
theorem
  for a be light positive Real holds 1+a < 1/(1 - a)
  proof
    let a be light positive Real;
    1 - a*a < 1 - 0 by XREAL_1:10; then
    (1+a)*(1-a) < 1 & 1 - a > 0;
    hence thesis by XREAL_1:81;
  end;
