Definition CReal_mult (x y : CReal) : CReal :=
{|
seq := CReal_mult_seq x y;
scale := CReal_mult_scale x y;
cauchy := CReal_mult_cauchy x y;
bound := CReal_mult_bound x y
|}.
Infix "*" := CReal_mult : CReal_scope.

Lemma CReal_scale_sep0_limit : forall (x : CReal) (n : Z),
(2 * (2^n)%Q < seq x n)%Q
-> (n <= scale x - 2)%Z.