 reserve X,a,b,c,x,y,z,t for set;
 reserve R for Relation;

theorem UApEmpty:
  for R being non empty RelStr holds
    (UAp R).{} = {}
  proof
    let R be non empty RelStr;
    (UAp R).{} = UAp {}R by ROUGHS_2:def 11
              .= {};
    hence thesis;
  end;
