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refactor: HashMap/TreeMap and their extensional variants to use getElem instance #11578

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Merged
wkrozowski merged 6 commits into from
Dec 10, 2025
Merged

refactor: HashMap/TreeMap and their extensional variants to use getElem instance #11578

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b9063c5
chore: Cleanup `HashMap.lemmas`
wkrozowski Dec 9, 2025
697fc8b
chore: `HashMap` done
wkrozowski Dec 9, 2025
e5f0b5c
Add `ExtHashMap` lemmas
wkrozowski Dec 9, 2025
076d432
chore: `TreeMap` depreciation is done
wkrozowski Dec 10, 2025
bb770e1
chore: finish refactoring `TreeMap.Raw`
wkrozowski Dec 10, 2025
dcc4908
chore: finish refactoring `ExtTreeMap`
wkrozowski Dec 10, 2025
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118 changes: 109 additions & 9 deletions src/Std/Data/ExtHashMap/Lemmas.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -1409,27 +1409,58 @@ theorem union_insert_right_eq_insert_union [EquivBEq α] [LawfulHashable α] {p
simp only [union, insert, ExtDHashMap.union_eq, mk.injEq]
exact ExtDHashMap.union_insert_right_eq_insert_union

/- getElem? -/
theorem getElem?_union [EquivBEq α] [LawfulHashable α] {k : α} :
(m₁ ∪ m₂)[k]? = (m₂[k]?).or (m₁[k]?) :=
ExtDHashMap.Const.get?_union

theorem getElem?_union_of_not_mem_left [EquivBEq α] [LawfulHashable α]
{k : α} (not_mem : ¬k ∈ m₁) :
(m₁ ∪ m₂)[k]? = m₂[k]? :=
ExtDHashMap.Const.get?_union_of_not_mem_left not_mem

theorem getElem?_union_of_not_mem_right [EquivBEq α] [LawfulHashable α]
{k : α} (not_mem : ¬k ∈ m₂) :
(m₁ ∪ m₂)[k]? = m₁[k]? :=
ExtDHashMap.Const.get?_union_of_not_mem_right not_mem

/- get? -/
@[deprecated getElem?_union (since := "2025-12-10")]
theorem get?_union [EquivBEq α] [LawfulHashable α] {k : α} :
(m₁ ∪ m₂).get? k = (m₂.get? k).or (m₁.get? k) :=
ExtDHashMap.Const.get?_union

@[deprecated getElem?_union_of_not_mem_left (since := "2025-12-10")]
theorem get?_union_of_not_mem_left [EquivBEq α] [LawfulHashable α]
{k : α} (not_mem : ¬k ∈ m₁) :
(m₁ ∪ m₂).get? k = m₂.get? k :=
ExtDHashMap.Const.get?_union_of_not_mem_left not_mem

@[deprecated getElem?_union_of_not_mem_right (since := "2025-12-10")]
theorem get?_union_of_not_mem_right [EquivBEq α] [LawfulHashable α]
{k : α} (not_mem : ¬k ∈ m₂) :
(m₁ ∪ m₂).get? k = m₁.get? k :=
ExtDHashMap.Const.get?_union_of_not_mem_right not_mem

/- getElem -/
theorem getElem_union_of_mem_right [EquivBEq α] [LawfulHashable α]
{k : α} (mem : k ∈ m₂) :
(m₁ ∪ m₂)[k]'(mem_union_of_right mem) = m₂[k]'mem :=
ExtDHashMap.Const.get_union_of_mem_right mem

theorem getElem_union_of_not_mem_left [EquivBEq α] [LawfulHashable α]
{k : α} (not_mem : ¬k ∈ m₁) {h'} :
(m₁ ∪ m₂)[k]'h' = m₂[k]'(mem_of_mem_union_of_not_mem_left h' not_mem) :=
ExtDHashMap.Const.get_union_of_not_mem_left not_mem (h' := h')

/- get -/
@[deprecated getElem_union_of_mem_right (since := "2025-12-10")]
theorem get_union_of_mem_right [EquivBEq α] [LawfulHashable α]
{k : α} (mem : k ∈ m₂) :
(m₁ ∪ m₂).get k (mem_union_of_right mem) = m₂.get k mem :=
ExtDHashMap.Const.get_union_of_mem_right mem

@[deprecated getElem_union_of_not_mem_left (since := "2025-12-10")]
theorem get_union_of_not_mem_left [EquivBEq α] [LawfulHashable α]
{k : α} (not_mem : ¬k ∈ m₁) {h'} :
(m₁ ∪ m₂).get k h' = m₂.get k (mem_of_mem_union_of_not_mem_left h' not_mem) :=
Expand All @@ -1450,16 +1481,33 @@ theorem getD_union_of_not_mem_right [EquivBEq α] [LawfulHashable α]
(m₁ ∪ m₂).getD k fallback = m₁.getD k fallback :=
ExtDHashMap.Const.getD_union_of_not_mem_right not_mem

/- getElem! -/
theorem getElem!_union [EquivBEq α] [LawfulHashable α] {k : α} [Inhabited β] :
(m₁ ∪ m₂)[k]! = m₂.getD k (m₁[k]!) :=
ExtDHashMap.Const.get!_union

theorem getElem!_union_of_not_mem_left [EquivBEq α] [LawfulHashable α]
{k : α} [Inhabited β] (not_mem : ¬k ∈ m₁) :
(m₁ ∪ m₂)[k]! = m₂[k]! :=
ExtDHashMap.Const.get!_union_of_not_mem_left not_mem

theorem getElem!_union_of_not_mem_right [EquivBEq α] [LawfulHashable α] {k : α} [Inhabited β] (not_mem : ¬k ∈ m₂) :
(m₁ ∪ m₂)[k]! = m₁[k]! :=
ExtDHashMap.Const.get!_union_of_not_mem_right not_mem

/- get! -/
@[deprecated getElem!_union (since := "2025-12-10")]
theorem get!_union [EquivBEq α] [LawfulHashable α] {k : α} [Inhabited β] :
(m₁ ∪ m₂).get! k = m₂.getD k (m₁.get! k) :=
ExtDHashMap.Const.get!_union

@[deprecated getElem!_union_of_not_mem_left (since := "2025-12-10")]
theorem get!_union_of_not_mem_left [EquivBEq α] [LawfulHashable α]
{k : α} [Inhabited β] (not_mem : ¬k ∈ m₁) :
(m₁ ∪ m₂).get! k = m₂.get! k :=
ExtDHashMap.Const.get!_union_of_not_mem_left not_mem

@[deprecated getElem!_union_of_not_mem_right (since := "2025-12-10")]
theorem get!_union_of_not_mem_right [EquivBEq α] [LawfulHashable α] {k : α} [Inhabited β] (not_mem : ¬k ∈ m₂) :
(m₁ ∪ m₂).get! k = m₁.get! k :=
ExtDHashMap.Const.get!_union_of_not_mem_right not_mem
Expand Down Expand Up @@ -1579,33 +1627,62 @@ theorem not_mem_inter_of_not_mem_right [EquivBEq α] [LawfulHashable α] {k : α
k ∉ m₁ ∩ m₂ :=
ExtDHashMap.not_mem_inter_of_not_mem_right not_mem

/- getElem? -/
theorem getElem?_inter [EquivBEq α] [LawfulHashable α] {k : α} :
(m₁ ∩ m₂)[k]? = if k ∈ m₂ then m₁[k]? else none :=
ExtDHashMap.Const.get?_inter

theorem getElem?_inter_of_mem_right [EquivBEq α] [LawfulHashable α]
{k : α} (mem : k ∈ m₂) :
(m₁ ∩ m₂)[k]? = m₁[k]? :=
ExtDHashMap.Const.get?_inter_of_mem_right mem

theorem getElem?_inter_of_not_mem_left [EquivBEq α] [LawfulHashable α]
{k : α} (not_mem : k ∉ m₁) :
(m₁ ∩ m₂)[k]? = none :=
ExtDHashMap.Const.get?_inter_of_not_mem_left not_mem

theorem getElem?_inter_of_not_mem_right [EquivBEq α] [LawfulHashable α]
{k : α} (not_mem : k ∉ m₂) :
(m₁ ∩ m₂)[k]? = none :=
ExtDHashMap.Const.get?_inter_of_not_mem_right not_mem

/- get? -/
@[deprecated getElem?_inter (since := "2025-12-10")]
theorem get?_inter [EquivBEq α] [LawfulHashable α] {k : α} :
(m₁ ∩ m₂).get? k =
if k ∈ m₂ then m₁.get? k else none :=
(m₁ ∩ m₂).get? k = if k ∈ m₂ then m₁.get? k else none :=
ExtDHashMap.Const.get?_inter

@[deprecated getElem?_inter_of_mem_right (since := "2025-12-10")]
theorem get?_inter_of_mem_right [EquivBEq α] [LawfulHashable α]
{k : α} (mem : k ∈ m₂) :
(m₁ ∩ m₂).get? k = m₁.get? k :=
ExtDHashMap.Const.get?_inter_of_mem_right mem

@[deprecated getElem?_inter_of_not_mem_left (since := "2025-12-10")]
theorem get?_inter_of_not_mem_left [EquivBEq α] [LawfulHashable α]
{k : α} (not_mem : k ∉ m₁) :
(m₁ ∩ m₂).get? k = none :=
ExtDHashMap.Const.get?_inter_of_not_mem_left not_mem

@[deprecated getElem?_inter_of_not_mem_right (since := "2025-12-10")]
theorem get?_inter_of_not_mem_right [EquivBEq α] [LawfulHashable α]
{k : α} (not_mem : k ∉ m₂) :
(m₁ ∩ m₂).get? k = none :=
ExtDHashMap.Const.get?_inter_of_not_mem_right not_mem

/- get -/
/- getElem -/
@[simp]
theorem getElem_inter [EquivBEq α] [LawfulHashable α]
{k : α} {h_mem : k ∈ m₁ ∩ m₂} :
(m₁ ∩ m₂)[k]'h_mem = m₁[k]'(mem_inter_iff.1 h_mem).1 :=
ExtDHashMap.Const.get_inter (h_mem := h_mem)

/- get -/
@[deprecated getElem_inter (since := "2025-12-10")]
theorem get_inter [EquivBEq α] [LawfulHashable α]
{k : α} {h_mem : k ∈ m₁ ∩ m₂} :
(m₁ ∩ m₂).get k h_mem =
m₁.get k (mem_inter_iff.1 h_mem).1 :=
(m₁ ∩ m₂).get k h_mem = m₁.get k (mem_inter_iff.1 h_mem).1 :=
ExtDHashMap.Const.get_inter

/- getD -/
Expand All @@ -1629,22 +1706,45 @@ theorem getD_inter_of_not_mem_left [EquivBEq α] [LawfulHashable α]
(m₁ ∩ m₂).getD k fallback = fallback :=
ExtDHashMap.Const.getD_inter_of_not_mem_left not_mem

/- getElem! -/
theorem getElem!_inter [EquivBEq α] [LawfulHashable α] {k : α} [Inhabited β] :
(m₁ ∩ m₂)[k]! = if k ∈ m₂ then m₁[k]! else default :=
ExtDHashMap.Const.get!_inter

theorem getElem!_inter_of_mem_right [EquivBEq α] [LawfulHashable α]
{k : α} [Inhabited β] (mem : k ∈ m₂) :
(m₁ ∩ m₂)[k]! = m₁[k]! :=
ExtDHashMap.Const.get!_inter_of_mem_right mem

theorem getElem!_inter_of_not_mem_right [EquivBEq α] [LawfulHashable α]
{k : α} [Inhabited β] (not_mem : k ∉ m₂) :
(m₁ ∩ m₂)[k]! = default :=
ExtDHashMap.Const.get!_inter_of_not_mem_right not_mem

theorem getElem!_inter_of_not_mem_left [EquivBEq α] [LawfulHashable α]
{k : α} [Inhabited β] (not_mem : k ∉ m₁) :
(m₁ ∩ m₂)[k]! = default :=
ExtDHashMap.Const.get!_inter_of_not_mem_left not_mem

/- get! -/
@[deprecated getElem!_inter (since := "2025-12-10")]
theorem get!_inter [EquivBEq α] [LawfulHashable α] {k : α} [Inhabited β] :
(m₁ ∩ m₂).get! k =
if k ∈ m₂ then m₁.get! k else default :=
(m₁ ∩ m₂).get! k = if k ∈ m₂ then m₁.get! k else default :=
ExtDHashMap.Const.get!_inter

@[deprecated getElem!_inter_of_mem_right (since := "2025-12-10")]
theorem get!_inter_of_mem_right [EquivBEq α] [LawfulHashable α]
{k : α} [Inhabited β] (mem : k ∈ m₂) :
(m₁ ∩ m₂).get! k = m₁.get! k :=
ExtDHashMap.Const.get!_inter_of_mem_right mem

@[deprecated getElem!_inter_of_not_mem_right (since := "2025-12-10")]
theorem get!_inter_of_not_mem_right [EquivBEq α] [LawfulHashable α]
{k : α} [Inhabited β] (not_mem : k ∉ m₂) :
(m₁ ∩ m₂).get! k = default :=
ExtDHashMap.Const.get!_inter_of_not_mem_right not_mem

@[deprecated getElem!_inter_of_not_mem_left (since := "2025-12-10")]
theorem get!_inter_of_not_mem_left [EquivBEq α] [LawfulHashable α]
{k : α} [Inhabited β] (not_mem : k ∉ m₁) :
(m₁ ∩ m₂).get! k = default :=
Expand Down Expand Up @@ -2490,12 +2590,12 @@ 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) :=
(m.filter f).size = m.size ↔ ∀ k h, f (m.getKey k h) (m[k]'h) :=
ExtDHashMap.Const.size_filter_eq_size_iff

theorem filter_eq_self_iff [EquivBEq α] [LawfulHashable α]
{f : α → β → Bool} :
m.filter f = m ↔ ∀ k h, f (m.getKey k h) (m.get k h) :=
m.filter f = m ↔ ∀ k h, f (m.getKey k h) (m[k]'h) :=
ext_iff.trans ExtDHashMap.Const.filter_eq_self_iff

theorem getElem?_filter [EquivBEq α] [LawfulHashable α]
Expand Down
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