max/lean4-htt
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions 2

feat: add @[grind] annotations for HashMap (#8246)

Browse source 
This PR add `@[grind]` annotations for HashMap and variants.
This commit is contained in:
Kim Morrison 2025-05-13 14:56:41 +10:00 • committed by GitHub
parent ef77434a49
commit a08d182359
No known key found for this signature in database
GPG key ID: B5690EEEBB952194
17 changed files with 1471 additions and 915 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

397
src/Std/Data/DHashMap/Lemmas.lean
View file

File diff suppressed because it is too large Load diff

414
src/Std/Data/DHashMap/RawLemmas.lean
View file

File diff suppressed because it is too large Load diff

2
src/Std/Data/DTreeMap/Lemmas.lean
View file

@ -1289,6 +1289,7 @@ theorem insertMany_cons {l : List ((a : α) × β a)} {k : α} {v : β k} :
t.insertMany (⟨k, v⟩ :: l) = (t.insert k v).insertMany l :=
ext <| Impl.insertMany_cons t.wf
@[grind _=_]
theorem insertMany_append {l₁ l₂ : List ((a : α) × β a)} :
insertMany t (l₁ ++ l₂) = insertMany (insertMany t l₁) l₂ := by
induction l₁ generalizing t with
@ -1469,6 +1470,7 @@ theorem insertMany_cons {l : List (α × β)} {k : α} {v : β} :
Const.insertMany t ((k, v) :: l) = Const.insertMany (t.insert k v) l :=
ext <| Impl.Const.insertMany_cons t.wf
@[grind _=_]
theorem insertMany_append {l₁ l₂ : List (α × β)} :
insertMany t (l₁ ++ l₂) = insertMany (insertMany t l₁) l₂ := by
induction l₁ generalizing t with

2
src/Std/Data/DTreeMap/Raw/Lemmas.lean
View file

@ -1296,6 +1296,7 @@ theorem insertMany_cons {l : List ((a : α) × β a)} {k : α} {v : β k} :
t.insertMany (⟨k, v⟩ :: l) = (t.insert k v).insertMany l :=
ext <| Impl.insertMany!_cons
@[grind _=_]
theorem insertMany_append {l₁ l₂ : List ((a : α) × β a)} :
insertMany t (l₁ ++ l₂) = insertMany (insertMany t l₁) l₂ := by
induction l₁ generalizing t with
@ -1476,6 +1477,7 @@ theorem insertMany_cons {l : List (α × β)} {k : α} {v : β} :
Const.insertMany t ((k, v) :: l) = Const.insertMany (t.insert k v) l :=
ext <| Impl.Const.insertMany!_cons
@[grind _=_]
theorem insertMany_append {l₁ l₂ : List (α × β)} :
insertMany t (l₁ ++ l₂) = insertMany (insertMany t l₁) l₂ := by
induction l₁ generalizing t with

360
src/Std/Data/ExtDHashMap/Lemmas.lean
View file

File diff suppressed because it is too large Load diff

247
src/Std/Data/ExtHashMap/Lemmas.lean
View file

@ -13,6 +13,8 @@ import Std.Data.ExtDHashMap.Lemmas
This module contains lemmas about `Std.ExtHashMap`.
-/
set_option trace.grind.ematch.pattern true
set_option linter.missingDocs true
set_option autoImplicit false
@ -32,7 +34,7 @@ private theorem ext {m m' : ExtHashMap α β} : m.inner = m'.inner → m = m' :=
private theorem ext_iff {m m' : ExtHashMap α β} : m = m' ↔ m.inner = m'.inner :=
⟨fun h => h ▸ rfl, ext⟩
@[simp]
@[simp, grind =]
theorem isEmpty_iff [EquivBEq α] [LawfulHashable α] : m.isEmpty ↔ m = ∅ :=
ExtDHashMap.isEmpty_iff.trans ext_iff.symm
@ -43,7 +45,7 @@ theorem isEmpty_eq_false_iff [EquivBEq α] [LawfulHashable α] : m.isEmpty = fal
@[simp]
theorem empty_eq : ∅ = m ↔ m = ∅ := eq_comm
@[simp]
@[simp, grind =]
theorem emptyWithCapacity_eq [EquivBEq α] [LawfulHashable α] {c} : (emptyWithCapacity c : ExtHashMap α β) = ∅ :=
ext ExtDHashMap.emptyWithCapacity_eq
@ -67,7 +69,7 @@ theorem mem_congr [EquivBEq α] [LawfulHashable α] {a b : α} (hab : a == b) :
a ∈ m ↔ b ∈ m :=
ExtDHashMap.mem_congr hab
@[simp] theorem contains_empty [EquivBEq α] [LawfulHashable α] {a : α} : (∅ : ExtHashMap α β).contains a = false :=
@[simp, grind =] theorem contains_empty [EquivBEq α] [LawfulHashable α] {a : α} : (∅ : ExtHashMap α β).contains a = false :=
ExtDHashMap.contains_empty
@[simp] theorem not_mem_empty [EquivBEq α] [LawfulHashable α] {a : α} : ¬a ∈ (∅ : ExtHashMap α β) :=
@ -87,12 +89,12 @@ theorem eq_empty_iff_forall_not_mem [EquivBEq α] [LawfulHashable α] : m = ∅
Singleton.singleton p = (∅ : ExtHashMap α β).insert p.1 p.2 :=
rfl
@[simp]
@[simp, grind =]
theorem contains_insert [EquivBEq α] [LawfulHashable α] {k a : α} {v : β} :
(m.insert k v).contains a = (k == a || m.contains a) :=
ExtDHashMap.contains_insert
@[simp]
@[simp, grind =]
theorem mem_insert [EquivBEq α] [LawfulHashable α] {k a : α} {v : β} :
a ∈ m.insert k v ↔ k == a ∨ a ∈ m :=
ExtDHashMap.mem_insert
@ -111,13 +113,14 @@ theorem contains_insert_self [EquivBEq α] [LawfulHashable α] {k : α} {v : β}
theorem mem_insert_self [EquivBEq α] [LawfulHashable α] {k : α} {v : β} : k ∈ m.insert k v := by
simp
@[simp]
@[simp, grind =]
theorem size_empty [EquivBEq α] [LawfulHashable α] : (∅ : ExtHashMap α β).size = 0 :=
ExtDHashMap.size_empty
theorem eq_empty_iff_size_eq_zero [EquivBEq α] [LawfulHashable α] : m = ∅ ↔ m.size = 0 :=
ext_iff.trans ExtDHashMap.eq_empty_iff_size_eq_zero
@[grind =]
theorem size_insert [EquivBEq α] [LawfulHashable α] {k : α} {v : β} :
(m.insert k v).size = if k ∈ m then m.size else m.size + 1 :=
ExtDHashMap.size_insert
@ -130,7 +133,7 @@ theorem size_insert_le [EquivBEq α] [LawfulHashable α] {k : α} {v : β} :
(m.insert k v).size ≤ m.size + 1 :=
ExtDHashMap.size_insert_le
@[simp]
@[simp, grind =]
theorem erase_empty [EquivBEq α] [LawfulHashable α] {a : α} : (∅ : ExtHashMap α β).erase a = ∅ :=
ext ExtDHashMap.erase_empty
@ -139,12 +142,12 @@ theorem erase_eq_empty_iff [EquivBEq α] [LawfulHashable α] {k : α} :
m.erase k = ∅ ↔ m = ∅ ∨ m.size = 1 ∧ k ∈ m := by
simpa only [ext_iff] using ExtDHashMap.erase_eq_empty_iff
@[simp]
@[simp, grind =]
theorem contains_erase [EquivBEq α] [LawfulHashable α] {k a : α} :
(m.erase k).contains a = (!(k == a) && m.contains a) :=
ExtDHashMap.contains_erase
@[simp]
@[simp, grind =]
theorem mem_erase [EquivBEq α] [LawfulHashable α] {k a : α} :
a ∈ m.erase k ↔ (k == a) = false ∧ a ∈ m :=
ExtDHashMap.mem_erase
@ -156,7 +159,7 @@ theorem contains_of_contains_erase [EquivBEq α] [LawfulHashable α] {k a : α}
theorem mem_of_mem_erase [EquivBEq α] [LawfulHashable α] {k a : α} : a ∈ m.erase k → a ∈ m :=
ExtDHashMap.mem_of_mem_erase
theorem size_erase [EquivBEq α] [LawfulHashable α] {k : α} :
@[grind =] theorem size_erase [EquivBEq α] [LawfulHashable α] {k : α} :
(m.erase k).size = if k ∈ m then m.size - 1 else m.size :=
ExtDHashMap.size_erase
@ -167,34 +170,35 @@ theorem size_le_size_erase [EquivBEq α] [LawfulHashable α] {k : α} :
m.size ≤ (m.erase k).size + 1 :=
ExtDHashMap.size_le_size_erase
@[simp]
@[simp, grind =]
theorem containsThenInsert_fst [EquivBEq α] [LawfulHashable α] {k : α} {v : β} :
(m.containsThenInsert k v).1 = m.contains k :=
ExtDHashMap.containsThenInsert_fst
@[simp]
@[simp, grind =]
theorem containsThenInsert_snd [EquivBEq α] [LawfulHashable α] {k : α} {v : β} :
(m.containsThenInsert k v).2 = m.insert k v :=
ext (ExtDHashMap.containsThenInsert_snd)
@[simp]
@[simp, grind =]
theorem containsThenInsertIfNew_fst [EquivBEq α] [LawfulHashable α] {k : α} {v : β} :
(m.containsThenInsertIfNew k v).1 = m.contains k :=
ExtDHashMap.containsThenInsertIfNew_fst
@[simp]
@[simp, grind =]
theorem containsThenInsertIfNew_snd [EquivBEq α] [LawfulHashable α] {k : α} {v : β} :
(m.containsThenInsertIfNew k v).2 = m.insertIfNew k v :=
ext ExtDHashMap.containsThenInsertIfNew_snd
@[simp] theorem get_eq_getElem [EquivBEq α] [LawfulHashable α] {a : α} {h} : get m a h = m[a]'h := rfl
@[simp] theorem get?_eq_getElem? [EquivBEq α] [LawfulHashable α] {a : α} : get? m a = m[a]? := rfl
@[simp] theorem get!_eq_getElem! [EquivBEq α] [LawfulHashable α] [Inhabited β] {a : α} : get! m a = m[a]! := rfl
@[simp, grind =] theorem get_eq_getElem [EquivBEq α] [LawfulHashable α] {a : α} {h} : get m a h = m[a]'h := rfl
@[simp, grind =] theorem get?_eq_getElem? [EquivBEq α] [LawfulHashable α] {a : α} : get? m a = m[a]? := rfl
@[simp, grind =] theorem get!_eq_getElem! [EquivBEq α] [LawfulHashable α] [Inhabited β] {a : α} : get! m a = m[a]! := rfl
@[simp]
@[simp, grind =]
theorem getElem?_empty [EquivBEq α] [LawfulHashable α] {a : α} : (∅ : ExtHashMap α β)[a]? = none :=
ExtDHashMap.Const.get?_empty
@[grind =]
theorem getElem?_insert [EquivBEq α] [LawfulHashable α] {k a : α} {v : β} :
(m.insert k v)[a]? = if k == a then some v else m[a]? :=
ExtDHashMap.Const.get?_insert
@ -229,7 +233,7 @@ theorem getElem?_eq_none_of_contains_eq_false [EquivBEq α] [LawfulHashable α]
theorem getElem?_eq_none [EquivBEq α] [LawfulHashable α] {a : α} : ¬a ∈ m → m[a]? = none :=
ExtDHashMap.Const.get?_eq_none
theorem getElem?_erase [EquivBEq α] [LawfulHashable α] {k a : α} :
@[grind =] theorem getElem?_erase [EquivBEq α] [LawfulHashable α] {k a : α} :
(m.erase k)[a]? = if k == a then none else m[a]? :=
ExtDHashMap.Const.get?_erase
@ -240,7 +244,7 @@ theorem getElem?_erase_self [EquivBEq α] [LawfulHashable α] {k : α} : (m.eras
theorem getElem?_congr [EquivBEq α] [LawfulHashable α] {a b : α} (hab : a == b) : m[a]? = m[b]? :=
ExtDHashMap.Const.get?_congr hab
theorem getElem_insert [EquivBEq α] [LawfulHashable α] {k a : α} {v : β} {h₁} :
@[grind =] theorem getElem_insert [EquivBEq α] [LawfulHashable α] {k a : α} {v : β} {h₁} :
(m.insert k v)[a]'h₁ =
if h₂ : k == a then v else m[a]'(mem_of_mem_insert h₁ (Bool.eq_false_iff.2 h₂)) :=
ExtDHashMap.Const.get_insert (h₁ := h₁)
@ -250,7 +254,7 @@ theorem getElem_insert_self [EquivBEq α] [LawfulHashable α] {k : α} {v : β}
(m.insert k v)[k]'mem_insert_self = v :=
ExtDHashMap.Const.get_insert_self
@[simp]
@[simp, grind =]
theorem getElem_erase [EquivBEq α] [LawfulHashable α] {k a : α} {h'} :
(m.erase k)[a]'h' = m[a]'(mem_of_mem_erase h') :=
ExtDHashMap.Const.get_erase (h' := h')
@ -263,7 +267,7 @@ theorem getElem_eq_get_getElem? [EquivBEq α] [LawfulHashable α] {a : α} {h} :
m[a]'h = m[a]?.get (mem_iff_isSome_getElem?.mp h) :=
ExtDHashMap.Const.get_eq_get_get? (h := h)
theorem get_getElem? [EquivBEq α] [LawfulHashable α] {a : α} {h} :
@[grind =] theorem get_getElem? [EquivBEq α] [LawfulHashable α] {a : α} {h} :
m[a]?.get h = m[a]'(mem_iff_isSome_getElem?.mpr h) :=
ExtDHashMap.Const.get_get?
@ -271,12 +275,12 @@ theorem getElem_congr [EquivBEq α] [LawfulHashable α] {a b : α} (hab : a == b
m[a]'h' = m[b]'((mem_congr hab).1 h') :=
ExtDHashMap.Const.get_congr hab (h' := h')
@[simp]
@[simp, grind =]
theorem getElem!_empty [EquivBEq α] [LawfulHashable α] [Inhabited β] {a : α} :
(∅ : ExtHashMap α β)[a]! = default :=
ExtDHashMap.Const.get!_empty
theorem getElem!_insert [EquivBEq α] [LawfulHashable α] [Inhabited β] {k a : α} {v : β} :
@[grind =] theorem getElem!_insert [EquivBEq α] [LawfulHashable α] [Inhabited β] {k a : α} {v : β} :
(m.insert k v)[a]! = if k == a then v else m[a]! :=
ExtDHashMap.Const.get!_insert
@ -293,7 +297,7 @@ theorem getElem!_eq_default [EquivBEq α] [LawfulHashable α] [Inhabited β] {a
¬a ∈ m → m[a]! = default :=
ExtDHashMap.Const.get!_eq_default
theorem getElem!_erase [EquivBEq α] [LawfulHashable α] [Inhabited β] {k a : α} :
@[grind =] theorem getElem!_erase [EquivBEq α] [LawfulHashable α] [Inhabited β] {k a : α} :
(m.erase k)[a]! = if k == a then default else m[a]! :=
ExtDHashMap.Const.get!_erase
@ -322,12 +326,12 @@ theorem getElem!_congr [EquivBEq α] [LawfulHashable α] [Inhabited β] {a b :
m[a]! = m[b]! :=
ExtDHashMap.Const.get!_congr hab
@[simp]
@[simp, grind =]
theorem getD_empty [EquivBEq α] [LawfulHashable α] {a : α} {fallback : β} :
(∅ : ExtHashMap α β).getD a fallback = fallback :=
ExtDHashMap.Const.getD_empty
theorem getD_insert [EquivBEq α] [LawfulHashable α] {k a : α} {fallback v : β} :
@[grind =] theorem getD_insert [EquivBEq α] [LawfulHashable α] {k a : α} {fallback v : β} :
(m.insert k v).getD a fallback = if k == a then v else m.getD a fallback :=
ExtDHashMap.Const.getD_insert
@ -344,7 +348,7 @@ theorem getD_eq_fallback [EquivBEq α] [LawfulHashable α] {a : α} {fallback :
¬a ∈ m → m.getD a fallback = fallback :=
ExtDHashMap.Const.getD_eq_fallback
theorem getD_erase [EquivBEq α] [LawfulHashable α] {k a : α} {fallback : β} :
@[grind =] theorem getD_erase [EquivBEq α] [LawfulHashable α] {k a : α} {fallback : β} :
(m.erase k).getD a fallback = if k == a then fallback else m.getD a fallback :=
ExtDHashMap.Const.getD_erase
@ -377,12 +381,12 @@ theorem getD_congr [EquivBEq α] [LawfulHashable α] {a b : α} {fallback : β}
m.getD a fallback = m.getD b fallback :=
ExtDHashMap.Const.getD_congr hab
@[simp]
@[simp, grind =]
theorem getKey?_empty [EquivBEq α] [LawfulHashable α] {a : α} :
(∅ : ExtHashMap α β).getKey? a = none :=
ExtDHashMap.getKey?_empty
theorem getKey?_insert [EquivBEq α] [LawfulHashable α] {k a : α} {v : β} :
@[grind =] theorem getKey?_insert [EquivBEq α] [LawfulHashable α] {k a : α} {v : β} :
(m.insert k v).getKey? a = if k == a then some k else m.getKey? a :=
ExtDHashMap.getKey?_insert
@ -420,7 +424,7 @@ theorem getKey?_eq_none_of_contains_eq_false [EquivBEq α] [LawfulHashable α] {
theorem getKey?_eq_none [EquivBEq α] [LawfulHashable α] {a : α} : ¬a ∈ m → m.getKey? a = none :=
ExtDHashMap.getKey?_eq_none
theorem getKey?_erase [EquivBEq α] [LawfulHashable α] {k a : α} :
@[grind =] theorem getKey?_erase [EquivBEq α] [LawfulHashable α] {k a : α} :
(m.erase k).getKey? a = if k == a then none else m.getKey? a :=
ExtDHashMap.getKey?_erase
@ -442,7 +446,7 @@ theorem getKey?_eq_some_of_contains [LawfulBEq α] {k : α} (h : m.contains k) :
theorem getKey?_eq_some [LawfulBEq α] {k : α} (h : k ∈ m) : m.getKey? k = some k := by
simpa only [mem_iff_contains] using getKey?_eq_some_of_contains h
theorem getKey_insert [EquivBEq α] [LawfulHashable α] {k a : α} {v : β} {h₁} :
@[grind =] theorem getKey_insert [EquivBEq α] [LawfulHashable α] {k a : α} {v : β} {h₁} :
(m.insert k v).getKey a h₁ =
if h₂ : k == a then k else m.getKey a ((mem_of_mem_insert h₁ (by simpa using h₂))) :=
ExtDHashMap.getKey_insert (h₁ := h₁)
@ -452,7 +456,7 @@ theorem getKey_insert_self [EquivBEq α] [LawfulHashable α] {k : α} {v : β} :
(m.insert k v).getKey k mem_insert_self = k :=
ExtDHashMap.getKey_insert_self
@[simp]
@[simp, grind =]
theorem getKey_erase [EquivBEq α] [LawfulHashable α] {k a : α} {h'} :
(m.erase k).getKey a h' = m.getKey a (mem_of_mem_erase h') :=
ExtDHashMap.getKey_erase (h' := h')
@ -465,7 +469,7 @@ theorem getKey_eq_get_getKey? [EquivBEq α] [LawfulHashable α] {a : α} {h} :
m.getKey a h = (m.getKey? a).get (mem_iff_isSome_getKey?.mp h) :=
ExtDHashMap.getKey_eq_get_getKey?
@[simp]
@[simp, grind =]
theorem get_getKey? [EquivBEq α] [LawfulHashable α] {a : α} {h} :
(m.getKey? a).get h = m.getKey a (mem_iff_isSome_getKey?.mpr h) :=
ExtDHashMap.get_getKey?
@ -477,16 +481,16 @@ theorem getKey_congr [EquivBEq α] [LawfulHashable α] {k₁ k₂ : α} (h : k
(h₁ : k₁ ∈ m) : m.getKey k₁ h₁ = m.getKey k₂ ((mem_congr h).mp h₁) :=
ExtDHashMap.getKey_congr h h₁
@[simp]
@[simp, grind =]
theorem getKey_eq [LawfulBEq α] {k : α} (h : k ∈ m) : m.getKey k h = k :=
ExtDHashMap.getKey_eq h
@[simp]
@[simp, grind =]
theorem getKey!_empty [EquivBEq α] [LawfulHashable α] [Inhabited α] {a : α} :
(∅ : ExtHashMap α β).getKey! a = default :=
ExtDHashMap.getKey!_empty
theorem getKey!_insert [EquivBEq α] [LawfulHashable α] [Inhabited α] {k a : α} {v : β} :
@[grind =] theorem getKey!_insert [EquivBEq α] [LawfulHashable α] [Inhabited α] {k a : α} {v : β} :
(m.insert k v).getKey! a = if k == a then k else m.getKey! a :=
ExtDHashMap.getKey!_insert
@ -503,7 +507,7 @@ theorem getKey!_eq_default [EquivBEq α] [LawfulHashable α] [Inhabited α] {a :
¬a ∈ m → m.getKey! a = default :=
ExtDHashMap.getKey!_eq_default
theorem getKey!_erase [EquivBEq α] [LawfulHashable α] [Inhabited α] {k a : α} :
@[grind =] theorem getKey!_erase [EquivBEq α] [LawfulHashable α] [Inhabited α] {k a : α} :
(m.erase k).getKey! a = if k == a then default else m.getKey! a :=
ExtDHashMap.getKey!_erase
@ -539,12 +543,12 @@ theorem getKey!_eq_of_contains [LawfulBEq α] [Inhabited α] {k : α} (h : m.con
theorem getKey!_eq_of_mem [LawfulBEq α] [Inhabited α] {k : α} (h : k ∈ m) : m.getKey! k = k :=
ExtDHashMap.getKey!_eq_of_mem h
@[simp]
@[simp, grind =]
theorem getKeyD_empty [EquivBEq α] [LawfulHashable α] {a : α} {fallback : α} :
(∅ : ExtHashMap α β).getKeyD a fallback = fallback :=
ExtDHashMap.getKeyD_empty
theorem getKeyD_insert [EquivBEq α] [LawfulHashable α] {k a fallback : α} {v : β} :
@[grind =] theorem getKeyD_insert [EquivBEq α] [LawfulHashable α] {k a fallback : α} {v : β} :
(m.insert k v).getKeyD a fallback = if k == a then k else m.getKeyD a fallback :=
ExtDHashMap.getKeyD_insert
@ -561,7 +565,7 @@ theorem getKeyD_eq_fallback [EquivBEq α] [LawfulHashable α] {a : α} {fallback
¬a ∈ m → m.getKeyD a fallback = fallback :=
ExtDHashMap.getKeyD_eq_fallback
theorem getKeyD_erase [EquivBEq α] [LawfulHashable α] {k a : α} {fallback : α} :
@[grind =] theorem getKeyD_erase [EquivBEq α] [LawfulHashable α] {k a : α} {fallback : α} :
(m.erase k).getKeyD a fallback = if k == a then fallback else m.getKeyD a fallback :=
ExtDHashMap.getKeyD_erase
@ -607,12 +611,12 @@ theorem not_insertIfNew_eq_empty [EquivBEq α] [LawfulHashable α] {k : α} {v :
¬m.insertIfNew k v = ∅ :=
(not_congr ext_iff).mpr ExtDHashMap.not_insertIfNew_eq_empty
@[simp]
@[simp, grind =]
theorem contains_insertIfNew [EquivBEq α] [LawfulHashable α] {k a : α} {v : β} :
(m.insertIfNew k v).contains a = (k == a || m.contains a) :=
ExtDHashMap.contains_insertIfNew
@[simp]
@[simp, grind =]
theorem mem_insertIfNew [EquivBEq α] [LawfulHashable α] {k a : α} {v : β} :
a ∈ m.insertIfNew k v ↔ k == a ∨ a ∈ m :=
ExtDHashMap.mem_insertIfNew
@ -645,7 +649,7 @@ theorem mem_of_mem_insertIfNew' [EquivBEq α] [LawfulHashable α] {k a : α} {v
a ∈ m.insertIfNew k v → ¬((k == a) ∧ ¬k ∈ m) → a ∈ m :=
ExtDHashMap.mem_of_mem_insertIfNew'
theorem size_insertIfNew [EquivBEq α] [LawfulHashable α] {k : α} {v : β} :
@[grind =] theorem size_insertIfNew [EquivBEq α] [LawfulHashable α] {k : α} {v : β} :
(m.insertIfNew k v).size = if k ∈ m then m.size else m.size + 1 :=
ExtDHashMap.size_insertIfNew
@ -657,47 +661,47 @@ theorem size_insertIfNew_le [EquivBEq α] [LawfulHashable α] {k : α} {v : β}
(m.insertIfNew k v).size ≤ m.size + 1 :=
ExtDHashMap.size_insertIfNew_le
theorem getElem?_insertIfNew [EquivBEq α] [LawfulHashable α] {k a : α} {v : β} :
@[grind =] theorem getElem?_insertIfNew [EquivBEq α] [LawfulHashable α] {k a : α} {v : β} :
(m.insertIfNew k v)[a]? = if k == a ∧ ¬k ∈ m then some v else m[a]? :=
ExtDHashMap.Const.get?_insertIfNew
theorem getElem_insertIfNew [EquivBEq α] [LawfulHashable α] {k a : α} {v : β} {h₁} :
@[grind =] theorem getElem_insertIfNew [EquivBEq α] [LawfulHashable α] {k a : α} {v : β} {h₁} :
(m.insertIfNew k v)[a]'h₁ =
if h₂ : k == a ∧ ¬k ∈ m then v else m[a]'(mem_of_mem_insertIfNew' h₁ h₂) :=
ExtDHashMap.Const.get_insertIfNew (h₁ := h₁)
theorem getElem!_insertIfNew [EquivBEq α] [LawfulHashable α] [Inhabited β] {k a : α} {v : β} :
@[grind =] theorem getElem!_insertIfNew [EquivBEq α] [LawfulHashable α] [Inhabited β] {k a : α} {v : β} :
(m.insertIfNew k v)[a]! = if k == a ∧ ¬k ∈ m then v else m[a]! :=
ExtDHashMap.Const.get!_insertIfNew
theorem getD_insertIfNew [EquivBEq α] [LawfulHashable α] {k a : α} {fallback v : β} :
@[grind =] theorem getD_insertIfNew [EquivBEq α] [LawfulHashable α] {k a : α} {fallback v : β} :
(m.insertIfNew k v).getD a fallback =
if k == a ∧ ¬k ∈ m then v else m.getD a fallback :=
ExtDHashMap.Const.getD_insertIfNew
theorem getKey?_insertIfNew [EquivBEq α] [LawfulHashable α] {k a : α} {v : β} :
@[grind =] theorem getKey?_insertIfNew [EquivBEq α] [LawfulHashable α] {k a : α} {v : β} :
getKey? (m.insertIfNew k v) a = if k == a ∧ ¬k ∈ m then some k else getKey? m a :=
ExtDHashMap.getKey?_insertIfNew
theorem getKey_insertIfNew [EquivBEq α] [LawfulHashable α] {k a : α} {v : β} {h₁} :
@[grind =] theorem getKey_insertIfNew [EquivBEq α] [LawfulHashable α] {k a : α} {v : β} {h₁} :
getKey (m.insertIfNew k v) a h₁ =
if h₂ : k == a ∧ ¬k ∈ m then k else getKey m a (mem_of_mem_insertIfNew' h₁ h₂) :=
ExtDHashMap.getKey_insertIfNew
theorem getKey!_insertIfNew [EquivBEq α] [LawfulHashable α] [Inhabited α] {k a : α} {v : β} :
@[grind =] theorem getKey!_insertIfNew [EquivBEq α] [LawfulHashable α] [Inhabited α] {k a : α} {v : β} :
getKey! (m.insertIfNew k v) a = if k == a ∧ ¬k ∈ m then k else getKey! m a :=
ExtDHashMap.getKey!_insertIfNew
theorem getKeyD_insertIfNew [EquivBEq α] [LawfulHashable α] {k a fallback : α} {v : β} :
@[grind =] theorem getKeyD_insertIfNew [EquivBEq α] [LawfulHashable α] {k a fallback : α} {v : β} :
getKeyD (m.insertIfNew k v) a fallback = if k == a ∧ ¬k ∈ m then k else getKeyD m a fallback :=
ExtDHashMap.getKeyD_insertIfNew
@[simp]
@[simp, grind =]
theorem getThenInsertIfNew?_fst [EquivBEq α] [LawfulHashable α] {k : α} {v : β} :
(getThenInsertIfNew? m k v).1 = get? m k :=
ExtDHashMap.Const.getThenInsertIfNew?_fst
@[simp]
@[simp, grind =]
theorem getThenInsertIfNew?_snd [EquivBEq α] [LawfulHashable α] {k : α} {v : β} :
(getThenInsertIfNew? m k v).2 = m.insertIfNew k v :=
ext (ExtDHashMap.Const.getThenInsertIfNew?_snd)
@ -713,20 +717,22 @@ instance [EquivBEq α] [LawfulHashable α] : LawfulGetElem (ExtHashMap α β) α
variable {ρ : Type w} [ForIn Id ρ (α × β)]
@[simp]
@[simp, grind =]
theorem insertMany_nil [EquivBEq α] [LawfulHashable α] :
insertMany m [] = m :=
ext ExtDHashMap.Const.insertMany_nil
@[simp]
@[simp, grind =]
theorem insertMany_list_singleton [EquivBEq α] [LawfulHashable α] {k : α} {v : β} :
insertMany m [⟨k, v⟩] = m.insert k v :=
ext ExtDHashMap.Const.insertMany_list_singleton
@[grind =]
theorem insertMany_cons [EquivBEq α] [LawfulHashable α] {l : List (α × β)} {k : α} {v : β} :
insertMany m (⟨k, v⟩ :: l) = insertMany (m.insert k v) l :=
ext ExtDHashMap.Const.insertMany_cons
@[grind _=_]
theorem insertMany_append [EquivBEq α] [LawfulHashable α] {l₁ l₂ : List (α × β)} :
insertMany m (l₁ ++ l₂) = insertMany (insertMany m l₁) l₂ := by
induction l₁ generalizing m with
@ -742,13 +748,13 @@ theorem insertMany_ind [EquivBEq α] [LawfulHashable α]
show motive ⟨ExtDHashMap.Const.insertMany m.1 l⟩ from
ExtDHashMap.Const.insertMany_ind m.inner l init fun m => insert ⟨m⟩
@[simp]
@[simp, grind =]
theorem contains_insertMany_list [EquivBEq α] [LawfulHashable α]
{l : List (α × β)} {k : α} :
(insertMany m l).contains k = (m.contains k || (l.map Prod.fst).contains k) :=
ExtDHashMap.Const.contains_insertMany_list
@[simp]
@[simp, grind =]
theorem mem_insertMany_list [EquivBEq α] [LawfulHashable α]
{l : List (α × β)} {k : α} :
k ∈ insertMany m l ↔ k ∈ m ∨ (l.map Prod.fst).contains k :=
@ -776,7 +782,7 @@ theorem getElem?_insertMany_list_of_mem [EquivBEq α] [LawfulHashable α]
(insertMany m l)[k']? = some v :=
ExtDHashMap.Const.get?_insertMany_list_of_mem k_beq distinct mem
theorem getElem?_insertMany_list [EquivBEq α] [LawfulHashable α]
@[grind =] theorem getElem?_insertMany_list [EquivBEq α] [LawfulHashable α]
{l : List (α × β)} {k : α} :
(insertMany m l)[k]? = (l.findSomeRev? (fun ⟨a, b⟩ => if a == k then some b else none)).or m[k]? :=
ExtDHashMap.Const.get?_insertMany_list
@ -893,11 +899,15 @@ theorem size_le_size_insertMany [EquivBEq α] [LawfulHashable α]
{l : ρ} : m.size ≤ (insertMany m l).size :=
ExtDHashMap.Const.size_le_size_insertMany
grind_pattern size_le_size_insertMany => (insertMany m l).size
theorem size_insertMany_list_le [EquivBEq α] [LawfulHashable α]
{l : List (α × β)} :
(insertMany m l).size ≤ m.size + l.length :=
ExtDHashMap.Const.size_insertMany_list_le
grind_pattern size_insertMany_list_le => (insertMany m l).size
@[simp]
theorem insertMany_list_eq_empty_iff [EquivBEq α] [LawfulHashable α] {l : List (α × β)} :
m.insertMany l = ∅ ↔ m = ∅ ∧ l = [] := by
@ -1079,16 +1089,17 @@ end
section
@[simp]
@[simp, grind =]
theorem ofList_nil [EquivBEq α] [LawfulHashable α] :
ofList ([] : List (α × β)) = ∅ :=
ext ExtDHashMap.Const.ofList_nil
@[simp]
@[simp, grind =]
theorem ofList_singleton [EquivBEq α] [LawfulHashable α] {k : α} {v : β} :
ofList [⟨k, v⟩] = (∅ : ExtHashMap α β).insert k v :=
ext ExtDHashMap.Const.ofList_singleton
@[grind _=_]
theorem ofList_cons [EquivBEq α] [LawfulHashable α] {k : α} {v : β} {tl : List (α × β)} :
ofList (⟨k, v⟩ :: tl) = insertMany ((∅ : ExtHashMap α β).insert k v) tl :=
ext ExtDHashMap.Const.ofList_cons
@ -1097,13 +1108,13 @@ theorem ofList_eq_insertMany_empty [EquivBEq α] [LawfulHashable α] {l : List (
ofList l = insertMany (∅ : ExtHashMap α β) l :=
ext ExtDHashMap.Const.ofList_eq_insertMany_empty
@[simp]
@[simp, grind =]
theorem contains_ofList [EquivBEq α] [LawfulHashable α]
{l : List (α × β)} {k : α} :
(ofList l).contains k = (l.map Prod.fst).contains k :=
ExtDHashMap.Const.contains_ofList
@[simp]
@[simp, grind =]
theorem mem_ofList [EquivBEq α] [LawfulHashable α]
{l : List (α × β)} {k : α} :
k ∈ ofList l ↔ (l.map Prod.fst).contains k :=
@ -1217,6 +1228,8 @@ theorem size_ofList_le [EquivBEq α] [LawfulHashable α]
(ofList l).size ≤ l.length :=
ExtDHashMap.Const.size_ofList_le
grind_pattern size_ofList => (ofList l).size
@[simp]
theorem ofList_eq_empty_iff [EquivBEq α] [LawfulHashable α] {l : List (α × β)} :
ofList l = ∅ ↔ l = [] :=
@ -1350,11 +1363,11 @@ theorem alter_eq_empty_iff [EquivBEq α] [LawfulHashable α] {k : α} {f : Optio
alter m k f = ∅ ↔ (m = ∅ ∨ (m.size = 1 ∧ k ∈ m)) ∧ f m[k]? = none := by
simpa only [ext_iff] using ExtDHashMap.Const.alter_eq_empty_iff
theorem contains_alter [EquivBEq α] [LawfulHashable α] {k k': α} {f : Option β → Option β} :
@[grind =] theorem contains_alter [EquivBEq α] [LawfulHashable α] {k k': α} {f : Option β → Option β} :
(alter m k f).contains k' = if k == k' then (f m[k]?).isSome else m.contains k' :=
ExtDHashMap.Const.contains_alter
theorem mem_alter [EquivBEq α] [LawfulHashable α] {k k': α} {f : Option β → Option β} :
@[grind =] theorem mem_alter [EquivBEq α] [LawfulHashable α] {k k': α} {f : Option β → Option β} :
k' ∈ alter m k f ↔ if k == k' then (f m[k]?).isSome = true else k' ∈ m :=
ExtDHashMap.Const.mem_alter
@ -1381,7 +1394,7 @@ theorem mem_alter_of_beq_eq_false [EquivBEq α] [LawfulHashable α] {k k' : α}
{f : Option β → Option β} (h : (k == k') = false) : k' ∈ alter m k f ↔ k' ∈ m :=
ExtDHashMap.Const.mem_alter_of_beq_eq_false h
theorem size_alter [EquivBEq α] [LawfulHashable α] {k : α} {f : Option β → Option β} :
@[grind =] theorem size_alter [EquivBEq α] [LawfulHashable α] {k : α} {f : Option β → Option β} :
(m.alter k f).size =
if k ∈ m ∧ (f m[k]?).isNone then
m.size - 1
@ -1419,7 +1432,7 @@ theorem size_le_size_alter [EquivBEq α] [LawfulHashable α] {k : α} {f : Optio
m.size - 1 ≤ (alter m k f).size :=
ExtDHashMap.Const.size_le_size_alter
theorem getElem?_alter [EquivBEq α] [LawfulHashable α] {k k' : α} {f : Option β → Option β} :
@[grind =] theorem getElem?_alter [EquivBEq α] [LawfulHashable α] {k k' : α} {f : Option β → Option β} :
(alter m k f)[k']? =
if k == k' then
f m[k]?
@ -1446,7 +1459,7 @@ theorem get?_alter_self [EquivBEq α] [LawfulHashable α] {k : α} {f : Option
get? (alter m k f) k = f (get? m k) :=
ExtDHashMap.Const.get?_alter_self
theorem getElem_alter [EquivBEq α] [LawfulHashable α] {k k' : α} {f : Option β → Option β}
@[grind =] theorem getElem_alter [EquivBEq α] [LawfulHashable α] {k k' : α} {f : Option β → Option β}
{h : k' ∈ alter m k f} :
(alter m k f)[k'] =
if heq : k == k' then
@ -1483,7 +1496,7 @@ theorem get_alter_self [EquivBEq α] [LawfulHashable α] {k : α} {f : Option β
get (alter m k f) k h = (f (get? m k)).get h' :=
ExtDHashMap.Const.get_alter_self
theorem getElem!_alter [EquivBEq α] [LawfulHashable α] {k k' : α} [Inhabited β]
@[grind =] theorem getElem!_alter [EquivBEq α] [LawfulHashable α] {k k' : α} [Inhabited β]
{f : Option β → Option β} : (alter m k f)[k']! =
if k == k' then
f m[k]? |>.get!
@ -1510,7 +1523,7 @@ theorem get!_alter_self [EquivBEq α] [LawfulHashable α] {k : α} [Inhabited β
{f : Option β → Option β} : get! (alter m k f) k = (f (get? m k)).get! :=
ExtDHashMap.Const.get!_alter_self
theorem getD_alter [EquivBEq α] [LawfulHashable α] {k k' : α} {fallback : β}
@[grind =] theorem getD_alter [EquivBEq α] [LawfulHashable α] {k k' : α} {fallback : β}
{f : Option β → Option β} :
getD (alter m k f) k' fallback =
if k == k' then
@ -1525,7 +1538,7 @@ theorem getD_alter_self [EquivBEq α] [LawfulHashable α] {k : α} {fallback :
getD (alter m k f) k fallback = (f m[k]?).getD fallback :=
ExtDHashMap.Const.getD_alter_self
theorem getKey?_alter [EquivBEq α] [LawfulHashable α] {k k' : α} {f : Option β → Option β} :
@[grind =] theorem getKey?_alter [EquivBEq α] [LawfulHashable α] {k k' : α} {f : Option β → Option β} :
(alter m k f).getKey? k' =
if k == k' then
if (f m[k]?).isSome then some k else none
@ -1537,7 +1550,7 @@ theorem getKey?_alter_self [EquivBEq α] [LawfulHashable α] {k : α} {f : Optio
(alter m k f).getKey? k = if (f m[k]?).isSome then some k else none :=
ExtDHashMap.Const.getKey?_alter_self
theorem getKey!_alter [EquivBEq α] [LawfulHashable α] [Inhabited α] {k k' : α}
@[grind =] theorem getKey!_alter [EquivBEq α] [LawfulHashable α] [Inhabited α] {k k' : α}
{f : Option β → Option β} : (alter m k f).getKey! k' =
if k == k' then
if (f m[k]?).isSome then k else default
@ -1550,7 +1563,7 @@ theorem getKey!_alter_self [EquivBEq α] [LawfulHashable α] [Inhabited α] {k :
(alter m k f).getKey! k = if (f m[k]?).isSome then k else default :=
ExtDHashMap.Const.getKey!_alter_self
theorem getKey_alter [EquivBEq α] [LawfulHashable α] [Inhabited α] {k k' : α}
@[grind =] theorem getKey_alter [EquivBEq α] [LawfulHashable α] [Inhabited α] {k k' : α}
{f : Option β → Option β} {h : k' ∈ alter m k f} :
(alter m k f).getKey k' h =
if heq : k == k' then
@ -1566,7 +1579,7 @@ theorem getKey_alter_self [EquivBEq α] [LawfulHashable α] [Inhabited α] {k :
(alter m k f).getKey k h = k :=
ExtDHashMap.Const.getKey_alter_self
theorem getKeyD_alter [EquivBEq α] [LawfulHashable α] {k k' fallback : α}
@[grind =] theorem getKeyD_alter [EquivBEq α] [LawfulHashable α] {k k' fallback : α}
{f : Option β → Option β} :
(alter m k f).getKeyD k' fallback =
if k == k' then
@ -1591,22 +1604,22 @@ theorem modify_eq_empty_iff [EquivBEq α] [LawfulHashable α] {k : α} {f : β
modify m k f = ∅ ↔ m = ∅ := by
simpa only [ext_iff] using ExtDHashMap.Const.modify_eq_empty_iff
@[simp]
@[simp, grind =]
theorem contains_modify [EquivBEq α] [LawfulHashable α] {k k': α} {f : β → β} :
(modify m k f).contains k' = m.contains k' :=
ExtDHashMap.Const.contains_modify
@[simp]
@[simp, grind =]
theorem mem_modify [EquivBEq α] [LawfulHashable α] {k k': α} {f : β → β} :
k' ∈ modify m k f ↔ k' ∈ m :=
ExtDHashMap.Const.mem_modify
@[simp]
@[simp, grind =]
theorem size_modify [EquivBEq α] [LawfulHashable α] {k : α} {f : β → β} :
(modify m k f).size = m.size :=
ExtDHashMap.Const.size_modify
theorem getElem?_modify [EquivBEq α] [LawfulHashable α] {k k' : α} {f : β → β} :
@[grind =] theorem getElem?_modify [EquivBEq α] [LawfulHashable α] {k k' : α} {f : β → β} :
(modify m k f)[k']? =
if k == k' then
m[k]?.map f
@ -1633,7 +1646,7 @@ theorem get?_modify_self [EquivBEq α] [LawfulHashable α] {k : α} {f : β →
get? (modify m k f) k = (get? m k).map f :=
ExtDHashMap.Const.get?_modify_self
theorem getElem_modify [EquivBEq α] [LawfulHashable α] {k k' : α} {f : β → β}
@[grind =] theorem getElem_modify [EquivBEq α] [LawfulHashable α] {k k' : α} {f : β → β}
{h : k' ∈ modify m k f} :
(modify m k f)[k'] =
if heq : k == k' then
@ -1670,7 +1683,7 @@ theorem get_modify_self [EquivBEq α] [LawfulHashable α] {k : α} {f : β →
get (modify m k f) k h = f (get m k h') :=
ExtDHashMap.Const.get_modify_self
theorem getElem!_modify [EquivBEq α] [LawfulHashable α] {k k' : α} [Inhabited β] {f : β → β} :
@[grind =] theorem getElem!_modify [EquivBEq α] [LawfulHashable α] {k k' : α} [Inhabited β] {f : β → β} :
(modify m k f)[k']! =
if k == k' then
m[k]?.map f |>.get!
@ -1697,7 +1710,7 @@ theorem get!_modify_self [EquivBEq α] [LawfulHashable α] {k : α} [Inhabited
get! (modify m k f) k = ((get? m k).map f).get! :=
ExtDHashMap.Const.get!_modify_self
theorem getD_modify [EquivBEq α] [LawfulHashable α] {k k' : α} {fallback : β} {f : β → β} :
@[grind =] theorem getD_modify [EquivBEq α] [LawfulHashable α] {k k' : α} {fallback : β} {f : β → β} :
getD (modify m k f) k' fallback =
if k == k' then
m[k]?.map f |>.getD fallback
@ -1710,7 +1723,7 @@ theorem getD_modify_self [EquivBEq α] [LawfulHashable α] {k : α} {fallback :
getD (modify m k f) k fallback = (m[k]?.map f).getD fallback :=
ExtDHashMap.Const.getD_modify_self
theorem getKey?_modify [EquivBEq α] [LawfulHashable α] {k k' : α} {f : β → β} :
@[grind =] theorem getKey?_modify [EquivBEq α] [LawfulHashable α] {k k' : α} {f : β → β} :
(modify m k f).getKey? k' =
if k == k' then
if k ∈ m then some k else none
@ -1722,7 +1735,7 @@ theorem getKey?_modify_self [EquivBEq α] [LawfulHashable α] {k : α} {f : β
(modify m k f).getKey? k = if k ∈ m then some k else none :=
ExtDHashMap.Const.getKey?_modify_self
theorem getKey!_modify [EquivBEq α] [LawfulHashable α] [Inhabited α] {k k' : α} {f : β → β} :
@[grind =] theorem getKey!_modify [EquivBEq α] [LawfulHashable α] [Inhabited α] {k k' : α} {f : β → β} :
(modify m k f).getKey! k' =
if k == k' then
if k ∈ m then k else default
@ -1734,7 +1747,7 @@ theorem getKey!_modify_self [EquivBEq α] [LawfulHashable α] [Inhabited α] {k
(modify m k f).getKey! k = if k ∈ m then k else default :=
ExtDHashMap.Const.getKey!_modify_self
theorem getKey_modify [EquivBEq α] [LawfulHashable α] [Inhabited α] {k k' : α} {f : β → β}
@[grind =] theorem getKey_modify [EquivBEq α] [LawfulHashable α] [Inhabited α] {k k' : α} {f : β → β}
{h : k' ∈ modify m k f} :
(modify m k f).getKey k' h =
if k == k' then
@ -1749,7 +1762,7 @@ theorem getKey_modify_self [EquivBEq α] [LawfulHashable α] [Inhabited α] {k :
{h : k ∈ modify m k f} : (modify m k f).getKey k h = k :=
ExtDHashMap.Const.getKey_modify_self
theorem getKeyD_modify [EquivBEq α] [LawfulHashable α] {k k' fallback : α} {f : β → β} :
@[grind =] theorem getKeyD_modify [EquivBEq α] [LawfulHashable α] {k k' fallback : α} {f : β → β} :
(modify m k f).getKeyD k' fallback =
if k == k' then
if k ∈ m then k else fallback
@ -1801,7 +1814,7 @@ theorem filterMap_eq_empty_iff [EquivBEq α] [LawfulHashable α] {f : α → β
m.filterMap f = ∅ ↔ ∀ k h, f (m.getKey k h) (m[k]'h) = none :=
ext_iff.trans ExtDHashMap.Const.filterMap_eq_empty_iff
theorem mem_filterMap [EquivBEq α] [LawfulHashable α]
@[grind =] theorem mem_filterMap [EquivBEq α] [LawfulHashable α]
{f : α → β → Option γ} {k : α} :
k ∈ m.filterMap f ↔ ∃ h, (f (m.getKey k h) m[k]).isSome :=
ExtDHashMap.Const.mem_filterMap
@ -1821,12 +1834,14 @@ theorem size_filterMap_le_size [EquivBEq α] [LawfulHashable α]
(m.filterMap f).size ≤ m.size :=
ExtDHashMap.size_filterMap_le_size
grind_pattern size_filterMap_le_size => (m.filterMap f).size
theorem size_filterMap_eq_size_iff [EquivBEq α] [LawfulHashable α]
{f : α → β → Option γ} :
(m.filterMap f).size = m.size ↔ ∀ k h, (f (m.getKey k h) m[k]).isSome :=
ExtDHashMap.Const.size_filterMap_eq_size_iff
theorem getElem?_filterMap [EquivBEq α] [LawfulHashable α]
@[grind =] theorem getElem?_filterMap [EquivBEq α] [LawfulHashable α]
{f : α → β → Option γ} {k : α} :
(m.filterMap f)[k]? = m[k]?.pbind (fun x h' =>
f (m.getKey k (mem_iff_isSome_getElem?.mpr (Option.isSome_of_eq_some h'))) x) :=
@ -1844,8 +1859,7 @@ theorem isSome_apply_of_mem_filterMap [EquivBEq α] [LawfulHashable α]
(m[k]'(mem_of_mem_filterMap h))).isSome :=
ExtDHashMap.Const.isSome_apply_of_mem_filterMap
@[simp]
theorem getElem_filterMap [EquivBEq α] [LawfulHashable α]
@[simp, grind =] theorem getElem_filterMap [EquivBEq α] [LawfulHashable α]
{f : α → β → Option γ} {k : α} {h} :
(m.filterMap f)[k]'h =
(f (m.getKey k (mem_of_mem_filterMap h))
@ -1853,7 +1867,7 @@ theorem getElem_filterMap [EquivBEq α] [LawfulHashable α]
(isSome_apply_of_mem_filterMap h) :=
ExtDHashMap.Const.get_filterMap (h := h)
theorem getElem!_filterMap [EquivBEq α] [LawfulHashable α] [Inhabited γ]
@[grind =] theorem getElem!_filterMap [EquivBEq α] [LawfulHashable α] [Inhabited γ]
{f : α → β → Option γ} {k : α} :
(m.filterMap f)[k]! =
(m[k]?.pbind (fun x h' =>
@ -1865,7 +1879,7 @@ theorem getElem!_filterMap_of_getKey?_eq_some [EquivBEq α] [LawfulHashable α]
(m.filterMap f)[k]! = (m[k]?.bind (f k')).get! :=
ExtDHashMap.Const.get!_filterMap_of_getKey?_eq_some h
theorem getD_filterMap [EquivBEq α] [LawfulHashable α]
@[grind =] theorem getD_filterMap [EquivBEq α] [LawfulHashable α]
{f : α → β → Option γ} {k : α} {fallback : γ} :
(m.filterMap f).getD k fallback =
(m[k]?.pbind (fun x h' =>
@ -1877,27 +1891,27 @@ theorem getD_filterMap_of_getKey?_eq_some [EquivBEq α] [LawfulHashable α]
(m.filterMap f).getD k fallback = (m[k]?.bind (f k')).getD fallback :=
ExtDHashMap.Const.getD_filterMap_of_getKey?_eq_some h
theorem getKey?_filterMap [EquivBEq α] [LawfulHashable α]
@[grind =] theorem getKey?_filterMap [EquivBEq α] [LawfulHashable α]
{f : α → β → Option γ} {k : α} :
(m.filterMap f).getKey? k =
(m.getKey? k).pfilter (fun x h' =>
(f x (m[x]'(mem_of_getKey?_eq_some h'))).isSome) :=
ExtDHashMap.Const.getKey?_filterMap
@[simp]
@[simp, grind =]
theorem getKey_filterMap [EquivBEq α] [LawfulHashable α]
{f : α → β → Option γ} {k : α} {h'} :
(m.filterMap f).getKey k h' = m.getKey k (mem_of_mem_filterMap h') :=
ExtDHashMap.getKey_filterMap
theorem getKey!_filterMap [EquivBEq α] [LawfulHashable α] [Inhabited α]
@[grind =] theorem getKey!_filterMap [EquivBEq α] [LawfulHashable α] [Inhabited α]
{f : α → β → Option γ} {k : α} :
(m.filterMap f).getKey! k =
((m.getKey? k).pfilter (fun x h' =>
(f x (m[x]'(mem_of_getKey?_eq_some h'))).isSome)).get! :=
ExtDHashMap.Const.getKey!_filterMap
theorem getKeyD_filterMap [EquivBEq α] [LawfulHashable α]
@[grind =] theorem getKeyD_filterMap [EquivBEq α] [LawfulHashable α]
{f : α → β → Option γ} {k fallback : α} :
(m.filterMap f).getKeyD k fallback =
((m.getKey? k).pfilter (fun x h' =>
@ -1918,7 +1932,7 @@ theorem filter_eq_empty_iff [EquivBEq α] [LawfulHashable α] {f : α → β →
m.filter f = ∅ ↔ ∀ k h, f (m.getKey k h) (m[k]'h) = false :=
ext_iff.trans ExtDHashMap.Const.filter_eq_empty_iff
theorem mem_filter [EquivBEq α] [LawfulHashable α]
@[grind =] theorem mem_filter [EquivBEq α] [LawfulHashable α]
{f : α → β → Bool} {k : α} :
k ∈ m.filter f ↔ ∃ (h' : k ∈ m), f (m.getKey k h') m[k] :=
ExtDHashMap.Const.mem_filter
@ -1938,6 +1952,8 @@ theorem size_filter_le_size [EquivBEq α] [LawfulHashable α]
(m.filter f).size ≤ m.size :=
ExtDHashMap.size_filter_le_size
grind_pattern size_filter_le_size => (m.filter f).size
theorem size_filter_eq_size_iff [EquivBEq α] [LawfulHashable α]
{f : α → β → Bool} :
(m.filter f).size = m.size ↔ ∀ k h, f (m.getKey k h) (m.get k h) :=
@ -1948,7 +1964,7 @@ theorem filter_eq_self_iff [EquivBEq α] [LawfulHashable α]
m.filter f = m ↔ ∀ k h, f (m.getKey k h) (m.get k h) :=
ext_iff.trans ExtDHashMap.Const.filter_eq_self_iff
theorem getElem?_filter [EquivBEq α] [LawfulHashable α]
@[grind =] theorem getElem?_filter [EquivBEq α] [LawfulHashable α]
{f : α → β → Bool} {k : α} :
(m.filter f)[k]? = m[k]?.pfilter (fun x h' =>
f (m.getKey k (mem_iff_isSome_getElem?.mpr (Option.isSome_of_eq_some h'))) x) :=
@ -1960,13 +1976,12 @@ theorem getElem?_filter_of_getKey?_eq_some [EquivBEq α] [LawfulHashable α]
(m.filter f)[k]? = m[k]?.filter (fun x => f k' x) :=
ExtDHashMap.Const.get?_filter_of_getKey?_eq_some
@[simp]
theorem getElem_filter [EquivBEq α] [LawfulHashable α]
@[simp, grind =] theorem getElem_filter [EquivBEq α] [LawfulHashable α]
{f : α → β → Bool} {k : α} {h'} :
(m.filter f)[k]'(h') = m[k]'(mem_of_mem_filter h') :=
ExtDHashMap.Const.get_filter (h' := h')
theorem getElem!_filter [EquivBEq α] [LawfulHashable α] [Inhabited β]
@[grind =] theorem getElem!_filter [EquivBEq α] [LawfulHashable α] [Inhabited β]
{f : α → β → Bool} {k : α} :
(m.filter f)[k]! =
(m[k]?.pfilter (fun x h' =>
@ -1979,7 +1994,7 @@ theorem getElem!_filter_of_getKey?_eq_some [EquivBEq α] [LawfulHashable α] [In
(m.filter f)[k]! = (m[k]?.filter (f k')).get! :=
ExtDHashMap.Const.get!_filter_of_getKey?_eq_some
theorem getD_filter [EquivBEq α] [LawfulHashable α]
@[grind =] theorem getD_filter [EquivBEq α] [LawfulHashable α]
{f : α → β → Bool} {k : α} {fallback : β} :
(m.filter f).getD k fallback = (m[k]?.pfilter (fun x h' =>
f (m.getKey k (mem_iff_isSome_getElem?.mpr (Option.isSome_of_eq_some h'))) x)).getD fallback :=
@ -1992,7 +2007,7 @@ theorem getD_filter_of_getKey?_eq_some [EquivBEq α] [LawfulHashable α]
(m[k]?.filter (fun x => f k' x)).getD fallback :=
ExtDHashMap.Const.getD_filter_of_getKey?_eq_some
theorem getKey?_filter [EquivBEq α] [LawfulHashable α]
@[grind =] theorem getKey?_filter [EquivBEq α] [LawfulHashable α]
{f : α → β → Bool} {k : α} :
(m.filter f).getKey? k =
(m.getKey? k).pfilter (fun x h' =>
@ -2004,13 +2019,13 @@ theorem getKey?_filter_key [EquivBEq α] [LawfulHashable α]
(m.filter fun k _ => f k).getKey? k = (m.getKey? k).filter f :=
ExtDHashMap.getKey?_filter_key
@[simp]
@[simp, grind =]
theorem getKey_filter [EquivBEq α] [LawfulHashable α]
{f : α → β → Bool} {k : α} {h'} :
(m.filter f).getKey k h' = m.getKey k (mem_of_mem_filter h') :=
ExtDHashMap.getKey_filter
theorem getKey!_filter [EquivBEq α] [LawfulHashable α] [Inhabited α]
@[grind =] theorem getKey!_filter [EquivBEq α] [LawfulHashable α] [Inhabited α]
{f : α → β → Bool} {k : α} :
(m.filter f).getKey! k =
((m.getKey? k).pfilter (fun x h' =>
@ -2022,7 +2037,7 @@ theorem getKey!_filter_key [EquivBEq α] [LawfulHashable α] [Inhabited α]
(m.filter fun k _ => f k).getKey! k = ((m.getKey? k).filter f).get! :=
ExtDHashMap.getKey!_filter_key
theorem getKeyD_filter [EquivBEq α] [LawfulHashable α]
@[grind =] theorem getKeyD_filter [EquivBEq α] [LawfulHashable α]
{f : α → β → Bool} {k fallback : α} :
(m.filter f).getKeyD k fallback =
((m.getKey? k).pfilter (fun x h' =>
@ -2059,7 +2074,7 @@ theorem map_eq_empty_iff [EquivBEq α] [LawfulHashable α] {f : α → β → γ
m.map f = ∅ ↔ m = ∅ := by
simpa only [ext_iff] using ExtDHashMap.map_eq_empty_iff
@[simp]
@[simp, grind =]
theorem contains_map [EquivBEq α] [LawfulHashable α]
{f : α → β → γ} {k : α} :
(m.map f).contains k = m.contains k :=
@ -2070,7 +2085,7 @@ theorem contains_of_contains_map [EquivBEq α] [LawfulHashable α]
(m.map f).contains k = true → m.contains k = true :=
ExtDHashMap.contains_of_contains_map
@[simp]
@[simp, grind =]
theorem mem_map [EquivBEq α] [LawfulHashable α]
{f : α → β → γ} {k : α} :
k ∈ m.map f ↔ k ∈ m := by
@ -2081,13 +2096,13 @@ theorem mem_of_mem_map [EquivBEq α] [LawfulHashable α]
k ∈ m.map f → k ∈ m :=
ExtDHashMap.contains_of_contains_map
@[simp]
@[simp, grind =]
theorem size_map [EquivBEq α] [LawfulHashable α]
{f : α → β → γ} :
(m.map f).size = m.size :=
ExtDHashMap.size_map
@[simp]
@[simp, grind =]
theorem getElem?_map [LawfulBEq α] [LawfulHashable α]
{f : α → β → γ} {k : α} :
(m.map f)[k]? = m[k]?.map (f k) :=
@ -2106,7 +2121,7 @@ theorem getElem?_map_of_getKey?_eq_some [EquivBEq α] [LawfulHashable α]
(m.map f)[k]? = m[k]?.map (f k') :=
ExtDHashMap.Const.get?_map_of_getKey?_eq_some h
@[simp]
@[simp, grind =]
theorem getElem_map [LawfulBEq α] [LawfulHashable α]
{f : α → β → γ} {k : α} {h'} :
(m.map f)[k]' h' =
@ -2121,7 +2136,7 @@ theorem getElem_map' [EquivBEq α] [LawfulHashable α]
f (m.getKey k (mem_of_mem_map h')) (m[k]'(mem_of_mem_map h')) :=
ExtDHashMap.Const.get_map' (h' := h')
theorem getElem!_map [LawfulBEq α] [LawfulHashable α] [Inhabited γ]
@[grind =] theorem getElem!_map [LawfulBEq α] [LawfulHashable α] [Inhabited γ]
{f : α → β → γ} {k : α} :
(m.map f)[k]! =
(m[k]?.map (f k)).get! :=
@ -2140,7 +2155,7 @@ theorem getElem!_map_of_getKey?_eq_some [EquivBEq α] [LawfulHashable α] [Inhab
(m.map f)[k]! = (m[k]?.map (f k')).get! :=
ExtDHashMap.Const.get!_map_of_getKey?_eq_some h
theorem getD_map [LawfulBEq α] [LawfulHashable α]
@[grind =] theorem getD_map [LawfulBEq α] [LawfulHashable α]
{f : α → β → γ} {k : α} {fallback : γ} :
(m.map f).getD k fallback =
(m[k]?.map (f k)).getD fallback :=
@ -2159,25 +2174,25 @@ theorem getD_map_of_getKey?_eq_some [EquivBEq α] [LawfulHashable α] [Inhabited
(m.map f).getD k fallback = (m[k]?.map (f k')).getD fallback :=
ExtDHashMap.Const.getD_map_of_getKey?_eq_some h
@[simp]
@[simp, grind =]
theorem getKey?_map [EquivBEq α] [LawfulHashable α]
{f : α → β → γ} {k : α} :
(m.map f).getKey? k = m.getKey? k :=
ExtDHashMap.getKey?_map
@[simp]
@[simp, grind =]
theorem getKey_map [EquivBEq α] [LawfulHashable α]
{f : α → β → γ} {k : α} {h'} :
(m.map f).getKey k h' = m.getKey k (mem_of_mem_map h') :=
ExtDHashMap.getKey_map
@[simp]
@[simp, grind =]
theorem getKey!_map [EquivBEq α] [LawfulHashable α] [Inhabited α]
{f : α → β → γ} {k : α} :
(m.map f).getKey! k = m.getKey! k :=
ExtDHashMap.getKey!_map
@[simp]
@[simp, grind =]
theorem getKeyD_map [EquivBEq α] [LawfulHashable α]
{f : α → β → γ} {k fallback : α} :
(m.map f).getKeyD k fallback = m.getKeyD k fallback :=

82
src/Std/Data/ExtHashSet/Lemmas.lean
View file

@ -13,6 +13,8 @@ import Std.Data.ExtHashSet.Basic
This module contains lemmas about `Std.ExtHashSet`.
-/
set_option trace.grind.ematch.pattern true
set_option linter.missingDocs true
set_option autoImplicit false
@ -32,7 +34,7 @@ private theorem ext {m m' : ExtHashSet α} : m.inner = m'.inner → m = m' := by
private theorem ext_iff {m m' : ExtHashSet α} : m = m' ↔ m.inner = m'.inner :=
⟨fun h => h ▸ rfl, ext⟩
@[simp]
@[simp, grind =]
theorem isEmpty_iff [EquivBEq α] [LawfulHashable α] : m.isEmpty ↔ m = ∅ :=
ExtHashMap.isEmpty_iff.trans ext_iff.symm
@ -43,7 +45,7 @@ theorem isEmpty_eq_false_iff [EquivBEq α] [LawfulHashable α] : m.isEmpty = fal
@[simp]
theorem empty_eq : ∅ = m ↔ m = ∅ := eq_comm
@[simp]
@[simp, grind =]
theorem emptyWithCapacity_eq [EquivBEq α] [LawfulHashable α] {c} : (emptyWithCapacity c : ExtHashSet α) = ∅ :=
ext ExtHashMap.emptyWithCapacity_eq
@ -66,7 +68,7 @@ theorem contains_congr [EquivBEq α] [LawfulHashable α] {a b : α} (hab : a ==
theorem mem_congr [EquivBEq α] [LawfulHashable α] {a b : α} (hab : a == b) : a ∈ m ↔ b ∈ m :=
ExtHashMap.mem_congr hab
@[simp] theorem contains_empty [EquivBEq α] [LawfulHashable α] {a : α} :
@[simp, grind =] theorem contains_empty [EquivBEq α] [LawfulHashable α] {a : α} :
(∅ : ExtHashSet α).contains a = false :=
ExtHashMap.contains_empty
@ -87,12 +89,12 @@ theorem eq_empty_iff_forall_not_mem [EquivBEq α] [LawfulHashable α] : m = ∅
Singleton.singleton a = (∅ : ExtHashSet α).insert a :=
rfl
@[simp]
@[simp, grind =]
theorem contains_insert [EquivBEq α] [LawfulHashable α] {k a : α} :
(m.insert k).contains a = (k == a || m.contains a) :=
ExtHashMap.contains_insertIfNew
@[simp]
@[simp, grind =]
theorem mem_insert [EquivBEq α] [LawfulHashable α] {k a : α} : a ∈ m.insert k ↔ k == a ∨ a ∈ m :=
ExtHashMap.mem_insertIfNew
@ -121,13 +123,14 @@ theorem contains_insert_self [EquivBEq α] [LawfulHashable α] {k : α} : (m.ins
theorem mem_insert_self [EquivBEq α] [LawfulHashable α] {k : α} : k ∈ m.insert k := by simp
@[simp]
@[simp, grind =]
theorem size_empty [EquivBEq α] [LawfulHashable α] : (∅ : ExtHashSet α).size = 0 :=
ExtHashMap.size_empty
theorem eq_empty_iff_size_eq_zero [EquivBEq α] [LawfulHashable α] : m = ∅ ↔ m.size = 0 :=
ext_iff.trans ExtHashMap.eq_empty_iff_size_eq_zero
@[grind =]
theorem size_insert [EquivBEq α] [LawfulHashable α] {k : α} :
(m.insert k).size = if k ∈ m then m.size else m.size + 1 :=
ExtHashMap.size_insertIfNew
@ -139,7 +142,7 @@ theorem size_insert_le [EquivBEq α] [LawfulHashable α] {k : α} :
(m.insert k).size ≤ m.size + 1 :=
ExtHashMap.size_insertIfNew_le
@[simp]
@[simp, grind =]
theorem erase_empty [EquivBEq α] [LawfulHashable α] {a : α} : (∅ : ExtHashSet α).erase a = ∅ :=
ext ExtHashMap.erase_empty
@ -148,12 +151,12 @@ theorem erase_eq_empty_iff [EquivBEq α] [LawfulHashable α] {k : α} :
m.erase k = ∅ ↔ m = ∅ ∨ m.size = 1 ∧ k ∈ m := by
simpa only [ext_iff] using ExtHashMap.erase_eq_empty_iff
@[simp]
@[simp, grind =]
theorem contains_erase [EquivBEq α] [LawfulHashable α] {k a : α} :
(m.erase k).contains a = (!(k == a) && m.contains a) :=
ExtHashMap.contains_erase
@[simp]
@[simp, grind =]
theorem mem_erase [EquivBEq α] [LawfulHashable α] {k a : α} :
a ∈ m.erase k ↔ (k == a) = false ∧ a ∈ m :=
ExtHashMap.mem_erase
@ -165,6 +168,7 @@ theorem contains_of_contains_erase [EquivBEq α] [LawfulHashable α] {k a : α}
theorem mem_of_mem_erase [EquivBEq α] [LawfulHashable α] {k a : α} : a ∈ m.erase k → a ∈ m :=
ExtHashMap.mem_of_mem_erase
@[grind =]
theorem size_erase [EquivBEq α] [LawfulHashable α] {k : α} :
(m.erase k).size = if k ∈ m then m.size - 1 else m.size :=
ExtHashMap.size_erase
@ -176,10 +180,11 @@ theorem size_le_size_erase [EquivBEq α] [LawfulHashable α] {k : α} :
m.size ≤ (m.erase k).size + 1 :=
ExtHashMap.size_le_size_erase
@[simp]
@[simp, grind =]
theorem get?_empty [EquivBEq α] [LawfulHashable α] {a : α} : (∅ : ExtHashSet α).get? a = none :=
ExtHashMap.getKey?_empty
@[grind =]
theorem get?_insert [EquivBEq α] [LawfulHashable α] {k a : α} :
(m.insert k).get? a = if k == a ∧ ¬k ∈ m then some k else m.get? a :=
ExtHashMap.getKey?_insertIfNew
@ -209,6 +214,7 @@ theorem get?_eq_none_of_contains_eq_false [EquivBEq α] [LawfulHashable α] {a :
theorem get?_eq_none [EquivBEq α] [LawfulHashable α] {a : α} : ¬a ∈ m → m.get? a = none :=
ExtHashMap.getKey?_eq_none
@[grind =]
theorem get?_erase [EquivBEq α] [LawfulHashable α] {k a : α} :
(m.erase k).get? a = if k == a then none else m.get? a :=
ExtHashMap.getKey?_erase
@ -230,12 +236,13 @@ theorem get?_eq_some_of_contains [LawfulBEq α] {k : α} (h : m.contains k) : m.
theorem get?_eq_some [LawfulBEq α] {k : α} (h : k ∈ m) : m.get? k = some k :=
ExtHashMap.getKey?_eq_some h
@[grind =]
theorem get_insert [EquivBEq α] [LawfulHashable α] {k a : α} {h₁} :
(m.insert k).get a h₁ =
if h₂ : k == a ∧ ¬k ∈ m then k else m.get a (mem_of_mem_insert' h₁ h₂) :=
ExtHashMap.getKey_insertIfNew (h₁ := h₁)
@[simp]
@[simp, grind =]
theorem get_erase [EquivBEq α] [LawfulHashable α] {k a : α} {h'} :
(m.erase k).get a h' = m.get a (mem_of_mem_erase h') :=
ExtHashMap.getKey_erase (h' := h')
@ -248,7 +255,7 @@ theorem get_eq_get_get? [EquivBEq α] [LawfulHashable α] {k : α} {h} :
m.get k h = (m.get? k).get (mem_iff_isSome_get?.mp h) :=
ExtHashMap.getKey_eq_get_getKey?
theorem get_get? [EquivBEq α] [LawfulHashable α] {k : α} {h} :
@[grind =] theorem get_get? [EquivBEq α] [LawfulHashable α] {k : α} {h} :
(m.get? k).get h = m.get k (mem_iff_isSome_get?.mpr h) :=
ExtHashMap.get_getKey?
@ -259,15 +266,16 @@ theorem get_congr [EquivBEq α] [LawfulHashable α] {k₁ k₂ : α} (h : k₁ =
(h₁ : k₁ ∈ m) : m.get k₁ h₁ = m.get k₂ ((mem_congr h).mp h₁) :=
ExtHashMap.getKey_congr h h₁
@[simp]
@[simp, grind =]
theorem get_eq [LawfulBEq α] {k : α} (h : k ∈ m) : m.get k h = k :=
ExtHashMap.getKey_eq h
@[simp]
@[simp, grind =]
theorem get!_empty [EquivBEq α] [LawfulHashable α] [Inhabited α] {a : α} :
(∅ : ExtHashSet α).get! a = default :=
ExtHashMap.getKey!_empty
@[grind =]
theorem get!_insert [Inhabited α] [EquivBEq α] [LawfulHashable α] {k a : α} :
(m.insert k).get! a = if k == a ∧ ¬k ∈ m then k else m.get! a :=
ExtHashMap.getKey!_insertIfNew
@ -280,6 +288,7 @@ theorem get!_eq_default [Inhabited α] [EquivBEq α] [LawfulHashable α] {a : α
¬a ∈ m → m.get! a = default :=
ExtHashMap.getKey!_eq_default
@[grind =]
theorem get!_erase [Inhabited α] [EquivBEq α] [LawfulHashable α] {k a : α} :
(m.erase k).get! a = if k == a then default else m.get! a :=
ExtHashMap.getKey!_erase
@ -315,12 +324,12 @@ theorem get!_eq_of_contains [LawfulBEq α] [Inhabited α] {k : α} (h : m.contai
theorem get!_eq_of_mem [LawfulBEq α] [Inhabited α] {k : α} (h : k ∈ m) : m.get! k = k :=
ExtHashMap.getKey!_eq_of_mem h
@[simp]
@[simp, grind =]
theorem getD_empty [EquivBEq α] [LawfulHashable α] {a fallback : α} :
(∅ : ExtHashSet α).getD a fallback = fallback :=
ExtHashMap.getKeyD_empty
theorem getD_insert [EquivBEq α] [LawfulHashable α] {k a fallback : α} :
@[grind] theorem getD_insert [EquivBEq α] [LawfulHashable α] {k a fallback : α} :
(m.insert k).getD a fallback = if k == a ∧ ¬k ∈ m then k else m.getD a fallback :=
ExtHashMap.getKeyD_insertIfNew
@ -333,7 +342,7 @@ theorem getD_eq_fallback [EquivBEq α] [LawfulHashable α] {a fallback : α} :
¬a ∈ m → m.getD a fallback = fallback :=
ExtHashMap.getKeyD_eq_fallback
theorem getD_erase [EquivBEq α] [LawfulHashable α] {k a fallback : α} :
@[grind =] theorem getD_erase [EquivBEq α] [LawfulHashable α] {k a fallback : α} :
(m.erase k).getD a fallback = if k == a then fallback else m.getD a fallback :=
ExtHashMap.getKeyD_erase
@ -373,32 +382,34 @@ theorem getD_eq_of_contains [LawfulBEq α] {k fallback : α} (h : m.contains k)
theorem getD_eq_of_mem [LawfulBEq α] {k fallback : α} (h : k ∈ m) : m.getD k fallback = k :=
ExtHashMap.getKeyD_eq_of_mem h
@[simp]
@[simp, grind =]
theorem containsThenInsert_fst [EquivBEq α] [LawfulHashable α] {k : α} :
(m.containsThenInsert k).1 = m.contains k :=
ExtHashMap.containsThenInsertIfNew_fst
@[simp]
@[simp, grind =]
theorem containsThenInsert_snd [EquivBEq α] [LawfulHashable α] {k : α} :
(m.containsThenInsert k).2 = m.insert k :=
ext ExtHashMap.containsThenInsertIfNew_snd
variable {ρ : Type v} [ForIn Id ρ α]
@[simp]
@[simp, grind =]
theorem insertMany_nil [EquivBEq α] [LawfulHashable α] :
insertMany m [] = m :=
ext ExtHashMap.insertManyIfNewUnit_nil
@[simp]
@[simp, grind =]
theorem insertMany_list_singleton [EquivBEq α] [LawfulHashable α] {k : α} :
insertMany m [k] = m.insert k :=
ext ExtHashMap.insertManyIfNewUnit_list_singleton
@[grind _=_]
theorem insertMany_cons [EquivBEq α] [LawfulHashable α] {l : List α} {k : α} :
insertMany m (k :: l) = insertMany (m.insert k) l :=
ext ExtHashMap.insertManyIfNewUnit_cons
@[grind _=_]
theorem insertMany_append [EquivBEq α] [LawfulHashable α] {l₁ l₂ : List α} :
insertMany m (l₁ ++ l₂) = insertMany (insertMany m l₁) l₂ := by
induction l₁ generalizing m with
@ -414,13 +425,13 @@ theorem insertMany_ind [EquivBEq α] [LawfulHashable α]
show motive ⟨m.1.insertManyIfNewUnit l⟩ from
ExtHashMap.insertManyIfNewUnit_ind m.inner l init fun m => insert ⟨m⟩
@[simp]
@[simp, grind =]
theorem contains_insertMany_list [EquivBEq α] [LawfulHashable α]
{l : List α} {k : α} :
(insertMany m l).contains k = (m.contains k || l.contains k) :=
ExtHashMap.contains_insertManyIfNewUnit_list
@[simp]
@[simp, grind =]
theorem mem_insertMany_list [EquivBEq α] [LawfulHashable α]
{l : List α} {k : α} :
k ∈ insertMany m l ↔ k ∈ m ∨ l.contains k :=
@ -525,11 +536,15 @@ theorem size_le_size_insertMany [EquivBEq α] [LawfulHashable α]
{l : ρ} : m.size ≤ (insertMany m l).size :=
ExtHashMap.size_le_size_insertManyIfNewUnit
grind_pattern size_le_size_insertMany => (insertMany m l).size
theorem size_insertMany_list_le [EquivBEq α] [LawfulHashable α]
{l : List α} :
(insertMany m l).size ≤ m.size + l.length :=
ExtHashMap.size_insertManyIfNewUnit_list_le
grind_pattern size_insertMany_list_le => (insertMany m l).size
@[simp]
theorem insertMany_list_eq_empty_iff [EquivBEq α] [LawfulHashable α] {l : List α} :
m.insertMany l = ∅ ↔ m = ∅ ∧ l = [] := by
@ -543,16 +558,17 @@ end
section
@[simp]
@[simp, grind =]
theorem ofList_nil [EquivBEq α] [LawfulHashable α] :
ofList ([] : List α) = ∅ :=
ext ExtHashMap.unitOfList_nil
@[simp]
@[simp, grind =]
theorem ofList_singleton [EquivBEq α] [LawfulHashable α] {k : α} :
ofList [k] = (∅ : ExtHashSet α).insert k :=
ext ExtHashMap.unitOfList_singleton
@[grind _=_]
theorem ofList_cons [EquivBEq α] [LawfulHashable α] {hd : α} {tl : List α} :
ofList (hd :: tl) =
insertMany ((∅ : ExtHashSet α).insert hd) tl :=
@ -564,13 +580,13 @@ theorem ofList_eq_insertMany_empty [EquivBEq α] [LawfulHashable α] {l : List
| [] => by simp
| hd :: tl => by simp [ofList_cons, insertMany_cons]
@[simp]
@[simp, grind =]
theorem contains_ofList [EquivBEq α] [LawfulHashable α]
{l : List α} {k : α} :
(ofList l).contains k = l.contains k :=
ExtHashMap.contains_unitOfList
@[simp]
@[simp, grind =]
theorem mem_ofList [EquivBEq α] [LawfulHashable α]
{l : List α} {k : α} :
k ∈ ofList l ↔ l.contains k :=
@ -632,6 +648,8 @@ theorem size_ofList_le [EquivBEq α] [LawfulHashable α]
(ofList l).size ≤ l.length :=
ExtHashMap.size_unitOfList_le
grind_pattern size_ofList_le => (ofList l).size
@[simp]
theorem ofList_eq_empty_iff [EquivBEq α] [LawfulHashable α] {l : List α} :
ofList l = ∅ ↔ l = [] :=
@ -664,7 +682,7 @@ theorem filter_eq_empty_iff [EquivBEq α] [LawfulHashable α] {f : α → Bool}
m.filter f = ∅ ↔ ∀ k h, f (m.get k h) = false :=
ext_iff.trans ExtHashMap.filter_eq_empty_iff
@[simp]
@[simp, grind =]
theorem mem_filter [EquivBEq α] [LawfulHashable α]
{f : α → Bool} {k : α} :
k ∈ m.filter f ↔ ∃ h, f (m.get k h) :=
@ -685,6 +703,8 @@ theorem size_filter_le_size [EquivBEq α] [LawfulHashable α]
(m.filter f).size ≤ m.size :=
ExtHashMap.size_filter_le_size
grind_pattern size_filter_le_size => (m.filter f).size
theorem size_filter_eq_size_iff [EquivBEq α] [LawfulHashable α]
{f : α → Bool} :
(m.filter f).size = m.size ↔ ∀ k h, f (m.get k h) :=
@ -695,23 +715,25 @@ theorem filter_eq_self_iff [EquivBEq α] [LawfulHashable α]
m.filter f = m ↔ ∀ k h, f (m.get k h) :=
ext_iff.trans ExtHashMap.filter_eq_self_iff
@[simp]
@[simp, grind =]
theorem get?_filter [EquivBEq α] [LawfulHashable α]
{f : α → Bool} {k : α} :
(m.filter f).get? k = (m.get? k).filter f :=
ExtHashMap.getKey?_filter_key
@[simp]
@[simp, grind =]
theorem get_filter [EquivBEq α] [LawfulHashable α]
{f : α → Bool} {k : α} {h} :
(m.filter f).get k h = m.get k (mem_of_mem_filter h) :=
ExtHashMap.getKey_filter
@[grind =]
theorem get!_filter [EquivBEq α] [LawfulHashable α] [Inhabited α]
{f : α → Bool} {k : α} :
(m.filter f).get! k = ((m.get? k).filter f).get! :=
ExtHashMap.getKey!_filter_key
@[grind =]
theorem getD_filter [EquivBEq α] [LawfulHashable α]
{f : α → Bool} {k fallback : α} :
(m.filter f).getD k fallback = ((m.get? k).filter f).getD fallback :=

282
src/Std/Data/HashMap/Lemmas.lean
View file

File diff suppressed because it is too large Load diff

268
src/Std/Data/HashMap/RawLemmas.lean
View file

File diff suppressed because it is too large Load diff

129
src/Std/Data/HashSet/Lemmas.lean
View file

@ -15,6 +15,8 @@ This module contains lemmas about `Std.Data.HashSet`. Most of the lemmas require
is to provide an instance of `LawfulBEq α`.
-/
set_option trace.grind.ematch.pattern true
set_option linter.missingDocs true
set_option autoImplicit false
@ -31,11 +33,11 @@ variable {m : HashSet α}
private theorem ext {m m' : HashSet α} : m.inner = m'.inner → m = m' := by
cases m; cases m'; rintro rfl; rfl
@[simp]
@[simp, grind =]
theorem isEmpty_emptyWithCapacity {c} : (emptyWithCapacity c : HashSet α).isEmpty :=
HashMap.isEmpty_emptyWithCapacity
@[simp]
@[simp, grind =]
theorem isEmpty_empty : (∅ : HashSet α).isEmpty :=
HashMap.isEmpty_empty
@ -43,7 +45,7 @@ set_option linter.missingDocs false in
@[deprecated isEmpty_empty (since := "2025-03-12")]
abbrev isEmpty_emptyc := @isEmpty_empty
@[simp]
@[simp, grind =]
theorem isEmpty_insert [EquivBEq α] [LawfulHashable α] {a : α} : (m.insert a).isEmpty = false :=
HashMap.isEmpty_insertIfNew
@ -61,14 +63,14 @@ theorem contains_congr [EquivBEq α] [LawfulHashable α] {a b : α} (hab : a ==
theorem mem_congr [EquivBEq α] [LawfulHashable α] {a b : α} (hab : a == b) : a ∈ m ↔ b ∈ m :=
HashMap.mem_congr hab
@[simp]
@[simp, grind =]
theorem contains_emptyWithCapacity {a : α} {c} : (emptyWithCapacity c : HashSet α).contains a = false :=
HashMap.contains_emptyWithCapacity
@[simp] theorem not_mem_emptyWithCapacity {a : α} {c} : ¬a ∈ (emptyWithCapacity c : HashSet α) :=
@[simp, grind] theorem not_mem_emptyWithCapacity {a : α} {c} : ¬a ∈ (emptyWithCapacity c : HashSet α) :=
HashMap.not_mem_emptyWithCapacity
@[simp] theorem contains_empty {a : α} : (∅ : HashSet α).contains a = false :=
@[simp, grind =] theorem contains_empty {a : α} : (∅ : HashSet α).contains a = false :=
HashMap.contains_empty
set_option linter.missingDocs false in
@ -110,12 +112,12 @@ theorem isEmpty_iff_forall_not_mem [EquivBEq α] [LawfulHashable α] :
@[simp] theorem singleton_eq_insert {a : α} : Singleton.singleton a = (∅ : HashSet α).insert a := rfl
@[simp]
@[simp, grind =]
theorem contains_insert [EquivBEq α] [LawfulHashable α] {k a : α} :
(m.insert k).contains a = (k == a || m.contains a) :=
HashMap.contains_insertIfNew
@[simp]
@[simp, grind =]
theorem mem_insert [EquivBEq α] [LawfulHashable α] {k a : α} : a ∈ m.insert k ↔ k == a ∨ a ∈ m :=
HashMap.mem_insertIfNew
@ -144,11 +146,11 @@ theorem contains_insert_self [EquivBEq α] [LawfulHashable α] {k : α} : (m.ins
theorem mem_insert_self [EquivBEq α] [LawfulHashable α] {k : α} : k ∈ m.insert k := by simp
@[simp]
@[simp, grind =]
theorem size_emptyWithCapacity {c} : (emptyWithCapacity c : HashSet α).size = 0 :=
HashMap.size_emptyWithCapacity
@[simp]
@[simp, grind =]
theorem size_empty : (∅ : HashSet α).size = 0 :=
HashMap.size_empty
@ -159,7 +161,7 @@ abbrev size_emptyc := @size_empty
theorem isEmpty_eq_size_eq_zero : m.isEmpty = (m.size == 0) :=
HashMap.isEmpty_eq_size_eq_zero
theorem size_insert [EquivBEq α] [LawfulHashable α] {k : α} :
@[grind =] theorem size_insert [EquivBEq α] [LawfulHashable α] {k : α} :
(m.insert k).size = if k ∈ m then m.size else m.size + 1 :=
HashMap.size_insertIfNew
@ -170,11 +172,11 @@ theorem size_insert_le [EquivBEq α] [LawfulHashable α] {k : α} :
(m.insert k).size ≤ m.size + 1 :=
HashMap.size_insertIfNew_le
@[simp]
@[simp, grind =]
theorem erase_emptyWithCapacity {a : α} {c : Nat} : (emptyWithCapacity c : HashSet α).erase a = emptyWithCapacity c :=
ext HashMap.erase_emptyWithCapacity
@[simp]
@[simp, grind =]
theorem erase_empty {a : α} : (∅ : HashSet α).erase a = ∅ :=
ext HashMap.erase_empty
@ -182,17 +184,17 @@ set_option linter.missingDocs false in
@[deprecated erase_empty (since := "2025-03-12")]
abbrev erase_emptyc := @erase_empty
@[simp]
@[simp, grind =]
theorem isEmpty_erase [EquivBEq α] [LawfulHashable α] {k : α} :
(m.erase k).isEmpty = (m.isEmpty || (m.size == 1 && m.contains k)) :=
HashMap.isEmpty_erase
@[simp]
@[simp, grind =]
theorem contains_erase [EquivBEq α] [LawfulHashable α] {k a : α} :
(m.erase k).contains a = (!(k == a) && m.contains a) :=
HashMap.contains_erase
@[simp]
@[simp, grind =]
theorem mem_erase [EquivBEq α] [LawfulHashable α] {k a : α} :
a ∈ m.erase k ↔ (k == a) = false ∧ a ∈ m :=
HashMap.mem_erase
@ -204,7 +206,7 @@ theorem contains_of_contains_erase [EquivBEq α] [LawfulHashable α] {k a : α}
theorem mem_of_mem_erase [EquivBEq α] [LawfulHashable α] {k a : α} : a ∈ m.erase k → a ∈ m :=
HashMap.mem_of_mem_erase
theorem size_erase [EquivBEq α] [LawfulHashable α] {k : α} :
@[grind =] theorem size_erase [EquivBEq α] [LawfulHashable α] {k : α} :
(m.erase k).size = if k ∈ m then m.size - 1 else m.size :=
HashMap.size_erase
@ -215,11 +217,11 @@ theorem size_le_size_erase [EquivBEq α] [LawfulHashable α] {k : α} :
m.size ≤ (m.erase k).size + 1 :=
HashMap.size_le_size_erase
@[simp]
@[simp, grind =]
theorem get?_emptyWithCapacity {a : α} {c} : (emptyWithCapacity c : HashSet α).get? a = none :=
HashMap.getKey?_emptyWithCapacity
@[simp]
@[simp, grind =]
theorem get?_empty {a : α} : (∅ : HashSet α).get? a = none :=
HashMap.getKey?_empty
@ -231,7 +233,7 @@ theorem get?_of_isEmpty [EquivBEq α] [LawfulHashable α] {a : α} :
m.isEmpty = true → m.get? a = none :=
HashMap.getKey?_of_isEmpty
theorem get?_insert [EquivBEq α] [LawfulHashable α] {k a : α} :
@[grind =] theorem get?_insert [EquivBEq α] [LawfulHashable α] {k a : α} :
(m.insert k).get? a = if k == a ∧ ¬k ∈ m then some k else m.get? a :=
HashMap.getKey?_insertIfNew
@ -260,7 +262,7 @@ theorem get?_eq_none_of_contains_eq_false [EquivBEq α] [LawfulHashable α] {a :
theorem get?_eq_none [EquivBEq α] [LawfulHashable α] {a : α} : ¬a ∈ m → m.get? a = none :=
HashMap.getKey?_eq_none
theorem get?_erase [EquivBEq α] [LawfulHashable α] {k a : α} :
@[grind =] theorem get?_erase [EquivBEq α] [LawfulHashable α] {k a : α} :
(m.erase k).get? a = if k == a then none else m.get? a :=
HashMap.getKey?_erase
@ -281,12 +283,12 @@ theorem get?_eq_some_of_contains [LawfulBEq α] {k : α} (h : m.contains k) : m.
theorem get?_eq_some [LawfulBEq α] {k : α} (h : k ∈ m) : m.get? k = some k :=
HashMap.getKey?_eq_some h
theorem get_insert [EquivBEq α] [LawfulHashable α] {k a : α} {h₁} :
@[grind =] theorem get_insert [EquivBEq α] [LawfulHashable α] {k a : α} {h₁} :
(m.insert k).get a h₁ =
if h₂ : k == a ∧ ¬k ∈ m then k else m.get a (mem_of_mem_insert' h₁ h₂) :=
HashMap.getKey_insertIfNew (h₁ := h₁)
@[simp]
@[simp, grind =]
theorem get_erase [EquivBEq α] [LawfulHashable α] {k a : α} {h'} :
(m.erase k).get a h' = m.get a (mem_of_mem_erase h') :=
HashMap.getKey_erase (h' := h')
@ -299,7 +301,7 @@ theorem get_eq_get_get? [EquivBEq α] [LawfulHashable α] {k : α} {h} :
m.get k h = (m.get? k).get (mem_iff_isSome_get?.mp h) :=
HashMap.getKey_eq_get_getKey?
theorem get_get? [EquivBEq α] [LawfulHashable α] {k : α} {h} :
@[grind =] theorem get_get? [EquivBEq α] [LawfulHashable α] {k : α} {h} :
(m.get? k).get h = m.get k (mem_iff_isSome_get?.mpr h) :=
HashMap.get_getKey?
@ -310,15 +312,15 @@ theorem get_congr [EquivBEq α] [LawfulHashable α] {k₁ k₂ : α} (h : k₁ =
(h₁ : k₁ ∈ m) : m.get k₁ h₁ = m.get k₂ ((mem_congr h).mp h₁) :=
HashMap.getKey_congr h h₁
@[simp]
@[simp, grind =]
theorem get_eq [LawfulBEq α] {k : α} (h : k ∈ m) : m.get k h = k :=
HashMap.getKey_eq h
@[simp]
@[simp, grind =]
theorem get!_emptyWithCapacity [Inhabited α] {a : α} {c} : (emptyWithCapacity c : HashSet α).get! a = default :=
HashMap.getKey!_emptyWithCapacity
@[simp]
@[simp, grind =]
theorem get!_empty [Inhabited α] {a : α} : (∅ : HashSet α).get! a = default :=
HashMap.getKey!_empty
@ -330,7 +332,7 @@ theorem get!_of_isEmpty [Inhabited α] [EquivBEq α] [LawfulHashable α] {a : α
m.isEmpty = true → m.get! a = default :=
HashMap.getKey!_of_isEmpty
theorem get!_insert [Inhabited α] [EquivBEq α] [LawfulHashable α] {k a : α} :
@[grind =] theorem get!_insert [Inhabited α] [EquivBEq α] [LawfulHashable α] {k a : α} :
(m.insert k).get! a = if k == a ∧ ¬k ∈ m then k else m.get! a :=
HashMap.getKey!_insertIfNew
@ -342,7 +344,7 @@ theorem get!_eq_default [Inhabited α] [EquivBEq α] [LawfulHashable α] {a : α
¬a ∈ m → m.get! a = default :=
HashMap.getKey!_eq_default
theorem get!_erase [Inhabited α] [EquivBEq α] [LawfulHashable α] {k a : α} :
@[grind =] theorem get!_erase [Inhabited α] [EquivBEq α] [LawfulHashable α] {k a : α} :
(m.erase k).get! a = if k == a then default else m.get! a :=
HashMap.getKey!_erase
@ -377,11 +379,11 @@ theorem get!_eq_of_contains [LawfulBEq α] [Inhabited α] {k : α} (h : m.contai
theorem get!_eq_of_mem [LawfulBEq α] [Inhabited α] {k : α} (h : k ∈ m) : m.get! k = k :=
HashMap.getKey!_eq_of_mem h
@[simp]
@[simp, grind =]
theorem getD_emptyWithCapacity {a fallback : α} {c} : (emptyWithCapacity c : HashSet α).getD a fallback = fallback :=
HashMap.getKeyD_emptyWithCapacity
@[simp]
@[simp, grind =]
theorem getD_empty {a fallback : α} : (∅ : HashSet α).getD a fallback = fallback :=
HashMap.getKeyD_empty
@ -393,7 +395,7 @@ theorem getD_of_isEmpty [EquivBEq α] [LawfulHashable α] {a fallback : α} :
m.isEmpty = true → m.getD a fallback = fallback :=
HashMap.getKeyD_of_isEmpty
theorem getD_insert [EquivBEq α] [LawfulHashable α] {k a fallback : α} :
@[grind =] theorem getD_insert [EquivBEq α] [LawfulHashable α] {k a fallback : α} :
(m.insert k).getD a fallback = if k == a ∧ ¬k ∈ m then k else m.getD a fallback :=
HashMap.getKeyD_insertIfNew
@ -406,7 +408,7 @@ theorem getD_eq_fallback [EquivBEq α] [LawfulHashable α] {a fallback : α} :
¬a ∈ m → m.getD a fallback = fallback :=
HashMap.getKeyD_eq_fallback
theorem getD_erase [EquivBEq α] [LawfulHashable α] {k a fallback : α} :
@[grind =] theorem getD_erase [EquivBEq α] [LawfulHashable α] {k a fallback : α} :
(m.erase k).getD a fallback = if k == a then fallback else m.getD a fallback :=
HashMap.getKeyD_erase
@ -446,30 +448,30 @@ theorem getD_eq_of_contains [LawfulBEq α] {k fallback : α} (h : m.contains k)
theorem getD_eq_of_mem [LawfulBEq α] {k fallback : α} (h : k ∈ m) : m.getD k fallback = k :=
HashMap.getKeyD_eq_of_mem h
@[simp]
@[simp, grind =]
theorem containsThenInsert_fst {k : α} : (m.containsThenInsert k).1 = m.contains k :=
HashMap.containsThenInsertIfNew_fst
@[simp]
@[simp, grind =]
theorem containsThenInsert_snd {k : α} : (m.containsThenInsert k).2 = m.insert k :=
ext HashMap.containsThenInsertIfNew_snd
@[simp]
@[simp, grind =]
theorem length_toList [EquivBEq α] [LawfulHashable α] :
m.toList.length = m.size :=
HashMap.length_keys
@[simp]
@[simp, grind =]
theorem isEmpty_toList [EquivBEq α] [LawfulHashable α] :
m.toList.isEmpty = m.isEmpty :=
HashMap.isEmpty_keys
@[simp]
@[simp, grind =]
theorem contains_toList [EquivBEq α] [LawfulHashable α] {k : α} :
m.toList.contains k = m.contains k :=
HashMap.contains_keys
@[simp]
@[simp, grind =]
theorem mem_toList [LawfulBEq α] [LawfulHashable α] {k : α} :
k ∈ m.toList ↔ k ∈ m :=
HashMap.mem_keys
@ -491,7 +493,7 @@ theorem fold_eq_foldl_toList {f : δ → α → δ} {init : δ} :
m.fold f init = m.toList.foldl f init :=
HashMap.fold_eq_foldl_keys
@[simp]
@[simp, grind =]
theorem forM_eq_forM [Monad m'] [LawfulMonad m'] {f : α → m' PUnit} :
m.forM f = ForM.forM m f := rfl
@ -499,7 +501,7 @@ theorem forM_eq_forM_toList [Monad m'] [LawfulMonad m'] {f : α → m' PUnit} :
ForM.forM m f = ForM.forM m.toList f :=
HashMap.forM_eq_forM_keys
@[simp]
@[simp, grind =]
theorem forIn_eq_forIn [Monad m'] [LawfulMonad m']
{f : α → δ → m' (ForInStep δ)} {init : δ} :
ForIn.forIn m init f = ForIn.forIn m init f := rfl
@ -513,20 +515,21 @@ end monadic
variable {ρ : Type v} [ForIn Id ρ α]
@[simp]
@[simp, grind =]
theorem insertMany_nil :
insertMany m [] = m :=
ext HashMap.insertManyIfNewUnit_nil
@[simp]
@[simp, grind =]
theorem insertMany_list_singleton {k : α} :
insertMany m [k] = m.insert k :=
ext HashMap.insertManyIfNewUnit_list_singleton
theorem insertMany_cons {l : List α} {k : α} :
@[grind _=_] theorem insertMany_cons {l : List α} {k : α} :
insertMany m (k :: l) = insertMany (m.insert k) l :=
ext HashMap.insertManyIfNewUnit_cons
@[grind _=_]
theorem insertMany_append {l₁ l₂ : List α} :
insertMany m (l₁ ++ l₂) = insertMany (insertMany m l₁) l₂ := by
induction l₁ generalizing m with
@ -541,13 +544,13 @@ theorem insertMany_ind {motive : HashSet α → Prop} (m : HashSet α) {l : ρ}
show motive ⟨m.1.insertManyIfNewUnit l⟩ from
HashMap.insertManyIfNewUnit_ind m.inner l init fun m => insert ⟨m⟩
@[simp]
@[simp, grind =]
theorem contains_insertMany_list [EquivBEq α] [LawfulHashable α]
{l : List α} {k : α} :
(insertMany m l).contains k = (m.contains k || l.contains k) :=
HashMap.contains_insertManyIfNewUnit_list
@[simp]
@[simp, grind =]
theorem mem_insertMany_list [EquivBEq α] [LawfulHashable α]
{l : List α} {k : α} :
k ∈ insertMany m l ↔ k ∈ m ∨ l.contains k :=
@ -652,12 +655,16 @@ theorem size_le_size_insertMany [EquivBEq α] [LawfulHashable α]
{l : ρ} : m.size ≤ (insertMany m l).size :=
HashMap.size_le_size_insertManyIfNewUnit
grind_pattern size_le_size_insertMany => (insertMany m l).size
theorem size_insertMany_list_le [EquivBEq α] [LawfulHashable α]
{l : List α} :
(insertMany m l).size ≤ m.size + l.length :=
HashMap.size_insertManyIfNewUnit_list_le
@[simp]
grind_pattern size_insertMany_list_le => (insertMany m l).size
@[simp, grind =]
theorem isEmpty_insertMany_list [EquivBEq α] [LawfulHashable α]
{l : List α} :
(insertMany m l).isEmpty = (m.isEmpty && l.isEmpty) :=
@ -671,17 +678,17 @@ end
section
@[simp]
@[simp, grind =]
theorem ofList_nil :
ofList ([] : List α) = ∅ :=
ext HashMap.unitOfList_nil
@[simp]
@[simp, grind =]
theorem ofList_singleton {k : α} :
ofList [k] = (∅ : HashSet α).insert k :=
ext HashMap.unitOfList_singleton
theorem ofList_cons {hd : α} {tl : List α} :
@[grind _=_] theorem ofList_cons {hd : α} {tl : List α} :
ofList (hd :: tl) =
insertMany ((∅ : HashSet α).insert hd) tl :=
ext HashMap.unitOfList_cons
@ -692,13 +699,13 @@ theorem ofList_eq_insertMany_empty {l : List α} :
| [] => by simp
| hd :: tl => by simp [ofList_cons, insertMany_cons]
@[simp]
@[simp, grind =]
theorem contains_ofList [EquivBEq α] [LawfulHashable α]
{l : List α} {k : α} :
(ofList l).contains k = l.contains k :=
HashMap.contains_unitOfList
@[simp]
@[simp, grind =]
theorem mem_ofList [EquivBEq α] [LawfulHashable α]
{l : List α} {k : α} :
k ∈ ofList l ↔ l.contains k :=
@ -760,7 +767,9 @@ theorem size_ofList_le [EquivBEq α] [LawfulHashable α]
(ofList l).size ≤ l.length :=
HashMap.size_unitOfList_le
@[simp]
grind_pattern size_ofList_le => (ofList l).size
@[simp, grind =]
theorem isEmpty_ofList [EquivBEq α] [LawfulHashable α]
{l : List α} :
(ofList l).isEmpty = l.isEmpty :=
@ -893,7 +902,7 @@ theorem toList_filter {f : α → Bool} :
(m.filter f).toList.Perm (m.toList.filter f) :=
HashMap.keys_filter_key
theorem isEmpty_filter_iff [EquivBEq α] [LawfulHashable α]
@[grind =] theorem isEmpty_filter_iff [EquivBEq α] [LawfulHashable α]
{f : α → Bool} :
(m.filter f).isEmpty ↔ ∀ k h, f (m.get k h) = false :=
HashMap.isEmpty_filter_iff
@ -903,7 +912,9 @@ theorem isEmpty_filter_eq_false_iff [EquivBEq α] [LawfulHashable α]
(m.filter f).isEmpty = false ↔ ∃ k h, f (m.get k h) :=
HashMap.isEmpty_filter_eq_false_iff
@[simp]
-- TODO: `contains_filter` is missing.
@[simp, grind =]
theorem mem_filter [EquivBEq α] [LawfulHashable α]
{f : α → Bool} {k : α} :
k ∈ m.filter f ↔ ∃ h, f (m.get k h) :=
@ -924,6 +935,8 @@ theorem size_filter_le_size [EquivBEq α] [LawfulHashable α]
(m.filter f).size ≤ m.size :=
HashMap.size_filter_le_size
grind_pattern size_filter_le_size => (m.filter f).size
theorem size_filter_eq_size_iff [EquivBEq α] [LawfulHashable α]
{f : α → Bool} :
(m.filter f).size = m.size ↔ ∀ k h, f (m.get k h) :=
@ -935,23 +948,25 @@ theorem filter_equiv_self_iff [EquivBEq α] [LawfulHashable α]
⟨fun h => HashMap.filter_equiv_self_iff.mp h.1,
fun h => ⟨HashMap.filter_equiv_self_iff.mpr h⟩⟩
@[simp]
@[simp, grind =]
theorem get?_filter [EquivBEq α] [LawfulHashable α]
{f : α → Bool} {k : α} :
(m.filter f).get? k = (m.get? k).filter f :=
HashMap.getKey?_filter_key
@[simp]
@[simp, grind =]
theorem get_filter [EquivBEq α] [LawfulHashable α]
{f : α → Bool} {k : α} {h} :
(m.filter f).get k h = m.get k (mem_of_mem_filter h) :=
HashMap.getKey_filter
@[grind =]
theorem get!_filter [EquivBEq α] [LawfulHashable α] [Inhabited α]
{f : α → Bool} {k : α} :
(m.filter f).get! k = ((m.get? k).filter f).get! :=
HashMap.getKey!_filter_key
@[grind =]
theorem getD_filter [EquivBEq α] [LawfulHashable α]
{f : α → Bool} {k fallback : α} :
(m.filter f).getD k fallback = ((m.get? k).filter f).getD fallback :=

128
src/Std/Data/HashSet/RawLemmas.lean
View file

@ -15,6 +15,8 @@ This module contains lemmas about `Std.Data.HashSet.Raw`. Most of the lemmas req
is to provide an instance of `LawfulBEq α`.
-/
set_option trace.grind.ematch.pattern true
set_option linter.missingDocs true
set_option autoImplicit false
@ -31,11 +33,11 @@ variable {m : Raw α}
private theorem ext {m m' : Raw α} : m.inner = m'.inner → m = m' := by
cases m; cases m'; rintro rfl; rfl
@[simp]
@[simp, grind =]
theorem size_emptyWithCapacity {c} : (emptyWithCapacity c : Raw α).size = 0 :=
HashMap.Raw.size_emptyWithCapacity
@[simp]
@[simp, grind =]
theorem size_empty : (∅ : Raw α).size = 0 :=
HashMap.Raw.size_empty
@ -48,11 +50,11 @@ theorem isEmpty_eq_size_eq_zero : m.isEmpty = (m.size == 0) :=
variable [BEq α] [Hashable α]
@[simp]
@[simp, grind =]
theorem isEmpty_emptyWithCapacity {c} : (emptyWithCapacity c : Raw α).isEmpty :=
HashMap.Raw.isEmpty_emptyWithCapacity
@[simp]
@[simp, grind =]
theorem isEmpty_empty : (∅ : Raw α).isEmpty :=
HashMap.Raw.isEmpty_empty
@ -60,7 +62,7 @@ set_option linter.missingDocs false in
@[deprecated isEmpty_empty (since := "2025-03-12")]
abbrev isEmpty_emptyc := @isEmpty_empty
@[simp]
@[simp, grind =]
theorem isEmpty_insert [EquivBEq α] [LawfulHashable α] (h : m.WF) {a : α} :
(m.insert a).isEmpty = false :=
HashMap.Raw.isEmpty_insertIfNew h.out
@ -80,13 +82,13 @@ theorem mem_congr [EquivBEq α] [LawfulHashable α] (h : m.WF) {a b : α} (hab :
a ∈ m ↔ b ∈ m :=
HashMap.Raw.mem_congr h.out hab
@[simp] theorem contains_emptyWithCapacity {a : α} {c} : (emptyWithCapacity c : Raw α).contains a = false :=
@[simp, grind =] theorem contains_emptyWithCapacity {a : α} {c} : (emptyWithCapacity c : Raw α).contains a = false :=
HashMap.Raw.contains_emptyWithCapacity
@[simp] theorem not_mem_emptyWithCapacity {a : α} {c} : ¬a ∈ (emptyWithCapacity c : Raw α) :=
@[simp, grind] theorem not_mem_emptyWithCapacity {a : α} {c} : ¬a ∈ (emptyWithCapacity c : Raw α) :=
HashMap.Raw.not_mem_emptyWithCapacity
@[simp] theorem contains_empty {a : α} : (∅ : Raw α).contains a = false :=
@[simp, grind =] theorem contains_empty {a : α} : (∅ : Raw α).contains a = false :=
HashMap.Raw.contains_empty
set_option linter.missingDocs false in
@ -128,12 +130,12 @@ theorem isEmpty_iff_forall_not_mem [EquivBEq α] [LawfulHashable α] (h : m.WF)
@[simp] theorem singleton_eq_insert {a : α} : Singleton.singleton a = (∅ : Raw α).insert a := rfl
@[simp]
@[simp, grind =]
theorem contains_insert [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a : α} :
(m.insert k).contains a = (k == a || m.contains a) :=
HashMap.Raw.contains_insertIfNew h.out
@[simp]
@[simp, grind =]
theorem mem_insert [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a : α} :
a ∈ m.insert k ↔ k == a ∨ a ∈ m :=
HashMap.Raw.mem_insertIfNew h.out
@ -167,7 +169,7 @@ theorem contains_insert_self [EquivBEq α] [LawfulHashable α] (h : m.WF) {k :
theorem mem_insert_self [EquivBEq α] [LawfulHashable α] (h : m.WF) {k : α} : k ∈ m.insert k :=
HashMap.Raw.mem_insertIfNew_self h.out
theorem size_insert [EquivBEq α] [LawfulHashable α] (h : m.WF) {k : α} :
@[grind =]theorem size_insert [EquivBEq α] [LawfulHashable α] (h : m.WF) {k : α} :
(m.insert k).size = if k ∈ m then m.size else m.size + 1 :=
HashMap.Raw.size_insertIfNew h.out
@ -179,11 +181,11 @@ theorem size_insert_le [EquivBEq α] [LawfulHashable α] (h : m.WF) {k : α} :
(m.insert k).size ≤ m.size + 1 :=
HashMap.Raw.size_insertIfNew_le h.out
@[simp]
@[simp, grind =]
theorem erase_emptyWithCapacity {k : α} {c : Nat} : (emptyWithCapacity c : Raw α).erase k = emptyWithCapacity c :=
ext HashMap.Raw.erase_emptyWithCapacity
@[simp]
@[simp, grind =]
theorem erase_empty {k : α} : (∅ : Raw α).erase k = ∅ :=
ext HashMap.Raw.erase_empty
@ -191,17 +193,17 @@ set_option linter.missingDocs false in
@[deprecated erase_empty (since := "2025-03-12")]
abbrev erase_emptyc := @erase_empty
@[simp]
@[simp, grind =]
theorem isEmpty_erase [EquivBEq α] [LawfulHashable α] (h : m.WF) {k : α} :
(m.erase k).isEmpty = (m.isEmpty || (m.size == 1 && m.contains k)) :=
HashMap.Raw.isEmpty_erase h.out
@[simp]
@[simp, grind =]
theorem contains_erase [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a : α} :
(m.erase k).contains a = (!(k == a) && m.contains a) :=
HashMap.Raw.contains_erase h.out
@[simp]
@[simp, grind =]
theorem mem_erase [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a : α} :
a ∈ m.erase k ↔ (k == a) = false ∧ a ∈ m :=
HashMap.Raw.mem_erase h.out
@ -214,6 +216,7 @@ theorem mem_of_mem_erase [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a : α}
a ∈ m.erase k → a ∈ m :=
HashMap.Raw.mem_of_mem_erase h.out
@[grind =]
theorem size_erase [EquivBEq α] [LawfulHashable α] (h : m.WF) {k : α} :
(m.erase k).size = if k ∈ m then m.size - 1 else m.size :=
HashMap.Raw.size_erase h.out
@ -226,11 +229,11 @@ theorem size_le_size_erase [EquivBEq α] [LawfulHashable α] (h : m.WF) {k : α}
m.size ≤ (m.erase k).size + 1 :=
HashMap.Raw.size_le_size_erase h.out
@[simp]
@[simp, grind =]
theorem get?_emptyWithCapacity {a : α} {c} : (emptyWithCapacity c : Raw α).get? a = none :=
HashMap.Raw.getKey?_emptyWithCapacity
@[simp]
@[simp, grind =]
theorem get?_empty {a : α} : (∅ : Raw α).get? a = none :=
HashMap.Raw.getKey?_empty
@ -242,7 +245,7 @@ theorem get?_of_isEmpty [EquivBEq α] [LawfulHashable α] (h : m.WF) {a : α} :
m.isEmpty = true → m.get? a = none :=
HashMap.Raw.getKey?_of_isEmpty h.out
theorem get?_insert [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a : α} :
@[grind =] theorem get?_insert [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a : α} :
(m.insert k).get? a = if k == a ∧ ¬k ∈ m then some k else m.get? a :=
HashMap.Raw.getKey?_insertIfNew h.out
@ -272,7 +275,7 @@ theorem get?_eq_none [EquivBEq α] [LawfulHashable α] (h : m.WF) {a : α} :
¬a ∈ m → m.get? a = none :=
HashMap.Raw.getKey?_eq_none h.out
theorem get?_erase [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a : α} :
@[grind =] theorem get?_erase [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a : α} :
(m.erase k).get? a = if k == a then none else m.get? a :=
HashMap.Raw.getKey?_erase h.out
@ -292,12 +295,12 @@ theorem get?_eq_some [LawfulBEq α] (h : m.WF) {k : α} (h' : k ∈ m) :
m.get? k = some k :=
HashMap.Raw.getKey?_eq_some h.out h'
theorem get_insert [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a : α} {h₁} :
@[grind =] theorem get_insert [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a : α} {h₁} :
(m.insert k).get a h₁ =
if h₂ : k == a ∧ ¬k ∈ m then k else m.get a (mem_of_mem_insert' h h₁ h₂) :=
HashMap.Raw.getKey_insertIfNew (h₁ := h₁) h.out
@[simp]
@[simp, grind =]
theorem get_erase [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a : α} {h'} :
(m.erase k).get a h' = m.get a (mem_of_mem_erase h h') :=
HashMap.Raw.getKey_erase (h' := h') h.out
@ -310,7 +313,7 @@ theorem get_eq_get_get? [EquivBEq α] [LawfulHashable α] (h : m.WF) {k : α} {h
m.get k h' = (m.get? k).get ((mem_iff_isSome_get? h).mp h') :=
HashMap.Raw.getKey_eq_get_getKey? h.out
theorem get_get? [EquivBEq α] [LawfulHashable α] (h : m.WF) {k : α} {h'} :
@[grind =] theorem get_get? [EquivBEq α] [LawfulHashable α] (h : m.WF) {k : α} {h'} :
(m.get? k).get h' = m.get k ((mem_iff_isSome_get? h).mpr h') :=
HashMap.Raw.get_getKey? h.out
@ -328,16 +331,16 @@ theorem get_congr [EquivBEq α] [LawfulHashable α] (h : m.WF) {k₁ k₂ : α}
m.get k₁ h₁ = m.get k₂ (((mem_congr h h').mp h₁)) :=
HashMap.Raw.getKey_congr h.out h' h₁
@[simp]
@[simp, grind =]
theorem get_eq [LawfulBEq α] (h : m.WF) {k : α} (h' : m.contains k) :
m.get k h' = k :=
HashMap.Raw.getKey_eq h.out h'
@[simp]
@[simp, grind =]
theorem get!_emptyWithCapacity [Inhabited α] {a : α} {c} : (emptyWithCapacity c : Raw α).get! a = default :=
HashMap.Raw.getKey!_emptyWithCapacity
@[simp]
@[simp, grind =]
theorem get!_empty [Inhabited α] {a : α} : (∅ : Raw α).get! a = default :=
HashMap.Raw.getKey!_empty
@ -349,7 +352,7 @@ theorem get!_of_isEmpty [Inhabited α] [EquivBEq α] [LawfulHashable α] (h : m.
m.isEmpty = true → m.get! a = default :=
HashMap.Raw.getKey!_of_isEmpty h.out
theorem get!_insert [Inhabited α] [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a : α} :
@[grind =] theorem get!_insert [Inhabited α] [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a : α} :
(m.insert k).get! a = if k == a ∧ ¬k ∈ m then k else m.get! a :=
HashMap.Raw.getKey!_insertIfNew h.out
@ -362,7 +365,7 @@ theorem get!_eq_default [Inhabited α] [EquivBEq α] [LawfulHashable α] (h : m.
¬a ∈ m → m.get! a = default :=
HashMap.Raw.getKey!_eq_default h.out
theorem get!_erase [Inhabited α] [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a : α} :
@[grind =] theorem get!_erase [Inhabited α] [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a : α} :
(m.erase k).get! a = if k == a then default else m.get! a :=
HashMap.Raw.getKey!_erase h.out
@ -398,11 +401,11 @@ theorem get!_eq_of_contains [LawfulBEq α] [Inhabited α] (h : m.WF) {k : α} (h
theorem get!_eq_of_mem [LawfulBEq α] [Inhabited α] (h : m.WF) {k : α} (h' : k ∈ m) : m.get! k = k :=
HashMap.Raw.getKey!_eq_of_mem h.out h'
@[simp]
@[simp, grind =]
theorem getD_emptyWithCapacity {a fallback : α} {c} : (emptyWithCapacity c : Raw α).getD a fallback = fallback :=
HashMap.Raw.getKeyD_emptyWithCapacity
@[simp]
@[simp, grind =]
theorem getD_empty {a fallback : α} : (∅ : Raw α).getD a fallback = fallback :=
HashMap.Raw.getKeyD_empty
@ -414,7 +417,7 @@ theorem getD_of_isEmpty [EquivBEq α] [LawfulHashable α] (h : m.WF) {a fallback
m.isEmpty = true → m.getD a fallback = fallback :=
HashMap.Raw.getKeyD_of_isEmpty h.out
theorem getD_insert [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a fallback : α} :
@[grind =] theorem getD_insert [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a fallback : α} :
(m.insert k).getD a fallback = if k == a ∧ ¬k ∈ m then k else m.getD a fallback :=
HashMap.Raw.getKeyD_insertIfNew h.out
@ -427,7 +430,7 @@ theorem getD_eq_fallback [EquivBEq α] [LawfulHashable α] (h : m.WF) {a fallbac
¬a ∈ m → m.getD a fallback = fallback :=
HashMap.Raw.getKeyD_eq_fallback h.out
theorem getD_erase [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a fallback : α} :
@[grind =] theorem getD_erase [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a fallback : α} :
(m.erase k).getD a fallback = if k == a then fallback else m.getD a fallback :=
HashMap.Raw.getKeyD_erase h.out
@ -469,30 +472,30 @@ theorem getD_eq_of_mem [LawfulBEq α] (h : m.WF) {k fallback : α} (h' : k ∈ m
m.getD k fallback = k :=
HashMap.Raw.getKeyD_eq_of_mem h.out h'
@[simp]
@[simp, grind =]
theorem containsThenInsert_fst (h : m.WF) {k : α} : (m.containsThenInsert k).1 = m.contains k :=
HashMap.Raw.containsThenInsertIfNew_fst h.out
@[simp]
@[simp, grind =]
theorem containsThenInsert_snd (h : m.WF) {k : α} : (m.containsThenInsert k).2 = m.insert k :=
ext (HashMap.Raw.containsThenInsertIfNew_snd h.out)
@[simp]
@[simp, grind =]
theorem length_toList [EquivBEq α] [LawfulHashable α] (h : m.WF) :
m.toList.length = m.size :=
HashMap.Raw.length_keys h.1
@[simp]
@[simp, grind =]
theorem isEmpty_toList [EquivBEq α] [LawfulHashable α] (h : m.WF) :
m.toList.isEmpty = m.isEmpty :=
HashMap.Raw.isEmpty_keys h.1
@[simp]
@[simp, grind =]
theorem contains_toList [EquivBEq α] [LawfulHashable α] {k : α} (h : m.WF) :
m.toList.contains k = m.contains k :=
HashMap.Raw.contains_keys h.1
@[simp]
@[simp, grind =]
theorem mem_toList [LawfulBEq α] [LawfulHashable α] (h : m.WF) {k : α} :
k ∈ m.toList ↔ k ∈ m :=
HashMap.Raw.mem_keys h.1
@ -515,7 +518,7 @@ theorem fold_eq_foldl_toList (h : m.WF) {f : δ → α → δ} {init : δ} :
HashMap.Raw.fold_eq_foldl_keys h.out
omit [BEq α] [Hashable α] in
@[simp]
@[simp, grind =]
theorem forM_eq_forM [Monad m'] [LawfulMonad m'] {f : α → m' PUnit} :
m.forM f = ForM.forM m f := rfl
@ -524,7 +527,7 @@ theorem forM_eq_forM_toList [Monad m'] [LawfulMonad m'] (h : m.WF) {f : α → m
HashMap.Raw.forM_eq_forM_keys h.out
omit [BEq α] [Hashable α] in
@[simp]
@[simp, grind =]
theorem forIn_eq_forIn [Monad m'] [LawfulMonad m']
{f : α → δ → m' (ForInStep δ)} {init : δ} :
m.forIn f init = ForIn.forIn m init f := rfl
@ -538,20 +541,22 @@ end monadic
variable {ρ : Type v} [ForIn Id ρ α]
@[simp]
@[simp, grind =]
theorem insertMany_nil (h : m.WF) :
insertMany m [] = m :=
ext (HashMap.Raw.insertManyIfNewUnit_nil h.1)
@[simp]
@[simp, grind =]
theorem insertMany_list_singleton (h : m.WF) {k : α} :
insertMany m [k] = m.insert k :=
ext (HashMap.Raw.insertManyIfNewUnit_list_singleton h.1)
@[grind _=_]
theorem insertMany_cons (h : m.WF) {l : List α} {k : α} :
insertMany m (k :: l) = insertMany (m.insert k) l :=
ext (HashMap.Raw.insertManyIfNewUnit_cons h.1)
@[grind _=_]
theorem insertMany_append (h : m.WF) {l₁ l₂ : List α} :
insertMany m (l₁ ++ l₂) = insertMany (insertMany m l₁) l₂ := by
induction l₁ generalizing m with
@ -566,13 +571,13 @@ theorem insertMany_ind {motive : Raw α → Prop} (m : Raw α) (l : ρ)
show motive ⟨m.1.insertManyIfNewUnit l⟩ from
HashMap.Raw.insertManyIfNewUnit_ind m.inner l init fun m => insert ⟨m⟩
@[simp]
@[simp, grind =]
theorem contains_insertMany_list [EquivBEq α] [LawfulHashable α] (h : m.WF)
{l : List α} {k : α} :
(insertMany m l).contains k = (m.contains k || l.contains k) :=
HashMap.Raw.contains_insertManyIfNewUnit_list h.1
@[simp]
@[simp, grind =]
theorem mem_insertMany_list [EquivBEq α] [LawfulHashable α] (h : m.WF)
{l : List α} {k : α} :
k ∈ insertMany m l ↔ k ∈ m ∨ l.contains k :=
@ -677,12 +682,16 @@ theorem size_le_size_insertMany [EquivBEq α] [LawfulHashable α] (h : m.WF)
{l : ρ} : m.size ≤ (insertMany m l).size :=
HashMap.Raw.size_le_size_insertManyIfNewUnit h.out
grind_pattern size_le_size_insertMany => (insertMany m l).size
theorem size_insertMany_list_le [EquivBEq α] [LawfulHashable α] (h : m.WF)
{l : List α} :
(insertMany m l).size ≤ m.size + l.length :=
HashMap.Raw.size_insertManyIfNewUnit_list_le h.1
@[simp]
grind_pattern size_insertMany_list_le => (insertMany m l).size
@[simp, grind =]
theorem isEmpty_insertMany_list [EquivBEq α] [LawfulHashable α] (h : m.WF)
{l : List α} :
(insertMany m l).isEmpty = (m.isEmpty && l.isEmpty) :=
@ -692,27 +701,28 @@ theorem isEmpty_of_isEmpty_insertMany [EquivBEq α] [LawfulHashable α] (h : m.W
{l : ρ} : (insertMany m l).isEmpty → m.isEmpty :=
HashMap.Raw.isEmpty_of_isEmpty_insertManyIfNewUnit h.out
@[simp]
@[simp, grind =]
theorem ofList_nil :
ofList ([] : List α) = ∅ :=
ext HashMap.Raw.unitOfList_nil
@[simp]
@[simp, grind =]
theorem ofList_singleton {k : α} :
ofList [k] = (∅ : Raw α).insert k :=
ext HashMap.Raw.unitOfList_singleton
@[grind _=_]
theorem ofList_cons {hd : α} {tl : List α} :
ofList (hd :: tl) = insertMany ((∅ : Raw α).insert hd) tl :=
ext HashMap.Raw.unitOfList_cons
@[simp]
@[simp, grind =]
theorem contains_ofList [EquivBEq α] [LawfulHashable α]
{l : List α} {k : α} :
(ofList l).contains k = l.contains k :=
HashMap.Raw.contains_unitOfList
@[simp]
@[simp, grind =]
theorem mem_ofList [EquivBEq α] [LawfulHashable α]
{l : List α} {k : α} :
k ∈ ofList l ↔ l.contains k :=
@ -774,7 +784,9 @@ theorem size_ofList_le [EquivBEq α] [LawfulHashable α]
(ofList l).size ≤ l.length :=
HashMap.Raw.size_unitOfList_le
@[simp]
grind_pattern size_ofList_le => (ofList l).size
@[simp, grind =]
theorem isEmpty_ofList [EquivBEq α] [LawfulHashable α]
{l : List α} :
(ofList l).isEmpty = l.isEmpty :=
@ -896,7 +908,7 @@ theorem toList_filter {f : α → Bool} (h : m.WF) :
(m.filter f).toList.Perm (m.toList.filter f) :=
HashMap.Raw.keys_filter_key h.1
theorem isEmpty_filter_iff [EquivBEq α] [LawfulHashable α]
@[grind =] theorem isEmpty_filter_iff [EquivBEq α] [LawfulHashable α]
{f : α → Bool} (h : m.WF) :
(m.filter f).isEmpty ↔
∀ (k : α) (h : k ∈ m), f (m.get k h) = false :=
@ -908,7 +920,9 @@ theorem isEmpty_filter_eq_false_iff [EquivBEq α] [LawfulHashable α]
∃ (k : α) (h : k ∈ m), f (m.get k h) :=
HashMap.Raw.isEmpty_filter_eq_false_iff h.out
@[simp]
-- TODO: `contains_filter` is missing.
@[simp, grind =]
theorem mem_filter [EquivBEq α] [LawfulHashable α]
{f : α → Bool} {k : α} (h : m.WF) :
(k ∈ m.filter f) ↔ ∃ (h' : k ∈ m), f (m.get k h') :=
@ -924,6 +938,8 @@ theorem size_filter_le_size [EquivBEq α] [LawfulHashable α]
(m.filter f).size ≤ m.size :=
HashMap.Raw.size_filter_le_size h.out
grind_pattern size_filter_le_size => (m.filter f).size
theorem size_filter_eq_size_iff [EquivBEq α] [LawfulHashable α]
{f : α → Bool} (h : m.WF) :
(m.filter f).size = m.size ↔ ∀ (k : α) (h : k ∈ m), f (m.get k h) :=
@ -935,24 +951,24 @@ theorem filter_equiv_self_iff [EquivBEq α] [LawfulHashable α]
⟨fun h' => (HashMap.Raw.filter_equiv_self_iff h.out).mp h'.1,
fun h' => ⟨(HashMap.Raw.filter_equiv_self_iff h.out).mpr h'⟩⟩
@[simp]
@[simp, grind =]
theorem get?_filter [EquivBEq α] [LawfulHashable α]
{f : α → Bool} {k : α} (h : m.WF) :
(m.filter f).get? k = (m.get? k).filter f :=
HashMap.Raw.getKey?_filter_key h.out
@[simp]
@[simp, grind =]
theorem get_filter [EquivBEq α] [LawfulHashable α]
{f : α → Bool} {k : α} {h'} (h : m.WF) :
(m.filter f).get k h' = (m.get k (mem_of_mem_filter h h')) :=
HashMap.Raw.getKey_filter h.out
theorem get!_filter [EquivBEq α] [LawfulHashable α] [Inhabited α]
@[grind =] theorem get!_filter [EquivBEq α] [LawfulHashable α] [Inhabited α]
{f : α → Bool} {k : α} (h : m.WF) :
(m.filter f).get! k = ((m.get? k).filter f).get! :=
HashMap.Raw.getKey!_filter_key h.out
theorem getD_filter [EquivBEq α] [LawfulHashable α]
@[grind =] theorem getD_filter [EquivBEq α] [LawfulHashable α]
{f : α → Bool} {k fallback : α} (h : m.WF) :
(m.filter f).getD k fallback = ((m.get? k).filter f).getD fallback :=
HashMap.Raw.getKeyD_filter_key h.out

1
src/Std/Data/TreeMap/Raw/Lemmas.lean
View file

@ -920,6 +920,7 @@ theorem insertMany_cons {l : List (α × β)} {k : α} {v : β} :
t.insertMany (⟨k, v⟩ :: l) = (t.insert k v).insertMany l :=
ext <| DTreeMap.Raw.Const.insertMany_cons
@[grind _=_]
theorem insertMany_append {l₁ l₂ : List (α × β)} :
insertMany t (l₁ ++ l₂) = insertMany (insertMany t l₁) l₂ := by
induction l₁ generalizing t with

1
src/Std/Data/TreeSet/Lemmas.lean
View file

@ -490,6 +490,7 @@ theorem insertMany_cons {l : List α} {k : α} :
t.insertMany (k :: l) = (t.insert k).insertMany l :=
ext TreeMap.insertManyIfNewUnit_cons
@[grind _=_]
theorem insertMany_append {l₁ l₂ : List α} :
insertMany t (l₁ ++ l₂) = insertMany (insertMany t l₁) l₂ := by
induction l₁ generalizing t with

1
src/Std/Data/TreeSet/Raw/Lemmas.lean
View file

@ -488,6 +488,7 @@ theorem insertMany_cons {l : List α} {k : α} :
t.insertMany (k :: l) = (t.insert k).insertMany l :=
ext TreeMap.Raw.insertManyIfNewUnit_cons
@[grind _=_]
theorem insertMany_append {l₁ l₂ : List α} :
insertMany t (l₁ ++ l₂) = insertMany (insertMany t l₁) l₂ := by
induction l₁ generalizing t with

26
tests/lean/grind/experiments/map.lean Normal file
View file

@ -0,0 +1,26 @@
import Std.Data.HashMap
import Std.Data.DHashMap
import Std.Data.ExtHashMap
set_option grind.warning false
open Std
-- Do we want this?
example (m : HashMap Nat Nat) (h : m.isEmpty) : m[3]? = none := by grind [HashMap.getElem?_of_isEmpty]
-- Don't just use `@[grind]`, instead add two patterns!
-- Do this for List etc?
-- attribute [grind] HashMap.getElem?_eq_some_getElem -- Do we do this for list?
grind_pattern HashMap.getElem?_eq_some_getElem => a ∈ m, m[a]?
example (m : HashMap Nat Nat) : ((m.alter 5 id).erase 7).size ≥ m.size - 1 := by grind
example (m : ExtHashMap Nat Nat) :
(m.insert 1 2).filter (fun k v => k > 1000) = (m.insert 1 3).filter fun k v => k > 1000 := by
ext1 k
grind
example (m : ExtHashMap Nat Nat) :
(((m.insert 1 2).insert 3 4).insert 5 6).filter (fun k v => k > 6) = m.filter fun k v => k > 6 := by
ext1 k
grind

34
tests/lean/run/grind_map.lean Normal file
View file

@ -0,0 +1,34 @@
import Std.Data.HashMap
import Std.Data.DHashMap
import Std.Data.ExtHashMap
import Std.Data.HashSet
set_option grind.warning false
open Std
section
variable [BEq α] [LawfulBEq α] [Hashable α] [LawfulHashable α ]
example : (∅ : DHashMap α β).isEmpty := by grind
example (m : DHashMap α β) (h : m = ∅) : m.isEmpty := by grind
example : (((∅ : HashMap Nat Nat).insert 3 6).insert 4 7).contains 3 := by grind
example : (((∅ : HashMap Nat Nat).insert 3 6).insert 4 7).contains 9 == false := by grind
example (m : HashMap Nat Nat) (h : m.contains 3) : (m.erase 2).contains 3 := by grind
example (m : HashMap Nat Nat) (h : (m.erase 2).contains 3) : m.contains 3 := by grind
example (m : HashMap Nat Nat) : (m.erase 3).contains 3 = false := by grind
example (m : HashMap Nat Nat) (h : m.contains 3 = false) : (m.erase 2).contains 3 = false := by grind
-- Insert twice
example (m : HashMap Nat Nat) : m.size ≤ ((m.insert 1 2).insert 3 4).size := by grind
example (m : HashMap Nat Nat) : ((m.insert 1 2).insert 3 4).size ≤ m.size + 2 := by grind
-- Insert the same key twice
example (m : HashMap Nat Nat) : m.size ≤ ((m.insert 1 2).insert 1 4).size := by grind
example (m : HashMap Nat Nat) : ((m.insert 1 2).insert 1 4).size ≤ m.size + 1 := by grind
example : (((∅ : HashMap Nat Nat).insert 3 6).erase 4)[3]? = some 6 := by grind
end

12
tests/lean/run/grind_map_uniform.lean Normal file
View file

@ -0,0 +1,12 @@
import Lean.Meta.Tactic.Grind
import Std.Data.DHashMap
import Std.Data.HashMap
import Std.Data.HashSet
import Std.Data.TreeMap
import Std.Data.TreeSet
#eval Lean.Meta.Grind.isEMatchTheorem `Std.DHashMap.isEmpty_emptyWithCapacity
#eval Lean.Meta.Grind.isEMatchTheorem `Std.HashMap.isEmpty_emptyWithCapacity
#eval Lean.Meta.Grind.isEMatchTheorem `Std.HashSet.isEmpty_emptyWithCapacity
#eval Lean.Meta.Grind.isEMatchTheorem `Std.TreeMap.isEmpty_emptyWithCapacity
#eval Lean.Meta.Grind.isEMatchTheorem `Std.TreeSet.isEmpty_emptyWithCapacity