content: {-# LANGUAGE BangPatterns              #-}
  {-# LANGUAGE EmptyCase                 #-}
  {-# LANGUAGE EmptyDataDecls            #-}
  {-# LANGUAGE ExistentialQuantification #-}
  {-# LANGUAGE NoMonomorphismRestriction #-}
  {-# LANGUAGE OverloadedStrings         #-}
  {-# LANGUAGE PatternSynonyms           #-}
  {-# LANGUAGE RankNTypes                #-}
  {-# LANGUAGE ScopedTypeVariables       #-}
  
  {-# OPTIONS_GHC -Wno-overlapping-patterns #-}
  
  module MAlonzo.Code.Algebra.Properties.QQuasigroup where
  
  import Data.Text qualified
  import MAlonzo.Code.Agda.Builtin.Sigma qualified
  import MAlonzo.Code.Agda.Primitive qualified
  import MAlonzo.Code.Algebra.Bundles qualified
  import MAlonzo.Code.Algebra.Structures qualified
  import MAlonzo.Code.Relation.Binary.Bundles qualified
  import MAlonzo.Code.Relation.Binary.Reasoning.Base.Single qualified
  import MAlonzo.Code.Relation.Binary.Reasoning.Syntax qualified
  import MAlonzo.Code.Relation.Binary.Structures qualified
  import MAlonzo.RTE (AgdaAny, add64, addInt, coe, eq64, eqInt, erased, geqInt, lt64, ltInt, mul64,
                      mulInt, quot64, quotInt, rem64, remInt, sub64, subInt, word64FromNat,
                      word64ToNat)
  import MAlonzo.RTE qualified
  
  -- Algebra.Properties.Quasigroup._.Cancellative
  d_Cancellative_112 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_Quasigroup_4246 ->
    (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d_Cancellative_112 = erased
  -- Algebra.Properties.Quasigroup._.LeftCancellative
  d_LeftCancellative_144 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_Quasigroup_4246 ->
    (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d_LeftCancellative_144 = erased
  -- Algebra.Properties.Quasigroup._.RightCancellative
  d_RightCancellative_174 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_Quasigroup_4246 ->
    (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d_RightCancellative_174 = erased
  -- Algebra.Properties.Quasigroup.cancelˡ
  d_cancel'737'_256 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_Quasigroup_4246 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_cancel'737'_256 ~v0 ~v1 v2 v3 v4 v5 v6
    = du_cancel'737'_256 v2 v3 v4 v5 v6
  du_cancel'737'_256 ::
    MAlonzo.Code.Algebra.Bundles.T_Quasigroup_4246 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_cancel'737'_256 v0 v1 v2 v3 v4
    = coe
        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
        (\ v5 v6 v7 ->
           coe
             MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 v7)
        v2 v3
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
              (coe
                 MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                 (coe
                    MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                    (let v5
                           = MAlonzo.Code.Algebra.Bundles.d_isQuasigroup_4274 (coe v0) in
                     coe
                       (coe
                          MAlonzo.Code.Algebra.Structures.du_setoid_200
                          (coe MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v5)))))))
           (MAlonzo.Code.Relation.Binary.Structures.d_sym_36
              (coe
                 MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                 (let v5
                        = MAlonzo.Code.Algebra.Bundles.d_isQuasigroup_4274 (coe v0) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_setoid_200
                       (coe MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v5))))))
           v2
           (coe
              MAlonzo.Code.Algebra.Bundles.d__'92''92'__4270 v0 v1
              (coe MAlonzo.Code.Algebra.Bundles.d__'8729'__4268 v0 v1 v2))
           v3
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                    (coe
                       MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                       (let v5
                              = MAlonzo.Code.Algebra.Bundles.d_isQuasigroup_4274 (coe v0) in
                        coe
                          (coe
                             MAlonzo.Code.Algebra.Structures.du_setoid_200
                             (coe MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v5)))))))
              (coe
                 MAlonzo.Code.Algebra.Bundles.d__'92''92'__4270 v0 v1
                 (coe MAlonzo.Code.Algebra.Bundles.d__'8729'__4268 v0 v1 v2))
              (coe
                 MAlonzo.Code.Algebra.Bundles.d__'92''92'__4270 v0 v1
                 (coe MAlonzo.Code.Algebra.Bundles.d__'8729'__4268 v0 v1 v3))
              v3
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                    (coe
                       MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                       (coe
                          MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                          (let v5
                                 = MAlonzo.Code.Algebra.Bundles.d_isQuasigroup_4274 (coe v0) in
                           coe
                             (coe
                                MAlonzo.Code.Algebra.Structures.du_setoid_200
                                (coe MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v5)))))))
                 (coe
                    MAlonzo.Code.Algebra.Bundles.d__'92''92'__4270 v0 v1
                    (coe MAlonzo.Code.Algebra.Bundles.d__'8729'__4268 v0 v1 v3))
                 v3 v3
                 (let v5
                        = MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                            (coe
                               MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                               (let v5
                                      = MAlonzo.Code.Algebra.Bundles.d_isQuasigroup_4274 (coe v0) in
                                coe
                                  (coe
                                     MAlonzo.Code.Algebra.Structures.du_setoid_200
                                     (coe
                                        MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v5))))) in
                  coe
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                       (coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                          (coe v5))
                       (coe v3)))
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_leftDivides'691'_3012
                    (MAlonzo.Code.Algebra.Bundles.d_isQuasigroup_4274 (coe v0)) v1 v3))
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'92''92''45'cong'737'_2994
                 (coe MAlonzo.Code.Algebra.Bundles.d_isQuasigroup_4274 (coe v0))
                 (coe v1)
                 (coe MAlonzo.Code.Algebra.Bundles.d__'8729'__4268 v0 v1 v2)
                 (coe MAlonzo.Code.Algebra.Bundles.d__'8729'__4268 v0 v1 v3)
                 (coe v4)))
           (coe
              MAlonzo.Code.Algebra.Structures.du_leftDivides'691'_3012
              (MAlonzo.Code.Algebra.Bundles.d_isQuasigroup_4274 (coe v0)) v1 v2))
  -- Algebra.Properties.Quasigroup.cancelʳ
  d_cancel'691'_266 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_Quasigroup_4246 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_cancel'691'_266 ~v0 ~v1 v2 v3 v4 v5 v6
    = du_cancel'691'_266 v2 v3 v4 v5 v6
  du_cancel'691'_266 ::
    MAlonzo.Code.Algebra.Bundles.T_Quasigroup_4246 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_cancel'691'_266 v0 v1 v2 v3 v4
    = coe
        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
        (\ v5 v6 v7 ->
           coe
             MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 v7)
        v2 v3
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
              (coe
                 MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                 (coe
                    MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                    (let v5
                           = MAlonzo.Code.Algebra.Bundles.d_isQuasigroup_4274 (coe v0) in
                     coe
                       (coe
                          MAlonzo.Code.Algebra.Structures.du_setoid_200
                          (coe MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v5)))))))
           (MAlonzo.Code.Relation.Binary.Structures.d_sym_36
              (coe
                 MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                 (let v5
                        = MAlonzo.Code.Algebra.Bundles.d_isQuasigroup_4274 (coe v0) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_setoid_200
                       (coe MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v5))))))
           v2
           (coe
              MAlonzo.Code.Algebra.Bundles.d__'47''47'__4272 v0
              (coe MAlonzo.Code.Algebra.Bundles.d__'8729'__4268 v0 v2 v1) v1)
           v3
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                    (coe
                       MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                       (let v5
                              = MAlonzo.Code.Algebra.Bundles.d_isQuasigroup_4274 (coe v0) in
                        coe
                          (coe
                             MAlonzo.Code.Algebra.Structures.du_setoid_200
                             (coe MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v5)))))))
              (coe
                 MAlonzo.Code.Algebra.Bundles.d__'47''47'__4272 v0
                 (coe MAlonzo.Code.Algebra.Bundles.d__'8729'__4268 v0 v2 v1) v1)
              (coe
                 MAlonzo.Code.Algebra.Bundles.d__'47''47'__4272 v0
                 (coe MAlonzo.Code.Algebra.Bundles.d__'8729'__4268 v0 v3 v1) v1)
              v3
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                    (coe
                       MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                       (coe
                          MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                          (let v5
                                 = MAlonzo.Code.Algebra.Bundles.d_isQuasigroup_4274 (coe v0) in
                           coe
                             (coe
                                MAlonzo.Code.Algebra.Structures.du_setoid_200
                                (coe MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v5)))))))
                 (coe
                    MAlonzo.Code.Algebra.Bundles.d__'47''47'__4272 v0
                    (coe MAlonzo.Code.Algebra.Bundles.d__'8729'__4268 v0 v3 v1) v1)
                 v3 v3
                 (let v5
                        = MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                            (coe
                               MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                               (let v5
                                      = MAlonzo.Code.Algebra.Bundles.d_isQuasigroup_4274 (coe v0) in
                                coe
                                  (coe
                                     MAlonzo.Code.Algebra.Structures.du_setoid_200
                                     (coe
                                        MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v5))))) in
                  coe
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                       (coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                          (coe v5))
                       (coe v3)))
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_rightDivides'691'_3016
                    (MAlonzo.Code.Algebra.Bundles.d_isQuasigroup_4274 (coe v0)) v1 v3))
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'47''47''45'cong'691'_3006
                 (coe MAlonzo.Code.Algebra.Bundles.d_isQuasigroup_4274 (coe v0))
                 (coe v1)
                 (coe MAlonzo.Code.Algebra.Bundles.d__'8729'__4268 v0 v2 v1)
                 (coe MAlonzo.Code.Algebra.Bundles.d__'8729'__4268 v0 v3 v1)
                 (coe v4)))
           (coe
              MAlonzo.Code.Algebra.Structures.du_rightDivides'691'_3016
              (MAlonzo.Code.Algebra.Bundles.d_isQuasigroup_4274 (coe v0)) v1 v2))
  -- Algebra.Properties.Quasigroup.cancel
  d_cancel_276 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_Quasigroup_4246 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_cancel_276 ~v0 ~v1 v2 = du_cancel_276 v2
  du_cancel_276 ::
    MAlonzo.Code.Algebra.Bundles.T_Quasigroup_4246 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_cancel_276 v0
    = coe
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
        (coe du_cancel'737'_256 (coe v0)) (coe du_cancel'691'_266 (coe v0))
  -- Algebra.Properties.Quasigroup.y≈x\\z
  d_y'8776'x'92''92'z_284 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_Quasigroup_4246 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_y'8776'x'92''92'z_284 ~v0 ~v1 v2 v3 v4 v5 v6
    = du_y'8776'x'92''92'z_284 v2 v3 v4 v5 v6
  du_y'8776'x'92''92'z_284 ::
    MAlonzo.Code.Algebra.Bundles.T_Quasigroup_4246 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_y'8776'x'92''92'z_284 v0 v1 v2 v3 v4
    = coe
        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
        (\ v5 v6 v7 ->
           coe
             MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 v7)
        v2 (coe MAlonzo.Code.Algebra.Bundles.d__'92''92'__4270 v0 v1 v3)
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
              (coe
                 MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                 (coe
                    MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                    (let v5
                           = MAlonzo.Code.Algebra.Bundles.d_isQuasigroup_4274 (coe v0) in
                     coe
                       (coe
                          MAlonzo.Code.Algebra.Structures.du_setoid_200
                          (coe MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v5)))))))
           (MAlonzo.Code.Relation.Binary.Structures.d_sym_36
              (coe
                 MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                 (let v5
                        = MAlonzo.Code.Algebra.Bundles.d_isQuasigroup_4274 (coe v0) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_setoid_200
                       (coe MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v5))))))
           v2
           (coe
              MAlonzo.Code.Algebra.Bundles.d__'92''92'__4270 v0 v1
              (coe MAlonzo.Code.Algebra.Bundles.d__'8729'__4268 v0 v1 v2))
           (coe MAlonzo.Code.Algebra.Bundles.d__'92''92'__4270 v0 v1 v3)
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                    (coe
                       MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                       (let v5
                              = MAlonzo.Code.Algebra.Bundles.d_isQuasigroup_4274 (coe v0) in
                        coe
                          (coe
                             MAlonzo.Code.Algebra.Structures.du_setoid_200
                             (coe MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v5)))))))
              (coe
                 MAlonzo.Code.Algebra.Bundles.d__'92''92'__4270 v0 v1
                 (coe MAlonzo.Code.Algebra.Bundles.d__'8729'__4268 v0 v1 v2))
              (coe MAlonzo.Code.Algebra.Bundles.d__'92''92'__4270 v0 v1 v3)
              (coe MAlonzo.Code.Algebra.Bundles.d__'92''92'__4270 v0 v1 v3)
              (let v5
                     = MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                         (coe
                            MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                            (let v5
                                   = MAlonzo.Code.Algebra.Bundles.d_isQuasigroup_4274 (coe v0) in
                             coe
                               (coe
                                  MAlonzo.Code.Algebra.Structures.du_setoid_200
                                  (coe MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v5))))) in
               coe
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                       (coe v5))
                    (coe MAlonzo.Code.Algebra.Bundles.d__'92''92'__4270 v0 v1 v3)))
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'92''92''45'cong'737'_2994
                 (coe MAlonzo.Code.Algebra.Bundles.d_isQuasigroup_4274 (coe v0))
                 (coe v1)
                 (coe MAlonzo.Code.Algebra.Bundles.d__'8729'__4268 v0 v1 v2)
                 (coe v3) (coe v4)))
           (coe
              MAlonzo.Code.Algebra.Structures.du_leftDivides'691'_3012
              (MAlonzo.Code.Algebra.Bundles.d_isQuasigroup_4274 (coe v0)) v1 v2))
  -- Algebra.Properties.Quasigroup.x≈z//y
  d_x'8776'z'47''47'y_300 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_Quasigroup_4246 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_x'8776'z'47''47'y_300 ~v0 ~v1 v2 v3 v4 v5 v6
    = du_x'8776'z'47''47'y_300 v2 v3 v4 v5 v6
  du_x'8776'z'47''47'y_300 ::
    MAlonzo.Code.Algebra.Bundles.T_Quasigroup_4246 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_x'8776'z'47''47'y_300 v0 v1 v2 v3 v4
    = coe
        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
        (\ v5 v6 v7 ->
           coe
             MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 v7)
        v1 (coe MAlonzo.Code.Algebra.Bundles.d__'47''47'__4272 v0 v3 v2)
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
              (coe
                 MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                 (coe
                    MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                    (let v5
                           = MAlonzo.Code.Algebra.Bundles.d_isQuasigroup_4274 (coe v0) in
                     coe
                       (coe
                          MAlonzo.Code.Algebra.Structures.du_setoid_200
                          (coe MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v5)))))))
           (MAlonzo.Code.Relation.Binary.Structures.d_sym_36
              (coe
                 MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                 (let v5
                        = MAlonzo.Code.Algebra.Bundles.d_isQuasigroup_4274 (coe v0) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_setoid_200
                       (coe MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v5))))))
           v1
           (coe
              MAlonzo.Code.Algebra.Bundles.d__'47''47'__4272 v0
              (coe MAlonzo.Code.Algebra.Bundles.d__'8729'__4268 v0 v1 v2) v2)
           (coe MAlonzo.Code.Algebra.Bundles.d__'47''47'__4272 v0 v3 v2)
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                    (coe
                       MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                       (let v5
                              = MAlonzo.Code.Algebra.Bundles.d_isQuasigroup_4274 (coe v0) in
                        coe
                          (coe
                             MAlonzo.Code.Algebra.Structures.du_setoid_200
                             (coe MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v5)))))))
              (coe
                 MAlonzo.Code.Algebra.Bundles.d__'47''47'__4272 v0
                 (coe MAlonzo.Code.Algebra.Bundles.d__'8729'__4268 v0 v1 v2) v2)
              (coe MAlonzo.Code.Algebra.Bundles.d__'47''47'__4272 v0 v3 v2)
              (coe MAlonzo.Code.Algebra.Bundles.d__'47''47'__4272 v0 v3 v2)
              (let v5
                     = MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                         (coe
                            MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                            (let v5
                                   = MAlonzo.Code.Algebra.Bundles.d_isQuasigroup_4274 (coe v0) in
                             coe
                               (coe
                                  MAlonzo.Code.Algebra.Structures.du_setoid_200
                                  (coe MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v5))))) in
               coe
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                       (coe v5))
                    (coe MAlonzo.Code.Algebra.Bundles.d__'47''47'__4272 v0 v3 v2)))
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'47''47''45'cong'691'_3006
                 (coe MAlonzo.Code.Algebra.Bundles.d_isQuasigroup_4274 (coe v0))
                 (coe v2)
                 (coe MAlonzo.Code.Algebra.Bundles.d__'8729'__4268 v0 v1 v2)
                 (coe v3) (coe v4)))
           (coe
              MAlonzo.Code.Algebra.Structures.du_rightDivides'691'_3016
              (MAlonzo.Code.Algebra.Bundles.d_isQuasigroup_4274 (coe v0)) v2 v1))
  