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_lt : forall (x:R) (z:Z), 0 < x -> 0 < x ^Z z.