Definition continuous_at(f : Rat -> Rat -> Prop)(c : Rat) :=
  forall v, f c v ->
    rat_limit f c v.

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.