(** ** Compatibility of Qpower with relational operators *)

(* Specifications: *)
Lemma Qpower_lt_compat_l:
forall (q : Q) (n m : Z), (n < m)%Z -> (1<q)%Q -> (q ^ n < q ^ m)%Q.
Lemma Qpower_le_compat_l:
forall (q : Q) (n m : Z), (n <= m)%Z -> (1<=q)%Q -> (q ^ n <= q ^ m)%Q.
Lemma Qpower_lt_compat_l_inv:
forall (q : Q) (n m : Z), (q ^ n < q ^ m)%Q -> (1<q)%Q -> (n < m)%Z.
Lemma Qpower_le_compat_l_inv:
forall (q : Q) (n m : Z), (q ^ n <= q ^ m)%Q -> (1<q)%Q -> (n <= m)%Z.