proposition: Theorem Zlt_powerRZ : forall (e : R) (n m : Z), (1 <= e)%R -> (powerRZ e n < powerRZ e m)%R -> (n < m)%Z.
proof: Proof. intros e n m H' H'0. case (Zle_or_lt m n); auto; intros Z1. contradict H'0. apply Rle_not_lt. apply Rle_powerRZ; auto. Qed.
imports: Reals ZArith List PeanoNat Psatz