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_red_scale: forall (a : Z -> Q) (b : Z) (c : QCauchySeq a) (d : QBound a b), scale (mkCReal a b c d) = b.