Documentation

Batteries.Data.Array.Lemmas

@[deprecated Array.forIn_toList (since := "2025-07-01")]
theorem Array.forIn_eq_forIn_toList {m : Type u_1 → Type u_2} {α : Type u_3} {β : Type u_1} [Monad m] (as : Array α) (b : β) (f : αβm (ForInStep β)) :
forIn as b f = forIn as.toList b f

idxOf? #

theorem Array.idxOf?_toList {α : Type u_1} [BEq α] {a : α} {l : Array α} :

erase #

@[deprecated List.eraseP_toArray (since := "2025-02-06")]
theorem Array.eraseP_toArray {α : Type u_1} {as : List α} {p : αBool} :

Alias of List.eraseP_toArray.

@[deprecated List.erase_toArray (since := "2025-02-06")]
theorem Array.erase_toArray {α : Type u_1} [BEq α] {as : List α} {a : α} :

Alias of List.erase_toArray.

@[simp]
theorem Array.toList_erase {α : Type u_1} [BEq α] (l : Array α) (a : α) :
@[simp]
theorem Array.size_eraseIdxIfInBounds {α : Type u_1} (a : Array α) (i : Nat) :

set #

theorem Array.size_set! {α : Type u_1} (a : Array α) (i : Nat) (v : α) :
(a.set! i v).size = a.size

map #

mem #

insertAt #

@[deprecated Array.getElem_insertIdx_of_lt (since := "2025-02-06")]
theorem Array.getElem_insertIdx_lt {α : Type u} {xs : Array α} {x : α} {i k : Nat} (w : i xs.size) (h : k < i) :
(xs.insertIdx i x w)[k] = xs[k]

Alias of Array.getElem_insertIdx_of_lt.

@[deprecated Array.getElem_insertIdx_self (since := "2025-02-06")]
theorem Array.getElem_insertIdx_eq {α : Type u} {xs : Array α} {x : α} {i : Nat} (w : i xs.size) :
(xs.insertIdx i x w)[i] = x

Alias of Array.getElem_insertIdx_self.

@[deprecated Array.getElem_insertIdx_of_gt (since := "2025-02-06")]
theorem Array.getElem_insertIdx_gt {α : Type u} {xs : Array α} {x : α} {i k : Nat} (w : k xs.size) (h : k > i) :
(xs.insertIdx i x )[k] = xs[k - 1]

Alias of Array.getElem_insertIdx_of_gt.

extract #

@[simp]
theorem Array.extract_empty_of_start_eq_stop {α : Type u_1} {i : Nat} {a : Array α} :
a.extract i i = #[]
theorem Array.extract_append_of_stop_le_size_left {α : Type u_1} {j i : Nat} {a b : Array α} (h : j a.size) :
(a ++ b).extract i j = a.extract i j
theorem Array.extract_append_of_size_left_le_start {α : Type u_1} {i j : Nat} {a b : Array α} (h : a.size i) :
(a ++ b).extract i j = b.extract (i - a.size) (j - a.size)
theorem Array.extract_eq_of_size_le_stop {α : Type u_1} {j i : Nat} {a : Array α} (h : a.size j) :
a.extract i j = a.extract i