∀ {ι : Type u_1} {ι' : Type u_2} {α : Type u_3} [inst : Preorder ι'] [Nonempty ι'] [IsDirectedOrder ι']
  [inst_3 : Order.Coframe α] {s : Set ι},
  s.Finite → ∀ {f : ι → ι' → α}, (∀ i ∈ s, Antitone (f i)) → ⨅ j, ⨆ i ∈ s, f i j = ⨆ i ∈ s, ⨅ j, f i j