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_mult_lt_0_compat_correct : forall (x y : CReal) (Hx : 0 < x) (Hy : 0 < y), (2 * 2^(proj1_sig Hx + proj1_sig Hy - 1)%Z < seq (x * y)%CReal (proj1_sig Hx + proj1_sig Hy - 1)%Z - seq (inject_Q 0) (proj1_sig Hx + proj1_sig Hy - 1)%Z)%Q.