∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {H : Type u_3} [inst_3 : TopologicalSpace H] {I : ModelWithCorners 𝕜 E H} {E' : Type u_5}
  [inst_4 : NormedAddCommGroup E'] [inst_5 : NormedSpace 𝕜 E'] {H' : Type u_6} [inst_6 : TopologicalSpace H']
  {I' : ModelWithCorners 𝕜 E' H'} (n : WithTop ℕ∞) ⦃s : Set H⦄ ⦃x : H⦄ ⦃t : Set H⦄ ⦃f : H → H'⦄,
  s ∈ nhdsWithin x t → ContDiffWithinAtProp I I' n f s x → ContDiffWithinAtProp I I' n f t x