Canonical Cnat_addrPred := AddrPred Cnat_semiring.
Canonical Cnat_mulrPred := MulrPred Cnat_semiring.
Canonical Cnat_semiringPred := SemiringPred Cnat_semiring.

(* Specifications: *)
Lemma Cnat_ge0 x : x \in Cnat -> 0 <= x.
Lemma Cnat_mul_eq1 x y :
x \in Cnat -> y \in Cnat -> (x * y == 1) = (x == 1) && (y == 1).