∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {f : 𝕜 → E} {g : 𝕜 → 𝕜} {z₀ : 𝕜},
  AnalyticAt 𝕜 g z₀ →
    deriv g z₀ ≠ 0 → ∀ [CompleteSpace 𝕜] [CharZero 𝕜], analyticOrderAt (f ∘ g) z₀ = analyticOrderAt f (g z₀)