intro v
n : ℕ
i : Fin n
this :
  ArithPart₁ fun v =>
    rfind fun x => Part.some (decide ((fun x x => x * x) v x ≤ v.get i ∧ v.get i < (fun x x => x * x) v (x + 1)))
⊢ ∀ (i_1 : Vector ℕ n),
    (rfind fun x =>
        Part.some (decide ((fun x x => x * x) i_1 x ≤ i_1.get i ∧ i_1.get i < (fun x x => x * x) i_1 (x + 1)))) =
      (↑fun v => (v.get i).sqrt) i_1
n : ℕ
i : Fin n
this :
  ArithPart₁ fun v =>
    rfind fun x => Part.some (decide ((fun x x => x * x) v x ≤ v.get i ∧ v.get i < (fun x x => x * x) v (x + 1)))
v : Vector ℕ n
⊢ (rfind fun x => Part.some (decide ((fun x x => x * x) v x ≤ v.get i ∧ v.get i < (fun x x => x * x) v (x + 1)))) =
    (↑fun v => (v.get i).sqrt) v