intros f' k l cvfk eps ep; destruct (cvfk eps ep) as [N Pn].
exists (N + k)%nat; intros n nN; assert (tmp: (n = (n - k) + k)%nat).
- rewrite Nat.sub_add;[ | apply Nat.le_trans with (N + k)%nat]; auto with arith.
- rewrite tmp; apply Pn; apply Nat.le_add_le_sub_r; assumption.
Qed.

Lemma CV_shift' :
forall f k l, Un_cv f l -> Un_cv (fun n => f (n + k)%nat) l.