∀ {ι : Type u_1} {π : ι → Type u_2} [inst : (i : ι) → CompleteAtomicBooleanAlgebra (π i)] {ι_1 : Type (max u_1 u_2)}
  {κ : ι_1 → Type (max u_1 u_2)} (f : (a : ι_1) → κ a → (i : ι) → π i), ⨅ a, ⨆ b, f a b = ⨆ g, ⨅ a, f a (g a)