case (Zle_lt_or_eq _ _ H'); clear H'; intros H'.
apply Rlt_le; auto with real.
rewrite <- H'; auto with real.
Qed.
Hint Resolve Rle_IZR: real.

Theorem Rlt_IZRO : forall p : Z, (0 < p)%Z -> (0 < IZR p)%R.
intros p H; replace 0%R with (IZR 0); auto with real.