intuition.
eapply rat_inf_limit_comp.
eauto.
symmetry.
trivial.
eapply ratInverse_continuous.
trivial.
trivial.
Qed.

Lemma rat_inf_limit_exp_0 : forall (f : nat -> Rat -> Prop) a,
rat_inf_limit f a ->
~ 1 <= a ->
(forall n, exists r, f n r) ->
rat_inf_limit (fun n => (expRat_rel (f n) n)) 0.