(** Monotonicity results, both ways *)

(* Specifications: *)
Lemma pow_lt_mono_l_iff : forall a b c, 0<=a -> 0<=b -> 0<c ->
(a<b <-> a^c < b^c).
Lemma pow_le_mono_l_iff : forall a b c, 0<=a -> 0<=b -> 0<c ->
(a<=b <-> a^c <= b^c).
Lemma pow_lt_mono_r_iff : forall a b c, 1<a -> 0<=c ->
(b<c <-> a^b < a^c).
Lemma pow_le_mono_r_iff : forall a b c, 1<a -> 0<=c ->
(b<=c <-> a^b <= a^c).