theorem
  L1 c= L2 & O1 c= O2 implies L1|O1 c= L2|O2
  proof
    assume L1 c= L2 & O1 c= O2; then
    L1|O1 c= L2|O1 & L2|O1 c= L2|O2 by RELAT_1:123,124;
    hence thesis;
  end;
