Canonical dvdz_oppPred d := OpprPred (dvdz_zmod_closed d).
Canonical dvdz_zmodPred d := ZmodPred (dvdz_zmod_closed d).

Lemma divzDl m n d :
(d %| m)%Z -> ((m + n) %/ d)%Z = (m %/ d)%Z + (n %/ d)%Z.