reserve x,y for Real,
  u,v,w for set,
  r for positive Real;

theorem Th13:
  for n being Element of NAT for a being Point of TOP-REAL n for r
  being positive Real holds a in Ball(a,r)
proof
  let n be Element of NAT;
  let a be Point of TOP-REAL n;
  let r be positive Real;
  a-a = 0.TOP-REAL n by RLVECT_1:5;
  then |.a-a.| = 0 by EUCLID_2:39;
  hence thesis by TOPREAL9:7;
end;
