(1) Let L be a non empty reflexive transitive relational structure and x, y be elements of L. If x ≤ y, then compactbelow(x)⊆ compactbelow(y). (2) For every non empty reflexive relational structure L and for every element x of L holds compactbelow(x) is a subset of CompactSublatt(L). (3) For every relational structure L and for every relational substructure S of L holds every subset of S is a s...
