intros n m; case m; simpl in |- *; auto with zarith.
intros p H'; elim (nat_of_P p); simpl in |- *; auto with zarith.
intros n0 H'0; rewrite <- H'0; simpl in |- *; auto with zarith.
rewrite <- Rmult_IZR; auto.
intros p H'; Contradict H'; auto with zarith.
Qed.

(* Specifications: *)
Theorem powerRZ_R1 : forall n : Z, powerRZ 1 n = 1%R.
intros n; case n; simpl in |- *; auto.