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 powerRZ_inv' x alpha : powerRZ (/ x) alpha = Rinv (powerRZ x alpha).