∀ {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] {F : Type u_5} [inst_6 : NormedAddCommGroup F]
  [inst_7 : NormedSpace 𝕜 F] {n : WithTop ℕ∞} {V : M → Type u_6} [inst_8 : TopologicalSpace (Bundle.TotalSpace F V)]
  [inst_9 : (x : M) → TopologicalSpace (V x)] [inst_10 : FiberBundle F V] [inst_11 : (x : M) → AddCommGroup (V x)]
  [inst_12 : (x : M) → Module 𝕜 (V x)] [VectorBundle 𝕜 F V] {ι : Type u_7} {t : ι → (x : M) → V x} {s : Finset ι}
  {x₀ : M},
  (∀ i ∈ s, ContMDiffAt I (I.prod (modelWithCornersSelf 𝕜 F)) n (fun x => Bundle.TotalSpace.mk' F x (t i x)) x₀) →
    ContMDiffAt I (I.prod (modelWithCornersSelf 𝕜 F)) n (fun x => Bundle.TotalSpace.mk' F x (∑ i ∈ s, t i x)) x₀