intros r n H'.
case (Req_dec (Rabs r) 1); auto; intros H'1.
case (Rdichotomy _ _ H'1); intros H'2.
generalize H'; case n; auto.
intros n0 H'0.
cut (r <> 0%R); [ intros Eq1 | idtac ].
2: Contradict H'0; auto with arith.
2: simpl in |- *; rewrite H'0; rewrite Rmult_0_l; auto with real.
cut (Rabs r <> 0%R); [ intros Eq2 | apply Rabs_no_R0 ]; auto.
absurd (Rabs (/ r) ^ 0 < Rabs (/ r) ^ S n0)%R; auto.
replace (Rabs (/ r) ^ S n0)%R with 1%R.
simpl in |- *; apply Rlt_irrefl; auto.
rewrite Rabs_Rinv; auto.
rewrite <- Rinv_pow; auto.
rewrite RPow_abs; auto.
rewrite H'0; rewrite Rabs_right; auto with real.
apply Rlt_pow; auto with arith.
rewrite Rabs_Rinv; auto.
apply Rmult_lt_reg_l with (r := Rabs r).
case (Rabs_pos r); auto.
intros H'3; case Eq2; auto.
rewrite Rmult_1_r; rewrite Rinv_r; auto with real.
generalize H'; case n; auto.
intros n0 H'0.
cut (r <> 0%R); [ intros Eq1 | auto with real ].
2: Contradict H'0; simpl in |- *; rewrite H'0; rewrite Rmult_0_l;
auto with real.
cut (Rabs r <> 0%R); [ intros Eq2 | apply Rabs_no_R0 ]; auto.
absurd (Rabs r ^ 0 < Rabs r ^ S n0)%R; auto with real arith.
repeat rewrite RPow_abs; rewrite H'0; simpl in |- *; auto with real.
Qed.

(* Specifications: *)
Theorem Zpower_NR0 :
forall (e : BinInt.Z) (n : nat), (0 <= e)%Z -> (0 <= Zpower_nat e n)%Z.
Theorem Zpower_NR0 :
forall (e : Z) (n : nat), (0 <= e)%Z -> (0 <= Zpower_nat e n)%Z.