{-# 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.Lattice.Bundles where

import MAlonzo.RTE (coe, erased, AgdaAny, addInt, subInt, mulInt,
                    quotInt, remInt, geqInt, ltInt, eqInt, add64, sub64, mul64, quot64,
                    rem64, lt64, eq64, word64FromNat, word64ToNat)
import qualified MAlonzo.RTE
import qualified Data.Text
import qualified MAlonzo.Code.Agda.Builtin.Equality
import qualified MAlonzo.Code.Agda.Builtin.Sigma
import qualified MAlonzo.Code.Agda.Primitive
import qualified MAlonzo.Code.Algebra.Bundles
import qualified MAlonzo.Code.Algebra.Bundles.Raw
import qualified MAlonzo.Code.Algebra.Consequences.Base
import qualified MAlonzo.Code.Algebra.Lattice.Bundles.Raw
import qualified MAlonzo.Code.Algebra.Lattice.Structures
import qualified MAlonzo.Code.Algebra.Structures
import qualified MAlonzo.Code.Relation.Binary.Bundles
import qualified MAlonzo.Code.Relation.Binary.Structures

-- Algebra.Lattice.Bundles.Semilattice
d_Semilattice_10 :: p -> p -> ()
d_Semilattice_10 p
a0 p
a1 = ()
data T_Semilattice_10
  = C_constructor_84 (AgdaAny -> AgdaAny -> AgdaAny)
                     MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
-- Algebra.Lattice.Bundles.Semilattice.Carrier
d_Carrier_24 :: T_Semilattice_10 -> ()
d_Carrier_24 :: T_Semilattice_10 -> ()
d_Carrier_24 = T_Semilattice_10 -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.Semilattice._≈_
d__'8776'__26 :: T_Semilattice_10 -> AgdaAny -> AgdaAny -> ()
d__'8776'__26 :: T_Semilattice_10 -> AgdaAny -> AgdaAny -> ()
d__'8776'__26 = T_Semilattice_10 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.Semilattice._∙_
d__'8729'__28 :: T_Semilattice_10 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__28 :: T_Semilattice_10 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__28 T_Semilattice_10
v0
  = case T_Semilattice_10 -> T_Semilattice_10
forall a b. a -> b
coe T_Semilattice_10
v0 of
      C_constructor_84 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsCommutativeBand_612
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_Semilattice_10
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.Semilattice.isSemilattice
d_isSemilattice_30 ::
  T_Semilattice_10 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
d_isSemilattice_30 :: T_Semilattice_10 -> T_IsCommutativeBand_612
d_isSemilattice_30 T_Semilattice_10
v0
  = case T_Semilattice_10 -> T_Semilattice_10
forall a b. a -> b
coe T_Semilattice_10
v0 of
      C_constructor_84 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsCommutativeBand_612
v4 -> T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v4
      T_Semilattice_10
_ -> T_IsCommutativeBand_612
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.Semilattice._.assoc
d_assoc_34 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semilattice_10 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_34 :: ()
-> ()
-> T_Semilattice_10
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_assoc_34 ~()
v0 ~()
v1 T_Semilattice_10
v2 = T_Semilattice_10 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_34 T_Semilattice_10
v2
du_assoc_34 ::
  T_Semilattice_10 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_34 :: T_Semilattice_10 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_34 T_Semilattice_10
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_Semilattice_10 -> T_IsCommutativeBand_612
d_isSemilattice_30 (T_Semilattice_10 -> T_Semilattice_10
forall a b. a -> b
coe T_Semilattice_10
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_498
         ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
            ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v1))))
-- Algebra.Lattice.Bundles.Semilattice._.comm
d_comm_36 :: T_Semilattice_10 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_36 :: T_Semilattice_10 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_36 T_Semilattice_10
v0
  = (T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_622
      ((T_Semilattice_10 -> T_IsCommutativeBand_612) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10 -> T_IsCommutativeBand_612
d_isSemilattice_30 (T_Semilattice_10 -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10
v0))
-- Algebra.Lattice.Bundles.Semilattice._.idem
d_idem_38 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semilattice_10 -> AgdaAny -> AgdaAny
d_idem_38 :: () -> () -> T_Semilattice_10 -> AgdaAny -> AgdaAny
d_idem_38 ~()
v0 ~()
v1 T_Semilattice_10
v2 = T_Semilattice_10 -> AgdaAny -> AgdaAny
du_idem_38 T_Semilattice_10
v2
du_idem_38 :: T_Semilattice_10 -> AgdaAny -> AgdaAny
du_idem_38 :: T_Semilattice_10 -> AgdaAny -> AgdaAny
du_idem_38 T_Semilattice_10
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_Semilattice_10 -> T_IsCommutativeBand_612
d_isSemilattice_30 (T_Semilattice_10 -> T_Semilattice_10
forall a b. a -> b
coe T_Semilattice_10
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsBand_526 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_526 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_536
         ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v1)))
-- Algebra.Lattice.Bundles.Semilattice._.isBand
d_isBand_40 ::
  T_Semilattice_10 -> MAlonzo.Code.Algebra.Structures.T_IsBand_526
d_isBand_40 :: T_Semilattice_10 -> T_IsBand_526
d_isBand_40 T_Semilattice_10
v0
  = (T_IsCommutativeBand_612 -> T_IsBand_526)
-> AgdaAny -> T_IsBand_526
forall a b. a -> b
coe
      T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620
      ((T_Semilattice_10 -> T_IsCommutativeBand_612) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10 -> T_IsCommutativeBand_612
d_isSemilattice_30 (T_Semilattice_10 -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10
v0))
-- Algebra.Lattice.Bundles.Semilattice._.isEquivalence
d_isEquivalence_42 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semilattice_10 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_42 :: () -> () -> T_Semilattice_10 -> T_IsEquivalence_28
d_isEquivalence_42 ~()
v0 ~()
v1 T_Semilattice_10
v2 = T_Semilattice_10 -> T_IsEquivalence_28
du_isEquivalence_42 T_Semilattice_10
v2
du_isEquivalence_42 ::
  T_Semilattice_10 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_42 :: T_Semilattice_10 -> T_IsEquivalence_28
du_isEquivalence_42 T_Semilattice_10
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_Semilattice_10 -> T_IsCommutativeBand_612
d_isSemilattice_30 (T_Semilattice_10 -> T_Semilattice_10
forall a b. a -> b
coe T_Semilattice_10
v0) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
               ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v1)))))
-- Algebra.Lattice.Bundles.Semilattice._.isMagma
d_isMagma_44 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semilattice_10 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_44 :: () -> () -> T_Semilattice_10 -> T_IsMagma_178
d_isMagma_44 ~()
v0 ~()
v1 T_Semilattice_10
v2 = T_Semilattice_10 -> T_IsMagma_178
du_isMagma_44 T_Semilattice_10
v2
du_isMagma_44 ::
  T_Semilattice_10 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_178
du_isMagma_44 :: T_Semilattice_10 -> T_IsMagma_178
du_isMagma_44 T_Semilattice_10
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_Semilattice_10 -> T_IsCommutativeBand_612
d_isSemilattice_30 (T_Semilattice_10 -> T_Semilattice_10
forall a b. a -> b
coe T_Semilattice_10
v0) in
    AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
            ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v1))))
-- Algebra.Lattice.Bundles.Semilattice._.isPartialEquivalence
d_isPartialEquivalence_46 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semilattice_10 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_46 :: () -> () -> T_Semilattice_10 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_46 ~()
v0 ~()
v1 T_Semilattice_10
v2
  = T_Semilattice_10 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_46 T_Semilattice_10
v2
du_isPartialEquivalence_46 ::
  T_Semilattice_10 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_46 :: T_Semilattice_10 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_46 T_Semilattice_10
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_Semilattice_10 -> T_IsCommutativeBand_612
d_isSemilattice_30 (T_Semilattice_10 -> T_Semilattice_10
forall a b. a -> b
coe T_Semilattice_10
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsBand_526
v2 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                  ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4))))))
-- Algebra.Lattice.Bundles.Semilattice._.isSemigroup
d_isSemigroup_48 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semilattice_10 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_48 :: () -> () -> T_Semilattice_10 -> T_IsSemigroup_488
d_isSemigroup_48 ~()
v0 ~()
v1 T_Semilattice_10
v2 = T_Semilattice_10 -> T_IsSemigroup_488
du_isSemigroup_48 T_Semilattice_10
v2
du_isSemigroup_48 ::
  T_Semilattice_10 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
du_isSemigroup_48 :: T_Semilattice_10 -> T_IsSemigroup_488
du_isSemigroup_48 T_Semilattice_10
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_Semilattice_10 -> T_IsCommutativeBand_612
d_isSemilattice_30 (T_Semilattice_10 -> T_Semilattice_10
forall a b. a -> b
coe T_Semilattice_10
v0) in
    AgdaAny -> T_IsSemigroup_488
forall a b. a -> b
coe
      ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
         ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v1)))
-- Algebra.Lattice.Bundles.Semilattice._.refl
d_refl_50 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semilattice_10 -> AgdaAny -> AgdaAny
d_refl_50 :: () -> () -> T_Semilattice_10 -> AgdaAny -> AgdaAny
d_refl_50 ~()
v0 ~()
v1 T_Semilattice_10
v2 = T_Semilattice_10 -> AgdaAny -> AgdaAny
du_refl_50 T_Semilattice_10
v2
du_refl_50 :: T_Semilattice_10 -> AgdaAny -> AgdaAny
du_refl_50 :: T_Semilattice_10 -> AgdaAny -> AgdaAny
du_refl_50 T_Semilattice_10
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_Semilattice_10 -> T_IsCommutativeBand_612
d_isSemilattice_30 (T_Semilattice_10 -> T_Semilattice_10
forall a b. a -> b
coe T_Semilattice_10
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
            ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
               ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
                  ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v1))))))
-- Algebra.Lattice.Bundles.Semilattice._.reflexive
d_reflexive_52 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semilattice_10 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_52 :: ()
-> ()
-> T_Semilattice_10
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_52 ~()
v0 ~()
v1 T_Semilattice_10
v2 = T_Semilattice_10 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_52 T_Semilattice_10
v2
du_reflexive_52 ::
  T_Semilattice_10 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_52 :: T_Semilattice_10 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_52 T_Semilattice_10
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_Semilattice_10 -> T_IsCommutativeBand_612
d_isSemilattice_30 (T_Semilattice_10 -> T_Semilattice_10
forall a b. a -> b
coe T_Semilattice_10
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBand_526
v2 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                    ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4))
                    AgdaAny
v5))))
-- Algebra.Lattice.Bundles.Semilattice._.setoid
d_setoid_54 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semilattice_10 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_54 :: () -> () -> T_Semilattice_10 -> T_Setoid_46
d_setoid_54 ~()
v0 ~()
v1 T_Semilattice_10
v2 = T_Semilattice_10 -> T_Setoid_46
du_setoid_54 T_Semilattice_10
v2
du_setoid_54 ::
  T_Semilattice_10 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_54 :: T_Semilattice_10 -> T_Setoid_46
du_setoid_54 T_Semilattice_10
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_Semilattice_10 -> T_IsCommutativeBand_612
d_isSemilattice_30 (T_Semilattice_10 -> T_Semilattice_10
forall a b. a -> b
coe T_Semilattice_10
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsBand_526
v2 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
               ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v3)))))
-- Algebra.Lattice.Bundles.Semilattice._.sym
d_sym_56 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semilattice_10 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_56 :: ()
-> ()
-> T_Semilattice_10
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_56 ~()
v0 ~()
v1 T_Semilattice_10
v2 = T_Semilattice_10 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_56 T_Semilattice_10
v2
du_sym_56 ::
  T_Semilattice_10 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_56 :: T_Semilattice_10 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_56 T_Semilattice_10
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_Semilattice_10 -> T_IsCommutativeBand_612
d_isSemilattice_30 (T_Semilattice_10 -> T_Semilattice_10
forall a b. a -> b
coe T_Semilattice_10
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
            ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
               ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
                  ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v1))))))
-- Algebra.Lattice.Bundles.Semilattice._.trans
d_trans_58 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semilattice_10 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_58 :: ()
-> ()
-> T_Semilattice_10
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_58 ~()
v0 ~()
v1 T_Semilattice_10
v2 = T_Semilattice_10
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_58 T_Semilattice_10
v2
du_trans_58 ::
  T_Semilattice_10 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_58 :: T_Semilattice_10
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_58 T_Semilattice_10
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_Semilattice_10 -> T_IsCommutativeBand_612
d_isSemilattice_30 (T_Semilattice_10 -> T_Semilattice_10
forall a b. a -> b
coe T_Semilattice_10
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
            ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
               ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
                  ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v1))))))
-- Algebra.Lattice.Bundles.Semilattice._.∙-cong
d_'8729''45'cong_60 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semilattice_10 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_60 :: ()
-> ()
-> T_Semilattice_10
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_60 ~()
v0 ~()
v1 T_Semilattice_10
v2 = T_Semilattice_10
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_60 T_Semilattice_10
v2
du_'8729''45'cong_60 ::
  T_Semilattice_10 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong_60 :: T_Semilattice_10
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_60 T_Semilattice_10
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_Semilattice_10 -> T_IsCommutativeBand_612
d_isSemilattice_30 (T_Semilattice_10 -> T_Semilattice_10
forall a b. a -> b
coe T_Semilattice_10
v0) in
    AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
               ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v1)))))
-- Algebra.Lattice.Bundles.Semilattice._.∙-congʳ
d_'8729''45'cong'691'_62 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semilattice_10 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_62 :: ()
-> ()
-> T_Semilattice_10
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_62 ~()
v0 ~()
v1 T_Semilattice_10
v2 = T_Semilattice_10
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_62 T_Semilattice_10
v2
du_'8729''45'cong'691'_62 ::
  T_Semilattice_10 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_62 :: T_Semilattice_10
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_62 T_Semilattice_10
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_Semilattice_10 -> T_IsCommutativeBand_612
d_isSemilattice_30 (T_Semilattice_10 -> T_Semilattice_10
forall a b. a -> b
coe T_Semilattice_10
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBand_526
v2 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
v5
                      = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6
                         = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v4) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                        ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6)
                        ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                           ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                              (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))))))
-- Algebra.Lattice.Bundles.Semilattice._.∙-congˡ
d_'8729''45'cong'737'_64 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semilattice_10 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_64 :: ()
-> ()
-> T_Semilattice_10
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_64 ~()
v0 ~()
v1 T_Semilattice_10
v2 = T_Semilattice_10
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_64 T_Semilattice_10
v2
du_'8729''45'cong'737'_64 ::
  T_Semilattice_10 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_64 :: T_Semilattice_10
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_64 T_Semilattice_10
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_Semilattice_10 -> T_IsCommutativeBand_612
d_isSemilattice_30 (T_Semilattice_10 -> T_Semilattice_10
forall a b. a -> b
coe T_Semilattice_10
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBand_526
v2 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
v5
                      = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6
                         = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v4) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                        ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6)
                        ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                           ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                              (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))))))
-- Algebra.Lattice.Bundles.Semilattice.band
d_band_66 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semilattice_10 -> MAlonzo.Code.Algebra.Bundles.T_Band_620
d_band_66 :: () -> () -> T_Semilattice_10 -> T_Band_620
d_band_66 ~()
v0 ~()
v1 T_Semilattice_10
v2 = T_Semilattice_10 -> T_Band_620
du_band_66 T_Semilattice_10
v2
du_band_66 ::
  T_Semilattice_10 -> MAlonzo.Code.Algebra.Bundles.T_Band_620
du_band_66 :: T_Semilattice_10 -> T_Band_620
du_band_66 T_Semilattice_10
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_IsBand_526 -> T_Band_620)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsBand_526 -> T_Band_620
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsBand_526 -> T_Band_620
MAlonzo.Code.Algebra.Bundles.C_constructor_682
      (T_Semilattice_10 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__28 (T_Semilattice_10 -> T_Semilattice_10
forall a b. a -> b
coe T_Semilattice_10
v0))
      (T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620
         ((T_Semilattice_10 -> T_IsCommutativeBand_612)
-> AgdaAny -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_Semilattice_10 -> T_IsCommutativeBand_612
d_isSemilattice_30 (T_Semilattice_10 -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10
v0)))
-- Algebra.Lattice.Bundles.Semilattice._._≉_
d__'8777'__70 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semilattice_10 -> AgdaAny -> AgdaAny -> ()
d__'8777'__70 :: () -> () -> T_Semilattice_10 -> AgdaAny -> AgdaAny -> ()
d__'8777'__70 = () -> () -> T_Semilattice_10 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.Semilattice._.isBand
d_isBand_72 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semilattice_10 -> MAlonzo.Code.Algebra.Structures.T_IsBand_526
d_isBand_72 :: () -> () -> T_Semilattice_10 -> T_IsBand_526
d_isBand_72 ~()
v0 ~()
v1 T_Semilattice_10
v2 = T_Semilattice_10 -> T_IsBand_526
du_isBand_72 T_Semilattice_10
v2
du_isBand_72 ::
  T_Semilattice_10 -> MAlonzo.Code.Algebra.Structures.T_IsBand_526
du_isBand_72 :: T_Semilattice_10 -> T_IsBand_526
du_isBand_72 T_Semilattice_10
v0
  = (T_IsCommutativeBand_612 -> T_IsBand_526)
-> AgdaAny -> T_IsBand_526
forall a b. a -> b
coe
      T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620
      ((T_Semilattice_10 -> T_IsCommutativeBand_612) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10 -> T_IsCommutativeBand_612
d_isSemilattice_30 (T_Semilattice_10 -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10
v0))
-- Algebra.Lattice.Bundles.Semilattice._.isMagma
d_isMagma_74 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semilattice_10 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_74 :: () -> () -> T_Semilattice_10 -> T_IsMagma_178
d_isMagma_74 ~()
v0 ~()
v1 T_Semilattice_10
v2 = T_Semilattice_10 -> T_IsMagma_178
du_isMagma_74 T_Semilattice_10
v2
du_isMagma_74 ::
  T_Semilattice_10 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_178
du_isMagma_74 :: T_Semilattice_10 -> T_IsMagma_178
du_isMagma_74 T_Semilattice_10
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
         ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620
            ((T_Semilattice_10 -> T_IsCommutativeBand_612) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10 -> T_IsCommutativeBand_612
d_isSemilattice_30 (T_Semilattice_10 -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10
v0))))
-- Algebra.Lattice.Bundles.Semilattice._.isSemigroup
d_isSemigroup_76 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semilattice_10 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_76 :: () -> () -> T_Semilattice_10 -> T_IsSemigroup_488
d_isSemigroup_76 ~()
v0 ~()
v1 T_Semilattice_10
v2 = T_Semilattice_10 -> T_IsSemigroup_488
du_isSemigroup_76 T_Semilattice_10
v2
du_isSemigroup_76 ::
  T_Semilattice_10 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
du_isSemigroup_76 :: T_Semilattice_10 -> T_IsSemigroup_488
du_isSemigroup_76 T_Semilattice_10
v0
  = (T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
      ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620
         ((T_Semilattice_10 -> T_IsCommutativeBand_612) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10 -> T_IsCommutativeBand_612
d_isSemilattice_30 (T_Semilattice_10 -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10
v0)))
-- Algebra.Lattice.Bundles.Semilattice._.magma
d_magma_78 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semilattice_10 -> MAlonzo.Code.Algebra.Bundles.T_Magma_74
d_magma_78 :: () -> () -> T_Semilattice_10 -> T_Magma_74
d_magma_78 ~()
v0 ~()
v1 T_Semilattice_10
v2 = T_Semilattice_10 -> T_Magma_74
du_magma_78 T_Semilattice_10
v2
du_magma_78 ::
  T_Semilattice_10 -> MAlonzo.Code.Algebra.Bundles.T_Magma_74
du_magma_78 :: T_Semilattice_10 -> T_Magma_74
du_magma_78 T_Semilattice_10
v0
  = let v1 :: AgdaAny
v1 = (T_Semilattice_10 -> T_Band_620) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_620
du_band_66 (T_Semilattice_10 -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10
v0) in
    AgdaAny -> T_Magma_74
forall a b. a -> b
coe
      ((T_Semigroup_558 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Semigroup_558 -> T_Magma_74
MAlonzo.Code.Algebra.Bundles.du_magma_606
         ((T_Band_620 -> T_Semigroup_558) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_620 -> T_Semigroup_558
MAlonzo.Code.Algebra.Bundles.du_semigroup_672 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Lattice.Bundles.Semilattice._.rawMagma
d_rawMagma_80 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semilattice_10 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
d_rawMagma_80 :: () -> () -> T_Semilattice_10 -> T_RawMagma_44
d_rawMagma_80 ~()
v0 ~()
v1 T_Semilattice_10
v2 = T_Semilattice_10 -> T_RawMagma_44
du_rawMagma_80 T_Semilattice_10
v2
du_rawMagma_80 ::
  T_Semilattice_10 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
du_rawMagma_80 :: T_Semilattice_10 -> T_RawMagma_44
du_rawMagma_80 T_Semilattice_10
v0
  = let v1 :: AgdaAny
v1 = (T_Semilattice_10 -> T_Band_620) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_620
du_band_66 (T_Semilattice_10 -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10
v0) in
    AgdaAny -> T_RawMagma_44
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_Band_620 -> T_Semigroup_558) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_620 -> T_Semigroup_558
MAlonzo.Code.Algebra.Bundles.du_semigroup_672 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Magma_74 -> T_RawMagma_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Magma_74 -> T_RawMagma_44
MAlonzo.Code.Algebra.Bundles.du_rawMagma_118
            ((T_Semigroup_558 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558 -> T_Magma_74
MAlonzo.Code.Algebra.Bundles.du_magma_606 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Lattice.Bundles.Semilattice._.semigroup
d_semigroup_82 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semilattice_10 -> MAlonzo.Code.Algebra.Bundles.T_Semigroup_558
d_semigroup_82 :: () -> () -> T_Semilattice_10 -> T_Semigroup_558
d_semigroup_82 ~()
v0 ~()
v1 T_Semilattice_10
v2 = T_Semilattice_10 -> T_Semigroup_558
du_semigroup_82 T_Semilattice_10
v2
du_semigroup_82 ::
  T_Semilattice_10 -> MAlonzo.Code.Algebra.Bundles.T_Semigroup_558
du_semigroup_82 :: T_Semilattice_10 -> T_Semigroup_558
du_semigroup_82 T_Semilattice_10
v0
  = (T_Band_620 -> T_Semigroup_558) -> AgdaAny -> T_Semigroup_558
forall a b. a -> b
coe
      T_Band_620 -> T_Semigroup_558
MAlonzo.Code.Algebra.Bundles.du_semigroup_672
      ((T_Semilattice_10 -> T_Band_620) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_620
du_band_66 (T_Semilattice_10 -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10
v0))
-- Algebra.Lattice.Bundles.MeetSemilattice
d_MeetSemilattice_90 :: p -> p -> ()
d_MeetSemilattice_90 p
a0 p
a1 = ()
data T_MeetSemilattice_90
  = C_constructor_158 (AgdaAny -> AgdaAny -> AgdaAny)
                      MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
-- Algebra.Lattice.Bundles.MeetSemilattice.Carrier
d_Carrier_104 :: T_MeetSemilattice_90 -> ()
d_Carrier_104 :: T_MeetSemilattice_90 -> ()
d_Carrier_104 = T_MeetSemilattice_90 -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.MeetSemilattice._≈_
d__'8776'__106 :: T_MeetSemilattice_90 -> AgdaAny -> AgdaAny -> ()
d__'8776'__106 :: T_MeetSemilattice_90 -> AgdaAny -> AgdaAny -> ()
d__'8776'__106 = T_MeetSemilattice_90 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.MeetSemilattice._∧_
d__'8743'__108 ::
  T_MeetSemilattice_90 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__108 :: T_MeetSemilattice_90 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__108 T_MeetSemilattice_90
v0
  = case T_MeetSemilattice_90 -> T_MeetSemilattice_90
forall a b. a -> b
coe T_MeetSemilattice_90
v0 of
      C_constructor_158 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsCommutativeBand_612
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_MeetSemilattice_90
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.MeetSemilattice.isMeetSemilattice
d_isMeetSemilattice_110 ::
  T_MeetSemilattice_90 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
d_isMeetSemilattice_110 :: T_MeetSemilattice_90 -> T_IsCommutativeBand_612
d_isMeetSemilattice_110 T_MeetSemilattice_90
v0
  = case T_MeetSemilattice_90 -> T_MeetSemilattice_90
forall a b. a -> b
coe T_MeetSemilattice_90
v0 of
      C_constructor_158 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsCommutativeBand_612
v4 -> T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v4
      T_MeetSemilattice_90
_ -> T_IsCommutativeBand_612
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.MeetSemilattice._.assoc
d_assoc_114 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_90 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_114 :: ()
-> ()
-> T_MeetSemilattice_90
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_assoc_114 ~()
v0 ~()
v1 T_MeetSemilattice_90
v2 = T_MeetSemilattice_90 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_114 T_MeetSemilattice_90
v2
du_assoc_114 ::
  T_MeetSemilattice_90 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_114 :: T_MeetSemilattice_90 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_114 T_MeetSemilattice_90
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_MeetSemilattice_90 -> T_IsCommutativeBand_612
d_isMeetSemilattice_110 (T_MeetSemilattice_90 -> T_MeetSemilattice_90
forall a b. a -> b
coe T_MeetSemilattice_90
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_498
         ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
            ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v1))))
-- Algebra.Lattice.Bundles.MeetSemilattice._.comm
d_comm_116 :: T_MeetSemilattice_90 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_116 :: T_MeetSemilattice_90 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_116 T_MeetSemilattice_90
v0
  = (T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_622
      ((T_MeetSemilattice_90 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_90 -> T_IsCommutativeBand_612
d_isMeetSemilattice_110 (T_MeetSemilattice_90 -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_90
v0))
-- Algebra.Lattice.Bundles.MeetSemilattice._.idem
d_idem_118 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_90 -> AgdaAny -> AgdaAny
d_idem_118 :: () -> () -> T_MeetSemilattice_90 -> AgdaAny -> AgdaAny
d_idem_118 ~()
v0 ~()
v1 T_MeetSemilattice_90
v2 = T_MeetSemilattice_90 -> AgdaAny -> AgdaAny
du_idem_118 T_MeetSemilattice_90
v2
du_idem_118 :: T_MeetSemilattice_90 -> AgdaAny -> AgdaAny
du_idem_118 :: T_MeetSemilattice_90 -> AgdaAny -> AgdaAny
du_idem_118 T_MeetSemilattice_90
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_MeetSemilattice_90 -> T_IsCommutativeBand_612
d_isMeetSemilattice_110 (T_MeetSemilattice_90 -> T_MeetSemilattice_90
forall a b. a -> b
coe T_MeetSemilattice_90
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsBand_526 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_526 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_536
         ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v1)))
-- Algebra.Lattice.Bundles.MeetSemilattice._.isBand
d_isBand_120 ::
  T_MeetSemilattice_90 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
d_isBand_120 :: T_MeetSemilattice_90 -> T_IsBand_526
d_isBand_120 T_MeetSemilattice_90
v0
  = (T_IsCommutativeBand_612 -> T_IsBand_526)
-> AgdaAny -> T_IsBand_526
forall a b. a -> b
coe
      T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620
      ((T_MeetSemilattice_90 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_90 -> T_IsCommutativeBand_612
d_isMeetSemilattice_110 (T_MeetSemilattice_90 -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_90
v0))
-- Algebra.Lattice.Bundles.MeetSemilattice._.isEquivalence
d_isEquivalence_122 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_90 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_122 :: () -> () -> T_MeetSemilattice_90 -> T_IsEquivalence_28
d_isEquivalence_122 ~()
v0 ~()
v1 T_MeetSemilattice_90
v2 = T_MeetSemilattice_90 -> T_IsEquivalence_28
du_isEquivalence_122 T_MeetSemilattice_90
v2
du_isEquivalence_122 ::
  T_MeetSemilattice_90 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_122 :: T_MeetSemilattice_90 -> T_IsEquivalence_28
du_isEquivalence_122 T_MeetSemilattice_90
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_MeetSemilattice_90 -> T_IsCommutativeBand_612
d_isMeetSemilattice_110 (T_MeetSemilattice_90 -> T_MeetSemilattice_90
forall a b. a -> b
coe T_MeetSemilattice_90
v0) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
               ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v1)))))
-- Algebra.Lattice.Bundles.MeetSemilattice._.isMagma
d_isMagma_124 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_90 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_124 :: () -> () -> T_MeetSemilattice_90 -> T_IsMagma_178
d_isMagma_124 ~()
v0 ~()
v1 T_MeetSemilattice_90
v2 = T_MeetSemilattice_90 -> T_IsMagma_178
du_isMagma_124 T_MeetSemilattice_90
v2
du_isMagma_124 ::
  T_MeetSemilattice_90 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
du_isMagma_124 :: T_MeetSemilattice_90 -> T_IsMagma_178
du_isMagma_124 T_MeetSemilattice_90
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_MeetSemilattice_90 -> T_IsCommutativeBand_612
d_isMeetSemilattice_110 (T_MeetSemilattice_90 -> T_MeetSemilattice_90
forall a b. a -> b
coe T_MeetSemilattice_90
v0) in
    AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
            ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v1))))
-- Algebra.Lattice.Bundles.MeetSemilattice._.isPartialEquivalence
d_isPartialEquivalence_126 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_90 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_126 :: () -> () -> T_MeetSemilattice_90 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_126 ~()
v0 ~()
v1 T_MeetSemilattice_90
v2
  = T_MeetSemilattice_90 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_126 T_MeetSemilattice_90
v2
du_isPartialEquivalence_126 ::
  T_MeetSemilattice_90 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_126 :: T_MeetSemilattice_90 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_126 T_MeetSemilattice_90
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_MeetSemilattice_90 -> T_IsCommutativeBand_612
d_isMeetSemilattice_110 (T_MeetSemilattice_90 -> T_MeetSemilattice_90
forall a b. a -> b
coe T_MeetSemilattice_90
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsBand_526
v2 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                  ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4))))))
-- Algebra.Lattice.Bundles.MeetSemilattice._.isSemigroup
d_isSemigroup_128 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_90 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_128 :: () -> () -> T_MeetSemilattice_90 -> T_IsSemigroup_488
d_isSemigroup_128 ~()
v0 ~()
v1 T_MeetSemilattice_90
v2 = T_MeetSemilattice_90 -> T_IsSemigroup_488
du_isSemigroup_128 T_MeetSemilattice_90
v2
du_isSemigroup_128 ::
  T_MeetSemilattice_90 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
du_isSemigroup_128 :: T_MeetSemilattice_90 -> T_IsSemigroup_488
du_isSemigroup_128 T_MeetSemilattice_90
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_MeetSemilattice_90 -> T_IsCommutativeBand_612
d_isMeetSemilattice_110 (T_MeetSemilattice_90 -> T_MeetSemilattice_90
forall a b. a -> b
coe T_MeetSemilattice_90
v0) in
    AgdaAny -> T_IsSemigroup_488
forall a b. a -> b
coe
      ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
         ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v1)))
-- Algebra.Lattice.Bundles.MeetSemilattice._.refl
d_refl_130 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_90 -> AgdaAny -> AgdaAny
d_refl_130 :: () -> () -> T_MeetSemilattice_90 -> AgdaAny -> AgdaAny
d_refl_130 ~()
v0 ~()
v1 T_MeetSemilattice_90
v2 = T_MeetSemilattice_90 -> AgdaAny -> AgdaAny
du_refl_130 T_MeetSemilattice_90
v2
du_refl_130 :: T_MeetSemilattice_90 -> AgdaAny -> AgdaAny
du_refl_130 :: T_MeetSemilattice_90 -> AgdaAny -> AgdaAny
du_refl_130 T_MeetSemilattice_90
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_MeetSemilattice_90 -> T_IsCommutativeBand_612
d_isMeetSemilattice_110 (T_MeetSemilattice_90 -> T_MeetSemilattice_90
forall a b. a -> b
coe T_MeetSemilattice_90
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
            ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
               ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
                  ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v1))))))
-- Algebra.Lattice.Bundles.MeetSemilattice._.reflexive
d_reflexive_132 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_90 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_132 :: ()
-> ()
-> T_MeetSemilattice_90
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_132 ~()
v0 ~()
v1 T_MeetSemilattice_90
v2 = T_MeetSemilattice_90
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_132 T_MeetSemilattice_90
v2
du_reflexive_132 ::
  T_MeetSemilattice_90 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_132 :: T_MeetSemilattice_90
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_132 T_MeetSemilattice_90
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_MeetSemilattice_90 -> T_IsCommutativeBand_612
d_isMeetSemilattice_110 (T_MeetSemilattice_90 -> T_MeetSemilattice_90
forall a b. a -> b
coe T_MeetSemilattice_90
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBand_526
v2 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                    ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4))
                    AgdaAny
v5))))
-- Algebra.Lattice.Bundles.MeetSemilattice._.setoid
d_setoid_134 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_90 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_134 :: () -> () -> T_MeetSemilattice_90 -> T_Setoid_46
d_setoid_134 ~()
v0 ~()
v1 T_MeetSemilattice_90
v2 = T_MeetSemilattice_90 -> T_Setoid_46
du_setoid_134 T_MeetSemilattice_90
v2
du_setoid_134 ::
  T_MeetSemilattice_90 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_134 :: T_MeetSemilattice_90 -> T_Setoid_46
du_setoid_134 T_MeetSemilattice_90
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_MeetSemilattice_90 -> T_IsCommutativeBand_612
d_isMeetSemilattice_110 (T_MeetSemilattice_90 -> T_MeetSemilattice_90
forall a b. a -> b
coe T_MeetSemilattice_90
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsBand_526
v2 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
               ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v3)))))
-- Algebra.Lattice.Bundles.MeetSemilattice._.sym
d_sym_136 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_90 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_136 :: ()
-> ()
-> T_MeetSemilattice_90
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_136 ~()
v0 ~()
v1 T_MeetSemilattice_90
v2 = T_MeetSemilattice_90 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_136 T_MeetSemilattice_90
v2
du_sym_136 ::
  T_MeetSemilattice_90 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_136 :: T_MeetSemilattice_90 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_136 T_MeetSemilattice_90
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_MeetSemilattice_90 -> T_IsCommutativeBand_612
d_isMeetSemilattice_110 (T_MeetSemilattice_90 -> T_MeetSemilattice_90
forall a b. a -> b
coe T_MeetSemilattice_90
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
            ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
               ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
                  ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v1))))))
-- Algebra.Lattice.Bundles.MeetSemilattice._.trans
d_trans_138 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_90 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_138 :: ()
-> ()
-> T_MeetSemilattice_90
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_138 ~()
v0 ~()
v1 T_MeetSemilattice_90
v2 = T_MeetSemilattice_90
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_138 T_MeetSemilattice_90
v2
du_trans_138 ::
  T_MeetSemilattice_90 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_138 :: T_MeetSemilattice_90
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_138 T_MeetSemilattice_90
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_MeetSemilattice_90 -> T_IsCommutativeBand_612
d_isMeetSemilattice_110 (T_MeetSemilattice_90 -> T_MeetSemilattice_90
forall a b. a -> b
coe T_MeetSemilattice_90
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
            ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
               ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
                  ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v1))))))
-- Algebra.Lattice.Bundles.MeetSemilattice._.∙-cong
d_'8729''45'cong_140 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_90 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_140 :: ()
-> ()
-> T_MeetSemilattice_90
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_140 ~()
v0 ~()
v1 T_MeetSemilattice_90
v2 = T_MeetSemilattice_90
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_140 T_MeetSemilattice_90
v2
du_'8729''45'cong_140 ::
  T_MeetSemilattice_90 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong_140 :: T_MeetSemilattice_90
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_140 T_MeetSemilattice_90
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_MeetSemilattice_90 -> T_IsCommutativeBand_612
d_isMeetSemilattice_110 (T_MeetSemilattice_90 -> T_MeetSemilattice_90
forall a b. a -> b
coe T_MeetSemilattice_90
v0) in
    AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
               ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v1)))))
-- Algebra.Lattice.Bundles.MeetSemilattice._.∙-congʳ
d_'8729''45'cong'691'_142 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_90 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_142 :: ()
-> ()
-> T_MeetSemilattice_90
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_142 ~()
v0 ~()
v1 T_MeetSemilattice_90
v2
  = T_MeetSemilattice_90
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_142 T_MeetSemilattice_90
v2
du_'8729''45'cong'691'_142 ::
  T_MeetSemilattice_90 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_142 :: T_MeetSemilattice_90
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_142 T_MeetSemilattice_90
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_MeetSemilattice_90 -> T_IsCommutativeBand_612
d_isMeetSemilattice_110 (T_MeetSemilattice_90 -> T_MeetSemilattice_90
forall a b. a -> b
coe T_MeetSemilattice_90
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBand_526
v2 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
v5
                      = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6
                         = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v4) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                        ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6)
                        ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                           ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                              (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))))))
-- Algebra.Lattice.Bundles.MeetSemilattice._.∙-congˡ
d_'8729''45'cong'737'_144 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_90 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_144 :: ()
-> ()
-> T_MeetSemilattice_90
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_144 ~()
v0 ~()
v1 T_MeetSemilattice_90
v2
  = T_MeetSemilattice_90
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_144 T_MeetSemilattice_90
v2
du_'8729''45'cong'737'_144 ::
  T_MeetSemilattice_90 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_144 :: T_MeetSemilattice_90
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_144 T_MeetSemilattice_90
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_MeetSemilattice_90 -> T_IsCommutativeBand_612
d_isMeetSemilattice_110 (T_MeetSemilattice_90 -> T_MeetSemilattice_90
forall a b. a -> b
coe T_MeetSemilattice_90
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBand_526
v2 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
v5
                      = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6
                         = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v4) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                        ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6)
                        ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                           ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                              (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))))))
-- Algebra.Lattice.Bundles.MeetSemilattice.semilattice
d_semilattice_146 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_90 -> T_Semilattice_10
d_semilattice_146 :: () -> () -> T_MeetSemilattice_90 -> T_Semilattice_10
d_semilattice_146 ~()
v0 ~()
v1 T_MeetSemilattice_90
v2 = T_MeetSemilattice_90 -> T_Semilattice_10
du_semilattice_146 T_MeetSemilattice_90
v2
du_semilattice_146 :: T_MeetSemilattice_90 -> T_Semilattice_10
du_semilattice_146 :: T_MeetSemilattice_90 -> T_Semilattice_10
du_semilattice_146 T_MeetSemilattice_90
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsCommutativeBand_612 -> T_Semilattice_10)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> T_Semilattice_10
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612 -> T_Semilattice_10
C_constructor_84 (T_MeetSemilattice_90 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__108 (T_MeetSemilattice_90 -> T_MeetSemilattice_90
forall a b. a -> b
coe T_MeetSemilattice_90
v0))
      (T_MeetSemilattice_90 -> T_IsCommutativeBand_612
d_isMeetSemilattice_110 (T_MeetSemilattice_90 -> T_MeetSemilattice_90
forall a b. a -> b
coe T_MeetSemilattice_90
v0))
-- Algebra.Lattice.Bundles.MeetSemilattice._.band
d_band_150 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_90 -> MAlonzo.Code.Algebra.Bundles.T_Band_620
d_band_150 :: () -> () -> T_MeetSemilattice_90 -> T_Band_620
d_band_150 ~()
v0 ~()
v1 T_MeetSemilattice_90
v2 = T_MeetSemilattice_90 -> T_Band_620
du_band_150 T_MeetSemilattice_90
v2
du_band_150 ::
  T_MeetSemilattice_90 -> MAlonzo.Code.Algebra.Bundles.T_Band_620
du_band_150 :: T_MeetSemilattice_90 -> T_Band_620
du_band_150 T_MeetSemilattice_90
v0 = (T_Semilattice_10 -> T_Band_620) -> AgdaAny -> T_Band_620
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_620
du_band_66 ((T_MeetSemilattice_90 -> T_Semilattice_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_90 -> T_Semilattice_10
du_semilattice_146 (T_MeetSemilattice_90 -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_90
v0))
-- Algebra.Lattice.Bundles.MeetSemilattice._.magma
d_magma_152 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_90 -> MAlonzo.Code.Algebra.Bundles.T_Magma_74
d_magma_152 :: () -> () -> T_MeetSemilattice_90 -> T_Magma_74
d_magma_152 ~()
v0 ~()
v1 T_MeetSemilattice_90
v2 = T_MeetSemilattice_90 -> T_Magma_74
du_magma_152 T_MeetSemilattice_90
v2
du_magma_152 ::
  T_MeetSemilattice_90 -> MAlonzo.Code.Algebra.Bundles.T_Magma_74
du_magma_152 :: T_MeetSemilattice_90 -> T_Magma_74
du_magma_152 T_MeetSemilattice_90
v0
  = let v1 :: AgdaAny
v1 = (T_MeetSemilattice_90 -> T_Semilattice_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_90 -> T_Semilattice_10
du_semilattice_146 (T_MeetSemilattice_90 -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_90
v0) in
    AgdaAny -> T_Magma_74
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_Semilattice_10 -> T_Band_620) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_620
du_band_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Semigroup_558 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Semigroup_558 -> T_Magma_74
MAlonzo.Code.Algebra.Bundles.du_magma_606
            ((T_Band_620 -> T_Semigroup_558) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_620 -> T_Semigroup_558
MAlonzo.Code.Algebra.Bundles.du_semigroup_672 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Lattice.Bundles.MeetSemilattice._.rawMagma
d_rawMagma_154 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_90 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
d_rawMagma_154 :: () -> () -> T_MeetSemilattice_90 -> T_RawMagma_44
d_rawMagma_154 ~()
v0 ~()
v1 T_MeetSemilattice_90
v2 = T_MeetSemilattice_90 -> T_RawMagma_44
du_rawMagma_154 T_MeetSemilattice_90
v2
du_rawMagma_154 ::
  T_MeetSemilattice_90 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
du_rawMagma_154 :: T_MeetSemilattice_90 -> T_RawMagma_44
du_rawMagma_154 T_MeetSemilattice_90
v0
  = let v1 :: AgdaAny
v1 = (T_MeetSemilattice_90 -> T_Semilattice_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_90 -> T_Semilattice_10
du_semilattice_146 (T_MeetSemilattice_90 -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_90
v0) in
    AgdaAny -> T_RawMagma_44
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_Semilattice_10 -> T_Band_620) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_620
du_band_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_Band_620 -> T_Semigroup_558) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_620 -> T_Semigroup_558
MAlonzo.Code.Algebra.Bundles.du_semigroup_672 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_Magma_74 -> T_RawMagma_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Magma_74 -> T_RawMagma_44
MAlonzo.Code.Algebra.Bundles.du_rawMagma_118
               ((T_Semigroup_558 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558 -> T_Magma_74
MAlonzo.Code.Algebra.Bundles.du_magma_606 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))
-- Algebra.Lattice.Bundles.MeetSemilattice._.semigroup
d_semigroup_156 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_90 ->
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_558
d_semigroup_156 :: () -> () -> T_MeetSemilattice_90 -> T_Semigroup_558
d_semigroup_156 ~()
v0 ~()
v1 T_MeetSemilattice_90
v2 = T_MeetSemilattice_90 -> T_Semigroup_558
du_semigroup_156 T_MeetSemilattice_90
v2
du_semigroup_156 ::
  T_MeetSemilattice_90 ->
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_558
du_semigroup_156 :: T_MeetSemilattice_90 -> T_Semigroup_558
du_semigroup_156 T_MeetSemilattice_90
v0
  = let v1 :: AgdaAny
v1 = (T_MeetSemilattice_90 -> T_Semilattice_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_90 -> T_Semilattice_10
du_semilattice_146 (T_MeetSemilattice_90 -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_90
v0) in
    AgdaAny -> T_Semigroup_558
forall a b. a -> b
coe
      ((T_Band_620 -> T_Semigroup_558) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Band_620 -> T_Semigroup_558
MAlonzo.Code.Algebra.Bundles.du_semigroup_672
         ((T_Semilattice_10 -> T_Band_620) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_620
du_band_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Lattice.Bundles.JoinSemilattice
d_JoinSemilattice_164 :: p -> p -> ()
d_JoinSemilattice_164 p
a0 p
a1 = ()
data T_JoinSemilattice_164
  = C_constructor_232 (AgdaAny -> AgdaAny -> AgdaAny)
                      MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
-- Algebra.Lattice.Bundles.JoinSemilattice.Carrier
d_Carrier_178 :: T_JoinSemilattice_164 -> ()
d_Carrier_178 :: T_JoinSemilattice_164 -> ()
d_Carrier_178 = T_JoinSemilattice_164 -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.JoinSemilattice._≈_
d__'8776'__180 :: T_JoinSemilattice_164 -> AgdaAny -> AgdaAny -> ()
d__'8776'__180 :: T_JoinSemilattice_164 -> AgdaAny -> AgdaAny -> ()
d__'8776'__180 = T_JoinSemilattice_164 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.JoinSemilattice._∨_
d__'8744'__182 ::
  T_JoinSemilattice_164 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__182 :: T_JoinSemilattice_164 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__182 T_JoinSemilattice_164
v0
  = case T_JoinSemilattice_164 -> T_JoinSemilattice_164
forall a b. a -> b
coe T_JoinSemilattice_164
v0 of
      C_constructor_232 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsCommutativeBand_612
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_JoinSemilattice_164
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.JoinSemilattice.isJoinSemilattice
d_isJoinSemilattice_184 ::
  T_JoinSemilattice_164 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
d_isJoinSemilattice_184 :: T_JoinSemilattice_164 -> T_IsCommutativeBand_612
d_isJoinSemilattice_184 T_JoinSemilattice_164
v0
  = case T_JoinSemilattice_164 -> T_JoinSemilattice_164
forall a b. a -> b
coe T_JoinSemilattice_164
v0 of
      C_constructor_232 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsCommutativeBand_612
v4 -> T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v4
      T_JoinSemilattice_164
_ -> T_IsCommutativeBand_612
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.JoinSemilattice._.assoc
d_assoc_188 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_164 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_188 :: ()
-> ()
-> T_JoinSemilattice_164
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_assoc_188 ~()
v0 ~()
v1 T_JoinSemilattice_164
v2 = T_JoinSemilattice_164 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_188 T_JoinSemilattice_164
v2
du_assoc_188 ::
  T_JoinSemilattice_164 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_188 :: T_JoinSemilattice_164 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_188 T_JoinSemilattice_164
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_JoinSemilattice_164 -> T_IsCommutativeBand_612
d_isJoinSemilattice_184 (T_JoinSemilattice_164 -> T_JoinSemilattice_164
forall a b. a -> b
coe T_JoinSemilattice_164
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_498
         ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
            ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v1))))
-- Algebra.Lattice.Bundles.JoinSemilattice._.comm
d_comm_190 ::
  T_JoinSemilattice_164 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_190 :: T_JoinSemilattice_164 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_190 T_JoinSemilattice_164
v0
  = (T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_622
      ((T_JoinSemilattice_164 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_164 -> T_IsCommutativeBand_612
d_isJoinSemilattice_184 (T_JoinSemilattice_164 -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_164
v0))
-- Algebra.Lattice.Bundles.JoinSemilattice._.idem
d_idem_192 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_164 -> AgdaAny -> AgdaAny
d_idem_192 :: () -> () -> T_JoinSemilattice_164 -> AgdaAny -> AgdaAny
d_idem_192 ~()
v0 ~()
v1 T_JoinSemilattice_164
v2 = T_JoinSemilattice_164 -> AgdaAny -> AgdaAny
du_idem_192 T_JoinSemilattice_164
v2
du_idem_192 :: T_JoinSemilattice_164 -> AgdaAny -> AgdaAny
du_idem_192 :: T_JoinSemilattice_164 -> AgdaAny -> AgdaAny
du_idem_192 T_JoinSemilattice_164
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_JoinSemilattice_164 -> T_IsCommutativeBand_612
d_isJoinSemilattice_184 (T_JoinSemilattice_164 -> T_JoinSemilattice_164
forall a b. a -> b
coe T_JoinSemilattice_164
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsBand_526 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_526 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_536
         ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v1)))
-- Algebra.Lattice.Bundles.JoinSemilattice._.isBand
d_isBand_194 ::
  T_JoinSemilattice_164 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
d_isBand_194 :: T_JoinSemilattice_164 -> T_IsBand_526
d_isBand_194 T_JoinSemilattice_164
v0
  = (T_IsCommutativeBand_612 -> T_IsBand_526)
-> AgdaAny -> T_IsBand_526
forall a b. a -> b
coe
      T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620
      ((T_JoinSemilattice_164 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_164 -> T_IsCommutativeBand_612
d_isJoinSemilattice_184 (T_JoinSemilattice_164 -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_164
v0))
-- Algebra.Lattice.Bundles.JoinSemilattice._.isEquivalence
d_isEquivalence_196 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_164 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_196 :: () -> () -> T_JoinSemilattice_164 -> T_IsEquivalence_28
d_isEquivalence_196 ~()
v0 ~()
v1 T_JoinSemilattice_164
v2 = T_JoinSemilattice_164 -> T_IsEquivalence_28
du_isEquivalence_196 T_JoinSemilattice_164
v2
du_isEquivalence_196 ::
  T_JoinSemilattice_164 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_196 :: T_JoinSemilattice_164 -> T_IsEquivalence_28
du_isEquivalence_196 T_JoinSemilattice_164
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_JoinSemilattice_164 -> T_IsCommutativeBand_612
d_isJoinSemilattice_184 (T_JoinSemilattice_164 -> T_JoinSemilattice_164
forall a b. a -> b
coe T_JoinSemilattice_164
v0) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
               ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v1)))))
-- Algebra.Lattice.Bundles.JoinSemilattice._.isMagma
d_isMagma_198 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_164 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_198 :: () -> () -> T_JoinSemilattice_164 -> T_IsMagma_178
d_isMagma_198 ~()
v0 ~()
v1 T_JoinSemilattice_164
v2 = T_JoinSemilattice_164 -> T_IsMagma_178
du_isMagma_198 T_JoinSemilattice_164
v2
du_isMagma_198 ::
  T_JoinSemilattice_164 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
du_isMagma_198 :: T_JoinSemilattice_164 -> T_IsMagma_178
du_isMagma_198 T_JoinSemilattice_164
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_JoinSemilattice_164 -> T_IsCommutativeBand_612
d_isJoinSemilattice_184 (T_JoinSemilattice_164 -> T_JoinSemilattice_164
forall a b. a -> b
coe T_JoinSemilattice_164
v0) in
    AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
            ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v1))))
-- Algebra.Lattice.Bundles.JoinSemilattice._.isPartialEquivalence
d_isPartialEquivalence_200 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_164 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_200 :: () -> () -> T_JoinSemilattice_164 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_200 ~()
v0 ~()
v1 T_JoinSemilattice_164
v2
  = T_JoinSemilattice_164 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_200 T_JoinSemilattice_164
v2
du_isPartialEquivalence_200 ::
  T_JoinSemilattice_164 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_200 :: T_JoinSemilattice_164 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_200 T_JoinSemilattice_164
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_JoinSemilattice_164 -> T_IsCommutativeBand_612
d_isJoinSemilattice_184 (T_JoinSemilattice_164 -> T_JoinSemilattice_164
forall a b. a -> b
coe T_JoinSemilattice_164
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsBand_526
v2 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                  ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4))))))
-- Algebra.Lattice.Bundles.JoinSemilattice._.isSemigroup
d_isSemigroup_202 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_164 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_202 :: () -> () -> T_JoinSemilattice_164 -> T_IsSemigroup_488
d_isSemigroup_202 ~()
v0 ~()
v1 T_JoinSemilattice_164
v2 = T_JoinSemilattice_164 -> T_IsSemigroup_488
du_isSemigroup_202 T_JoinSemilattice_164
v2
du_isSemigroup_202 ::
  T_JoinSemilattice_164 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
du_isSemigroup_202 :: T_JoinSemilattice_164 -> T_IsSemigroup_488
du_isSemigroup_202 T_JoinSemilattice_164
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_JoinSemilattice_164 -> T_IsCommutativeBand_612
d_isJoinSemilattice_184 (T_JoinSemilattice_164 -> T_JoinSemilattice_164
forall a b. a -> b
coe T_JoinSemilattice_164
v0) in
    AgdaAny -> T_IsSemigroup_488
forall a b. a -> b
coe
      ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
         ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v1)))
-- Algebra.Lattice.Bundles.JoinSemilattice._.refl
d_refl_204 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_164 -> AgdaAny -> AgdaAny
d_refl_204 :: () -> () -> T_JoinSemilattice_164 -> AgdaAny -> AgdaAny
d_refl_204 ~()
v0 ~()
v1 T_JoinSemilattice_164
v2 = T_JoinSemilattice_164 -> AgdaAny -> AgdaAny
du_refl_204 T_JoinSemilattice_164
v2
du_refl_204 :: T_JoinSemilattice_164 -> AgdaAny -> AgdaAny
du_refl_204 :: T_JoinSemilattice_164 -> AgdaAny -> AgdaAny
du_refl_204 T_JoinSemilattice_164
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_JoinSemilattice_164 -> T_IsCommutativeBand_612
d_isJoinSemilattice_184 (T_JoinSemilattice_164 -> T_JoinSemilattice_164
forall a b. a -> b
coe T_JoinSemilattice_164
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
            ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
               ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
                  ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v1))))))
-- Algebra.Lattice.Bundles.JoinSemilattice._.reflexive
d_reflexive_206 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_164 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_206 :: ()
-> ()
-> T_JoinSemilattice_164
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_206 ~()
v0 ~()
v1 T_JoinSemilattice_164
v2 = T_JoinSemilattice_164
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_206 T_JoinSemilattice_164
v2
du_reflexive_206 ::
  T_JoinSemilattice_164 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_206 :: T_JoinSemilattice_164
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_206 T_JoinSemilattice_164
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_JoinSemilattice_164 -> T_IsCommutativeBand_612
d_isJoinSemilattice_184 (T_JoinSemilattice_164 -> T_JoinSemilattice_164
forall a b. a -> b
coe T_JoinSemilattice_164
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBand_526
v2 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                    ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4))
                    AgdaAny
v5))))
-- Algebra.Lattice.Bundles.JoinSemilattice._.setoid
d_setoid_208 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_164 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_208 :: () -> () -> T_JoinSemilattice_164 -> T_Setoid_46
d_setoid_208 ~()
v0 ~()
v1 T_JoinSemilattice_164
v2 = T_JoinSemilattice_164 -> T_Setoid_46
du_setoid_208 T_JoinSemilattice_164
v2
du_setoid_208 ::
  T_JoinSemilattice_164 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_208 :: T_JoinSemilattice_164 -> T_Setoid_46
du_setoid_208 T_JoinSemilattice_164
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_JoinSemilattice_164 -> T_IsCommutativeBand_612
d_isJoinSemilattice_184 (T_JoinSemilattice_164 -> T_JoinSemilattice_164
forall a b. a -> b
coe T_JoinSemilattice_164
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsBand_526
v2 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
               ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v3)))))
-- Algebra.Lattice.Bundles.JoinSemilattice._.sym
d_sym_210 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_164 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_210 :: ()
-> ()
-> T_JoinSemilattice_164
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_210 ~()
v0 ~()
v1 T_JoinSemilattice_164
v2 = T_JoinSemilattice_164 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_210 T_JoinSemilattice_164
v2
du_sym_210 ::
  T_JoinSemilattice_164 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_210 :: T_JoinSemilattice_164 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_210 T_JoinSemilattice_164
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_JoinSemilattice_164 -> T_IsCommutativeBand_612
d_isJoinSemilattice_184 (T_JoinSemilattice_164 -> T_JoinSemilattice_164
forall a b. a -> b
coe T_JoinSemilattice_164
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
            ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
               ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
                  ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v1))))))
-- Algebra.Lattice.Bundles.JoinSemilattice._.trans
d_trans_212 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_164 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_212 :: ()
-> ()
-> T_JoinSemilattice_164
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_212 ~()
v0 ~()
v1 T_JoinSemilattice_164
v2 = T_JoinSemilattice_164
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_212 T_JoinSemilattice_164
v2
du_trans_212 ::
  T_JoinSemilattice_164 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_212 :: T_JoinSemilattice_164
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_212 T_JoinSemilattice_164
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_JoinSemilattice_164 -> T_IsCommutativeBand_612
d_isJoinSemilattice_184 (T_JoinSemilattice_164 -> T_JoinSemilattice_164
forall a b. a -> b
coe T_JoinSemilattice_164
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
            ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
               ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
                  ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v1))))))
-- Algebra.Lattice.Bundles.JoinSemilattice._.∙-cong
d_'8729''45'cong_214 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_164 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_214 :: ()
-> ()
-> T_JoinSemilattice_164
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_214 ~()
v0 ~()
v1 T_JoinSemilattice_164
v2 = T_JoinSemilattice_164
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_214 T_JoinSemilattice_164
v2
du_'8729''45'cong_214 ::
  T_JoinSemilattice_164 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong_214 :: T_JoinSemilattice_164
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_214 T_JoinSemilattice_164
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_JoinSemilattice_164 -> T_IsCommutativeBand_612
d_isJoinSemilattice_184 (T_JoinSemilattice_164 -> T_JoinSemilattice_164
forall a b. a -> b
coe T_JoinSemilattice_164
v0) in
    AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
               ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v1)))))
-- Algebra.Lattice.Bundles.JoinSemilattice._.∙-congʳ
d_'8729''45'cong'691'_216 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_164 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_216 :: ()
-> ()
-> T_JoinSemilattice_164
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_216 ~()
v0 ~()
v1 T_JoinSemilattice_164
v2
  = T_JoinSemilattice_164
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_216 T_JoinSemilattice_164
v2
du_'8729''45'cong'691'_216 ::
  T_JoinSemilattice_164 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_216 :: T_JoinSemilattice_164
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_216 T_JoinSemilattice_164
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_JoinSemilattice_164 -> T_IsCommutativeBand_612
d_isJoinSemilattice_184 (T_JoinSemilattice_164 -> T_JoinSemilattice_164
forall a b. a -> b
coe T_JoinSemilattice_164
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBand_526
v2 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
v5
                      = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6
                         = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v4) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                        ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6)
                        ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                           ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                              (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))))))
-- Algebra.Lattice.Bundles.JoinSemilattice._.∙-congˡ
d_'8729''45'cong'737'_218 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_164 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_218 :: ()
-> ()
-> T_JoinSemilattice_164
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_218 ~()
v0 ~()
v1 T_JoinSemilattice_164
v2
  = T_JoinSemilattice_164
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_218 T_JoinSemilattice_164
v2
du_'8729''45'cong'737'_218 ::
  T_JoinSemilattice_164 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_218 :: T_JoinSemilattice_164
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_218 T_JoinSemilattice_164
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_JoinSemilattice_164 -> T_IsCommutativeBand_612
d_isJoinSemilattice_184 (T_JoinSemilattice_164 -> T_JoinSemilattice_164
forall a b. a -> b
coe T_JoinSemilattice_164
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBand_526
v2 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
v5
                      = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6
                         = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v4) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                        ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6)
                        ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                           ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                              (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))))))
-- Algebra.Lattice.Bundles.JoinSemilattice.semilattice
d_semilattice_220 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_164 -> T_Semilattice_10
d_semilattice_220 :: () -> () -> T_JoinSemilattice_164 -> T_Semilattice_10
d_semilattice_220 ~()
v0 ~()
v1 T_JoinSemilattice_164
v2 = T_JoinSemilattice_164 -> T_Semilattice_10
du_semilattice_220 T_JoinSemilattice_164
v2
du_semilattice_220 :: T_JoinSemilattice_164 -> T_Semilattice_10
du_semilattice_220 :: T_JoinSemilattice_164 -> T_Semilattice_10
du_semilattice_220 T_JoinSemilattice_164
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsCommutativeBand_612 -> T_Semilattice_10)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> T_Semilattice_10
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612 -> T_Semilattice_10
C_constructor_84 (T_JoinSemilattice_164 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__182 (T_JoinSemilattice_164 -> T_JoinSemilattice_164
forall a b. a -> b
coe T_JoinSemilattice_164
v0))
      (T_JoinSemilattice_164 -> T_IsCommutativeBand_612
d_isJoinSemilattice_184 (T_JoinSemilattice_164 -> T_JoinSemilattice_164
forall a b. a -> b
coe T_JoinSemilattice_164
v0))
-- Algebra.Lattice.Bundles.JoinSemilattice._.band
d_band_224 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_164 -> MAlonzo.Code.Algebra.Bundles.T_Band_620
d_band_224 :: () -> () -> T_JoinSemilattice_164 -> T_Band_620
d_band_224 ~()
v0 ~()
v1 T_JoinSemilattice_164
v2 = T_JoinSemilattice_164 -> T_Band_620
du_band_224 T_JoinSemilattice_164
v2
du_band_224 ::
  T_JoinSemilattice_164 -> MAlonzo.Code.Algebra.Bundles.T_Band_620
du_band_224 :: T_JoinSemilattice_164 -> T_Band_620
du_band_224 T_JoinSemilattice_164
v0 = (T_Semilattice_10 -> T_Band_620) -> AgdaAny -> T_Band_620
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_620
du_band_66 ((T_JoinSemilattice_164 -> T_Semilattice_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_164 -> T_Semilattice_10
du_semilattice_220 (T_JoinSemilattice_164 -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_164
v0))
-- Algebra.Lattice.Bundles.JoinSemilattice._.magma
d_magma_226 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_164 -> MAlonzo.Code.Algebra.Bundles.T_Magma_74
d_magma_226 :: () -> () -> T_JoinSemilattice_164 -> T_Magma_74
d_magma_226 ~()
v0 ~()
v1 T_JoinSemilattice_164
v2 = T_JoinSemilattice_164 -> T_Magma_74
du_magma_226 T_JoinSemilattice_164
v2
du_magma_226 ::
  T_JoinSemilattice_164 -> MAlonzo.Code.Algebra.Bundles.T_Magma_74
du_magma_226 :: T_JoinSemilattice_164 -> T_Magma_74
du_magma_226 T_JoinSemilattice_164
v0
  = let v1 :: AgdaAny
v1 = (T_JoinSemilattice_164 -> T_Semilattice_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_164 -> T_Semilattice_10
du_semilattice_220 (T_JoinSemilattice_164 -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_164
v0) in
    AgdaAny -> T_Magma_74
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_Semilattice_10 -> T_Band_620) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_620
du_band_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Semigroup_558 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Semigroup_558 -> T_Magma_74
MAlonzo.Code.Algebra.Bundles.du_magma_606
            ((T_Band_620 -> T_Semigroup_558) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_620 -> T_Semigroup_558
MAlonzo.Code.Algebra.Bundles.du_semigroup_672 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Lattice.Bundles.JoinSemilattice._.rawMagma
d_rawMagma_228 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_164 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
d_rawMagma_228 :: () -> () -> T_JoinSemilattice_164 -> T_RawMagma_44
d_rawMagma_228 ~()
v0 ~()
v1 T_JoinSemilattice_164
v2 = T_JoinSemilattice_164 -> T_RawMagma_44
du_rawMagma_228 T_JoinSemilattice_164
v2
du_rawMagma_228 ::
  T_JoinSemilattice_164 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
du_rawMagma_228 :: T_JoinSemilattice_164 -> T_RawMagma_44
du_rawMagma_228 T_JoinSemilattice_164
v0
  = let v1 :: AgdaAny
v1 = (T_JoinSemilattice_164 -> T_Semilattice_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_164 -> T_Semilattice_10
du_semilattice_220 (T_JoinSemilattice_164 -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_164
v0) in
    AgdaAny -> T_RawMagma_44
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_Semilattice_10 -> T_Band_620) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_620
du_band_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_Band_620 -> T_Semigroup_558) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_620 -> T_Semigroup_558
MAlonzo.Code.Algebra.Bundles.du_semigroup_672 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_Magma_74 -> T_RawMagma_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Magma_74 -> T_RawMagma_44
MAlonzo.Code.Algebra.Bundles.du_rawMagma_118
               ((T_Semigroup_558 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558 -> T_Magma_74
MAlonzo.Code.Algebra.Bundles.du_magma_606 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))
-- Algebra.Lattice.Bundles.JoinSemilattice._.semigroup
d_semigroup_230 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_164 ->
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_558
d_semigroup_230 :: () -> () -> T_JoinSemilattice_164 -> T_Semigroup_558
d_semigroup_230 ~()
v0 ~()
v1 T_JoinSemilattice_164
v2 = T_JoinSemilattice_164 -> T_Semigroup_558
du_semigroup_230 T_JoinSemilattice_164
v2
du_semigroup_230 ::
  T_JoinSemilattice_164 ->
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_558
du_semigroup_230 :: T_JoinSemilattice_164 -> T_Semigroup_558
du_semigroup_230 T_JoinSemilattice_164
v0
  = let v1 :: AgdaAny
v1 = (T_JoinSemilattice_164 -> T_Semilattice_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_164 -> T_Semilattice_10
du_semilattice_220 (T_JoinSemilattice_164 -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_164
v0) in
    AgdaAny -> T_Semigroup_558
forall a b. a -> b
coe
      ((T_Band_620 -> T_Semigroup_558) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Band_620 -> T_Semigroup_558
MAlonzo.Code.Algebra.Bundles.du_semigroup_672
         ((T_Semilattice_10 -> T_Band_620) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_620
du_band_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Lattice.Bundles.BoundedSemilattice
d_BoundedSemilattice_238 :: p -> p -> ()
d_BoundedSemilattice_238 p
a0 p
a1 = ()
data T_BoundedSemilattice_238
  = C_constructor_330 (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny
                      MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884
-- Algebra.Lattice.Bundles.BoundedSemilattice.Carrier
d_Carrier_254 :: T_BoundedSemilattice_238 -> ()
d_Carrier_254 :: T_BoundedSemilattice_238 -> ()
d_Carrier_254 = T_BoundedSemilattice_238 -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.BoundedSemilattice._≈_
d__'8776'__256 ::
  T_BoundedSemilattice_238 -> AgdaAny -> AgdaAny -> ()
d__'8776'__256 :: T_BoundedSemilattice_238 -> AgdaAny -> AgdaAny -> ()
d__'8776'__256 = T_BoundedSemilattice_238 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.BoundedSemilattice._∙_
d__'8729'__258 ::
  T_BoundedSemilattice_238 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__258 :: T_BoundedSemilattice_238 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__258 T_BoundedSemilattice_238
v0
  = case T_BoundedSemilattice_238 -> T_BoundedSemilattice_238
forall a b. a -> b
coe T_BoundedSemilattice_238
v0 of
      C_constructor_330 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsIdempotentCommutativeMonoid_884
v5 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_BoundedSemilattice_238
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.BoundedSemilattice.ε
d_ε_260 :: T_BoundedSemilattice_238 -> AgdaAny
d_ε_260 :: T_BoundedSemilattice_238 -> AgdaAny
d_ε_260 T_BoundedSemilattice_238
v0
  = case T_BoundedSemilattice_238 -> T_BoundedSemilattice_238
forall a b. a -> b
coe T_BoundedSemilattice_238
v0 of
      C_constructor_330 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsIdempotentCommutativeMonoid_884
v5 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4
      T_BoundedSemilattice_238
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.BoundedSemilattice.isBoundedSemilattice
d_isBoundedSemilattice_262 ::
  T_BoundedSemilattice_238 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884
d_isBoundedSemilattice_262 :: T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedSemilattice_262 T_BoundedSemilattice_238
v0
  = case T_BoundedSemilattice_238 -> T_BoundedSemilattice_238
forall a b. a -> b
coe T_BoundedSemilattice_238
v0 of
      C_constructor_330 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsIdempotentCommutativeMonoid_884
v5 -> T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v5
      T_BoundedSemilattice_238
_ -> T_IsIdempotentCommutativeMonoid_884
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.BoundedSemilattice._.assoc
d_assoc_266 ::
  T_BoundedSemilattice_238 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_266 :: T_BoundedSemilattice_238
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_266 T_BoundedSemilattice_238
v0
  = (T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_498
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
         ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
            ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
               ((T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedSemilattice_262 (T_BoundedSemilattice_238 -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238
v0)))))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.comm
d_comm_268 ::
  T_BoundedSemilattice_238 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_268 :: T_BoundedSemilattice_238 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_268 T_BoundedSemilattice_238
v0
  = (T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_776
      ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
         ((T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedSemilattice_262 (T_BoundedSemilattice_238 -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238
v0)))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.idem
d_idem_270 :: T_BoundedSemilattice_238 -> AgdaAny -> AgdaAny
d_idem_270 :: T_BoundedSemilattice_238 -> AgdaAny -> AgdaAny
d_idem_270 T_BoundedSemilattice_238
v0
  = (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_896
      ((T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedSemilattice_262 (T_BoundedSemilattice_238 -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238
v0))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.identity
d_identity_272 ::
  T_BoundedSemilattice_238 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_272 :: T_BoundedSemilattice_238 -> T_Σ_14
d_identity_272 T_BoundedSemilattice_238
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_724
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
         ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
            ((T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedSemilattice_262 (T_BoundedSemilattice_238 -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238
v0))))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.identityʳ
d_identity'691'_274 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedSemilattice_238 -> AgdaAny -> AgdaAny
d_identity'691'_274 :: () -> () -> T_BoundedSemilattice_238 -> AgdaAny -> AgdaAny
d_identity'691'_274 ~()
v0 ~()
v1 T_BoundedSemilattice_238
v2 = T_BoundedSemilattice_238 -> AgdaAny -> AgdaAny
du_identity'691'_274 T_BoundedSemilattice_238
v2
du_identity'691'_274 ::
  T_BoundedSemilattice_238 -> AgdaAny -> AgdaAny
du_identity'691'_274 :: T_BoundedSemilattice_238 -> AgdaAny -> AgdaAny
du_identity'691'_274 T_BoundedSemilattice_238
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedSemilattice_262 (T_BoundedSemilattice_238 -> T_BoundedSemilattice_238
forall a b. a -> b
coe T_BoundedSemilattice_238
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2
             = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_712 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_754
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2))))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.identityˡ
d_identity'737'_276 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedSemilattice_238 -> AgdaAny -> AgdaAny
d_identity'737'_276 :: () -> () -> T_BoundedSemilattice_238 -> AgdaAny -> AgdaAny
d_identity'737'_276 ~()
v0 ~()
v1 T_BoundedSemilattice_238
v2 = T_BoundedSemilattice_238 -> AgdaAny -> AgdaAny
du_identity'737'_276 T_BoundedSemilattice_238
v2
du_identity'737'_276 ::
  T_BoundedSemilattice_238 -> AgdaAny -> AgdaAny
du_identity'737'_276 :: T_BoundedSemilattice_238 -> AgdaAny -> AgdaAny
du_identity'737'_276 T_BoundedSemilattice_238
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedSemilattice_262 (T_BoundedSemilattice_238 -> T_BoundedSemilattice_238
forall a b. a -> b
coe T_BoundedSemilattice_238
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2
             = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_712 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_752
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2))))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.isBand
d_isBand_278 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedSemilattice_238 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
d_isBand_278 :: () -> () -> T_BoundedSemilattice_238 -> T_IsBand_526
d_isBand_278 ~()
v0 ~()
v1 T_BoundedSemilattice_238
v2 = T_BoundedSemilattice_238 -> T_IsBand_526
du_isBand_278 T_BoundedSemilattice_238
v2
du_isBand_278 ::
  T_BoundedSemilattice_238 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
du_isBand_278 :: T_BoundedSemilattice_238 -> T_IsBand_526
du_isBand_278 T_BoundedSemilattice_238
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedSemilattice_262 (T_BoundedSemilattice_238 -> T_BoundedSemilattice_238
forall a b. a -> b
coe T_BoundedSemilattice_238
v0) in
    AgdaAny -> T_IsBand_526
forall a b. a -> b
coe
      ((T_IsIdempotentMonoid_826 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentMonoid_826 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.du_isBand_876
         ((T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_942
            (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1)))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.isCommutativeMagma
d_isCommutativeMagma_280 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedSemilattice_238 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
d_isCommutativeMagma_280 :: () -> () -> T_BoundedSemilattice_238 -> T_IsCommutativeMagma_214
d_isCommutativeMagma_280 ~()
v0 ~()
v1 T_BoundedSemilattice_238
v2 = T_BoundedSemilattice_238 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_280 T_BoundedSemilattice_238
v2
du_isCommutativeMagma_280 ::
  T_BoundedSemilattice_238 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
du_isCommutativeMagma_280 :: T_BoundedSemilattice_238 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_280 T_BoundedSemilattice_238
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedSemilattice_262 (T_BoundedSemilattice_238 -> T_BoundedSemilattice_238
forall a b. a -> b
coe T_BoundedSemilattice_238
v0) in
    AgdaAny -> T_IsCommutativeMagma_214
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2
             = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_606
            ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
               (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2))))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.isCommutativeMonoid
d_isCommutativeMonoid_282 ::
  T_BoundedSemilattice_238 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764
d_isCommutativeMonoid_282 :: T_BoundedSemilattice_238 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_282 T_BoundedSemilattice_238
v0
  = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
      ((T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedSemilattice_262 (T_BoundedSemilattice_238 -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238
v0))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.isCommutativeSemigroup
d_isCommutativeSemigroup_284 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedSemilattice_238 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_284 :: ()
-> () -> T_BoundedSemilattice_238 -> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_284 ~()
v0 ~()
v1 T_BoundedSemilattice_238
v2
  = T_BoundedSemilattice_238 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_284 T_BoundedSemilattice_238
v2
du_isCommutativeSemigroup_284 ::
  T_BoundedSemilattice_238 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_284 :: T_BoundedSemilattice_238 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_284 T_BoundedSemilattice_238
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedSemilattice_262 (T_BoundedSemilattice_238 -> T_BoundedSemilattice_238
forall a b. a -> b
coe T_BoundedSemilattice_238
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe
      ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
         ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
            (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1)))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.isEquivalence
d_isEquivalence_286 ::
  T_BoundedSemilattice_238 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_286 :: T_BoundedSemilattice_238 -> T_IsEquivalence_28
d_isEquivalence_286 T_BoundedSemilattice_238
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
               ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                  ((T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedSemilattice_262 (T_BoundedSemilattice_238 -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238
v0))))))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.isIdempotentMonoid
d_isIdempotentMonoid_288 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedSemilattice_238 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826
d_isIdempotentMonoid_288 :: () -> () -> T_BoundedSemilattice_238 -> T_IsIdempotentMonoid_826
d_isIdempotentMonoid_288 ~()
v0 ~()
v1 T_BoundedSemilattice_238
v2 = T_BoundedSemilattice_238 -> T_IsIdempotentMonoid_826
du_isIdempotentMonoid_288 T_BoundedSemilattice_238
v2
du_isIdempotentMonoid_288 ::
  T_BoundedSemilattice_238 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826
du_isIdempotentMonoid_288 :: T_BoundedSemilattice_238 -> T_IsIdempotentMonoid_826
du_isIdempotentMonoid_288 T_BoundedSemilattice_238
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedSemilattice_262 (T_BoundedSemilattice_238 -> T_BoundedSemilattice_238
forall a b. a -> b
coe T_BoundedSemilattice_238
v0) in
    AgdaAny -> T_IsIdempotentMonoid_826
forall a b. a -> b
coe
      ((T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_942 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.isMagma
d_isMagma_290 ::
  T_BoundedSemilattice_238 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_290 :: T_BoundedSemilattice_238 -> T_IsMagma_178
d_isMagma_290 T_BoundedSemilattice_238
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
         ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
            ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
               ((T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedSemilattice_262 (T_BoundedSemilattice_238 -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238
v0)))))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.isMonoid
d_isMonoid_292 ::
  T_BoundedSemilattice_238 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_isMonoid_292 :: T_BoundedSemilattice_238 -> T_IsMonoid_712
d_isMonoid_292 T_BoundedSemilattice_238
v0
  = (T_IsCommutativeMonoid_764 -> T_IsMonoid_712)
-> AgdaAny -> T_IsMonoid_712
forall a b. a -> b
coe
      T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
      ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
         ((T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedSemilattice_262 (T_BoundedSemilattice_238 -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238
v0)))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.isPartialEquivalence
d_isPartialEquivalence_294 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedSemilattice_238 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_294 :: () -> () -> T_BoundedSemilattice_238 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_294 ~()
v0 ~()
v1 T_BoundedSemilattice_238
v2
  = T_BoundedSemilattice_238 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_294 T_BoundedSemilattice_238
v2
du_isPartialEquivalence_294 ::
  T_BoundedSemilattice_238 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_294 :: T_BoundedSemilattice_238 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_294 T_BoundedSemilattice_238
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedSemilattice_262 (T_BoundedSemilattice_238 -> T_BoundedSemilattice_238
forall a b. a -> b
coe T_BoundedSemilattice_238
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2
             = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_712
v3
                = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_488
v4
                   = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_178
v5 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                     ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v5)))))))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.isSemigroup
d_isSemigroup_296 ::
  T_BoundedSemilattice_238 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_296 :: T_BoundedSemilattice_238 -> T_IsSemigroup_488
d_isSemigroup_296 T_BoundedSemilattice_238
v0
  = (T_IsMonoid_712 -> T_IsSemigroup_488)
-> AgdaAny -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
         ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
            ((T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedSemilattice_262 (T_BoundedSemilattice_238 -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238
v0))))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.isCommutativeBand
d_isCommutativeBand_298 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedSemilattice_238 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
d_isCommutativeBand_298 :: () -> () -> T_BoundedSemilattice_238 -> T_IsCommutativeBand_612
d_isCommutativeBand_298 ~()
v0 ~()
v1 T_BoundedSemilattice_238
v2 = T_BoundedSemilattice_238 -> T_IsCommutativeBand_612
du_isCommutativeBand_298 T_BoundedSemilattice_238
v2
du_isCommutativeBand_298 ::
  T_BoundedSemilattice_238 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
du_isCommutativeBand_298 :: T_BoundedSemilattice_238 -> T_IsCommutativeBand_612
du_isCommutativeBand_298 T_BoundedSemilattice_238
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedSemilattice_262 (T_BoundedSemilattice_238 -> T_BoundedSemilattice_238
forall a b. a -> b
coe T_BoundedSemilattice_238
v0) in
    AgdaAny -> T_IsCommutativeBand_612
forall a b. a -> b
coe
      ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.isUnitalMagma
d_isUnitalMagma_300 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedSemilattice_238 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
d_isUnitalMagma_300 :: () -> () -> T_BoundedSemilattice_238 -> T_IsUnitalMagma_666
d_isUnitalMagma_300 ~()
v0 ~()
v1 T_BoundedSemilattice_238
v2 = T_BoundedSemilattice_238 -> T_IsUnitalMagma_666
du_isUnitalMagma_300 T_BoundedSemilattice_238
v2
du_isUnitalMagma_300 ::
  T_BoundedSemilattice_238 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
du_isUnitalMagma_300 :: T_BoundedSemilattice_238 -> T_IsUnitalMagma_666
du_isUnitalMagma_300 T_BoundedSemilattice_238
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedSemilattice_262 (T_BoundedSemilattice_238 -> T_BoundedSemilattice_238
forall a b. a -> b
coe T_BoundedSemilattice_238
v0) in
    AgdaAny -> T_IsUnitalMagma_666
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2
             = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_712 -> T_IsUnitalMagma_666) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsUnitalMagma_666
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_756
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2))))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.refl
d_refl_302 :: T_BoundedSemilattice_238 -> AgdaAny -> AgdaAny
d_refl_302 :: T_BoundedSemilattice_238 -> AgdaAny -> AgdaAny
d_refl_302 T_BoundedSemilattice_238
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
               ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
                  ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                     ((T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedSemilattice_262 (T_BoundedSemilattice_238 -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238
v0)))))))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.reflexive
d_reflexive_304 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedSemilattice_238 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_304 :: ()
-> ()
-> T_BoundedSemilattice_238
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_304 ~()
v0 ~()
v1 T_BoundedSemilattice_238
v2 = T_BoundedSemilattice_238
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_304 T_BoundedSemilattice_238
v2
du_reflexive_304 ::
  T_BoundedSemilattice_238 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_304 :: T_BoundedSemilattice_238
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_304 T_BoundedSemilattice_238
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedSemilattice_262 (T_BoundedSemilattice_238 -> T_BoundedSemilattice_238
forall a b. a -> b
coe T_BoundedSemilattice_238
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2
             = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_712
v3
                = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_488
v4
                   = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_178
v5 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v4) in
                (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                  (\ AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 ->
                     (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                       ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v5))
                       AgdaAny
v6)))))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.setoid
d_setoid_306 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedSemilattice_238 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_306 :: () -> () -> T_BoundedSemilattice_238 -> T_Setoid_46
d_setoid_306 ~()
v0 ~()
v1 T_BoundedSemilattice_238
v2 = T_BoundedSemilattice_238 -> T_Setoid_46
du_setoid_306 T_BoundedSemilattice_238
v2
du_setoid_306 ::
  T_BoundedSemilattice_238 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_306 :: T_BoundedSemilattice_238 -> T_Setoid_46
du_setoid_306 T_BoundedSemilattice_238
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedSemilattice_262 (T_BoundedSemilattice_238 -> T_BoundedSemilattice_238
forall a b. a -> b
coe T_BoundedSemilattice_238
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2
             = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_712
v3
                = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_488
v4
                   = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
                  ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v4))))))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.sym
d_sym_308 ::
  T_BoundedSemilattice_238 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_308 :: T_BoundedSemilattice_238
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_308 T_BoundedSemilattice_238
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
               ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
                  ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                     ((T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedSemilattice_262 (T_BoundedSemilattice_238 -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238
v0)))))))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.trans
d_trans_310 ::
  T_BoundedSemilattice_238 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_310 :: T_BoundedSemilattice_238
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_310 T_BoundedSemilattice_238
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
               ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
                  ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                     ((T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedSemilattice_262 (T_BoundedSemilattice_238 -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238
v0)))))))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.∙-cong
d_'8729''45'cong_312 ::
  T_BoundedSemilattice_238 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_312 :: T_BoundedSemilattice_238
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_312 T_BoundedSemilattice_238
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
               ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                  ((T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedSemilattice_262 (T_BoundedSemilattice_238 -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238
v0))))))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.∙-congʳ
d_'8729''45'cong'691'_314 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedSemilattice_238 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_314 :: ()
-> ()
-> T_BoundedSemilattice_238
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_314 ~()
v0 ~()
v1 T_BoundedSemilattice_238
v2
  = T_BoundedSemilattice_238
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_314 T_BoundedSemilattice_238
v2
du_'8729''45'cong'691'_314 ::
  T_BoundedSemilattice_238 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_314 :: T_BoundedSemilattice_238
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_314 T_BoundedSemilattice_238
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedSemilattice_262 (T_BoundedSemilattice_238 -> T_BoundedSemilattice_238
forall a b. a -> b
coe T_BoundedSemilattice_238
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2
             = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_712
v3
                = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_488
v4
                   = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_178
v5 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
v6
                         = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7
                            = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v5) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                           ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7)
                           ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                              ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                                 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6))))))))))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.∙-congˡ
d_'8729''45'cong'737'_316 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedSemilattice_238 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_316 :: ()
-> ()
-> T_BoundedSemilattice_238
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_316 ~()
v0 ~()
v1 T_BoundedSemilattice_238
v2
  = T_BoundedSemilattice_238
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_316 T_BoundedSemilattice_238
v2
du_'8729''45'cong'737'_316 ::
  T_BoundedSemilattice_238 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_316 :: T_BoundedSemilattice_238
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_316 T_BoundedSemilattice_238
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedSemilattice_262 (T_BoundedSemilattice_238 -> T_BoundedSemilattice_238
forall a b. a -> b
coe T_BoundedSemilattice_238
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2
             = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_712
v3
                = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_488
v4
                   = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_178
v5 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
v6
                         = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7
                            = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v5) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                           ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7)
                           ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                              ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                                 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6))))))))))
-- Algebra.Lattice.Bundles.BoundedSemilattice.semilattice
d_semilattice_318 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedSemilattice_238 -> T_Semilattice_10
d_semilattice_318 :: () -> () -> T_BoundedSemilattice_238 -> T_Semilattice_10
d_semilattice_318 ~()
v0 ~()
v1 T_BoundedSemilattice_238
v2 = T_BoundedSemilattice_238 -> T_Semilattice_10
du_semilattice_318 T_BoundedSemilattice_238
v2
du_semilattice_318 :: T_BoundedSemilattice_238 -> T_Semilattice_10
du_semilattice_318 :: T_BoundedSemilattice_238 -> T_Semilattice_10
du_semilattice_318 T_BoundedSemilattice_238
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsCommutativeBand_612 -> T_Semilattice_10)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> T_Semilattice_10
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612 -> T_Semilattice_10
C_constructor_84 (T_BoundedSemilattice_238 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__258 (T_BoundedSemilattice_238 -> T_BoundedSemilattice_238
forall a b. a -> b
coe T_BoundedSemilattice_238
v0))
      ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
         ((T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedSemilattice_262 (T_BoundedSemilattice_238 -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238
v0)))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.band
d_band_322 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedSemilattice_238 -> MAlonzo.Code.Algebra.Bundles.T_Band_620
d_band_322 :: () -> () -> T_BoundedSemilattice_238 -> T_Band_620
d_band_322 ~()
v0 ~()
v1 T_BoundedSemilattice_238
v2 = T_BoundedSemilattice_238 -> T_Band_620
du_band_322 T_BoundedSemilattice_238
v2
du_band_322 ::
  T_BoundedSemilattice_238 -> MAlonzo.Code.Algebra.Bundles.T_Band_620
du_band_322 :: T_BoundedSemilattice_238 -> T_Band_620
du_band_322 T_BoundedSemilattice_238
v0 = (T_Semilattice_10 -> T_Band_620) -> AgdaAny -> T_Band_620
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_620
du_band_66 ((T_BoundedSemilattice_238 -> T_Semilattice_10)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238 -> T_Semilattice_10
du_semilattice_318 (T_BoundedSemilattice_238 -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238
v0))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.magma
d_magma_324 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedSemilattice_238 -> MAlonzo.Code.Algebra.Bundles.T_Magma_74
d_magma_324 :: () -> () -> T_BoundedSemilattice_238 -> T_Magma_74
d_magma_324 ~()
v0 ~()
v1 T_BoundedSemilattice_238
v2 = T_BoundedSemilattice_238 -> T_Magma_74
du_magma_324 T_BoundedSemilattice_238
v2
du_magma_324 ::
  T_BoundedSemilattice_238 -> MAlonzo.Code.Algebra.Bundles.T_Magma_74
du_magma_324 :: T_BoundedSemilattice_238 -> T_Magma_74
du_magma_324 T_BoundedSemilattice_238
v0
  = let v1 :: AgdaAny
v1 = (T_BoundedSemilattice_238 -> T_Semilattice_10)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238 -> T_Semilattice_10
du_semilattice_318 (T_BoundedSemilattice_238 -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238
v0) in
    AgdaAny -> T_Magma_74
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_Semilattice_10 -> T_Band_620) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_620
du_band_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Semigroup_558 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Semigroup_558 -> T_Magma_74
MAlonzo.Code.Algebra.Bundles.du_magma_606
            ((T_Band_620 -> T_Semigroup_558) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_620 -> T_Semigroup_558
MAlonzo.Code.Algebra.Bundles.du_semigroup_672 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.rawMagma
d_rawMagma_326 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedSemilattice_238 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
d_rawMagma_326 :: () -> () -> T_BoundedSemilattice_238 -> T_RawMagma_44
d_rawMagma_326 ~()
v0 ~()
v1 T_BoundedSemilattice_238
v2 = T_BoundedSemilattice_238 -> T_RawMagma_44
du_rawMagma_326 T_BoundedSemilattice_238
v2
du_rawMagma_326 ::
  T_BoundedSemilattice_238 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
du_rawMagma_326 :: T_BoundedSemilattice_238 -> T_RawMagma_44
du_rawMagma_326 T_BoundedSemilattice_238
v0
  = let v1 :: AgdaAny
v1 = (T_BoundedSemilattice_238 -> T_Semilattice_10)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238 -> T_Semilattice_10
du_semilattice_318 (T_BoundedSemilattice_238 -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238
v0) in
    AgdaAny -> T_RawMagma_44
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_Semilattice_10 -> T_Band_620) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_620
du_band_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_Band_620 -> T_Semigroup_558) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_620 -> T_Semigroup_558
MAlonzo.Code.Algebra.Bundles.du_semigroup_672 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_Magma_74 -> T_RawMagma_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Magma_74 -> T_RawMagma_44
MAlonzo.Code.Algebra.Bundles.du_rawMagma_118
               ((T_Semigroup_558 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558 -> T_Magma_74
MAlonzo.Code.Algebra.Bundles.du_magma_606 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.semigroup
d_semigroup_328 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedSemilattice_238 ->
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_558
d_semigroup_328 :: () -> () -> T_BoundedSemilattice_238 -> T_Semigroup_558
d_semigroup_328 ~()
v0 ~()
v1 T_BoundedSemilattice_238
v2 = T_BoundedSemilattice_238 -> T_Semigroup_558
du_semigroup_328 T_BoundedSemilattice_238
v2
du_semigroup_328 ::
  T_BoundedSemilattice_238 ->
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_558
du_semigroup_328 :: T_BoundedSemilattice_238 -> T_Semigroup_558
du_semigroup_328 T_BoundedSemilattice_238
v0
  = let v1 :: AgdaAny
v1 = (T_BoundedSemilattice_238 -> T_Semilattice_10)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238 -> T_Semilattice_10
du_semilattice_318 (T_BoundedSemilattice_238 -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238
v0) in
    AgdaAny -> T_Semigroup_558
forall a b. a -> b
coe
      ((T_Band_620 -> T_Semigroup_558) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Band_620 -> T_Semigroup_558
MAlonzo.Code.Algebra.Bundles.du_semigroup_672
         ((T_Semilattice_10 -> T_Band_620) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_620
du_band_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice
d_BoundedMeetSemilattice_336 :: p -> p -> ()
d_BoundedMeetSemilattice_336 p
a0 p
a1 = ()
data T_BoundedMeetSemilattice_336
  = C_constructor_418 (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny
                      MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice.Carrier
d_Carrier_352 :: T_BoundedMeetSemilattice_336 -> ()
d_Carrier_352 :: T_BoundedMeetSemilattice_336 -> ()
d_Carrier_352 = T_BoundedMeetSemilattice_336 -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._≈_
d__'8776'__354 ::
  T_BoundedMeetSemilattice_336 -> AgdaAny -> AgdaAny -> ()
d__'8776'__354 :: T_BoundedMeetSemilattice_336 -> AgdaAny -> AgdaAny -> ()
d__'8776'__354 = T_BoundedMeetSemilattice_336 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._∧_
d__'8743'__356 ::
  T_BoundedMeetSemilattice_336 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__356 :: T_BoundedMeetSemilattice_336 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__356 T_BoundedMeetSemilattice_336
v0
  = case T_BoundedMeetSemilattice_336 -> T_BoundedMeetSemilattice_336
forall a b. a -> b
coe T_BoundedMeetSemilattice_336
v0 of
      C_constructor_418 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsIdempotentCommutativeMonoid_884
v5 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_BoundedMeetSemilattice_336
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice.⊤
d_'8868'_358 :: T_BoundedMeetSemilattice_336 -> AgdaAny
d_'8868'_358 :: T_BoundedMeetSemilattice_336 -> AgdaAny
d_'8868'_358 T_BoundedMeetSemilattice_336
v0
  = case T_BoundedMeetSemilattice_336 -> T_BoundedMeetSemilattice_336
forall a b. a -> b
coe T_BoundedMeetSemilattice_336
v0 of
      C_constructor_418 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsIdempotentCommutativeMonoid_884
v5 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4
      T_BoundedMeetSemilattice_336
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice.isBoundedMeetSemilattice
d_isBoundedMeetSemilattice_360 ::
  T_BoundedMeetSemilattice_336 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884
d_isBoundedMeetSemilattice_360 :: T_BoundedMeetSemilattice_336 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedMeetSemilattice_360 T_BoundedMeetSemilattice_336
v0
  = case T_BoundedMeetSemilattice_336 -> T_BoundedMeetSemilattice_336
forall a b. a -> b
coe T_BoundedMeetSemilattice_336
v0 of
      C_constructor_418 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsIdempotentCommutativeMonoid_884
v5 -> T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v5
      T_BoundedMeetSemilattice_336
_ -> T_IsIdempotentCommutativeMonoid_884
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.assoc
d_assoc_364 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_336 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_364 :: ()
-> ()
-> T_BoundedMeetSemilattice_336
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_assoc_364 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_336
v2 = T_BoundedMeetSemilattice_336
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_364 T_BoundedMeetSemilattice_336
v2
du_assoc_364 ::
  T_BoundedMeetSemilattice_336 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_364 :: T_BoundedMeetSemilattice_336
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_364 T_BoundedMeetSemilattice_336
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedMeetSemilattice_336 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedMeetSemilattice_360 (T_BoundedMeetSemilattice_336 -> T_BoundedMeetSemilattice_336
forall a b. a -> b
coe T_BoundedMeetSemilattice_336
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
                 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_498
            ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
               ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.comm
d_comm_366 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_336 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_366 :: ()
-> ()
-> T_BoundedMeetSemilattice_336
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_comm_366 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_336
v2 = T_BoundedMeetSemilattice_336 -> AgdaAny -> AgdaAny -> AgdaAny
du_comm_366 T_BoundedMeetSemilattice_336
v2
du_comm_366 ::
  T_BoundedMeetSemilattice_336 -> AgdaAny -> AgdaAny -> AgdaAny
du_comm_366 :: T_BoundedMeetSemilattice_336 -> AgdaAny -> AgdaAny -> AgdaAny
du_comm_366 T_BoundedMeetSemilattice_336
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedMeetSemilattice_336 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedMeetSemilattice_360 (T_BoundedMeetSemilattice_336 -> T_BoundedMeetSemilattice_336
forall a b. a -> b
coe T_BoundedMeetSemilattice_336
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_776
         ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
            (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1)))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.idem
d_idem_368 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_336 -> AgdaAny -> AgdaAny
d_idem_368 :: () -> () -> T_BoundedMeetSemilattice_336 -> AgdaAny -> AgdaAny
d_idem_368 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_336
v2 = T_BoundedMeetSemilattice_336 -> AgdaAny -> AgdaAny
du_idem_368 T_BoundedMeetSemilattice_336
v2
du_idem_368 :: T_BoundedMeetSemilattice_336 -> AgdaAny -> AgdaAny
du_idem_368 :: T_BoundedMeetSemilattice_336 -> AgdaAny -> AgdaAny
du_idem_368 T_BoundedMeetSemilattice_336
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedMeetSemilattice_336 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedMeetSemilattice_360 (T_BoundedMeetSemilattice_336 -> T_BoundedMeetSemilattice_336
forall a b. a -> b
coe T_BoundedMeetSemilattice_336
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
                 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsBand_526 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_526 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_536
            ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.identity
d_identity_370 ::
  T_BoundedMeetSemilattice_336 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_370 :: T_BoundedMeetSemilattice_336 -> T_Σ_14
d_identity_370 T_BoundedMeetSemilattice_336
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_724
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
         ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
            ((T_BoundedMeetSemilattice_336
 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_336 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedMeetSemilattice_360 (T_BoundedMeetSemilattice_336 -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_336
v0))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.identityʳ
d_identity'691'_372 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_336 -> AgdaAny -> AgdaAny
d_identity'691'_372 :: () -> () -> T_BoundedMeetSemilattice_336 -> AgdaAny -> AgdaAny
d_identity'691'_372 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_336
v2 = T_BoundedMeetSemilattice_336 -> AgdaAny -> AgdaAny
du_identity'691'_372 T_BoundedMeetSemilattice_336
v2
du_identity'691'_372 ::
  T_BoundedMeetSemilattice_336 -> AgdaAny -> AgdaAny
du_identity'691'_372 :: T_BoundedMeetSemilattice_336 -> AgdaAny -> AgdaAny
du_identity'691'_372 T_BoundedMeetSemilattice_336
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedMeetSemilattice_336 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedMeetSemilattice_360 (T_BoundedMeetSemilattice_336 -> T_BoundedMeetSemilattice_336
forall a b. a -> b
coe T_BoundedMeetSemilattice_336
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2
             = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_712 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_754
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.identityˡ
d_identity'737'_374 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_336 -> AgdaAny -> AgdaAny
d_identity'737'_374 :: () -> () -> T_BoundedMeetSemilattice_336 -> AgdaAny -> AgdaAny
d_identity'737'_374 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_336
v2 = T_BoundedMeetSemilattice_336 -> AgdaAny -> AgdaAny
du_identity'737'_374 T_BoundedMeetSemilattice_336
v2
du_identity'737'_374 ::
  T_BoundedMeetSemilattice_336 -> AgdaAny -> AgdaAny
du_identity'737'_374 :: T_BoundedMeetSemilattice_336 -> AgdaAny -> AgdaAny
du_identity'737'_374 T_BoundedMeetSemilattice_336
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedMeetSemilattice_336 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedMeetSemilattice_360 (T_BoundedMeetSemilattice_336 -> T_BoundedMeetSemilattice_336
forall a b. a -> b
coe T_BoundedMeetSemilattice_336
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2
             = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_712 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_752
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.isBand
d_isBand_376 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_336 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
d_isBand_376 :: () -> () -> T_BoundedMeetSemilattice_336 -> T_IsBand_526
d_isBand_376 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_336
v2 = T_BoundedMeetSemilattice_336 -> T_IsBand_526
du_isBand_376 T_BoundedMeetSemilattice_336
v2
du_isBand_376 ::
  T_BoundedMeetSemilattice_336 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
du_isBand_376 :: T_BoundedMeetSemilattice_336 -> T_IsBand_526
du_isBand_376 T_BoundedMeetSemilattice_336
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedMeetSemilattice_336 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedMeetSemilattice_360 (T_BoundedMeetSemilattice_336 -> T_BoundedMeetSemilattice_336
forall a b. a -> b
coe T_BoundedMeetSemilattice_336
v0) in
    AgdaAny -> T_IsBand_526
forall a b. a -> b
coe
      ((T_IsIdempotentMonoid_826 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentMonoid_826 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.du_isBand_876
         ((T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_942
            (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1)))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.isEquivalence
d_isEquivalence_378 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_336 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_378 :: () -> () -> T_BoundedMeetSemilattice_336 -> T_IsEquivalence_28
d_isEquivalence_378 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_336
v2 = T_BoundedMeetSemilattice_336 -> T_IsEquivalence_28
du_isEquivalence_378 T_BoundedMeetSemilattice_336
v2
du_isEquivalence_378 ::
  T_BoundedMeetSemilattice_336 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_378 :: T_BoundedMeetSemilattice_336 -> T_IsEquivalence_28
du_isEquivalence_378 T_BoundedMeetSemilattice_336
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedMeetSemilattice_336 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedMeetSemilattice_360 (T_BoundedMeetSemilattice_336 -> T_BoundedMeetSemilattice_336
forall a b. a -> b
coe T_BoundedMeetSemilattice_336
v0) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
                 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
            ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
               ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
                  ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.isMagma
d_isMagma_380 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_336 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_380 :: () -> () -> T_BoundedMeetSemilattice_336 -> T_IsMagma_178
d_isMagma_380 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_336
v2 = T_BoundedMeetSemilattice_336 -> T_IsMagma_178
du_isMagma_380 T_BoundedMeetSemilattice_336
v2
du_isMagma_380 ::
  T_BoundedMeetSemilattice_336 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
du_isMagma_380 :: T_BoundedMeetSemilattice_336 -> T_IsMagma_178
du_isMagma_380 T_BoundedMeetSemilattice_336
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedMeetSemilattice_336 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedMeetSemilattice_360 (T_BoundedMeetSemilattice_336 -> T_BoundedMeetSemilattice_336
forall a b. a -> b
coe T_BoundedMeetSemilattice_336
v0) in
    AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
                 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
               ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.isCommutativeBand
d_isCommutativeBand_382 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_336 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
d_isCommutativeBand_382 :: () -> () -> T_BoundedMeetSemilattice_336 -> T_IsCommutativeBand_612
d_isCommutativeBand_382 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_336
v2 = T_BoundedMeetSemilattice_336 -> T_IsCommutativeBand_612
du_isCommutativeBand_382 T_BoundedMeetSemilattice_336
v2
du_isCommutativeBand_382 ::
  T_BoundedMeetSemilattice_336 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
du_isCommutativeBand_382 :: T_BoundedMeetSemilattice_336 -> T_IsCommutativeBand_612
du_isCommutativeBand_382 T_BoundedMeetSemilattice_336
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedMeetSemilattice_336 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedMeetSemilattice_360 (T_BoundedMeetSemilattice_336 -> T_BoundedMeetSemilattice_336
forall a b. a -> b
coe T_BoundedMeetSemilattice_336
v0) in
    AgdaAny -> T_IsCommutativeBand_612
forall a b. a -> b
coe
      ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.isPartialEquivalence
d_isPartialEquivalence_384 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_336 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_384 :: ()
-> () -> T_BoundedMeetSemilattice_336 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_384 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_336
v2
  = T_BoundedMeetSemilattice_336 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_384 T_BoundedMeetSemilattice_336
v2
du_isPartialEquivalence_384 ::
  T_BoundedMeetSemilattice_336 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_384 :: T_BoundedMeetSemilattice_336 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_384 T_BoundedMeetSemilattice_336
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedMeetSemilattice_336 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedMeetSemilattice_360 (T_BoundedMeetSemilattice_336 -> T_BoundedMeetSemilattice_336
forall a b. a -> b
coe T_BoundedMeetSemilattice_336
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
                 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsBand_526
v3 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> T_IsCommutativeBand_612
forall a b. a -> b
coe AgdaAny
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_488
v4
                   = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_178
v5 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                     ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v5)))))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.isSemigroup
d_isSemigroup_386 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_336 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_386 :: () -> () -> T_BoundedMeetSemilattice_336 -> T_IsSemigroup_488
d_isSemigroup_386 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_336
v2 = T_BoundedMeetSemilattice_336 -> T_IsSemigroup_488
du_isSemigroup_386 T_BoundedMeetSemilattice_336
v2
du_isSemigroup_386 ::
  T_BoundedMeetSemilattice_336 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
du_isSemigroup_386 :: T_BoundedMeetSemilattice_336 -> T_IsSemigroup_488
du_isSemigroup_386 T_BoundedMeetSemilattice_336
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedMeetSemilattice_336 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedMeetSemilattice_360 (T_BoundedMeetSemilattice_336 -> T_BoundedMeetSemilattice_336
forall a b. a -> b
coe T_BoundedMeetSemilattice_336
v0) in
    AgdaAny -> T_IsSemigroup_488
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
                 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
            ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.refl
d_refl_388 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_336 -> AgdaAny -> AgdaAny
d_refl_388 :: () -> () -> T_BoundedMeetSemilattice_336 -> AgdaAny -> AgdaAny
d_refl_388 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_336
v2 = T_BoundedMeetSemilattice_336 -> AgdaAny -> AgdaAny
du_refl_388 T_BoundedMeetSemilattice_336
v2
du_refl_388 :: T_BoundedMeetSemilattice_336 -> AgdaAny -> AgdaAny
du_refl_388 :: T_BoundedMeetSemilattice_336 -> AgdaAny -> AgdaAny
du_refl_388 T_BoundedMeetSemilattice_336
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedMeetSemilattice_336 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedMeetSemilattice_360 (T_BoundedMeetSemilattice_336 -> T_BoundedMeetSemilattice_336
forall a b. a -> b
coe T_BoundedMeetSemilattice_336
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
                 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
            ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
               ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
                  ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
                     ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)))))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.reflexive
d_reflexive_390 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_336 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_390 :: ()
-> ()
-> T_BoundedMeetSemilattice_336
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_390 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_336
v2 = T_BoundedMeetSemilattice_336
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_390 T_BoundedMeetSemilattice_336
v2
du_reflexive_390 ::
  T_BoundedMeetSemilattice_336 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_390 :: T_BoundedMeetSemilattice_336
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_390 T_BoundedMeetSemilattice_336
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedMeetSemilattice_336 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedMeetSemilattice_360 (T_BoundedMeetSemilattice_336 -> T_BoundedMeetSemilattice_336
forall a b. a -> b
coe T_BoundedMeetSemilattice_336
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
                 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsBand_526
v3 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> T_IsCommutativeBand_612
forall a b. a -> b
coe AgdaAny
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_488
v4
                   = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_178
v5 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v4) in
                (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                  (\ AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 ->
                     (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                       ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v5))
                       AgdaAny
v6)))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.setoid
d_setoid_392 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_336 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_392 :: () -> () -> T_BoundedMeetSemilattice_336 -> T_Setoid_46
d_setoid_392 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_336
v2 = T_BoundedMeetSemilattice_336 -> T_Setoid_46
du_setoid_392 T_BoundedMeetSemilattice_336
v2
du_setoid_392 ::
  T_BoundedMeetSemilattice_336 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_392 :: T_BoundedMeetSemilattice_336 -> T_Setoid_46
du_setoid_392 T_BoundedMeetSemilattice_336
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedMeetSemilattice_336 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedMeetSemilattice_360 (T_BoundedMeetSemilattice_336 -> T_BoundedMeetSemilattice_336
forall a b. a -> b
coe T_BoundedMeetSemilattice_336
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
                 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsBand_526
v3 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> T_IsCommutativeBand_612
forall a b. a -> b
coe AgdaAny
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_488
v4
                   = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
                  ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v4))))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.sym
d_sym_394 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_336 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_394 :: ()
-> ()
-> T_BoundedMeetSemilattice_336
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_394 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_336
v2 = T_BoundedMeetSemilattice_336
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_394 T_BoundedMeetSemilattice_336
v2
du_sym_394 ::
  T_BoundedMeetSemilattice_336 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_394 :: T_BoundedMeetSemilattice_336
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_394 T_BoundedMeetSemilattice_336
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedMeetSemilattice_336 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedMeetSemilattice_360 (T_BoundedMeetSemilattice_336 -> T_BoundedMeetSemilattice_336
forall a b. a -> b
coe T_BoundedMeetSemilattice_336
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
                 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
            ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
               ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
                  ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
                     ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)))))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.trans
d_trans_396 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_336 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_396 :: ()
-> ()
-> T_BoundedMeetSemilattice_336
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_396 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_336
v2 = T_BoundedMeetSemilattice_336
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_396 T_BoundedMeetSemilattice_336
v2
du_trans_396 ::
  T_BoundedMeetSemilattice_336 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_396 :: T_BoundedMeetSemilattice_336
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_396 T_BoundedMeetSemilattice_336
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedMeetSemilattice_336 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedMeetSemilattice_360 (T_BoundedMeetSemilattice_336 -> T_BoundedMeetSemilattice_336
forall a b. a -> b
coe T_BoundedMeetSemilattice_336
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
                 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
            ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
               ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
                  ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
                     ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)))))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.∙-cong
d_'8729''45'cong_398 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_336 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_398 :: ()
-> ()
-> T_BoundedMeetSemilattice_336
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_398 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_336
v2 = T_BoundedMeetSemilattice_336
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_398 T_BoundedMeetSemilattice_336
v2
du_'8729''45'cong_398 ::
  T_BoundedMeetSemilattice_336 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong_398 :: T_BoundedMeetSemilattice_336
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_398 T_BoundedMeetSemilattice_336
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedMeetSemilattice_336 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedMeetSemilattice_360 (T_BoundedMeetSemilattice_336 -> T_BoundedMeetSemilattice_336
forall a b. a -> b
coe T_BoundedMeetSemilattice_336
v0) in
    AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
                 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188
            ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
               ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
                  ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.∙-congʳ
d_'8729''45'cong'691'_400 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_336 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_400 :: ()
-> ()
-> T_BoundedMeetSemilattice_336
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_400 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_336
v2
  = T_BoundedMeetSemilattice_336
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_400 T_BoundedMeetSemilattice_336
v2
du_'8729''45'cong'691'_400 ::
  T_BoundedMeetSemilattice_336 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_400 :: T_BoundedMeetSemilattice_336
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_400 T_BoundedMeetSemilattice_336
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedMeetSemilattice_336 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedMeetSemilattice_360 (T_BoundedMeetSemilattice_336 -> T_BoundedMeetSemilattice_336
forall a b. a -> b
coe T_BoundedMeetSemilattice_336
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
                 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsBand_526
v3 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> T_IsCommutativeBand_612
forall a b. a -> b
coe AgdaAny
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_488
v4
                   = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_178
v5 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
v6
                         = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7
                            = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v5) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                           ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7)
                           ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                              ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                                 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6))))))))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.∙-congˡ
d_'8729''45'cong'737'_402 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_336 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_402 :: ()
-> ()
-> T_BoundedMeetSemilattice_336
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_402 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_336
v2
  = T_BoundedMeetSemilattice_336
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_402 T_BoundedMeetSemilattice_336
v2
du_'8729''45'cong'737'_402 ::
  T_BoundedMeetSemilattice_336 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_402 :: T_BoundedMeetSemilattice_336
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_402 T_BoundedMeetSemilattice_336
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedMeetSemilattice_336 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedMeetSemilattice_360 (T_BoundedMeetSemilattice_336 -> T_BoundedMeetSemilattice_336
forall a b. a -> b
coe T_BoundedMeetSemilattice_336
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
                 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsBand_526
v3 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> T_IsCommutativeBand_612
forall a b. a -> b
coe AgdaAny
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_488
v4
                   = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_178
v5 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
v6
                         = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7
                            = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v5) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                           ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7)
                           ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                              ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                                 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6))))))))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice.boundedSemilattice
d_boundedSemilattice_404 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_336 -> T_BoundedSemilattice_238
d_boundedSemilattice_404 :: ()
-> () -> T_BoundedMeetSemilattice_336 -> T_BoundedSemilattice_238
d_boundedSemilattice_404 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_336
v2 = T_BoundedMeetSemilattice_336 -> T_BoundedSemilattice_238
du_boundedSemilattice_404 T_BoundedMeetSemilattice_336
v2
du_boundedSemilattice_404 ::
  T_BoundedMeetSemilattice_336 -> T_BoundedSemilattice_238
du_boundedSemilattice_404 :: T_BoundedMeetSemilattice_336 -> T_BoundedSemilattice_238
du_boundedSemilattice_404 T_BoundedMeetSemilattice_336
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsIdempotentCommutativeMonoid_884
 -> T_BoundedSemilattice_238)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_BoundedSemilattice_238
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_BoundedSemilattice_238
C_constructor_330 (T_BoundedMeetSemilattice_336 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__356 (T_BoundedMeetSemilattice_336 -> T_BoundedMeetSemilattice_336
forall a b. a -> b
coe T_BoundedMeetSemilattice_336
v0)) (T_BoundedMeetSemilattice_336 -> AgdaAny
d_'8868'_358 (T_BoundedMeetSemilattice_336 -> T_BoundedMeetSemilattice_336
forall a b. a -> b
coe T_BoundedMeetSemilattice_336
v0))
      (T_BoundedMeetSemilattice_336 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedMeetSemilattice_360 (T_BoundedMeetSemilattice_336 -> T_BoundedMeetSemilattice_336
forall a b. a -> b
coe T_BoundedMeetSemilattice_336
v0))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.band
d_band_408 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_336 ->
  MAlonzo.Code.Algebra.Bundles.T_Band_620
d_band_408 :: () -> () -> T_BoundedMeetSemilattice_336 -> T_Band_620
d_band_408 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_336
v2 = T_BoundedMeetSemilattice_336 -> T_Band_620
du_band_408 T_BoundedMeetSemilattice_336
v2
du_band_408 ::
  T_BoundedMeetSemilattice_336 ->
  MAlonzo.Code.Algebra.Bundles.T_Band_620
du_band_408 :: T_BoundedMeetSemilattice_336 -> T_Band_620
du_band_408 T_BoundedMeetSemilattice_336
v0
  = let v1 :: AgdaAny
v1 = (T_BoundedMeetSemilattice_336 -> T_BoundedSemilattice_238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_336 -> T_BoundedSemilattice_238
du_boundedSemilattice_404 (T_BoundedMeetSemilattice_336 -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_336
v0) in
    AgdaAny -> T_Band_620
forall a b. a -> b
coe ((T_Semilattice_10 -> T_Band_620) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_620
du_band_66 ((T_BoundedSemilattice_238 -> T_Semilattice_10)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238 -> T_Semilattice_10
du_semilattice_318 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.magma
d_magma_410 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_336 ->
  MAlonzo.Code.Algebra.Bundles.T_Magma_74
d_magma_410 :: () -> () -> T_BoundedMeetSemilattice_336 -> T_Magma_74
d_magma_410 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_336
v2 = T_BoundedMeetSemilattice_336 -> T_Magma_74
du_magma_410 T_BoundedMeetSemilattice_336
v2
du_magma_410 ::
  T_BoundedMeetSemilattice_336 ->
  MAlonzo.Code.Algebra.Bundles.T_Magma_74
du_magma_410 :: T_BoundedMeetSemilattice_336 -> T_Magma_74
du_magma_410 T_BoundedMeetSemilattice_336
v0
  = let v1 :: AgdaAny
v1 = (T_BoundedMeetSemilattice_336 -> T_BoundedSemilattice_238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_336 -> T_BoundedSemilattice_238
du_boundedSemilattice_404 (T_BoundedMeetSemilattice_336 -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_336
v0) in
    AgdaAny -> T_Magma_74
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_BoundedSemilattice_238 -> T_Semilattice_10)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238 -> T_Semilattice_10
du_semilattice_318 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_Semilattice_10 -> T_Band_620) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_620
du_band_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_Semigroup_558 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Semigroup_558 -> T_Magma_74
MAlonzo.Code.Algebra.Bundles.du_magma_606
               ((T_Band_620 -> T_Semigroup_558) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_620 -> T_Semigroup_558
MAlonzo.Code.Algebra.Bundles.du_semigroup_672 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.rawMagma
d_rawMagma_412 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_336 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
d_rawMagma_412 :: () -> () -> T_BoundedMeetSemilattice_336 -> T_RawMagma_44
d_rawMagma_412 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_336
v2 = T_BoundedMeetSemilattice_336 -> T_RawMagma_44
du_rawMagma_412 T_BoundedMeetSemilattice_336
v2
du_rawMagma_412 ::
  T_BoundedMeetSemilattice_336 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
du_rawMagma_412 :: T_BoundedMeetSemilattice_336 -> T_RawMagma_44
du_rawMagma_412 T_BoundedMeetSemilattice_336
v0
  = let v1 :: AgdaAny
v1 = (T_BoundedMeetSemilattice_336 -> T_BoundedSemilattice_238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_336 -> T_BoundedSemilattice_238
du_boundedSemilattice_404 (T_BoundedMeetSemilattice_336 -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_336
v0) in
    AgdaAny -> T_RawMagma_44
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_BoundedSemilattice_238 -> T_Semilattice_10)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238 -> T_Semilattice_10
du_semilattice_318 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_Semilattice_10 -> T_Band_620) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_620
du_band_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4
                   = (T_Band_620 -> T_Semigroup_558) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_620 -> T_Semigroup_558
MAlonzo.Code.Algebra.Bundles.du_semigroup_672 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_Magma_74 -> T_RawMagma_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Magma_74 -> T_RawMagma_44
MAlonzo.Code.Algebra.Bundles.du_rawMagma_118
                  ((T_Semigroup_558 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558 -> T_Magma_74
MAlonzo.Code.Algebra.Bundles.du_magma_606 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.semigroup
d_semigroup_414 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_336 ->
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_558
d_semigroup_414 :: () -> () -> T_BoundedMeetSemilattice_336 -> T_Semigroup_558
d_semigroup_414 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_336
v2 = T_BoundedMeetSemilattice_336 -> T_Semigroup_558
du_semigroup_414 T_BoundedMeetSemilattice_336
v2
du_semigroup_414 ::
  T_BoundedMeetSemilattice_336 ->
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_558
du_semigroup_414 :: T_BoundedMeetSemilattice_336 -> T_Semigroup_558
du_semigroup_414 T_BoundedMeetSemilattice_336
v0
  = let v1 :: AgdaAny
v1 = (T_BoundedMeetSemilattice_336 -> T_BoundedSemilattice_238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_336 -> T_BoundedSemilattice_238
du_boundedSemilattice_404 (T_BoundedMeetSemilattice_336 -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_336
v0) in
    AgdaAny -> T_Semigroup_558
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_BoundedSemilattice_238 -> T_Semilattice_10)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238 -> T_Semilattice_10
du_semilattice_318 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Band_620 -> T_Semigroup_558) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Band_620 -> T_Semigroup_558
MAlonzo.Code.Algebra.Bundles.du_semigroup_672
            ((T_Semilattice_10 -> T_Band_620) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_620
du_band_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.semilattice
d_semilattice_416 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_336 -> T_Semilattice_10
d_semilattice_416 :: () -> () -> T_BoundedMeetSemilattice_336 -> T_Semilattice_10
d_semilattice_416 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_336
v2 = T_BoundedMeetSemilattice_336 -> T_Semilattice_10
du_semilattice_416 T_BoundedMeetSemilattice_336
v2
du_semilattice_416 ::
  T_BoundedMeetSemilattice_336 -> T_Semilattice_10
du_semilattice_416 :: T_BoundedMeetSemilattice_336 -> T_Semilattice_10
du_semilattice_416 T_BoundedMeetSemilattice_336
v0
  = (T_BoundedSemilattice_238 -> T_Semilattice_10)
-> AgdaAny -> T_Semilattice_10
forall a b. a -> b
coe T_BoundedSemilattice_238 -> T_Semilattice_10
du_semilattice_318 ((T_BoundedMeetSemilattice_336 -> T_BoundedSemilattice_238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_336 -> T_BoundedSemilattice_238
du_boundedSemilattice_404 (T_BoundedMeetSemilattice_336 -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_336
v0))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice
d_BoundedJoinSemilattice_424 :: p -> p -> ()
d_BoundedJoinSemilattice_424 p
a0 p
a1 = ()
data T_BoundedJoinSemilattice_424
  = C_constructor_506 (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny
                      MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice.Carrier
d_Carrier_440 :: T_BoundedJoinSemilattice_424 -> ()
d_Carrier_440 :: T_BoundedJoinSemilattice_424 -> ()
d_Carrier_440 = T_BoundedJoinSemilattice_424 -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._≈_
d__'8776'__442 ::
  T_BoundedJoinSemilattice_424 -> AgdaAny -> AgdaAny -> ()
d__'8776'__442 :: T_BoundedJoinSemilattice_424 -> AgdaAny -> AgdaAny -> ()
d__'8776'__442 = T_BoundedJoinSemilattice_424 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._∨_
d__'8744'__444 ::
  T_BoundedJoinSemilattice_424 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__444 :: T_BoundedJoinSemilattice_424 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__444 T_BoundedJoinSemilattice_424
v0
  = case T_BoundedJoinSemilattice_424 -> T_BoundedJoinSemilattice_424
forall a b. a -> b
coe T_BoundedJoinSemilattice_424
v0 of
      C_constructor_506 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsIdempotentCommutativeMonoid_884
v5 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_BoundedJoinSemilattice_424
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice.⊥
d_'8869'_446 :: T_BoundedJoinSemilattice_424 -> AgdaAny
d_'8869'_446 :: T_BoundedJoinSemilattice_424 -> AgdaAny
d_'8869'_446 T_BoundedJoinSemilattice_424
v0
  = case T_BoundedJoinSemilattice_424 -> T_BoundedJoinSemilattice_424
forall a b. a -> b
coe T_BoundedJoinSemilattice_424
v0 of
      C_constructor_506 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsIdempotentCommutativeMonoid_884
v5 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4
      T_BoundedJoinSemilattice_424
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice.isBoundedJoinSemilattice
d_isBoundedJoinSemilattice_448 ::
  T_BoundedJoinSemilattice_424 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884
d_isBoundedJoinSemilattice_448 :: T_BoundedJoinSemilattice_424 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedJoinSemilattice_448 T_BoundedJoinSemilattice_424
v0
  = case T_BoundedJoinSemilattice_424 -> T_BoundedJoinSemilattice_424
forall a b. a -> b
coe T_BoundedJoinSemilattice_424
v0 of
      C_constructor_506 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsIdempotentCommutativeMonoid_884
v5 -> T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v5
      T_BoundedJoinSemilattice_424
_ -> T_IsIdempotentCommutativeMonoid_884
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.assoc
d_assoc_452 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_424 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_452 :: ()
-> ()
-> T_BoundedJoinSemilattice_424
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_assoc_452 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_424
v2 = T_BoundedJoinSemilattice_424
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_452 T_BoundedJoinSemilattice_424
v2
du_assoc_452 ::
  T_BoundedJoinSemilattice_424 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_452 :: T_BoundedJoinSemilattice_424
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_452 T_BoundedJoinSemilattice_424
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedJoinSemilattice_424 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedJoinSemilattice_448 (T_BoundedJoinSemilattice_424 -> T_BoundedJoinSemilattice_424
forall a b. a -> b
coe T_BoundedJoinSemilattice_424
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
                 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_498
            ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
               ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.comm
d_comm_454 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_424 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_454 :: ()
-> ()
-> T_BoundedJoinSemilattice_424
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_comm_454 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_424
v2 = T_BoundedJoinSemilattice_424 -> AgdaAny -> AgdaAny -> AgdaAny
du_comm_454 T_BoundedJoinSemilattice_424
v2
du_comm_454 ::
  T_BoundedJoinSemilattice_424 -> AgdaAny -> AgdaAny -> AgdaAny
du_comm_454 :: T_BoundedJoinSemilattice_424 -> AgdaAny -> AgdaAny -> AgdaAny
du_comm_454 T_BoundedJoinSemilattice_424
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedJoinSemilattice_424 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedJoinSemilattice_448 (T_BoundedJoinSemilattice_424 -> T_BoundedJoinSemilattice_424
forall a b. a -> b
coe T_BoundedJoinSemilattice_424
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_776
         ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
            (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1)))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.idem
d_idem_456 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_424 -> AgdaAny -> AgdaAny
d_idem_456 :: () -> () -> T_BoundedJoinSemilattice_424 -> AgdaAny -> AgdaAny
d_idem_456 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_424
v2 = T_BoundedJoinSemilattice_424 -> AgdaAny -> AgdaAny
du_idem_456 T_BoundedJoinSemilattice_424
v2
du_idem_456 :: T_BoundedJoinSemilattice_424 -> AgdaAny -> AgdaAny
du_idem_456 :: T_BoundedJoinSemilattice_424 -> AgdaAny -> AgdaAny
du_idem_456 T_BoundedJoinSemilattice_424
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedJoinSemilattice_424 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedJoinSemilattice_448 (T_BoundedJoinSemilattice_424 -> T_BoundedJoinSemilattice_424
forall a b. a -> b
coe T_BoundedJoinSemilattice_424
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
                 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsBand_526 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_526 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_536
            ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.identity
d_identity_458 ::
  T_BoundedJoinSemilattice_424 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_458 :: T_BoundedJoinSemilattice_424 -> T_Σ_14
d_identity_458 T_BoundedJoinSemilattice_424
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_724
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
         ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
            ((T_BoundedJoinSemilattice_424
 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_424 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedJoinSemilattice_448 (T_BoundedJoinSemilattice_424 -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_424
v0))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.identityʳ
d_identity'691'_460 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_424 -> AgdaAny -> AgdaAny
d_identity'691'_460 :: () -> () -> T_BoundedJoinSemilattice_424 -> AgdaAny -> AgdaAny
d_identity'691'_460 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_424
v2 = T_BoundedJoinSemilattice_424 -> AgdaAny -> AgdaAny
du_identity'691'_460 T_BoundedJoinSemilattice_424
v2
du_identity'691'_460 ::
  T_BoundedJoinSemilattice_424 -> AgdaAny -> AgdaAny
du_identity'691'_460 :: T_BoundedJoinSemilattice_424 -> AgdaAny -> AgdaAny
du_identity'691'_460 T_BoundedJoinSemilattice_424
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedJoinSemilattice_424 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedJoinSemilattice_448 (T_BoundedJoinSemilattice_424 -> T_BoundedJoinSemilattice_424
forall a b. a -> b
coe T_BoundedJoinSemilattice_424
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2
             = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_712 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_754
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.identityˡ
d_identity'737'_462 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_424 -> AgdaAny -> AgdaAny
d_identity'737'_462 :: () -> () -> T_BoundedJoinSemilattice_424 -> AgdaAny -> AgdaAny
d_identity'737'_462 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_424
v2 = T_BoundedJoinSemilattice_424 -> AgdaAny -> AgdaAny
du_identity'737'_462 T_BoundedJoinSemilattice_424
v2
du_identity'737'_462 ::
  T_BoundedJoinSemilattice_424 -> AgdaAny -> AgdaAny
du_identity'737'_462 :: T_BoundedJoinSemilattice_424 -> AgdaAny -> AgdaAny
du_identity'737'_462 T_BoundedJoinSemilattice_424
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedJoinSemilattice_424 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedJoinSemilattice_448 (T_BoundedJoinSemilattice_424 -> T_BoundedJoinSemilattice_424
forall a b. a -> b
coe T_BoundedJoinSemilattice_424
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2
             = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_712 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_752
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.isBand
d_isBand_464 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_424 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
d_isBand_464 :: () -> () -> T_BoundedJoinSemilattice_424 -> T_IsBand_526
d_isBand_464 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_424
v2 = T_BoundedJoinSemilattice_424 -> T_IsBand_526
du_isBand_464 T_BoundedJoinSemilattice_424
v2
du_isBand_464 ::
  T_BoundedJoinSemilattice_424 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
du_isBand_464 :: T_BoundedJoinSemilattice_424 -> T_IsBand_526
du_isBand_464 T_BoundedJoinSemilattice_424
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedJoinSemilattice_424 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedJoinSemilattice_448 (T_BoundedJoinSemilattice_424 -> T_BoundedJoinSemilattice_424
forall a b. a -> b
coe T_BoundedJoinSemilattice_424
v0) in
    AgdaAny -> T_IsBand_526
forall a b. a -> b
coe
      ((T_IsIdempotentMonoid_826 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentMonoid_826 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.du_isBand_876
         ((T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_942
            (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1)))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.isEquivalence
d_isEquivalence_466 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_424 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_466 :: () -> () -> T_BoundedJoinSemilattice_424 -> T_IsEquivalence_28
d_isEquivalence_466 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_424
v2 = T_BoundedJoinSemilattice_424 -> T_IsEquivalence_28
du_isEquivalence_466 T_BoundedJoinSemilattice_424
v2
du_isEquivalence_466 ::
  T_BoundedJoinSemilattice_424 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_466 :: T_BoundedJoinSemilattice_424 -> T_IsEquivalence_28
du_isEquivalence_466 T_BoundedJoinSemilattice_424
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedJoinSemilattice_424 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedJoinSemilattice_448 (T_BoundedJoinSemilattice_424 -> T_BoundedJoinSemilattice_424
forall a b. a -> b
coe T_BoundedJoinSemilattice_424
v0) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
                 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
            ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
               ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
                  ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.isCommutativeBand
d_isCommutativeBand_468 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_424 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
d_isCommutativeBand_468 :: () -> () -> T_BoundedJoinSemilattice_424 -> T_IsCommutativeBand_612
d_isCommutativeBand_468 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_424
v2 = T_BoundedJoinSemilattice_424 -> T_IsCommutativeBand_612
du_isCommutativeBand_468 T_BoundedJoinSemilattice_424
v2
du_isCommutativeBand_468 ::
  T_BoundedJoinSemilattice_424 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
du_isCommutativeBand_468 :: T_BoundedJoinSemilattice_424 -> T_IsCommutativeBand_612
du_isCommutativeBand_468 T_BoundedJoinSemilattice_424
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedJoinSemilattice_424 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedJoinSemilattice_448 (T_BoundedJoinSemilattice_424 -> T_BoundedJoinSemilattice_424
forall a b. a -> b
coe T_BoundedJoinSemilattice_424
v0) in
    AgdaAny -> T_IsCommutativeBand_612
forall a b. a -> b
coe
      ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.isMagma
d_isMagma_470 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_424 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_470 :: () -> () -> T_BoundedJoinSemilattice_424 -> T_IsMagma_178
d_isMagma_470 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_424
v2 = T_BoundedJoinSemilattice_424 -> T_IsMagma_178
du_isMagma_470 T_BoundedJoinSemilattice_424
v2
du_isMagma_470 ::
  T_BoundedJoinSemilattice_424 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
du_isMagma_470 :: T_BoundedJoinSemilattice_424 -> T_IsMagma_178
du_isMagma_470 T_BoundedJoinSemilattice_424
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedJoinSemilattice_424 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedJoinSemilattice_448 (T_BoundedJoinSemilattice_424 -> T_BoundedJoinSemilattice_424
forall a b. a -> b
coe T_BoundedJoinSemilattice_424
v0) in
    AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
                 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
               ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.isPartialEquivalence
d_isPartialEquivalence_472 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_424 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_472 :: ()
-> () -> T_BoundedJoinSemilattice_424 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_472 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_424
v2
  = T_BoundedJoinSemilattice_424 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_472 T_BoundedJoinSemilattice_424
v2
du_isPartialEquivalence_472 ::
  T_BoundedJoinSemilattice_424 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_472 :: T_BoundedJoinSemilattice_424 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_472 T_BoundedJoinSemilattice_424
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedJoinSemilattice_424 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedJoinSemilattice_448 (T_BoundedJoinSemilattice_424 -> T_BoundedJoinSemilattice_424
forall a b. a -> b
coe T_BoundedJoinSemilattice_424
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
                 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsBand_526
v3 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> T_IsCommutativeBand_612
forall a b. a -> b
coe AgdaAny
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_488
v4
                   = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_178
v5 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                     ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v5)))))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.isSemigroup
d_isSemigroup_474 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_424 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_474 :: () -> () -> T_BoundedJoinSemilattice_424 -> T_IsSemigroup_488
d_isSemigroup_474 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_424
v2 = T_BoundedJoinSemilattice_424 -> T_IsSemigroup_488
du_isSemigroup_474 T_BoundedJoinSemilattice_424
v2
du_isSemigroup_474 ::
  T_BoundedJoinSemilattice_424 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
du_isSemigroup_474 :: T_BoundedJoinSemilattice_424 -> T_IsSemigroup_488
du_isSemigroup_474 T_BoundedJoinSemilattice_424
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedJoinSemilattice_424 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedJoinSemilattice_448 (T_BoundedJoinSemilattice_424 -> T_BoundedJoinSemilattice_424
forall a b. a -> b
coe T_BoundedJoinSemilattice_424
v0) in
    AgdaAny -> T_IsSemigroup_488
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
                 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
            ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.refl
d_refl_476 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_424 -> AgdaAny -> AgdaAny
d_refl_476 :: () -> () -> T_BoundedJoinSemilattice_424 -> AgdaAny -> AgdaAny
d_refl_476 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_424
v2 = T_BoundedJoinSemilattice_424 -> AgdaAny -> AgdaAny
du_refl_476 T_BoundedJoinSemilattice_424
v2
du_refl_476 :: T_BoundedJoinSemilattice_424 -> AgdaAny -> AgdaAny
du_refl_476 :: T_BoundedJoinSemilattice_424 -> AgdaAny -> AgdaAny
du_refl_476 T_BoundedJoinSemilattice_424
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedJoinSemilattice_424 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedJoinSemilattice_448 (T_BoundedJoinSemilattice_424 -> T_BoundedJoinSemilattice_424
forall a b. a -> b
coe T_BoundedJoinSemilattice_424
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
                 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
            ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
               ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
                  ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
                     ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)))))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.reflexive
d_reflexive_478 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_424 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_478 :: ()
-> ()
-> T_BoundedJoinSemilattice_424
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_478 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_424
v2 = T_BoundedJoinSemilattice_424
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_478 T_BoundedJoinSemilattice_424
v2
du_reflexive_478 ::
  T_BoundedJoinSemilattice_424 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_478 :: T_BoundedJoinSemilattice_424
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_478 T_BoundedJoinSemilattice_424
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedJoinSemilattice_424 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedJoinSemilattice_448 (T_BoundedJoinSemilattice_424 -> T_BoundedJoinSemilattice_424
forall a b. a -> b
coe T_BoundedJoinSemilattice_424
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
                 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsBand_526
v3 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> T_IsCommutativeBand_612
forall a b. a -> b
coe AgdaAny
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_488
v4
                   = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_178
v5 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v4) in
                (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                  (\ AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 ->
                     (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                       ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v5))
                       AgdaAny
v6)))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.setoid
d_setoid_480 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_424 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_480 :: () -> () -> T_BoundedJoinSemilattice_424 -> T_Setoid_46
d_setoid_480 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_424
v2 = T_BoundedJoinSemilattice_424 -> T_Setoid_46
du_setoid_480 T_BoundedJoinSemilattice_424
v2
du_setoid_480 ::
  T_BoundedJoinSemilattice_424 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_480 :: T_BoundedJoinSemilattice_424 -> T_Setoid_46
du_setoid_480 T_BoundedJoinSemilattice_424
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedJoinSemilattice_424 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedJoinSemilattice_448 (T_BoundedJoinSemilattice_424 -> T_BoundedJoinSemilattice_424
forall a b. a -> b
coe T_BoundedJoinSemilattice_424
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
                 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsBand_526
v3 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> T_IsCommutativeBand_612
forall a b. a -> b
coe AgdaAny
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_488
v4
                   = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
                  ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v4))))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.sym
d_sym_482 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_424 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_482 :: ()
-> ()
-> T_BoundedJoinSemilattice_424
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_482 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_424
v2 = T_BoundedJoinSemilattice_424
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_482 T_BoundedJoinSemilattice_424
v2
du_sym_482 ::
  T_BoundedJoinSemilattice_424 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_482 :: T_BoundedJoinSemilattice_424
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_482 T_BoundedJoinSemilattice_424
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedJoinSemilattice_424 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedJoinSemilattice_448 (T_BoundedJoinSemilattice_424 -> T_BoundedJoinSemilattice_424
forall a b. a -> b
coe T_BoundedJoinSemilattice_424
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
                 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
            ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
               ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
                  ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
                     ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)))))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.trans
d_trans_484 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_424 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_484 :: ()
-> ()
-> T_BoundedJoinSemilattice_424
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_484 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_424
v2 = T_BoundedJoinSemilattice_424
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_484 T_BoundedJoinSemilattice_424
v2
du_trans_484 ::
  T_BoundedJoinSemilattice_424 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_484 :: T_BoundedJoinSemilattice_424
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_484 T_BoundedJoinSemilattice_424
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedJoinSemilattice_424 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedJoinSemilattice_448 (T_BoundedJoinSemilattice_424 -> T_BoundedJoinSemilattice_424
forall a b. a -> b
coe T_BoundedJoinSemilattice_424
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
                 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
            ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
               ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
                  ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
                     ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)))))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.∙-cong
d_'8729''45'cong_486 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_424 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_486 :: ()
-> ()
-> T_BoundedJoinSemilattice_424
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_486 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_424
v2 = T_BoundedJoinSemilattice_424
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_486 T_BoundedJoinSemilattice_424
v2
du_'8729''45'cong_486 ::
  T_BoundedJoinSemilattice_424 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong_486 :: T_BoundedJoinSemilattice_424
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_486 T_BoundedJoinSemilattice_424
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedJoinSemilattice_424 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedJoinSemilattice_448 (T_BoundedJoinSemilattice_424 -> T_BoundedJoinSemilattice_424
forall a b. a -> b
coe T_BoundedJoinSemilattice_424
v0) in
    AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
                 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188
            ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
               ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
                  ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.∙-congʳ
d_'8729''45'cong'691'_488 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_424 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_488 :: ()
-> ()
-> T_BoundedJoinSemilattice_424
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_488 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_424
v2
  = T_BoundedJoinSemilattice_424
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_488 T_BoundedJoinSemilattice_424
v2
du_'8729''45'cong'691'_488 ::
  T_BoundedJoinSemilattice_424 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_488 :: T_BoundedJoinSemilattice_424
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_488 T_BoundedJoinSemilattice_424
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedJoinSemilattice_424 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedJoinSemilattice_448 (T_BoundedJoinSemilattice_424 -> T_BoundedJoinSemilattice_424
forall a b. a -> b
coe T_BoundedJoinSemilattice_424
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
                 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsBand_526
v3 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> T_IsCommutativeBand_612
forall a b. a -> b
coe AgdaAny
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_488
v4
                   = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_178
v5 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
v6
                         = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7
                            = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v5) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                           ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7)
                           ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                              ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                                 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6))))))))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.∙-congˡ
d_'8729''45'cong'737'_490 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_424 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_490 :: ()
-> ()
-> T_BoundedJoinSemilattice_424
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_490 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_424
v2
  = T_BoundedJoinSemilattice_424
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_490 T_BoundedJoinSemilattice_424
v2
du_'8729''45'cong'737'_490 ::
  T_BoundedJoinSemilattice_424 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_490 :: T_BoundedJoinSemilattice_424
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_490 T_BoundedJoinSemilattice_424
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_BoundedJoinSemilattice_424 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedJoinSemilattice_448 (T_BoundedJoinSemilattice_424 -> T_BoundedJoinSemilattice_424
forall a b. a -> b
coe T_BoundedJoinSemilattice_424
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
                 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsBand_526
v3 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> T_IsCommutativeBand_612
forall a b. a -> b
coe AgdaAny
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_488
v4
                   = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_178
v5 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
v6
                         = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7
                            = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v5) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                           ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7)
                           ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                              ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                                 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6))))))))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice.boundedSemilattice
d_boundedSemilattice_492 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_424 -> T_BoundedSemilattice_238
d_boundedSemilattice_492 :: ()
-> () -> T_BoundedJoinSemilattice_424 -> T_BoundedSemilattice_238
d_boundedSemilattice_492 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_424
v2 = T_BoundedJoinSemilattice_424 -> T_BoundedSemilattice_238
du_boundedSemilattice_492 T_BoundedJoinSemilattice_424
v2
du_boundedSemilattice_492 ::
  T_BoundedJoinSemilattice_424 -> T_BoundedSemilattice_238
du_boundedSemilattice_492 :: T_BoundedJoinSemilattice_424 -> T_BoundedSemilattice_238
du_boundedSemilattice_492 T_BoundedJoinSemilattice_424
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsIdempotentCommutativeMonoid_884
 -> T_BoundedSemilattice_238)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_BoundedSemilattice_238
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_BoundedSemilattice_238
C_constructor_330 (T_BoundedJoinSemilattice_424 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__444 (T_BoundedJoinSemilattice_424 -> T_BoundedJoinSemilattice_424
forall a b. a -> b
coe T_BoundedJoinSemilattice_424
v0)) (T_BoundedJoinSemilattice_424 -> AgdaAny
d_'8869'_446 (T_BoundedJoinSemilattice_424 -> T_BoundedJoinSemilattice_424
forall a b. a -> b
coe T_BoundedJoinSemilattice_424
v0))
      (T_BoundedJoinSemilattice_424 -> T_IsIdempotentCommutativeMonoid_884
d_isBoundedJoinSemilattice_448 (T_BoundedJoinSemilattice_424 -> T_BoundedJoinSemilattice_424
forall a b. a -> b
coe T_BoundedJoinSemilattice_424
v0))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.band
d_band_496 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_424 ->
  MAlonzo.Code.Algebra.Bundles.T_Band_620
d_band_496 :: () -> () -> T_BoundedJoinSemilattice_424 -> T_Band_620
d_band_496 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_424
v2 = T_BoundedJoinSemilattice_424 -> T_Band_620
du_band_496 T_BoundedJoinSemilattice_424
v2
du_band_496 ::
  T_BoundedJoinSemilattice_424 ->
  MAlonzo.Code.Algebra.Bundles.T_Band_620
du_band_496 :: T_BoundedJoinSemilattice_424 -> T_Band_620
du_band_496 T_BoundedJoinSemilattice_424
v0
  = let v1 :: AgdaAny
v1 = (T_BoundedJoinSemilattice_424 -> T_BoundedSemilattice_238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_424 -> T_BoundedSemilattice_238
du_boundedSemilattice_492 (T_BoundedJoinSemilattice_424 -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_424
v0) in
    AgdaAny -> T_Band_620
forall a b. a -> b
coe ((T_Semilattice_10 -> T_Band_620) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_620
du_band_66 ((T_BoundedSemilattice_238 -> T_Semilattice_10)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238 -> T_Semilattice_10
du_semilattice_318 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.magma
d_magma_498 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_424 ->
  MAlonzo.Code.Algebra.Bundles.T_Magma_74
d_magma_498 :: () -> () -> T_BoundedJoinSemilattice_424 -> T_Magma_74
d_magma_498 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_424
v2 = T_BoundedJoinSemilattice_424 -> T_Magma_74
du_magma_498 T_BoundedJoinSemilattice_424
v2
du_magma_498 ::
  T_BoundedJoinSemilattice_424 ->
  MAlonzo.Code.Algebra.Bundles.T_Magma_74
du_magma_498 :: T_BoundedJoinSemilattice_424 -> T_Magma_74
du_magma_498 T_BoundedJoinSemilattice_424
v0
  = let v1 :: AgdaAny
v1 = (T_BoundedJoinSemilattice_424 -> T_BoundedSemilattice_238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_424 -> T_BoundedSemilattice_238
du_boundedSemilattice_492 (T_BoundedJoinSemilattice_424 -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_424
v0) in
    AgdaAny -> T_Magma_74
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_BoundedSemilattice_238 -> T_Semilattice_10)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238 -> T_Semilattice_10
du_semilattice_318 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_Semilattice_10 -> T_Band_620) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_620
du_band_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_Semigroup_558 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Semigroup_558 -> T_Magma_74
MAlonzo.Code.Algebra.Bundles.du_magma_606
               ((T_Band_620 -> T_Semigroup_558) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_620 -> T_Semigroup_558
MAlonzo.Code.Algebra.Bundles.du_semigroup_672 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.rawMagma
d_rawMagma_500 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_424 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
d_rawMagma_500 :: () -> () -> T_BoundedJoinSemilattice_424 -> T_RawMagma_44
d_rawMagma_500 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_424
v2 = T_BoundedJoinSemilattice_424 -> T_RawMagma_44
du_rawMagma_500 T_BoundedJoinSemilattice_424
v2
du_rawMagma_500 ::
  T_BoundedJoinSemilattice_424 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
du_rawMagma_500 :: T_BoundedJoinSemilattice_424 -> T_RawMagma_44
du_rawMagma_500 T_BoundedJoinSemilattice_424
v0
  = let v1 :: AgdaAny
v1 = (T_BoundedJoinSemilattice_424 -> T_BoundedSemilattice_238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_424 -> T_BoundedSemilattice_238
du_boundedSemilattice_492 (T_BoundedJoinSemilattice_424 -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_424
v0) in
    AgdaAny -> T_RawMagma_44
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_BoundedSemilattice_238 -> T_Semilattice_10)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238 -> T_Semilattice_10
du_semilattice_318 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_Semilattice_10 -> T_Band_620) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_620
du_band_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4
                   = (T_Band_620 -> T_Semigroup_558) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_620 -> T_Semigroup_558
MAlonzo.Code.Algebra.Bundles.du_semigroup_672 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_Magma_74 -> T_RawMagma_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Magma_74 -> T_RawMagma_44
MAlonzo.Code.Algebra.Bundles.du_rawMagma_118
                  ((T_Semigroup_558 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558 -> T_Magma_74
MAlonzo.Code.Algebra.Bundles.du_magma_606 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.semigroup
d_semigroup_502 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_424 ->
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_558
d_semigroup_502 :: () -> () -> T_BoundedJoinSemilattice_424 -> T_Semigroup_558
d_semigroup_502 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_424
v2 = T_BoundedJoinSemilattice_424 -> T_Semigroup_558
du_semigroup_502 T_BoundedJoinSemilattice_424
v2
du_semigroup_502 ::
  T_BoundedJoinSemilattice_424 ->
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_558
du_semigroup_502 :: T_BoundedJoinSemilattice_424 -> T_Semigroup_558
du_semigroup_502 T_BoundedJoinSemilattice_424
v0
  = let v1 :: AgdaAny
v1 = (T_BoundedJoinSemilattice_424 -> T_BoundedSemilattice_238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_424 -> T_BoundedSemilattice_238
du_boundedSemilattice_492 (T_BoundedJoinSemilattice_424 -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_424
v0) in
    AgdaAny -> T_Semigroup_558
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_BoundedSemilattice_238 -> T_Semilattice_10)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_238 -> T_Semilattice_10
du_semilattice_318 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Band_620 -> T_Semigroup_558) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Band_620 -> T_Semigroup_558
MAlonzo.Code.Algebra.Bundles.du_semigroup_672
            ((T_Semilattice_10 -> T_Band_620) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_620
du_band_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.semilattice
d_semilattice_504 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_424 -> T_Semilattice_10
d_semilattice_504 :: () -> () -> T_BoundedJoinSemilattice_424 -> T_Semilattice_10
d_semilattice_504 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_424
v2 = T_BoundedJoinSemilattice_424 -> T_Semilattice_10
du_semilattice_504 T_BoundedJoinSemilattice_424
v2
du_semilattice_504 ::
  T_BoundedJoinSemilattice_424 -> T_Semilattice_10
du_semilattice_504 :: T_BoundedJoinSemilattice_424 -> T_Semilattice_10
du_semilattice_504 T_BoundedJoinSemilattice_424
v0
  = (T_BoundedSemilattice_238 -> T_Semilattice_10)
-> AgdaAny -> T_Semilattice_10
forall a b. a -> b
coe T_BoundedSemilattice_238 -> T_Semilattice_10
du_semilattice_318 ((T_BoundedJoinSemilattice_424 -> T_BoundedSemilattice_238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_424 -> T_BoundedSemilattice_238
du_boundedSemilattice_492 (T_BoundedJoinSemilattice_424 -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_424
v0))
-- Algebra.Lattice.Bundles.Lattice
d_Lattice_512 :: p -> p -> ()
d_Lattice_512 p
a0 p
a1 = ()
data T_Lattice_512
  = C_constructor_592 (AgdaAny -> AgdaAny -> AgdaAny)
                      (AgdaAny -> AgdaAny -> AgdaAny)
                      MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_3070
-- Algebra.Lattice.Bundles.Lattice.Carrier
d_Carrier_528 :: T_Lattice_512 -> ()
d_Carrier_528 :: T_Lattice_512 -> ()
d_Carrier_528 = T_Lattice_512 -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.Lattice._≈_
d__'8776'__530 :: T_Lattice_512 -> AgdaAny -> AgdaAny -> ()
d__'8776'__530 :: T_Lattice_512 -> AgdaAny -> AgdaAny -> ()
d__'8776'__530 = T_Lattice_512 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.Lattice._∨_
d__'8744'__532 :: T_Lattice_512 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__532 :: T_Lattice_512 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__532 T_Lattice_512
v0
  = case T_Lattice_512 -> T_Lattice_512
forall a b. a -> b
coe T_Lattice_512
v0 of
      C_constructor_592 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsLattice_3070
v5 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_Lattice_512
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.Lattice._∧_
d__'8743'__534 :: T_Lattice_512 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__534 :: T_Lattice_512 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__534 T_Lattice_512
v0
  = case T_Lattice_512 -> T_Lattice_512
forall a b. a -> b
coe T_Lattice_512
v0 of
      C_constructor_592 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsLattice_3070
v5 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_Lattice_512
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.Lattice.isLattice
d_isLattice_536 ::
  T_Lattice_512 ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_3070
d_isLattice_536 :: T_Lattice_512 -> T_IsLattice_3070
d_isLattice_536 T_Lattice_512
v0
  = case T_Lattice_512 -> T_Lattice_512
forall a b. a -> b
coe T_Lattice_512
v0 of
      C_constructor_592 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsLattice_3070
v5 -> T_IsLattice_3070 -> T_IsLattice_3070
forall a b. a -> b
coe T_IsLattice_3070
v5
      T_Lattice_512
_ -> T_IsLattice_3070
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.Lattice._.absorptive
d_absorptive_540 ::
  T_Lattice_512 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_absorptive_540 :: T_Lattice_512 -> T_Σ_14
d_absorptive_540 T_Lattice_512
v0
  = (T_IsLattice_3070 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsLattice_3070 -> T_Σ_14
MAlonzo.Code.Algebra.Lattice.Structures.d_absorptive_3106
      ((T_Lattice_512 -> T_IsLattice_3070) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_512 -> T_IsLattice_3070
d_isLattice_536 (T_Lattice_512 -> AgdaAny
forall a b. a -> b
coe T_Lattice_512
v0))
-- Algebra.Lattice.Bundles.Lattice._.isEquivalence
d_isEquivalence_542 ::
  T_Lattice_512 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_542 :: T_Lattice_512 -> T_IsEquivalence_28
d_isEquivalence_542 T_Lattice_512
v0
  = (T_IsLattice_3070 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
      ((T_Lattice_512 -> T_IsLattice_3070) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_512 -> T_IsLattice_3070
d_isLattice_536 (T_Lattice_512 -> AgdaAny
forall a b. a -> b
coe T_Lattice_512
v0))
-- Algebra.Lattice.Bundles.Lattice._.isPartialEquivalence
d_isPartialEquivalence_544 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_512 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_544 :: () -> () -> T_Lattice_512 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_544 ~()
v0 ~()
v1 T_Lattice_512
v2
  = T_Lattice_512 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_544 T_Lattice_512
v2
du_isPartialEquivalence_544 ::
  T_Lattice_512 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_544 :: T_Lattice_512 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_544 T_Lattice_512
v0
  = let v1 :: T_IsLattice_3070
v1 = T_Lattice_512 -> T_IsLattice_3070
d_isLattice_536 (T_Lattice_512 -> T_Lattice_512
forall a b. a -> b
coe T_Lattice_512
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
         ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
            (T_IsLattice_3070 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070
v1)))
-- Algebra.Lattice.Bundles.Lattice._.refl
d_refl_546 :: T_Lattice_512 -> AgdaAny -> AgdaAny
d_refl_546 :: T_Lattice_512 -> AgdaAny -> AgdaAny
d_refl_546 T_Lattice_512
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
         ((T_Lattice_512 -> T_IsLattice_3070) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_512 -> T_IsLattice_3070
d_isLattice_536 (T_Lattice_512 -> AgdaAny
forall a b. a -> b
coe T_Lattice_512
v0)))
-- Algebra.Lattice.Bundles.Lattice._.reflexive
d_reflexive_548 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_512 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_548 :: ()
-> ()
-> T_Lattice_512
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_548 ~()
v0 ~()
v1 T_Lattice_512
v2 = T_Lattice_512 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_548 T_Lattice_512
v2
du_reflexive_548 ::
  T_Lattice_512 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_548 :: T_Lattice_512 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_548 T_Lattice_512
v0
  = let v1 :: T_IsLattice_3070
v1 = T_Lattice_512 -> T_IsLattice_3070
d_isLattice_536 (T_Lattice_512 -> T_Lattice_512
forall a b. a -> b
coe T_Lattice_512
v0) in
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (\ AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 ->
         (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
           ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
              (T_IsLattice_3070 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070
v1))
           AgdaAny
v2)
-- Algebra.Lattice.Bundles.Lattice._.sym
d_sym_550 ::
  T_Lattice_512 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_550 :: T_Lattice_512 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_550 T_Lattice_512
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
         ((T_Lattice_512 -> T_IsLattice_3070) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_512 -> T_IsLattice_3070
d_isLattice_536 (T_Lattice_512 -> AgdaAny
forall a b. a -> b
coe T_Lattice_512
v0)))
-- Algebra.Lattice.Bundles.Lattice._.trans
d_trans_552 ::
  T_Lattice_512 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_552 :: T_Lattice_512
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_552 T_Lattice_512
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
         ((T_Lattice_512 -> T_IsLattice_3070) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_512 -> T_IsLattice_3070
d_isLattice_536 (T_Lattice_512 -> AgdaAny
forall a b. a -> b
coe T_Lattice_512
v0)))
-- Algebra.Lattice.Bundles.Lattice._.∧-absorbs-∨
d_'8743''45'absorbs'45''8744'_554 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_512 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'absorbs'45''8744'_554 :: () -> () -> T_Lattice_512 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'absorbs'45''8744'_554 ~()
v0 ~()
v1 T_Lattice_512
v2
  = T_Lattice_512 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_554 T_Lattice_512
v2
du_'8743''45'absorbs'45''8744'_554 ::
  T_Lattice_512 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_554 :: T_Lattice_512 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_554 T_Lattice_512
v0
  = (T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'absorbs'45''8744'_3122
      ((T_Lattice_512 -> T_IsLattice_3070) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_512 -> T_IsLattice_3070
d_isLattice_536 (T_Lattice_512 -> AgdaAny
forall a b. a -> b
coe T_Lattice_512
v0))
-- Algebra.Lattice.Bundles.Lattice._.∧-assoc
d_'8743''45'assoc_556 ::
  T_Lattice_512 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_556 :: T_Lattice_512 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_556 T_Lattice_512
v0
  = (T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'assoc_3102
      ((T_Lattice_512 -> T_IsLattice_3070) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_512 -> T_IsLattice_3070
d_isLattice_536 (T_Lattice_512 -> AgdaAny
forall a b. a -> b
coe T_Lattice_512
v0))
-- Algebra.Lattice.Bundles.Lattice._.∧-comm
d_'8743''45'comm_558 ::
  T_Lattice_512 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_558 :: T_Lattice_512 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_558 T_Lattice_512
v0
  = (T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'comm_3100
      ((T_Lattice_512 -> T_IsLattice_3070) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_512 -> T_IsLattice_3070
d_isLattice_536 (T_Lattice_512 -> AgdaAny
forall a b. a -> b
coe T_Lattice_512
v0))
-- Algebra.Lattice.Bundles.Lattice._.∧-cong
d_'8743''45'cong_560 ::
  T_Lattice_512 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong_560 :: T_Lattice_512
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong_560 T_Lattice_512
v0
  = (T_IsLattice_3070
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_3070
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'cong_3104
      ((T_Lattice_512 -> T_IsLattice_3070) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_512 -> T_IsLattice_3070
d_isLattice_536 (T_Lattice_512 -> AgdaAny
forall a b. a -> b
coe T_Lattice_512
v0))
-- Algebra.Lattice.Bundles.Lattice._.∧-congʳ
d_'8743''45'cong'691'_562 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_512 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong'691'_562 :: ()
-> ()
-> T_Lattice_512
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong'691'_562 ~()
v0 ~()
v1 T_Lattice_512
v2
  = T_Lattice_512
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_562 T_Lattice_512
v2
du_'8743''45'cong'691'_562 ::
  T_Lattice_512 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_562 :: T_Lattice_512
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_562 T_Lattice_512
v0
  = (T_IsLattice_3070
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'cong'691'_3128
      ((T_Lattice_512 -> T_IsLattice_3070) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_512 -> T_IsLattice_3070
d_isLattice_536 (T_Lattice_512 -> AgdaAny
forall a b. a -> b
coe T_Lattice_512
v0))
-- Algebra.Lattice.Bundles.Lattice._.∧-congˡ
d_'8743''45'cong'737'_564 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_512 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong'737'_564 :: ()
-> ()
-> T_Lattice_512
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong'737'_564 ~()
v0 ~()
v1 T_Lattice_512
v2
  = T_Lattice_512
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_564 T_Lattice_512
v2
du_'8743''45'cong'737'_564 ::
  T_Lattice_512 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_564 :: T_Lattice_512
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_564 T_Lattice_512
v0
  = (T_IsLattice_3070
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'cong'737'_3124
      ((T_Lattice_512 -> T_IsLattice_3070) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_512 -> T_IsLattice_3070
d_isLattice_536 (T_Lattice_512 -> AgdaAny
forall a b. a -> b
coe T_Lattice_512
v0))
-- Algebra.Lattice.Bundles.Lattice._.∨-absorbs-∧
d_'8744''45'absorbs'45''8743'_566 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_512 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'absorbs'45''8743'_566 :: () -> () -> T_Lattice_512 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'absorbs'45''8743'_566 ~()
v0 ~()
v1 T_Lattice_512
v2
  = T_Lattice_512 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_566 T_Lattice_512
v2
du_'8744''45'absorbs'45''8743'_566 ::
  T_Lattice_512 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_566 :: T_Lattice_512 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_566 T_Lattice_512
v0
  = (T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'absorbs'45''8743'_3120
      ((T_Lattice_512 -> T_IsLattice_3070) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_512 -> T_IsLattice_3070
d_isLattice_536 (T_Lattice_512 -> AgdaAny
forall a b. a -> b
coe T_Lattice_512
v0))
-- Algebra.Lattice.Bundles.Lattice._.∨-assoc
d_'8744''45'assoc_568 ::
  T_Lattice_512 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_568 :: T_Lattice_512 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_568 T_Lattice_512
v0
  = (T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'assoc_3096
      ((T_Lattice_512 -> T_IsLattice_3070) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_512 -> T_IsLattice_3070
d_isLattice_536 (T_Lattice_512 -> AgdaAny
forall a b. a -> b
coe T_Lattice_512
v0))
-- Algebra.Lattice.Bundles.Lattice._.∨-comm
d_'8744''45'comm_570 ::
  T_Lattice_512 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_570 :: T_Lattice_512 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_570 T_Lattice_512
v0
  = (T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'comm_3094
      ((T_Lattice_512 -> T_IsLattice_3070) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_512 -> T_IsLattice_3070
d_isLattice_536 (T_Lattice_512 -> AgdaAny
forall a b. a -> b
coe T_Lattice_512
v0))
-- Algebra.Lattice.Bundles.Lattice._.∨-cong
d_'8744''45'cong_572 ::
  T_Lattice_512 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong_572 :: T_Lattice_512
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong_572 T_Lattice_512
v0
  = (T_IsLattice_3070
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_3070
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'cong_3098
      ((T_Lattice_512 -> T_IsLattice_3070) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_512 -> T_IsLattice_3070
d_isLattice_536 (T_Lattice_512 -> AgdaAny
forall a b. a -> b
coe T_Lattice_512
v0))
-- Algebra.Lattice.Bundles.Lattice._.∨-congʳ
d_'8744''45'cong'691'_574 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_512 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong'691'_574 :: ()
-> ()
-> T_Lattice_512
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong'691'_574 ~()
v0 ~()
v1 T_Lattice_512
v2
  = T_Lattice_512
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_574 T_Lattice_512
v2
du_'8744''45'cong'691'_574 ::
  T_Lattice_512 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_574 :: T_Lattice_512
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_574 T_Lattice_512
v0
  = (T_IsLattice_3070
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'cong'691'_3136
      ((T_Lattice_512 -> T_IsLattice_3070) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_512 -> T_IsLattice_3070
d_isLattice_536 (T_Lattice_512 -> AgdaAny
forall a b. a -> b
coe T_Lattice_512
v0))
-- Algebra.Lattice.Bundles.Lattice._.∨-congˡ
d_'8744''45'cong'737'_576 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_512 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong'737'_576 :: ()
-> ()
-> T_Lattice_512
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong'737'_576 ~()
v0 ~()
v1 T_Lattice_512
v2
  = T_Lattice_512
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_576 T_Lattice_512
v2
du_'8744''45'cong'737'_576 ::
  T_Lattice_512 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_576 :: T_Lattice_512
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_576 T_Lattice_512
v0
  = (T_IsLattice_3070
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'cong'737'_3132
      ((T_Lattice_512 -> T_IsLattice_3070) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_512 -> T_IsLattice_3070
d_isLattice_536 (T_Lattice_512 -> AgdaAny
forall a b. a -> b
coe T_Lattice_512
v0))
-- Algebra.Lattice.Bundles.Lattice.rawLattice
d_rawLattice_578 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_512 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.Raw.T_RawLattice_12
d_rawLattice_578 :: () -> () -> T_Lattice_512 -> T_RawLattice_12
d_rawLattice_578 ~()
v0 ~()
v1 T_Lattice_512
v2 = T_Lattice_512 -> T_RawLattice_12
du_rawLattice_578 T_Lattice_512
v2
du_rawLattice_578 ::
  T_Lattice_512 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.Raw.T_RawLattice_12
du_rawLattice_578 :: T_Lattice_512 -> T_RawLattice_12
du_rawLattice_578 T_Lattice_512
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_RawLattice_12)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_RawLattice_12
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_RawLattice_12
MAlonzo.Code.Algebra.Lattice.Bundles.Raw.C_constructor_42
      (T_Lattice_512 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__534 (T_Lattice_512 -> T_Lattice_512
forall a b. a -> b
coe T_Lattice_512
v0)) (T_Lattice_512 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__532 (T_Lattice_512 -> T_Lattice_512
forall a b. a -> b
coe T_Lattice_512
v0))
-- Algebra.Lattice.Bundles.Lattice._.∧-rawMagma
d_'8743''45'rawMagma_582 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_512 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
d_'8743''45'rawMagma_582 :: () -> () -> T_Lattice_512 -> T_RawMagma_44
d_'8743''45'rawMagma_582 ~()
v0 ~()
v1 T_Lattice_512
v2 = T_Lattice_512 -> T_RawMagma_44
du_'8743''45'rawMagma_582 T_Lattice_512
v2
du_'8743''45'rawMagma_582 ::
  T_Lattice_512 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
du_'8743''45'rawMagma_582 :: T_Lattice_512 -> T_RawMagma_44
du_'8743''45'rawMagma_582 T_Lattice_512
v0
  = (T_RawLattice_12 -> T_RawMagma_44) -> AgdaAny -> T_RawMagma_44
forall a b. a -> b
coe
      T_RawLattice_12 -> T_RawMagma_44
MAlonzo.Code.Algebra.Lattice.Bundles.Raw.du_'8743''45'rawMagma_36
      ((T_Lattice_512 -> T_RawLattice_12) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_512 -> T_RawLattice_12
du_rawLattice_578 (T_Lattice_512 -> AgdaAny
forall a b. a -> b
coe T_Lattice_512
v0))
-- Algebra.Lattice.Bundles.Lattice._.∨-rawMagma
d_'8744''45'rawMagma_584 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_512 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
d_'8744''45'rawMagma_584 :: () -> () -> T_Lattice_512 -> T_RawMagma_44
d_'8744''45'rawMagma_584 ~()
v0 ~()
v1 T_Lattice_512
v2 = T_Lattice_512 -> T_RawMagma_44
du_'8744''45'rawMagma_584 T_Lattice_512
v2
du_'8744''45'rawMagma_584 ::
  T_Lattice_512 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
du_'8744''45'rawMagma_584 :: T_Lattice_512 -> T_RawMagma_44
du_'8744''45'rawMagma_584 T_Lattice_512
v0
  = (T_RawLattice_12 -> T_RawMagma_44) -> AgdaAny -> T_RawMagma_44
forall a b. a -> b
coe
      T_RawLattice_12 -> T_RawMagma_44
MAlonzo.Code.Algebra.Lattice.Bundles.Raw.du_'8744''45'rawMagma_34
      ((T_Lattice_512 -> T_RawLattice_12) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_512 -> T_RawLattice_12
du_rawLattice_578 (T_Lattice_512 -> AgdaAny
forall a b. a -> b
coe T_Lattice_512
v0))
-- Algebra.Lattice.Bundles.Lattice.setoid
d_setoid_586 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_512 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_586 :: () -> () -> T_Lattice_512 -> T_Setoid_46
d_setoid_586 ~()
v0 ~()
v1 T_Lattice_512
v2 = T_Lattice_512 -> T_Setoid_46
du_setoid_586 T_Lattice_512
v2
du_setoid_586 ::
  T_Lattice_512 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_586 :: T_Lattice_512 -> T_Setoid_46
du_setoid_586 T_Lattice_512
v0
  = (T_IsEquivalence_28 -> T_Setoid_46)
-> T_IsEquivalence_28 -> T_Setoid_46
forall a b. a -> b
coe
      T_IsEquivalence_28 -> T_Setoid_46
MAlonzo.Code.Relation.Binary.Bundles.C_constructor_84
      (T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
         ((T_Lattice_512 -> T_IsLattice_3070) -> AgdaAny -> T_IsLattice_3070
forall a b. a -> b
coe T_Lattice_512 -> T_IsLattice_3070
d_isLattice_536 (T_Lattice_512 -> AgdaAny
forall a b. a -> b
coe T_Lattice_512
v0)))
-- Algebra.Lattice.Bundles.Lattice._._≉_
d__'8777'__590 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_512 -> AgdaAny -> AgdaAny -> ()
d__'8777'__590 :: () -> () -> T_Lattice_512 -> AgdaAny -> AgdaAny -> ()
d__'8777'__590 = () -> () -> T_Lattice_512 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.DistributiveLattice
d_DistributiveLattice_598 :: p -> p -> ()
d_DistributiveLattice_598 p
a0 p
a1 = ()
data T_DistributiveLattice_598
  = C_constructor_692 (AgdaAny -> AgdaAny -> AgdaAny)
                      (AgdaAny -> AgdaAny -> AgdaAny)
                      MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3146
-- Algebra.Lattice.Bundles.DistributiveLattice.Carrier
d_Carrier_614 :: T_DistributiveLattice_598 -> ()
d_Carrier_614 :: T_DistributiveLattice_598 -> ()
d_Carrier_614 = T_DistributiveLattice_598 -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.DistributiveLattice._≈_
d__'8776'__616 ::
  T_DistributiveLattice_598 -> AgdaAny -> AgdaAny -> ()
d__'8776'__616 :: T_DistributiveLattice_598 -> AgdaAny -> AgdaAny -> ()
d__'8776'__616 = T_DistributiveLattice_598 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.DistributiveLattice._∨_
d__'8744'__618 ::
  T_DistributiveLattice_598 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__618 :: T_DistributiveLattice_598 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__618 T_DistributiveLattice_598
v0
  = case T_DistributiveLattice_598 -> T_DistributiveLattice_598
forall a b. a -> b
coe T_DistributiveLattice_598
v0 of
      C_constructor_692 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsDistributiveLattice_3146
v5 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_DistributiveLattice_598
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.DistributiveLattice._∧_
d__'8743'__620 ::
  T_DistributiveLattice_598 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__620 :: T_DistributiveLattice_598 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__620 T_DistributiveLattice_598
v0
  = case T_DistributiveLattice_598 -> T_DistributiveLattice_598
forall a b. a -> b
coe T_DistributiveLattice_598
v0 of
      C_constructor_692 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsDistributiveLattice_3146
v5 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_DistributiveLattice_598
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.DistributiveLattice.isDistributiveLattice
d_isDistributiveLattice_622 ::
  T_DistributiveLattice_598 ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3146
d_isDistributiveLattice_622 :: T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_622 T_DistributiveLattice_598
v0
  = case T_DistributiveLattice_598 -> T_DistributiveLattice_598
forall a b. a -> b
coe T_DistributiveLattice_598
v0 of
      C_constructor_692 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsDistributiveLattice_3146
v5 -> T_IsDistributiveLattice_3146 -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v5
      T_DistributiveLattice_598
_ -> T_IsDistributiveLattice_3146
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.DistributiveLattice._.absorptive
d_absorptive_626 ::
  T_DistributiveLattice_598 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_absorptive_626 :: T_DistributiveLattice_598 -> T_Σ_14
d_absorptive_626 T_DistributiveLattice_598
v0
  = (T_IsLattice_3070 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsLattice_3070 -> T_Σ_14
MAlonzo.Code.Algebra.Lattice.Structures.d_absorptive_3106
      ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
         ((T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_622 (T_DistributiveLattice_598 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598
v0)))
-- Algebra.Lattice.Bundles.DistributiveLattice._.isEquivalence
d_isEquivalence_628 ::
  T_DistributiveLattice_598 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_628 :: T_DistributiveLattice_598 -> T_IsEquivalence_28
d_isEquivalence_628 T_DistributiveLattice_598
v0
  = (T_IsLattice_3070 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
      ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
         ((T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_622 (T_DistributiveLattice_598 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598
v0)))
-- Algebra.Lattice.Bundles.DistributiveLattice._.isLattice
d_isLattice_630 ::
  T_DistributiveLattice_598 ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_3070
d_isLattice_630 :: T_DistributiveLattice_598 -> T_IsLattice_3070
d_isLattice_630 T_DistributiveLattice_598
v0
  = (T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> T_IsLattice_3070
forall a b. a -> b
coe
      T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
      ((T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_622 (T_DistributiveLattice_598 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598
v0))
-- Algebra.Lattice.Bundles.DistributiveLattice._.isPartialEquivalence
d_isPartialEquivalence_632 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_598 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_632 :: () -> () -> T_DistributiveLattice_598 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_632 ~()
v0 ~()
v1 T_DistributiveLattice_598
v2
  = T_DistributiveLattice_598 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_632 T_DistributiveLattice_598
v2
du_isPartialEquivalence_632 ::
  T_DistributiveLattice_598 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_632 :: T_DistributiveLattice_598 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_632 T_DistributiveLattice_598
v0
  = let v1 :: T_IsDistributiveLattice_3146
v1 = T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_622 (T_DistributiveLattice_598 -> T_DistributiveLattice_598
forall a b. a -> b
coe T_DistributiveLattice_598
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_3070
v2
             = T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                 (T_IsDistributiveLattice_3146 -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
               (T_IsLattice_3070 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070
v2))))
-- Algebra.Lattice.Bundles.DistributiveLattice._.refl
d_refl_634 :: T_DistributiveLattice_598 -> AgdaAny -> AgdaAny
d_refl_634 :: T_DistributiveLattice_598 -> AgdaAny -> AgdaAny
d_refl_634 T_DistributiveLattice_598
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
         ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
            ((T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_622 (T_DistributiveLattice_598 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598
v0))))
-- Algebra.Lattice.Bundles.DistributiveLattice._.reflexive
d_reflexive_636 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_598 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_636 :: ()
-> ()
-> T_DistributiveLattice_598
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_636 ~()
v0 ~()
v1 T_DistributiveLattice_598
v2 = T_DistributiveLattice_598
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_636 T_DistributiveLattice_598
v2
du_reflexive_636 ::
  T_DistributiveLattice_598 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_636 :: T_DistributiveLattice_598
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_636 T_DistributiveLattice_598
v0
  = let v1 :: T_IsDistributiveLattice_3146
v1 = T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_622 (T_DistributiveLattice_598 -> T_DistributiveLattice_598
forall a b. a -> b
coe T_DistributiveLattice_598
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_3070
v2
             = T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                 (T_IsDistributiveLattice_3146 -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                 (T_IsLattice_3070 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070
v2))
              AgdaAny
v3))
-- Algebra.Lattice.Bundles.DistributiveLattice._.sym
d_sym_638 ::
  T_DistributiveLattice_598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_638 :: T_DistributiveLattice_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_638 T_DistributiveLattice_598
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
         ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
            ((T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_622 (T_DistributiveLattice_598 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598
v0))))
-- Algebra.Lattice.Bundles.DistributiveLattice._.trans
d_trans_640 ::
  T_DistributiveLattice_598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_640 :: T_DistributiveLattice_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_640 T_DistributiveLattice_598
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
         ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
            ((T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_622 (T_DistributiveLattice_598 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598
v0))))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∧-absorbs-∨
d_'8743''45'absorbs'45''8744'_642 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_598 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'absorbs'45''8744'_642 :: ()
-> () -> T_DistributiveLattice_598 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'absorbs'45''8744'_642 ~()
v0 ~()
v1 T_DistributiveLattice_598
v2
  = T_DistributiveLattice_598 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_642 T_DistributiveLattice_598
v2
du_'8743''45'absorbs'45''8744'_642 ::
  T_DistributiveLattice_598 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_642 :: T_DistributiveLattice_598 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_642 T_DistributiveLattice_598
v0
  = let v1 :: T_IsDistributiveLattice_3146
v1 = T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_622 (T_DistributiveLattice_598 -> T_DistributiveLattice_598
forall a b. a -> b
coe T_DistributiveLattice_598
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'absorbs'45''8744'_3122
         ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158 (T_IsDistributiveLattice_3146 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v1)))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∧-assoc
d_'8743''45'assoc_644 ::
  T_DistributiveLattice_598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_644 :: T_DistributiveLattice_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_644 T_DistributiveLattice_598
v0
  = (T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'assoc_3102
      ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
         ((T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_622 (T_DistributiveLattice_598 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598
v0)))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∧-comm
d_'8743''45'comm_646 ::
  T_DistributiveLattice_598 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_646 :: T_DistributiveLattice_598 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_646 T_DistributiveLattice_598
v0
  = (T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'comm_3100
      ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
         ((T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_622 (T_DistributiveLattice_598 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598
v0)))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∧-cong
d_'8743''45'cong_648 ::
  T_DistributiveLattice_598 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong_648 :: T_DistributiveLattice_598
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong_648 T_DistributiveLattice_598
v0
  = (T_IsLattice_3070
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_3070
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'cong_3104
      ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
         ((T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_622 (T_DistributiveLattice_598 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598
v0)))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∧-congʳ
d_'8743''45'cong'691'_650 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong'691'_650 :: ()
-> ()
-> T_DistributiveLattice_598
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong'691'_650 ~()
v0 ~()
v1 T_DistributiveLattice_598
v2
  = T_DistributiveLattice_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_650 T_DistributiveLattice_598
v2
du_'8743''45'cong'691'_650 ::
  T_DistributiveLattice_598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_650 :: T_DistributiveLattice_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_650 T_DistributiveLattice_598
v0
  = let v1 :: T_IsDistributiveLattice_3146
v1 = T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_622 (T_DistributiveLattice_598 -> T_DistributiveLattice_598
forall a b. a -> b
coe T_DistributiveLattice_598
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsLattice_3070
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'cong'691'_3128
         ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158 (T_IsDistributiveLattice_3146 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v1)))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∧-congˡ
d_'8743''45'cong'737'_652 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong'737'_652 :: ()
-> ()
-> T_DistributiveLattice_598
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong'737'_652 ~()
v0 ~()
v1 T_DistributiveLattice_598
v2
  = T_DistributiveLattice_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_652 T_DistributiveLattice_598
v2
du_'8743''45'cong'737'_652 ::
  T_DistributiveLattice_598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_652 :: T_DistributiveLattice_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_652 T_DistributiveLattice_598
v0
  = let v1 :: T_IsDistributiveLattice_3146
v1 = T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_622 (T_DistributiveLattice_598 -> T_DistributiveLattice_598
forall a b. a -> b
coe T_DistributiveLattice_598
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsLattice_3070
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'cong'737'_3124
         ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158 (T_IsDistributiveLattice_3146 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v1)))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∧-distrib-∨
d_'8743''45'distrib'45''8744'_654 ::
  T_DistributiveLattice_598 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8743''45'distrib'45''8744'_654 :: T_DistributiveLattice_598 -> T_Σ_14
d_'8743''45'distrib'45''8744'_654 T_DistributiveLattice_598
v0
  = (T_IsDistributiveLattice_3146 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsDistributiveLattice_3146 -> T_Σ_14
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'distrib'45''8744'_3162
      ((T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_622 (T_DistributiveLattice_598 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598
v0))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∧-distribʳ-∨
d_'8743''45'distrib'691''45''8744'_656 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'distrib'691''45''8744'_656 :: ()
-> ()
-> T_DistributiveLattice_598
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'distrib'691''45''8744'_656 ~()
v0 ~()
v1 T_DistributiveLattice_598
v2
  = T_DistributiveLattice_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'691''45''8744'_656 T_DistributiveLattice_598
v2
du_'8743''45'distrib'691''45''8744'_656 ::
  T_DistributiveLattice_598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'691''45''8744'_656 :: T_DistributiveLattice_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'691''45''8744'_656 T_DistributiveLattice_598
v0
  = (T_IsDistributiveLattice_3146
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'distrib'691''45''8744'_3210
      ((T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_622 (T_DistributiveLattice_598 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598
v0))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∧-distribˡ-∨
d_'8743''45'distrib'737''45''8744'_658 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'distrib'737''45''8744'_658 :: ()
-> ()
-> T_DistributiveLattice_598
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'distrib'737''45''8744'_658 ~()
v0 ~()
v1 T_DistributiveLattice_598
v2
  = T_DistributiveLattice_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'737''45''8744'_658 T_DistributiveLattice_598
v2
du_'8743''45'distrib'737''45''8744'_658 ::
  T_DistributiveLattice_598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'737''45''8744'_658 :: T_DistributiveLattice_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'737''45''8744'_658 T_DistributiveLattice_598
v0
  = (T_IsDistributiveLattice_3146
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'distrib'737''45''8744'_3208
      ((T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_622 (T_DistributiveLattice_598 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598
v0))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∨-absorbs-∧
d_'8744''45'absorbs'45''8743'_660 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_598 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'absorbs'45''8743'_660 :: ()
-> () -> T_DistributiveLattice_598 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'absorbs'45''8743'_660 ~()
v0 ~()
v1 T_DistributiveLattice_598
v2
  = T_DistributiveLattice_598 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_660 T_DistributiveLattice_598
v2
du_'8744''45'absorbs'45''8743'_660 ::
  T_DistributiveLattice_598 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_660 :: T_DistributiveLattice_598 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_660 T_DistributiveLattice_598
v0
  = let v1 :: T_IsDistributiveLattice_3146
v1 = T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_622 (T_DistributiveLattice_598 -> T_DistributiveLattice_598
forall a b. a -> b
coe T_DistributiveLattice_598
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'absorbs'45''8743'_3120
         ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158 (T_IsDistributiveLattice_3146 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v1)))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∨-assoc
d_'8744''45'assoc_662 ::
  T_DistributiveLattice_598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_662 :: T_DistributiveLattice_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_662 T_DistributiveLattice_598
v0
  = (T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'assoc_3096
      ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
         ((T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_622 (T_DistributiveLattice_598 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598
v0)))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∨-comm
d_'8744''45'comm_664 ::
  T_DistributiveLattice_598 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_664 :: T_DistributiveLattice_598 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_664 T_DistributiveLattice_598
v0
  = (T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'comm_3094
      ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
         ((T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_622 (T_DistributiveLattice_598 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598
v0)))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∨-cong
d_'8744''45'cong_666 ::
  T_DistributiveLattice_598 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong_666 :: T_DistributiveLattice_598
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong_666 T_DistributiveLattice_598
v0
  = (T_IsLattice_3070
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_3070
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'cong_3098
      ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
         ((T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_622 (T_DistributiveLattice_598 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598
v0)))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∨-congʳ
d_'8744''45'cong'691'_668 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong'691'_668 :: ()
-> ()
-> T_DistributiveLattice_598
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong'691'_668 ~()
v0 ~()
v1 T_DistributiveLattice_598
v2
  = T_DistributiveLattice_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_668 T_DistributiveLattice_598
v2
du_'8744''45'cong'691'_668 ::
  T_DistributiveLattice_598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_668 :: T_DistributiveLattice_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_668 T_DistributiveLattice_598
v0
  = let v1 :: T_IsDistributiveLattice_3146
v1 = T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_622 (T_DistributiveLattice_598 -> T_DistributiveLattice_598
forall a b. a -> b
coe T_DistributiveLattice_598
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsLattice_3070
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'cong'691'_3136
         ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158 (T_IsDistributiveLattice_3146 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v1)))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∨-congˡ
d_'8744''45'cong'737'_670 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong'737'_670 :: ()
-> ()
-> T_DistributiveLattice_598
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong'737'_670 ~()
v0 ~()
v1 T_DistributiveLattice_598
v2
  = T_DistributiveLattice_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_670 T_DistributiveLattice_598
v2
du_'8744''45'cong'737'_670 ::
  T_DistributiveLattice_598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_670 :: T_DistributiveLattice_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_670 T_DistributiveLattice_598
v0
  = let v1 :: T_IsDistributiveLattice_3146
v1 = T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_622 (T_DistributiveLattice_598 -> T_DistributiveLattice_598
forall a b. a -> b
coe T_DistributiveLattice_598
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsLattice_3070
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'cong'737'_3132
         ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158 (T_IsDistributiveLattice_3146 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v1)))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∨-distrib-∧
d_'8744''45'distrib'45''8743'_672 ::
  T_DistributiveLattice_598 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8744''45'distrib'45''8743'_672 :: T_DistributiveLattice_598 -> T_Σ_14
d_'8744''45'distrib'45''8743'_672 T_DistributiveLattice_598
v0
  = (T_IsDistributiveLattice_3146 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsDistributiveLattice_3146 -> T_Σ_14
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'distrib'45''8743'_3160
      ((T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_622 (T_DistributiveLattice_598 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598
v0))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∨-distribʳ-∧
d_'8744''45'distrib'691''45''8743'_674 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'distrib'691''45''8743'_674 :: ()
-> ()
-> T_DistributiveLattice_598
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'distrib'691''45''8743'_674 ~()
v0 ~()
v1 T_DistributiveLattice_598
v2
  = T_DistributiveLattice_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'691''45''8743'_674 T_DistributiveLattice_598
v2
du_'8744''45'distrib'691''45''8743'_674 ::
  T_DistributiveLattice_598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'691''45''8743'_674 :: T_DistributiveLattice_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'691''45''8743'_674 T_DistributiveLattice_598
v0
  = (T_IsDistributiveLattice_3146
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'distrib'691''45''8743'_3206
      ((T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_622 (T_DistributiveLattice_598 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598
v0))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∨-distribˡ-∧
d_'8744''45'distrib'737''45''8743'_676 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'distrib'737''45''8743'_676 :: ()
-> ()
-> T_DistributiveLattice_598
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'distrib'737''45''8743'_676 ~()
v0 ~()
v1 T_DistributiveLattice_598
v2
  = T_DistributiveLattice_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'737''45''8743'_676 T_DistributiveLattice_598
v2
du_'8744''45'distrib'737''45''8743'_676 ::
  T_DistributiveLattice_598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'737''45''8743'_676 :: T_DistributiveLattice_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'737''45''8743'_676 T_DistributiveLattice_598
v0
  = (T_IsDistributiveLattice_3146
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'distrib'737''45''8743'_3204
      ((T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_622 (T_DistributiveLattice_598 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598
v0))
-- Algebra.Lattice.Bundles.DistributiveLattice.lattice
d_lattice_678 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_598 -> T_Lattice_512
d_lattice_678 :: () -> () -> T_DistributiveLattice_598 -> T_Lattice_512
d_lattice_678 ~()
v0 ~()
v1 T_DistributiveLattice_598
v2 = T_DistributiveLattice_598 -> T_Lattice_512
du_lattice_678 T_DistributiveLattice_598
v2
du_lattice_678 :: T_DistributiveLattice_598 -> T_Lattice_512
du_lattice_678 :: T_DistributiveLattice_598 -> T_Lattice_512
du_lattice_678 T_DistributiveLattice_598
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsLattice_3070
 -> T_Lattice_512)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_3070
-> T_Lattice_512
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_3070
-> T_Lattice_512
C_constructor_592 (T_DistributiveLattice_598 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__618 (T_DistributiveLattice_598 -> T_DistributiveLattice_598
forall a b. a -> b
coe T_DistributiveLattice_598
v0))
      (T_DistributiveLattice_598 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__620 (T_DistributiveLattice_598 -> T_DistributiveLattice_598
forall a b. a -> b
coe T_DistributiveLattice_598
v0))
      (T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
         ((T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_622 (T_DistributiveLattice_598 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598
v0)))
-- Algebra.Lattice.Bundles.DistributiveLattice._._≉_
d__'8777'__682 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_598 -> AgdaAny -> AgdaAny -> ()
d__'8777'__682 :: () -> () -> T_DistributiveLattice_598 -> AgdaAny -> AgdaAny -> ()
d__'8777'__682 = () -> () -> T_DistributiveLattice_598 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.DistributiveLattice._.rawLattice
d_rawLattice_684 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_598 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.Raw.T_RawLattice_12
d_rawLattice_684 :: () -> () -> T_DistributiveLattice_598 -> T_RawLattice_12
d_rawLattice_684 ~()
v0 ~()
v1 T_DistributiveLattice_598
v2 = T_DistributiveLattice_598 -> T_RawLattice_12
du_rawLattice_684 T_DistributiveLattice_598
v2
du_rawLattice_684 ::
  T_DistributiveLattice_598 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.Raw.T_RawLattice_12
du_rawLattice_684 :: T_DistributiveLattice_598 -> T_RawLattice_12
du_rawLattice_684 T_DistributiveLattice_598
v0
  = (T_Lattice_512 -> T_RawLattice_12) -> AgdaAny -> T_RawLattice_12
forall a b. a -> b
coe T_Lattice_512 -> T_RawLattice_12
du_rawLattice_578 ((T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_Lattice_512
du_lattice_678 (T_DistributiveLattice_598 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598
v0))
-- Algebra.Lattice.Bundles.DistributiveLattice._.setoid
d_setoid_686 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_598 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_686 :: () -> () -> T_DistributiveLattice_598 -> T_Setoid_46
d_setoid_686 ~()
v0 ~()
v1 T_DistributiveLattice_598
v2 = T_DistributiveLattice_598 -> T_Setoid_46
du_setoid_686 T_DistributiveLattice_598
v2
du_setoid_686 ::
  T_DistributiveLattice_598 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_686 :: T_DistributiveLattice_598 -> T_Setoid_46
du_setoid_686 T_DistributiveLattice_598
v0 = (T_Lattice_512 -> T_Setoid_46) -> AgdaAny -> T_Setoid_46
forall a b. a -> b
coe T_Lattice_512 -> T_Setoid_46
du_setoid_586 ((T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_Lattice_512
du_lattice_678 (T_DistributiveLattice_598 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598
v0))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∧-rawMagma
d_'8743''45'rawMagma_688 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_598 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
d_'8743''45'rawMagma_688 :: () -> () -> T_DistributiveLattice_598 -> T_RawMagma_44
d_'8743''45'rawMagma_688 ~()
v0 ~()
v1 T_DistributiveLattice_598
v2 = T_DistributiveLattice_598 -> T_RawMagma_44
du_'8743''45'rawMagma_688 T_DistributiveLattice_598
v2
du_'8743''45'rawMagma_688 ::
  T_DistributiveLattice_598 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
du_'8743''45'rawMagma_688 :: T_DistributiveLattice_598 -> T_RawMagma_44
du_'8743''45'rawMagma_688 T_DistributiveLattice_598
v0
  = let v1 :: AgdaAny
v1 = (T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_Lattice_512
du_lattice_678 (T_DistributiveLattice_598 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598
v0) in
    AgdaAny -> T_RawMagma_44
forall a b. a -> b
coe
      ((T_RawLattice_12 -> T_RawMagma_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_RawLattice_12 -> T_RawMagma_44
MAlonzo.Code.Algebra.Lattice.Bundles.Raw.du_'8743''45'rawMagma_36
         ((T_Lattice_512 -> T_RawLattice_12) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_512 -> T_RawLattice_12
du_rawLattice_578 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∨-rawMagma
d_'8744''45'rawMagma_690 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_598 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
d_'8744''45'rawMagma_690 :: () -> () -> T_DistributiveLattice_598 -> T_RawMagma_44
d_'8744''45'rawMagma_690 ~()
v0 ~()
v1 T_DistributiveLattice_598
v2 = T_DistributiveLattice_598 -> T_RawMagma_44
du_'8744''45'rawMagma_690 T_DistributiveLattice_598
v2
du_'8744''45'rawMagma_690 ::
  T_DistributiveLattice_598 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
du_'8744''45'rawMagma_690 :: T_DistributiveLattice_598 -> T_RawMagma_44
du_'8744''45'rawMagma_690 T_DistributiveLattice_598
v0
  = let v1 :: AgdaAny
v1 = (T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_Lattice_512
du_lattice_678 (T_DistributiveLattice_598 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598
v0) in
    AgdaAny -> T_RawMagma_44
forall a b. a -> b
coe
      ((T_RawLattice_12 -> T_RawMagma_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_RawLattice_12 -> T_RawMagma_44
MAlonzo.Code.Algebra.Lattice.Bundles.Raw.du_'8744''45'rawMagma_34
         ((T_Lattice_512 -> T_RawLattice_12) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_512 -> T_RawLattice_12
du_rawLattice_578 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Lattice.Bundles.BooleanAlgebra
d_BooleanAlgebra_698 :: p -> p -> ()
d_BooleanAlgebra_698 p
a0 p
a1 = ()
data T_BooleanAlgebra_698
  = C_constructor_822 (AgdaAny -> AgdaAny -> AgdaAny)
                      (AgdaAny -> AgdaAny -> AgdaAny) (AgdaAny -> AgdaAny) AgdaAny
                      AgdaAny
                      MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224
-- Algebra.Lattice.Bundles.BooleanAlgebra.Carrier
d_Carrier_720 :: T_BooleanAlgebra_698 -> ()
d_Carrier_720 :: T_BooleanAlgebra_698 -> ()
d_Carrier_720 = T_BooleanAlgebra_698 -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.BooleanAlgebra._≈_
d__'8776'__722 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> ()
d__'8776'__722 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> ()
d__'8776'__722 = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.BooleanAlgebra._∨_
d__'8744'__724 ::
  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__724 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__724 T_BooleanAlgebra_698
v0
  = case T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0 of
      C_constructor_822 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsBooleanAlgebra_3224
v8 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_BooleanAlgebra_698
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.BooleanAlgebra._∧_
d__'8743'__726 ::
  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__726 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__726 T_BooleanAlgebra_698
v0
  = case T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0 of
      C_constructor_822 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsBooleanAlgebra_3224
v8 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_BooleanAlgebra_698
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.BooleanAlgebra.¬_
d_'172'__728 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
d_'172'__728 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
d_'172'__728 T_BooleanAlgebra_698
v0
  = case T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0 of
      C_constructor_822 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsBooleanAlgebra_3224
v8 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v5
      T_BooleanAlgebra_698
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.BooleanAlgebra.⊤
d_'8868'_730 :: T_BooleanAlgebra_698 -> AgdaAny
d_'8868'_730 :: T_BooleanAlgebra_698 -> AgdaAny
d_'8868'_730 T_BooleanAlgebra_698
v0
  = case T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0 of
      C_constructor_822 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsBooleanAlgebra_3224
v8 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6
      T_BooleanAlgebra_698
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.BooleanAlgebra.⊥
d_'8869'_732 :: T_BooleanAlgebra_698 -> AgdaAny
d_'8869'_732 :: T_BooleanAlgebra_698 -> AgdaAny
d_'8869'_732 T_BooleanAlgebra_698
v0
  = case T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0 of
      C_constructor_822 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsBooleanAlgebra_3224
v8 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v7
      T_BooleanAlgebra_698
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.BooleanAlgebra.isBooleanAlgebra
d_isBooleanAlgebra_734 ::
  T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224
d_isBooleanAlgebra_734 :: T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
d_isBooleanAlgebra_734 T_BooleanAlgebra_698
v0
  = case T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0 of
      C_constructor_822 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsBooleanAlgebra_3224
v8 -> T_IsBooleanAlgebra_3224 -> T_IsBooleanAlgebra_3224
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v8
      T_BooleanAlgebra_698
_ -> T_IsBooleanAlgebra_3224
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.BooleanAlgebra._.absorptive
d_absorptive_738 ::
  T_BooleanAlgebra_698 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_absorptive_738 :: T_BooleanAlgebra_698 -> T_Σ_14
d_absorptive_738 T_BooleanAlgebra_698
v0
  = (T_IsLattice_3070 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsLattice_3070 -> T_Σ_14
MAlonzo.Code.Algebra.Lattice.Structures.d_absorptive_3106
      ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
         ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
            ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
d_isBooleanAlgebra_734 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.isDistributiveLattice
d_isDistributiveLattice_740 ::
  T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3146
d_isDistributiveLattice_740 :: T_BooleanAlgebra_698 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_740 T_BooleanAlgebra_698
v0
  = (T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe
      T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
      ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
d_isBooleanAlgebra_734 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.isEquivalence
d_isEquivalence_742 ::
  T_BooleanAlgebra_698 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_742 :: T_BooleanAlgebra_698 -> T_IsEquivalence_28
d_isEquivalence_742 T_BooleanAlgebra_698
v0
  = (T_IsLattice_3070 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
      ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
         ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
            ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
d_isBooleanAlgebra_734 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.isLattice
d_isLattice_744 ::
  T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_3070
d_isLattice_744 :: T_BooleanAlgebra_698 -> T_IsLattice_3070
d_isLattice_744 T_BooleanAlgebra_698
v0
  = (T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> T_IsLattice_3070
forall a b. a -> b
coe
      T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
      ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
         ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
d_isBooleanAlgebra_734 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.isPartialEquivalence
d_isPartialEquivalence_746 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_698 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_746 :: () -> () -> T_BooleanAlgebra_698 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_746 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_746 T_BooleanAlgebra_698
v2
du_isPartialEquivalence_746 ::
  T_BooleanAlgebra_698 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_746 :: T_BooleanAlgebra_698 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_746 T_BooleanAlgebra_698
v0
  = let v1 :: T_IsBooleanAlgebra_3224
v1 = T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
d_isBooleanAlgebra_734 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsDistributiveLattice_3146
v2
             = T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                 (T_IsBooleanAlgebra_3224 -> T_IsBooleanAlgebra_3224
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_3070
v3
                = T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                    (T_IsDistributiveLattice_3146 -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                  (T_IsLattice_3070 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070
v3)))))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.refl
d_refl_748 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
d_refl_748 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
d_refl_748 T_BooleanAlgebra_698
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
         ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
            ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
               ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
d_isBooleanAlgebra_734 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.reflexive
d_reflexive_750 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_698 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_750 :: ()
-> ()
-> T_BooleanAlgebra_698
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_750 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 = T_BooleanAlgebra_698
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_750 T_BooleanAlgebra_698
v2
du_reflexive_750 ::
  T_BooleanAlgebra_698 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_750 :: T_BooleanAlgebra_698
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_750 T_BooleanAlgebra_698
v0
  = let v1 :: T_IsBooleanAlgebra_3224
v1 = T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
d_isBooleanAlgebra_734 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsDistributiveLattice_3146
v2
             = T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                 (T_IsBooleanAlgebra_3224 -> T_IsBooleanAlgebra_3224
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_3070
v3
                = T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                    (T_IsDistributiveLattice_3146 -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                    (T_IsLattice_3070 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070
v3))
                 AgdaAny
v4)))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.sym
d_sym_752 ::
  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_752 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_752 T_BooleanAlgebra_698
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
         ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
            ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
               ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
d_isBooleanAlgebra_734 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.trans
d_trans_754 ::
  T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_754 :: T_BooleanAlgebra_698
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_754 T_BooleanAlgebra_698
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
         ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
            ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
               ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
d_isBooleanAlgebra_734 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.¬-cong
d_'172''45'cong_756 ::
  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'172''45'cong_756 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'172''45'cong_756 T_BooleanAlgebra_698
v0
  = (T_IsBooleanAlgebra_3224
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'172''45'cong_3250
      ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
d_isBooleanAlgebra_734 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∧-absorbs-∨
d_'8743''45'absorbs'45''8744'_758 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'absorbs'45''8744'_758 :: () -> () -> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'absorbs'45''8744'_758 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_758 T_BooleanAlgebra_698
v2
du_'8743''45'absorbs'45''8744'_758 ::
  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_758 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_758 T_BooleanAlgebra_698
v0
  = let v1 :: T_IsBooleanAlgebra_3224
v1 = T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
d_isBooleanAlgebra_734 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsDistributiveLattice_3146
v2
             = T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                 (T_IsBooleanAlgebra_3224 -> T_IsBooleanAlgebra_3224
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'absorbs'45''8744'_3122
            ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
               (T_IsDistributiveLattice_3146 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v2))))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∧-assoc
d_'8743''45'assoc_760 ::
  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_760 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_760 T_BooleanAlgebra_698
v0
  = (T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'assoc_3102
      ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
         ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
            ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
d_isBooleanAlgebra_734 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∧-comm
d_'8743''45'comm_762 ::
  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_762 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_762 T_BooleanAlgebra_698
v0
  = (T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'comm_3100
      ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
         ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
            ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
d_isBooleanAlgebra_734 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∧-complement
d_'8743''45'complement_764 ::
  T_BooleanAlgebra_698 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8743''45'complement_764 :: T_BooleanAlgebra_698 -> T_Σ_14
d_'8743''45'complement_764 T_BooleanAlgebra_698
v0
  = (T_IsBooleanAlgebra_3224 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsBooleanAlgebra_3224 -> T_Σ_14
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'complement_3248
      ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
d_isBooleanAlgebra_734 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∧-complementʳ
d_'8743''45'complement'691'_766 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
d_'8743''45'complement'691'_766 :: () -> () -> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
d_'8743''45'complement'691'_766 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8743''45'complement'691'_766 T_BooleanAlgebra_698
v2
du_'8743''45'complement'691'_766 ::
  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8743''45'complement'691'_766 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8743''45'complement'691'_766 T_BooleanAlgebra_698
v0
  = (T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'complement'691'_3312
      ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
d_isBooleanAlgebra_734 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∧-complementˡ
d_'8743''45'complement'737'_768 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
d_'8743''45'complement'737'_768 :: () -> () -> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
d_'8743''45'complement'737'_768 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8743''45'complement'737'_768 T_BooleanAlgebra_698
v2
du_'8743''45'complement'737'_768 ::
  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8743''45'complement'737'_768 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8743''45'complement'737'_768 T_BooleanAlgebra_698
v0
  = (T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'complement'737'_3310
      ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
d_isBooleanAlgebra_734 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∧-cong
d_'8743''45'cong_770 ::
  T_BooleanAlgebra_698 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong_770 :: T_BooleanAlgebra_698
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong_770 T_BooleanAlgebra_698
v0
  = (T_IsLattice_3070
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_3070
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'cong_3104
      ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
         ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
            ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
d_isBooleanAlgebra_734 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∧-congʳ
d_'8743''45'cong'691'_772 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong'691'_772 :: ()
-> ()
-> T_BooleanAlgebra_698
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong'691'_772 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_772 T_BooleanAlgebra_698
v2
du_'8743''45'cong'691'_772 ::
  T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_772 :: T_BooleanAlgebra_698
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_772 T_BooleanAlgebra_698
v0
  = let v1 :: T_IsBooleanAlgebra_3224
v1 = T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
d_isBooleanAlgebra_734 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsDistributiveLattice_3146
v2
             = T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                 (T_IsBooleanAlgebra_3224 -> T_IsBooleanAlgebra_3224
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsLattice_3070
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'cong'691'_3128
            ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
               (T_IsDistributiveLattice_3146 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v2))))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∧-congˡ
d_'8743''45'cong'737'_774 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong'737'_774 :: ()
-> ()
-> T_BooleanAlgebra_698
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong'737'_774 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_774 T_BooleanAlgebra_698
v2
du_'8743''45'cong'737'_774 ::
  T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_774 :: T_BooleanAlgebra_698
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_774 T_BooleanAlgebra_698
v0
  = let v1 :: T_IsBooleanAlgebra_3224
v1 = T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
d_isBooleanAlgebra_734 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsDistributiveLattice_3146
v2
             = T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                 (T_IsBooleanAlgebra_3224 -> T_IsBooleanAlgebra_3224
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsLattice_3070
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'cong'737'_3124
            ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
               (T_IsDistributiveLattice_3146 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v2))))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∧-distrib-∨
d_'8743''45'distrib'45''8744'_776 ::
  T_BooleanAlgebra_698 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8743''45'distrib'45''8744'_776 :: T_BooleanAlgebra_698 -> T_Σ_14
d_'8743''45'distrib'45''8744'_776 T_BooleanAlgebra_698
v0
  = (T_IsDistributiveLattice_3146 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsDistributiveLattice_3146 -> T_Σ_14
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'distrib'45''8744'_3162
      ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
         ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
d_isBooleanAlgebra_734 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∧-distribʳ-∨
d_'8743''45'distrib'691''45''8744'_778 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'distrib'691''45''8744'_778 :: ()
-> ()
-> T_BooleanAlgebra_698
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'distrib'691''45''8744'_778 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'691''45''8744'_778 T_BooleanAlgebra_698
v2
du_'8743''45'distrib'691''45''8744'_778 ::
  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'691''45''8744'_778 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'691''45''8744'_778 T_BooleanAlgebra_698
v0
  = let v1 :: T_IsBooleanAlgebra_3224
v1 = T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
d_isBooleanAlgebra_734 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsDistributiveLattice_3146
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'distrib'691''45''8744'_3210
         ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
            (T_IsBooleanAlgebra_3224 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v1)))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∧-distribˡ-∨
d_'8743''45'distrib'737''45''8744'_780 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'distrib'737''45''8744'_780 :: ()
-> ()
-> T_BooleanAlgebra_698
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'distrib'737''45''8744'_780 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'737''45''8744'_780 T_BooleanAlgebra_698
v2
du_'8743''45'distrib'737''45''8744'_780 ::
  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'737''45''8744'_780 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'737''45''8744'_780 T_BooleanAlgebra_698
v0
  = let v1 :: T_IsBooleanAlgebra_3224
v1 = T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
d_isBooleanAlgebra_734 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsDistributiveLattice_3146
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'distrib'737''45''8744'_3208
         ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
            (T_IsBooleanAlgebra_3224 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v1)))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∨-absorbs-∧
d_'8744''45'absorbs'45''8743'_782 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'absorbs'45''8743'_782 :: () -> () -> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'absorbs'45''8743'_782 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_782 T_BooleanAlgebra_698
v2
du_'8744''45'absorbs'45''8743'_782 ::
  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_782 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_782 T_BooleanAlgebra_698
v0
  = let v1 :: T_IsBooleanAlgebra_3224
v1 = T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
d_isBooleanAlgebra_734 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsDistributiveLattice_3146
v2
             = T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                 (T_IsBooleanAlgebra_3224 -> T_IsBooleanAlgebra_3224
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'absorbs'45''8743'_3120
            ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
               (T_IsDistributiveLattice_3146 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v2))))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∨-assoc
d_'8744''45'assoc_784 ::
  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_784 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_784 T_BooleanAlgebra_698
v0
  = (T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'assoc_3096
      ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
         ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
            ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
d_isBooleanAlgebra_734 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∨-comm
d_'8744''45'comm_786 ::
  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_786 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_786 T_BooleanAlgebra_698
v0
  = (T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'comm_3094
      ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
         ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
            ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
d_isBooleanAlgebra_734 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∨-complement
d_'8744''45'complement_788 ::
  T_BooleanAlgebra_698 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8744''45'complement_788 :: T_BooleanAlgebra_698 -> T_Σ_14
d_'8744''45'complement_788 T_BooleanAlgebra_698
v0
  = (T_IsBooleanAlgebra_3224 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsBooleanAlgebra_3224 -> T_Σ_14
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'complement_3246
      ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
d_isBooleanAlgebra_734 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∨-complementʳ
d_'8744''45'complement'691'_790 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
d_'8744''45'complement'691'_790 :: () -> () -> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
d_'8744''45'complement'691'_790 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8744''45'complement'691'_790 T_BooleanAlgebra_698
v2
du_'8744''45'complement'691'_790 ::
  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8744''45'complement'691'_790 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8744''45'complement'691'_790 T_BooleanAlgebra_698
v0
  = (T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'complement'691'_3308
      ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
d_isBooleanAlgebra_734 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∨-complementˡ
d_'8744''45'complement'737'_792 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
d_'8744''45'complement'737'_792 :: () -> () -> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
d_'8744''45'complement'737'_792 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8744''45'complement'737'_792 T_BooleanAlgebra_698
v2
du_'8744''45'complement'737'_792 ::
  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8744''45'complement'737'_792 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8744''45'complement'737'_792 T_BooleanAlgebra_698
v0
  = (T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'complement'737'_3306
      ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
d_isBooleanAlgebra_734 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∨-cong
d_'8744''45'cong_794 ::
  T_BooleanAlgebra_698 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong_794 :: T_BooleanAlgebra_698
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong_794 T_BooleanAlgebra_698
v0
  = (T_IsLattice_3070
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_3070
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'cong_3098
      ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
         ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
            ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
d_isBooleanAlgebra_734 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∨-congʳ
d_'8744''45'cong'691'_796 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong'691'_796 :: ()
-> ()
-> T_BooleanAlgebra_698
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong'691'_796 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_796 T_BooleanAlgebra_698
v2
du_'8744''45'cong'691'_796 ::
  T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_796 :: T_BooleanAlgebra_698
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_796 T_BooleanAlgebra_698
v0
  = let v1 :: T_IsBooleanAlgebra_3224
v1 = T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
d_isBooleanAlgebra_734 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsDistributiveLattice_3146
v2
             = T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                 (T_IsBooleanAlgebra_3224 -> T_IsBooleanAlgebra_3224
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsLattice_3070
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'cong'691'_3136
            ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
               (T_IsDistributiveLattice_3146 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v2))))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∨-congˡ
d_'8744''45'cong'737'_798 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong'737'_798 :: ()
-> ()
-> T_BooleanAlgebra_698
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong'737'_798 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_798 T_BooleanAlgebra_698
v2
du_'8744''45'cong'737'_798 ::
  T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_798 :: T_BooleanAlgebra_698
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_798 T_BooleanAlgebra_698
v0
  = let v1 :: T_IsBooleanAlgebra_3224
v1 = T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
d_isBooleanAlgebra_734 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsDistributiveLattice_3146
v2
             = T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                 (T_IsBooleanAlgebra_3224 -> T_IsBooleanAlgebra_3224
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsLattice_3070
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'cong'737'_3132
            ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
               (T_IsDistributiveLattice_3146 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v2))))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∨-distrib-∧
d_'8744''45'distrib'45''8743'_800 ::
  T_BooleanAlgebra_698 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8744''45'distrib'45''8743'_800 :: T_BooleanAlgebra_698 -> T_Σ_14
d_'8744''45'distrib'45''8743'_800 T_BooleanAlgebra_698
v0
  = (T_IsDistributiveLattice_3146 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsDistributiveLattice_3146 -> T_Σ_14
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'distrib'45''8743'_3160
      ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
         ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
d_isBooleanAlgebra_734 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∨-distribʳ-∧
d_'8744''45'distrib'691''45''8743'_802 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'distrib'691''45''8743'_802 :: ()
-> ()
-> T_BooleanAlgebra_698
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'distrib'691''45''8743'_802 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'691''45''8743'_802 T_BooleanAlgebra_698
v2
du_'8744''45'distrib'691''45''8743'_802 ::
  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'691''45''8743'_802 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'691''45''8743'_802 T_BooleanAlgebra_698
v0
  = let v1 :: T_IsBooleanAlgebra_3224
v1 = T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
d_isBooleanAlgebra_734 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsDistributiveLattice_3146
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'distrib'691''45''8743'_3206
         ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
            (T_IsBooleanAlgebra_3224 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v1)))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∨-distribˡ-∧
d_'8744''45'distrib'737''45''8743'_804 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'distrib'737''45''8743'_804 :: ()
-> ()
-> T_BooleanAlgebra_698
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'distrib'737''45''8743'_804 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'737''45''8743'_804 T_BooleanAlgebra_698
v2
du_'8744''45'distrib'737''45''8743'_804 ::
  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'737''45''8743'_804 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'737''45''8743'_804 T_BooleanAlgebra_698
v0
  = let v1 :: T_IsBooleanAlgebra_3224
v1 = T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
d_isBooleanAlgebra_734 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsDistributiveLattice_3146
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'distrib'737''45''8743'_3204
         ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
            (T_IsBooleanAlgebra_3224 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v1)))
-- Algebra.Lattice.Bundles.BooleanAlgebra.distributiveLattice
d_distributiveLattice_806 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_698 -> T_DistributiveLattice_598
d_distributiveLattice_806 :: () -> () -> T_BooleanAlgebra_698 -> T_DistributiveLattice_598
d_distributiveLattice_806 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_DistributiveLattice_598
du_distributiveLattice_806 T_BooleanAlgebra_698
v2
du_distributiveLattice_806 ::
  T_BooleanAlgebra_698 -> T_DistributiveLattice_598
du_distributiveLattice_806 :: T_BooleanAlgebra_698 -> T_DistributiveLattice_598
du_distributiveLattice_806 T_BooleanAlgebra_698
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsDistributiveLattice_3146
 -> T_DistributiveLattice_598)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_3146
-> T_DistributiveLattice_598
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_3146
-> T_DistributiveLattice_598
C_constructor_692 (T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__724 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      (T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__726 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      (T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
         ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> T_IsBooleanAlgebra_3224
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
d_isBooleanAlgebra_734 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
-- Algebra.Lattice.Bundles.BooleanAlgebra._._≉_
d__'8777'__810 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> ()
d__'8777'__810 :: () -> () -> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> ()
d__'8777'__810 = () -> () -> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.BooleanAlgebra._.lattice
d_lattice_812 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_698 -> T_Lattice_512
d_lattice_812 :: () -> () -> T_BooleanAlgebra_698 -> T_Lattice_512
d_lattice_812 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 = T_BooleanAlgebra_698 -> T_Lattice_512
du_lattice_812 T_BooleanAlgebra_698
v2
du_lattice_812 :: T_BooleanAlgebra_698 -> T_Lattice_512
du_lattice_812 :: T_BooleanAlgebra_698 -> T_Lattice_512
du_lattice_812 T_BooleanAlgebra_698
v0
  = (T_DistributiveLattice_598 -> T_Lattice_512)
-> AgdaAny -> T_Lattice_512
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_Lattice_512
du_lattice_678 ((T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_DistributiveLattice_598
du_distributiveLattice_806 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.rawLattice
d_rawLattice_814 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.Raw.T_RawLattice_12
d_rawLattice_814 :: () -> () -> T_BooleanAlgebra_698 -> T_RawLattice_12
d_rawLattice_814 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 = T_BooleanAlgebra_698 -> T_RawLattice_12
du_rawLattice_814 T_BooleanAlgebra_698
v2
du_rawLattice_814 ::
  T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.Raw.T_RawLattice_12
du_rawLattice_814 :: T_BooleanAlgebra_698 -> T_RawLattice_12
du_rawLattice_814 T_BooleanAlgebra_698
v0
  = let v1 :: AgdaAny
v1 = (T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_DistributiveLattice_598
du_distributiveLattice_806 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> T_RawLattice_12
forall a b. a -> b
coe ((T_Lattice_512 -> T_RawLattice_12) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_512 -> T_RawLattice_12
du_rawLattice_578 ((T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_Lattice_512
du_lattice_678 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.setoid
d_setoid_816 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_698 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_816 :: () -> () -> T_BooleanAlgebra_698 -> T_Setoid_46
d_setoid_816 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 = T_BooleanAlgebra_698 -> T_Setoid_46
du_setoid_816 T_BooleanAlgebra_698
v2
du_setoid_816 ::
  T_BooleanAlgebra_698 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_816 :: T_BooleanAlgebra_698 -> T_Setoid_46
du_setoid_816 T_BooleanAlgebra_698
v0
  = let v1 :: AgdaAny
v1 = (T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_DistributiveLattice_598
du_distributiveLattice_806 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe ((T_Lattice_512 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_512 -> T_Setoid_46
du_setoid_586 ((T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_Lattice_512
du_lattice_678 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∧-rawMagma
d_'8743''45'rawMagma_818 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
d_'8743''45'rawMagma_818 :: () -> () -> T_BooleanAlgebra_698 -> T_RawMagma_44
d_'8743''45'rawMagma_818 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 = T_BooleanAlgebra_698 -> T_RawMagma_44
du_'8743''45'rawMagma_818 T_BooleanAlgebra_698
v2
du_'8743''45'rawMagma_818 ::
  T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
du_'8743''45'rawMagma_818 :: T_BooleanAlgebra_698 -> T_RawMagma_44
du_'8743''45'rawMagma_818 T_BooleanAlgebra_698
v0
  = let v1 :: AgdaAny
v1 = (T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_DistributiveLattice_598
du_distributiveLattice_806 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> T_RawMagma_44
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_Lattice_512
du_lattice_678 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_RawLattice_12 -> T_RawMagma_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_RawLattice_12 -> T_RawMagma_44
MAlonzo.Code.Algebra.Lattice.Bundles.Raw.du_'8743''45'rawMagma_36
            ((T_Lattice_512 -> T_RawLattice_12) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_512 -> T_RawLattice_12
du_rawLattice_578 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∨-rawMagma
d_'8744''45'rawMagma_820 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
d_'8744''45'rawMagma_820 :: () -> () -> T_BooleanAlgebra_698 -> T_RawMagma_44
d_'8744''45'rawMagma_820 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 = T_BooleanAlgebra_698 -> T_RawMagma_44
du_'8744''45'rawMagma_820 T_BooleanAlgebra_698
v2
du_'8744''45'rawMagma_820 ::
  T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
du_'8744''45'rawMagma_820 :: T_BooleanAlgebra_698 -> T_RawMagma_44
du_'8744''45'rawMagma_820 T_BooleanAlgebra_698
v0
  = let v1 :: AgdaAny
v1 = (T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_DistributiveLattice_598
du_distributiveLattice_806 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> T_RawMagma_44
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_Lattice_512
du_lattice_678 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_RawLattice_12 -> T_RawMagma_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_RawLattice_12 -> T_RawMagma_44
MAlonzo.Code.Algebra.Lattice.Bundles.Raw.du_'8744''45'rawMagma_34
            ((T_Lattice_512 -> T_RawLattice_12) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_512 -> T_RawLattice_12
du_rawLattice_578 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))