∀ {α : Type u_2} {β : Type u_3} [inst : Min α] [inst_1 : Min β],
  InfHom.dual =
    { toFun := fun f => { toFun := ⇑f, map_sup' := ⋯ }, invFun := fun f => { toFun := ⇑f, map_inf' := ⋯ },
      left_inv := ⋯, right_inv := ⋯ }