∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {f g : 𝕜 → E} {z₀ : 𝕜},
  analyticOrderAt f z₀ < analyticOrderAt g z₀ → analyticOrderAt (f + g) z₀ = analyticOrderAt f z₀