I am looking at linear combination of two forecasts (Bates and Granger, 1969). I would like to understand how to prove that the expected squared error associated with the optimal combination weight is smaller than the minimum of 2 forecast variances. I have come across it quite a number of times in literature and textbook. However, after giving it much thought, I am still unable to prove it.
Below I have attached the proof. I have successfully managed to prove up to step 7.28. I am just left the last line boxed in blue to understand. Thank you!