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 bpow_plus_1 :
forall e : Z, (bpow (e + 1) = IZR r * bpow e)%R.