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.