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chore: move @[simp] from back_eq_back? to back_push #5896

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Oct 31, 2024
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chore: move @[simp] from back_eq_back? to back_push #5896

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5 changes: 3 additions & 2 deletions src/Init/Data/Array/Lemmas.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -506,13 +506,14 @@ theorem getElem?_eq_some_iff {as : Array α} : as[n]? = some a ↔ ∃ h : n < a
cases as
simp [List.getElem?_eq_some_iff]

@[simp] theorem back_eq_back? [Inhabited α] (a : Array α) : a.back = a.back?.getD default := by
theorem back_eq_back? [Inhabited α] (a : Array α) : a.back = a.back?.getD default := by
simp only [back, get!_eq_getElem?, get?_eq_getElem?, back?]

@[simp] theorem back?_push (a : Array α) : (a.push x).back? = some x := by
simp [back?, getElem?_eq_getElem?_toList]

theorem back_push [Inhabited α] (a : Array α) : (a.push x).back = x := by simp
@[simp] theorem back_push [Inhabited α] (a : Array α) : (a.push x).back = x := by
simp [back_eq_back?]

theorem getElem?_push_lt (a : Array α) (x : α) (i : Nat) (h : i < a.size) :
(a.push x)[i]? = some a[i] := by
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