∀ {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} {M : Type u_4}
  [inst_4 : TopologicalSpace M] [inst_5 : ChartedSpace H M] {s : Set M} {x : M} {n : WithTop ℕ∞} {ι : Type u_16}
  [inst_6 : Fintype ι] {Fi : ι → Type u_17} [inst_7 : (i : ι) → NormedAddCommGroup (Fi i)]
  [inst_8 : (i : ι) → NormedSpace 𝕜 (Fi i)] {φ : M → (i : ι) → Fi i},
  ContMDiffWithinAt I (modelWithCornersSelf 𝕜 ((i : ι) → Fi i)) n φ s x ↔
    ∀ (i : ι), ContMDiffWithinAt I (modelWithCornersSelf 𝕜 (Fi i)) n (fun x => φ x i) s x