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 Rcauchy_complete : forall (xn : nat -> CReal),
Un_cauchy_mod xn
-> { l : CReal  &  seq_cv xn l }.