∀ {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} {F' : Type u_21} [inst_6 : NormedCommRing F']
  [inst_7 : NormedAlgebra 𝕜 F'] {ι : Type} {t : Finset ι} {f : ι → M → F'},
  (∀ i ∈ t, MDifferentiableOn I (modelWithCornersSelf 𝕜 F') (f i) s) →
    MDifferentiableOn I (modelWithCornersSelf 𝕜 F') (∏ i ∈ t, f i) s