intros e n m H' H'0.
case H'; intros E1.
case (Zle_lt_or_eq _ _ H'0); intros E2.
apply Rlt_le; auto with real.
rewrite <- E2; auto with real.
repeat rewrite <- E1; repeat rewrite powerRZ_R1; auto with real.
Qed.

(* Specifications: *)
Theorem Zlt_powerRZ :
forall (e : R) (n m : BinInt.Z),
(1 <= e)%R -> (powerRZ e n < powerRZ e m)%R -> (n < m)%Z.
Theorem Zlt_powerRZ :
forall (e : R) (n m : Z),
(1 <= e)%R -> (powerRZ e n < powerRZ e m)%R -> (n < m)%Z.