(** Note: the <= in the conclusion is likely tight *)

Lemma CReal_from_cauchy_seq_bound :
forall (xn : nat -> CReal) (xcau : Un_cauchy_mod xn) (i j : Z),
(Qabs (CReal_from_cauchy_seq xn xcau i - CReal_from_cauchy_seq xn xcau j) <= 1)%Q.