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.