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

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This PR refactors the usage of `get` operation on
`HashMap`/`TreeMap`/`ExtHashMap`/`ExtTreeMap` to `getElem` instace.
This commit is contained in:
Wojciech Różowski 2025-12-10 18:52:34 +01:00 • committed by GitHub
parent 2b257854f9
commit 361bfdbc5c
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6 changed files with 1077 additions and 167 deletions
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126
src/Std/Data/ExtHashMap/Lemmas.lean
View file

@ -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) :=
@ -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
@ -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
/- get? -/
theorem get?_inter [EquivBEq α] [LawfulHashable α] {k : α} :
(m₁ ∩ m₂).get? k =
if k ∈ m₂ then m₁.get? k else none :=
/- 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 :=
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 -/
@ -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
/- get! -/
theorem get!_inter [EquivBEq α] [LawfulHashable α] {k : α} [Inhabited β] :
(m₁ ∩ m₂).get! k =
if k ∈ m₂ then m₁.get! k else default :=
/- 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 :=
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 :=
@ -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]

222
src/Std/Data/ExtTreeMap/Lemmas.lean
View file

@ -271,7 +271,7 @@ theorem getElem?_congr [TransCmp cmp] {a b : α} (hab : cmp a b = .eq) :
@[grind =] theorem getElem_insert [TransCmp cmp] {k a : α} {v : β} {h₁} :
(t.insert k v)[a]'h₁ =
if h₂ : cmp k a = .eq then v
else get t a (mem_of_mem_insert h₁ h₂) :=
else t[a]'(mem_of_mem_insert h₁ h₂) :=
ExtDTreeMap.Const.get_insert (h₁ := h₁)
@[simp]
@ -386,7 +386,7 @@ theorem getD_erase_self [TransCmp cmp] {k : α} {fallback : β} :
ExtDTreeMap.Const.getD_erase_self
theorem getElem?_eq_some_getD_of_contains [TransCmp cmp] {a : α} {fallback : β} :
t.contains a = true → get? t a = some (getD t a fallback) :=
t.contains a = true → t[a]? = some (getD t a fallback) :=
ExtDTreeMap.Const.get?_eq_some_getD_of_contains
theorem getElem?_eq_some_getD [TransCmp cmp] {a : α} {fallback : β} :
@ -743,7 +743,7 @@ theorem size_insertIfNew_le [TransCmp cmp] {k : α} {v : β} :
@[simp, grind =]
theorem getThenInsertIfNew?_fst [TransCmp cmp] {k : α} {v : β} :
(getThenInsertIfNew? t k v).1 = get? t k :=
(getThenInsertIfNew? t k v).1 = t[k]? :=
ExtDTreeMap.Const.getThenInsertIfNew?_fst
@[simp, grind =]
@ -1071,7 +1071,7 @@ theorem getElem_insertMany_list_of_contains_eq_false [TransCmp cmp] [BEq α]
(contains : (l.map Prod.fst).contains k = false)
{h'} :
(t.insertMany l)[k]'h' =
t.get k (mem_of_mem_insertMany_list h' contains) :=
t[k]'(mem_of_mem_insertMany_list h' contains) :=
ExtDTreeMap.Const.get_insertMany_list_of_contains_eq_false contains (h' := h')
theorem getElem_insertMany_list_of_mem [TransCmp cmp]
@ -1086,7 +1086,7 @@ theorem getElem!_insertMany_list_of_contains_eq_false [TransCmp cmp]
[BEq α] [LawfulBEqCmp cmp]
{l : List (α × β)} {k : α} [Inhabited β]
(contains_eq_false : (l.map Prod.fst).contains k = false) :
(t.insertMany l)[k]! = t.get! k :=
(t.insertMany l)[k]! = t[k]! :=
ExtDTreeMap.Const.get!_insertMany_list_of_contains_eq_false contains_eq_false
theorem getElem!_insertMany_list_of_mem [TransCmp cmp]
@ -1553,27 +1553,58 @@ theorem union_insert_right_eq_insert_union [TransCmp cmp] {p : (_ : α) × β} :
simp only [union, insert, ExtDTreeMap.union_eq, mk.injEq]
exact ExtDTreeMap.union_insert_right_eq_insert_union
/- getElem? -/
theorem getElem?_union [TransCmp cmp] {k : α} :
(t₁ ∪ t₂)[k]? = (t₂[k]?).or (t₁[k]?) :=
ExtDTreeMap.Const.get?_union
theorem getElem?_union_of_not_mem_left [TransCmp cmp]
{k : α} (not_mem : ¬k ∈ t₁) :
(t₁ ∪ t₂)[k]? = t₂[k]? :=
ExtDTreeMap.Const.get?_union_of_not_mem_left not_mem
theorem getElem?_union_of_not_mem_right [TransCmp cmp]
{k : α} (not_mem : ¬k ∈ t₂) :
(t₁ ∪ t₂)[k]? = t₁[k]? :=
ExtDTreeMap.Const.get?_union_of_not_mem_right not_mem
/- get? -/
@[deprecated getElem?_union (since := "2025-12-10")]
theorem get?_union [TransCmp cmp] {k : α} :
(t₁ ∪ t₂).get? k = (t₂.get? k).or (t₁.get? k) :=
ExtDTreeMap.Const.get?_union
@[deprecated getElem?_union_of_not_mem_left (since := "2025-12-10")]
theorem get?_union_of_not_mem_left [TransCmp cmp]
{k : α} (not_mem : ¬k ∈ t₁) :
(t₁ ∪ t₂).get? k = t₂.get? k :=
ExtDTreeMap.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 [TransCmp cmp]
{k : α} (not_mem : ¬k ∈ t₂) :
(t₁ ∪ t₂).get? k = t₁.get? k :=
ExtDTreeMap.Const.get?_union_of_not_mem_right not_mem
/- getElem -/
theorem getElem_union_of_mem_right [TransCmp cmp]
{k : α} (mem : k ∈ t₂) :
(t₁ ∪ t₂)[k]'(mem_union_of_right mem) = t₂[k]'mem :=
ExtDTreeMap.Const.get_union_of_mem_right mem
theorem getElem_union_of_not_mem_left [TransCmp cmp]
{k : α} (not_mem : ¬k ∈ t₁) {h'} :
(t₁ ∪ t₂)[k]'h' = t₂[k]'(mem_of_mem_union_of_not_mem_left h' not_mem) :=
ExtDTreeMap.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 [TransCmp cmp]
{k : α} (mem : k ∈ t₂) :
(t₁ ∪ t₂).get k (mem_union_of_right mem) = t₂.get k mem :=
ExtDTreeMap.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 [TransCmp cmp]
{k : α} (not_mem : ¬k ∈ t₁) {h'} :
(t₁ ∪ t₂).get k h' = t₂.get k (mem_of_mem_union_of_not_mem_left h' not_mem) :=
@ -1594,16 +1625,33 @@ theorem getD_union_of_not_mem_right [TransCmp cmp]
(t₁ ∪ t₂).getD k fallback = t₁.getD k fallback :=
ExtDTreeMap.Const.getD_union_of_not_mem_right not_mem
/- getElem! -/
theorem getElem!_union [TransCmp cmp] {k : α} [Inhabited β] :
(t₁ ∪ t₂)[k]! = t₂.getD k (t₁[k]!) :=
ExtDTreeMap.Const.get!_union
theorem getElem!_union_of_not_mem_left [TransCmp cmp]
{k : α} [Inhabited β] (not_mem : ¬k ∈ t₁) :
(t₁ ∪ t₂)[k]! = t₂[k]! :=
ExtDTreeMap.Const.get!_union_of_not_mem_left not_mem
theorem getElem!_union_of_not_mem_right [TransCmp cmp] {k : α} [Inhabited β] (not_mem : ¬k ∈ t₂) :
(t₁ ∪ t₂)[k]! = t₁[k]! :=
ExtDTreeMap.Const.get!_union_of_not_mem_right not_mem
/- get! -/
@[deprecated getElem!_union (since := "2025-12-10")]
theorem get!_union [TransCmp cmp] {k : α} [Inhabited β] :
(t₁ ∪ t₂).get! k = t₂.getD k (t₁.get! k) :=
ExtDTreeMap.Const.get!_union
@[deprecated getElem!_union_of_not_mem_left (since := "2025-12-10")]
theorem get!_union_of_not_mem_left [TransCmp cmp]
{k : α} [Inhabited β] (not_mem : ¬k ∈ t₁) :
(t₁ ∪ t₂).get! k = t₂.get! k :=
ExtDTreeMap.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 [TransCmp cmp] {k : α} [Inhabited β] (not_mem : ¬k ∈ t₂) :
(t₁ ∪ t₂).get! k = t₁.get! k :=
ExtDTreeMap.Const.get!_union_of_not_mem_right not_mem
@ -1720,33 +1768,62 @@ theorem not_mem_inter_of_not_mem_right [TransCmp cmp] {k : α}
k ∉ t₁ ∩ t₂ :=
ExtDTreeMap.not_mem_inter_of_not_mem_right not_mem
/- get? -/
theorem get?_inter [TransCmp cmp] {k : α} :
(t₁ ∩ t₂).get? k =
if k ∈ t₂ then t₁.get? k else none :=
/- getElem? -/
theorem getElem?_inter [TransCmp cmp] {k : α} :
(t₁ ∩ t₂)[k]? = if k ∈ t₂ then t₁[k]? else none :=
ExtDTreeMap.Const.get?_inter
theorem getElem?_inter_of_mem_right [TransCmp cmp]
{k : α} (mem : k ∈ t₂) :
(t₁ ∩ t₂)[k]? = t₁[k]? :=
ExtDTreeMap.Const.get?_inter_of_mem_right mem
theorem getElem?_inter_of_not_mem_left [TransCmp cmp]
{k : α} (not_mem : k ∉ t₁) :
(t₁ ∩ t₂)[k]? = none :=
ExtDTreeMap.Const.get?_inter_of_not_mem_left not_mem
theorem getElem?_inter_of_not_mem_right [TransCmp cmp]
{k : α} (not_mem : k ∉ t₂) :
(t₁ ∩ t₂)[k]? = none :=
ExtDTreeMap.Const.get?_inter_of_not_mem_right not_mem
/- get? -/
@[deprecated getElem?_inter (since := "2025-12-10")]
theorem get?_inter [TransCmp cmp] {k : α} :
(t₁ ∩ t₂).get? k = if k ∈ t₂ then t₁.get? k else none :=
ExtDTreeMap.Const.get?_inter
@[deprecated getElem?_inter_of_mem_right (since := "2025-12-10")]
theorem get?_inter_of_mem_right [TransCmp cmp]
{k : α} (mem : k ∈ t₂) :
(t₁ ∩ t₂).get? k = t₁.get? k :=
ExtDTreeMap.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 [TransCmp cmp]
{k : α} (not_mem : k ∉ t₁) :
(t₁ ∩ t₂).get? k = none :=
ExtDTreeMap.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 [TransCmp cmp]
{k : α} (not_mem : k ∉ t₂) :
(t₁ ∩ t₂).get? k = none :=
ExtDTreeMap.Const.get?_inter_of_not_mem_right not_mem
/- get -/
/- getElem -/
@[simp]
theorem getElem_inter [TransCmp cmp]
{k : α} {h_mem : k ∈ t₁ ∩ t₂} :
(t₁ ∩ t₂)[k]'h_mem = t₁[k]'(mem_inter_iff.1 h_mem).1 :=
ExtDTreeMap.Const.get_inter (h_mem := h_mem)
/- get -/
@[deprecated getElem_inter (since := "2025-12-10")]
theorem get_inter [TransCmp cmp]
{k : α} {h_mem : k ∈ t₁ ∩ t₂} :
(t₁ ∩ t₂).get k h_mem =
t₁.get k (mem_inter_iff.1 h_mem).1 :=
(t₁ ∩ t₂).get k h_mem = t₁.get k (mem_inter_iff.1 h_mem).1 :=
ExtDTreeMap.Const.get_inter
/- getD -/
@ -1770,22 +1847,45 @@ theorem getD_inter_of_not_mem_left [TransCmp cmp]
(t₁ ∩ t₂).getD k fallback = fallback :=
ExtDTreeMap.Const.getD_inter_of_not_mem_left not_mem
/- get! -/
theorem get!_inter [TransCmp cmp] {k : α} [Inhabited β] :
(t₁ ∩ t₂).get! k =
if k ∈ t₂ then t₁.get! k else default :=
/- getElem! -/
theorem getElem!_inter [TransCmp cmp] {k : α} [Inhabited β] :
(t₁ ∩ t₂)[k]! = if k ∈ t₂ then t₁[k]! else default :=
ExtDTreeMap.Const.get!_inter
theorem getElem!_inter_of_mem_right [TransCmp cmp]
{k : α} [Inhabited β] (mem : k ∈ t₂) :
(t₁ ∩ t₂)[k]! = t₁[k]! :=
ExtDTreeMap.Const.get!_inter_of_mem_right mem
theorem getElem!_inter_of_not_mem_right [TransCmp cmp]
{k : α} [Inhabited β] (not_mem : k ∉ t₂) :
(t₁ ∩ t₂)[k]! = default :=
ExtDTreeMap.Const.get!_inter_of_not_mem_right not_mem
theorem getElem!_inter_of_not_mem_left [TransCmp cmp]
{k : α} [Inhabited β] (not_mem : k ∉ t₁) :
(t₁ ∩ t₂)[k]! = default :=
ExtDTreeMap.Const.get!_inter_of_not_mem_left not_mem
/- get! -/
@[deprecated getElem!_inter (since := "2025-12-10")]
theorem get!_inter [TransCmp cmp] {k : α} [Inhabited β] :
(t₁ ∩ t₂).get! k = if k ∈ t₂ then t₁.get! k else default :=
ExtDTreeMap.Const.get!_inter
@[deprecated getElem!_inter_of_mem_right (since := "2025-12-10")]
theorem get!_inter_of_mem_right [TransCmp cmp]
{k : α} [Inhabited β] (mem : k ∈ t₂) :
(t₁ ∩ t₂).get! k = t₁.get! k :=
ExtDTreeMap.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 [TransCmp cmp]
{k : α} [Inhabited β] (not_mem : k ∉ t₂) :
(t₁ ∩ t₂).get! k = default :=
ExtDTreeMap.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 [TransCmp cmp]
{k : α} [Inhabited β] (not_mem : k ∉ t₁) :
(t₁ ∩ t₂).get! k = default :=
@ -1932,32 +2032,61 @@ theorem not_mem_diff_of_mem_right [TransCmp cmp] {k : α}
k ∉ t₁ \ t₂ :=
ExtDTreeMap.not_mem_diff_of_mem_right mem
/- get? -/
theorem get?_diff [TransCmp cmp] {k : α} :
(t₁ \ t₂).get? k =
if k ∈ t₂ then none else t₁.get? k :=
/- getElem? -/
theorem getElem?_diff [TransCmp cmp] {k : α} :
(t₁ \ t₂)[k]? = if k ∈ t₂ then none else t₁[k]? :=
ExtDTreeMap.Const.get?_diff
theorem getElem?_diff_of_not_mem_right [TransCmp cmp]
{k : α} (not_mem : k ∉ t₂) :
(t₁ \ t₂)[k]? = t₁[k]? :=
ExtDTreeMap.Const.get?_diff_of_not_mem_right not_mem
theorem getElem?_diff_of_not_mem_left [TransCmp cmp]
{k : α} (not_mem : k ∉ t₁) :
(t₁ \ t₂)[k]? = none :=
ExtDTreeMap.Const.get?_diff_of_not_mem_left not_mem
theorem getElem?_diff_of_mem_right [TransCmp cmp]
{k : α} (mem : k ∈ t₂) :
(t₁ \ t₂)[k]? = none :=
ExtDTreeMap.Const.get?_diff_of_mem_right mem
/- get? -/
@[deprecated getElem?_diff (since := "2025-12-10")]
theorem get?_diff [TransCmp cmp] {k : α} :
(t₁ \ t₂).get? k = if k ∈ t₂ then none else t₁.get? k :=
ExtDTreeMap.Const.get?_diff
@[deprecated getElem?_diff_of_not_mem_right (since := "2025-12-10")]
theorem get?_diff_of_not_mem_right [TransCmp cmp]
{k : α} (not_mem : k ∉ t₂) :
(t₁ \ t₂).get? k = t₁.get? k :=
ExtDTreeMap.Const.get?_diff_of_not_mem_right not_mem
@[deprecated getElem?_diff_of_not_mem_left (since := "2025-12-10")]
theorem get?_diff_of_not_mem_left [TransCmp cmp]
{k : α} (not_mem : k ∉ t₁) :
(t₁ \ t₂).get? k = none :=
ExtDTreeMap.Const.get?_diff_of_not_mem_left not_mem
@[deprecated getElem?_diff_of_mem_right (since := "2025-12-10")]
theorem get?_diff_of_mem_right [TransCmp cmp]
{k : α} (mem : k ∈ t₂) :
(t₁ \ t₂).get? k = none :=
ExtDTreeMap.Const.get?_diff_of_mem_right mem
/- getElem -/
theorem getElem_diff [TransCmp cmp]
{k : α} {h_mem : k ∈ t₁ \ t₂} :
(t₁ \ t₂)[k]'h_mem = t₁[k]'(mem_diff_iff.1 h_mem).1 :=
ExtDTreeMap.Const.get_diff (h_mem := h_mem)
/- get -/
@[deprecated getElem_diff (since := "2025-12-10")]
theorem get_diff [TransCmp cmp]
{k : α} {h_mem : k ∈ t₁ \ t₂} :
(t₁ \ t₂).get k h_mem =
t₁.get k (mem_diff_iff.1 h_mem).1 :=
(t₁ \ t₂).get k h_mem = t₁.get k (mem_diff_iff.1 h_mem).1 :=
ExtDTreeMap.Const.get_diff
/- getD -/
@ -1981,22 +2110,45 @@ theorem getD_diff_of_not_mem_left [TransCmp cmp]
(t₁ \ t₂).getD k fallback = fallback :=
ExtDTreeMap.Const.getD_diff_of_not_mem_left not_mem
/- get! -/
theorem get!_diff [TransCmp cmp] {k : α} [Inhabited β] :
(t₁ \ t₂).get! k =
if k ∈ t₂ then default else t₁.get! k :=
/- getElem! -/
theorem getElem!_diff [TransCmp cmp] {k : α} [Inhabited β] :
(t₁ \ t₂)[k]! = if k ∈ t₂ then default else t₁[k]! :=
ExtDTreeMap.Const.get!_diff
theorem getElem!_diff_of_not_mem_right [TransCmp cmp]
{k : α} [Inhabited β] (not_mem : k ∉ t₂) :
(t₁ \ t₂)[k]! = t₁[k]! :=
ExtDTreeMap.Const.get!_diff_of_not_mem_right not_mem
theorem getElem!_diff_of_mem_right [TransCmp cmp]
{k : α} [Inhabited β] (mem : k ∈ t₂) :
(t₁ \ t₂)[k]! = default :=
ExtDTreeMap.Const.get!_diff_of_mem_right mem
theorem getElem!_diff_of_not_mem_left [TransCmp cmp]
{k : α} [Inhabited β] (not_mem : k ∉ t₁) :
(t₁ \ t₂)[k]! = default :=
ExtDTreeMap.Const.get!_diff_of_not_mem_left not_mem
/- get! -/
@[deprecated getElem!_diff (since := "2025-12-10")]
theorem get!_diff [TransCmp cmp] {k : α} [Inhabited β] :
(t₁ \ t₂).get! k = if k ∈ t₂ then default else t₁.get! k :=
ExtDTreeMap.Const.get!_diff
@[deprecated getElem!_diff_of_not_mem_right (since := "2025-12-10")]
theorem get!_diff_of_not_mem_right [TransCmp cmp]
{k : α} [Inhabited β] (not_mem : k ∉ t₂) :
(t₁ \ t₂).get! k = t₁.get! k :=
ExtDTreeMap.Const.get!_diff_of_not_mem_right not_mem
@[deprecated getElem!_diff_of_mem_right (since := "2025-12-10")]
theorem get!_diff_of_mem_right [TransCmp cmp]
{k : α} [Inhabited β] (mem : k ∈ t₂) :
(t₁ \ t₂).get! k = default :=
ExtDTreeMap.Const.get!_diff_of_mem_right mem
@[deprecated getElem!_diff_of_not_mem_left (since := "2025-12-10")]
theorem get!_diff_of_not_mem_left [TransCmp cmp]
{k : α} [Inhabited β] (not_mem : k ∉ t₁) :
(t₁ \ t₂).get! k = default :=
@ -2102,12 +2254,12 @@ section Alter
theorem alter_eq_empty_iff_erase_eq_empty [TransCmp cmp] {k : α}
{f : Option β → Option β} :
alter t k f = ∅ ↔ t.erase k = ∅ ∧ f (get? t k) = none := by
alter t k f = ∅ ↔ t.erase k = ∅ ∧ f t[k]? = none := by
simpa only [ext_iff] using ExtDTreeMap.Const.alter_eq_empty_iff_erase_eq_empty
@[simp]
theorem alter_eq_empty_iff [TransCmp cmp] {k : α} {f : Option β → Option β} :
alter t k f = ∅ ↔ (t = ∅ ∨ (t.size = 1 ∧ k ∈ t)) ∧ (f (get? t k)) = none := by
alter t k f = ∅ ↔ (t = ∅ ∨ (t.size = 1 ∧ k ∈ t)) ∧ (f t[k]?) = none := by
simpa only [ext_iff] using ExtDTreeMap.Const.alter_eq_empty_iff
@[grind =]
@ -2922,7 +3074,7 @@ theorem ordCompare_minKey!_modify_eq [Ord α] [TransOrd α] {t : ExtTreeMap α
theorem minKey!_alter_eq_self [TransCmp cmp] [Inhabited α] {k f}
(he : alter t k f ≠ ∅) :
(alter t k f).minKey! = k ↔
(f (get? t k)).isSome ∧ ∀ k', k' ∈ t → (cmp k k').isLE :=
(f t[k]?).isSome ∧ ∀ k', k' ∈ t → (cmp k k').isLE :=
ExtDTreeMap.Const.minKey!_alter_eq_self (mt ext he)
theorem minKey?_eq_some_minKeyD [TransCmp cmp] (he : t ≠ ∅) {fallback} :
@ -3049,7 +3201,7 @@ theorem ordCompare_minKeyD_modify_eq [Ord α] [TransOrd α] {t : ExtTreeMap α
theorem minKeyD_alter_eq_self [TransCmp cmp] {k f}
(he : alter t k f ≠ ∅) {fallback} :
(alter t k f |>.minKeyD fallback) = k ↔
(f (get? t k)).isSome ∧ ∀ k', k' ∈ t → (cmp k k').isLE :=
(f t[k]?).isSome ∧ ∀ k', k' ∈ t → (cmp k k').isLE :=
ExtDTreeMap.Const.minKeyD_alter_eq_self (mt ext he)
end Min
@ -3499,7 +3651,7 @@ theorem ordCompare_maxKey!_modify_eq [Ord α] [TransOrd α] {t : ExtTreeMap α
theorem maxKey!_alter_eq_self [TransCmp cmp] [Inhabited α] {k f}
(he : alter t k f ≠ ∅) :
(alter t k f).maxKey! = k ↔
(f (get? t k)).isSome ∧ ∀ k', k' ∈ t → (cmp k' k).isLE :=
(f t[k]?).isSome ∧ ∀ k', k' ∈ t → (cmp k' k).isLE :=
ExtDTreeMap.Const.maxKey!_alter_eq_self (mt ext he)
theorem maxKey?_eq_some_maxKeyD [TransCmp cmp] (he : t ≠ ∅) {fallback} :
@ -3626,7 +3778,7 @@ theorem ordCompare_maxKeyD_modify_eq [Ord α] [TransOrd α] {t : ExtTreeMap α
theorem maxKeyD_alter_eq_self [TransCmp cmp] {k f}
(he : alter t k f ≠ ∅) {fallback} :
(alter t k f |>.maxKeyD fallback) = k ↔
(f (get? t k)).isSome ∧ ∀ k', k' ∈ t → (cmp k' k).isLE :=
(f t[k]?).isSome ∧ ∀ k', k' ∈ t → (cmp k' k).isLE :=
ExtDTreeMap.Const.maxKeyD_alter_eq_self (mt ext he)
end Max
@ -3877,12 +4029,12 @@ grind_pattern size_filter_le_size => (t.filter f).size
theorem size_filter_eq_size_iff [TransCmp cmp]
{f : α → β → Bool} :
(t.filter f).size = t.size ↔ ∀ k h, f (t.getKey k h) (t.get k h) :=
(t.filter f).size = t.size ↔ ∀ k h, f (t.getKey k h) (t[k]'h) :=
ExtDTreeMap.Const.size_filter_eq_size_iff
theorem filter_eq_self_iff [TransCmp cmp]
{f : α → β → Bool} :
t.filter f = t ↔ ∀ k h, f (t.getKey k h) (t.get k h) :=
t.filter f = t ↔ ∀ k h, f (t.getKey k h) (t[k]'h) :=
ext_iff.trans ExtDTreeMap.Const.filter_eq_self_iff
@[simp]
@ -3953,7 +4105,7 @@ theorem getD_filter_of_getKey?_eq_some [TransCmp cmp]
theorem keys_filter [TransCmp cmp] {f : α → β → Bool} :
(t.filter f).keys =
(t.keys.attach.filter (fun ⟨x, h'⟩ => f x (get t x (mem_of_mem_keys h')))).unattach :=
(t.keys.attach.filter (fun ⟨x, h'⟩ => f x (t[x]'(mem_of_mem_keys h')))).unattach :=
ExtDTreeMap.Const.keys_filter
@[grind =]

224
src/Std/Data/HashMap/Lemmas.lean
View file

@ -810,7 +810,7 @@ theorem size_insertIfNew_le [EquivBEq α] [LawfulHashable α] {k : α} {v : β}
DHashMap.getKeyD_insertIfNew
@[simp, grind =]
theorem getThenInsertIfNew?_fst {k : α} {v : β} : (getThenInsertIfNew? m k v).1 = get? m k :=
theorem getThenInsertIfNew?_fst {k : α} {v : β} : (getThenInsertIfNew? m k v).1 = m[k]? :=
DHashMap.Const.getThenInsertIfNew?_fst
@[simp, grind =]
@ -986,6 +986,13 @@ theorem getElem?_eq_some_iff_exists_beq_and_mem_toArray [EquivBEq α] [LawfulHas
m[k]? = some v ↔ ∃ (k' : α), k == k' ∧ (k', v) ∈ m.toArray :=
DHashMap.Const.get?_eq_some_iff_exists_beq_and_mem_toArray
theorem find?_toArray_eq_some_iff_getKey?_eq_some_and_getElem?_eq_some
[EquivBEq α] [LawfulHashable α] {k k' : α} {v : β} :
m.toArray.find? (fun a => a.1 == k) = some ⟨k', v⟩ ↔
m.getKey? k = some k' ∧ m[k]? = some v :=
DHashMap.Const.find?_toArray_eq_some_iff_getKey?_eq_some_and_get?_eq_some
@[deprecated find?_toArray_eq_some_iff_getKey?_eq_some_and_getElem?_eq_some (since := "2025-12-10")]
theorem find?_toArray_eq_some_iff_getKey?_eq_some_and_get?_eq_some
[EquivBEq α] [LawfulHashable α] {k k' : α} {v : β} :
m.toArray.find? (fun a => a.1 == k) = some ⟨k', v⟩ ↔
@ -1435,32 +1442,69 @@ theorem union_insert_right_equiv_union_insert [EquivBEq α] [LawfulHashable α]
(m₁ ∪ (m₂.insert p.fst p.snd)) ~m ((m₁ ∪ m₂).insert p.fst p.snd) :=
union_insert_right_equiv_insert_union
/- getElem? -/
theorem getElem?_union [EquivBEq α] [LawfulHashable α] {k : α} :
(m₁ ∪ m₂)[k]? = m₂[k]?.or m₁[k]? :=
@DHashMap.Const.get?_union _ _ _ _ m₁.inner m₂.inner _ _ k
theorem getElem?_union_of_not_mem_left [EquivBEq α] [LawfulHashable α]
{k : α} (not_mem : ¬k ∈ m₁) :
(m₁ ∪ m₂)[k]? = m₂[k]? :=
@DHashMap.Const.get?_union_of_not_mem_left _ _ _ _ m₁.inner m₂.inner _ _ k not_mem
theorem getElem?_union_of_not_mem_right [EquivBEq α] [LawfulHashable α]
{k : α} (not_mem : ¬k ∈ m₂) :
(m₁ ∪ m₂)[k]? = m₁[k]? :=
@DHashMap.Const.get?_union_of_not_mem_right _ _ _ _ m₁.inner m₂.inner _ _ k 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) :=
@DHashMap.Const.get?_union _ _ _ _ m₁.inner m₂.inner _ _ k
@[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 :=
@DHashMap.Const.get?_union_of_not_mem_left _ _ _ _ m₁.inner m₂.inner _ _ k 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 :=
@DHashMap.Const.get?_union_of_not_mem_right _ _ _ _ m₁.inner m₂.inner _ _ k not_mem
/- getElem -/
theorem getElem_union_of_mem_right [EquivBEq α] [LawfulHashable α]
{k : α} (contains_right : k ∈ m₂) :
(m₁ ∪ m₂)[k]'(mem_union_of_right contains_right) = m₂[k]'contains_right :=
@DHashMap.Const.get_union_of_mem_right _ _ _ _ m₁.inner m₂.inner _ _ k contains_right
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) :=
@DHashMap.Const.get_union_of_not_mem_left _ _ _ _ m₁.inner m₂.inner _ _ k not_mem h'
theorem getElem_union_of_not_mem_right [EquivBEq α] [LawfulHashable α]
{k : α} (not_mem : ¬k ∈ m₂) {h'} :
(m₁ ∪ m₂)[k]'h' = m₁[k]'(mem_of_mem_union_of_not_mem_right h' not_mem) :=
@DHashMap.Const.get_union_of_not_mem_right _ _ _ _ m₁.inner m₂.inner _ _ k not_mem h'
/- get -/
@[deprecated getElem_union_of_mem_right (since := "2025-12-10")]
theorem get_union_of_mem_right [EquivBEq α] [LawfulHashable α]
{k : α} (contains_right : k ∈ m₂) :
(m₁ ∪ m₂).get k (mem_union_of_right contains_right) = m₂.get k contains_right :=
@DHashMap.Const.get_union_of_mem_right _ _ _ _ m₁.inner m₂.inner _ _ k contains_right
@[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) :=
@DHashMap.Const.get_union_of_not_mem_left _ _ _ _ m₁.inner m₂.inner _ _ k not_mem h'
@[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) {h'} :
(m₁ ∪ m₂).get k h' = m₁.get k (mem_of_mem_union_of_not_mem_right h' not_mem) :=
@ -1481,16 +1525,34 @@ theorem getD_union_of_not_mem_right [EquivBEq α] [LawfulHashable α]
(m₁ ∪ m₂).getD k fallback = m₁.getD k fallback :=
@DHashMap.Const.getD_union_of_not_mem_right _ _ _ _ m₁.inner m₂.inner _ _ k fallback not_mem
/- getElem! -/
theorem getElem!_union [EquivBEq α] [LawfulHashable α] {k : α} [Inhabited β] :
(m₁ ∪ m₂)[k]! = m₂.getD k m₁[k]! :=
@DHashMap.Const.get!_union _ _ _ _ m₁.inner m₂.inner _ _ _ k
theorem getElem!_union_of_not_mem_left [EquivBEq α] [LawfulHashable α]
{k : α} [Inhabited β] (not_mem : ¬k ∈ m₁) :
(m₁ ∪ m₂)[k]! = m₂[k]! :=
@DHashMap.Const.get!_union_of_not_mem_left _ _ _ _ m₁.inner m₂.inner _ _ _ k 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]! :=
@DHashMap.Const.get!_union_of_not_mem_right _ _ _ _ m₁.inner m₂.inner _ _ _ k 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) :=
@DHashMap.Const.get!_union _ _ _ _ m₁.inner m₂.inner _ _ _ k
@[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 :=
@DHashMap.Const.get!_union_of_not_mem_left _ _ _ _ m₁.inner m₂.inner _ _ _ k 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 :=
@ -1632,32 +1694,62 @@ theorem Equiv.inter_congr {m₃ m₄ : HashMap α β} [EquivBEq α] [LawfulHasha
(m₁ ∩ m₂) ~m (m₃ ∩ m₄) :=
⟨DHashMap.Equiv.inter_congr equiv₁.1 equiv₂.1⟩
/- get? -/
theorem get?_inter [EquivBEq α] [LawfulHashable α] {k : α} :
(m₁ ∩ m₂).get? k =
if k ∈ m₂ then m₁.get? k else none :=
/- getElem? -/
theorem getElem?_inter [EquivBEq α] [LawfulHashable α] {k : α} :
(m₁ ∩ m₂)[k]? = if k ∈ m₂ then m₁[k]? else none :=
@DHashMap.Const.get?_inter _ _ _ _ m₁.inner m₂.inner _ _ k
theorem getElem?_inter_of_mem_right [EquivBEq α] [LawfulHashable α]
{k : α} (mem : k ∈ m₂) :
(m₁ ∩ m₂)[k]? = m₁[k]? :=
@DHashMap.Const.get?_inter_of_mem_right _ _ _ _ m₁.inner m₂.inner _ _ k mem
theorem getElem?_inter_of_not_mem_left [EquivBEq α] [LawfulHashable α]
{k : α} (not_mem : k ∉ m₁) :
(m₁ ∩ m₂)[k]? = none :=
@DHashMap.Const.get?_inter_of_not_mem_left _ _ _ _ m₁.inner m₂.inner _ _ k not_mem
theorem getElem?_inter_of_not_mem_right [EquivBEq α] [LawfulHashable α]
{k : α} (not_mem : k ∉ m₂) :
(m₁ ∩ m₂)[k]? = none :=
@DHashMap.Const.get?_inter_of_not_mem_right _ _ _ _ m₁.inner m₂.inner _ _ k 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 :=
@DHashMap.Const.get?_inter _ _ _ _ m₁.inner m₂.inner _ _ k
@[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 :=
@DHashMap.Const.get?_inter_of_mem_right _ _ _ _ m₁.inner m₂.inner _ _ k 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 :=
@DHashMap.Const.get?_inter_of_not_mem_left _ _ _ _ m₁.inner m₂.inner _ _ k 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 :=
@DHashMap.Const.get?_inter_of_not_mem_right _ _ _ _ m₁.inner m₂.inner _ _ k not_mem
/- get -/
@[simp] theorem get_inter [EquivBEq α] [LawfulHashable α]
/- getElem -/
@[simp]
theorem getElem_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)[k]'h_mem = m₁[k]'((mem_inter_iff.1 h_mem).1) :=
@DHashMap.Const.get_inter _ _ _ _ m₁.inner m₂.inner _ _ k 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) :=
@DHashMap.Const.get_inter _ _ _ _ m₁.inner m₂.inner _ _ k h_mem
/- getD -/
@ -1681,22 +1773,45 @@ theorem getD_inter_of_not_mem_left [EquivBEq α] [LawfulHashable α]
(m₁ ∩ m₂).getD k fallback = fallback :=
@DHashMap.Const.getD_inter_of_not_mem_left _ _ _ _ m₁.inner m₂.inner _ _ k fallback not_mem
/- get! -/
theorem get!_inter [EquivBEq α] [LawfulHashable α] {k : α} [Inhabited β] :
(m₁ ∩ m₂).get! k =
if k ∈ m₂ then m₁.get! k else default :=
/- getElem! -/
theorem getElem!_inter [EquivBEq α] [LawfulHashable α] {k : α} [Inhabited β] :
(m₁ ∩ m₂)[k]! = if k ∈ m₂ then m₁[k]! else default :=
@DHashMap.Const.get!_inter _ _ _ _ m₁.inner m₂.inner _ _ _ k
theorem getElem!_inter_of_mem_right [EquivBEq α] [LawfulHashable α]
{k : α} [Inhabited β] (mem : k ∈ m₂) :
(m₁ ∩ m₂)[k]! = m₁[k]! :=
@DHashMap.Const.get!_inter_of_mem_right _ _ _ _ m₁.inner m₂.inner _ _ _ k mem
theorem getElem!_inter_of_not_mem_right [EquivBEq α] [LawfulHashable α]
{k : α} [Inhabited β] (not_mem : k ∉ m₂) :
(m₁ ∩ m₂)[k]! = default :=
@DHashMap.Const.get!_inter_of_not_mem_right _ _ _ _ m₁.inner m₂.inner _ _ _ k 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 :=
@DHashMap.Const.get!_inter_of_not_mem_left _ _ _ _ m₁.inner m₂.inner _ _ _ k 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 :=
@DHashMap.Const.get!_inter _ _ _ _ m₁.inner m₂.inner _ _ _ k
@[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 :=
@DHashMap.Const.get!_inter_of_mem_right _ _ _ _ m₁.inner m₂.inner _ _ _ k 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 :=
@DHashMap.Const.get!_inter_of_not_mem_right _ _ _ _ m₁.inner m₂.inner _ _ _ k 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 :=
@ -1844,22 +1959,45 @@ theorem not_mem_diff_of_mem_right [EquivBEq α] [LawfulHashable α] {k : α}
k ∉ m₁ \ m₂ :=
@DHashMap.not_mem_diff_of_mem_right _ _ _ _ m₁.inner m₂.inner _ _ k mem
/- get? -/
theorem get?_diff [EquivBEq α] [LawfulHashable α] {k : α} :
(m₁ \ m₂).get? k =
if k ∈ m₂ then none else m₁.get? k :=
/- getElem? -/
theorem getElem?_diff [EquivBEq α] [LawfulHashable α] {k : α} :
(m₁ \ m₂)[k]? = if k ∈ m₂ then none else m₁[k]? :=
@DHashMap.Const.get?_diff _ _ _ _ m₁.inner m₂.inner _ _ k
theorem getElem?_diff_of_not_mem_right [EquivBEq α] [LawfulHashable α]
{k : α} (not_mem : k ∉ m₂) :
(m₁ \ m₂)[k]? = m₁[k]? :=
@DHashMap.Const.get?_diff_of_not_mem_right _ _ _ _ m₁.inner m₂.inner _ _ k not_mem
theorem getElem?_diff_of_not_mem_left [EquivBEq α] [LawfulHashable α]
{k : α} (not_mem : k ∉ m₁) :
(m₁ \ m₂)[k]? = none :=
@DHashMap.Const.get?_diff_of_not_mem_left _ _ _ _ m₁.inner m₂.inner _ _ k not_mem
theorem getElem?_diff_of_mem_right [EquivBEq α] [LawfulHashable α]
{k : α} (mem : k ∈ m₂) :
(m₁ \ m₂)[k]? = none :=
@DHashMap.Const.get?_diff_of_mem_right _ _ _ _ m₁.inner m₂.inner _ _ k mem
/- get? -/
@[deprecated getElem?_diff (since := "2025-12-10")]
theorem get?_diff [EquivBEq α] [LawfulHashable α] {k : α} :
(m₁ \ m₂).get? k = if k ∈ m₂ then none else m₁.get? k :=
@DHashMap.Const.get?_diff _ _ _ _ m₁.inner m₂.inner _ _ k
@[deprecated getElem?_diff_of_not_mem_right (since := "2025-12-10")]
theorem get?_diff_of_not_mem_right [EquivBEq α] [LawfulHashable α]
{k : α} (not_mem : k ∉ m₂) :
(m₁ \ m₂).get? k = m₁.get? k :=
@DHashMap.Const.get?_diff_of_not_mem_right _ _ _ _ m₁.inner m₂.inner _ _ k not_mem
@[deprecated getElem?_diff_of_not_mem_left (since := "2025-12-10")]
theorem get?_diff_of_not_mem_left [EquivBEq α] [LawfulHashable α]
{k : α} (not_mem : k ∉ m₁) :
(m₁ \ m₂).get? k = none :=
@DHashMap.Const.get?_diff_of_not_mem_left _ _ _ _ m₁.inner m₂.inner _ _ k not_mem
@[deprecated getElem?_diff_of_mem_right (since := "2025-12-10")]
theorem get?_diff_of_mem_right [EquivBEq α] [LawfulHashable α]
{k : α} (mem : k ∈ m₂) :
(m₁ \ m₂).get? k = none :=
@ -1881,11 +2019,18 @@ theorem Equiv.diff_congr {m₃ m₄ : HashMap α β} [EquivBEq α] [LawfulHashab
(m₁ \ m₂) ~m (m₃ \ m₄) :=
⟨DHashMap.Equiv.diff_congr equiv₁.1 equiv₂.1⟩
/- get -/
@[simp] theorem get_diff [EquivBEq α] [LawfulHashable α]
/- getElem -/
@[simp]
theorem getElem_diff [EquivBEq α] [LawfulHashable α]
{k : α} {h_mem : k ∈ m₁ \ m₂} :
(m₁ \ m₂).get k h_mem =
m₁.get k ((mem_diff_iff.1 h_mem).1) :=
(m₁ \ m₂)[k]'h_mem = m₁[k]'(mem_diff_iff.1 h_mem).1 :=
@DHashMap.Const.get_diff _ _ _ _ m₁.inner m₂.inner _ _ k h_mem
/- get -/
@[deprecated getElem_diff (since := "2025-12-10")]
theorem get_diff [EquivBEq α] [LawfulHashable α]
{k : α} {h_mem : k ∈ m₁ \ m₂} :
(m₁ \ m₂).get k h_mem = m₁.get k ((mem_diff_iff.1 h_mem).1) :=
@DHashMap.Const.get_diff _ _ _ _ m₁.inner m₂.inner _ _ k h_mem
/- getD -/
@ -1909,22 +2054,45 @@ theorem getD_diff_of_not_mem_left [EquivBEq α] [LawfulHashable α]
(m₁ \ m₂).getD k fallback = fallback :=
@DHashMap.Const.getD_diff_of_not_mem_left _ _ _ _ m₁.inner m₂.inner _ _ k fallback not_mem
/- get! -/
theorem get!_diff [EquivBEq α] [LawfulHashable α] {k : α} [Inhabited β] :
(m₁ \ m₂).get! k =
if k ∈ m₂ then default else m₁.get! k :=
/- getElem! -/
theorem getElem!_diff [EquivBEq α] [LawfulHashable α] {k : α} [Inhabited β] :
(m₁ \ m₂)[k]! = if k ∈ m₂ then default else m₁[k]! :=
@DHashMap.Const.get!_diff _ _ _ _ m₁.inner m₂.inner _ _ _ k
theorem getElem!_diff_of_not_mem_right [EquivBEq α] [LawfulHashable α]
{k : α} [Inhabited β] (not_mem : k ∉ m₂) :
(m₁ \ m₂)[k]! = m₁[k]! :=
@DHashMap.Const.get!_diff_of_not_mem_right _ _ _ _ m₁.inner m₂.inner _ _ _ k not_mem
theorem getElem!_diff_of_mem_right [EquivBEq α] [LawfulHashable α]
{k : α} [Inhabited β] (mem : k ∈ m₂) :
(m₁ \ m₂)[k]! = default :=
@DHashMap.Const.get!_diff_of_mem_right _ _ _ _ m₁.inner m₂.inner _ _ _ k mem
theorem getElem!_diff_of_not_mem_left [EquivBEq α] [LawfulHashable α]
{k : α} [Inhabited β] (not_mem : k ∉ m₁) :
(m₁ \ m₂)[k]! = default :=
@DHashMap.Const.get!_diff_of_not_mem_left _ _ _ _ m₁.inner m₂.inner _ _ _ k not_mem
/- get! -/
@[deprecated getElem!_diff (since := "2025-12-10")]
theorem get!_diff [EquivBEq α] [LawfulHashable α] {k : α} [Inhabited β] :
(m₁ \ m₂).get! k = if k ∈ m₂ then default else m₁.get! k :=
@DHashMap.Const.get!_diff _ _ _ _ m₁.inner m₂.inner _ _ _ k
@[deprecated getElem!_diff_of_not_mem_right (since := "2025-12-10")]
theorem get!_diff_of_not_mem_right [EquivBEq α] [LawfulHashable α]
{k : α} [Inhabited β] (not_mem : k ∉ m₂) :
(m₁ \ m₂).get! k = m₁.get! k :=
@DHashMap.Const.get!_diff_of_not_mem_right _ _ _ _ m₁.inner m₂.inner _ _ _ k not_mem
@[deprecated getElem!_diff_of_mem_right (since := "2025-12-10")]
theorem get!_diff_of_mem_right [EquivBEq α] [LawfulHashable α]
{k : α} [Inhabited β] (mem : k ∈ m₂) :
(m₁ \ m₂).get! k = default :=
@DHashMap.Const.get!_diff_of_mem_right _ _ _ _ m₁.inner m₂.inner _ _ _ k mem
@[deprecated getElem!_diff_of_not_mem_left (since := "2025-12-10")]
theorem get!_diff_of_not_mem_left [EquivBEq α] [LawfulHashable α]
{k : α} [Inhabited β] (not_mem : k ∉ m₁) :
(m₁ \ m₂).get! k = default :=
@ -3217,12 +3385,12 @@ 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) :=
DHashMap.Const.size_filter_eq_size_iff
theorem filter_equiv_self_iff [EquivBEq α] [LawfulHashable α]
{f : α → β → Bool} :
m.filter f ~m m ↔ ∀ k h, f (m.getKey k h) (m.get k h) :=
m.filter f ~m m ↔ ∀ k h, f (m.getKey k h) (m[k]'h) :=
⟨fun h => DHashMap.Const.filter_equiv_self_iff.mp h.1,
fun h => ⟨DHashMap.Const.filter_equiv_self_iff.mpr h⟩⟩
@ -3294,7 +3462,7 @@ theorem getD_filter_of_getKey?_eq_some [EquivBEq α] [LawfulHashable α]
theorem keys_filter [EquivBEq α] [LawfulHashable α] {f : α → β → Bool} :
(m.filter f).keys.Perm
(m.keys.attach.filter (fun ⟨x, h'⟩ => f x (get m x (mem_of_mem_keys h')))).unattach :=
(m.keys.attach.filter (fun ⟨x, h'⟩ => f x (m[x]'(mem_of_mem_keys h')))).unattach :=
DHashMap.Const.keys_filter
@[grind =]

222
src/Std/Data/HashMap/RawLemmas.lean
View file

@ -828,7 +828,7 @@ theorem size_insertIfNew_le [EquivBEq α] [LawfulHashable α] (h : m.WF) {k : α
@[simp, grind =]
theorem getThenInsertIfNew?_fst (h : m.WF) {k : α} {v : β} :
(getThenInsertIfNew? m k v).1 = get? m k :=
(getThenInsertIfNew? m k v).1 = m[k]? :=
DHashMap.Raw.Const.getThenInsertIfNew?_fst h.out
@[simp, grind =]
@ -991,6 +991,12 @@ theorem mem_toArray_iff_getElem?_eq_some [LawfulBEq α]
(k, v) ∈ m.toArray ↔ m[k]? = some v :=
DHashMap.Raw.Const.mem_toArray_iff_get?_eq_some h.out
theorem getElem?_eq_some_iff_exists_beq_and_mem_toArray [EquivBEq α] [LawfulHashable α]
{k : α} {v : β} (h : m.WF) :
m[k]? = some v ↔ ∃ (k' : α), k == k' ∧ (k', v) ∈ m.toArray :=
DHashMap.Raw.Const.get?_eq_some_iff_exists_beq_and_mem_toArray h.out
@[deprecated getElem?_eq_some_iff_exists_beq_and_mem_toArray (since := "2025-12-10")]
theorem get?_eq_some_iff_exists_beq_and_mem_toArray [EquivBEq α] [LawfulHashable α]
{k : α} {v : β} (h : m.WF) :
get? m k = some v ↔ ∃ (k' : α), k == k' ∧ (k', v) ∈ m.toArray :=
@ -1401,31 +1407,69 @@ theorem union_insert_right_equiv_union_insert [EquivBEq α] [LawfulHashable α]
(m₁ ∪ (m₂.insert p.fst p.snd)).Equiv ((m₁ ∪ m₂).insert p.fst p.snd) :=
union_insert_right_equiv_insert_union h₁ h₂
/- getElem? -/
theorem getElem?_union [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF) (h₂ : m₂.WF) {k : α} :
(m₁ ∪ m₂)[k]? = m₂[k]?.or m₁[k]? :=
@DHashMap.Raw.Const.get?_union _ _ _ _ m₁.inner m₂.inner _ _ h₁.out h₂.out k
theorem getElem?_union_of_not_mem_left [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} (not_mem : ¬k ∈ m₁) :
(m₁ ∪ m₂)[k]? = m₂[k]? :=
@DHashMap.Raw.Const.get?_union_of_not_mem_left _ _ _ _ m₁.inner m₂.inner _ _ h₁.out h₂.out k not_mem
theorem getElem?_union_of_not_mem_right [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} (not_mem : ¬k ∈ m₂) :
(m₁ ∪ m₂)[k]? = m₁[k]? :=
@DHashMap.Raw.Const.get?_union_of_not_mem_right _ _ _ _ m₁.inner m₂.inner _ _ h₁.out h₂.out k not_mem
/- get? -/
@[deprecated getElem?_union (since := "2025-12-10")]
theorem get?_union [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF) (h₂ : m₂.WF) {k : α} :
get? (m₁ ∪ m₂) k = (get? m₂ k).or (get? m₁ k) :=
@DHashMap.Raw.Const.get?_union _ _ _ _ m₁.inner m₂.inner _ _ h₁.out h₂.out k
@[deprecated getElem?_union_of_not_mem_left (since := "2025-12-10")]
theorem get?_union_of_not_mem_left [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} (not_mem : ¬k ∈ m₁) :
get? (m₁ ∪ m₂) k = get? m₂ k :=
@DHashMap.Raw.Const.get?_union_of_not_mem_left _ _ _ _ m₁.inner m₂.inner _ _ h₁.out h₂.out k not_mem
@[deprecated getElem?_union_of_not_mem_right (since := "2025-12-10")]
theorem get?_union_of_not_mem_right [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} (not_mem : ¬k ∈ m₂) :
get? (m₁ ∪ m₂) k = get? m₁ k :=
@DHashMap.Raw.Const.get?_union_of_not_mem_right _ _ _ _ m₁.inner m₂.inner _ _ h₁.out h₂.out k not_mem
/- getElem -/
theorem getElem_union_of_mem_right [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} (mem : k ∈ m₂) :
(m₁ ∪ m₂)[k]'(mem_union_of_right h₁ h₂ mem) = m₂[k]'mem :=
@DHashMap.Raw.Const.get_union_of_mem_right _ _ _ _ m₁.inner m₂.inner _ _ h₁.out h₂.out k mem
theorem getElem_union_of_not_mem_left [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} (not_mem : ¬k ∈ m₁) {h'} :
(m₁ ∪ m₂)[k]'h' = m₂[k]'(mem_of_mem_union_of_not_mem_left h₁ h₂ h' not_mem) :=
@DHashMap.Raw.Const.get_union_of_not_mem_left _ _ _ _ m₁.inner m₂.inner _ _ h₁.out h₂.out k not_mem h'
theorem getElem_union_of_not_mem_right [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} (not_mem : ¬k ∈ m₂) {h'} :
(m₁ ∪ m₂)[k]'h' = m₁[k]'(mem_of_mem_union_of_not_mem_right h₁ h₂ h' not_mem) :=
@DHashMap.Raw.Const.get_union_of_not_mem_right _ _ _ _ m₁.inner m₂.inner _ _ h₁.out h₂.out k not_mem h'
/- get -/
@[deprecated getElem_union_of_mem_right (since := "2025-12-10")]
theorem get_union_of_mem_right [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} (mem : k ∈ m₂) :
get (m₁ ∪ m₂) k (mem_union_of_right h₁ h₂ mem) = get m₂ k mem :=
@DHashMap.Raw.Const.get_union_of_mem_right _ _ _ _ m₁.inner m₂.inner _ _ h₁.out h₂.out k mem
@[deprecated getElem_union_of_not_mem_left (since := "2025-12-10")]
theorem get_union_of_not_mem_left [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} (not_mem : ¬k ∈ m₁) {h'} :
get (m₁ ∪ m₂) k h' = get m₂ k (mem_of_mem_union_of_not_mem_left h₁ h₂ h' not_mem) :=
@DHashMap.Raw.Const.get_union_of_not_mem_left _ _ _ _ m₁.inner m₂.inner _ _ h₁.out h₂.out k not_mem h'
@[deprecated getElem_union_of_not_mem_right (since := "2025-12-10")]
theorem get_union_of_not_mem_right [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} (not_mem : ¬k ∈ m₂) {h'} :
get (m₁ ∪ m₂) k h' = get m₁ k (mem_of_mem_union_of_not_mem_right h₁ h₂ h' not_mem) :=
@ -1446,16 +1490,34 @@ theorem getD_union_of_not_mem_right [EquivBEq α] [LawfulHashable α] (h₁ : m
getD (m₁ ∪ m₂) k fallback = getD m₁ k fallback :=
@DHashMap.Raw.Const.getD_union_of_not_mem_right _ _ _ _ m₁.inner m₂.inner _ _ h₁.out h₂.out k fallback not_mem
/- getElem! -/
theorem getElem!_union [EquivBEq α] [LawfulHashable α] [Inhabited β] (h₁ : m₁.WF) (h₂ : m₂.WF) {k : α} :
(m₁ ∪ m₂)[k]! = getD m₂ k m₁[k]! :=
@DHashMap.Raw.Const.get!_union _ _ _ _ m₁.inner m₂.inner _ _ _ h₁.out h₂.out k
theorem getElem!_union_of_not_mem_left [EquivBEq α] [LawfulHashable α] [Inhabited β] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} (not_mem : ¬k ∈ m₁) :
(m₁ ∪ m₂)[k]! = m₂[k]! :=
@DHashMap.Raw.Const.get!_union_of_not_mem_left _ _ _ _ m₁.inner m₂.inner _ _ _ h₁.out h₂.out k not_mem
theorem getElem!_union_of_not_mem_right [EquivBEq α] [LawfulHashable α] [Inhabited β] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} (not_mem : ¬k ∈ m₂) :
(m₁ ∪ m₂)[k]! = m₁[k]! :=
@DHashMap.Raw.Const.get!_union_of_not_mem_right _ _ _ _ m₁.inner m₂.inner _ _ _ h₁.out h₂.out k not_mem
/- get! -/
@[deprecated getElem!_union (since := "2025-12-10")]
theorem get!_union [EquivBEq α] [LawfulHashable α] [Inhabited β] (h₁ : m₁.WF) (h₂ : m₂.WF) {k : α} :
get! (m₁ ∪ m₂) k = getD m₂ k (get! m₁ k) :=
@DHashMap.Raw.Const.get!_union _ _ _ _ m₁.inner m₂.inner _ _ _ h₁.out h₂.out k
@[deprecated getElem!_union_of_not_mem_left (since := "2025-12-10")]
theorem get!_union_of_not_mem_left [EquivBEq α] [LawfulHashable α] [Inhabited β] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} (not_mem : ¬k ∈ m₁) :
get! (m₁ ∪ m₂) k = get! m₂ k :=
@DHashMap.Raw.Const.get!_union_of_not_mem_left _ _ _ _ m₁.inner m₂.inner _ _ _ h₁.out h₂.out k not_mem
@[deprecated getElem!_union_of_not_mem_right (since := "2025-12-10")]
theorem get!_union_of_not_mem_right [EquivBEq α] [LawfulHashable α] [Inhabited β] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} (not_mem : ¬k ∈ m₂) :
get! (m₁ ∪ m₂) k = get! m₁ k :=
@ -1611,32 +1673,62 @@ theorem Equiv.inter_congr {m₃ m₄ : Raw α β} [EquivBEq α] [LawfulHashable
(m₁ ∩ m₂) ~m (m₃ ∩ m₄) :=
⟨@DHashMap.Raw.Equiv.inter_congr _ _ _ _ m₁.inner m₂.inner m₃.inner m₄.inner _ _ h₁.out h₂.out h₃.out h₄.out equiv₁.1 equiv₂.1⟩
/- get? -/
theorem get?_inter [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF) (h₂ : m₂.WF) {k : α} :
get? (m₁ ∩ m₂) k =
if k ∈ m₂ then get? m₁ k else none :=
/- getElem? -/
theorem getElem?_inter [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF) (h₂ : m₂.WF) {k : α} :
(m₁ ∩ m₂)[k]? = if k ∈ m₂ then m₁[k]? else none :=
@DHashMap.Raw.Const.get?_inter _ _ _ _ m₁.inner m₂.inner _ _ h₁.out h₂.out k
theorem getElem?_inter_of_mem_right [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} (mem : k ∈ m₂) :
(m₁ ∩ m₂)[k]? = m₁[k]? :=
@DHashMap.Raw.Const.get?_inter_of_mem_right _ _ _ _ m₁.inner m₂.inner _ _ h₁.out h₂.out k mem
theorem getElem?_inter_of_not_mem_left [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} (not_mem : k ∉ m₁) :
(m₁ ∩ m₂)[k]? = none :=
@DHashMap.Raw.Const.get?_inter_of_not_mem_left _ _ _ _ m₁.inner m₂.inner _ _ h₁.out h₂.out k not_mem
theorem getElem?_inter_of_not_mem_right [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} (not_mem : k ∉ m₂) :
(m₁ ∩ m₂)[k]? = none :=
@DHashMap.Raw.Const.get?_inter_of_not_mem_right _ _ _ _ m₁.inner m₂.inner _ _ h₁.out h₂.out k not_mem
/- get? -/
@[deprecated getElem?_inter (since := "2025-12-10")]
theorem get?_inter [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF) (h₂ : m₂.WF) {k : α} :
get? (m₁ ∩ m₂) k = if k ∈ m₂ then get? m₁ k else none :=
@DHashMap.Raw.Const.get?_inter _ _ _ _ m₁.inner m₂.inner _ _ h₁.out h₂.out k
@[deprecated getElem?_inter_of_mem_right (since := "2025-12-10")]
theorem get?_inter_of_mem_right [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} (mem : k ∈ m₂) :
get? (m₁ ∩ m₂) k = get? m₁ k :=
@DHashMap.Raw.Const.get?_inter_of_mem_right _ _ _ _ m₁.inner m₂.inner _ _ h₁.out h₂.out k mem
@[deprecated getElem?_inter_of_not_mem_left (since := "2025-12-10")]
theorem get?_inter_of_not_mem_left [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} (not_mem : k ∉ m₁) :
get? (m₁ ∩ m₂) k = none :=
@DHashMap.Raw.Const.get?_inter_of_not_mem_left _ _ _ _ m₁.inner m₂.inner _ _ h₁.out h₂.out k not_mem
@[deprecated getElem?_inter_of_not_mem_right (since := "2025-12-10")]
theorem get?_inter_of_not_mem_right [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} (not_mem : k ∉ m₂) :
get? (m₁ ∩ m₂) k = none :=
@DHashMap.Raw.Const.get?_inter_of_not_mem_right _ _ _ _ m₁.inner m₂.inner _ _ h₁.out h₂.out k not_mem
/- get -/
@[simp] theorem get_inter [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF) (h₂ : m₂.WF)
/- getElem -/
@[simp]
theorem getElem_inter [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} {h_mem : k ∈ m₁ ∩ m₂} :
get (m₁ ∩ m₂) k h_mem =
get m₁ k ((mem_inter_iff h₁ h₂).1 h_mem).1 :=
(m₁ ∩ m₂)[k]'h_mem = m₁[k]'((mem_inter_iff h₁ h₂).1 h_mem).1 :=
@DHashMap.Raw.Const.get_inter _ _ _ _ m₁.inner m₂.inner _ _ h₁.out h₂.out k h_mem
/- get -/
@[deprecated getElem_inter (since := "2025-12-10")]
theorem get_inter [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} {h_mem : k ∈ m₁ ∩ m₂} :
get (m₁ ∩ m₂) k h_mem = get m₁ k ((mem_inter_iff h₁ h₂).1 h_mem).1 :=
@DHashMap.Raw.Const.get_inter _ _ _ _ m₁.inner m₂.inner _ _ h₁.out h₂.out k h_mem
/- getD -/
@ -1661,22 +1753,45 @@ theorem getD_inter_of_not_mem_left [EquivBEq α] [LawfulHashable α] (h₁ : m
getD (m₁ ∩ m₂) k fallback = fallback :=
@DHashMap.Raw.Const.getD_inter_of_not_mem_left _ _ _ _ m₁.inner m₂.inner _ _ h₁.out h₂.out k fallback not_mem
/- get! -/
theorem get!_inter [EquivBEq α] [LawfulHashable α] [Inhabited β] (h₁ : m₁.WF) (h₂ : m₂.WF) {k : α} :
get! (m₁ ∩ m₂) k =
if k ∈ m₂ then get! m₁ k else default :=
/- getElem! -/
theorem getElem!_inter [EquivBEq α] [LawfulHashable α] [Inhabited β] (h₁ : m₁.WF) (h₂ : m₂.WF) {k : α} :
(m₁ ∩ m₂)[k]! = if k ∈ m₂ then m₁[k]! else default :=
@DHashMap.Raw.Const.get!_inter _ _ _ _ m₁.inner m₂.inner _ _ _ h₁.out h₂.out k
theorem getElem!_inter_of_mem_right [EquivBEq α] [LawfulHashable α] [Inhabited β] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} (mem : k ∈ m₂) :
(m₁ ∩ m₂)[k]! = m₁[k]! :=
@DHashMap.Raw.Const.get!_inter_of_mem_right _ _ _ _ m₁.inner m₂.inner _ _ _ h₁.out h₂.out k mem
theorem getElem!_inter_of_not_mem_right [EquivBEq α] [LawfulHashable α] [Inhabited β] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} (not_mem : k ∉ m₂) :
(m₁ ∩ m₂)[k]! = default :=
@DHashMap.Raw.Const.get!_inter_of_not_mem_right _ _ _ _ m₁.inner m₂.inner _ _ _ h₁.out h₂.out k not_mem
theorem getElem!_inter_of_not_mem_left [EquivBEq α] [LawfulHashable α] [Inhabited β] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} (not_mem : k ∉ m₁) :
(m₁ ∩ m₂)[k]! = default :=
@DHashMap.Raw.Const.get!_inter_of_not_mem_left _ _ _ _ m₁.inner m₂.inner _ _ _ h₁.out h₂.out k not_mem
/- get! -/
@[deprecated getElem!_inter (since := "2025-12-10")]
theorem get!_inter [EquivBEq α] [LawfulHashable α] [Inhabited β] (h₁ : m₁.WF) (h₂ : m₂.WF) {k : α} :
get! (m₁ ∩ m₂) k = if k ∈ m₂ then get! m₁ k else default :=
@DHashMap.Raw.Const.get!_inter _ _ _ _ m₁.inner m₂.inner _ _ _ h₁.out h₂.out k
@[deprecated getElem!_inter_of_mem_right (since := "2025-12-10")]
theorem get!_inter_of_mem_right [EquivBEq α] [LawfulHashable α] [Inhabited β] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} (mem : k ∈ m₂) :
get! (m₁ ∩ m₂) k = get! m₁ k :=
@DHashMap.Raw.Const.get!_inter_of_mem_right _ _ _ _ m₁.inner m₂.inner _ _ _ h₁.out h₂.out k mem
@[deprecated getElem!_inter_of_not_mem_right (since := "2025-12-10")]
theorem get!_inter_of_not_mem_right [EquivBEq α] [LawfulHashable α] [Inhabited β] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} (not_mem : k ∉ m₂) :
get! (m₁ ∩ m₂) k = default :=
@DHashMap.Raw.Const.get!_inter_of_not_mem_right _ _ _ _ m₁.inner m₂.inner _ _ _ h₁.out h₂.out k not_mem
@[deprecated getElem!_inter_of_not_mem_left (since := "2025-12-10")]
theorem get!_inter_of_not_mem_left [EquivBEq α] [LawfulHashable α] [Inhabited β] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} (not_mem : k ∉ m₁) :
get! (m₁ ∩ m₂) k = default :=
@ -1852,32 +1967,62 @@ theorem Equiv.diff_congr {m₃ m₄ : Raw α β} [EquivBEq α] [LawfulHashable
(m₁ \ m₂) ~m (m₃ \ m₄) :=
⟨@DHashMap.Raw.Equiv.diff_congr _ _ _ _ m₁.inner m₂.inner m₃.inner m₄.inner _ _ h₁.out h₂.out h₃.out h₄.out equiv₁.1 equiv₂.1⟩
/- get? -/
theorem get?_diff [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF) (h₂ : m₂.WF) {k : α} :
get? (m₁ \ m₂) k =
if k ∈ m₂ then none else get? m₁ k :=
/- getElem? -/
theorem getElem?_diff [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF) (h₂ : m₂.WF) {k : α} :
(m₁ \ m₂)[k]? = if k ∈ m₂ then none else m₁[k]? :=
@DHashMap.Raw.Const.get?_diff _ _ _ _ m₁.inner m₂.inner _ _ h₁.out h₂.out k
theorem getElem?_diff_of_not_mem_right [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} (not_mem : k ∉ m₂) :
(m₁ \ m₂)[k]? = m₁[k]? :=
@DHashMap.Raw.Const.get?_diff_of_not_mem_right _ _ _ _ m₁.inner m₂.inner _ _ h₁.out h₂.out k not_mem
theorem getElem?_diff_of_not_mem_left [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} (not_mem : k ∉ m₁) :
(m₁ \ m₂)[k]? = none :=
@DHashMap.Raw.Const.get?_diff_of_not_mem_left _ _ _ _ m₁.inner m₂.inner _ _ h₁.out h₂.out k not_mem
theorem getElem?_diff_of_mem_right [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} (mem : k ∈ m₂) :
(m₁ \ m₂)[k]? = none :=
@DHashMap.Raw.Const.get?_diff_of_mem_right _ _ _ _ m₁.inner m₂.inner _ _ h₁.out h₂.out k mem
/- get? -/
@[deprecated getElem?_diff (since := "2025-12-10")]
theorem get?_diff [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF) (h₂ : m₂.WF) {k : α} :
get? (m₁ \ m₂) k = if k ∈ m₂ then none else get? m₁ k :=
@DHashMap.Raw.Const.get?_diff _ _ _ _ m₁.inner m₂.inner _ _ h₁.out h₂.out k
@[deprecated getElem?_diff_of_not_mem_right (since := "2025-12-10")]
theorem get?_diff_of_not_mem_right [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} (not_mem : k ∉ m₂) :
get? (m₁ \ m₂) k = get? m₁ k :=
@DHashMap.Raw.Const.get?_diff_of_not_mem_right _ _ _ _ m₁.inner m₂.inner _ _ h₁.out h₂.out k not_mem
@[deprecated getElem?_diff_of_not_mem_left (since := "2025-12-10")]
theorem get?_diff_of_not_mem_left [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} (not_mem : k ∉ m₁) :
get? (m₁ \ m₂) k = none :=
@DHashMap.Raw.Const.get?_diff_of_not_mem_left _ _ _ _ m₁.inner m₂.inner _ _ h₁.out h₂.out k not_mem
@[deprecated getElem?_diff_of_mem_right (since := "2025-12-10")]
theorem get?_diff_of_mem_right [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} (mem : k ∈ m₂) :
get? (m₁ \ m₂) k = none :=
@DHashMap.Raw.Const.get?_diff_of_mem_right _ _ _ _ m₁.inner m₂.inner _ _ h₁.out h₂.out k mem
/- get -/
@[simp] theorem get_diff [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF) (h₂ : m₂.WF)
/- getElem -/
@[simp]
theorem getElem_diff [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} {h_mem : k ∈ m₁ \ m₂} :
get (m₁ \ m₂) k h_mem =
get m₁ k ((mem_diff_iff h₁ h₂).1 h_mem).1 :=
(m₁ \ m₂)[k]'h_mem = m₁[k]'((mem_diff_iff h₁ h₂).1 h_mem).1 :=
@DHashMap.Raw.Const.get_diff _ _ _ _ m₁.inner m₂.inner _ _ h₁.out h₂.out k h_mem
/- get -/
@[deprecated getElem_diff (since := "2025-12-10")]
theorem get_diff [EquivBEq α] [LawfulHashable α] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} {h_mem : k ∈ m₁ \ m₂} :
get (m₁ \ m₂) k h_mem = get m₁ k ((mem_diff_iff h₁ h₂).1 h_mem).1 :=
@DHashMap.Raw.Const.get_diff _ _ _ _ m₁.inner m₂.inner _ _ h₁.out h₂.out k h_mem
/- getD -/
@ -1902,22 +2047,45 @@ theorem getD_diff_of_not_mem_left [EquivBEq α] [LawfulHashable α] (h₁ : m₁
getD (m₁ \ m₂) k fallback = fallback :=
@DHashMap.Raw.Const.getD_diff_of_not_mem_left _ _ _ _ m₁.inner m₂.inner _ _ h₁.out h₂.out k fallback not_mem
/- get! -/
theorem get!_diff [EquivBEq α] [LawfulHashable α] [Inhabited β] (h₁ : m₁.WF) (h₂ : m₂.WF) {k : α} :
get! (m₁ \ m₂) k =
if k ∈ m₂ then default else get! m₁ k :=
/- getElem! -/
theorem getElem!_diff [EquivBEq α] [LawfulHashable α] [Inhabited β] (h₁ : m₁.WF) (h₂ : m₂.WF) {k : α} :
(m₁ \ m₂)[k]! = if k ∈ m₂ then default else m₁[k]! :=
@DHashMap.Raw.Const.get!_diff _ _ _ _ m₁.inner m₂.inner _ _ _ h₁.out h₂.out k
theorem getElem!_diff_of_not_mem_right [EquivBEq α] [LawfulHashable α] [Inhabited β] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} (not_mem : k ∉ m₂) :
(m₁ \ m₂)[k]! = m₁[k]! :=
@DHashMap.Raw.Const.get!_diff_of_not_mem_right _ _ _ _ m₁.inner m₂.inner _ _ _ h₁.out h₂.out k not_mem
theorem getElem!_diff_of_mem_right [EquivBEq α] [LawfulHashable α] [Inhabited β] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} (mem : k ∈ m₂) :
(m₁ \ m₂)[k]! = default :=
@DHashMap.Raw.Const.get!_diff_of_mem_right _ _ _ _ m₁.inner m₂.inner _ _ _ h₁.out h₂.out k mem
theorem getElem!_diff_of_not_mem_left [EquivBEq α] [LawfulHashable α] [Inhabited β] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} (not_mem : k ∉ m₁) :
(m₁ \ m₂)[k]! = default :=
@DHashMap.Raw.Const.get!_diff_of_not_mem_left _ _ _ _ m₁.inner m₂.inner _ _ _ h₁.out h₂.out k not_mem
/- get! -/
@[deprecated getElem!_diff (since := "2025-12-10")]
theorem get!_diff [EquivBEq α] [LawfulHashable α] [Inhabited β] (h₁ : m₁.WF) (h₂ : m₂.WF) {k : α} :
get! (m₁ \ m₂) k = if k ∈ m₂ then default else get! m₁ k :=
@DHashMap.Raw.Const.get!_diff _ _ _ _ m₁.inner m₂.inner _ _ _ h₁.out h₂.out k
@[deprecated getElem!_diff_of_not_mem_right (since := "2025-12-10")]
theorem get!_diff_of_not_mem_right [EquivBEq α] [LawfulHashable α] [Inhabited β] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} (not_mem : k ∉ m₂) :
get! (m₁ \ m₂) k = get! m₁ k :=
@DHashMap.Raw.Const.get!_diff_of_not_mem_right _ _ _ _ m₁.inner m₂.inner _ _ _ h₁.out h₂.out k not_mem
@[deprecated getElem!_diff_of_mem_right (since := "2025-12-10")]
theorem get!_diff_of_mem_right [EquivBEq α] [LawfulHashable α] [Inhabited β] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} (mem : k ∈ m₂) :
get! (m₁ \ m₂) k = default :=
@DHashMap.Raw.Const.get!_diff_of_mem_right _ _ _ _ m₁.inner m₂.inner _ _ _ h₁.out h₂.out k mem
@[deprecated getElem!_diff_of_not_mem_left (since := "2025-12-10")]
theorem get!_diff_of_not_mem_left [EquivBEq α] [LawfulHashable α] [Inhabited β] (h₁ : m₁.WF) (h₂ : m₂.WF)
{k : α} (not_mem : k ∉ m₁) :
get! (m₁ \ m₂) k = default :=
@ -3530,7 +3698,7 @@ theorem getElem!_map [LawfulBEq α] [Inhabited γ]
theorem getElem!_map' [EquivBEq α] [LawfulHashable α] [Inhabited γ]
{f : α → β → γ} {k : α} (h : m.WF) :
(m.map f)[k]! =
((get? m k).pmap (fun v h => f (m.getKey k h) v)
(m[k]?.pmap (fun v h => f (m.getKey k h) v)
(fun _ h' => (mem_iff_isSome_getElem? h).mpr (Option.isSome_of_eq_some h'))).get! :=
DHashMap.Raw.Const.get!_map' h.out
@ -3550,7 +3718,7 @@ theorem getD_map [LawfulBEq α]
theorem getD_map' [EquivBEq α] [LawfulHashable α]
{f : α → β → γ} {k : α} {fallback : γ} (h : m.WF) :
getD (m.map f) k fallback =
((get? m k).pmap (fun v h => f (m.getKey k h) v)
(m[k]?.pmap (fun v h => f (m.getKey k h) v)
(fun _ h' => (mem_iff_isSome_getElem? h).mpr (Option.isSome_of_eq_some h'))).getD fallback :=
DHashMap.Raw.Const.getD_map' h.out

227
src/Std/Data/TreeMap/Lemmas.lean
View file

@ -290,7 +290,7 @@ theorem getElem?_congr [TransCmp cmp] {a b : α} (hab : cmp a b = .eq) :
@[grind =] theorem getElem_insert [TransCmp cmp] {k a : α} {v : β} {h₁} :
(t.insert k v)[a]'h₁ =
if h₂ : cmp k a = .eq then v
else get t a (mem_of_mem_insert h₁ h₂) :=
else t[a]'(mem_of_mem_insert h₁ h₂) :=
DTreeMap.Const.get_insert
theorem toList_insert_perm [BEq α] [TransCmp cmp] [LawfulBEqCmp cmp] {k : α} {v : β} :
@ -420,7 +420,7 @@ theorem getD_erase_self [TransCmp cmp] {k : α} {fallback : β} :
DTreeMap.Const.getD_erase_self
theorem getElem?_eq_some_getD_of_contains [TransCmp cmp] {a : α} {fallback : β} :
t.contains a = true → get? t a = some (getD t a fallback) :=
t.contains a = true → t[a]? = some (getD t a fallback) :=
DTreeMap.Const.get?_eq_some_getD_of_contains
theorem getElem?_eq_some_getD [TransCmp cmp] {a : α} {fallback : β} :
@ -781,7 +781,7 @@ theorem size_insertIfNew_le [TransCmp cmp] {k : α} {v : β} :
@[simp, grind =]
theorem getThenInsertIfNew?_fst [TransCmp cmp] {k : α} {v : β} :
(getThenInsertIfNew? t k v).1 = get? t k :=
(getThenInsertIfNew? t k v).1 = t[k]? :=
DTreeMap.Const.getThenInsertIfNew?_fst
@[simp, grind =]
@ -1096,7 +1096,7 @@ theorem getElem_insertMany_list_of_contains_eq_false [TransCmp cmp] [BEq α]
(contains : (l.map Prod.fst).contains k = false)
{h'} :
(t.insertMany l)[k]'h' =
t.get k (mem_of_mem_insertMany_list h' contains) :=
t[k]'(mem_of_mem_insertMany_list h' contains) :=
DTreeMap.Const.get_insertMany_list_of_contains_eq_false contains
theorem getElem_insertMany_list_of_mem [TransCmp cmp]
@ -1111,7 +1111,7 @@ theorem getElem!_insertMany_list_of_contains_eq_false [TransCmp cmp]
[BEq α] [LawfulBEqCmp cmp]
{l : List (α × β)} {k : α} [Inhabited β]
(contains_eq_false : (l.map Prod.fst).contains k = false) :
(t.insertMany l)[k]! = t.get! k :=
(t.insertMany l)[k]! = t[k]! :=
DTreeMap.Const.get!_insertMany_list_of_contains_eq_false contains_eq_false
theorem getElem!_insertMany_list_of_mem [TransCmp cmp]
@ -1586,33 +1586,71 @@ theorem union_insert_right_equiv_insert_union [TransCmp cmp] {p : (_ : α) × β
(t₁ ∪ (t₂.insert p.fst p.snd)).Equiv ((t₁ ∪ t₂).insert p.fst p.snd) :=
⟨DTreeMap.union_insert_right_equiv_insert_union⟩
/- getElem? -/
theorem getElem?_union [TransCmp cmp]
{k : α} :
(t₁ ∪ t₂)[k]? = (t₂[k]?).or (t₁[k]?) :=
DTreeMap.Const.get?_union
theorem getElem?_union_of_not_mem_left [TransCmp cmp]
{k : α} (not_mem : ¬k ∈ t₁) :
(t₁ ∪ t₂)[k]? = t₂[k]? :=
DTreeMap.Const.get?_union_of_not_mem_left not_mem
theorem getElem?_union_of_not_mem_right [TransCmp cmp]
{k : α} (not_mem : ¬k ∈ t₂) :
(t₁ ∪ t₂)[k]? = t₁[k]? :=
DTreeMap.Const.get?_union_of_not_mem_right not_mem
/- get? -/
@[deprecated getElem?_union (since := "2025-12-10")]
theorem get?_union [TransCmp cmp]
{k : α} :
(t₁ ∪ t₂).get? k = (t₂.get? k).or (t₁.get? k) :=
DTreeMap.Const.get?_union
@[deprecated getElem?_union_of_not_mem_left (since := "2025-12-10")]
theorem get?_union_of_not_mem_left [TransCmp cmp]
{k : α} (not_mem : ¬k ∈ t₁) :
(t₁ ∪ t₂).get? k = t₂.get? k :=
DTreeMap.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 [TransCmp cmp]
{k : α} (not_mem : ¬k ∈ t₂) :
(t₁ ∪ t₂).get? k = t₁.get? k :=
DTreeMap.Const.get?_union_of_not_mem_right not_mem
/- getElem -/
theorem getElem_union_of_mem_right [TransCmp cmp]
{k : α} (mem : k ∈ t₂) :
(t₁ ∪ t₂)[k]'(mem_union_of_right mem) = t₂[k]'mem :=
DTreeMap.Const.get_union_of_mem_right mem
theorem getElem_union_of_not_mem_left [TransCmp cmp]
{k : α} (not_mem : ¬k ∈ t₁) {h'} :
(t₁ ∪ t₂)[k]'h' = t₂[k]'(mem_of_mem_union_of_not_mem_left h' not_mem) :=
DTreeMap.Const.get_union_of_not_mem_left not_mem
theorem getElem_union_of_not_mem_right [TransCmp cmp]
{k : α} (not_mem : ¬k ∈ t₂) {h'} :
(t₁ ∪ t₂)[k]'h' = t₁[k]'(mem_of_mem_union_of_not_mem_right h' not_mem) :=
DTreeMap.Const.get_union_of_not_mem_right not_mem
/- get -/
@[deprecated getElem_union_of_mem_right (since := "2025-12-10")]
theorem get_union_of_mem_right [TransCmp cmp]
{k : α} (mem : k ∈ t₂) :
(t₁ ∪ t₂).get k (mem_union_of_right mem) = t₂.get k mem :=
DTreeMap.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 [TransCmp cmp]
{k : α} (not_mem : ¬k ∈ t₁) {h'} :
(t₁ ∪ t₂).get k h' = t₂.get k (mem_of_mem_union_of_not_mem_left h' not_mem) :=
DTreeMap.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 [TransCmp cmp]
{k : α} (not_mem : ¬k ∈ t₂) {h'} :
(t₁ ∪ t₂).get k h' = t₁.get k (mem_of_mem_union_of_not_mem_right h' not_mem) :=
@ -1634,17 +1672,36 @@ theorem getD_union_of_not_mem_right [TransCmp cmp]
(t₁ ∪ t₂).getD k fallback = t₁.getD k fallback :=
DTreeMap.Const.getD_union_of_not_mem_right not_mem
/- getElem! -/
theorem getElem!_union [TransCmp cmp]
{k : α} [Inhabited β] :
(t₁ ∪ t₂)[k]! = t₂.getD k (t₁[k]!) :=
DTreeMap.Const.get!_union
theorem getElem!_union_of_not_mem_left [TransCmp cmp]
{k : α} [Inhabited β] (not_mem : ¬k ∈ t₁) :
(t₁ ∪ t₂)[k]! = t₂[k]! :=
DTreeMap.Const.get!_union_of_not_mem_left not_mem
theorem getElem!_union_of_not_mem_right [TransCmp cmp]
{k : α} [Inhabited β] (not_mem : ¬k ∈ t₂) :
(t₁ ∪ t₂)[k]! = t₁[k]! :=
DTreeMap.Const.get!_union_of_not_mem_right not_mem
/- get! -/
@[deprecated getElem!_union (since := "2025-12-10")]
theorem get!_union [TransCmp cmp]
{k : α} [Inhabited β] :
(t₁ ∪ t₂).get! k = t₂.getD k (t₁.get! k) :=
DTreeMap.Const.get!_union
@[deprecated getElem!_union_of_not_mem_left (since := "2025-12-10")]
theorem get!_union_of_not_mem_left [TransCmp cmp]
{k : α} [Inhabited β] (not_mem : ¬k ∈ t₁) :
(t₁ ∪ t₂).get! k = t₂.get! k :=
DTreeMap.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 [TransCmp cmp]
{k : α} [Inhabited β] (not_mem : ¬k ∈ t₂) :
(t₁ ∪ t₂).get! k = t₁.get! k :=
@ -1786,33 +1843,62 @@ theorem Equiv.inter_congr {t₃ t₄ : TreeMap α β cmp} [TransCmp cmp]
constructor
apply DTreeMap.Equiv.inter_congr equiv₁.1 equiv₂.1
/- get? -/
theorem get?_inter [TransCmp cmp] {k : α} :
(t₁ ∩ t₂).get? k =
if k ∈ t₂ then t₁.get? k else none :=
/- getElem? -/
theorem getElem?_inter [TransCmp cmp] {k : α} :
(t₁ ∩ t₂)[k]? = if k ∈ t₂ then t₁[k]? else none :=
DTreeMap.Const.get?_inter
theorem getElem?_inter_of_mem_right [TransCmp cmp]
{k : α} (mem : k ∈ t₂) :
(t₁ ∩ t₂)[k]? = t₁[k]? :=
DTreeMap.Const.get?_inter_of_mem_right mem
theorem getElem?_inter_of_not_mem_left [TransCmp cmp]
{k : α} (not_mem : k ∉ t₁) :
(t₁ ∩ t₂)[k]? = none :=
DTreeMap.Const.get?_inter_of_not_mem_left not_mem
theorem getElem?_inter_of_not_mem_right [TransCmp cmp]
{k : α} (not_mem : k ∉ t₂) :
(t₁ ∩ t₂)[k]? = none :=
DTreeMap.Const.get?_inter_of_not_mem_right not_mem
/- get? -/
@[deprecated getElem?_inter (since := "2025-12-10")]
theorem get?_inter [TransCmp cmp] {k : α} :
(t₁ ∩ t₂).get? k = if k ∈ t₂ then t₁.get? k else none :=
DTreeMap.Const.get?_inter
@[deprecated getElem?_inter_of_mem_right (since := "2025-12-10")]
theorem get?_inter_of_mem_right [TransCmp cmp]
{k : α} (mem : k ∈ t₂) :
(t₁ ∩ t₂).get? k = t₁.get? k :=
DTreeMap.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 [TransCmp cmp]
{k : α} (not_mem : k ∉ t₁) :
(t₁ ∩ t₂).get? k = none :=
DTreeMap.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 [TransCmp cmp]
{k : α} (not_mem : k ∉ t₂) :
(t₁ ∩ t₂).get? k = none :=
DTreeMap.Const.get?_inter_of_not_mem_right not_mem
/- get -/
/- getElem -/
@[simp]
theorem getElem_inter [TransCmp cmp]
{k : α} {h_mem : k ∈ t₁ ∩ t₂} :
(t₁ ∩ t₂)[k]'h_mem = t₁[k]'(mem_inter_iff.1 h_mem).1 :=
DTreeMap.Const.get_inter
/- get -/
@[deprecated getElem_inter (since := "2025-12-10")]
theorem get_inter [TransCmp cmp]
{k : α} {h_mem : k ∈ t₁ ∩ t₂} :
(t₁ ∩ t₂).get k h_mem =
t₁.get k (mem_inter_iff.1 h_mem).1 :=
(t₁ ∩ t₂).get k h_mem = t₁.get k (mem_inter_iff.1 h_mem).1 :=
DTreeMap.Const.get_inter
/- getD -/
@ -1836,22 +1922,45 @@ theorem getD_inter_of_not_mem_left [TransCmp cmp]
(t₁ ∩ t₂).getD k fallback = fallback :=
DTreeMap.Const.getD_inter_of_not_mem_left not_mem
/- get! -/
theorem get!_inter [TransCmp cmp] {k : α} [Inhabited β] :
(t₁ ∩ t₂).get! k =
if k ∈ t₂ then t₁.get! k else default :=
/- getElem! -/
theorem getElem!_inter [TransCmp cmp] {k : α} [Inhabited β] :
(t₁ ∩ t₂)[k]! = if k ∈ t₂ then t₁[k]! else default :=
DTreeMap.Const.get!_inter
theorem getElem!_inter_of_mem_right [TransCmp cmp]
{k : α} [Inhabited β] (mem : k ∈ t₂) :
(t₁ ∩ t₂)[k]! = t₁[k]! :=
DTreeMap.Const.get!_inter_of_mem_right mem
theorem getElem!_inter_of_not_mem_right [TransCmp cmp]
{k : α} [Inhabited β] (not_mem : k ∉ t₂) :
(t₁ ∩ t₂)[k]! = default :=
DTreeMap.Const.get!_inter_of_not_mem_right not_mem
theorem getElem!_inter_of_not_mem_left [TransCmp cmp]
{k : α} [Inhabited β] (not_mem : k ∉ t₁) :
(t₁ ∩ t₂)[k]! = default :=
DTreeMap.Const.get!_inter_of_not_mem_left not_mem
/- get! -/
@[deprecated getElem!_inter (since := "2025-12-10")]
theorem get!_inter [TransCmp cmp] {k : α} [Inhabited β] :
(t₁ ∩ t₂).get! k = if k ∈ t₂ then t₁.get! k else default :=
DTreeMap.Const.get!_inter
@[deprecated getElem!_inter_of_mem_right (since := "2025-12-10")]
theorem get!_inter_of_mem_right [TransCmp cmp]
{k : α} [Inhabited β] (mem : k ∈ t₂) :
(t₁ ∩ t₂).get! k = t₁.get! k :=
DTreeMap.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 [TransCmp cmp]
{k : α} [Inhabited β] (not_mem : k ∉ t₂) :
(t₁ ∩ t₂).get! k = default :=
DTreeMap.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 [TransCmp cmp]
{k : α} [Inhabited β] (not_mem : k ∉ t₁) :
(t₁ ∩ t₂).get! k = default :=
@ -2017,32 +2126,61 @@ theorem Equiv.diff_congr {t₃ t₄ : TreeMap α β cmp} [TransCmp cmp]
constructor
apply DTreeMap.Equiv.diff_congr equiv₁.1 equiv₂.1
/- get? -/
theorem get?_diff [TransCmp cmp] {k : α} :
(t₁ \ t₂).get? k =
if k ∈ t₂ then none else t₁.get? k :=
/- getElem? -/
theorem getElem?_diff [TransCmp cmp] {k : α} :
(t₁ \ t₂)[k]? = if k ∈ t₂ then none else t₁[k]? :=
DTreeMap.Const.get?_diff
theorem getElem?_diff_of_not_mem_right [TransCmp cmp]
{k : α} (not_mem : k ∉ t₂) :
(t₁ \ t₂)[k]? = t₁[k]? :=
DTreeMap.Const.get?_diff_of_not_mem_right not_mem
theorem getElem?_diff_of_not_mem_left [TransCmp cmp]
{k : α} (not_mem : k ∉ t₁) :
(t₁ \ t₂)[k]? = none :=
DTreeMap.Const.get?_diff_of_not_mem_left not_mem
theorem getElem?_diff_of_mem_right [TransCmp cmp]
{k : α} (mem : k ∈ t₂) :
(t₁ \ t₂)[k]? = none :=
DTreeMap.Const.get?_diff_of_mem_right mem
/- get? -/
@[deprecated getElem?_diff (since := "2025-12-10")]
theorem get?_diff [TransCmp cmp] {k : α} :
(t₁ \ t₂).get? k = if k ∈ t₂ then none else t₁.get? k :=
DTreeMap.Const.get?_diff
@[deprecated getElem?_diff_of_not_mem_right (since := "2025-12-10")]
theorem get?_diff_of_not_mem_right [TransCmp cmp]
{k : α} (not_mem : k ∉ t₂) :
(t₁ \ t₂).get? k = t₁.get? k :=
DTreeMap.Const.get?_diff_of_not_mem_right not_mem
@[deprecated getElem?_diff_of_not_mem_left (since := "2025-12-10")]
theorem get?_diff_of_not_mem_left [TransCmp cmp]
{k : α} (not_mem : k ∉ t₁) :
(t₁ \ t₂).get? k = none :=
DTreeMap.Const.get?_diff_of_not_mem_left not_mem
@[deprecated getElem?_diff_of_mem_right (since := "2025-12-10")]
theorem get?_diff_of_mem_right [TransCmp cmp]
{k : α} (mem : k ∈ t₂) :
(t₁ \ t₂).get? k = none :=
DTreeMap.Const.get?_diff_of_mem_right mem
/- getElem -/
theorem getElem_diff [TransCmp cmp]
{k : α} {h_mem : k ∈ t₁ \ t₂} :
(t₁ \ t₂)[k]'h_mem = t₁[k]'(mem_diff_iff.1 h_mem).1 :=
DTreeMap.Const.get_diff
/- get -/
@[deprecated getElem_diff (since := "2025-12-10")]
theorem get_diff [TransCmp cmp]
{k : α} {h_mem : k ∈ t₁ \ t₂} :
(t₁ \ t₂).get k h_mem =
t₁.get k (mem_diff_iff.1 h_mem).1 :=
(t₁ \ t₂).get k h_mem = t₁.get k (mem_diff_iff.1 h_mem).1 :=
DTreeMap.Const.get_diff
/- getD -/
@ -2066,22 +2204,45 @@ theorem getD_diff_of_not_mem_left [TransCmp cmp]
(t₁ \ t₂).getD k fallback = fallback :=
DTreeMap.Const.getD_diff_of_not_mem_left not_mem
/- get! -/
theorem get!_diff [TransCmp cmp] {k : α} [Inhabited β] :
(t₁ \ t₂).get! k =
if k ∈ t₂ then default else t₁.get! k :=
/- getElem! -/
theorem getElem!_diff [TransCmp cmp] {k : α} [Inhabited β] :
(t₁ \ t₂)[k]! = if k ∈ t₂ then default else t₁[k]! :=
DTreeMap.Const.get!_diff
theorem getElem!_diff_of_not_mem_right [TransCmp cmp]
{k : α} [Inhabited β] (not_mem : k ∉ t₂) :
(t₁ \ t₂)[k]! = t₁[k]! :=
DTreeMap.Const.get!_diff_of_not_mem_right not_mem
theorem getElem!_diff_of_mem_right [TransCmp cmp]
{k : α} [Inhabited β] (mem : k ∈ t₂) :
(t₁ \ t₂)[k]! = default :=
DTreeMap.Const.get!_diff_of_mem_right mem
theorem getElem!_diff_of_not_mem_left [TransCmp cmp]
{k : α} [Inhabited β] (not_mem : k ∉ t₁) :
(t₁ \ t₂)[k]! = default :=
DTreeMap.Const.get!_diff_of_not_mem_left not_mem
/- get! -/
@[deprecated getElem!_diff (since := "2025-12-10")]
theorem get!_diff [TransCmp cmp] {k : α} [Inhabited β] :
(t₁ \ t₂).get! k = if k ∈ t₂ then default else t₁.get! k :=
DTreeMap.Const.get!_diff
@[deprecated getElem!_diff_of_not_mem_right (since := "2025-12-10")]
theorem get!_diff_of_not_mem_right [TransCmp cmp]
{k : α} [Inhabited β] (not_mem : k ∉ t₂) :
(t₁ \ t₂).get! k = t₁.get! k :=
DTreeMap.Const.get!_diff_of_not_mem_right not_mem
@[deprecated getElem!_diff_of_mem_right (since := "2025-12-10")]
theorem get!_diff_of_mem_right [TransCmp cmp]
{k : α} [Inhabited β] (mem : k ∈ t₂) :
(t₁ \ t₂).get! k = default :=
DTreeMap.Const.get!_diff_of_mem_right mem
@[deprecated getElem!_diff_of_not_mem_left (since := "2025-12-10")]
theorem get!_diff_of_not_mem_left [TransCmp cmp]
{k : α} [Inhabited β] (not_mem : k ∉ t₁) :
(t₁ \ t₂).get! k = default :=
@ -3011,7 +3172,7 @@ theorem ordCompare_minKey!_modify_eq [Ord α] [TransOrd α] {t : TreeMap α β}
theorem minKey!_alter_eq_self [TransCmp cmp] [Inhabited α] {k f}
(he : (alter t k f).isEmpty = false) :
(alter t k f).minKey! = k ↔
(f (get? t k)).isSome ∧ ∀ k', k' ∈ t → (cmp k k').isLE :=
(f t[k]?).isSome ∧ ∀ k', k' ∈ t → (cmp k k').isLE :=
DTreeMap.Const.minKey!_alter_eq_self he
theorem minKey?_eq_some_minKeyD [TransCmp cmp] (he : t.isEmpty = false) {fallback} :
@ -3139,7 +3300,7 @@ theorem ordCompare_minKeyD_modify_eq [Ord α] [TransOrd α] {t : TreeMap α β}
theorem minKeyD_alter_eq_self [TransCmp cmp] {k f}
(he : (alter t k f).isEmpty = false) {fallback} :
(alter t k f |>.minKeyD fallback) = k ↔
(f (get? t k)).isSome ∧ ∀ k', k' ∈ t → (cmp k k').isLE :=
(f t[k]?).isSome ∧ ∀ k', k' ∈ t → (cmp k k').isLE :=
DTreeMap.Const.minKeyD_alter_eq_self he
end Min
@ -3592,7 +3753,7 @@ theorem ordCompare_maxKey!_modify_eq [Ord α] [TransOrd α] {t : TreeMap α β}
theorem maxKey!_alter_eq_self [TransCmp cmp] [Inhabited α] {k f}
(he : (alter t k f).isEmpty = false) :
(alter t k f).maxKey! = k ↔
(f (get? t k)).isSome ∧ ∀ k', k' ∈ t → (cmp k' k).isLE :=
(f t[k]?).isSome ∧ ∀ k', k' ∈ t → (cmp k' k).isLE :=
DTreeMap.Const.maxKey!_alter_eq_self he
theorem maxKey?_eq_some_maxKeyD [TransCmp cmp] (he : t.isEmpty = false) {fallback} :
@ -3720,7 +3881,7 @@ theorem ordCompare_maxKeyD_modify_eq [Ord α] [TransOrd α] {t : TreeMap α β}
theorem maxKeyD_alter_eq_self [TransCmp cmp] {k f}
(he : (alter t k f).isEmpty = false) {fallback} :
(alter t k f |>.maxKeyD fallback) = k ↔
(f (get? t k)).isSome ∧ ∀ k', k' ∈ t → (cmp k' k).isLE :=
(f t[k]?).isSome ∧ ∀ k', k' ∈ t → (cmp k' k).isLE :=
DTreeMap.Const.maxKeyD_alter_eq_self he
end Max
@ -4388,12 +4549,12 @@ grind_pattern size_filter_le_size => (t.filter f).size
theorem size_filter_eq_size_iff [TransCmp cmp]
{f : α → β → Bool} :
(t.filter f).size = t.size ↔ ∀ k h, f (t.getKey k h) (t.get k h) :=
(t.filter f).size = t.size ↔ ∀ k h, f (t.getKey k h) (t[k]'h) :=
DTreeMap.Const.size_filter_eq_size_iff
theorem filter_equiv_self_iff [TransCmp cmp]
{f : α → β → Bool} :
t.filter f ~m t ↔ ∀ k h, f (t.getKey k h) (t.get k h) :=
t.filter f ~m t ↔ ∀ k h, f (t.getKey k h) (t[k]'h) :=
⟨fun h => DTreeMap.Const.filter_equiv_self_iff.mp h.1,
fun h => ⟨DTreeMap.Const.filter_equiv_self_iff.mpr h⟩⟩
@ -4465,7 +4626,7 @@ theorem getD_filter_of_getKey?_eq_some [TransCmp cmp]
theorem keys_filter [TransCmp cmp] {f : α → β → Bool} :
(t.filter f).keys =
(t.keys.attach.filter (fun ⟨x, h'⟩ => f x (get t x (mem_of_mem_keys h')))).unattach :=
(t.keys.attach.filter (fun ⟨x, h'⟩ => f x (t[x]'(mem_of_mem_keys h')))).unattach :=
DTreeMap.Const.keys_filter
@[grind =]

223
src/Std/Data/TreeMap/Raw/Lemmas.lean
View file

@ -413,7 +413,7 @@ theorem getD_erase_self [TransCmp cmp] (h : t.WF) {k : α} {fallback : β} :
DTreeMap.Raw.Const.getD_erase_self h
theorem getElem?_eq_some_getD_of_contains [TransCmp cmp] (h : t.WF) {a : α} {fallback : β} :
t.contains a = true → get? t a = some (getD t a fallback) :=
t.contains a = true → t[a]? = some (getD t a fallback) :=
DTreeMap.Raw.Const.get?_eq_some_getD_of_contains h
theorem getElem?_eq_some_getD [TransCmp cmp] (h : t.WF) {a : α} {fallback : β} :
@ -789,7 +789,7 @@ theorem size_insertIfNew_le [TransCmp cmp] (h : t.WF) {k : α} {v : β} :
@[simp, grind =]
theorem getThenInsertIfNew?_fst [TransCmp cmp] (h : t.WF) {k : α} {v : β} :
(getThenInsertIfNew? t k v).1 = get? t k :=
(getThenInsertIfNew? t k v).1 = t[k]? :=
DTreeMap.Raw.Const.getThenInsertIfNew?_fst h
@[simp, grind =]
@ -1616,33 +1616,71 @@ theorem union_insert_right_equiv_insert_union [TransCmp cmp] {p : (_ : α) × β
(t₁ ∪ (t₂.insert p.fst p.snd)).Equiv ((t₁ ∪ t₂).insert p.fst p.snd) :=
⟨DTreeMap.Raw.union_insert_right_equiv_insert_union h₁ h₂⟩
/- getElem? -/
theorem getElem?_union [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} :
(t₁ ∪ t₂)[k]? = (t₂[k]?).or (t₁[k]?) :=
DTreeMap.Raw.Const.get?_union h₁ h₂
theorem getElem?_union_of_not_mem_left [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} (not_mem : ¬k ∈ t₁) :
(t₁ ∪ t₂)[k]? = t₂[k]? :=
DTreeMap.Raw.Const.get?_union_of_not_mem_left h₁ h₂ not_mem
theorem getElem?_union_of_not_mem_right [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} (not_mem : ¬k ∈ t₂) :
(t₁ ∪ t₂)[k]? = t₁[k]? :=
DTreeMap.Raw.Const.get?_union_of_not_mem_right h₁ h₂ not_mem
/- get? -/
@[deprecated getElem?_union (since := "2025-12-10")]
theorem get?_union [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} :
(t₁ ∪ t₂).get? k = (t₂.get? k).or (t₁.get? k) :=
DTreeMap.Raw.Const.get?_union h₁ h₂
@[deprecated getElem?_union_of_not_mem_left (since := "2025-12-10")]
theorem get?_union_of_not_mem_left [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} (not_mem : ¬k ∈ t₁) :
(t₁ ∪ t₂).get? k = t₂.get? k :=
DTreeMap.Raw.Const.get?_union_of_not_mem_left h₁ h₂ not_mem
@[deprecated getElem?_union_of_not_mem_right (since := "2025-12-10")]
theorem get?_union_of_not_mem_right [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} (not_mem : ¬k ∈ t₂) :
(t₁ ∪ t₂).get? k = t₁.get? k :=
DTreeMap.Raw.Const.get?_union_of_not_mem_right h₁ h₂ not_mem
/- getElem -/
theorem getElem_union_of_mem_right [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} (mem : k ∈ t₂) :
(t₁ ∪ t₂)[k]'(mem_union_of_right h₁ h₂ mem) = t₂[k]'mem :=
DTreeMap.Raw.Const.get_union_of_mem_right h₁ h₂ mem
theorem getElem_union_of_not_mem_left [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} (not_mem : ¬k ∈ t₁) {h'} :
(t₁ ∪ t₂)[k]'h' = t₂[k]'(mem_of_mem_union_of_not_mem_left h₁ h₂ h' not_mem) :=
DTreeMap.Raw.Const.get_union_of_not_mem_left h₁ h₂ not_mem
theorem getElem_union_of_not_mem_right [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} (not_mem : ¬k ∈ t₂) {h'} :
(t₁ ∪ t₂)[k]'h' = t₁[k]'(mem_of_mem_union_of_not_mem_right h₁ h₂ h' not_mem) :=
DTreeMap.Raw.Const.get_union_of_not_mem_right h₁ h₂ not_mem
/- get -/
@[deprecated getElem_union_of_mem_right (since := "2025-12-10")]
theorem get_union_of_mem_right [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} (mem : k ∈ t₂) :
(t₁ ∪ t₂).get k (mem_union_of_right h₁ h₂ mem) = t₂.get k mem :=
DTreeMap.Raw.Const.get_union_of_mem_right h₁ h₂ mem
@[deprecated getElem_union_of_not_mem_left (since := "2025-12-10")]
theorem get_union_of_not_mem_left [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} (not_mem : ¬k ∈ t₁) {h'} :
(t₁ ∪ t₂).get k h' = t₂.get k (mem_of_mem_union_of_not_mem_left h₁ h₂ h' not_mem) :=
DTreeMap.Raw.Const.get_union_of_not_mem_left h₁ h₂ not_mem
@[deprecated getElem_union_of_not_mem_right (since := "2025-12-10")]
theorem get_union_of_not_mem_right [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} (not_mem : ¬k ∈ t₂) {h'} :
(t₁ ∪ t₂).get k h' = t₁.get k (mem_of_mem_union_of_not_mem_right h₁ h₂ h' not_mem) :=
@ -1664,17 +1702,36 @@ theorem getD_union_of_not_mem_right [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂
(t₁ ∪ t₂).getD k fallback = t₁.getD k fallback :=
DTreeMap.Raw.Const.getD_union_of_not_mem_right h₁ h₂ not_mem
/- getElem! -/
theorem getElem!_union [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} [Inhabited β] :
(t₁ ∪ t₂)[k]! = t₂.getD k (t₁[k]!) :=
DTreeMap.Raw.Const.get!_union h₁ h₂
theorem getElem!_union_of_not_mem_left [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} [Inhabited β] (not_mem : ¬k ∈ t₁) :
(t₁ ∪ t₂)[k]! = t₂[k]! :=
DTreeMap.Raw.Const.get!_union_of_not_mem_left h₁ h₂ not_mem
theorem getElem!_union_of_not_mem_right [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} [Inhabited β] (not_mem : ¬k ∈ t₂) :
(t₁ ∪ t₂)[k]! = t₁[k]! :=
DTreeMap.Raw.Const.get!_union_of_not_mem_right h₁ h₂ not_mem
/- get! -/
@[deprecated getElem!_union (since := "2025-12-10")]
theorem get!_union [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} [Inhabited β] :
(t₁ ∪ t₂).get! k = t₂.getD k (t₁.get! k) :=
DTreeMap.Raw.Const.get!_union h₁ h₂
@[deprecated getElem!_union_of_not_mem_left (since := "2025-12-10")]
theorem get!_union_of_not_mem_left [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} [Inhabited β] (not_mem : ¬k ∈ t₁) :
(t₁ ∪ t₂).get! k = t₂.get! k :=
DTreeMap.Raw.Const.get!_union_of_not_mem_left h₁ h₂ not_mem
@[deprecated getElem!_union_of_not_mem_right (since := "2025-12-10")]
theorem get!_union_of_not_mem_right [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} [Inhabited β] (not_mem : ¬k ∈ t₂) :
(t₁ ∪ t₂).get! k = t₁.get! k :=
@ -1829,33 +1886,62 @@ theorem Equiv.inter_congr [TransCmp cmp] {t₃ t₄ : Raw α β cmp}
(t₁ ∩ t₂).Equiv (t₃ ∩ t₄) :=
⟨DTreeMap.Raw.Equiv.inter_congr h₁ h₂ h₃ h₄ equiv₁.1 equiv₂.1⟩
/- get? -/
theorem get?_inter [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF) {k : α} :
(t₁ ∩ t₂).get? k =
if k ∈ t₂ then t₁.get? k else none :=
/- getElem? -/
theorem getElem?_inter [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF) {k : α} :
(t₁ ∩ t₂)[k]? = if k ∈ t₂ then t₁[k]? else none :=
DTreeMap.Raw.Const.get?_inter h₁ h₂
theorem getElem?_inter_of_mem_right [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} (mem : k ∈ t₂) :
(t₁ ∩ t₂)[k]? = t₁[k]? :=
DTreeMap.Raw.Const.get?_inter_of_mem_right h₁ h₂ mem
theorem getElem?_inter_of_not_mem_left [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} (not_mem : k ∉ t₁) :
(t₁ ∩ t₂)[k]? = none :=
DTreeMap.Raw.Const.get?_inter_of_not_mem_left h₁ h₂ not_mem
theorem getElem?_inter_of_not_mem_right [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} (not_mem : k ∉ t₂) :
(t₁ ∩ t₂)[k]? = none :=
DTreeMap.Raw.Const.get?_inter_of_not_mem_right h₁ h₂ not_mem
/- get? -/
@[deprecated getElem?_inter (since := "2025-12-10")]
theorem get?_inter [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF) {k : α} :
(t₁ ∩ t₂).get? k = if k ∈ t₂ then t₁.get? k else none :=
DTreeMap.Raw.Const.get?_inter h₁ h₂
@[deprecated getElem?_inter_of_mem_right (since := "2025-12-10")]
theorem get?_inter_of_mem_right [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} (mem : k ∈ t₂) :
(t₁ ∩ t₂).get? k = t₁.get? k :=
DTreeMap.Raw.Const.get?_inter_of_mem_right h₁ h₂ mem
@[deprecated getElem?_inter_of_not_mem_left (since := "2025-12-10")]
theorem get?_inter_of_not_mem_left [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} (not_mem : k ∉ t₁) :
(t₁ ∩ t₂).get? k = none :=
DTreeMap.Raw.Const.get?_inter_of_not_mem_left h₁ h₂ not_mem
@[deprecated getElem?_inter_of_not_mem_right (since := "2025-12-10")]
theorem get?_inter_of_not_mem_right [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} (not_mem : k ∉ t₂) :
(t₁ ∩ t₂).get? k = none :=
DTreeMap.Raw.Const.get?_inter_of_not_mem_right h₁ h₂ not_mem
/- get -/
/- getElem -/
@[simp]
theorem getElem_inter [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} {h_mem : k ∈ t₁ ∩ t₂} :
(t₁ ∩ t₂)[k]'h_mem = t₁[k]'((mem_inter_iff h₁ h₂).1 h_mem).1 :=
DTreeMap.Raw.Const.get_inter h₁ h₂
/- get -/
@[deprecated getElem_inter (since := "2025-12-10")]
theorem get_inter [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} {h_mem : k ∈ t₁ ∩ t₂} :
(t₁ ∩ t₂).get k h_mem =
t₁.get k ((mem_inter_iff h₁ h₂).1 h_mem).1 :=
(t₁ ∩ t₂).get k h_mem = t₁.get k ((mem_inter_iff h₁ h₂).1 h_mem).1 :=
DTreeMap.Raw.Const.get_inter h₁ h₂
/- getD -/
@ -1880,22 +1966,45 @@ theorem getD_inter_of_not_mem_left [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.
(t₁ ∩ t₂).getD k fallback = fallback :=
DTreeMap.Raw.Const.getD_inter_of_not_mem_left h₁ h₂ not_mem
/- get! -/
theorem get!_inter [TransCmp cmp] [Inhabited β] (h₁ : t₁.WF) (h₂ : t₂.WF) {k : α} :
(t₁ ∩ t₂).get! k =
if k ∈ t₂ then t₁.get! k else default :=
/- getElem! -/
theorem getElem!_inter [TransCmp cmp] [Inhabited β] (h₁ : t₁.WF) (h₂ : t₂.WF) {k : α} :
(t₁ ∩ t₂)[k]! = if k ∈ t₂ then t₁[k]! else default :=
DTreeMap.Raw.Const.get!_inter h₁ h₂
theorem getElem!_inter_of_mem_right [TransCmp cmp] [Inhabited β] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} (mem : k ∈ t₂) :
(t₁ ∩ t₂)[k]! = t₁[k]! :=
DTreeMap.Raw.Const.get!_inter_of_mem_right h₁ h₂ mem
theorem getElem!_inter_of_not_mem_right [TransCmp cmp] [Inhabited β] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} (not_mem : k ∉ t₂) :
(t₁ ∩ t₂)[k]! = default :=
DTreeMap.Raw.Const.get!_inter_of_not_mem_right h₁ h₂ not_mem
theorem getElem!_inter_of_not_mem_left [TransCmp cmp] [Inhabited β] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} (not_mem : k ∉ t₁) :
(t₁ ∩ t₂)[k]! = default :=
DTreeMap.Raw.Const.get!_inter_of_not_mem_left h₁ h₂ not_mem
/- get! -/
@[deprecated getElem!_inter (since := "2025-12-10")]
theorem get!_inter [TransCmp cmp] [Inhabited β] (h₁ : t₁.WF) (h₂ : t₂.WF) {k : α} :
(t₁ ∩ t₂).get! k = if k ∈ t₂ then t₁.get! k else default :=
DTreeMap.Raw.Const.get!_inter h₁ h₂
@[deprecated getElem!_inter_of_mem_right (since := "2025-12-10")]
theorem get!_inter_of_mem_right [TransCmp cmp] [Inhabited β] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} (mem : k ∈ t₂) :
(t₁ ∩ t₂).get! k = t₁.get! k :=
DTreeMap.Raw.Const.get!_inter_of_mem_right h₁ h₂ mem
@[deprecated getElem!_inter_of_not_mem_right (since := "2025-12-10")]
theorem get!_inter_of_not_mem_right [TransCmp cmp] [Inhabited β] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} (not_mem : k ∉ t₂) :
(t₁ ∩ t₂).get! k = default :=
DTreeMap.Raw.Const.get!_inter_of_not_mem_right h₁ h₂ not_mem
@[deprecated getElem!_inter_of_not_mem_left (since := "2025-12-10")]
theorem get!_inter_of_not_mem_left [TransCmp cmp] [Inhabited β] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} (not_mem : k ∉ t₁) :
(t₁ ∩ t₂).get! k = default :=
@ -2072,32 +2181,61 @@ theorem Equiv.diff_congr [TransCmp cmp] {t₃ t₄ : Raw α β cmp}
(t₁ \ t₂).Equiv (t₃ \ t₄) :=
⟨DTreeMap.Raw.Equiv.diff_congr h₁ h₂ h₃ h₄ equiv₁.1 equiv₂.1⟩
/- get? -/
theorem get?_diff [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF) {k : α} :
(t₁ \ t₂).get? k =
if k ∈ t₂ then none else t₁.get? k :=
/- getElem? -/
theorem getElem?_diff [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF) {k : α} :
(t₁ \ t₂)[k]? = if k ∈ t₂ then none else t₁[k]? :=
DTreeMap.Raw.Const.get?_diff h₁ h₂
theorem getElem?_diff_of_not_mem_right [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} (not_mem : k ∉ t₂) :
(t₁ \ t₂)[k]? = t₁[k]? :=
DTreeMap.Raw.Const.get?_diff_of_not_mem_right h₁ h₂ not_mem
theorem getElem?_diff_of_not_mem_left [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} (not_mem : k ∉ t₁) :
(t₁ \ t₂)[k]? = none :=
DTreeMap.Raw.Const.get?_diff_of_not_mem_left h₁ h₂ not_mem
theorem getElem?_diff_of_mem_right [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} (mem : k ∈ t₂) :
(t₁ \ t₂)[k]? = none :=
DTreeMap.Raw.Const.get?_diff_of_mem_right h₁ h₂ mem
/- get? -/
@[deprecated getElem?_diff (since := "2025-12-10")]
theorem get?_diff [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF) {k : α} :
(t₁ \ t₂).get? k = if k ∈ t₂ then none else t₁.get? k :=
DTreeMap.Raw.Const.get?_diff h₁ h₂
@[deprecated getElem?_diff_of_not_mem_right (since := "2025-12-10")]
theorem get?_diff_of_not_mem_right [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} (not_mem : k ∉ t₂) :
(t₁ \ t₂).get? k = t₁.get? k :=
DTreeMap.Raw.Const.get?_diff_of_not_mem_right h₁ h₂ not_mem
@[deprecated getElem?_diff_of_not_mem_left (since := "2025-12-10")]
theorem get?_diff_of_not_mem_left [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} (not_mem : k ∉ t₁) :
(t₁ \ t₂).get? k = none :=
DTreeMap.Raw.Const.get?_diff_of_not_mem_left h₁ h₂ not_mem
@[deprecated getElem?_diff_of_mem_right (since := "2025-12-10")]
theorem get?_diff_of_mem_right [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} (mem : k ∈ t₂) :
(t₁ \ t₂).get? k = none :=
DTreeMap.Raw.Const.get?_diff_of_mem_right h₁ h₂ mem
/- getElem -/
theorem getElem_diff [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} {h_mem : k ∈ t₁ \ t₂} :
(t₁ \ t₂)[k]'h_mem = t₁[k]'((mem_diff_iff h₁ h₂).1 h_mem).1 :=
DTreeMap.Raw.Const.get_diff h₁ h₂
/- get -/
@[deprecated getElem_diff (since := "2025-12-10")]
theorem get_diff [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} {h_mem : k ∈ t₁ \ t₂} :
(t₁ \ t₂).get k h_mem =
t₁.get k ((mem_diff_iff h₁ h₂).1 h_mem).1 :=
(t₁ \ t₂).get k h_mem = t₁.get k ((mem_diff_iff h₁ h₂).1 h_mem).1 :=
DTreeMap.Raw.Const.get_diff h₁ h₂
/- getD -/
@ -2122,22 +2260,45 @@ theorem getD_diff_of_not_mem_left [TransCmp cmp] (h₁ : t₁.WF) (h₂ : t₂.W
(t₁ \ t₂).getD k fallback = fallback :=
DTreeMap.Raw.Const.getD_diff_of_not_mem_left h₁ h₂ not_mem
/- get! -/
theorem get!_diff [TransCmp cmp] [Inhabited β] (h₁ : t₁.WF) (h₂ : t₂.WF) {k : α} :
(t₁ \ t₂).get! k =
if k ∈ t₂ then default else t₁.get! k :=
/- getElem! -/
theorem getElem!_diff [TransCmp cmp] [Inhabited β] (h₁ : t₁.WF) (h₂ : t₂.WF) {k : α} :
(t₁ \ t₂)[k]! = if k ∈ t₂ then default else t₁[k]! :=
DTreeMap.Raw.Const.get!_diff h₁ h₂
theorem getElem!_diff_of_not_mem_right [TransCmp cmp] [Inhabited β] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} (not_mem : k ∉ t₂) :
(t₁ \ t₂)[k]! = t₁[k]! :=
DTreeMap.Raw.Const.get!_diff_of_not_mem_right h₁ h₂ not_mem
theorem getElem!_diff_of_mem_right [TransCmp cmp] [Inhabited β] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} (mem : k ∈ t₂) :
(t₁ \ t₂)[k]! = default :=
DTreeMap.Raw.Const.get!_diff_of_mem_right h₁ h₂ mem
theorem getElem!_diff_of_not_mem_left [TransCmp cmp] [Inhabited β] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} (not_mem : k ∉ t₁) :
(t₁ \ t₂)[k]! = default :=
DTreeMap.Raw.Const.get!_diff_of_not_mem_left h₁ h₂ not_mem
/- get! -/
@[deprecated getElem!_diff (since := "2025-12-10")]
theorem get!_diff [TransCmp cmp] [Inhabited β] (h₁ : t₁.WF) (h₂ : t₂.WF) {k : α} :
(t₁ \ t₂).get! k = if k ∈ t₂ then default else t₁.get! k :=
DTreeMap.Raw.Const.get!_diff h₁ h₂
@[deprecated getElem!_diff_of_not_mem_right (since := "2025-12-10")]
theorem get!_diff_of_not_mem_right [TransCmp cmp] [Inhabited β] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} (not_mem : k ∉ t₂) :
(t₁ \ t₂).get! k = t₁.get! k :=
DTreeMap.Raw.Const.get!_diff_of_not_mem_right h₁ h₂ not_mem
@[deprecated getElem!_diff_of_mem_right (since := "2025-12-10")]
theorem get!_diff_of_mem_right [TransCmp cmp] [Inhabited β] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} (mem : k ∈ t₂) :
(t₁ \ t₂).get! k = default :=
DTreeMap.Raw.Const.get!_diff_of_mem_right h₁ h₂ mem
@[deprecated getElem!_diff_of_not_mem_left (since := "2025-12-10")]
theorem get!_diff_of_not_mem_left [TransCmp cmp] [Inhabited β] (h₁ : t₁.WF) (h₂ : t₂.WF)
{k : α} (not_mem : k ∉ t₁) :
(t₁ \ t₂).get! k = default :=
@ -2802,7 +2963,7 @@ theorem compare_minKey?_modify_eq [TransCmp cmp] (h : t.WF) {k f km kmm} :
theorem minKey?_alter_eq_self [TransCmp cmp] (h : t.WF) {k f} :
(t.alter k f).minKey? = some k ↔
(f (t.get? k)).isSome ∧ ∀ k', k' ∈ t → (cmp k k').isLE :=
(f t[k]?).isSome ∧ ∀ k', k' ∈ t → (cmp k k').isLE :=
DTreeMap.Raw.Const.minKey?_alter_eq_self h
theorem minKey?_eq_some_minKey! [TransCmp cmp] [Inhabited α] (h : t.WF) (he : t.isEmpty = false) :
@ -2924,7 +3085,7 @@ theorem ordCompare_minKey!_modify_eq [Ord α] [TransOrd α] {t : Raw α β} [Inh
theorem minKey!_alter_eq_self [TransCmp cmp] [Inhabited α] (h : t.WF) {k f}
(he : (alter t k f).isEmpty = false) :
(alter t k f).minKey! = k ↔
(f (get? t k)).isSome ∧ ∀ k', k' ∈ t → (cmp k k').isLE :=
(f t[k]?).isSome ∧ ∀ k', k' ∈ t → (cmp k k').isLE :=
DTreeMap.Raw.Const.minKey!_alter_eq_self h he
theorem minKey?_eq_some_minKeyD [TransCmp cmp] (h : t.WF) (he : t.isEmpty = false) {fallback} :
@ -3052,7 +3213,7 @@ theorem ordCompare_minKeyD_modify_eq [Ord α] [TransOrd α] {t : Raw α β} (h :
theorem minKeyD_alter_eq_self [TransCmp cmp] (h : t.WF) {k f}
(he : (alter t k f).isEmpty = false) {fallback} :
(alter t k f |>.minKeyD fallback) = k ↔
(f (get? t k)).isSome ∧ ∀ k', k' ∈ t → (cmp k k').isLE :=
(f t[k]?).isSome ∧ ∀ k', k' ∈ t → (cmp k k').isLE :=
DTreeMap.Raw.Const.minKeyD_alter_eq_self h he
end Min
@ -3240,7 +3401,7 @@ theorem compare_maxKey?_modify_eq [TransCmp cmp] (h : t.WF) {k f km kmm} :
theorem maxKey?_alter_eq_self [TransCmp cmp] (h : t.WF) {k f} :
(t.alter k f).maxKey? = some k ↔
(f (t.get? k)).isSome ∧ ∀ k', k' ∈ t → (cmp k' k).isLE :=
(f t[k]?).isSome ∧ ∀ k', k' ∈ t → (cmp k' k).isLE :=
DTreeMap.Raw.Const.maxKey?_alter_eq_self h
theorem maxKey?_eq_some_maxKey! [TransCmp cmp] [Inhabited α] (h : t.WF) (he : t.isEmpty = false) :
@ -3364,7 +3525,7 @@ theorem ordCompare_maxKey!_modify_eq [Ord α] [TransOrd α] {t : Raw α β} [Inh
theorem maxKey!_alter_eq_self [TransCmp cmp] [Inhabited α] (h : t.WF) {k f}
(he : (alter t k f).isEmpty = false) :
(alter t k f).maxKey! = k ↔
(f (get? t k)).isSome ∧ ∀ k', k' ∈ t → (cmp k' k).isLE :=
(f t[k]?).isSome ∧ ∀ k', k' ∈ t → (cmp k' k).isLE :=
DTreeMap.Raw.Const.maxKey!_alter_eq_self h he
theorem maxKey?_eq_some_maxKeyD [TransCmp cmp] (h : t.WF) (he : t.isEmpty = false) {fallback} :
@ -3492,7 +3653,7 @@ theorem ordCompare_maxKeyD_modify_eq [Ord α] [TransOrd α] {t : Raw α β} (h :
theorem maxKeyD_alter_eq_self [TransCmp cmp] (h : t.WF) {k f}
(he : (alter t k f).isEmpty = false) {fallback} :
(alter t k f |>.maxKeyD fallback) = k ↔
(f (get? t k)).isSome ∧ ∀ k', k' ∈ t → (cmp k' k).isLE :=
(f t[k]?).isSome ∧ ∀ k', k' ∈ t → (cmp k' k).isLE :=
DTreeMap.Raw.Const.maxKeyD_alter_eq_self h he
end Max
@ -4373,7 +4534,7 @@ theorem getElem!_map [TransCmp cmp] [LawfulEqCmp cmp] [Inhabited γ]
theorem getElem!_map' [TransCmp cmp] [Inhabited γ]
{f : α → β → γ} {k : α} (h : t.WF) :
(t.map f)[k]! =
((get? t k).pmap (fun v h => f (t.getKey k h) v)
((t[k]?).pmap (fun v h => f (t.getKey k h) v)
(fun _ h' => (mem_iff_isSome_getElem? h).mpr (Option.isSome_of_eq_some h'))).get! :=
DTreeMap.Raw.Const.get!_map' h.out
@ -4393,7 +4554,7 @@ theorem getD_map [TransCmp cmp] [LawfulEqCmp cmp]
theorem getD_map' [TransCmp cmp]
{f : α → β → γ} {k : α} {fallback : γ} (h : t.WF) :
getD (t.map f) k fallback =
((get? t k).pmap (fun v h => f (t.getKey k h) v)
(t[k]?.pmap (fun v h => f (t.getKey k h) v)
(fun _ h' => (mem_iff_isSome_getElem? h).mpr (Option.isSome_of_eq_some h'))).getD fallback :=
DTreeMap.Raw.Const.getD_map' h.out