
theorem Th57:
  for V being RealUnitarySpace holds LattStr (# Subspaces(V),
    SubJoin(V), SubMeet(V) #) is 01_Lattice
proof
  let V be RealUnitarySpace;
  LattStr (# Subspaces(V), SubJoin(V), SubMeet(V) #) is lower-bounded
  upper-bounded Lattice by Th55,Th56;
  hence thesis;
end;
