Let L be a relational structure and x be a set. Then x is a directed subset of L op if and only if x is a filtered subset of L . Let L be a relational structure and x be a set. Let L be a relational structure and x be a set. L op is upper-bounded.
L is upper-bounded.
For every relational structure L holds L is bounded iff L op is bounded. Let L be a bounded lattice and x , y be elements of L . Then y is a complement of x if and only if y is a complement of x . For every bounded lattice L holds L is complemented iff L op is complemented. Let L be a lower-bounded relational structure.