theorem Th24:
  for r being non zero Real holds Fr Ball(x,r) = Sphere(x,r)
proof
  let r be non zero Real;
  set P = Ball(x,r);
  thus Fr P = Cl P \ P by TOPS_1:42
    .= cl_Ball(x,r) \ P by Th23
    .= Sphere(x,r) by Th19;
end;
