Definition CReal_from_cauchy_cm (n : Z) : positive :=
  match n with
    | Z0
    | Zpos _ => 1%positive
    | Zneg p => p
    end.

Lemma CReal_from_cauchy_cm_mono : forall (n p : Z), (p <= n)%Z -> (CReal_from_cauchy_cm n <= CReal_from_cauchy_cm p)%positive.