Definition C_Ring_mixin :=
  Ring.Mixin _ _ _ Cmult_assoc Cmult_1_r Cmult_1_l Cmult_plus_distr_r Cmult_plus_distr_l.Canonical C_Ring :=
  Ring.Pack C (Ring.Class _ _ C_Ring_mixin) C.

Lemma Cmod_eq_0 : forall x, Cmod x = 0 -> x = 0.