Canonical pi_unit_quot_morph rqT := PiMono1 (pi_unitr rqT).Canonical pi_inv_quot_morph rqT := PiMorph1 (pi_invr rqT).Notation UnitRingQuotType u i Q mix :=
  (@UnitRingQuotType_pack _ _ _ _ _ _ _ u i Q _ _ _ _ id id mix).Notation UnitRingQuotMixin Q mU mV :=
  (@UnitRingQuotMixin_pack _ _ _ _ _ _ _ _ _ Q
    _ _ id _ _ id (zmod_quot_mixinP _) mU mV).

Lemma idealr_closed_nontrivial R S : @idealr_closed R S -> proper_ideal S.