intros e n m; case n; case m; simpl in |- *;
try (unfold Zlt in |- *; intros; discriminate); auto with real.
intros p p0 H' H'0; apply Rlt_pow; auto with real.
apply Pnat.nat_of_P_lt_Lt_compare_morphism; auto.
intros p H' H'0; replace 1%R with (/ 1)%R; auto with real.
intros p p0 H' H'0; apply Rlt_trans with (r2 := 1%R).
replace 1%R with (/ 1)%R; auto with real.
apply Rlt_pow_R1; auto with real.
intros p p0 H' H'0; apply Rinv_1_lt_contravar; auto with real.
apply Rlt_pow; auto with real.
apply Pnat.nat_of_P_lt_Lt_compare_morphism; rewrite BinPos.ZC4; auto.
Qed.
Hint Resolve Rlt_powerRZ: real.

Theorem Rpow_R1 :
forall (r : R) (z : BinInt.Z),
r <> 0%R -> powerRZ r z = 1%R -> Rabs r = 1%R \/ z = 0%Z.