∀ {ι : Type u_1} {α : Type u_2} {s : ι → Set α} [inst : SizeOf ι] [inst_1 : SizeOf α]
  [inst_2 : (a : ι) → (a_1 : α) → SizeOf (s a a_1)] (eq_of_mem : ∀ {x : α} {i j : ι}, x ∈ s i → x ∈ s j → i = j)
  (some : ι → α) (some_mem : ∀ (i : ι), some i ∈ s i) (index : α → ι) (mem_index : ∀ (x : α), x ∈ s (index x)),
  sizeOf { eq_of_mem := eq_of_mem, some := some, some_mem := some_mem, index := index, mem_index := mem_index } = 1