∀ {α : Type u_2} {β : Type u_3} [inst : Lattice α] [inst_1 : BoundedOrder α] [inst_2 : Lattice β]
  [inst_3 : BoundedOrder β] (f : BoundedLatticeHom αᵒᵈ βᵒᵈ) (a : αᵒᵈ), (BoundedLatticeHom.dual.symm f) a = f a