∀ {α : Type u_1} {ι : Type u_2} [inst : GeneralizedBooleanAlgebra α] [inst_1 : Preorder ι]
  [inst_2 : LocallyFiniteOrderBot ι] {f : ι → α} {i : ι}, (∀ j < i, Disjoint (f j) (f i)) → disjointed f i = f i