
theorem Th26:
  for L be with_suprema antisymmetric transitive RelStr for S be
  non empty join-closed Subset of L holds subrelstr S is with_suprema
proof
  let L be with_suprema antisymmetric transitive RelStr;
  let S be non empty join-closed Subset of L;
  subrelstr S is non empty join-inheriting full SubRelStr of L by Def2;
  hence thesis;
end;
