Definition CReal_from_cauchy (xn : nat -> CReal) (xcau : Un_cauchy_mod xn) : CReal :=
{|
  seq := CReal_from_cauchy_seq xn xcau;
  scale := CReal_from_cauchy_scale xn xcau;
  cauchy := CReal_from_cauchy_cauchy xn xcau;
  bound := CReal_from_cauchy_bound xn xcau
|}.

Lemma CRealAbsLUB : forall x y : CReal, x <= y /\ (- x) <= y <-> (CReal_abs x) <= y.