Show that if , then
The corresponding problem replacing the s with is shown here:
How to prove ?
The proof is not staggeringly difficult: The idea is to show (the tough part) that if then . The result then easily follows.
A pair of observations, both under the constraint of :
If then . This is proven for but I don't see how for
If then there are positive satisfying the constraint such that
So one would hope that the case, lying farther within the "valid" region, might be easier than but I have not been able to prove it.
Note that it is not always true, under our constraint, that , which if true would prove the case immediately.