(** Well-used function called bpow for computing the power function #&beta;#^e *)
Definition bpow e :=
  match e with
  | Zpos p => Z2R (Zpower_pos r p)
  | Zneg p => Rinv (Z2R (Zpower_pos r p))
  | Z0 => 1%R
  end.

Theorem lt_bpow : forall e1 e2 : Z, (bpow e1 < bpow e2)%R -> (e1 < e2)%Z.