Note that L is lattice-like. Suppose a b . Let a' , b' be elements of the carrier of L . Let a' , b' be elements of the carrier of L . Then b a .
L is upper-bounded.
L is lower-bounded. L is a distributive lattice. In the sequel L denotes a lower bound lattice, f , g denote functions from A into the carrier of L , and u denotes an element of the carrier of L . The join operation of L has a unity. In the sequel L denotes an upper bound lattice, f , g denote functions from A into the carrier of L , and u denotes an element of the carrier of L .