(** This upper bound can also be seen as a convexity proof for x^c : image of (a+b)/2 is below the middle of the images of a and b *)

(* Specifications: *)
Lemma pow_add_upper : forall a b c, 0<=a -> 0<=b -> 0<c ->
(a+b)^c <= 2^(pred c) * (a^c + b^c).