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.