∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {R : Type u_5} [inst_3 : NormedDivisionRing R] [inst_4 : NormedAlgebra 𝕜 R] {h : E → R}
  {z : E} {S : Set E}, DifferentiableWithinAt 𝕜 h S z → h z ≠ 0 → DifferentiableWithinAt 𝕜 h⁻¹ S z