(*******************************)
(** *       Power              *)
(*******************************)
(*********)
Infix "^" := pow : R_scope.

Lemma pow_lt_1_zero :
forall x:R,
Rabs x < 1 ->
forall y:R,
0 < y ->
exists N : nat, (forall n:nat, (n >= N)%nat -> Rabs (x ^ n) < y).