∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {f : 𝕜 → E} {x : 𝕜},
  AnalyticAt 𝕜 f x →
    ∀ [CompleteSpace E] [CharZero 𝕜], analyticOrderAt (deriv f) x + 1 = analyticOrderAt (fun x_1 => f x_1 - f x) x