Definition CReal_abs (x : CReal) : CReal :=
{|
  seq := CReal_abs_seq x;
  scale := CReal_abs_scale x;
  cauchy := CReal_abs_cauchy x;
  bound := CReal_abs_bound x
|}.

Lemma CRealLt_RQ_from_single_dist : forall (r : CReal) (q : Q) (n :Z), (2^n < q - seq r n)%Q -> r < inject_Q q.