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

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