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.AbelianGroup 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.Properties.Group qualified
  import MAlonzo.Code.Algebra.Properties.Loop qualified
  import MAlonzo.Code.Algebra.Properties.QQuasigroup 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.AbelianGroup._._//_
  d__'47''47'__14 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d__'47''47'__14 ~v0 ~v1 v2 = du__'47''47'__14 v2
  du__'47''47'__14 ::
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny
  du__'47''47'__14 v0
    = let v1 = MAlonzo.Code.Algebra.Bundles.d__'8729'__1658 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Bundles.d__'8315''185'_1662 (coe v0) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du__'47''47'__1098 (coe v1)
              (coe v2)))
  -- Algebra.Properties.AbelianGroup._.//-cong₂
  d_'47''47''45'cong'8322'_158 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'47''47''45'cong'8322'_158 ~v0 ~v1 v2
    = du_'47''47''45'cong'8322'_158 v2
  du_'47''47''45'cong'8322'_158 ::
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'47''47''45'cong'8322'_158 v0
    = coe
        MAlonzo.Code.Algebra.Properties.Group.du_'47''47''45'cong'8322'_522
        (coe MAlonzo.Code.Algebra.Bundles.du_group_1732 (coe v0))
  -- Algebra.Properties.AbelianGroup._.//-rightDivides
  d_'47''47''45'rightDivides_160 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'47''47''45'rightDivides_160 ~v0 ~v1 v2
    = du_'47''47''45'rightDivides_160 v2
  du_'47''47''45'rightDivides_160 ::
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'47''47''45'rightDivides_160 v0
    = coe
        MAlonzo.Code.Algebra.Properties.Group.du_'47''47''45'rightDivides_554
        (coe MAlonzo.Code.Algebra.Bundles.du_group_1732 (coe v0))
  -- Algebra.Properties.AbelianGroup._.//-rightDividesʳ
  d_'47''47''45'rightDivides'691'_162 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_'47''47''45'rightDivides'691'_162 ~v0 ~v1 v2
    = du_'47''47''45'rightDivides'691'_162 v2
  du_'47''47''45'rightDivides'691'_162 ::
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny
  du_'47''47''45'rightDivides'691'_162 v0
    = coe
        MAlonzo.Code.Algebra.Properties.Group.du_'47''47''45'rightDivides'691'_548
        (coe MAlonzo.Code.Algebra.Bundles.du_group_1732 (coe v0))
  -- Algebra.Properties.AbelianGroup._.//-rightDividesˡ
  d_'47''47''45'rightDivides'737'_164 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_'47''47''45'rightDivides'737'_164 ~v0 ~v1 v2
    = du_'47''47''45'rightDivides'737'_164 v2
  du_'47''47''45'rightDivides'737'_164 ::
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny
  du_'47''47''45'rightDivides'737'_164 v0
    = coe
        MAlonzo.Code.Algebra.Properties.Group.du_'47''47''45'rightDivides'737'_542
        (coe MAlonzo.Code.Algebra.Bundles.du_group_1732 (coe v0))
  -- Algebra.Properties.AbelianGroup._.\\-cong₂
  d_'92''92''45'cong'8322'_166 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'92''92''45'cong'8322'_166 ~v0 ~v1 v2
    = du_'92''92''45'cong'8322'_166 v2
  du_'92''92''45'cong'8322'_166 ::
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'92''92''45'cong'8322'_166 v0
    = coe
        MAlonzo.Code.Algebra.Properties.Group.du_'92''92''45'cong'8322'_516
        (coe MAlonzo.Code.Algebra.Bundles.du_group_1732 (coe v0))
  -- Algebra.Properties.AbelianGroup._.\\-leftDivides
  d_'92''92''45'leftDivides_168 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'92''92''45'leftDivides_168 ~v0 ~v1 v2
    = du_'92''92''45'leftDivides_168 v2
  du_'92''92''45'leftDivides_168 ::
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'92''92''45'leftDivides_168 v0
    = coe
        MAlonzo.Code.Algebra.Properties.Group.du_'92''92''45'leftDivides_540
        (coe MAlonzo.Code.Algebra.Bundles.du_group_1732 (coe v0))
  -- Algebra.Properties.AbelianGroup._.\\-leftDividesʳ
  d_'92''92''45'leftDivides'691'_170 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_'92''92''45'leftDivides'691'_170 ~v0 ~v1 v2
    = du_'92''92''45'leftDivides'691'_170 v2
  du_'92''92''45'leftDivides'691'_170 ::
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny
  du_'92''92''45'leftDivides'691'_170 v0
    = coe
        MAlonzo.Code.Algebra.Properties.Group.du_'92''92''45'leftDivides'691'_534
        (coe MAlonzo.Code.Algebra.Bundles.du_group_1732 (coe v0))
  -- Algebra.Properties.AbelianGroup._.\\-leftDividesˡ
  d_'92''92''45'leftDivides'737'_172 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_'92''92''45'leftDivides'737'_172 ~v0 ~v1 v2
    = du_'92''92''45'leftDivides'737'_172 v2
  du_'92''92''45'leftDivides'737'_172 ::
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny
  du_'92''92''45'leftDivides'737'_172 v0
    = coe
        MAlonzo.Code.Algebra.Properties.Group.du_'92''92''45'leftDivides'737'_528
        (coe MAlonzo.Code.Algebra.Bundles.du_group_1732 (coe v0))
  -- Algebra.Properties.AbelianGroup._.\\≗flip-//⇒comm
  d_'92''92''8791'flip'45''47''47''8658'comm_174 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
  d_'92''92''8791'flip'45''47''47''8658'comm_174 ~v0 ~v1 v2
    = du_'92''92''8791'flip'45''47''47''8658'comm_174 v2
  du_'92''92''8791'flip'45''47''47''8658'comm_174 ::
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
  du_'92''92''8791'flip'45''47''47''8658'comm_174 v0
    = coe
        MAlonzo.Code.Algebra.Properties.Group.du_'92''92''8791'flip'45''47''47''8658'comm_680
        (coe MAlonzo.Code.Algebra.Bundles.du_group_1732 (coe v0))
  -- Algebra.Properties.AbelianGroup._.comm⇒\\≗flip-//
  d_comm'8658''92''92''8791'flip'45''47''47'_176 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
  d_comm'8658''92''92''8791'flip'45''47''47'_176 ~v0 ~v1 v2
    = du_comm'8658''92''92''8791'flip'45''47''47'_176 v2
  du_comm'8658''92''92''8791'flip'45''47''47'_176 ::
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
  du_comm'8658''92''92''8791'flip'45''47''47'_176 v0
    = coe
        MAlonzo.Code.Algebra.Properties.Group.du_comm'8658''92''92''8791'flip'45''47''47'_692
        (coe MAlonzo.Code.Algebra.Bundles.du_group_1732 (coe v0))
  -- Algebra.Properties.AbelianGroup._.identity-unique
  d_identity'45'unique_178 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 -> AgdaAny
  d_identity'45'unique_178 ~v0 ~v1 v2 = du_identity'45'unique_178 v2
  du_identity'45'unique_178 ::
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 -> AgdaAny
  du_identity'45'unique_178 v0
    = let v1
            = coe MAlonzo.Code.Algebra.Bundles.du_group_1732 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Properties.Loop.du_identity'45'unique_326
           (coe MAlonzo.Code.Algebra.Properties.Group.du_loop_574 (coe v1)))
  -- Algebra.Properties.AbelianGroup._.identityʳ-unique
  d_identity'691''45'unique_180 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_identity'691''45'unique_180 ~v0 ~v1 v2
    = du_identity'691''45'unique_180 v2
  du_identity'691''45'unique_180 ::
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_identity'691''45'unique_180 v0
    = let v1
            = coe MAlonzo.Code.Algebra.Bundles.du_group_1732 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Properties.Loop.du_identity'691''45'unique_316
           (coe MAlonzo.Code.Algebra.Properties.Group.du_loop_574 (coe v1)))
  -- Algebra.Properties.AbelianGroup._.identityˡ-unique
  d_identity'737''45'unique_182 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_identity'737''45'unique_182 ~v0 ~v1 v2
    = du_identity'737''45'unique_182 v2
  du_identity'737''45'unique_182 ::
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_identity'737''45'unique_182 v0
    = let v1
            = coe MAlonzo.Code.Algebra.Bundles.du_group_1732 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Properties.Loop.du_identity'737''45'unique_304
           (coe MAlonzo.Code.Algebra.Properties.Group.du_loop_574 (coe v1)))
  -- Algebra.Properties.AbelianGroup._.inverseʳ-unique
  d_inverse'691''45'unique_184 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_inverse'691''45'unique_184 ~v0 ~v1 v2
    = du_inverse'691''45'unique_184 v2
  du_inverse'691''45'unique_184 ::
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_inverse'691''45'unique_184 v0
    = coe
        MAlonzo.Code.Algebra.Properties.Group.du_inverse'691''45'unique_600
        (coe MAlonzo.Code.Algebra.Bundles.du_group_1732 (coe v0))
  -- Algebra.Properties.AbelianGroup._.inverseˡ-unique
  d_inverse'737''45'unique_186 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_inverse'737''45'unique_186 ~v0 ~v1 v2
    = du_inverse'737''45'unique_186 v2
  du_inverse'737''45'unique_186 ::
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_inverse'737''45'unique_186 v0
    = coe
        MAlonzo.Code.Algebra.Properties.Group.du_inverse'737''45'unique_588
        (coe MAlonzo.Code.Algebra.Bundles.du_group_1732 (coe v0))
  -- Algebra.Properties.AbelianGroup._.isLoop
  d_isLoop_188 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    MAlonzo.Code.Algebra.Structures.T_IsLoop_3026
  d_isLoop_188 ~v0 ~v1 v2 = du_isLoop_188 v2
  du_isLoop_188 ::
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    MAlonzo.Code.Algebra.Structures.T_IsLoop_3026
  du_isLoop_188 v0
    = coe
        MAlonzo.Code.Algebra.Properties.Group.du_isLoop_572
        (coe MAlonzo.Code.Algebra.Bundles.du_group_1732 (coe v0))
  -- Algebra.Properties.AbelianGroup._.isQuasigroup
  d_isQuasigroup_190 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_2944
  d_isQuasigroup_190 ~v0 ~v1 v2 = du_isQuasigroup_190 v2
  du_isQuasigroup_190 ::
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_2944
  du_isQuasigroup_190 v0
    = coe
        MAlonzo.Code.Algebra.Properties.Group.du_isQuasigroup_556
        (coe MAlonzo.Code.Algebra.Bundles.du_group_1732 (coe v0))
  -- Algebra.Properties.AbelianGroup._.loop
  d_loop_192 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    MAlonzo.Code.Algebra.Bundles.T_Loop_4346
  d_loop_192 ~v0 ~v1 v2 = du_loop_192 v2
  du_loop_192 ::
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    MAlonzo.Code.Algebra.Bundles.T_Loop_4346
  du_loop_192 v0
    = coe
        MAlonzo.Code.Algebra.Properties.Group.du_loop_574
        (coe MAlonzo.Code.Algebra.Bundles.du_group_1732 (coe v0))
  -- Algebra.Properties.AbelianGroup._.quasigroup
  d_quasigroup_194 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    MAlonzo.Code.Algebra.Bundles.T_Quasigroup_4246
  d_quasigroup_194 ~v0 ~v1 v2 = du_quasigroup_194 v2
  du_quasigroup_194 ::
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    MAlonzo.Code.Algebra.Bundles.T_Quasigroup_4246
  du_quasigroup_194 v0
    = coe
        MAlonzo.Code.Algebra.Properties.Group.du_quasigroup_558
        (coe MAlonzo.Code.Algebra.Bundles.du_group_1732 (coe v0))
  -- Algebra.Properties.AbelianGroup._.x∙y⁻¹≈ε⇒x≈y
  d_x'8729'y'8315''185''8776'ε'8658'x'8776'y_196 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_x'8729'y'8315''185''8776'ε'8658'x'8776'y_196 ~v0 ~v1 v2
    = du_x'8729'y'8315''185''8776'ε'8658'x'8776'y_196 v2
  du_x'8729'y'8315''185''8776'ε'8658'x'8776'y_196 ::
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_x'8729'y'8315''185''8776'ε'8658'x'8776'y_196 v0
    = coe
        MAlonzo.Code.Algebra.Properties.Group.du_x'8729'y'8315''185''8776'ε'8658'x'8776'y_624
        (coe MAlonzo.Code.Algebra.Bundles.du_group_1732 (coe v0))
  -- Algebra.Properties.AbelianGroup._.x≈y⇒x∙y⁻¹≈ε
  d_x'8776'y'8658'x'8729'y'8315''185''8776'ε_198 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_x'8776'y'8658'x'8729'y'8315''185''8776'ε_198 ~v0 ~v1 v2
    = du_x'8776'y'8658'x'8729'y'8315''185''8776'ε_198 v2
  du_x'8776'y'8658'x'8729'y'8315''185''8776'ε_198 ::
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_x'8776'y'8658'x'8729'y'8315''185''8776'ε_198 v0
    = coe
        MAlonzo.Code.Algebra.Properties.Group.du_x'8776'y'8658'x'8729'y'8315''185''8776'ε_636
        (coe MAlonzo.Code.Algebra.Bundles.du_group_1732 (coe v0))
  -- Algebra.Properties.AbelianGroup._.x≈z//y
  d_x'8776'z'47''47'y_200 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_x'8776'z'47''47'y_200 ~v0 ~v1 v2 = du_x'8776'z'47''47'y_200 v2
  du_x'8776'z'47''47'y_200 ::
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_x'8776'z'47''47'y_200 v0
    = let v1
            = coe MAlonzo.Code.Algebra.Bundles.du_group_1732 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Properties.QQuasigroup.du_x'8776'z'47''47'y_300
           (coe
              MAlonzo.Code.Algebra.Properties.Group.du_quasigroup_558 (coe v1)))
  -- Algebra.Properties.AbelianGroup._.y≈x\\z
  d_y'8776'x'92''92'z_202 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_y'8776'x'92''92'z_202 ~v0 ~v1 v2 = du_y'8776'x'92''92'z_202 v2
  du_y'8776'x'92''92'z_202 ::
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_y'8776'x'92''92'z_202 v0
    = let v1
            = coe MAlonzo.Code.Algebra.Bundles.du_group_1732 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Properties.QQuasigroup.du_y'8776'x'92''92'z_284
           (coe
              MAlonzo.Code.Algebra.Properties.Group.du_quasigroup_558 (coe v1)))
  -- Algebra.Properties.AbelianGroup._.ε⁻¹≈ε
  d_ε'8315''185''8776'ε_204 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 -> AgdaAny
  d_ε'8315''185''8776'ε_204 ~v0 ~v1 v2
    = du_ε'8315''185''8776'ε_204 v2
  du_ε'8315''185''8776'ε_204 ::
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 -> AgdaAny
  du_ε'8315''185''8776'ε_204 v0
    = coe
        MAlonzo.Code.Algebra.Properties.Group.du_ε'8315''185''8776'ε_608
        (coe MAlonzo.Code.Algebra.Bundles.du_group_1732 (coe v0))
  -- Algebra.Properties.AbelianGroup._.⁻¹-anti-homo-//
  d_'8315''185''45'anti'45'homo'45''47''47'_206 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_'8315''185''45'anti'45'homo'45''47''47'_206 ~v0 ~v1 v2
    = du_'8315''185''45'anti'45'homo'45''47''47'_206 v2
  du_'8315''185''45'anti'45'homo'45''47''47'_206 ::
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny
  du_'8315''185''45'anti'45'homo'45''47''47'_206 v0
    = coe
        MAlonzo.Code.Algebra.Properties.Group.du_'8315''185''45'anti'45'homo'45''47''47'_660
        (coe MAlonzo.Code.Algebra.Bundles.du_group_1732 (coe v0))
  -- Algebra.Properties.AbelianGroup._.⁻¹-anti-homo-\\
  d_'8315''185''45'anti'45'homo'45''92''92'_208 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_'8315''185''45'anti'45'homo'45''92''92'_208 ~v0 ~v1 v2
    = du_'8315''185''45'anti'45'homo'45''92''92'_208 v2
  du_'8315''185''45'anti'45'homo'45''92''92'_208 ::
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny
  du_'8315''185''45'anti'45'homo'45''92''92'_208 v0
    = coe
        MAlonzo.Code.Algebra.Properties.Group.du_'8315''185''45'anti'45'homo'45''92''92'_670
        (coe MAlonzo.Code.Algebra.Bundles.du_group_1732 (coe v0))
  -- Algebra.Properties.AbelianGroup._.⁻¹-anti-homo-∙
  d_'8315''185''45'anti'45'homo'45''8729'_210 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_'8315''185''45'anti'45'homo'45''8729'_210 ~v0 ~v1 v2
    = du_'8315''185''45'anti'45'homo'45''8729'_210 v2
  du_'8315''185''45'anti'45'homo'45''8729'_210 ::
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny
  du_'8315''185''45'anti'45'homo'45''8729'_210 v0
    = coe
        MAlonzo.Code.Algebra.Properties.Group.du_'8315''185''45'anti'45'homo'45''8729'_650
        (coe MAlonzo.Code.Algebra.Bundles.du_group_1732 (coe v0))
  -- Algebra.Properties.AbelianGroup._.⁻¹-injective
  d_'8315''185''45'injective_212 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8315''185''45'injective_212 ~v0 ~v1 v2
    = du_'8315''185''45'injective_212 v2
  du_'8315''185''45'injective_212 ::
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8315''185''45'injective_212 v0
    = coe
        MAlonzo.Code.Algebra.Properties.Group.du_'8315''185''45'injective_644
        (coe MAlonzo.Code.Algebra.Bundles.du_group_1732 (coe v0))
  -- Algebra.Properties.AbelianGroup._.⁻¹-involutive
  d_'8315''185''45'involutive_214 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny
  d_'8315''185''45'involutive_214 ~v0 ~v1 v2
    = du_'8315''185''45'involutive_214 v2
  du_'8315''185''45'involutive_214 ::
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny
  du_'8315''185''45'involutive_214 v0
    = coe
        MAlonzo.Code.Algebra.Properties.Group.du_'8315''185''45'involutive_618
        (coe MAlonzo.Code.Algebra.Bundles.du_group_1732 (coe v0))
  -- Algebra.Properties.AbelianGroup._.⁻¹-selfInverse
  d_'8315''185''45'selfInverse_216 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8315''185''45'selfInverse_216 ~v0 ~v1 v2
    = du_'8315''185''45'selfInverse_216 v2
  du_'8315''185''45'selfInverse_216 ::
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8315''185''45'selfInverse_216 v0
    = coe
        MAlonzo.Code.Algebra.Properties.Group.du_'8315''185''45'selfInverse_610
        (coe MAlonzo.Code.Algebra.Bundles.du_group_1732 (coe v0))
  -- Algebra.Properties.AbelianGroup._.cancel
  d_cancel_218 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_cancel_218 ~v0 ~v1 v2 = du_cancel_218 v2
  du_cancel_218 ::
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_cancel_218 v0
    = let v1
            = coe MAlonzo.Code.Algebra.Bundles.du_group_1732 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Properties.QQuasigroup.du_cancel_276
           (coe
              MAlonzo.Code.Algebra.Properties.Group.du_quasigroup_558 (coe v1)))
  -- Algebra.Properties.AbelianGroup._.cancelʳ
  d_cancel'691'_220 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_cancel'691'_220 ~v0 ~v1 v2 = du_cancel'691'_220 v2
  du_cancel'691'_220 ::
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_cancel'691'_220 v0
    = let v1
            = coe MAlonzo.Code.Algebra.Bundles.du_group_1732 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Properties.QQuasigroup.du_cancel'691'_266
           (coe
              MAlonzo.Code.Algebra.Properties.Group.du_quasigroup_558 (coe v1)))
  -- Algebra.Properties.AbelianGroup._.cancelˡ
  d_cancel'737'_222 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_cancel'737'_222 ~v0 ~v1 v2 = du_cancel'737'_222 v2
  du_cancel'737'_222 ::
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_cancel'737'_222 v0
    = let v1
            = coe MAlonzo.Code.Algebra.Bundles.du_group_1732 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Properties.QQuasigroup.du_cancel'737'_256
           (coe
              MAlonzo.Code.Algebra.Properties.Group.du_quasigroup_558 (coe v1)))
  -- Algebra.Properties.AbelianGroup.⁻¹-anti-homo‿-
  d_'8315''185''45'anti'45'homo'8255''45'_228 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_'8315''185''45'anti'45'homo'8255''45'_228 ~v0 ~v1 v2
    = du_'8315''185''45'anti'45'homo'8255''45'_228 v2
  du_'8315''185''45'anti'45'homo'8255''45'_228 ::
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny
  du_'8315''185''45'anti'45'homo'8255''45'_228 v0
    = coe
        MAlonzo.Code.Algebra.Properties.Group.du_'8315''185''45'anti'45'homo'45''47''47'_660
        (coe MAlonzo.Code.Algebra.Bundles.du_group_1732 (coe v0))
  -- Algebra.Properties.AbelianGroup.xyx⁻¹≈y
  d_xyx'8315''185''8776'y_234 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_xyx'8315''185''8776'y_234 ~v0 ~v1 v2 v3 v4
    = du_xyx'8315''185''8776'y_234 v2 v3 v4
  du_xyx'8315''185''8776'y_234 ::
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny
  du_xyx'8315''185''8776'y_234 v0 v1 v2
    = coe
        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
        (\ v3 v4 v5 ->
           coe
             MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 v5)
        (coe
           MAlonzo.Code.Algebra.Bundles.d__'8729'__1658 v0
           (coe MAlonzo.Code.Algebra.Bundles.d__'8729'__1658 v0 v1 v2)
           (coe MAlonzo.Code.Algebra.Bundles.d__'8315''185'_1662 v0 v1))
        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 v3
                           = MAlonzo.Code.Algebra.Bundles.d_isAbelianGroup_1664 (coe v0) in
                     coe
                       (let v4
                              = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v3) in
                        coe
                          (let v5
                                 = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v4) in
                           coe
                             (let v6
                                    = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v5) in
                              coe
                                (coe
                                   MAlonzo.Code.Algebra.Structures.du_setoid_200
                                   (coe
                                      MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v6))))))))))
           (coe
              MAlonzo.Code.Algebra.Bundles.d__'8729'__1658 v0
              (coe MAlonzo.Code.Algebra.Bundles.d__'8729'__1658 v0 v1 v2)
              (coe MAlonzo.Code.Algebra.Bundles.d__'8315''185'_1662 v0 v1))
           (coe
              MAlonzo.Code.Algebra.Bundles.d__'8729'__1658 v0
              (coe MAlonzo.Code.Algebra.Bundles.d__'8729'__1658 v0 v2 v1)
              (coe MAlonzo.Code.Algebra.Bundles.d__'8315''185'_1662 v0 v1))
           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 v3
                              = MAlonzo.Code.Algebra.Bundles.d_isAbelianGroup_1664 (coe v0) in
                        coe
                          (let v4
                                 = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v3) in
                           coe
                             (let v5
                                    = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v4) in
                              coe
                                (let v6
                                       = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v5) in
                                 coe
                                   (coe
                                      MAlonzo.Code.Algebra.Structures.du_setoid_200
                                      (coe
                                         MAlonzo.Code.Algebra.Structures.d_isMagma_480
                                         (coe v6))))))))))
              (coe
                 MAlonzo.Code.Algebra.Bundles.d__'8729'__1658 v0
                 (coe MAlonzo.Code.Algebra.Bundles.d__'8729'__1658 v0 v2 v1)
                 (coe MAlonzo.Code.Algebra.Bundles.d__'8315''185'_1662 v0 v1))
              (coe
                 MAlonzo.Code.Algebra.Bundles.d__'8729'__1658 v0 v2
                 (coe
                    MAlonzo.Code.Algebra.Bundles.d__'8729'__1658 v0 v1
                    (coe MAlonzo.Code.Algebra.Bundles.d__'8315''185'_1662 v0 v1)))
              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 v3
                                 = MAlonzo.Code.Algebra.Bundles.d_isAbelianGroup_1664 (coe v0) in
                           coe
                             (let v4
                                    = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v3) in
                              coe
                                (let v5
                                       = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v4) in
                                 coe
                                   (let v6
                                          = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                                              (coe v5) in
                                    coe
                                      (coe
                                         MAlonzo.Code.Algebra.Structures.du_setoid_200
                                         (coe
                                            MAlonzo.Code.Algebra.Structures.d_isMagma_480
                                            (coe v6))))))))))
                 (coe
                    MAlonzo.Code.Algebra.Bundles.d__'8729'__1658 v0 v2
                    (coe
                       MAlonzo.Code.Algebra.Bundles.d__'8729'__1658 v0 v1
                       (coe MAlonzo.Code.Algebra.Bundles.d__'8315''185'_1662 v0 v1)))
                 (coe
                    MAlonzo.Code.Algebra.Bundles.d__'8729'__1658 v0 v2
                    (MAlonzo.Code.Algebra.Bundles.d_ε_1660 (coe v0)))
                 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 v3
                                    = MAlonzo.Code.Algebra.Bundles.d_isAbelianGroup_1664 (coe v0) in
                              coe
                                (let v4
                                       = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v3) in
                                 coe
                                   (let v5
                                          = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                                              (coe v4) in
                                    coe
                                      (let v6
                                             = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                                                 (coe v5) in
                                       coe
                                         (coe
                                            MAlonzo.Code.Algebra.Structures.du_setoid_200
                                            (coe
                                               MAlonzo.Code.Algebra.Structures.d_isMagma_480
                                               (coe v6))))))))))
                    (coe
                       MAlonzo.Code.Algebra.Bundles.d__'8729'__1658 v0 v2
                       (MAlonzo.Code.Algebra.Bundles.d_ε_1660 (coe v0)))
                    v2 v2
                    (let v3
                           = MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                               (coe
                                  MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                                  (let v3
                                         = MAlonzo.Code.Algebra.Bundles.d_isAbelianGroup_1664
                                             (coe v0) in
                                   coe
                                     (let v4
                                            = MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                                                (coe v3) in
                                      coe
                                        (let v5
                                               = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                                                   (coe v4) in
                                         coe
                                           (let v6
                                                  = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                                                      (coe v5) in
                                            coe
                                              (coe
                                                 MAlonzo.Code.Algebra.Structures.du_setoid_200
                                                 (coe
                                                    MAlonzo.Code.Algebra.Structures.d_isMagma_480
                                                    (coe v6)))))))) in
                     coe
                       (coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                          (coe
                             MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                             (coe v3))
                          (coe v2)))
                    (let v3
                           = MAlonzo.Code.Algebra.Bundles.d_isAbelianGroup_1664 (coe v0) in
                     coe
                       (let v4
                              = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v3) in
                        coe
                          (coe
                             MAlonzo.Code.Algebra.Structures.du_identity'691'_728
                             (MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v4)) v2))))
                 (let v3
                        = MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                            (coe
                               MAlonzo.Code.Algebra.Bundles.d_isAbelianGroup_1664 (coe v0)) in
                  coe
                    (let v4
                           = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v3) in
                     coe
                       (let v5
                              = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v4) in
                        coe
                          (coe
                             MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                             (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v5))
                             (coe v2)
                             (coe
                                MAlonzo.Code.Algebra.Bundles.d__'8729'__1658 v0 v1
                                (coe MAlonzo.Code.Algebra.Bundles.d__'8315''185'_1662 v0 v1))
                             (coe MAlonzo.Code.Algebra.Bundles.d_ε_1660 (coe v0))
                             (let v6
                                    = MAlonzo.Code.Algebra.Bundles.d_isAbelianGroup_1664 (coe v0) in
                              coe
                                (coe
                                   MAlonzo.Code.Algebra.Structures.du_inverse'691'_1108
                                   (MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v6)) v1)))))))
              (coe
                 MAlonzo.Code.Algebra.Structures.d_assoc_482
                 (MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                          (coe
                             MAlonzo.Code.Algebra.Bundles.d_isAbelianGroup_1664 (coe v0)))))
                 v2 v1
                 (coe MAlonzo.Code.Algebra.Bundles.d__'8315''185'_1662 v0 v1)))
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                      (coe
                         MAlonzo.Code.Algebra.Bundles.d_isAbelianGroup_1664 (coe v0)) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v4) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                       (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v5))
                       (coe MAlonzo.Code.Algebra.Bundles.d__'8315''185'_1662 v0 v1)
                       (coe MAlonzo.Code.Algebra.Bundles.d__'8729'__1658 v0 v1 v2)
                       (coe MAlonzo.Code.Algebra.Bundles.d__'8729'__1658 v0 v2 v1)
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_comm_1146
                          (MAlonzo.Code.Algebra.Bundles.d_isAbelianGroup_1664 (coe v0)) v1
                          v2))))))
  -- Algebra.Properties.AbelianGroup.⁻¹-∙-comm
  d_'8315''185''45''8729''45'comm_244 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_'8315''185''45''8729''45'comm_244 ~v0 ~v1 v2 v3 v4
    = du_'8315''185''45''8729''45'comm_244 v2 v3 v4
  du_'8315''185''45''8729''45'comm_244 ::
    MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny
  du_'8315''185''45''8729''45'comm_244 v0 v1 v2
    = coe
        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
        (\ v3 v4 v5 ->
           coe
             MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 v5)
        (coe
           MAlonzo.Code.Algebra.Bundles.d__'8729'__1658 v0
           (coe MAlonzo.Code.Algebra.Bundles.d__'8315''185'_1662 v0 v1)
           (coe MAlonzo.Code.Algebra.Bundles.d__'8315''185'_1662 v0 v2))
        (coe
           MAlonzo.Code.Algebra.Bundles.d__'8315''185'_1662 v0
           (coe MAlonzo.Code.Algebra.Bundles.d__'8729'__1658 v0 v1 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 v3
                           = MAlonzo.Code.Algebra.Bundles.d_isAbelianGroup_1664 (coe v0) in
                     coe
                       (let v4
                              = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v3) in
                        coe
                          (let v5
                                 = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v4) in
                           coe
                             (let v6
                                    = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v5) in
                              coe
                                (coe
                                   MAlonzo.Code.Algebra.Structures.du_setoid_200
                                   (coe
                                      MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v6))))))))))
           (MAlonzo.Code.Relation.Binary.Structures.d_sym_36
              (coe
                 MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                 (let v3
                        = MAlonzo.Code.Algebra.Bundles.d_isAbelianGroup_1664 (coe v0) in
                  coe
                    (let v4
                           = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v3) in
                     coe
                       (let v5
                              = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v4) in
                        coe
                          (let v6
                                 = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v5) in
                           coe
                             (coe
                                MAlonzo.Code.Algebra.Structures.du_setoid_200
                                (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v6)))))))))
           (coe
              MAlonzo.Code.Algebra.Bundles.d__'8729'__1658 v0
              (coe MAlonzo.Code.Algebra.Bundles.d__'8315''185'_1662 v0 v1)
              (coe MAlonzo.Code.Algebra.Bundles.d__'8315''185'_1662 v0 v2))
           (coe
              MAlonzo.Code.Algebra.Bundles.d__'8315''185'_1662 v0
              (coe MAlonzo.Code.Algebra.Bundles.d__'8729'__1658 v0 v2 v1))
           (coe
              MAlonzo.Code.Algebra.Bundles.d__'8315''185'_1662 v0
              (coe MAlonzo.Code.Algebra.Bundles.d__'8729'__1658 v0 v1 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 v3
                              = MAlonzo.Code.Algebra.Bundles.d_isAbelianGroup_1664 (coe v0) in
                        coe
                          (let v4
                                 = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v3) in
                           coe
                             (let v5
                                    = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v4) in
                              coe
                                (let v6
                                       = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v5) in
                                 coe
                                   (coe
                                      MAlonzo.Code.Algebra.Structures.du_setoid_200
                                      (coe
                                         MAlonzo.Code.Algebra.Structures.d_isMagma_480
                                         (coe v6))))))))))
              (coe
                 MAlonzo.Code.Algebra.Bundles.d__'8315''185'_1662 v0
                 (coe MAlonzo.Code.Algebra.Bundles.d__'8729'__1658 v0 v2 v1))
              (coe
                 MAlonzo.Code.Algebra.Bundles.d__'8315''185'_1662 v0
                 (coe MAlonzo.Code.Algebra.Bundles.d__'8729'__1658 v0 v1 v2))
              (coe
                 MAlonzo.Code.Algebra.Bundles.d__'8315''185'_1662 v0
                 (coe MAlonzo.Code.Algebra.Bundles.d__'8729'__1658 v0 v1 v2))
              (let v3
                     = MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                         (coe
                            MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                            (let v3
                                   = MAlonzo.Code.Algebra.Bundles.d_isAbelianGroup_1664 (coe v0) in
                             coe
                               (let v4
                                      = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v3) in
                                coe
                                  (let v5
                                         = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v4) in
                                   coe
                                     (let v6
                                            = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                                                (coe v5) in
                                      coe
                                        (coe
                                           MAlonzo.Code.Algebra.Structures.du_setoid_200
                                           (coe
                                              MAlonzo.Code.Algebra.Structures.d_isMagma_480
                                              (coe v6)))))))) in
               coe
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                       (coe v3))
                    (coe
                       MAlonzo.Code.Algebra.Bundles.d__'8315''185'_1662 v0
                       (coe MAlonzo.Code.Algebra.Bundles.d__'8729'__1658 v0 v1 v2))))
              (coe
                 MAlonzo.Code.Algebra.Structures.d_'8315''185''45'cong_1054
                 (MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                    (coe MAlonzo.Code.Algebra.Bundles.d_isAbelianGroup_1664 (coe v0)))
                 (coe MAlonzo.Code.Algebra.Bundles.d__'8729'__1658 v0 v2 v1)
                 (coe MAlonzo.Code.Algebra.Bundles.d__'8729'__1658 v0 v1 v2)
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_comm_1146
                    (MAlonzo.Code.Algebra.Bundles.d_isAbelianGroup_1664 (coe v0)) v2
                    v1)))
           (coe
              MAlonzo.Code.Algebra.Properties.Group.du_'8315''185''45'anti'45'homo'45''8729'_650
              (coe MAlonzo.Code.Algebra.Bundles.du_group_1732 (coe v0)) (coe v2)
              (coe v1)))
  