(* Strict inequality on CReal is in sort Type, for example
   used in the computation of division. *)
Definition CReal_mult_lt_0_compat : forall x y : CReal,
    0 < x -> 0 < y -> 0 < x * y
  := fun x y Hx Hy => exist _ (proj1_sig Hx + proj1_sig Hy - 1)%Z
                        (CReal_mult_lt_0_compat_correct
                           x y Hx Hy).

Lemma CReal_mult_proper_r : forall x y z : CReal, y == z -> y * x == z * x.