∀ {α : Type u_1} {β : Type u_2} [inst : Min α] [inst_1 : Top α] [inst_2 : Min β] [inst_3 : Top β],
  Function.RightInverse (fun f => { toInfHom := InfHom.dual.symm f.toSupHom, map_top' := ⋯ }) fun f =>
    { toSupHom := InfHom.dual f.toInfHom, map_bot' := ⋯ }