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.