∀ {α : Type u_1} {β : Type u_2} [inst : CompleteLattice α] [inst_1 : CompleteLattice β],
  Function.RightInverse (fun f => { tosInfHom := sSupHom.dual f.tosSupHom, map_sSup' := ⋯ }) fun f =>
    { tosInfHom := sSupHom.dual f.tosSupHom, map_sSup' := ⋯ }