMap.Raw.Const.isSome_apply_of_mem_filterMap h.out
@[simp]
theorem getElem_filterMap [EquivBEq α] [LawfulHashable α]
{f : α → β → Option γ} {k : α} {g} (h : m.WF) :
(m.filterMap f)[k]'g =
(f (m.getKey k (mem_of_mem_filterMap h g))
(m[k]'(mem_of_... |
15,097 | lean_file_chunk | 85b0f4abbd7b0980d4ed82db60d1414d3bbc97b268b533eb63bc10d52499a0f4 | 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: Markus Himmel
-/
module
prelude
public import Std.Data.DHashMap.Raw
@[expose] public section
set_option linter.missingDocs true
set_option autoImplicit false
/-!
# Hash maps with un... |
5,122 | lean_file_chunk | 7e5bfb36613c8b79096fbd87bdf3d9d274490945c422d7b1008cc8a26a059fac | 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
import Init.Data.Iterators.Lemmas.Combinators
import Std.Data.DHashMap.IteratorLemmas
public import Std.Data.HashMap.Iterator
import all Std.Data.HashM... |
708 | lean_file_chunk | 140da1e603befa6c1b56abe122a082691a4af4721902d70cb8761e62029af6fb | 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: Wojciech Różowski
-/
module
prelude
public import Std.Data.DHashMap.RawDecidableEquiv
public import Std.Data.HashMap.Raw
public section
/-!
# Decidable equivalence for `HashMap.Raw`
... |
2,050 | lean_file_chunk | 372a779a9bd81906f856d94f44cde7f318113a9b312ab4291a7ffa7bbfff3712 | 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 Std.Data.DHashMap.Iterator
public import Std.Data.HashMap.Basic
public import Std.Data.HashMap.Raw
import Init.Data.Iterators.Combinators.... |
23,999 | lean_file_chunk | 7efd2007b5a8733f753b1b135ef800300d55be1e1aba0b2ef8ce6defc2225871 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2025 Robin Arnez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robin Arnez, Markus Himmel, Paul Reichert
-/
module
prelude
public import Std.Data.ExtTreeMap.Lemmas
public import Std.Data.ExtTreeSet.Basic
@[expose] public section
/-!
# Tree set lem... |
23,966 | lean_file_chunk | 23777dc9e81d3c8a9dd6e2902ea2d51dc7e4663e093b47d87d95786e40fa3335 | lean_source_file | lean_toolchain_source_file_chunks | theorem get?_diff_of_not_mem_right [TransCmp cmp]
{k : α} (not_mem : k ∉ t₂) :
(t₁ \ t₂).get? k = t₁.get? k :=
ExtTreeMap.getKey?_diff_of_not_mem_right not_mem
theorem get?_diff_of_not_mem_left [TransCmp cmp]
{k : α} (not_mem : k ∉ t₁) :
(t₁ \ t₂).get? k = none :=
ExtTreeMap.getKey?_diff_of_not_mem... |
22,998 | lean_file_chunk | 7cca5947357ecf566193bc3e395070448765c9802658baa8e45aa9cbdbef21ab | lean_source_file | lean_toolchain_source_file_chunks | ExtTreeMap.minKey!_insertIfNew_le_self
@[grind =] theorem contains_min! [TransCmp cmp] [Inhabited α] (he : t ≠ ∅) :
t.contains t.min! :=
ExtTreeMap.contains_minKey! (mt ext he)
theorem min!_mem [TransCmp cmp] [Inhabited α] (he : t ≠ ∅) :
t.min! ∈ t :=
ExtTreeMap.minKey!_mem (mt ext he)
grind_pattern min!... |
20,106 | lean_file_chunk | 4a24161ea0441cd9556520c201d4acae20654d2e85a17bb95c357ae79d84d2c0 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2025 Robin Arnez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robin Arnez, Markus Himmel, Paul Reichert
-/
module
prelude
public import Std.Data.ExtTreeMap.Basic
@[expose] public section
/-!
# Extensional tree sets
This file develops the type `S... |
1,743 | lean_file_chunk | deedf095fec0417479f7f5c886205ae464fab74e8017ad439abbed140add27c4 | 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 Std.Data.TreeSet.Raw.Basic
public import Std.Data.TreeMap.AdditionalOperations
@[expose] public section
/-!
# Additional tree set operat... |
579 | lean_file_chunk | 5cbd6c669489e9c822330368de5bd15f77e7185ed419ce94ad3e3014f7397309 | 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: Wojciech Różowski
-/
module
prelude
public import Std.Data.TreeMap.DecidableEquiv
public import Std.Data.TreeSet.Basic
public section
/-!
# Decidable equivalence for `TreeSet`
-/
op... |
23,946 | lean_file_chunk | 8dfc0f4b1fffae3a1a5e775302c34f598e3249ed1f84b5cccf3403fb70debf3d | 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
-/
module
prelude
import Std.Data.TreeMap.Lemmas
import Std.Data.DTreeMap.Lemmas
public import Init.Data.Array.Perm
public import Std.Data.TreeSet.Addition... |
23,987 | lean_file_chunk | d7d72cb24ba8d4d31acabc6f0ee45307447825145462ee3e5bfc07bec0ddcd0a | lean_source_file | lean_toolchain_source_file_chunks | theorem get!_inter_of_mem_right [TransCmp cmp] [Inhabited α]
{k : α} (mem : k ∈ t₂) :
(t₁ ∩ t₂).get! k = t₁.get! k :=
TreeMap.getKey!_inter_of_mem_right mem
theorem get!_inter_of_not_mem_right [TransCmp cmp] [Inhabited α]
{k : α} (not_mem : k ∉ t₂) :
(t₁ ∩ t₂).get! k = default :=
TreeMap.getKey!_in... |
23,977 | lean_file_chunk | c29c2ed7112e5eafa8c0d7b11708d5ed35b9c068502ffdd73a04b30184ad9f05 | lean_source_file | lean_toolchain_source_file_chunks | TreeMap.minKey_insertIfNew_le_minKey
theorem min_insert_le_self [TransCmp cmp] {k} :
cmp (t.insert k |>.min <| isEmpty_insert) k |>.isLE :=
TreeMap.minKey_insertIfNew_le_self
@[grind =] theorem contains_min [TransCmp cmp] {he} :
t.contains (t.min he) :=
TreeMap.contains_minKey
theorem min_mem [TransCmp c... |
12,820 | lean_file_chunk | e19f378f0d170cd709a3fcb0786dfc27a0f043ab658d36b32f5c7be3a5d05b96 | lean_source_file | lean_toolchain_source_file_chunks | t.get! (t.maxD fallback) = t.maxD fallback :=
TreeMap.getKey!_maxKeyD he
theorem getD_maxD [TransCmp cmp] (he : t.isEmpty = false) {fallback fallback'} :
t.getD (t.maxD fallback) fallback' = t.maxD fallback :=
TreeMap.getKeyD_maxKeyD he
theorem maxD_erase_eq_of_not_compare_maxD_eq [TransCmp cmp] {k fallback}
... |
17,496 | lean_file_chunk | 43dae47abbc28c834d8653850d3badde39878d31545f5d607ccb1a262fab9ff3 | 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: Markus Himmel, Paul Reichert
-/
module
prelude
public import Std.Data.TreeMap.Basic
@[expose] public section
/-!
# Tree sets
This file develops the type `Std.TreeSet` of tree sets.
... |
423 | lean_file_chunk | da6d61b9ba06016594c6e4a54153577e3666cc62e56604ddb45da406f9939f59 | 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 Std.Data.TreeSet.Raw.Basic
public import Std.Data.TreeSet.Raw.Lemmas
public import Std.Data.TreeSet.Raw.WF
public import Std.Data.TreeSet.... |
1,049 | lean_file_chunk | 6d02214443e361d4b233aa95032db38d8da2c95ca0d909cec1be612686bb0d80 | 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: Wojciech Różowski
-/
module
prelude
public import Std.Data.TreeSet.Basic
public import Std.Data.TreeMap.Iterator
public import Std.Data.DTreeMap.Lemmas
import Init.Data.Iterators.Lemma... |
5,897 | lean_file_chunk | 4430f4b3db79696f09729be7d22b7c945beae48a164dd9090f0a5e1381d19206 | 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: Wojciech Różowski
-/
module
prelude
public import Std.Data.TreeSet.Raw.Slice
/-!
This module provides slice notation for `TreeSet` slices and implements an iterator
for those slices.
... |
23,969 | lean_file_chunk | 5e05f4eedfa15b208916f21aee0ad3bb4a4c29d15cd122c7ed85f1dee057b08e | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2025 Robin Arnez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robin Arnez
-/
module
prelude
public import Std.Data.ExtDTreeMap.Basic
import Init.Data.List.Pairwise
@[expose] public section
/-!
# Extensional dependent tree map lemmas
This file co... |
23,964 | lean_file_chunk | 191abda5e9304a35e91903e067cc8886cdba20e504a0e4e07f50e49e42df63c6 | lean_source_file | lean_toolchain_source_file_chunks | getD t a fallback = getD t b fallback :=
t.inductionOn (fun _ hab => DTreeMap.Const.getD_congr hab) hab
end Const
@[simp, grind =]
theorem getKey?_empty [TransCmp cmp] {a : α} : (∅ : ExtDTreeMap α β cmp).getKey? a = none :=
DTreeMap.getKey?_emptyc
@[grind =] theorem getKey?_insert [TransCmp cmp] {a k : α} {v : β... |
23,995 | lean_file_chunk | 2e728ae8f0ad6a2f19d132fb99edf98d8f7e1455899629a46f3a28a51454b0fc | lean_source_file | lean_toolchain_source_file_chunks | {f : (a : α) × β a → δ → m (ForInStep δ)} {init : δ} :
ForIn.forIn t init f = ForIn.forIn t.toList init f :=
t.inductionOn fun _ => DTreeMap.forIn_eq_forIn_toList
theorem foldlM_eq_foldlM_keys [TransCmp cmp] [Monad m] [LawfulMonad m] {f : δ → α → m δ} {init : δ} :
t.foldlM (fun d a _ => f d a) init = t.keys.... |
23,967 | lean_file_chunk | 4003132725d5c31f9e73c8660e4f4a6e5afcb207c2e265120a87b51a1030c406 | lean_source_file | lean_toolchain_source_file_chunks | get (insertMany t l) k h' = get t k (mem_of_mem_insertMany_list h' contains_eq_false) := by
refine t.inductionOn (fun _ contains_eq_false _ => ?_) contains_eq_false h'
simp only [insertMany_list_mk]
exact DTreeMap.Const.get_insertMany_list_of_contains_eq_false contains_eq_false
theorem get_insertMany_list_of_mem... |
23,965 | lean_file_chunk | 0665c8aa37a40c53e5adf08b67535c96683d07db29c0e51d6bcb1b99b6acf969 | lean_source_file | lean_toolchain_source_file_chunks | (ofList l cmp).size = l.length :=
DTreeMap.Const.size_ofList distinct
theorem size_ofList_le [TransCmp cmp] {l : List (α × β)} :
(ofList l cmp).size ≤ l.length :=
DTreeMap.Const.size_ofList_le
grind_pattern size_ofList_le => (ofList l cmp).size
@[simp]
theorem ofList_eq_empty_iff [TransCmp cmp] {l : List (α ... |
23,970 | lean_file_chunk | 99794a6698dcb53bdc0bf7033f95a52454023a152acf3f31e56643481c0d72f2 | lean_source_file | lean_toolchain_source_file_chunks | (t₁ ∩ t₂).isEmpty = true := by
revert h
exact t₁.inductionOn₂ t₂ fun _ _ h => DTreeMap.isEmpty_inter_left h
@[simp]
theorem isEmpty_inter_right [TransCmp cmp] (h : t₂.isEmpty) :
(t₁ ∩ t₂).isEmpty = true := by
revert h
exact t₁.inductionOn₂ t₂ fun _ _ h => DTreeMap.isEmpty_inter_right h
theorem isEmpty_int... |
23,996 | lean_file_chunk | d18a5004783a767abe4673dc309ad98ae7fa472ceb82c4d2e1bd3dab38ea208a | lean_source_file | lean_toolchain_source_file_chunks | t.inductionOn fun _ => DTreeMap.Const.contains_alter
@[grind =]
theorem mem_alter [TransCmp cmp] {k k' : α} {f : Option β → Option β} :
k' ∈ alter t k f ↔
if cmp k k' = .eq then (f (get? t k)).isSome = true else k' ∈ t :=
t.inductionOn fun _ => DTreeMap.Const.mem_alter
theorem mem_alter_of_compare_eq [Tra... |
23,997 | lean_file_chunk | be1c8b6fd52c18235b9bda5a764d2f94f5bda5faa69a9720a6dda415f5a48e4f | lean_source_file | lean_toolchain_source_file_chunks | t.inductionOn fun _ => DTreeMap.minKey?_le_minKey?_erase
@[grind =] theorem minKey?_insertIfNew [TransCmp cmp] {k v} :
(t.insertIfNew k v).minKey? =
some (t.minKey?.elim k fun k' => if cmp k k' = .lt then k else k') :=
t.inductionOn fun _ => DTreeMap.minKey?_insertIfNew
@[grind =] theorem isSome_minKey?_i... |
23,979 | lean_file_chunk | 18537906be008533a18bef36a3ff822a4fbaec0b31417dafa3b6d9ee2d573cde | lean_source_file | lean_toolchain_source_file_chunks | theorem isSome_maxKey?_eq_not_isEmpty [TransCmp cmp] :
t.maxKey?.isSome = !t.isEmpty :=
t.inductionOn fun _ => DTreeMap.isSome_maxKey?_eq_not_isEmpty
theorem isSome_maxKey?_iff_ne_empty [TransCmp cmp] :
t.maxKey?.isSome ↔ t ≠ ∅ := by
simp
@[grind =] theorem maxKey?_insert [TransCmp cmp] {k v} :
(t.ins... |
23,983 | lean_file_chunk | bee888a021dc680fb19e676f3468a95460800a0a76f629c2bdc8be1765cb111a | lean_source_file | lean_toolchain_source_file_chunks | t.inductionOn (fun _ he heq => DTreeMap.maxKeyD_erase_eq_of_not_compare_maxKeyD_eq (isEmpty_eq_false_iff.mpr he) heq) he heq
theorem maxKeyD_erase_le_maxKeyD [TransCmp cmp] {k}
(he : t.erase k ≠ ∅) {fallback} :
cmp (t.erase k |>.maxKeyD fallback) (t.maxKeyD fallback) |>.isLE :=
t.inductionOn (fun _ he => DTr... |
10,405 | lean_file_chunk | 903a7b4a3a3b7fec2a3f4c548ee2e60acad9b3c6281612e61093a137bcf8b569 | lean_source_file | lean_toolchain_source_file_chunks | @[simp, grind =]
theorem get_filter [TransCmp cmp]
{f : α → β → Bool} {k : α} {h'} :
Const.get (t.filter f) k h' = Const.get t k (mem_of_mem_filter h') :=
t.inductionOn (fun _ _ => DTreeMap.Const.get_filter) h'
theorem get!_filter [TransCmp cmp] [Inhabited β]
{f : α → β → Bool} {k : α} :
Const.get! (... |
23,977 | lean_file_chunk | 267045fec3072a21577862c1678583250827efb80ac1280439412a3cfff9d3c1 | lean_source_file | lean_toolchain_source_file_chunks | /-
Copyright (c) 2025 Robin Arnez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robin Arnez, Markus Himmel, Paul Reichert
-/
module
prelude
public import Std.Data.DTreeMap.Lemmas
@[expose] public section
/-!
# Extensional dependent tree maps
This file develops th... |
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