
theorem
  for a be light positive Real, n be heavy positive Real holds
  ((1+a) to_power n) /(1 + a to_power n) <
    (1 - a to_power n)/((1-a) to_power n)
  proof
    let a be light positive Real, n be heavy positive Real;
    ((1+a) to_power n)*((1-a) to_power n) <
      (1 + a to_power n)*(1 - a to_power n) by IL1;
    hence thesis by XREAL_1:106;
  end;
