(** For any a>1, the a^x function is above the identity function *)

(* Specifications: *)
Lemma pow_gt_lin_r : forall a b, 1<a -> 0<=b -> b < a^b.
(** Someday, we should say something about the full Newton formula. In the meantime, we can at least provide some inequalities about (a+b)^c. *)
Lemma pow_add_lower : forall a b c, 0<=a -> 0<=b -> 0<c ->
a^c + b^c <= (a+b)^c.