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 CRealLt_QR_to_single_dist : forall (q : Q) (x : CReal) (n : Z), inject_Q q < x -> (-(2^n) <= seq x n - q)%Q.