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

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