Definition CReal_from_cauchy_seq (xn : nat -> CReal) (xcau : Un_cauchy_mod xn) (n : Z) : Q :=
  let p := CReal_from_cauchy_cm n in
  let (q, _) := xcau (4 * 2^p)%positive in
  seq (xn q) (Z.neg p - 2)%Z.

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.