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 Th15:
  Sphere(x,r) c= cl_Ball(x,r)
proof
  reconsider e = x as Point of Euclid n by TOPREAL3:8;
  Sphere(x,r) = Sphere(e,r) & cl_Ball(x,r) = cl_Ball(e,r) by Th12,Th13;
  hence thesis by METRIC_1:15;
end;
