Definition CReal_from_cauchy_scale (xn : nat -> CReal) (xcau : Un_cauchy_mod xn) : Z :=
  Qbound_lt_ZExp2 (Qabs (CReal_from_cauchy_seq xn xcau (-1)) + 2)%Q.

Lemma CReal_from_cauchy_bound : forall (xn : nat -> CReal) (xcau : Un_cauchy_mod xn), QBound (CReal_from_cauchy_seq xn xcau) (CReal_from_cauchy_scale xn xcau).