theorem Th4:
  ex i st frac(r-s) = frac(r) - frac(s) + i & (i = 0 or i = 1)
  proof
    frac(r-s) = frac(r)-frac(s)+Q or frac(r-s) = frac(r)-frac(s)+1
    by Th2,Th3;
    hence thesis;
  end;
