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 Qnot_le_iff_lt: forall x y : Q, ~ (x <= y)%Q <-> (y < x)%Q.