A kind of converse of this theorem was proved by Anne C. Davis: If every order preserving function f : L → L on a lattice L has a fixed point, then L is a complete lattice.
这个定理的一种逆命题由 Anne C. Davis 证明了: 如果所有次序保持函数 f : L → L 有不动点，则 L 是完全格。