(** ** Conversion from scientific notation *)
(** Russian peasant exponentiation *)
Fixpoint pos_pow (x y: positive) : positive :=
match y with
| xH => x
| xO y => Pos.square (pos_pow x y)
| xI y => Pos.mul x (Pos.square (pos_pow x y))
end.

(* Specifications: *)
Lemma pos_pow_spec:
forall x y, Z.pos (pos_pow x y) = Z.pos x ^ Z.pos y.