reserve a,b,c,x,y,z for object,X,Y,Z for set,
  n for Nat,
  i,j for Integer,
  r,r1,r2,r3,s for Real,
  c1,c2 for Complex,
  p for Point of TOP-REAL n;

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;
