∀ {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] {F₁ : Type u_14} [inst_6 : NormedAddCommGroup F₁]
  [inst_7 : NormedSpace 𝕜 F₁] {F₂ : Type u_15} [inst_8 : NormedAddCommGroup F₂] [inst_9 : NormedSpace 𝕜 F₂] {x : M}
  {n : WithTop ℕ∞} (f : M → F₁ × F₂),
  ContMDiffAt I (modelWithCornersSelf 𝕜 (F₁ × F₂)) n f x ↔
    ContMDiffAt I (modelWithCornersSelf 𝕜 F₁) n (Prod.fst ∘ f) x ∧
      ContMDiffAt I (modelWithCornersSelf 𝕜 F₂) n (Prod.snd ∘ f) x