∀ {α : Type u_1} [inst : SizeOf α] (sets : Set (Set α)) (univ_sets : Set.univ ∈ sets)
  (sets_of_superset : ∀ {x y : Set α}, x ∈ sets → x ⊆ y → y ∈ sets)
  (inter_sets : ∀ {x y : Set α}, x ∈ sets → y ∈ sets → x ∩ y ∈ sets),
  sizeOf { sets := sets, univ_sets := univ_sets, sets_of_superset := sets_of_superset, inter_sets := inter_sets } =
    1 + sizeOf univ_sets