(** Power and nullity *)

(* Specifications: *)
Lemma pow_eq_0 : forall a b, 0<=b -> a^b == 0 -> a == 0.
Lemma pow_nonzero : forall a b, a~=0 -> 0<=b -> a^b ~= 0.
Lemma pow_eq_0_iff : forall a b, a^b == 0 <-> b<0 \/ (0<b /\ a==0).
(** Power and addition, multiplication *)
Lemma pow_add_r : forall a b c, 0<=b -> 0<=c ->
a^(b+c) == a^b * a^c.
Lemma pow_mul_l : forall a b c,
(a*b)^c == a^c * b^c.
Lemma pow_mul_r : forall a b c, 0<=b -> 0<=c ->
a^(b*c) == (a^b)^c.