Canonical pi_one_quot_morph rqT := PiMorph (pi_oner rqT).Canonical pi_mul_quot_morph rqT := PiMorph2 (pi_mulr rqT).Notation RingQuotType o mul Q mix :=
  (@RingQuotType_pack _ _ _ _ _ o mul Q _ _ _ _ id id mix).Notation RingQuotMixin Q m1 mM :=
  (@RingQuotMixin_pack _ _ _ _ _ _ _ Q _ _ id _ _ id (zmod_quot_mixinP _) m1 mM).Canonical pi_rmorphism := AddRMorphism pi_is_multiplicative.Record unit_ring_quot_class_of (Q : Type) : Type := UnitRingQuotClass {
  unit_ring_quot_quot_class :> quot_class_of T Q;
  unit_ring_quot_ring_class :> GRing.UnitRing.class_of Q;
  unit_ring_quot_mixin :> unit_ring_quot_mixin_of
    unit_ring_quot_quot_class unit_ring_quot_ring_class
}.Record unit_ring_quot_class_of (Q : Type) : Type := UnitRingQuotClass {
  unit_ring_quot_quot_class :> quot_class_of T Q;
  unit_ring_quot_ring_class :> GRing.UnitRing.class_of Q;
  unit_ring_quot_mixin :> unit_ring_quot_mixin_of
    unit_ring_quot_quot_class unit_ring_quot_ring_class
}.Record unit_ring_quot_class_of (Q : Type) : Type := UnitRingQuotClass {
  unit_ring_quot_quot_class :> quot_class_of T Q;
  unit_ring_quot_ring_class :> GRing.UnitRing.class_of Q;
  unit_ring_quot_mixin :> unit_ring_quot_mixin_of
    unit_ring_quot_quot_class unit_ring_quot_ring_class
}.Record unit_ring_quot_class_of (Q : Type) : Type := UnitRingQuotClass {
  unit_ring_quot_quot_class :> quot_class_of T Q;
  unit_ring_quot_ring_class :> GRing.UnitRing.class_of Q;
  unit_ring_quot_mixin :> unit_ring_quot_mixin_of
    unit_ring_quot_quot_class unit_ring_quot_ring_class
}.Record unit_ring_quot_class_of (Q : Type) : Type := UnitRingQuotClass {
  unit_ring_quot_quot_class :> quot_class_of T Q;
  unit_ring_quot_ring_class :> GRing.UnitRing.class_of Q;
  unit_ring_quot_mixin :> unit_ring_quot_mixin_of
    unit_ring_quot_quot_class unit_ring_quot_ring_class
}.Structure unitRingQuotType : Type := UnitRingQuotTypePack {
  unit_ring_quot_sort :> Type;
  _ : unit_ring_quot_class_of unit_ring_quot_sort;
 
}.Structure unitRingQuotType : Type := UnitRingQuotTypePack {
  unit_ring_quot_sort :> Type;
  _ : unit_ring_quot_class_of unit_ring_quot_sort;
 
}.Structure unitRingQuotType : Type := UnitRingQuotTypePack {
  unit_ring_quot_sort :> Type;
  _ : unit_ring_quot_class_of unit_ring_quot_sort;
 
}.Definition unit_ring_ring_quot_class rqT (rqc : unit_ring_quot_class_of rqT) :
  ring_quot_class_of eqT zeroT oppT addT oneT mulT rqT := RingQuotClass rqc.Definition unit_ring_zmod_quot_class rqT (rqc : unit_ring_quot_class_of rqT) :
  zmod_quot_class_of eqT zeroT oppT addT rqT := ZmodQuotClass rqc.Definition unit_ring_eq_quot_class rqT (rqc : unit_ring_quot_class_of rqT) :
  eq_quot_class_of eqT rqT := EqQuotClass rqc.Canonical unitRingQuotType_eqType rqT :=
  Equality.Pack (unit_ring_quot_class rqT).Canonical unitRingQuotType_choiceType rqT :=
  Choice.Pack (unit_ring_quot_class rqT).Canonical unitRingQuotType_zmodType rqT :=
  GRing.Zmodule.Pack (unit_ring_quot_class rqT).Canonical unitRingQuotType_ringType rqT :=
  GRing.Ring.Pack (unit_ring_quot_class rqT).Canonical unitRingQuotType_unitRingType rqT :=
  GRing.UnitRing.Pack (unit_ring_quot_class rqT).Canonical unitRingQuotType_quotType rqT :=
  QuotTypePack (unit_ring_quot_class rqT).Canonical unitRingQuotType_eqQuotType rqT :=
  EqQuotTypePack (unit_ring_eq_quot_class (unit_ring_quot_class rqT)).Canonical unitRingQuotType_zmodQuotType rqT :=
  ZmodQuotTypePack (unit_ring_zmod_quot_class (unit_ring_quot_class rqT)).Canonical unitRingQuotType_ringQuotType rqT :=
  RingQuotTypePack (unit_ring_ring_quot_class (unit_ring_quot_class rqT)).

Lemma unit_ring_quot_mixinP rqT : unit_ring_quot_mixin_of (unit_ring_quot_class rqT) (unit_ring_quot_class rqT).