reserve n for Nat,
  a, b, r, w for Real,
  x, y, z for Point of TOP-REAL n,
  e for Point of Euclid n;

theorem Th16:
  Ball(x,r) \/ Sphere(x,r) = cl_Ball(x,r)
proof
  reconsider e = x as Point of Euclid n by TOPREAL3:8;
A1: cl_Ball(x,r) = cl_Ball(e,r) by Th12;
  Sphere(x,r) = Sphere(e,r) & Ball(x,r) = Ball(e,r) by Th11,Th13;
  hence thesis by A1,METRIC_1:16;
end;
