theorem Th48:
  Ball(|[a,b]|,r) = inside_of_circle(a,b,r)
proof
  reconsider e = |[a,b]| as Point of Euclid 2 by TOPREAL3:8;
  thus Ball(|[a,b]|,r) = Ball(e,r) by Th11
    .= inside_of_circle(a,b,r) by Th46;
end;
