∀ {α : Type u_3} {α' : Type u_2} {β : α → Type u_4} {β' : α' → Type u_1} [inst : DecidableEq α]
  [inst_1 : DecidableEq α'] {f : α → α'} (g : (a : α) → β a → β' (f a)) (a : α),
  List.dlookup (f a) (List.map (Sigma.map f g) []) = Option.map (g a) (List.dlookup a [])