∀ {𝕜 : Type u_2} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {𝕝 : Type u_8} [inst_3 : NormedDivisionRing 𝕝] [inst_4 : NormedAlgebra 𝕜 𝕝] {f : E → 𝕝}
  {x : E} {s : Set E}, AnalyticWithinAt 𝕜 f s x → f x ≠ 0 → AnalyticWithinAt 𝕜 (fun i => (f i)⁻¹) s x