Definition powerRZ (x:R) (n:Z) :=
  match n with
    | Z0 => 1
    | Zpos p => x ^ Pos.to_nat p
    | Zneg p => / x ^ Pos.to_nat p
  end.Local Infix "^Z" := powerRZ (at level 30, right associativity) : R_scope.

Lemma Zpower_pos_powerRZ : forall n m, IZR (Z.pow_pos n m) = IZR n ^Z Zpos m.