(* This notation will be deprecated with a planned larger rework of Q lemma naming *)

(* Specifications: *)
Lemma Qpower_0_lt: forall (a : Q) (z : Z), 0 < a -> 0 < Qpower a z.
(** ** Relation of Qpower to 1 *)
Lemma Qpower_1_lt_pos:
forall (q : Q) (n : positive), (1<q)%Q -> (1 < q ^ (Z.pos n))%Q.
Lemma Qpower_1_lt:
forall (q : Q) (n : Z), (1<q)%Q -> (0<n)%Z -> (1 < q ^ n)%Q.
Lemma Qpower_1_le_pos:
forall (q : Q) (n : positive), (1<=q)%Q -> (1 <= q ^ (Z.pos n))%Q.
Lemma Qpower_1_le:
forall (q : Q) (n : Z), (1<=q)%Q -> (0<=n)%Z -> (1 <= q ^ n)%Q.