 The dual notion is often called antitone, anti-monotone, or order-reversing.Hence, an antitone function "f" satisfies the property

for all "x" and "y" in its domain.A constant function is both monotone and antitone; conversely, if "f" is both monotone and antitone, and if the domain of "f" is a lattice, then "f" must be constant.