∀ {𝕜 : Type u_2} [inst : NontriviallyNormedField 𝕜] {n : WithTop ℕ∞} {H : Type u_3} [inst_1 : TopologicalSpace H]
  {E : Type u_4} [inst_2 : NormedAddCommGroup E] [inst_3 : NormedSpace 𝕜 E] {I : ModelWithCorners 𝕜 E H} {G : Type u_5}
  [inst_4 : CommMonoid G] [inst_5 : TopologicalSpace G] [inst_6 : ChartedSpace H G] [ContMDiffMul I n G] {E' : Type u_6}
  [inst_8 : NormedAddCommGroup E'] [inst_9 : NormedSpace 𝕜 E'] {H' : Type u_7} [inst_10 : TopologicalSpace H']
  {I' : ModelWithCorners 𝕜 E' H'} {M : Type u_8} [inst_11 : TopologicalSpace M] [inst_12 : ChartedSpace H' M]
  {s : Set M} {x : M} {g : M → G},
  ContMDiffWithinAt I' I n g s x → ∀ (m : ℕ), ContMDiffWithinAt I' I n (fun x => g x ^ m) s x