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_NR0 :
forall (x:Z) (n:nat), (0 <= x)%Z -> (0 <= Zpower_nat x n)%Z.