{-# 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.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_Semilattice'46'constructor_193 (AgdaAny -> AgdaAny -> AgdaAny)
                                     MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
-- 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_Semilattice'46'constructor_193 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsCommutativeBand_590
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_590
d_isSemilattice_30 :: T_Semilattice_10 -> T_IsCommutativeBand_590
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_Semilattice'46'constructor_193 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsCommutativeBand_590
v4 -> T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v4
      T_Semilattice_10
_ -> T_IsCommutativeBand_590
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_590
v1 = T_Semilattice_10 -> T_IsCommutativeBand_590
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_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_482
         ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
            ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
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_590 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_600
      ((T_Semilattice_10 -> T_IsCommutativeBand_590) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10 -> T_IsCommutativeBand_590
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_590
v1 = T_Semilattice_10 -> T_IsCommutativeBand_590
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_508 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_508 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_518
         ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1)))
-- Algebra.Lattice.Bundles.Semilattice._.isBand
d_isBand_40 ::
  T_Semilattice_10 -> MAlonzo.Code.Algebra.Structures.T_IsBand_508
d_isBand_40 :: T_Semilattice_10 -> T_IsBand_508
d_isBand_40 T_Semilattice_10
v0
  = (T_IsCommutativeBand_590 -> T_IsBand_508)
-> AgdaAny -> T_IsBand_508
forall a b. a -> b
coe
      T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598
      ((T_Semilattice_10 -> T_IsCommutativeBand_590) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10 -> T_IsCommutativeBand_590
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_26
d_isEquivalence_42 :: () -> () -> T_Semilattice_10 -> T_IsEquivalence_26
d_isEquivalence_42 ~()
v0 ~()
v1 T_Semilattice_10
v2 = T_Semilattice_10 -> T_IsEquivalence_26
du_isEquivalence_42 T_Semilattice_10
v2
du_isEquivalence_42 ::
  T_Semilattice_10 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_42 :: T_Semilattice_10 -> T_IsEquivalence_26
du_isEquivalence_42 T_Semilattice_10
v0
  = let v1 :: T_IsCommutativeBand_590
v1 = T_Semilattice_10 -> T_IsCommutativeBand_590
d_isSemilattice_30 (T_Semilattice_10 -> T_Semilattice_10
forall a b. a -> b
coe T_Semilattice_10
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
               ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
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_176
d_isMagma_44 :: () -> () -> T_Semilattice_10 -> T_IsMagma_176
d_isMagma_44 ~()
v0 ~()
v1 T_Semilattice_10
v2 = T_Semilattice_10 -> T_IsMagma_176
du_isMagma_44 T_Semilattice_10
v2
du_isMagma_44 ::
  T_Semilattice_10 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
du_isMagma_44 :: T_Semilattice_10 -> T_IsMagma_176
du_isMagma_44 T_Semilattice_10
v0
  = let v1 :: T_IsCommutativeBand_590
v1 = T_Semilattice_10 -> T_IsCommutativeBand_590
d_isSemilattice_30 (T_Semilattice_10 -> T_Semilattice_10
forall a b. a -> b
coe T_Semilattice_10
v0) in
    AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
            ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
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_590
v1 = T_Semilattice_10 -> T_IsCommutativeBand_590
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_508
v2 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                  ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
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_472
d_isSemigroup_48 :: () -> () -> T_Semilattice_10 -> T_IsSemigroup_472
d_isSemigroup_48 ~()
v0 ~()
v1 T_Semilattice_10
v2 = T_Semilattice_10 -> T_IsSemigroup_472
du_isSemigroup_48 T_Semilattice_10
v2
du_isSemigroup_48 ::
  T_Semilattice_10 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
du_isSemigroup_48 :: T_Semilattice_10 -> T_IsSemigroup_472
du_isSemigroup_48 T_Semilattice_10
v0
  = let v1 :: T_IsCommutativeBand_590
v1 = T_Semilattice_10 -> T_IsCommutativeBand_590
d_isSemilattice_30 (T_Semilattice_10 -> T_Semilattice_10
forall a b. a -> b
coe T_Semilattice_10
v0) in
    AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
         ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
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_590
v1 = T_Semilattice_10 -> T_IsCommutativeBand_590
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_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
               ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                  ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
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_590
v1 = T_Semilattice_10 -> T_IsCommutativeBand_590
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_508
v2 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                    ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
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_44
d_setoid_54 :: () -> () -> T_Semilattice_10 -> T_Setoid_44
d_setoid_54 ~()
v0 ~()
v1 T_Semilattice_10
v2 = T_Semilattice_10 -> T_Setoid_44
du_setoid_54 T_Semilattice_10
v2
du_setoid_54 ::
  T_Semilattice_10 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_54 :: T_Semilattice_10 -> T_Setoid_44
du_setoid_54 T_Semilattice_10
v0
  = let v1 :: T_IsCommutativeBand_590
v1 = T_Semilattice_10 -> T_IsCommutativeBand_590
d_isSemilattice_30 (T_Semilattice_10 -> T_Semilattice_10
forall a b. a -> b
coe T_Semilattice_10
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsBand_508
v2 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
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_590
v1 = T_Semilattice_10 -> T_IsCommutativeBand_590
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_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
         ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
               ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                  ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
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_590
v1 = T_Semilattice_10 -> T_IsCommutativeBand_590
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_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
         ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
               ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                  ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
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_590
v1 = T_Semilattice_10 -> T_IsCommutativeBand_590
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_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
               ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
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_590
v1 = T_Semilattice_10 -> T_IsCommutativeBand_590
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_508
v2 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- 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_590
v1 = T_Semilattice_10 -> T_IsCommutativeBand_590
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_508
v2 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- 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_596
d_band_66 :: () -> () -> T_Semilattice_10 -> T_Band_596
d_band_66 ~()
v0 ~()
v1 T_Semilattice_10
v2 = T_Semilattice_10 -> T_Band_596
du_band_66 T_Semilattice_10
v2
du_band_66 ::
  T_Semilattice_10 -> MAlonzo.Code.Algebra.Bundles.T_Band_596
du_band_66 :: T_Semilattice_10 -> T_Band_596
du_band_66 T_Semilattice_10
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_IsBand_508 -> T_Band_596)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsBand_508 -> T_Band_596
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsBand_508 -> T_Band_596
MAlonzo.Code.Algebra.Bundles.C_Band'46'constructor_10881
      (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_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598
         ((T_Semilattice_10 -> T_IsCommutativeBand_590)
-> AgdaAny -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_Semilattice_10 -> T_IsCommutativeBand_590
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_508
d_isBand_72 :: () -> () -> T_Semilattice_10 -> T_IsBand_508
d_isBand_72 ~()
v0 ~()
v1 T_Semilattice_10
v2 = T_Semilattice_10 -> T_IsBand_508
du_isBand_72 T_Semilattice_10
v2
du_isBand_72 ::
  T_Semilattice_10 -> MAlonzo.Code.Algebra.Structures.T_IsBand_508
du_isBand_72 :: T_Semilattice_10 -> T_IsBand_508
du_isBand_72 T_Semilattice_10
v0
  = (T_IsCommutativeBand_590 -> T_IsBand_508)
-> AgdaAny -> T_IsBand_508
forall a b. a -> b
coe
      T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598
      ((T_Semilattice_10 -> T_IsCommutativeBand_590) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10 -> T_IsCommutativeBand_590
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_176
d_isMagma_74 :: () -> () -> T_Semilattice_10 -> T_IsMagma_176
d_isMagma_74 ~()
v0 ~()
v1 T_Semilattice_10
v2 = T_Semilattice_10 -> T_IsMagma_176
du_isMagma_74 T_Semilattice_10
v2
du_isMagma_74 ::
  T_Semilattice_10 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
du_isMagma_74 :: T_Semilattice_10 -> T_IsMagma_176
du_isMagma_74 T_Semilattice_10
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
      ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
         ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598
            ((T_Semilattice_10 -> T_IsCommutativeBand_590) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10 -> T_IsCommutativeBand_590
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_472
d_isSemigroup_76 :: () -> () -> T_Semilattice_10 -> T_IsSemigroup_472
d_isSemigroup_76 ~()
v0 ~()
v1 T_Semilattice_10
v2 = T_Semilattice_10 -> T_IsSemigroup_472
du_isSemigroup_76 T_Semilattice_10
v2
du_isSemigroup_76 ::
  T_Semilattice_10 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
du_isSemigroup_76 :: T_Semilattice_10 -> T_IsSemigroup_472
du_isSemigroup_76 T_Semilattice_10
v0
  = (T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
      ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598
         ((T_Semilattice_10 -> T_IsCommutativeBand_590) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10 -> T_IsCommutativeBand_590
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_68
d_magma_78 :: () -> () -> T_Semilattice_10 -> T_Magma_68
d_magma_78 ~()
v0 ~()
v1 T_Semilattice_10
v2 = T_Semilattice_10 -> T_Magma_68
du_magma_78 T_Semilattice_10
v2
du_magma_78 ::
  T_Semilattice_10 -> MAlonzo.Code.Algebra.Bundles.T_Magma_68
du_magma_78 :: T_Semilattice_10 -> T_Magma_68
du_magma_78 T_Semilattice_10
v0
  = let v1 :: t
v1 = (T_Semilattice_10 -> T_Band_596) -> AgdaAny -> t
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_596
du_band_66 (T_Semilattice_10 -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10
v0) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe
      ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Semigroup_536 -> T_Magma_68
MAlonzo.Code.Algebra.Bundles.du_magma_584
         ((T_Band_596 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_596 -> T_Semigroup_536
MAlonzo.Code.Algebra.Bundles.du_semigroup_648 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
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_36
d_rawMagma_80 :: () -> () -> T_Semilattice_10 -> T_RawMagma_36
d_rawMagma_80 ~()
v0 ~()
v1 T_Semilattice_10
v2 = T_Semilattice_10 -> T_RawMagma_36
du_rawMagma_80 T_Semilattice_10
v2
du_rawMagma_80 ::
  T_Semilattice_10 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_80 :: T_Semilattice_10 -> T_RawMagma_36
du_rawMagma_80 T_Semilattice_10
v0
  = let v1 :: t
v1 = (T_Semilattice_10 -> T_Band_596) -> AgdaAny -> t
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_596
du_band_66 (T_Semilattice_10 -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_Band_596 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_Band_596 -> T_Semigroup_536
MAlonzo.Code.Algebra.Bundles.du_semigroup_648 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Magma_68 -> T_RawMagma_36
MAlonzo.Code.Algebra.Bundles.du_rawMagma_112
            ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
MAlonzo.Code.Algebra.Bundles.du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
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_536
d_semigroup_82 :: () -> () -> T_Semilattice_10 -> T_Semigroup_536
d_semigroup_82 ~()
v0 ~()
v1 T_Semilattice_10
v2 = T_Semilattice_10 -> T_Semigroup_536
du_semigroup_82 T_Semilattice_10
v2
du_semigroup_82 ::
  T_Semilattice_10 -> MAlonzo.Code.Algebra.Bundles.T_Semigroup_536
du_semigroup_82 :: T_Semilattice_10 -> T_Semigroup_536
du_semigroup_82 T_Semilattice_10
v0
  = (T_Band_596 -> T_Semigroup_536) -> AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe
      T_Band_596 -> T_Semigroup_536
MAlonzo.Code.Algebra.Bundles.du_semigroup_648
      ((T_Semilattice_10 -> T_Band_596) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_596
du_band_66 (T_Semilattice_10 -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10
v0))
-- Algebra.Lattice.Bundles.MeetSemilattice
d_MeetSemilattice_88 :: p -> p -> ()
d_MeetSemilattice_88 p
a0 p
a1 = ()
data T_MeetSemilattice_88
  = C_MeetSemilattice'46'constructor_1393 (AgdaAny ->
                                           AgdaAny -> AgdaAny)
                                          MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
-- Algebra.Lattice.Bundles.MeetSemilattice.Carrier
d_Carrier_102 :: T_MeetSemilattice_88 -> ()
d_Carrier_102 :: T_MeetSemilattice_88 -> ()
d_Carrier_102 = T_MeetSemilattice_88 -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.MeetSemilattice._≈_
d__'8776'__104 :: T_MeetSemilattice_88 -> AgdaAny -> AgdaAny -> ()
d__'8776'__104 :: T_MeetSemilattice_88 -> AgdaAny -> AgdaAny -> ()
d__'8776'__104 = T_MeetSemilattice_88 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.MeetSemilattice._∧_
d__'8743'__106 ::
  T_MeetSemilattice_88 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__106 :: T_MeetSemilattice_88 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__106 T_MeetSemilattice_88
v0
  = case T_MeetSemilattice_88 -> T_MeetSemilattice_88
forall a b. a -> b
coe T_MeetSemilattice_88
v0 of
      C_MeetSemilattice'46'constructor_1393 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsCommutativeBand_590
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_MeetSemilattice_88
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.MeetSemilattice.isMeetSemilattice
d_isMeetSemilattice_108 ::
  T_MeetSemilattice_88 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
d_isMeetSemilattice_108 :: T_MeetSemilattice_88 -> T_IsCommutativeBand_590
d_isMeetSemilattice_108 T_MeetSemilattice_88
v0
  = case T_MeetSemilattice_88 -> T_MeetSemilattice_88
forall a b. a -> b
coe T_MeetSemilattice_88
v0 of
      C_MeetSemilattice'46'constructor_1393 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsCommutativeBand_590
v4 -> T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v4
      T_MeetSemilattice_88
_ -> T_IsCommutativeBand_590
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.MeetSemilattice._.assoc
d_assoc_112 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_88 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_112 :: ()
-> ()
-> T_MeetSemilattice_88
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_assoc_112 ~()
v0 ~()
v1 T_MeetSemilattice_88
v2 = T_MeetSemilattice_88 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_112 T_MeetSemilattice_88
v2
du_assoc_112 ::
  T_MeetSemilattice_88 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_112 :: T_MeetSemilattice_88 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_112 T_MeetSemilattice_88
v0
  = let v1 :: T_IsCommutativeBand_590
v1 = T_MeetSemilattice_88 -> T_IsCommutativeBand_590
d_isMeetSemilattice_108 (T_MeetSemilattice_88 -> T_MeetSemilattice_88
forall a b. a -> b
coe T_MeetSemilattice_88
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_482
         ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
            ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1))))
-- Algebra.Lattice.Bundles.MeetSemilattice._.comm
d_comm_114 :: T_MeetSemilattice_88 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_114 :: T_MeetSemilattice_88 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_114 T_MeetSemilattice_88
v0
  = (T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_600
      ((T_MeetSemilattice_88 -> T_IsCommutativeBand_590)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_88 -> T_IsCommutativeBand_590
d_isMeetSemilattice_108 (T_MeetSemilattice_88 -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_88
v0))
-- Algebra.Lattice.Bundles.MeetSemilattice._.idem
d_idem_116 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_88 -> AgdaAny -> AgdaAny
d_idem_116 :: () -> () -> T_MeetSemilattice_88 -> AgdaAny -> AgdaAny
d_idem_116 ~()
v0 ~()
v1 T_MeetSemilattice_88
v2 = T_MeetSemilattice_88 -> AgdaAny -> AgdaAny
du_idem_116 T_MeetSemilattice_88
v2
du_idem_116 :: T_MeetSemilattice_88 -> AgdaAny -> AgdaAny
du_idem_116 :: T_MeetSemilattice_88 -> AgdaAny -> AgdaAny
du_idem_116 T_MeetSemilattice_88
v0
  = let v1 :: T_IsCommutativeBand_590
v1 = T_MeetSemilattice_88 -> T_IsCommutativeBand_590
d_isMeetSemilattice_108 (T_MeetSemilattice_88 -> T_MeetSemilattice_88
forall a b. a -> b
coe T_MeetSemilattice_88
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsBand_508 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_508 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_518
         ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1)))
-- Algebra.Lattice.Bundles.MeetSemilattice._.isBand
d_isBand_118 ::
  T_MeetSemilattice_88 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_508
d_isBand_118 :: T_MeetSemilattice_88 -> T_IsBand_508
d_isBand_118 T_MeetSemilattice_88
v0
  = (T_IsCommutativeBand_590 -> T_IsBand_508)
-> AgdaAny -> T_IsBand_508
forall a b. a -> b
coe
      T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598
      ((T_MeetSemilattice_88 -> T_IsCommutativeBand_590)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_88 -> T_IsCommutativeBand_590
d_isMeetSemilattice_108 (T_MeetSemilattice_88 -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_88
v0))
-- Algebra.Lattice.Bundles.MeetSemilattice._.isEquivalence
d_isEquivalence_120 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_88 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_120 :: () -> () -> T_MeetSemilattice_88 -> T_IsEquivalence_26
d_isEquivalence_120 ~()
v0 ~()
v1 T_MeetSemilattice_88
v2 = T_MeetSemilattice_88 -> T_IsEquivalence_26
du_isEquivalence_120 T_MeetSemilattice_88
v2
du_isEquivalence_120 ::
  T_MeetSemilattice_88 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_120 :: T_MeetSemilattice_88 -> T_IsEquivalence_26
du_isEquivalence_120 T_MeetSemilattice_88
v0
  = let v1 :: T_IsCommutativeBand_590
v1 = T_MeetSemilattice_88 -> T_IsCommutativeBand_590
d_isMeetSemilattice_108 (T_MeetSemilattice_88 -> T_MeetSemilattice_88
forall a b. a -> b
coe T_MeetSemilattice_88
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
               ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1)))))
-- Algebra.Lattice.Bundles.MeetSemilattice._.isMagma
d_isMagma_122 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_88 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_122 :: () -> () -> T_MeetSemilattice_88 -> T_IsMagma_176
d_isMagma_122 ~()
v0 ~()
v1 T_MeetSemilattice_88
v2 = T_MeetSemilattice_88 -> T_IsMagma_176
du_isMagma_122 T_MeetSemilattice_88
v2
du_isMagma_122 ::
  T_MeetSemilattice_88 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
du_isMagma_122 :: T_MeetSemilattice_88 -> T_IsMagma_176
du_isMagma_122 T_MeetSemilattice_88
v0
  = let v1 :: T_IsCommutativeBand_590
v1 = T_MeetSemilattice_88 -> T_IsCommutativeBand_590
d_isMeetSemilattice_108 (T_MeetSemilattice_88 -> T_MeetSemilattice_88
forall a b. a -> b
coe T_MeetSemilattice_88
v0) in
    AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
            ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1))))
-- Algebra.Lattice.Bundles.MeetSemilattice._.isPartialEquivalence
d_isPartialEquivalence_124 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_88 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_124 :: () -> () -> T_MeetSemilattice_88 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_124 ~()
v0 ~()
v1 T_MeetSemilattice_88
v2
  = T_MeetSemilattice_88 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_124 T_MeetSemilattice_88
v2
du_isPartialEquivalence_124 ::
  T_MeetSemilattice_88 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_124 :: T_MeetSemilattice_88 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_124 T_MeetSemilattice_88
v0
  = let v1 :: T_IsCommutativeBand_590
v1 = T_MeetSemilattice_88 -> T_IsCommutativeBand_590
d_isMeetSemilattice_108 (T_MeetSemilattice_88 -> T_MeetSemilattice_88
forall a b. a -> b
coe T_MeetSemilattice_88
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsBand_508
v2 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                  ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4))))))
-- Algebra.Lattice.Bundles.MeetSemilattice._.isSemigroup
d_isSemigroup_126 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_88 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_126 :: () -> () -> T_MeetSemilattice_88 -> T_IsSemigroup_472
d_isSemigroup_126 ~()
v0 ~()
v1 T_MeetSemilattice_88
v2 = T_MeetSemilattice_88 -> T_IsSemigroup_472
du_isSemigroup_126 T_MeetSemilattice_88
v2
du_isSemigroup_126 ::
  T_MeetSemilattice_88 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
du_isSemigroup_126 :: T_MeetSemilattice_88 -> T_IsSemigroup_472
du_isSemigroup_126 T_MeetSemilattice_88
v0
  = let v1 :: T_IsCommutativeBand_590
v1 = T_MeetSemilattice_88 -> T_IsCommutativeBand_590
d_isMeetSemilattice_108 (T_MeetSemilattice_88 -> T_MeetSemilattice_88
forall a b. a -> b
coe T_MeetSemilattice_88
v0) in
    AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
         ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1)))
-- Algebra.Lattice.Bundles.MeetSemilattice._.refl
d_refl_128 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_88 -> AgdaAny -> AgdaAny
d_refl_128 :: () -> () -> T_MeetSemilattice_88 -> AgdaAny -> AgdaAny
d_refl_128 ~()
v0 ~()
v1 T_MeetSemilattice_88
v2 = T_MeetSemilattice_88 -> AgdaAny -> AgdaAny
du_refl_128 T_MeetSemilattice_88
v2
du_refl_128 :: T_MeetSemilattice_88 -> AgdaAny -> AgdaAny
du_refl_128 :: T_MeetSemilattice_88 -> AgdaAny -> AgdaAny
du_refl_128 T_MeetSemilattice_88
v0
  = let v1 :: T_IsCommutativeBand_590
v1 = T_MeetSemilattice_88 -> T_IsCommutativeBand_590
d_isMeetSemilattice_108 (T_MeetSemilattice_88 -> T_MeetSemilattice_88
forall a b. a -> b
coe T_MeetSemilattice_88
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
               ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                  ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1))))))
-- Algebra.Lattice.Bundles.MeetSemilattice._.reflexive
d_reflexive_130 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_88 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_130 :: ()
-> ()
-> T_MeetSemilattice_88
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_130 ~()
v0 ~()
v1 T_MeetSemilattice_88
v2 = T_MeetSemilattice_88
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_130 T_MeetSemilattice_88
v2
du_reflexive_130 ::
  T_MeetSemilattice_88 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_130 :: T_MeetSemilattice_88
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_130 T_MeetSemilattice_88
v0
  = let v1 :: T_IsCommutativeBand_590
v1 = T_MeetSemilattice_88 -> T_IsCommutativeBand_590
d_isMeetSemilattice_108 (T_MeetSemilattice_88 -> T_MeetSemilattice_88
forall a b. a -> b
coe T_MeetSemilattice_88
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBand_508
v2 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                    ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4))
                    AgdaAny
v5))))
-- Algebra.Lattice.Bundles.MeetSemilattice._.setoid
d_setoid_132 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_88 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_132 :: () -> () -> T_MeetSemilattice_88 -> T_Setoid_44
d_setoid_132 ~()
v0 ~()
v1 T_MeetSemilattice_88
v2 = T_MeetSemilattice_88 -> T_Setoid_44
du_setoid_132 T_MeetSemilattice_88
v2
du_setoid_132 ::
  T_MeetSemilattice_88 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_132 :: T_MeetSemilattice_88 -> T_Setoid_44
du_setoid_132 T_MeetSemilattice_88
v0
  = let v1 :: T_IsCommutativeBand_590
v1 = T_MeetSemilattice_88 -> T_IsCommutativeBand_590
d_isMeetSemilattice_108 (T_MeetSemilattice_88 -> T_MeetSemilattice_88
forall a b. a -> b
coe T_MeetSemilattice_88
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsBand_508
v2 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Lattice.Bundles.MeetSemilattice._.sym
d_sym_134 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_88 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_134 :: ()
-> ()
-> T_MeetSemilattice_88
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_134 ~()
v0 ~()
v1 T_MeetSemilattice_88
v2 = T_MeetSemilattice_88 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_134 T_MeetSemilattice_88
v2
du_sym_134 ::
  T_MeetSemilattice_88 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_134 :: T_MeetSemilattice_88 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_134 T_MeetSemilattice_88
v0
  = let v1 :: T_IsCommutativeBand_590
v1 = T_MeetSemilattice_88 -> T_IsCommutativeBand_590
d_isMeetSemilattice_108 (T_MeetSemilattice_88 -> T_MeetSemilattice_88
forall a b. a -> b
coe T_MeetSemilattice_88
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
         ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
               ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                  ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1))))))
-- Algebra.Lattice.Bundles.MeetSemilattice._.trans
d_trans_136 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_88 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_136 :: ()
-> ()
-> T_MeetSemilattice_88
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_136 ~()
v0 ~()
v1 T_MeetSemilattice_88
v2 = T_MeetSemilattice_88
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_136 T_MeetSemilattice_88
v2
du_trans_136 ::
  T_MeetSemilattice_88 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_136 :: T_MeetSemilattice_88
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_136 T_MeetSemilattice_88
v0
  = let v1 :: T_IsCommutativeBand_590
v1 = T_MeetSemilattice_88 -> T_IsCommutativeBand_590
d_isMeetSemilattice_108 (T_MeetSemilattice_88 -> T_MeetSemilattice_88
forall a b. a -> b
coe T_MeetSemilattice_88
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
         ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
               ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                  ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1))))))
-- Algebra.Lattice.Bundles.MeetSemilattice._.∙-cong
d_'8729''45'cong_138 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_88 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_138 :: ()
-> ()
-> T_MeetSemilattice_88
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_138 ~()
v0 ~()
v1 T_MeetSemilattice_88
v2 = T_MeetSemilattice_88
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_138 T_MeetSemilattice_88
v2
du_'8729''45'cong_138 ::
  T_MeetSemilattice_88 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong_138 :: T_MeetSemilattice_88
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_138 T_MeetSemilattice_88
v0
  = let v1 :: T_IsCommutativeBand_590
v1 = T_MeetSemilattice_88 -> T_IsCommutativeBand_590
d_isMeetSemilattice_108 (T_MeetSemilattice_88 -> T_MeetSemilattice_88
forall a b. a -> b
coe T_MeetSemilattice_88
v0) in
    AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
               ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1)))))
-- Algebra.Lattice.Bundles.MeetSemilattice._.∙-congʳ
d_'8729''45'cong'691'_140 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_88 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_140 :: ()
-> ()
-> T_MeetSemilattice_88
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_140 ~()
v0 ~()
v1 T_MeetSemilattice_88
v2
  = T_MeetSemilattice_88
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_140 T_MeetSemilattice_88
v2
du_'8729''45'cong'691'_140 ::
  T_MeetSemilattice_88 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_140 :: T_MeetSemilattice_88
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_140 T_MeetSemilattice_88
v0
  = let v1 :: T_IsCommutativeBand_590
v1 = T_MeetSemilattice_88 -> T_IsCommutativeBand_590
d_isMeetSemilattice_108 (T_MeetSemilattice_88 -> T_MeetSemilattice_88
forall a b. a -> b
coe T_MeetSemilattice_88
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBand_508
v2 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Lattice.Bundles.MeetSemilattice._.∙-congˡ
d_'8729''45'cong'737'_142 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_88 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_142 :: ()
-> ()
-> T_MeetSemilattice_88
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_142 ~()
v0 ~()
v1 T_MeetSemilattice_88
v2
  = T_MeetSemilattice_88
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_142 T_MeetSemilattice_88
v2
du_'8729''45'cong'737'_142 ::
  T_MeetSemilattice_88 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_142 :: T_MeetSemilattice_88
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_142 T_MeetSemilattice_88
v0
  = let v1 :: T_IsCommutativeBand_590
v1 = T_MeetSemilattice_88 -> T_IsCommutativeBand_590
d_isMeetSemilattice_108 (T_MeetSemilattice_88 -> T_MeetSemilattice_88
forall a b. a -> b
coe T_MeetSemilattice_88
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBand_508
v2 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Lattice.Bundles.MeetSemilattice.semilattice
d_semilattice_144 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_88 -> T_Semilattice_10
d_semilattice_144 :: () -> () -> T_MeetSemilattice_88 -> T_Semilattice_10
d_semilattice_144 ~()
v0 ~()
v1 T_MeetSemilattice_88
v2 = T_MeetSemilattice_88 -> T_Semilattice_10
du_semilattice_144 T_MeetSemilattice_88
v2
du_semilattice_144 :: T_MeetSemilattice_88 -> T_Semilattice_10
du_semilattice_144 :: T_MeetSemilattice_88 -> T_Semilattice_10
du_semilattice_144 T_MeetSemilattice_88
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsCommutativeBand_590 -> T_Semilattice_10)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> T_Semilattice_10
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590 -> T_Semilattice_10
C_Semilattice'46'constructor_193 (T_MeetSemilattice_88 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__106 (T_MeetSemilattice_88 -> T_MeetSemilattice_88
forall a b. a -> b
coe T_MeetSemilattice_88
v0))
      (T_MeetSemilattice_88 -> T_IsCommutativeBand_590
d_isMeetSemilattice_108 (T_MeetSemilattice_88 -> T_MeetSemilattice_88
forall a b. a -> b
coe T_MeetSemilattice_88
v0))
-- Algebra.Lattice.Bundles.MeetSemilattice._.band
d_band_148 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_88 -> MAlonzo.Code.Algebra.Bundles.T_Band_596
d_band_148 :: () -> () -> T_MeetSemilattice_88 -> T_Band_596
d_band_148 ~()
v0 ~()
v1 T_MeetSemilattice_88
v2 = T_MeetSemilattice_88 -> T_Band_596
du_band_148 T_MeetSemilattice_88
v2
du_band_148 ::
  T_MeetSemilattice_88 -> MAlonzo.Code.Algebra.Bundles.T_Band_596
du_band_148 :: T_MeetSemilattice_88 -> T_Band_596
du_band_148 T_MeetSemilattice_88
v0 = (T_Semilattice_10 -> T_Band_596) -> AgdaAny -> T_Band_596
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_596
du_band_66 ((T_MeetSemilattice_88 -> T_Semilattice_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_88 -> T_Semilattice_10
du_semilattice_144 (T_MeetSemilattice_88 -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_88
v0))
-- Algebra.Lattice.Bundles.MeetSemilattice._.magma
d_magma_150 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_88 -> MAlonzo.Code.Algebra.Bundles.T_Magma_68
d_magma_150 :: () -> () -> T_MeetSemilattice_88 -> T_Magma_68
d_magma_150 ~()
v0 ~()
v1 T_MeetSemilattice_88
v2 = T_MeetSemilattice_88 -> T_Magma_68
du_magma_150 T_MeetSemilattice_88
v2
du_magma_150 ::
  T_MeetSemilattice_88 -> MAlonzo.Code.Algebra.Bundles.T_Magma_68
du_magma_150 :: T_MeetSemilattice_88 -> T_Magma_68
du_magma_150 T_MeetSemilattice_88
v0
  = let v1 :: t
v1 = (T_MeetSemilattice_88 -> T_Semilattice_10) -> AgdaAny -> t
forall a b. a -> b
coe T_MeetSemilattice_88 -> T_Semilattice_10
du_semilattice_144 (T_MeetSemilattice_88 -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_88
v0) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semilattice_10 -> T_Band_596) -> AgdaAny -> t
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_596
du_band_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Semigroup_536 -> T_Magma_68
MAlonzo.Code.Algebra.Bundles.du_magma_584
            ((T_Band_596 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_596 -> T_Semigroup_536
MAlonzo.Code.Algebra.Bundles.du_semigroup_648 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Lattice.Bundles.MeetSemilattice._.rawMagma
d_rawMagma_152 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_88 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_152 :: () -> () -> T_MeetSemilattice_88 -> T_RawMagma_36
d_rawMagma_152 ~()
v0 ~()
v1 T_MeetSemilattice_88
v2 = T_MeetSemilattice_88 -> T_RawMagma_36
du_rawMagma_152 T_MeetSemilattice_88
v2
du_rawMagma_152 ::
  T_MeetSemilattice_88 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_152 :: T_MeetSemilattice_88 -> T_RawMagma_36
du_rawMagma_152 T_MeetSemilattice_88
v0
  = let v1 :: t
v1 = (T_MeetSemilattice_88 -> T_Semilattice_10) -> AgdaAny -> t
forall a b. a -> b
coe T_MeetSemilattice_88 -> T_Semilattice_10
du_semilattice_144 (T_MeetSemilattice_88 -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_88
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semilattice_10 -> T_Band_596) -> AgdaAny -> t
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_596
du_band_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_Band_596 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_Band_596 -> T_Semigroup_536
MAlonzo.Code.Algebra.Bundles.du_semigroup_648 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Magma_68 -> T_RawMagma_36
MAlonzo.Code.Algebra.Bundles.du_rawMagma_112
               ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
MAlonzo.Code.Algebra.Bundles.du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Lattice.Bundles.MeetSemilattice._.semigroup
d_semigroup_154 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_88 ->
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_536
d_semigroup_154 :: () -> () -> T_MeetSemilattice_88 -> T_Semigroup_536
d_semigroup_154 ~()
v0 ~()
v1 T_MeetSemilattice_88
v2 = T_MeetSemilattice_88 -> T_Semigroup_536
du_semigroup_154 T_MeetSemilattice_88
v2
du_semigroup_154 ::
  T_MeetSemilattice_88 ->
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_536
du_semigroup_154 :: T_MeetSemilattice_88 -> T_Semigroup_536
du_semigroup_154 T_MeetSemilattice_88
v0
  = let v1 :: t
v1 = (T_MeetSemilattice_88 -> T_Semilattice_10) -> AgdaAny -> t
forall a b. a -> b
coe T_MeetSemilattice_88 -> T_Semilattice_10
du_semilattice_144 (T_MeetSemilattice_88 -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_88
v0) in
    AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe
      ((T_Band_596 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Band_596 -> T_Semigroup_536
MAlonzo.Code.Algebra.Bundles.du_semigroup_648
         ((T_Semilattice_10 -> T_Band_596) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_596
du_band_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Lattice.Bundles.JoinSemilattice
d_JoinSemilattice_160 :: p -> p -> ()
d_JoinSemilattice_160 p
a0 p
a1 = ()
data T_JoinSemilattice_160
  = C_JoinSemilattice'46'constructor_2531 (AgdaAny ->
                                           AgdaAny -> AgdaAny)
                                          MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
-- Algebra.Lattice.Bundles.JoinSemilattice.Carrier
d_Carrier_174 :: T_JoinSemilattice_160 -> ()
d_Carrier_174 :: T_JoinSemilattice_160 -> ()
d_Carrier_174 = T_JoinSemilattice_160 -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.JoinSemilattice._≈_
d__'8776'__176 :: T_JoinSemilattice_160 -> AgdaAny -> AgdaAny -> ()
d__'8776'__176 :: T_JoinSemilattice_160 -> AgdaAny -> AgdaAny -> ()
d__'8776'__176 = T_JoinSemilattice_160 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.JoinSemilattice._∨_
d__'8744'__178 ::
  T_JoinSemilattice_160 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__178 :: T_JoinSemilattice_160 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__178 T_JoinSemilattice_160
v0
  = case T_JoinSemilattice_160 -> T_JoinSemilattice_160
forall a b. a -> b
coe T_JoinSemilattice_160
v0 of
      C_JoinSemilattice'46'constructor_2531 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsCommutativeBand_590
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_JoinSemilattice_160
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.JoinSemilattice.isJoinSemilattice
d_isJoinSemilattice_180 ::
  T_JoinSemilattice_160 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
d_isJoinSemilattice_180 :: T_JoinSemilattice_160 -> T_IsCommutativeBand_590
d_isJoinSemilattice_180 T_JoinSemilattice_160
v0
  = case T_JoinSemilattice_160 -> T_JoinSemilattice_160
forall a b. a -> b
coe T_JoinSemilattice_160
v0 of
      C_JoinSemilattice'46'constructor_2531 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsCommutativeBand_590
v4 -> T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v4
      T_JoinSemilattice_160
_ -> T_IsCommutativeBand_590
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.JoinSemilattice._.assoc
d_assoc_184 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_160 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_184 :: ()
-> ()
-> T_JoinSemilattice_160
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_assoc_184 ~()
v0 ~()
v1 T_JoinSemilattice_160
v2 = T_JoinSemilattice_160 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_184 T_JoinSemilattice_160
v2
du_assoc_184 ::
  T_JoinSemilattice_160 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_184 :: T_JoinSemilattice_160 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_184 T_JoinSemilattice_160
v0
  = let v1 :: T_IsCommutativeBand_590
v1 = T_JoinSemilattice_160 -> T_IsCommutativeBand_590
d_isJoinSemilattice_180 (T_JoinSemilattice_160 -> T_JoinSemilattice_160
forall a b. a -> b
coe T_JoinSemilattice_160
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_482
         ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
            ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1))))
-- Algebra.Lattice.Bundles.JoinSemilattice._.comm
d_comm_186 ::
  T_JoinSemilattice_160 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_186 :: T_JoinSemilattice_160 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_186 T_JoinSemilattice_160
v0
  = (T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_600
      ((T_JoinSemilattice_160 -> T_IsCommutativeBand_590)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_160 -> T_IsCommutativeBand_590
d_isJoinSemilattice_180 (T_JoinSemilattice_160 -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_160
v0))
-- Algebra.Lattice.Bundles.JoinSemilattice._.idem
d_idem_188 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_160 -> AgdaAny -> AgdaAny
d_idem_188 :: () -> () -> T_JoinSemilattice_160 -> AgdaAny -> AgdaAny
d_idem_188 ~()
v0 ~()
v1 T_JoinSemilattice_160
v2 = T_JoinSemilattice_160 -> AgdaAny -> AgdaAny
du_idem_188 T_JoinSemilattice_160
v2
du_idem_188 :: T_JoinSemilattice_160 -> AgdaAny -> AgdaAny
du_idem_188 :: T_JoinSemilattice_160 -> AgdaAny -> AgdaAny
du_idem_188 T_JoinSemilattice_160
v0
  = let v1 :: T_IsCommutativeBand_590
v1 = T_JoinSemilattice_160 -> T_IsCommutativeBand_590
d_isJoinSemilattice_180 (T_JoinSemilattice_160 -> T_JoinSemilattice_160
forall a b. a -> b
coe T_JoinSemilattice_160
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsBand_508 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_508 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_518
         ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1)))
-- Algebra.Lattice.Bundles.JoinSemilattice._.isBand
d_isBand_190 ::
  T_JoinSemilattice_160 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_508
d_isBand_190 :: T_JoinSemilattice_160 -> T_IsBand_508
d_isBand_190 T_JoinSemilattice_160
v0
  = (T_IsCommutativeBand_590 -> T_IsBand_508)
-> AgdaAny -> T_IsBand_508
forall a b. a -> b
coe
      T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598
      ((T_JoinSemilattice_160 -> T_IsCommutativeBand_590)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_160 -> T_IsCommutativeBand_590
d_isJoinSemilattice_180 (T_JoinSemilattice_160 -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_160
v0))
-- Algebra.Lattice.Bundles.JoinSemilattice._.isEquivalence
d_isEquivalence_192 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_160 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_192 :: () -> () -> T_JoinSemilattice_160 -> T_IsEquivalence_26
d_isEquivalence_192 ~()
v0 ~()
v1 T_JoinSemilattice_160
v2 = T_JoinSemilattice_160 -> T_IsEquivalence_26
du_isEquivalence_192 T_JoinSemilattice_160
v2
du_isEquivalence_192 ::
  T_JoinSemilattice_160 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_192 :: T_JoinSemilattice_160 -> T_IsEquivalence_26
du_isEquivalence_192 T_JoinSemilattice_160
v0
  = let v1 :: T_IsCommutativeBand_590
v1 = T_JoinSemilattice_160 -> T_IsCommutativeBand_590
d_isJoinSemilattice_180 (T_JoinSemilattice_160 -> T_JoinSemilattice_160
forall a b. a -> b
coe T_JoinSemilattice_160
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
               ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1)))))
-- Algebra.Lattice.Bundles.JoinSemilattice._.isMagma
d_isMagma_194 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_160 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_194 :: () -> () -> T_JoinSemilattice_160 -> T_IsMagma_176
d_isMagma_194 ~()
v0 ~()
v1 T_JoinSemilattice_160
v2 = T_JoinSemilattice_160 -> T_IsMagma_176
du_isMagma_194 T_JoinSemilattice_160
v2
du_isMagma_194 ::
  T_JoinSemilattice_160 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
du_isMagma_194 :: T_JoinSemilattice_160 -> T_IsMagma_176
du_isMagma_194 T_JoinSemilattice_160
v0
  = let v1 :: T_IsCommutativeBand_590
v1 = T_JoinSemilattice_160 -> T_IsCommutativeBand_590
d_isJoinSemilattice_180 (T_JoinSemilattice_160 -> T_JoinSemilattice_160
forall a b. a -> b
coe T_JoinSemilattice_160
v0) in
    AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
            ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1))))
-- Algebra.Lattice.Bundles.JoinSemilattice._.isPartialEquivalence
d_isPartialEquivalence_196 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_160 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_196 :: () -> () -> T_JoinSemilattice_160 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_196 ~()
v0 ~()
v1 T_JoinSemilattice_160
v2
  = T_JoinSemilattice_160 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_196 T_JoinSemilattice_160
v2
du_isPartialEquivalence_196 ::
  T_JoinSemilattice_160 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_196 :: T_JoinSemilattice_160 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_196 T_JoinSemilattice_160
v0
  = let v1 :: T_IsCommutativeBand_590
v1 = T_JoinSemilattice_160 -> T_IsCommutativeBand_590
d_isJoinSemilattice_180 (T_JoinSemilattice_160 -> T_JoinSemilattice_160
forall a b. a -> b
coe T_JoinSemilattice_160
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsBand_508
v2 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                  ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4))))))
-- Algebra.Lattice.Bundles.JoinSemilattice._.isSemigroup
d_isSemigroup_198 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_160 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_198 :: () -> () -> T_JoinSemilattice_160 -> T_IsSemigroup_472
d_isSemigroup_198 ~()
v0 ~()
v1 T_JoinSemilattice_160
v2 = T_JoinSemilattice_160 -> T_IsSemigroup_472
du_isSemigroup_198 T_JoinSemilattice_160
v2
du_isSemigroup_198 ::
  T_JoinSemilattice_160 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
du_isSemigroup_198 :: T_JoinSemilattice_160 -> T_IsSemigroup_472
du_isSemigroup_198 T_JoinSemilattice_160
v0
  = let v1 :: T_IsCommutativeBand_590
v1 = T_JoinSemilattice_160 -> T_IsCommutativeBand_590
d_isJoinSemilattice_180 (T_JoinSemilattice_160 -> T_JoinSemilattice_160
forall a b. a -> b
coe T_JoinSemilattice_160
v0) in
    AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
         ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1)))
-- Algebra.Lattice.Bundles.JoinSemilattice._.refl
d_refl_200 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_160 -> AgdaAny -> AgdaAny
d_refl_200 :: () -> () -> T_JoinSemilattice_160 -> AgdaAny -> AgdaAny
d_refl_200 ~()
v0 ~()
v1 T_JoinSemilattice_160
v2 = T_JoinSemilattice_160 -> AgdaAny -> AgdaAny
du_refl_200 T_JoinSemilattice_160
v2
du_refl_200 :: T_JoinSemilattice_160 -> AgdaAny -> AgdaAny
du_refl_200 :: T_JoinSemilattice_160 -> AgdaAny -> AgdaAny
du_refl_200 T_JoinSemilattice_160
v0
  = let v1 :: T_IsCommutativeBand_590
v1 = T_JoinSemilattice_160 -> T_IsCommutativeBand_590
d_isJoinSemilattice_180 (T_JoinSemilattice_160 -> T_JoinSemilattice_160
forall a b. a -> b
coe T_JoinSemilattice_160
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
               ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                  ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1))))))
-- Algebra.Lattice.Bundles.JoinSemilattice._.reflexive
d_reflexive_202 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_160 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_202 :: ()
-> ()
-> T_JoinSemilattice_160
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_202 ~()
v0 ~()
v1 T_JoinSemilattice_160
v2 = T_JoinSemilattice_160
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_202 T_JoinSemilattice_160
v2
du_reflexive_202 ::
  T_JoinSemilattice_160 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_202 :: T_JoinSemilattice_160
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_202 T_JoinSemilattice_160
v0
  = let v1 :: T_IsCommutativeBand_590
v1 = T_JoinSemilattice_160 -> T_IsCommutativeBand_590
d_isJoinSemilattice_180 (T_JoinSemilattice_160 -> T_JoinSemilattice_160
forall a b. a -> b
coe T_JoinSemilattice_160
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBand_508
v2 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                    ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4))
                    AgdaAny
v5))))
-- Algebra.Lattice.Bundles.JoinSemilattice._.setoid
d_setoid_204 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_160 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_204 :: () -> () -> T_JoinSemilattice_160 -> T_Setoid_44
d_setoid_204 ~()
v0 ~()
v1 T_JoinSemilattice_160
v2 = T_JoinSemilattice_160 -> T_Setoid_44
du_setoid_204 T_JoinSemilattice_160
v2
du_setoid_204 ::
  T_JoinSemilattice_160 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_204 :: T_JoinSemilattice_160 -> T_Setoid_44
du_setoid_204 T_JoinSemilattice_160
v0
  = let v1 :: T_IsCommutativeBand_590
v1 = T_JoinSemilattice_160 -> T_IsCommutativeBand_590
d_isJoinSemilattice_180 (T_JoinSemilattice_160 -> T_JoinSemilattice_160
forall a b. a -> b
coe T_JoinSemilattice_160
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsBand_508
v2 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Lattice.Bundles.JoinSemilattice._.sym
d_sym_206 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_160 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_206 :: ()
-> ()
-> T_JoinSemilattice_160
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_206 ~()
v0 ~()
v1 T_JoinSemilattice_160
v2 = T_JoinSemilattice_160 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_206 T_JoinSemilattice_160
v2
du_sym_206 ::
  T_JoinSemilattice_160 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_206 :: T_JoinSemilattice_160 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_206 T_JoinSemilattice_160
v0
  = let v1 :: T_IsCommutativeBand_590
v1 = T_JoinSemilattice_160 -> T_IsCommutativeBand_590
d_isJoinSemilattice_180 (T_JoinSemilattice_160 -> T_JoinSemilattice_160
forall a b. a -> b
coe T_JoinSemilattice_160
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
         ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
               ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                  ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1))))))
-- Algebra.Lattice.Bundles.JoinSemilattice._.trans
d_trans_208 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_160 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_208 :: ()
-> ()
-> T_JoinSemilattice_160
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_208 ~()
v0 ~()
v1 T_JoinSemilattice_160
v2 = T_JoinSemilattice_160
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_208 T_JoinSemilattice_160
v2
du_trans_208 ::
  T_JoinSemilattice_160 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_208 :: T_JoinSemilattice_160
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_208 T_JoinSemilattice_160
v0
  = let v1 :: T_IsCommutativeBand_590
v1 = T_JoinSemilattice_160 -> T_IsCommutativeBand_590
d_isJoinSemilattice_180 (T_JoinSemilattice_160 -> T_JoinSemilattice_160
forall a b. a -> b
coe T_JoinSemilattice_160
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
         ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
               ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                  ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1))))))
-- Algebra.Lattice.Bundles.JoinSemilattice._.∙-cong
d_'8729''45'cong_210 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_160 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_210 :: ()
-> ()
-> T_JoinSemilattice_160
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_210 ~()
v0 ~()
v1 T_JoinSemilattice_160
v2 = T_JoinSemilattice_160
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_210 T_JoinSemilattice_160
v2
du_'8729''45'cong_210 ::
  T_JoinSemilattice_160 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong_210 :: T_JoinSemilattice_160
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_210 T_JoinSemilattice_160
v0
  = let v1 :: T_IsCommutativeBand_590
v1 = T_JoinSemilattice_160 -> T_IsCommutativeBand_590
d_isJoinSemilattice_180 (T_JoinSemilattice_160 -> T_JoinSemilattice_160
forall a b. a -> b
coe T_JoinSemilattice_160
v0) in
    AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
               ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1)))))
-- Algebra.Lattice.Bundles.JoinSemilattice._.∙-congʳ
d_'8729''45'cong'691'_212 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_160 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_212 :: ()
-> ()
-> T_JoinSemilattice_160
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_212 ~()
v0 ~()
v1 T_JoinSemilattice_160
v2
  = T_JoinSemilattice_160
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_212 T_JoinSemilattice_160
v2
du_'8729''45'cong'691'_212 ::
  T_JoinSemilattice_160 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_212 :: T_JoinSemilattice_160
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_212 T_JoinSemilattice_160
v0
  = let v1 :: T_IsCommutativeBand_590
v1 = T_JoinSemilattice_160 -> T_IsCommutativeBand_590
d_isJoinSemilattice_180 (T_JoinSemilattice_160 -> T_JoinSemilattice_160
forall a b. a -> b
coe T_JoinSemilattice_160
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBand_508
v2 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Lattice.Bundles.JoinSemilattice._.∙-congˡ
d_'8729''45'cong'737'_214 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_160 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_214 :: ()
-> ()
-> T_JoinSemilattice_160
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_214 ~()
v0 ~()
v1 T_JoinSemilattice_160
v2
  = T_JoinSemilattice_160
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_214 T_JoinSemilattice_160
v2
du_'8729''45'cong'737'_214 ::
  T_JoinSemilattice_160 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_214 :: T_JoinSemilattice_160
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_214 T_JoinSemilattice_160
v0
  = let v1 :: T_IsCommutativeBand_590
v1 = T_JoinSemilattice_160 -> T_IsCommutativeBand_590
d_isJoinSemilattice_180 (T_JoinSemilattice_160 -> T_JoinSemilattice_160
forall a b. a -> b
coe T_JoinSemilattice_160
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBand_508
v2 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Lattice.Bundles.JoinSemilattice.semilattice
d_semilattice_216 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_160 -> T_Semilattice_10
d_semilattice_216 :: () -> () -> T_JoinSemilattice_160 -> T_Semilattice_10
d_semilattice_216 ~()
v0 ~()
v1 T_JoinSemilattice_160
v2 = T_JoinSemilattice_160 -> T_Semilattice_10
du_semilattice_216 T_JoinSemilattice_160
v2
du_semilattice_216 :: T_JoinSemilattice_160 -> T_Semilattice_10
du_semilattice_216 :: T_JoinSemilattice_160 -> T_Semilattice_10
du_semilattice_216 T_JoinSemilattice_160
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsCommutativeBand_590 -> T_Semilattice_10)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> T_Semilattice_10
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590 -> T_Semilattice_10
C_Semilattice'46'constructor_193 (T_JoinSemilattice_160 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__178 (T_JoinSemilattice_160 -> T_JoinSemilattice_160
forall a b. a -> b
coe T_JoinSemilattice_160
v0))
      (T_JoinSemilattice_160 -> T_IsCommutativeBand_590
d_isJoinSemilattice_180 (T_JoinSemilattice_160 -> T_JoinSemilattice_160
forall a b. a -> b
coe T_JoinSemilattice_160
v0))
-- Algebra.Lattice.Bundles.JoinSemilattice._.band
d_band_220 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_160 -> MAlonzo.Code.Algebra.Bundles.T_Band_596
d_band_220 :: () -> () -> T_JoinSemilattice_160 -> T_Band_596
d_band_220 ~()
v0 ~()
v1 T_JoinSemilattice_160
v2 = T_JoinSemilattice_160 -> T_Band_596
du_band_220 T_JoinSemilattice_160
v2
du_band_220 ::
  T_JoinSemilattice_160 -> MAlonzo.Code.Algebra.Bundles.T_Band_596
du_band_220 :: T_JoinSemilattice_160 -> T_Band_596
du_band_220 T_JoinSemilattice_160
v0 = (T_Semilattice_10 -> T_Band_596) -> AgdaAny -> T_Band_596
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_596
du_band_66 ((T_JoinSemilattice_160 -> T_Semilattice_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_160 -> T_Semilattice_10
du_semilattice_216 (T_JoinSemilattice_160 -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_160
v0))
-- Algebra.Lattice.Bundles.JoinSemilattice._.magma
d_magma_222 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_160 -> MAlonzo.Code.Algebra.Bundles.T_Magma_68
d_magma_222 :: () -> () -> T_JoinSemilattice_160 -> T_Magma_68
d_magma_222 ~()
v0 ~()
v1 T_JoinSemilattice_160
v2 = T_JoinSemilattice_160 -> T_Magma_68
du_magma_222 T_JoinSemilattice_160
v2
du_magma_222 ::
  T_JoinSemilattice_160 -> MAlonzo.Code.Algebra.Bundles.T_Magma_68
du_magma_222 :: T_JoinSemilattice_160 -> T_Magma_68
du_magma_222 T_JoinSemilattice_160
v0
  = let v1 :: t
v1 = (T_JoinSemilattice_160 -> T_Semilattice_10) -> AgdaAny -> t
forall a b. a -> b
coe T_JoinSemilattice_160 -> T_Semilattice_10
du_semilattice_216 (T_JoinSemilattice_160 -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_160
v0) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semilattice_10 -> T_Band_596) -> AgdaAny -> t
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_596
du_band_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Semigroup_536 -> T_Magma_68
MAlonzo.Code.Algebra.Bundles.du_magma_584
            ((T_Band_596 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_596 -> T_Semigroup_536
MAlonzo.Code.Algebra.Bundles.du_semigroup_648 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Lattice.Bundles.JoinSemilattice._.rawMagma
d_rawMagma_224 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_160 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_224 :: () -> () -> T_JoinSemilattice_160 -> T_RawMagma_36
d_rawMagma_224 ~()
v0 ~()
v1 T_JoinSemilattice_160
v2 = T_JoinSemilattice_160 -> T_RawMagma_36
du_rawMagma_224 T_JoinSemilattice_160
v2
du_rawMagma_224 ::
  T_JoinSemilattice_160 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_224 :: T_JoinSemilattice_160 -> T_RawMagma_36
du_rawMagma_224 T_JoinSemilattice_160
v0
  = let v1 :: t
v1 = (T_JoinSemilattice_160 -> T_Semilattice_10) -> AgdaAny -> t
forall a b. a -> b
coe T_JoinSemilattice_160 -> T_Semilattice_10
du_semilattice_216 (T_JoinSemilattice_160 -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_160
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semilattice_10 -> T_Band_596) -> AgdaAny -> t
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_596
du_band_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_Band_596 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_Band_596 -> T_Semigroup_536
MAlonzo.Code.Algebra.Bundles.du_semigroup_648 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Magma_68 -> T_RawMagma_36
MAlonzo.Code.Algebra.Bundles.du_rawMagma_112
               ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
MAlonzo.Code.Algebra.Bundles.du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Lattice.Bundles.JoinSemilattice._.semigroup
d_semigroup_226 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_160 ->
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_536
d_semigroup_226 :: () -> () -> T_JoinSemilattice_160 -> T_Semigroup_536
d_semigroup_226 ~()
v0 ~()
v1 T_JoinSemilattice_160
v2 = T_JoinSemilattice_160 -> T_Semigroup_536
du_semigroup_226 T_JoinSemilattice_160
v2
du_semigroup_226 ::
  T_JoinSemilattice_160 ->
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_536
du_semigroup_226 :: T_JoinSemilattice_160 -> T_Semigroup_536
du_semigroup_226 T_JoinSemilattice_160
v0
  = let v1 :: t
v1 = (T_JoinSemilattice_160 -> T_Semilattice_10) -> AgdaAny -> t
forall a b. a -> b
coe T_JoinSemilattice_160 -> T_Semilattice_10
du_semilattice_216 (T_JoinSemilattice_160 -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_160
v0) in
    AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe
      ((T_Band_596 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Band_596 -> T_Semigroup_536
MAlonzo.Code.Algebra.Bundles.du_semigroup_648
         ((T_Semilattice_10 -> T_Band_596) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_596
du_band_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Lattice.Bundles.BoundedSemilattice
d_BoundedSemilattice_232 :: p -> p -> ()
d_BoundedSemilattice_232 p
a0 p
a1 = ()
data T_BoundedSemilattice_232
  = C_BoundedSemilattice'46'constructor_3703 (AgdaAny ->
                                              AgdaAny -> AgdaAny)
                                             AgdaAny
                                             MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852
-- Algebra.Lattice.Bundles.BoundedSemilattice.Carrier
d_Carrier_248 :: T_BoundedSemilattice_232 -> ()
d_Carrier_248 :: T_BoundedSemilattice_232 -> ()
d_Carrier_248 = T_BoundedSemilattice_232 -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.BoundedSemilattice._≈_
d__'8776'__250 ::
  T_BoundedSemilattice_232 -> AgdaAny -> AgdaAny -> ()
d__'8776'__250 :: T_BoundedSemilattice_232 -> AgdaAny -> AgdaAny -> ()
d__'8776'__250 = T_BoundedSemilattice_232 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.BoundedSemilattice._∙_
d__'8729'__252 ::
  T_BoundedSemilattice_232 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__252 :: T_BoundedSemilattice_232 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__252 T_BoundedSemilattice_232
v0
  = case T_BoundedSemilattice_232 -> T_BoundedSemilattice_232
forall a b. a -> b
coe T_BoundedSemilattice_232
v0 of
      C_BoundedSemilattice'46'constructor_3703 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsIdempotentCommutativeMonoid_852
v5 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_BoundedSemilattice_232
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.BoundedSemilattice.ε
d_ε_254 :: T_BoundedSemilattice_232 -> AgdaAny
d_ε_254 :: T_BoundedSemilattice_232 -> AgdaAny
d_ε_254 T_BoundedSemilattice_232
v0
  = case T_BoundedSemilattice_232 -> T_BoundedSemilattice_232
forall a b. a -> b
coe T_BoundedSemilattice_232
v0 of
      C_BoundedSemilattice'46'constructor_3703 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsIdempotentCommutativeMonoid_852
v5 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4
      T_BoundedSemilattice_232
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.BoundedSemilattice.isBoundedSemilattice
d_isBoundedSemilattice_256 ::
  T_BoundedSemilattice_232 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852
d_isBoundedSemilattice_256 :: T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedSemilattice_256 T_BoundedSemilattice_232
v0
  = case T_BoundedSemilattice_232 -> T_BoundedSemilattice_232
forall a b. a -> b
coe T_BoundedSemilattice_232
v0 of
      C_BoundedSemilattice'46'constructor_3703 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsIdempotentCommutativeMonoid_852
v5 -> T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v5
      T_BoundedSemilattice_232
_ -> T_IsIdempotentCommutativeMonoid_852
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.BoundedSemilattice._.assoc
d_assoc_260 ::
  T_BoundedSemilattice_232 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_260 :: T_BoundedSemilattice_232
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_260 T_BoundedSemilattice_232
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_482
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
            ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
               ((T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedSemilattice_256 (T_BoundedSemilattice_232 -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_232
v0)))))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.comm
d_comm_262 ::
  T_BoundedSemilattice_232 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_262 :: T_BoundedSemilattice_232 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_262 T_BoundedSemilattice_232
v0
  = (T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_748
      ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
         ((T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedSemilattice_256 (T_BoundedSemilattice_232 -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_232
v0)))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.idem
d_idem_264 :: T_BoundedSemilattice_232 -> AgdaAny -> AgdaAny
d_idem_264 :: T_BoundedSemilattice_232 -> AgdaAny -> AgdaAny
d_idem_264 T_BoundedSemilattice_232
v0
  = (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_864
      ((T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedSemilattice_256 (T_BoundedSemilattice_232 -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_232
v0))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.identity
d_identity_266 ::
  T_BoundedSemilattice_232 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_266 :: T_BoundedSemilattice_232 -> T_Σ_14
d_identity_266 T_BoundedSemilattice_232
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_698
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
         ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
            ((T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedSemilattice_256 (T_BoundedSemilattice_232 -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_232
v0))))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.identityʳ
d_identity'691'_268 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedSemilattice_232 -> AgdaAny -> AgdaAny
d_identity'691'_268 :: () -> () -> T_BoundedSemilattice_232 -> AgdaAny -> AgdaAny
d_identity'691'_268 ~()
v0 ~()
v1 T_BoundedSemilattice_232
v2 = T_BoundedSemilattice_232 -> AgdaAny -> AgdaAny
du_identity'691'_268 T_BoundedSemilattice_232
v2
du_identity'691'_268 ::
  T_BoundedSemilattice_232 -> AgdaAny -> AgdaAny
du_identity'691'_268 :: T_BoundedSemilattice_232 -> AgdaAny -> AgdaAny
du_identity'691'_268 T_BoundedSemilattice_232
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedSemilattice_256 (T_BoundedSemilattice_232 -> T_BoundedSemilattice_232
forall a b. a -> b
coe T_BoundedSemilattice_232
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_728
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2))))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.identityˡ
d_identity'737'_270 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedSemilattice_232 -> AgdaAny -> AgdaAny
d_identity'737'_270 :: () -> () -> T_BoundedSemilattice_232 -> AgdaAny -> AgdaAny
d_identity'737'_270 ~()
v0 ~()
v1 T_BoundedSemilattice_232
v2 = T_BoundedSemilattice_232 -> AgdaAny -> AgdaAny
du_identity'737'_270 T_BoundedSemilattice_232
v2
du_identity'737'_270 ::
  T_BoundedSemilattice_232 -> AgdaAny -> AgdaAny
du_identity'737'_270 :: T_BoundedSemilattice_232 -> AgdaAny -> AgdaAny
du_identity'737'_270 T_BoundedSemilattice_232
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedSemilattice_256 (T_BoundedSemilattice_232 -> T_BoundedSemilattice_232
forall a b. a -> b
coe T_BoundedSemilattice_232
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_726
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2))))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.isBand
d_isBand_272 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedSemilattice_232 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_508
d_isBand_272 :: () -> () -> T_BoundedSemilattice_232 -> T_IsBand_508
d_isBand_272 ~()
v0 ~()
v1 T_BoundedSemilattice_232
v2 = T_BoundedSemilattice_232 -> T_IsBand_508
du_isBand_272 T_BoundedSemilattice_232
v2
du_isBand_272 ::
  T_BoundedSemilattice_232 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_508
du_isBand_272 :: T_BoundedSemilattice_232 -> T_IsBand_508
du_isBand_272 T_BoundedSemilattice_232
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedSemilattice_256 (T_BoundedSemilattice_232 -> T_BoundedSemilattice_232
forall a b. a -> b
coe T_BoundedSemilattice_232
v0) in
    AgdaAny -> T_IsBand_508
forall a b. a -> b
coe
      ((T_IsIdempotentMonoid_796 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentMonoid_796 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.du_isBand_846
         ((T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_910
            (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1)))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.isCommutativeMagma
d_isCommutativeMagma_274 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedSemilattice_232 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
d_isCommutativeMagma_274 :: () -> () -> T_BoundedSemilattice_232 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_274 ~()
v0 ~()
v1 T_BoundedSemilattice_232
v2 = T_BoundedSemilattice_232 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_274 T_BoundedSemilattice_232
v2
du_isCommutativeMagma_274 ::
  T_BoundedSemilattice_232 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
du_isCommutativeMagma_274 :: T_BoundedSemilattice_232 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_274 T_BoundedSemilattice_232
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedSemilattice_256 (T_BoundedSemilattice_232 -> T_BoundedSemilattice_232
forall a b. a -> b
coe T_BoundedSemilattice_232
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
            ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
               (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2))))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.isCommutativeMonoid
d_isCommutativeMonoid_276 ::
  T_BoundedSemilattice_232 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
d_isCommutativeMonoid_276 :: T_BoundedSemilattice_232 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_276 T_BoundedSemilattice_232
v0
  = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
      ((T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedSemilattice_256 (T_BoundedSemilattice_232 -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_232
v0))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.isCommutativeSemigroup
d_isCommutativeSemigroup_278 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedSemilattice_232 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_278 :: ()
-> () -> T_BoundedSemilattice_232 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_278 ~()
v0 ~()
v1 T_BoundedSemilattice_232
v2
  = T_BoundedSemilattice_232 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_278 T_BoundedSemilattice_232
v2
du_isCommutativeSemigroup_278 ::
  T_BoundedSemilattice_232 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_278 :: T_BoundedSemilattice_232 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_278 T_BoundedSemilattice_232
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedSemilattice_256 (T_BoundedSemilattice_232 -> T_BoundedSemilattice_232
forall a b. a -> b
coe T_BoundedSemilattice_232
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
         ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
            (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1)))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.isEquivalence
d_isEquivalence_280 ::
  T_BoundedSemilattice_232 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_280 :: T_BoundedSemilattice_232 -> T_IsEquivalence_26
d_isEquivalence_280 T_BoundedSemilattice_232
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
               ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                  ((T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedSemilattice_256 (T_BoundedSemilattice_232 -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_232
v0))))))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.isIdempotentMonoid
d_isIdempotentMonoid_282 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedSemilattice_232 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_796
d_isIdempotentMonoid_282 :: () -> () -> T_BoundedSemilattice_232 -> T_IsIdempotentMonoid_796
d_isIdempotentMonoid_282 ~()
v0 ~()
v1 T_BoundedSemilattice_232
v2 = T_BoundedSemilattice_232 -> T_IsIdempotentMonoid_796
du_isIdempotentMonoid_282 T_BoundedSemilattice_232
v2
du_isIdempotentMonoid_282 ::
  T_BoundedSemilattice_232 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_796
du_isIdempotentMonoid_282 :: T_BoundedSemilattice_232 -> T_IsIdempotentMonoid_796
du_isIdempotentMonoid_282 T_BoundedSemilattice_232
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedSemilattice_256 (T_BoundedSemilattice_232 -> T_BoundedSemilattice_232
forall a b. a -> b
coe T_BoundedSemilattice_232
v0) in
    AgdaAny -> T_IsIdempotentMonoid_796
forall a b. a -> b
coe
      ((T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_910 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.isMagma
d_isMagma_284 ::
  T_BoundedSemilattice_232 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_284 :: T_BoundedSemilattice_232 -> T_IsMagma_176
d_isMagma_284 T_BoundedSemilattice_232
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
            ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
               ((T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedSemilattice_256 (T_BoundedSemilattice_232 -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_232
v0)))))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.isMonoid
d_isMonoid_286 ::
  T_BoundedSemilattice_232 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_isMonoid_286 :: T_BoundedSemilattice_232 -> T_IsMonoid_686
d_isMonoid_286 T_BoundedSemilattice_232
v0
  = (T_IsCommutativeMonoid_736 -> T_IsMonoid_686)
-> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
      ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
         ((T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedSemilattice_256 (T_BoundedSemilattice_232 -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_232
v0)))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.isPartialEquivalence
d_isPartialEquivalence_288 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedSemilattice_232 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_288 :: () -> () -> T_BoundedSemilattice_232 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_288 ~()
v0 ~()
v1 T_BoundedSemilattice_232
v2
  = T_BoundedSemilattice_232 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_288 T_BoundedSemilattice_232
v2
du_isPartialEquivalence_288 ::
  T_BoundedSemilattice_232 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_288 :: T_BoundedSemilattice_232 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_288 T_BoundedSemilattice_232
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedSemilattice_256 (T_BoundedSemilattice_232 -> T_BoundedSemilattice_232
forall a b. a -> b
coe T_BoundedSemilattice_232
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3
                = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_176
v5 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                     ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v5)))))))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.isSemigroup
d_isSemigroup_290 ::
  T_BoundedSemilattice_232 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_290 :: T_BoundedSemilattice_232 -> T_IsSemigroup_472
d_isSemigroup_290 T_BoundedSemilattice_232
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
         ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
            ((T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedSemilattice_256 (T_BoundedSemilattice_232 -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_232
v0))))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.isCommutativeBand
d_isCommutativeBand_292 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedSemilattice_232 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
d_isCommutativeBand_292 :: () -> () -> T_BoundedSemilattice_232 -> T_IsCommutativeBand_590
d_isCommutativeBand_292 ~()
v0 ~()
v1 T_BoundedSemilattice_232
v2 = T_BoundedSemilattice_232 -> T_IsCommutativeBand_590
du_isCommutativeBand_292 T_BoundedSemilattice_232
v2
du_isCommutativeBand_292 ::
  T_BoundedSemilattice_232 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
du_isCommutativeBand_292 :: T_BoundedSemilattice_232 -> T_IsCommutativeBand_590
du_isCommutativeBand_292 T_BoundedSemilattice_232
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedSemilattice_256 (T_BoundedSemilattice_232 -> T_BoundedSemilattice_232
forall a b. a -> b
coe T_BoundedSemilattice_232
v0) in
    AgdaAny -> T_IsCommutativeBand_590
forall a b. a -> b
coe
      ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.isUnitalMagma
d_isUnitalMagma_294 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedSemilattice_232 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
d_isUnitalMagma_294 :: () -> () -> T_BoundedSemilattice_232 -> T_IsUnitalMagma_642
d_isUnitalMagma_294 ~()
v0 ~()
v1 T_BoundedSemilattice_232
v2 = T_BoundedSemilattice_232 -> T_IsUnitalMagma_642
du_isUnitalMagma_294 T_BoundedSemilattice_232
v2
du_isUnitalMagma_294 ::
  T_BoundedSemilattice_232 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
du_isUnitalMagma_294 :: T_BoundedSemilattice_232 -> T_IsUnitalMagma_642
du_isUnitalMagma_294 T_BoundedSemilattice_232
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedSemilattice_256 (T_BoundedSemilattice_232 -> T_BoundedSemilattice_232
forall a b. a -> b
coe T_BoundedSemilattice_232
v0) in
    AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_686 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsUnitalMagma_642
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2))))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.refl
d_refl_296 :: T_BoundedSemilattice_232 -> AgdaAny -> AgdaAny
d_refl_296 :: T_BoundedSemilattice_232 -> AgdaAny -> AgdaAny
d_refl_296 T_BoundedSemilattice_232
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                  ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                     ((T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedSemilattice_256 (T_BoundedSemilattice_232 -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_232
v0)))))))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.reflexive
d_reflexive_298 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedSemilattice_232 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_298 :: ()
-> ()
-> T_BoundedSemilattice_232
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_298 ~()
v0 ~()
v1 T_BoundedSemilattice_232
v2 = T_BoundedSemilattice_232
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_298 T_BoundedSemilattice_232
v2
du_reflexive_298 ::
  T_BoundedSemilattice_232 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_298 :: T_BoundedSemilattice_232
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_298 T_BoundedSemilattice_232
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedSemilattice_256 (T_BoundedSemilattice_232 -> T_BoundedSemilattice_232
forall a b. a -> b
coe T_BoundedSemilattice_232
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3
                = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_176
v5 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v4) in
                (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                  (\ AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 ->
                     (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                       ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v5))
                       AgdaAny
v6)))))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.setoid
d_setoid_300 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedSemilattice_232 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_300 :: () -> () -> T_BoundedSemilattice_232 -> T_Setoid_44
d_setoid_300 ~()
v0 ~()
v1 T_BoundedSemilattice_232
v2 = T_BoundedSemilattice_232 -> T_Setoid_44
du_setoid_300 T_BoundedSemilattice_232
v2
du_setoid_300 ::
  T_BoundedSemilattice_232 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_300 :: T_BoundedSemilattice_232 -> T_Setoid_44
du_setoid_300 T_BoundedSemilattice_232
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedSemilattice_256 (T_BoundedSemilattice_232 -> T_BoundedSemilattice_232
forall a b. a -> b
coe T_BoundedSemilattice_232
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3
                = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                  ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.sym
d_sym_302 ::
  T_BoundedSemilattice_232 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_302 :: T_BoundedSemilattice_232
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_302 T_BoundedSemilattice_232
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                  ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                     ((T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedSemilattice_256 (T_BoundedSemilattice_232 -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_232
v0)))))))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.trans
d_trans_304 ::
  T_BoundedSemilattice_232 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_304 :: T_BoundedSemilattice_232
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_304 T_BoundedSemilattice_232
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                  ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                     ((T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedSemilattice_256 (T_BoundedSemilattice_232 -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_232
v0)))))))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.∙-cong
d_'8729''45'cong_306 ::
  T_BoundedSemilattice_232 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_306 :: T_BoundedSemilattice_232
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_306 T_BoundedSemilattice_232
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
               ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                  ((T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedSemilattice_256 (T_BoundedSemilattice_232 -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_232
v0))))))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.∙-congʳ
d_'8729''45'cong'691'_308 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedSemilattice_232 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_308 :: ()
-> ()
-> T_BoundedSemilattice_232
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_308 ~()
v0 ~()
v1 T_BoundedSemilattice_232
v2
  = T_BoundedSemilattice_232
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_308 T_BoundedSemilattice_232
v2
du_'8729''45'cong'691'_308 ::
  T_BoundedSemilattice_232 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_308 :: T_BoundedSemilattice_232
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_308 T_BoundedSemilattice_232
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedSemilattice_256 (T_BoundedSemilattice_232 -> T_BoundedSemilattice_232
forall a b. a -> b
coe T_BoundedSemilattice_232
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3
                = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                  ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.∙-congˡ
d_'8729''45'cong'737'_310 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedSemilattice_232 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_310 :: ()
-> ()
-> T_BoundedSemilattice_232
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_310 ~()
v0 ~()
v1 T_BoundedSemilattice_232
v2
  = T_BoundedSemilattice_232
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_310 T_BoundedSemilattice_232
v2
du_'8729''45'cong'737'_310 ::
  T_BoundedSemilattice_232 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_310 :: T_BoundedSemilattice_232
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_310 T_BoundedSemilattice_232
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedSemilattice_256 (T_BoundedSemilattice_232 -> T_BoundedSemilattice_232
forall a b. a -> b
coe T_BoundedSemilattice_232
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3
                = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                  ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Lattice.Bundles.BoundedSemilattice.semilattice
d_semilattice_312 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedSemilattice_232 -> T_Semilattice_10
d_semilattice_312 :: () -> () -> T_BoundedSemilattice_232 -> T_Semilattice_10
d_semilattice_312 ~()
v0 ~()
v1 T_BoundedSemilattice_232
v2 = T_BoundedSemilattice_232 -> T_Semilattice_10
du_semilattice_312 T_BoundedSemilattice_232
v2
du_semilattice_312 :: T_BoundedSemilattice_232 -> T_Semilattice_10
du_semilattice_312 :: T_BoundedSemilattice_232 -> T_Semilattice_10
du_semilattice_312 T_BoundedSemilattice_232
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsCommutativeBand_590 -> T_Semilattice_10)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> T_Semilattice_10
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590 -> T_Semilattice_10
C_Semilattice'46'constructor_193 (T_BoundedSemilattice_232 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__252 (T_BoundedSemilattice_232 -> T_BoundedSemilattice_232
forall a b. a -> b
coe T_BoundedSemilattice_232
v0))
      ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
         ((T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_232 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedSemilattice_256 (T_BoundedSemilattice_232 -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_232
v0)))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.band
d_band_316 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedSemilattice_232 -> MAlonzo.Code.Algebra.Bundles.T_Band_596
d_band_316 :: () -> () -> T_BoundedSemilattice_232 -> T_Band_596
d_band_316 ~()
v0 ~()
v1 T_BoundedSemilattice_232
v2 = T_BoundedSemilattice_232 -> T_Band_596
du_band_316 T_BoundedSemilattice_232
v2
du_band_316 ::
  T_BoundedSemilattice_232 -> MAlonzo.Code.Algebra.Bundles.T_Band_596
du_band_316 :: T_BoundedSemilattice_232 -> T_Band_596
du_band_316 T_BoundedSemilattice_232
v0 = (T_Semilattice_10 -> T_Band_596) -> AgdaAny -> T_Band_596
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_596
du_band_66 ((T_BoundedSemilattice_232 -> T_Semilattice_10)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_232 -> T_Semilattice_10
du_semilattice_312 (T_BoundedSemilattice_232 -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_232
v0))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.magma
d_magma_318 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedSemilattice_232 -> MAlonzo.Code.Algebra.Bundles.T_Magma_68
d_magma_318 :: () -> () -> T_BoundedSemilattice_232 -> T_Magma_68
d_magma_318 ~()
v0 ~()
v1 T_BoundedSemilattice_232
v2 = T_BoundedSemilattice_232 -> T_Magma_68
du_magma_318 T_BoundedSemilattice_232
v2
du_magma_318 ::
  T_BoundedSemilattice_232 -> MAlonzo.Code.Algebra.Bundles.T_Magma_68
du_magma_318 :: T_BoundedSemilattice_232 -> T_Magma_68
du_magma_318 T_BoundedSemilattice_232
v0
  = let v1 :: t
v1 = (T_BoundedSemilattice_232 -> T_Semilattice_10) -> AgdaAny -> t
forall a b. a -> b
coe T_BoundedSemilattice_232 -> T_Semilattice_10
du_semilattice_312 (T_BoundedSemilattice_232 -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_232
v0) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semilattice_10 -> T_Band_596) -> AgdaAny -> t
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_596
du_band_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Semigroup_536 -> T_Magma_68
MAlonzo.Code.Algebra.Bundles.du_magma_584
            ((T_Band_596 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_596 -> T_Semigroup_536
MAlonzo.Code.Algebra.Bundles.du_semigroup_648 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.rawMagma
d_rawMagma_320 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedSemilattice_232 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_320 :: () -> () -> T_BoundedSemilattice_232 -> T_RawMagma_36
d_rawMagma_320 ~()
v0 ~()
v1 T_BoundedSemilattice_232
v2 = T_BoundedSemilattice_232 -> T_RawMagma_36
du_rawMagma_320 T_BoundedSemilattice_232
v2
du_rawMagma_320 ::
  T_BoundedSemilattice_232 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_320 :: T_BoundedSemilattice_232 -> T_RawMagma_36
du_rawMagma_320 T_BoundedSemilattice_232
v0
  = let v1 :: t
v1 = (T_BoundedSemilattice_232 -> T_Semilattice_10) -> AgdaAny -> t
forall a b. a -> b
coe T_BoundedSemilattice_232 -> T_Semilattice_10
du_semilattice_312 (T_BoundedSemilattice_232 -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_232
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semilattice_10 -> T_Band_596) -> AgdaAny -> t
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_596
du_band_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_Band_596 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_Band_596 -> T_Semigroup_536
MAlonzo.Code.Algebra.Bundles.du_semigroup_648 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Magma_68 -> T_RawMagma_36
MAlonzo.Code.Algebra.Bundles.du_rawMagma_112
               ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
MAlonzo.Code.Algebra.Bundles.du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Lattice.Bundles.BoundedSemilattice._.semigroup
d_semigroup_322 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedSemilattice_232 ->
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_536
d_semigroup_322 :: () -> () -> T_BoundedSemilattice_232 -> T_Semigroup_536
d_semigroup_322 ~()
v0 ~()
v1 T_BoundedSemilattice_232
v2 = T_BoundedSemilattice_232 -> T_Semigroup_536
du_semigroup_322 T_BoundedSemilattice_232
v2
du_semigroup_322 ::
  T_BoundedSemilattice_232 ->
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_536
du_semigroup_322 :: T_BoundedSemilattice_232 -> T_Semigroup_536
du_semigroup_322 T_BoundedSemilattice_232
v0
  = let v1 :: t
v1 = (T_BoundedSemilattice_232 -> T_Semilattice_10) -> AgdaAny -> t
forall a b. a -> b
coe T_BoundedSemilattice_232 -> T_Semilattice_10
du_semilattice_312 (T_BoundedSemilattice_232 -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_232
v0) in
    AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe
      ((T_Band_596 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Band_596 -> T_Semigroup_536
MAlonzo.Code.Algebra.Bundles.du_semigroup_648
         ((T_Semilattice_10 -> T_Band_596) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_596
du_band_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice
d_BoundedMeetSemilattice_328 :: p -> p -> ()
d_BoundedMeetSemilattice_328 p
a0 p
a1 = ()
data T_BoundedMeetSemilattice_328
  = C_BoundedMeetSemilattice'46'constructor_5171 (AgdaAny ->
                                                  AgdaAny -> AgdaAny)
                                                 AgdaAny
                                                 MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice.Carrier
d_Carrier_344 :: T_BoundedMeetSemilattice_328 -> ()
d_Carrier_344 :: T_BoundedMeetSemilattice_328 -> ()
d_Carrier_344 = T_BoundedMeetSemilattice_328 -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._≈_
d__'8776'__346 ::
  T_BoundedMeetSemilattice_328 -> AgdaAny -> AgdaAny -> ()
d__'8776'__346 :: T_BoundedMeetSemilattice_328 -> AgdaAny -> AgdaAny -> ()
d__'8776'__346 = T_BoundedMeetSemilattice_328 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._∧_
d__'8743'__348 ::
  T_BoundedMeetSemilattice_328 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__348 :: T_BoundedMeetSemilattice_328 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__348 T_BoundedMeetSemilattice_328
v0
  = case T_BoundedMeetSemilattice_328 -> T_BoundedMeetSemilattice_328
forall a b. a -> b
coe T_BoundedMeetSemilattice_328
v0 of
      C_BoundedMeetSemilattice'46'constructor_5171 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsIdempotentCommutativeMonoid_852
v5 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_BoundedMeetSemilattice_328
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice.⊤
d_'8868'_350 :: T_BoundedMeetSemilattice_328 -> AgdaAny
d_'8868'_350 :: T_BoundedMeetSemilattice_328 -> AgdaAny
d_'8868'_350 T_BoundedMeetSemilattice_328
v0
  = case T_BoundedMeetSemilattice_328 -> T_BoundedMeetSemilattice_328
forall a b. a -> b
coe T_BoundedMeetSemilattice_328
v0 of
      C_BoundedMeetSemilattice'46'constructor_5171 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsIdempotentCommutativeMonoid_852
v5 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4
      T_BoundedMeetSemilattice_328
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice.isBoundedMeetSemilattice
d_isBoundedMeetSemilattice_352 ::
  T_BoundedMeetSemilattice_328 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852
d_isBoundedMeetSemilattice_352 :: T_BoundedMeetSemilattice_328 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedMeetSemilattice_352 T_BoundedMeetSemilattice_328
v0
  = case T_BoundedMeetSemilattice_328 -> T_BoundedMeetSemilattice_328
forall a b. a -> b
coe T_BoundedMeetSemilattice_328
v0 of
      C_BoundedMeetSemilattice'46'constructor_5171 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsIdempotentCommutativeMonoid_852
v5 -> T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v5
      T_BoundedMeetSemilattice_328
_ -> T_IsIdempotentCommutativeMonoid_852
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.assoc
d_assoc_356 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_328 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_356 :: ()
-> ()
-> T_BoundedMeetSemilattice_328
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_assoc_356 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_328
v2 = T_BoundedMeetSemilattice_328
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_356 T_BoundedMeetSemilattice_328
v2
du_assoc_356 ::
  T_BoundedMeetSemilattice_328 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_356 :: T_BoundedMeetSemilattice_328
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_356 T_BoundedMeetSemilattice_328
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedMeetSemilattice_328 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedMeetSemilattice_352 (T_BoundedMeetSemilattice_328 -> T_BoundedMeetSemilattice_328
forall a b. a -> b
coe T_BoundedMeetSemilattice_328
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
                 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_482
            ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
               ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2)))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.comm
d_comm_358 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_328 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_358 :: ()
-> ()
-> T_BoundedMeetSemilattice_328
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_comm_358 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_328
v2 = T_BoundedMeetSemilattice_328 -> AgdaAny -> AgdaAny -> AgdaAny
du_comm_358 T_BoundedMeetSemilattice_328
v2
du_comm_358 ::
  T_BoundedMeetSemilattice_328 -> AgdaAny -> AgdaAny -> AgdaAny
du_comm_358 :: T_BoundedMeetSemilattice_328 -> AgdaAny -> AgdaAny -> AgdaAny
du_comm_358 T_BoundedMeetSemilattice_328
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedMeetSemilattice_328 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedMeetSemilattice_352 (T_BoundedMeetSemilattice_328 -> T_BoundedMeetSemilattice_328
forall a b. a -> b
coe T_BoundedMeetSemilattice_328
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_600
         ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1)))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.idem
d_idem_360 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_328 -> AgdaAny -> AgdaAny
d_idem_360 :: () -> () -> T_BoundedMeetSemilattice_328 -> AgdaAny -> AgdaAny
d_idem_360 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_328
v2 = T_BoundedMeetSemilattice_328 -> AgdaAny -> AgdaAny
du_idem_360 T_BoundedMeetSemilattice_328
v2
du_idem_360 :: T_BoundedMeetSemilattice_328 -> AgdaAny -> AgdaAny
du_idem_360 :: T_BoundedMeetSemilattice_328 -> AgdaAny -> AgdaAny
du_idem_360 T_BoundedMeetSemilattice_328
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedMeetSemilattice_328 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedMeetSemilattice_352 (T_BoundedMeetSemilattice_328 -> T_BoundedMeetSemilattice_328
forall a b. a -> b
coe T_BoundedMeetSemilattice_328
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
                 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsBand_508 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_508 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_518
            ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.identity
d_identity_362 ::
  T_BoundedMeetSemilattice_328 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_362 :: T_BoundedMeetSemilattice_328 -> T_Σ_14
d_identity_362 T_BoundedMeetSemilattice_328
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_698
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
         ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
            ((T_BoundedMeetSemilattice_328
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_328 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedMeetSemilattice_352 (T_BoundedMeetSemilattice_328 -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_328
v0))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.identityʳ
d_identity'691'_364 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_328 -> AgdaAny -> AgdaAny
d_identity'691'_364 :: () -> () -> T_BoundedMeetSemilattice_328 -> AgdaAny -> AgdaAny
d_identity'691'_364 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_328
v2 = T_BoundedMeetSemilattice_328 -> AgdaAny -> AgdaAny
du_identity'691'_364 T_BoundedMeetSemilattice_328
v2
du_identity'691'_364 ::
  T_BoundedMeetSemilattice_328 -> AgdaAny -> AgdaAny
du_identity'691'_364 :: T_BoundedMeetSemilattice_328 -> AgdaAny -> AgdaAny
du_identity'691'_364 T_BoundedMeetSemilattice_328
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedMeetSemilattice_328 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedMeetSemilattice_352 (T_BoundedMeetSemilattice_328 -> T_BoundedMeetSemilattice_328
forall a b. a -> b
coe T_BoundedMeetSemilattice_328
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_728
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.identityˡ
d_identity'737'_366 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_328 -> AgdaAny -> AgdaAny
d_identity'737'_366 :: () -> () -> T_BoundedMeetSemilattice_328 -> AgdaAny -> AgdaAny
d_identity'737'_366 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_328
v2 = T_BoundedMeetSemilattice_328 -> AgdaAny -> AgdaAny
du_identity'737'_366 T_BoundedMeetSemilattice_328
v2
du_identity'737'_366 ::
  T_BoundedMeetSemilattice_328 -> AgdaAny -> AgdaAny
du_identity'737'_366 :: T_BoundedMeetSemilattice_328 -> AgdaAny -> AgdaAny
du_identity'737'_366 T_BoundedMeetSemilattice_328
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedMeetSemilattice_328 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedMeetSemilattice_352 (T_BoundedMeetSemilattice_328 -> T_BoundedMeetSemilattice_328
forall a b. a -> b
coe T_BoundedMeetSemilattice_328
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_726
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.isBand
d_isBand_368 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_328 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_508
d_isBand_368 :: () -> () -> T_BoundedMeetSemilattice_328 -> T_IsBand_508
d_isBand_368 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_328
v2 = T_BoundedMeetSemilattice_328 -> T_IsBand_508
du_isBand_368 T_BoundedMeetSemilattice_328
v2
du_isBand_368 ::
  T_BoundedMeetSemilattice_328 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_508
du_isBand_368 :: T_BoundedMeetSemilattice_328 -> T_IsBand_508
du_isBand_368 T_BoundedMeetSemilattice_328
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedMeetSemilattice_328 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedMeetSemilattice_352 (T_BoundedMeetSemilattice_328 -> T_BoundedMeetSemilattice_328
forall a b. a -> b
coe T_BoundedMeetSemilattice_328
v0) in
    AgdaAny -> T_IsBand_508
forall a b. a -> b
coe
      ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598
         ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1)))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.isEquivalence
d_isEquivalence_370 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_328 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_370 :: () -> () -> T_BoundedMeetSemilattice_328 -> T_IsEquivalence_26
d_isEquivalence_370 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_328
v2 = T_BoundedMeetSemilattice_328 -> T_IsEquivalence_26
du_isEquivalence_370 T_BoundedMeetSemilattice_328
v2
du_isEquivalence_370 ::
  T_BoundedMeetSemilattice_328 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_370 :: T_BoundedMeetSemilattice_328 -> T_IsEquivalence_26
du_isEquivalence_370 T_BoundedMeetSemilattice_328
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedMeetSemilattice_328 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedMeetSemilattice_352 (T_BoundedMeetSemilattice_328 -> T_BoundedMeetSemilattice_328
forall a b. a -> b
coe T_BoundedMeetSemilattice_328
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
                 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
               ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                  ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.isMagma
d_isMagma_372 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_328 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_372 :: () -> () -> T_BoundedMeetSemilattice_328 -> T_IsMagma_176
d_isMagma_372 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_328
v2 = T_BoundedMeetSemilattice_328 -> T_IsMagma_176
du_isMagma_372 T_BoundedMeetSemilattice_328
v2
du_isMagma_372 ::
  T_BoundedMeetSemilattice_328 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
du_isMagma_372 :: T_BoundedMeetSemilattice_328 -> T_IsMagma_176
du_isMagma_372 T_BoundedMeetSemilattice_328
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedMeetSemilattice_328 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedMeetSemilattice_352 (T_BoundedMeetSemilattice_328 -> T_BoundedMeetSemilattice_328
forall a b. a -> b
coe T_BoundedMeetSemilattice_328
v0) in
    AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
                 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
               ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2)))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.isCommutativeBand
d_isCommutativeBand_374 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_328 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
d_isCommutativeBand_374 :: () -> () -> T_BoundedMeetSemilattice_328 -> T_IsCommutativeBand_590
d_isCommutativeBand_374 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_328
v2 = T_BoundedMeetSemilattice_328 -> T_IsCommutativeBand_590
du_isCommutativeBand_374 T_BoundedMeetSemilattice_328
v2
du_isCommutativeBand_374 ::
  T_BoundedMeetSemilattice_328 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
du_isCommutativeBand_374 :: T_BoundedMeetSemilattice_328 -> T_IsCommutativeBand_590
du_isCommutativeBand_374 T_BoundedMeetSemilattice_328
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedMeetSemilattice_328 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedMeetSemilattice_352 (T_BoundedMeetSemilattice_328 -> T_BoundedMeetSemilattice_328
forall a b. a -> b
coe T_BoundedMeetSemilattice_328
v0) in
    AgdaAny -> T_IsCommutativeBand_590
forall a b. a -> b
coe
      ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.isPartialEquivalence
d_isPartialEquivalence_376 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_328 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_376 :: ()
-> () -> T_BoundedMeetSemilattice_328 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_376 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_328
v2
  = T_BoundedMeetSemilattice_328 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_376 T_BoundedMeetSemilattice_328
v2
du_isPartialEquivalence_376 ::
  T_BoundedMeetSemilattice_328 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_376 :: T_BoundedMeetSemilattice_328 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_376 T_BoundedMeetSemilattice_328
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedMeetSemilattice_328 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedMeetSemilattice_352 (T_BoundedMeetSemilattice_328 -> T_BoundedMeetSemilattice_328
forall a b. a -> b
coe T_BoundedMeetSemilattice_328
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
                 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsBand_508
v3 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> T_IsCommutativeBand_590
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_176
v5 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                     ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v5)))))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.isSemigroup
d_isSemigroup_378 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_328 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_378 :: () -> () -> T_BoundedMeetSemilattice_328 -> T_IsSemigroup_472
d_isSemigroup_378 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_328
v2 = T_BoundedMeetSemilattice_328 -> T_IsSemigroup_472
du_isSemigroup_378 T_BoundedMeetSemilattice_328
v2
du_isSemigroup_378 ::
  T_BoundedMeetSemilattice_328 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
du_isSemigroup_378 :: T_BoundedMeetSemilattice_328 -> T_IsSemigroup_472
du_isSemigroup_378 T_BoundedMeetSemilattice_328
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedMeetSemilattice_328 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedMeetSemilattice_352 (T_BoundedMeetSemilattice_328 -> T_BoundedMeetSemilattice_328
forall a b. a -> b
coe T_BoundedMeetSemilattice_328
v0) in
    AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
                 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
            ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.refl
d_refl_380 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_328 -> AgdaAny -> AgdaAny
d_refl_380 :: () -> () -> T_BoundedMeetSemilattice_328 -> AgdaAny -> AgdaAny
d_refl_380 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_328
v2 = T_BoundedMeetSemilattice_328 -> AgdaAny -> AgdaAny
du_refl_380 T_BoundedMeetSemilattice_328
v2
du_refl_380 :: T_BoundedMeetSemilattice_328 -> AgdaAny -> AgdaAny
du_refl_380 :: T_BoundedMeetSemilattice_328 -> AgdaAny -> AgdaAny
du_refl_380 T_BoundedMeetSemilattice_328
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedMeetSemilattice_328 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedMeetSemilattice_352 (T_BoundedMeetSemilattice_328 -> T_BoundedMeetSemilattice_328
forall a b. a -> b
coe T_BoundedMeetSemilattice_328
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
                 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
            ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
                  ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                     ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2)))))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.reflexive
d_reflexive_382 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_328 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_382 :: ()
-> ()
-> T_BoundedMeetSemilattice_328
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_382 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_328
v2 = T_BoundedMeetSemilattice_328
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_382 T_BoundedMeetSemilattice_328
v2
du_reflexive_382 ::
  T_BoundedMeetSemilattice_328 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_382 :: T_BoundedMeetSemilattice_328
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_382 T_BoundedMeetSemilattice_328
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedMeetSemilattice_328 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedMeetSemilattice_352 (T_BoundedMeetSemilattice_328 -> T_BoundedMeetSemilattice_328
forall a b. a -> b
coe T_BoundedMeetSemilattice_328
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
                 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsBand_508
v3 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> T_IsCommutativeBand_590
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_176
v5 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v4) in
                (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                  (\ AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 ->
                     (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                       ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v5))
                       AgdaAny
v6)))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.setoid
d_setoid_384 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_328 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_384 :: () -> () -> T_BoundedMeetSemilattice_328 -> T_Setoid_44
d_setoid_384 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_328
v2 = T_BoundedMeetSemilattice_328 -> T_Setoid_44
du_setoid_384 T_BoundedMeetSemilattice_328
v2
du_setoid_384 ::
  T_BoundedMeetSemilattice_328 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_384 :: T_BoundedMeetSemilattice_328 -> T_Setoid_44
du_setoid_384 T_BoundedMeetSemilattice_328
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedMeetSemilattice_328 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedMeetSemilattice_352 (T_BoundedMeetSemilattice_328 -> T_BoundedMeetSemilattice_328
forall a b. a -> b
coe T_BoundedMeetSemilattice_328
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
                 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsBand_508
v3 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> T_IsCommutativeBand_590
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                  ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.sym
d_sym_386 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_328 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_386 :: ()
-> ()
-> T_BoundedMeetSemilattice_328
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_386 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_328
v2 = T_BoundedMeetSemilattice_328
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_386 T_BoundedMeetSemilattice_328
v2
du_sym_386 ::
  T_BoundedMeetSemilattice_328 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_386 :: T_BoundedMeetSemilattice_328
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_386 T_BoundedMeetSemilattice_328
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedMeetSemilattice_328 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedMeetSemilattice_352 (T_BoundedMeetSemilattice_328 -> T_BoundedMeetSemilattice_328
forall a b. a -> b
coe T_BoundedMeetSemilattice_328
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
                 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
            ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
                  ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                     ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2)))))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.trans
d_trans_388 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_328 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_388 :: ()
-> ()
-> T_BoundedMeetSemilattice_328
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_388 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_328
v2 = T_BoundedMeetSemilattice_328
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_388 T_BoundedMeetSemilattice_328
v2
du_trans_388 ::
  T_BoundedMeetSemilattice_328 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_388 :: T_BoundedMeetSemilattice_328
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_388 T_BoundedMeetSemilattice_328
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedMeetSemilattice_328 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedMeetSemilattice_352 (T_BoundedMeetSemilattice_328 -> T_BoundedMeetSemilattice_328
forall a b. a -> b
coe T_BoundedMeetSemilattice_328
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
                 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
            ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
                  ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                     ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2)))))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.∙-cong
d_'8729''45'cong_390 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_328 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_390 :: ()
-> ()
-> T_BoundedMeetSemilattice_328
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_390 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_328
v2 = T_BoundedMeetSemilattice_328
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_390 T_BoundedMeetSemilattice_328
v2
du_'8729''45'cong_390 ::
  T_BoundedMeetSemilattice_328 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong_390 :: T_BoundedMeetSemilattice_328
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_390 T_BoundedMeetSemilattice_328
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedMeetSemilattice_328 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedMeetSemilattice_352 (T_BoundedMeetSemilattice_328 -> T_BoundedMeetSemilattice_328
forall a b. a -> b
coe T_BoundedMeetSemilattice_328
v0) in
    AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
                 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
               ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                  ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.∙-congʳ
d_'8729''45'cong'691'_392 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_328 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_392 :: ()
-> ()
-> T_BoundedMeetSemilattice_328
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_392 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_328
v2
  = T_BoundedMeetSemilattice_328
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_392 T_BoundedMeetSemilattice_328
v2
du_'8729''45'cong'691'_392 ::
  T_BoundedMeetSemilattice_328 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_392 :: T_BoundedMeetSemilattice_328
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_392 T_BoundedMeetSemilattice_328
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedMeetSemilattice_328 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedMeetSemilattice_352 (T_BoundedMeetSemilattice_328 -> T_BoundedMeetSemilattice_328
forall a b. a -> b
coe T_BoundedMeetSemilattice_328
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
                 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsBand_508
v3 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> T_IsCommutativeBand_590
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                  ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.∙-congˡ
d_'8729''45'cong'737'_394 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_328 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_394 :: ()
-> ()
-> T_BoundedMeetSemilattice_328
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_394 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_328
v2
  = T_BoundedMeetSemilattice_328
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_394 T_BoundedMeetSemilattice_328
v2
du_'8729''45'cong'737'_394 ::
  T_BoundedMeetSemilattice_328 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_394 :: T_BoundedMeetSemilattice_328
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_394 T_BoundedMeetSemilattice_328
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedMeetSemilattice_328 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedMeetSemilattice_352 (T_BoundedMeetSemilattice_328 -> T_BoundedMeetSemilattice_328
forall a b. a -> b
coe T_BoundedMeetSemilattice_328
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
                 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsBand_508
v3 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> T_IsCommutativeBand_590
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                  ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice.boundedSemilattice
d_boundedSemilattice_396 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_328 -> T_BoundedSemilattice_232
d_boundedSemilattice_396 :: ()
-> () -> T_BoundedMeetSemilattice_328 -> T_BoundedSemilattice_232
d_boundedSemilattice_396 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_328
v2 = T_BoundedMeetSemilattice_328 -> T_BoundedSemilattice_232
du_boundedSemilattice_396 T_BoundedMeetSemilattice_328
v2
du_boundedSemilattice_396 ::
  T_BoundedMeetSemilattice_328 -> T_BoundedSemilattice_232
du_boundedSemilattice_396 :: T_BoundedMeetSemilattice_328 -> T_BoundedSemilattice_232
du_boundedSemilattice_396 T_BoundedMeetSemilattice_328
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsIdempotentCommutativeMonoid_852
 -> T_BoundedSemilattice_232)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_BoundedSemilattice_232
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_BoundedSemilattice_232
C_BoundedSemilattice'46'constructor_3703 (T_BoundedMeetSemilattice_328 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__348 (T_BoundedMeetSemilattice_328 -> T_BoundedMeetSemilattice_328
forall a b. a -> b
coe T_BoundedMeetSemilattice_328
v0))
      (T_BoundedMeetSemilattice_328 -> AgdaAny
d_'8868'_350 (T_BoundedMeetSemilattice_328 -> T_BoundedMeetSemilattice_328
forall a b. a -> b
coe T_BoundedMeetSemilattice_328
v0)) (T_BoundedMeetSemilattice_328 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedMeetSemilattice_352 (T_BoundedMeetSemilattice_328 -> T_BoundedMeetSemilattice_328
forall a b. a -> b
coe T_BoundedMeetSemilattice_328
v0))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.band
d_band_400 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_328 ->
  MAlonzo.Code.Algebra.Bundles.T_Band_596
d_band_400 :: () -> () -> T_BoundedMeetSemilattice_328 -> T_Band_596
d_band_400 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_328
v2 = T_BoundedMeetSemilattice_328 -> T_Band_596
du_band_400 T_BoundedMeetSemilattice_328
v2
du_band_400 ::
  T_BoundedMeetSemilattice_328 ->
  MAlonzo.Code.Algebra.Bundles.T_Band_596
du_band_400 :: T_BoundedMeetSemilattice_328 -> T_Band_596
du_band_400 T_BoundedMeetSemilattice_328
v0
  = let v1 :: t
v1 = (T_BoundedMeetSemilattice_328 -> T_BoundedSemilattice_232)
-> AgdaAny -> t
forall a b. a -> b
coe T_BoundedMeetSemilattice_328 -> T_BoundedSemilattice_232
du_boundedSemilattice_396 (T_BoundedMeetSemilattice_328 -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_328
v0) in
    AgdaAny -> T_Band_596
forall a b. a -> b
coe ((T_Semilattice_10 -> T_Band_596) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_596
du_band_66 ((T_BoundedSemilattice_232 -> T_Semilattice_10)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_232 -> T_Semilattice_10
du_semilattice_312 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.magma
d_magma_402 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_328 ->
  MAlonzo.Code.Algebra.Bundles.T_Magma_68
d_magma_402 :: () -> () -> T_BoundedMeetSemilattice_328 -> T_Magma_68
d_magma_402 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_328
v2 = T_BoundedMeetSemilattice_328 -> T_Magma_68
du_magma_402 T_BoundedMeetSemilattice_328
v2
du_magma_402 ::
  T_BoundedMeetSemilattice_328 ->
  MAlonzo.Code.Algebra.Bundles.T_Magma_68
du_magma_402 :: T_BoundedMeetSemilattice_328 -> T_Magma_68
du_magma_402 T_BoundedMeetSemilattice_328
v0
  = let v1 :: t
v1 = (T_BoundedMeetSemilattice_328 -> T_BoundedSemilattice_232)
-> AgdaAny -> t
forall a b. a -> b
coe T_BoundedMeetSemilattice_328 -> T_BoundedSemilattice_232
du_boundedSemilattice_396 (T_BoundedMeetSemilattice_328 -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_328
v0) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_BoundedSemilattice_232 -> T_Semilattice_10) -> AgdaAny -> t
forall a b. a -> b
coe T_BoundedSemilattice_232 -> T_Semilattice_10
du_semilattice_312 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semilattice_10 -> T_Band_596) -> AgdaAny -> t
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_596
du_band_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Semigroup_536 -> T_Magma_68
MAlonzo.Code.Algebra.Bundles.du_magma_584
               ((T_Band_596 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_596 -> T_Semigroup_536
MAlonzo.Code.Algebra.Bundles.du_semigroup_648 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.rawMagma
d_rawMagma_404 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_328 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_404 :: () -> () -> T_BoundedMeetSemilattice_328 -> T_RawMagma_36
d_rawMagma_404 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_328
v2 = T_BoundedMeetSemilattice_328 -> T_RawMagma_36
du_rawMagma_404 T_BoundedMeetSemilattice_328
v2
du_rawMagma_404 ::
  T_BoundedMeetSemilattice_328 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_404 :: T_BoundedMeetSemilattice_328 -> T_RawMagma_36
du_rawMagma_404 T_BoundedMeetSemilattice_328
v0
  = let v1 :: t
v1 = (T_BoundedMeetSemilattice_328 -> T_BoundedSemilattice_232)
-> AgdaAny -> t
forall a b. a -> b
coe T_BoundedMeetSemilattice_328 -> T_BoundedSemilattice_232
du_boundedSemilattice_396 (T_BoundedMeetSemilattice_328 -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_328
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_BoundedSemilattice_232 -> T_Semilattice_10) -> AgdaAny -> t
forall a b. a -> b
coe T_BoundedSemilattice_232 -> T_Semilattice_10
du_semilattice_312 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semilattice_10 -> T_Band_596) -> AgdaAny -> t
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_596
du_band_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4
                   = (T_Band_596 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_Band_596 -> T_Semigroup_536
MAlonzo.Code.Algebra.Bundles.du_semigroup_648 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Magma_68 -> T_RawMagma_36
MAlonzo.Code.Algebra.Bundles.du_rawMagma_112
                  ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
MAlonzo.Code.Algebra.Bundles.du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.semigroup
d_semigroup_406 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_328 ->
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_536
d_semigroup_406 :: () -> () -> T_BoundedMeetSemilattice_328 -> T_Semigroup_536
d_semigroup_406 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_328
v2 = T_BoundedMeetSemilattice_328 -> T_Semigroup_536
du_semigroup_406 T_BoundedMeetSemilattice_328
v2
du_semigroup_406 ::
  T_BoundedMeetSemilattice_328 ->
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_536
du_semigroup_406 :: T_BoundedMeetSemilattice_328 -> T_Semigroup_536
du_semigroup_406 T_BoundedMeetSemilattice_328
v0
  = let v1 :: t
v1 = (T_BoundedMeetSemilattice_328 -> T_BoundedSemilattice_232)
-> AgdaAny -> t
forall a b. a -> b
coe T_BoundedMeetSemilattice_328 -> T_BoundedSemilattice_232
du_boundedSemilattice_396 (T_BoundedMeetSemilattice_328 -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_328
v0) in
    AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_BoundedSemilattice_232 -> T_Semilattice_10) -> AgdaAny -> t
forall a b. a -> b
coe T_BoundedSemilattice_232 -> T_Semilattice_10
du_semilattice_312 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Band_596 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Band_596 -> T_Semigroup_536
MAlonzo.Code.Algebra.Bundles.du_semigroup_648
            ((T_Semilattice_10 -> T_Band_596) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_596
du_band_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Lattice.Bundles.BoundedMeetSemilattice._.semilattice
d_semilattice_408 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_328 -> T_Semilattice_10
d_semilattice_408 :: () -> () -> T_BoundedMeetSemilattice_328 -> T_Semilattice_10
d_semilattice_408 ~()
v0 ~()
v1 T_BoundedMeetSemilattice_328
v2 = T_BoundedMeetSemilattice_328 -> T_Semilattice_10
du_semilattice_408 T_BoundedMeetSemilattice_328
v2
du_semilattice_408 ::
  T_BoundedMeetSemilattice_328 -> T_Semilattice_10
du_semilattice_408 :: T_BoundedMeetSemilattice_328 -> T_Semilattice_10
du_semilattice_408 T_BoundedMeetSemilattice_328
v0
  = (T_BoundedSemilattice_232 -> T_Semilattice_10)
-> AgdaAny -> T_Semilattice_10
forall a b. a -> b
coe T_BoundedSemilattice_232 -> T_Semilattice_10
du_semilattice_312 ((T_BoundedMeetSemilattice_328 -> T_BoundedSemilattice_232)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_328 -> T_BoundedSemilattice_232
du_boundedSemilattice_396 (T_BoundedMeetSemilattice_328 -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_328
v0))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice
d_BoundedJoinSemilattice_414 :: p -> p -> ()
d_BoundedJoinSemilattice_414 p
a0 p
a1 = ()
data T_BoundedJoinSemilattice_414
  = C_BoundedJoinSemilattice'46'constructor_6531 (AgdaAny ->
                                                  AgdaAny -> AgdaAny)
                                                 AgdaAny
                                                 MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice.Carrier
d_Carrier_430 :: T_BoundedJoinSemilattice_414 -> ()
d_Carrier_430 :: T_BoundedJoinSemilattice_414 -> ()
d_Carrier_430 = T_BoundedJoinSemilattice_414 -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._≈_
d__'8776'__432 ::
  T_BoundedJoinSemilattice_414 -> AgdaAny -> AgdaAny -> ()
d__'8776'__432 :: T_BoundedJoinSemilattice_414 -> AgdaAny -> AgdaAny -> ()
d__'8776'__432 = T_BoundedJoinSemilattice_414 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._∨_
d__'8744'__434 ::
  T_BoundedJoinSemilattice_414 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__434 :: T_BoundedJoinSemilattice_414 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__434 T_BoundedJoinSemilattice_414
v0
  = case T_BoundedJoinSemilattice_414 -> T_BoundedJoinSemilattice_414
forall a b. a -> b
coe T_BoundedJoinSemilattice_414
v0 of
      C_BoundedJoinSemilattice'46'constructor_6531 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsIdempotentCommutativeMonoid_852
v5 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_BoundedJoinSemilattice_414
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice.⊥
d_'8869'_436 :: T_BoundedJoinSemilattice_414 -> AgdaAny
d_'8869'_436 :: T_BoundedJoinSemilattice_414 -> AgdaAny
d_'8869'_436 T_BoundedJoinSemilattice_414
v0
  = case T_BoundedJoinSemilattice_414 -> T_BoundedJoinSemilattice_414
forall a b. a -> b
coe T_BoundedJoinSemilattice_414
v0 of
      C_BoundedJoinSemilattice'46'constructor_6531 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsIdempotentCommutativeMonoid_852
v5 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4
      T_BoundedJoinSemilattice_414
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice.isBoundedJoinSemilattice
d_isBoundedJoinSemilattice_438 ::
  T_BoundedJoinSemilattice_414 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852
d_isBoundedJoinSemilattice_438 :: T_BoundedJoinSemilattice_414 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedJoinSemilattice_438 T_BoundedJoinSemilattice_414
v0
  = case T_BoundedJoinSemilattice_414 -> T_BoundedJoinSemilattice_414
forall a b. a -> b
coe T_BoundedJoinSemilattice_414
v0 of
      C_BoundedJoinSemilattice'46'constructor_6531 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsIdempotentCommutativeMonoid_852
v5 -> T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v5
      T_BoundedJoinSemilattice_414
_ -> T_IsIdempotentCommutativeMonoid_852
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.assoc
d_assoc_442 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_414 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_442 :: ()
-> ()
-> T_BoundedJoinSemilattice_414
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_assoc_442 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_414
v2 = T_BoundedJoinSemilattice_414
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_442 T_BoundedJoinSemilattice_414
v2
du_assoc_442 ::
  T_BoundedJoinSemilattice_414 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_442 :: T_BoundedJoinSemilattice_414
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_442 T_BoundedJoinSemilattice_414
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedJoinSemilattice_414 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedJoinSemilattice_438 (T_BoundedJoinSemilattice_414 -> T_BoundedJoinSemilattice_414
forall a b. a -> b
coe T_BoundedJoinSemilattice_414
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
                 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_482
            ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
               ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2)))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.comm
d_comm_444 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_414 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_444 :: ()
-> ()
-> T_BoundedJoinSemilattice_414
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_comm_444 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_414
v2 = T_BoundedJoinSemilattice_414 -> AgdaAny -> AgdaAny -> AgdaAny
du_comm_444 T_BoundedJoinSemilattice_414
v2
du_comm_444 ::
  T_BoundedJoinSemilattice_414 -> AgdaAny -> AgdaAny -> AgdaAny
du_comm_444 :: T_BoundedJoinSemilattice_414 -> AgdaAny -> AgdaAny -> AgdaAny
du_comm_444 T_BoundedJoinSemilattice_414
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedJoinSemilattice_414 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedJoinSemilattice_438 (T_BoundedJoinSemilattice_414 -> T_BoundedJoinSemilattice_414
forall a b. a -> b
coe T_BoundedJoinSemilattice_414
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_600
         ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1)))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.idem
d_idem_446 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_414 -> AgdaAny -> AgdaAny
d_idem_446 :: () -> () -> T_BoundedJoinSemilattice_414 -> AgdaAny -> AgdaAny
d_idem_446 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_414
v2 = T_BoundedJoinSemilattice_414 -> AgdaAny -> AgdaAny
du_idem_446 T_BoundedJoinSemilattice_414
v2
du_idem_446 :: T_BoundedJoinSemilattice_414 -> AgdaAny -> AgdaAny
du_idem_446 :: T_BoundedJoinSemilattice_414 -> AgdaAny -> AgdaAny
du_idem_446 T_BoundedJoinSemilattice_414
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedJoinSemilattice_414 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedJoinSemilattice_438 (T_BoundedJoinSemilattice_414 -> T_BoundedJoinSemilattice_414
forall a b. a -> b
coe T_BoundedJoinSemilattice_414
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
                 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsBand_508 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_508 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_518
            ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.identity
d_identity_448 ::
  T_BoundedJoinSemilattice_414 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_448 :: T_BoundedJoinSemilattice_414 -> T_Σ_14
d_identity_448 T_BoundedJoinSemilattice_414
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_698
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
         ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
            ((T_BoundedJoinSemilattice_414
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_414 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedJoinSemilattice_438 (T_BoundedJoinSemilattice_414 -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_414
v0))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.identityʳ
d_identity'691'_450 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_414 -> AgdaAny -> AgdaAny
d_identity'691'_450 :: () -> () -> T_BoundedJoinSemilattice_414 -> AgdaAny -> AgdaAny
d_identity'691'_450 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_414
v2 = T_BoundedJoinSemilattice_414 -> AgdaAny -> AgdaAny
du_identity'691'_450 T_BoundedJoinSemilattice_414
v2
du_identity'691'_450 ::
  T_BoundedJoinSemilattice_414 -> AgdaAny -> AgdaAny
du_identity'691'_450 :: T_BoundedJoinSemilattice_414 -> AgdaAny -> AgdaAny
du_identity'691'_450 T_BoundedJoinSemilattice_414
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedJoinSemilattice_414 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedJoinSemilattice_438 (T_BoundedJoinSemilattice_414 -> T_BoundedJoinSemilattice_414
forall a b. a -> b
coe T_BoundedJoinSemilattice_414
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_728
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.identityˡ
d_identity'737'_452 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_414 -> AgdaAny -> AgdaAny
d_identity'737'_452 :: () -> () -> T_BoundedJoinSemilattice_414 -> AgdaAny -> AgdaAny
d_identity'737'_452 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_414
v2 = T_BoundedJoinSemilattice_414 -> AgdaAny -> AgdaAny
du_identity'737'_452 T_BoundedJoinSemilattice_414
v2
du_identity'737'_452 ::
  T_BoundedJoinSemilattice_414 -> AgdaAny -> AgdaAny
du_identity'737'_452 :: T_BoundedJoinSemilattice_414 -> AgdaAny -> AgdaAny
du_identity'737'_452 T_BoundedJoinSemilattice_414
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedJoinSemilattice_414 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedJoinSemilattice_438 (T_BoundedJoinSemilattice_414 -> T_BoundedJoinSemilattice_414
forall a b. a -> b
coe T_BoundedJoinSemilattice_414
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_726
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.isBand
d_isBand_454 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_414 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_508
d_isBand_454 :: () -> () -> T_BoundedJoinSemilattice_414 -> T_IsBand_508
d_isBand_454 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_414
v2 = T_BoundedJoinSemilattice_414 -> T_IsBand_508
du_isBand_454 T_BoundedJoinSemilattice_414
v2
du_isBand_454 ::
  T_BoundedJoinSemilattice_414 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_508
du_isBand_454 :: T_BoundedJoinSemilattice_414 -> T_IsBand_508
du_isBand_454 T_BoundedJoinSemilattice_414
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedJoinSemilattice_414 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedJoinSemilattice_438 (T_BoundedJoinSemilattice_414 -> T_BoundedJoinSemilattice_414
forall a b. a -> b
coe T_BoundedJoinSemilattice_414
v0) in
    AgdaAny -> T_IsBand_508
forall a b. a -> b
coe
      ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598
         ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1)))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.isEquivalence
d_isEquivalence_456 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_414 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_456 :: () -> () -> T_BoundedJoinSemilattice_414 -> T_IsEquivalence_26
d_isEquivalence_456 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_414
v2 = T_BoundedJoinSemilattice_414 -> T_IsEquivalence_26
du_isEquivalence_456 T_BoundedJoinSemilattice_414
v2
du_isEquivalence_456 ::
  T_BoundedJoinSemilattice_414 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_456 :: T_BoundedJoinSemilattice_414 -> T_IsEquivalence_26
du_isEquivalence_456 T_BoundedJoinSemilattice_414
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedJoinSemilattice_414 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedJoinSemilattice_438 (T_BoundedJoinSemilattice_414 -> T_BoundedJoinSemilattice_414
forall a b. a -> b
coe T_BoundedJoinSemilattice_414
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
                 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
               ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                  ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.isCommutativeBand
d_isCommutativeBand_458 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_414 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
d_isCommutativeBand_458 :: () -> () -> T_BoundedJoinSemilattice_414 -> T_IsCommutativeBand_590
d_isCommutativeBand_458 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_414
v2 = T_BoundedJoinSemilattice_414 -> T_IsCommutativeBand_590
du_isCommutativeBand_458 T_BoundedJoinSemilattice_414
v2
du_isCommutativeBand_458 ::
  T_BoundedJoinSemilattice_414 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
du_isCommutativeBand_458 :: T_BoundedJoinSemilattice_414 -> T_IsCommutativeBand_590
du_isCommutativeBand_458 T_BoundedJoinSemilattice_414
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedJoinSemilattice_414 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedJoinSemilattice_438 (T_BoundedJoinSemilattice_414 -> T_BoundedJoinSemilattice_414
forall a b. a -> b
coe T_BoundedJoinSemilattice_414
v0) in
    AgdaAny -> T_IsCommutativeBand_590
forall a b. a -> b
coe
      ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.isMagma
d_isMagma_460 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_414 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_460 :: () -> () -> T_BoundedJoinSemilattice_414 -> T_IsMagma_176
d_isMagma_460 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_414
v2 = T_BoundedJoinSemilattice_414 -> T_IsMagma_176
du_isMagma_460 T_BoundedJoinSemilattice_414
v2
du_isMagma_460 ::
  T_BoundedJoinSemilattice_414 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
du_isMagma_460 :: T_BoundedJoinSemilattice_414 -> T_IsMagma_176
du_isMagma_460 T_BoundedJoinSemilattice_414
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedJoinSemilattice_414 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedJoinSemilattice_438 (T_BoundedJoinSemilattice_414 -> T_BoundedJoinSemilattice_414
forall a b. a -> b
coe T_BoundedJoinSemilattice_414
v0) in
    AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
                 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
               ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2)))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.isPartialEquivalence
d_isPartialEquivalence_462 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_414 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_462 :: ()
-> () -> T_BoundedJoinSemilattice_414 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_462 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_414
v2
  = T_BoundedJoinSemilattice_414 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_462 T_BoundedJoinSemilattice_414
v2
du_isPartialEquivalence_462 ::
  T_BoundedJoinSemilattice_414 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_462 :: T_BoundedJoinSemilattice_414 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_462 T_BoundedJoinSemilattice_414
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedJoinSemilattice_414 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedJoinSemilattice_438 (T_BoundedJoinSemilattice_414 -> T_BoundedJoinSemilattice_414
forall a b. a -> b
coe T_BoundedJoinSemilattice_414
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
                 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsBand_508
v3 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> T_IsCommutativeBand_590
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_176
v5 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                     ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v5)))))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.isSemigroup
d_isSemigroup_464 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_414 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_464 :: () -> () -> T_BoundedJoinSemilattice_414 -> T_IsSemigroup_472
d_isSemigroup_464 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_414
v2 = T_BoundedJoinSemilattice_414 -> T_IsSemigroup_472
du_isSemigroup_464 T_BoundedJoinSemilattice_414
v2
du_isSemigroup_464 ::
  T_BoundedJoinSemilattice_414 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
du_isSemigroup_464 :: T_BoundedJoinSemilattice_414 -> T_IsSemigroup_472
du_isSemigroup_464 T_BoundedJoinSemilattice_414
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedJoinSemilattice_414 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedJoinSemilattice_438 (T_BoundedJoinSemilattice_414 -> T_BoundedJoinSemilattice_414
forall a b. a -> b
coe T_BoundedJoinSemilattice_414
v0) in
    AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
                 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
            ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.refl
d_refl_466 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_414 -> AgdaAny -> AgdaAny
d_refl_466 :: () -> () -> T_BoundedJoinSemilattice_414 -> AgdaAny -> AgdaAny
d_refl_466 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_414
v2 = T_BoundedJoinSemilattice_414 -> AgdaAny -> AgdaAny
du_refl_466 T_BoundedJoinSemilattice_414
v2
du_refl_466 :: T_BoundedJoinSemilattice_414 -> AgdaAny -> AgdaAny
du_refl_466 :: T_BoundedJoinSemilattice_414 -> AgdaAny -> AgdaAny
du_refl_466 T_BoundedJoinSemilattice_414
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedJoinSemilattice_414 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedJoinSemilattice_438 (T_BoundedJoinSemilattice_414 -> T_BoundedJoinSemilattice_414
forall a b. a -> b
coe T_BoundedJoinSemilattice_414
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
                 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
            ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
                  ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                     ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2)))))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.reflexive
d_reflexive_468 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_414 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_468 :: ()
-> ()
-> T_BoundedJoinSemilattice_414
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_468 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_414
v2 = T_BoundedJoinSemilattice_414
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_468 T_BoundedJoinSemilattice_414
v2
du_reflexive_468 ::
  T_BoundedJoinSemilattice_414 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_468 :: T_BoundedJoinSemilattice_414
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_468 T_BoundedJoinSemilattice_414
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedJoinSemilattice_414 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedJoinSemilattice_438 (T_BoundedJoinSemilattice_414 -> T_BoundedJoinSemilattice_414
forall a b. a -> b
coe T_BoundedJoinSemilattice_414
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
                 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsBand_508
v3 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> T_IsCommutativeBand_590
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_176
v5 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v4) in
                (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                  (\ AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 ->
                     (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                       ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v5))
                       AgdaAny
v6)))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.setoid
d_setoid_470 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_414 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_470 :: () -> () -> T_BoundedJoinSemilattice_414 -> T_Setoid_44
d_setoid_470 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_414
v2 = T_BoundedJoinSemilattice_414 -> T_Setoid_44
du_setoid_470 T_BoundedJoinSemilattice_414
v2
du_setoid_470 ::
  T_BoundedJoinSemilattice_414 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_470 :: T_BoundedJoinSemilattice_414 -> T_Setoid_44
du_setoid_470 T_BoundedJoinSemilattice_414
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedJoinSemilattice_414 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedJoinSemilattice_438 (T_BoundedJoinSemilattice_414 -> T_BoundedJoinSemilattice_414
forall a b. a -> b
coe T_BoundedJoinSemilattice_414
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
                 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsBand_508
v3 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> T_IsCommutativeBand_590
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                  ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.sym
d_sym_472 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_414 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_472 :: ()
-> ()
-> T_BoundedJoinSemilattice_414
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_472 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_414
v2 = T_BoundedJoinSemilattice_414
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_472 T_BoundedJoinSemilattice_414
v2
du_sym_472 ::
  T_BoundedJoinSemilattice_414 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_472 :: T_BoundedJoinSemilattice_414
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_472 T_BoundedJoinSemilattice_414
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedJoinSemilattice_414 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedJoinSemilattice_438 (T_BoundedJoinSemilattice_414 -> T_BoundedJoinSemilattice_414
forall a b. a -> b
coe T_BoundedJoinSemilattice_414
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
                 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
            ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
                  ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                     ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2)))))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.trans
d_trans_474 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_414 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_474 :: ()
-> ()
-> T_BoundedJoinSemilattice_414
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_474 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_414
v2 = T_BoundedJoinSemilattice_414
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_474 T_BoundedJoinSemilattice_414
v2
du_trans_474 ::
  T_BoundedJoinSemilattice_414 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_474 :: T_BoundedJoinSemilattice_414
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_474 T_BoundedJoinSemilattice_414
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedJoinSemilattice_414 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedJoinSemilattice_438 (T_BoundedJoinSemilattice_414 -> T_BoundedJoinSemilattice_414
forall a b. a -> b
coe T_BoundedJoinSemilattice_414
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
                 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
            ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
                  ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                     ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2)))))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.∙-cong
d_'8729''45'cong_476 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_414 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_476 :: ()
-> ()
-> T_BoundedJoinSemilattice_414
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_476 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_414
v2 = T_BoundedJoinSemilattice_414
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_476 T_BoundedJoinSemilattice_414
v2
du_'8729''45'cong_476 ::
  T_BoundedJoinSemilattice_414 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong_476 :: T_BoundedJoinSemilattice_414
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_476 T_BoundedJoinSemilattice_414
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedJoinSemilattice_414 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedJoinSemilattice_438 (T_BoundedJoinSemilattice_414 -> T_BoundedJoinSemilattice_414
forall a b. a -> b
coe T_BoundedJoinSemilattice_414
v0) in
    AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
                 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
               ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                  ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.∙-congʳ
d_'8729''45'cong'691'_478 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_414 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_478 :: ()
-> ()
-> T_BoundedJoinSemilattice_414
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_478 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_414
v2
  = T_BoundedJoinSemilattice_414
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_478 T_BoundedJoinSemilattice_414
v2
du_'8729''45'cong'691'_478 ::
  T_BoundedJoinSemilattice_414 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_478 :: T_BoundedJoinSemilattice_414
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_478 T_BoundedJoinSemilattice_414
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedJoinSemilattice_414 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedJoinSemilattice_438 (T_BoundedJoinSemilattice_414 -> T_BoundedJoinSemilattice_414
forall a b. a -> b
coe T_BoundedJoinSemilattice_414
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
                 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsBand_508
v3 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> T_IsCommutativeBand_590
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                  ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.∙-congˡ
d_'8729''45'cong'737'_480 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_414 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_480 :: ()
-> ()
-> T_BoundedJoinSemilattice_414
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_480 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_414
v2
  = T_BoundedJoinSemilattice_414
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_480 T_BoundedJoinSemilattice_414
v2
du_'8729''45'cong'737'_480 ::
  T_BoundedJoinSemilattice_414 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_480 :: T_BoundedJoinSemilattice_414
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_480 T_BoundedJoinSemilattice_414
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_BoundedJoinSemilattice_414 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedJoinSemilattice_438 (T_BoundedJoinSemilattice_414 -> T_BoundedJoinSemilattice_414
forall a b. a -> b
coe T_BoundedJoinSemilattice_414
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
                 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsBand_508
v3 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> T_IsCommutativeBand_590
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                  ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice.boundedSemilattice
d_boundedSemilattice_482 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_414 -> T_BoundedSemilattice_232
d_boundedSemilattice_482 :: ()
-> () -> T_BoundedJoinSemilattice_414 -> T_BoundedSemilattice_232
d_boundedSemilattice_482 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_414
v2 = T_BoundedJoinSemilattice_414 -> T_BoundedSemilattice_232
du_boundedSemilattice_482 T_BoundedJoinSemilattice_414
v2
du_boundedSemilattice_482 ::
  T_BoundedJoinSemilattice_414 -> T_BoundedSemilattice_232
du_boundedSemilattice_482 :: T_BoundedJoinSemilattice_414 -> T_BoundedSemilattice_232
du_boundedSemilattice_482 T_BoundedJoinSemilattice_414
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsIdempotentCommutativeMonoid_852
 -> T_BoundedSemilattice_232)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_BoundedSemilattice_232
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_BoundedSemilattice_232
C_BoundedSemilattice'46'constructor_3703 (T_BoundedJoinSemilattice_414 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__434 (T_BoundedJoinSemilattice_414 -> T_BoundedJoinSemilattice_414
forall a b. a -> b
coe T_BoundedJoinSemilattice_414
v0))
      (T_BoundedJoinSemilattice_414 -> AgdaAny
d_'8869'_436 (T_BoundedJoinSemilattice_414 -> T_BoundedJoinSemilattice_414
forall a b. a -> b
coe T_BoundedJoinSemilattice_414
v0)) (T_BoundedJoinSemilattice_414 -> T_IsIdempotentCommutativeMonoid_852
d_isBoundedJoinSemilattice_438 (T_BoundedJoinSemilattice_414 -> T_BoundedJoinSemilattice_414
forall a b. a -> b
coe T_BoundedJoinSemilattice_414
v0))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.band
d_band_486 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_414 ->
  MAlonzo.Code.Algebra.Bundles.T_Band_596
d_band_486 :: () -> () -> T_BoundedJoinSemilattice_414 -> T_Band_596
d_band_486 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_414
v2 = T_BoundedJoinSemilattice_414 -> T_Band_596
du_band_486 T_BoundedJoinSemilattice_414
v2
du_band_486 ::
  T_BoundedJoinSemilattice_414 ->
  MAlonzo.Code.Algebra.Bundles.T_Band_596
du_band_486 :: T_BoundedJoinSemilattice_414 -> T_Band_596
du_band_486 T_BoundedJoinSemilattice_414
v0
  = let v1 :: t
v1 = (T_BoundedJoinSemilattice_414 -> T_BoundedSemilattice_232)
-> AgdaAny -> t
forall a b. a -> b
coe T_BoundedJoinSemilattice_414 -> T_BoundedSemilattice_232
du_boundedSemilattice_482 (T_BoundedJoinSemilattice_414 -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_414
v0) in
    AgdaAny -> T_Band_596
forall a b. a -> b
coe ((T_Semilattice_10 -> T_Band_596) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_596
du_band_66 ((T_BoundedSemilattice_232 -> T_Semilattice_10)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedSemilattice_232 -> T_Semilattice_10
du_semilattice_312 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.magma
d_magma_488 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_414 ->
  MAlonzo.Code.Algebra.Bundles.T_Magma_68
d_magma_488 :: () -> () -> T_BoundedJoinSemilattice_414 -> T_Magma_68
d_magma_488 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_414
v2 = T_BoundedJoinSemilattice_414 -> T_Magma_68
du_magma_488 T_BoundedJoinSemilattice_414
v2
du_magma_488 ::
  T_BoundedJoinSemilattice_414 ->
  MAlonzo.Code.Algebra.Bundles.T_Magma_68
du_magma_488 :: T_BoundedJoinSemilattice_414 -> T_Magma_68
du_magma_488 T_BoundedJoinSemilattice_414
v0
  = let v1 :: t
v1 = (T_BoundedJoinSemilattice_414 -> T_BoundedSemilattice_232)
-> AgdaAny -> t
forall a b. a -> b
coe T_BoundedJoinSemilattice_414 -> T_BoundedSemilattice_232
du_boundedSemilattice_482 (T_BoundedJoinSemilattice_414 -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_414
v0) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_BoundedSemilattice_232 -> T_Semilattice_10) -> AgdaAny -> t
forall a b. a -> b
coe T_BoundedSemilattice_232 -> T_Semilattice_10
du_semilattice_312 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semilattice_10 -> T_Band_596) -> AgdaAny -> t
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_596
du_band_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Semigroup_536 -> T_Magma_68
MAlonzo.Code.Algebra.Bundles.du_magma_584
               ((T_Band_596 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_596 -> T_Semigroup_536
MAlonzo.Code.Algebra.Bundles.du_semigroup_648 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.rawMagma
d_rawMagma_490 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_414 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_490 :: () -> () -> T_BoundedJoinSemilattice_414 -> T_RawMagma_36
d_rawMagma_490 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_414
v2 = T_BoundedJoinSemilattice_414 -> T_RawMagma_36
du_rawMagma_490 T_BoundedJoinSemilattice_414
v2
du_rawMagma_490 ::
  T_BoundedJoinSemilattice_414 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_490 :: T_BoundedJoinSemilattice_414 -> T_RawMagma_36
du_rawMagma_490 T_BoundedJoinSemilattice_414
v0
  = let v1 :: t
v1 = (T_BoundedJoinSemilattice_414 -> T_BoundedSemilattice_232)
-> AgdaAny -> t
forall a b. a -> b
coe T_BoundedJoinSemilattice_414 -> T_BoundedSemilattice_232
du_boundedSemilattice_482 (T_BoundedJoinSemilattice_414 -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_414
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_BoundedSemilattice_232 -> T_Semilattice_10) -> AgdaAny -> t
forall a b. a -> b
coe T_BoundedSemilattice_232 -> T_Semilattice_10
du_semilattice_312 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semilattice_10 -> T_Band_596) -> AgdaAny -> t
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_596
du_band_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4
                   = (T_Band_596 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_Band_596 -> T_Semigroup_536
MAlonzo.Code.Algebra.Bundles.du_semigroup_648 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Magma_68 -> T_RawMagma_36
MAlonzo.Code.Algebra.Bundles.du_rawMagma_112
                  ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
MAlonzo.Code.Algebra.Bundles.du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.semigroup
d_semigroup_492 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_414 ->
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_536
d_semigroup_492 :: () -> () -> T_BoundedJoinSemilattice_414 -> T_Semigroup_536
d_semigroup_492 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_414
v2 = T_BoundedJoinSemilattice_414 -> T_Semigroup_536
du_semigroup_492 T_BoundedJoinSemilattice_414
v2
du_semigroup_492 ::
  T_BoundedJoinSemilattice_414 ->
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_536
du_semigroup_492 :: T_BoundedJoinSemilattice_414 -> T_Semigroup_536
du_semigroup_492 T_BoundedJoinSemilattice_414
v0
  = let v1 :: t
v1 = (T_BoundedJoinSemilattice_414 -> T_BoundedSemilattice_232)
-> AgdaAny -> t
forall a b. a -> b
coe T_BoundedJoinSemilattice_414 -> T_BoundedSemilattice_232
du_boundedSemilattice_482 (T_BoundedJoinSemilattice_414 -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_414
v0) in
    AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_BoundedSemilattice_232 -> T_Semilattice_10) -> AgdaAny -> t
forall a b. a -> b
coe T_BoundedSemilattice_232 -> T_Semilattice_10
du_semilattice_312 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Band_596 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Band_596 -> T_Semigroup_536
MAlonzo.Code.Algebra.Bundles.du_semigroup_648
            ((T_Semilattice_10 -> T_Band_596) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_10 -> T_Band_596
du_band_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Lattice.Bundles.BoundedJoinSemilattice._.semilattice
d_semilattice_494 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_414 -> T_Semilattice_10
d_semilattice_494 :: () -> () -> T_BoundedJoinSemilattice_414 -> T_Semilattice_10
d_semilattice_494 ~()
v0 ~()
v1 T_BoundedJoinSemilattice_414
v2 = T_BoundedJoinSemilattice_414 -> T_Semilattice_10
du_semilattice_494 T_BoundedJoinSemilattice_414
v2
du_semilattice_494 ::
  T_BoundedJoinSemilattice_414 -> T_Semilattice_10
du_semilattice_494 :: T_BoundedJoinSemilattice_414 -> T_Semilattice_10
du_semilattice_494 T_BoundedJoinSemilattice_414
v0
  = (T_BoundedSemilattice_232 -> T_Semilattice_10)
-> AgdaAny -> T_Semilattice_10
forall a b. a -> b
coe T_BoundedSemilattice_232 -> T_Semilattice_10
du_semilattice_312 ((T_BoundedJoinSemilattice_414 -> T_BoundedSemilattice_232)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_414 -> T_BoundedSemilattice_232
du_boundedSemilattice_482 (T_BoundedJoinSemilattice_414 -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_414
v0))
-- Algebra.Lattice.Bundles.Lattice
d_Lattice_500 :: p -> p -> ()
d_Lattice_500 p
a0 p
a1 = ()
data T_Lattice_500
  = C_Lattice'46'constructor_7925 (AgdaAny -> AgdaAny -> AgdaAny)
                                  (AgdaAny -> AgdaAny -> AgdaAny)
                                  MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_2962
-- Algebra.Lattice.Bundles.Lattice.Carrier
d_Carrier_516 :: T_Lattice_500 -> ()
d_Carrier_516 :: T_Lattice_500 -> ()
d_Carrier_516 = T_Lattice_500 -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.Lattice._≈_
d__'8776'__518 :: T_Lattice_500 -> AgdaAny -> AgdaAny -> ()
d__'8776'__518 :: T_Lattice_500 -> AgdaAny -> AgdaAny -> ()
d__'8776'__518 = T_Lattice_500 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.Lattice._∨_
d__'8744'__520 :: T_Lattice_500 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__520 :: T_Lattice_500 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__520 T_Lattice_500
v0
  = case T_Lattice_500 -> T_Lattice_500
forall a b. a -> b
coe T_Lattice_500
v0 of
      C_Lattice'46'constructor_7925 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsLattice_2962
v5 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_Lattice_500
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.Lattice._∧_
d__'8743'__522 :: T_Lattice_500 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__522 :: T_Lattice_500 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__522 T_Lattice_500
v0
  = case T_Lattice_500 -> T_Lattice_500
forall a b. a -> b
coe T_Lattice_500
v0 of
      C_Lattice'46'constructor_7925 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsLattice_2962
v5 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_Lattice_500
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.Lattice.isLattice
d_isLattice_524 ::
  T_Lattice_500 ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_2962
d_isLattice_524 :: T_Lattice_500 -> T_IsLattice_2962
d_isLattice_524 T_Lattice_500
v0
  = case T_Lattice_500 -> T_Lattice_500
forall a b. a -> b
coe T_Lattice_500
v0 of
      C_Lattice'46'constructor_7925 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsLattice_2962
v5 -> T_IsLattice_2962 -> T_IsLattice_2962
forall a b. a -> b
coe T_IsLattice_2962
v5
      T_Lattice_500
_ -> T_IsLattice_2962
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.Lattice._.absorptive
d_absorptive_528 ::
  T_Lattice_500 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_absorptive_528 :: T_Lattice_500 -> T_Σ_14
d_absorptive_528 T_Lattice_500
v0
  = (T_IsLattice_2962 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsLattice_2962 -> T_Σ_14
MAlonzo.Code.Algebra.Lattice.Structures.d_absorptive_2998
      ((T_Lattice_500 -> T_IsLattice_2962) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_500 -> T_IsLattice_2962
d_isLattice_524 (T_Lattice_500 -> AgdaAny
forall a b. a -> b
coe T_Lattice_500
v0))
-- Algebra.Lattice.Bundles.Lattice._.isEquivalence
d_isEquivalence_530 ::
  T_Lattice_500 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_530 :: T_Lattice_500 -> T_IsEquivalence_26
d_isEquivalence_530 T_Lattice_500
v0
  = (T_IsLattice_2962 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsLattice_2962 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
      ((T_Lattice_500 -> T_IsLattice_2962) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_500 -> T_IsLattice_2962
d_isLattice_524 (T_Lattice_500 -> AgdaAny
forall a b. a -> b
coe T_Lattice_500
v0))
-- Algebra.Lattice.Bundles.Lattice._.isPartialEquivalence
d_isPartialEquivalence_532 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_500 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_532 :: () -> () -> T_Lattice_500 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_532 ~()
v0 ~()
v1 T_Lattice_500
v2
  = T_Lattice_500 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_532 T_Lattice_500
v2
du_isPartialEquivalence_532 ::
  T_Lattice_500 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_532 :: T_Lattice_500 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_532 T_Lattice_500
v0
  = let v1 :: T_IsLattice_2962
v1 = T_Lattice_500 -> T_IsLattice_2962
d_isLattice_524 (T_Lattice_500 -> T_Lattice_500
forall a b. a -> b
coe T_Lattice_500
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
         ((T_IsLattice_2962 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_2962 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
            (T_IsLattice_2962 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962
v1)))
-- Algebra.Lattice.Bundles.Lattice._.refl
d_refl_534 :: T_Lattice_500 -> AgdaAny -> AgdaAny
d_refl_534 :: T_Lattice_500 -> AgdaAny -> AgdaAny
d_refl_534 T_Lattice_500
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsLattice_2962 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_2962 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
         ((T_Lattice_500 -> T_IsLattice_2962) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_500 -> T_IsLattice_2962
d_isLattice_524 (T_Lattice_500 -> AgdaAny
forall a b. a -> b
coe T_Lattice_500
v0)))
-- Algebra.Lattice.Bundles.Lattice._.reflexive
d_reflexive_536 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_500 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_536 :: ()
-> ()
-> T_Lattice_500
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_536 ~()
v0 ~()
v1 T_Lattice_500
v2 = T_Lattice_500 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_536 T_Lattice_500
v2
du_reflexive_536 ::
  T_Lattice_500 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_536 :: T_Lattice_500 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_536 T_Lattice_500
v0
  = let v1 :: T_IsLattice_2962
v1 = T_Lattice_500 -> T_IsLattice_2962
d_isLattice_524 (T_Lattice_500 -> T_Lattice_500
forall a b. a -> b
coe T_Lattice_500
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_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
           ((T_IsLattice_2962 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsLattice_2962 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
              (T_IsLattice_2962 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962
v1))
           AgdaAny
v2)
-- Algebra.Lattice.Bundles.Lattice._.sym
d_sym_538 ::
  T_Lattice_500 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_538 :: T_Lattice_500 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_538 T_Lattice_500
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsLattice_2962 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_2962 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
         ((T_Lattice_500 -> T_IsLattice_2962) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_500 -> T_IsLattice_2962
d_isLattice_524 (T_Lattice_500 -> AgdaAny
forall a b. a -> b
coe T_Lattice_500
v0)))
-- Algebra.Lattice.Bundles.Lattice._.trans
d_trans_540 ::
  T_Lattice_500 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_540 :: T_Lattice_500
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_540 T_Lattice_500
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsLattice_2962 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_2962 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
         ((T_Lattice_500 -> T_IsLattice_2962) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_500 -> T_IsLattice_2962
d_isLattice_524 (T_Lattice_500 -> AgdaAny
forall a b. a -> b
coe T_Lattice_500
v0)))
-- Algebra.Lattice.Bundles.Lattice._.∧-absorbs-∨
d_'8743''45'absorbs'45''8744'_542 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_500 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'absorbs'45''8744'_542 :: () -> () -> T_Lattice_500 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'absorbs'45''8744'_542 ~()
v0 ~()
v1 T_Lattice_500
v2
  = T_Lattice_500 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_542 T_Lattice_500
v2
du_'8743''45'absorbs'45''8744'_542 ::
  T_Lattice_500 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_542 :: T_Lattice_500 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_542 T_Lattice_500
v0
  = (T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'absorbs'45''8744'_3014
      ((T_Lattice_500 -> T_IsLattice_2962) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_500 -> T_IsLattice_2962
d_isLattice_524 (T_Lattice_500 -> AgdaAny
forall a b. a -> b
coe T_Lattice_500
v0))
-- Algebra.Lattice.Bundles.Lattice._.∧-assoc
d_'8743''45'assoc_544 ::
  T_Lattice_500 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_544 :: T_Lattice_500 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_544 T_Lattice_500
v0
  = (T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'assoc_2994
      ((T_Lattice_500 -> T_IsLattice_2962) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_500 -> T_IsLattice_2962
d_isLattice_524 (T_Lattice_500 -> AgdaAny
forall a b. a -> b
coe T_Lattice_500
v0))
-- Algebra.Lattice.Bundles.Lattice._.∧-comm
d_'8743''45'comm_546 ::
  T_Lattice_500 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_546 :: T_Lattice_500 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_546 T_Lattice_500
v0
  = (T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'comm_2992
      ((T_Lattice_500 -> T_IsLattice_2962) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_500 -> T_IsLattice_2962
d_isLattice_524 (T_Lattice_500 -> AgdaAny
forall a b. a -> b
coe T_Lattice_500
v0))
-- Algebra.Lattice.Bundles.Lattice._.∧-cong
d_'8743''45'cong_548 ::
  T_Lattice_500 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong_548 :: T_Lattice_500
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong_548 T_Lattice_500
v0
  = (T_IsLattice_2962
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_2962
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'cong_2996
      ((T_Lattice_500 -> T_IsLattice_2962) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_500 -> T_IsLattice_2962
d_isLattice_524 (T_Lattice_500 -> AgdaAny
forall a b. a -> b
coe T_Lattice_500
v0))
-- Algebra.Lattice.Bundles.Lattice._.∧-congʳ
d_'8743''45'cong'691'_550 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_500 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong'691'_550 :: ()
-> ()
-> T_Lattice_500
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong'691'_550 ~()
v0 ~()
v1 T_Lattice_500
v2
  = T_Lattice_500
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_550 T_Lattice_500
v2
du_'8743''45'cong'691'_550 ::
  T_Lattice_500 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_550 :: T_Lattice_500
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_550 T_Lattice_500
v0
  = (T_IsLattice_2962
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_2962
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'cong'691'_3020
      ((T_Lattice_500 -> T_IsLattice_2962) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_500 -> T_IsLattice_2962
d_isLattice_524 (T_Lattice_500 -> AgdaAny
forall a b. a -> b
coe T_Lattice_500
v0))
-- Algebra.Lattice.Bundles.Lattice._.∧-congˡ
d_'8743''45'cong'737'_552 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_500 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong'737'_552 :: ()
-> ()
-> T_Lattice_500
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong'737'_552 ~()
v0 ~()
v1 T_Lattice_500
v2
  = T_Lattice_500
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_552 T_Lattice_500
v2
du_'8743''45'cong'737'_552 ::
  T_Lattice_500 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_552 :: T_Lattice_500
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_552 T_Lattice_500
v0
  = (T_IsLattice_2962
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_2962
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'cong'737'_3016
      ((T_Lattice_500 -> T_IsLattice_2962) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_500 -> T_IsLattice_2962
d_isLattice_524 (T_Lattice_500 -> AgdaAny
forall a b. a -> b
coe T_Lattice_500
v0))
-- Algebra.Lattice.Bundles.Lattice._.∨-absorbs-∧
d_'8744''45'absorbs'45''8743'_554 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_500 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'absorbs'45''8743'_554 :: () -> () -> T_Lattice_500 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'absorbs'45''8743'_554 ~()
v0 ~()
v1 T_Lattice_500
v2
  = T_Lattice_500 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_554 T_Lattice_500
v2
du_'8744''45'absorbs'45''8743'_554 ::
  T_Lattice_500 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_554 :: T_Lattice_500 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_554 T_Lattice_500
v0
  = (T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'absorbs'45''8743'_3012
      ((T_Lattice_500 -> T_IsLattice_2962) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_500 -> T_IsLattice_2962
d_isLattice_524 (T_Lattice_500 -> AgdaAny
forall a b. a -> b
coe T_Lattice_500
v0))
-- Algebra.Lattice.Bundles.Lattice._.∨-assoc
d_'8744''45'assoc_556 ::
  T_Lattice_500 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_556 :: T_Lattice_500 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_556 T_Lattice_500
v0
  = (T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'assoc_2988
      ((T_Lattice_500 -> T_IsLattice_2962) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_500 -> T_IsLattice_2962
d_isLattice_524 (T_Lattice_500 -> AgdaAny
forall a b. a -> b
coe T_Lattice_500
v0))
-- Algebra.Lattice.Bundles.Lattice._.∨-comm
d_'8744''45'comm_558 ::
  T_Lattice_500 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_558 :: T_Lattice_500 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_558 T_Lattice_500
v0
  = (T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'comm_2986
      ((T_Lattice_500 -> T_IsLattice_2962) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_500 -> T_IsLattice_2962
d_isLattice_524 (T_Lattice_500 -> AgdaAny
forall a b. a -> b
coe T_Lattice_500
v0))
-- Algebra.Lattice.Bundles.Lattice._.∨-cong
d_'8744''45'cong_560 ::
  T_Lattice_500 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong_560 :: T_Lattice_500
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong_560 T_Lattice_500
v0
  = (T_IsLattice_2962
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_2962
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'cong_2990
      ((T_Lattice_500 -> T_IsLattice_2962) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_500 -> T_IsLattice_2962
d_isLattice_524 (T_Lattice_500 -> AgdaAny
forall a b. a -> b
coe T_Lattice_500
v0))
-- Algebra.Lattice.Bundles.Lattice._.∨-congʳ
d_'8744''45'cong'691'_562 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_500 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong'691'_562 :: ()
-> ()
-> T_Lattice_500
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong'691'_562 ~()
v0 ~()
v1 T_Lattice_500
v2
  = T_Lattice_500
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_562 T_Lattice_500
v2
du_'8744''45'cong'691'_562 ::
  T_Lattice_500 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_562 :: T_Lattice_500
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_562 T_Lattice_500
v0
  = (T_IsLattice_2962
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_2962
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'cong'691'_3028
      ((T_Lattice_500 -> T_IsLattice_2962) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_500 -> T_IsLattice_2962
d_isLattice_524 (T_Lattice_500 -> AgdaAny
forall a b. a -> b
coe T_Lattice_500
v0))
-- Algebra.Lattice.Bundles.Lattice._.∨-congˡ
d_'8744''45'cong'737'_564 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_500 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong'737'_564 :: ()
-> ()
-> T_Lattice_500
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong'737'_564 ~()
v0 ~()
v1 T_Lattice_500
v2
  = T_Lattice_500
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_564 T_Lattice_500
v2
du_'8744''45'cong'737'_564 ::
  T_Lattice_500 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_564 :: T_Lattice_500
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_564 T_Lattice_500
v0
  = (T_IsLattice_2962
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_2962
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'cong'737'_3024
      ((T_Lattice_500 -> T_IsLattice_2962) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_500 -> T_IsLattice_2962
d_isLattice_524 (T_Lattice_500 -> AgdaAny
forall a b. a -> b
coe T_Lattice_500
v0))
-- Algebra.Lattice.Bundles.Lattice.rawLattice
d_rawLattice_566 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_500 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.Raw.T_RawLattice_12
d_rawLattice_566 :: () -> () -> T_Lattice_500 -> T_RawLattice_12
d_rawLattice_566 ~()
v0 ~()
v1 T_Lattice_500
v2 = T_Lattice_500 -> T_RawLattice_12
du_rawLattice_566 T_Lattice_500
v2
du_rawLattice_566 ::
  T_Lattice_500 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.Raw.T_RawLattice_12
du_rawLattice_566 :: T_Lattice_500 -> T_RawLattice_12
du_rawLattice_566 T_Lattice_500
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_RawLattice'46'constructor_121
      (T_Lattice_500 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__522 (T_Lattice_500 -> T_Lattice_500
forall a b. a -> b
coe T_Lattice_500
v0)) (T_Lattice_500 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__520 (T_Lattice_500 -> T_Lattice_500
forall a b. a -> b
coe T_Lattice_500
v0))
-- Algebra.Lattice.Bundles.Lattice._.∧-rawMagma
d_'8743''45'rawMagma_570 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_500 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_'8743''45'rawMagma_570 :: () -> () -> T_Lattice_500 -> T_RawMagma_36
d_'8743''45'rawMagma_570 ~()
v0 ~()
v1 T_Lattice_500
v2 = T_Lattice_500 -> T_RawMagma_36
du_'8743''45'rawMagma_570 T_Lattice_500
v2
du_'8743''45'rawMagma_570 ::
  T_Lattice_500 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_'8743''45'rawMagma_570 :: T_Lattice_500 -> T_RawMagma_36
du_'8743''45'rawMagma_570 T_Lattice_500
v0
  = (T_RawLattice_12 -> T_RawMagma_36) -> AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      T_RawLattice_12 -> T_RawMagma_36
MAlonzo.Code.Algebra.Lattice.Bundles.Raw.du_'8743''45'rawMagma_36
      ((T_Lattice_500 -> T_RawLattice_12) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_500 -> T_RawLattice_12
du_rawLattice_566 (T_Lattice_500 -> AgdaAny
forall a b. a -> b
coe T_Lattice_500
v0))
-- Algebra.Lattice.Bundles.Lattice._.∨-rawMagma
d_'8744''45'rawMagma_572 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_500 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_'8744''45'rawMagma_572 :: () -> () -> T_Lattice_500 -> T_RawMagma_36
d_'8744''45'rawMagma_572 ~()
v0 ~()
v1 T_Lattice_500
v2 = T_Lattice_500 -> T_RawMagma_36
du_'8744''45'rawMagma_572 T_Lattice_500
v2
du_'8744''45'rawMagma_572 ::
  T_Lattice_500 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_'8744''45'rawMagma_572 :: T_Lattice_500 -> T_RawMagma_36
du_'8744''45'rawMagma_572 T_Lattice_500
v0
  = (T_RawLattice_12 -> T_RawMagma_36) -> AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      T_RawLattice_12 -> T_RawMagma_36
MAlonzo.Code.Algebra.Lattice.Bundles.Raw.du_'8744''45'rawMagma_34
      ((T_Lattice_500 -> T_RawLattice_12) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_500 -> T_RawLattice_12
du_rawLattice_566 (T_Lattice_500 -> AgdaAny
forall a b. a -> b
coe T_Lattice_500
v0))
-- Algebra.Lattice.Bundles.Lattice.setoid
d_setoid_574 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_500 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_574 :: () -> () -> T_Lattice_500 -> T_Setoid_44
d_setoid_574 ~()
v0 ~()
v1 T_Lattice_500
v2 = T_Lattice_500 -> T_Setoid_44
du_setoid_574 T_Lattice_500
v2
du_setoid_574 ::
  T_Lattice_500 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_574 :: T_Lattice_500 -> T_Setoid_44
du_setoid_574 T_Lattice_500
v0
  = (T_IsEquivalence_26 -> T_Setoid_44)
-> T_IsEquivalence_26 -> T_Setoid_44
forall a b. a -> b
coe
      T_IsEquivalence_26 -> T_Setoid_44
MAlonzo.Code.Relation.Binary.Bundles.C_Setoid'46'constructor_733
      (T_IsLattice_2962 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
         ((T_Lattice_500 -> T_IsLattice_2962) -> AgdaAny -> T_IsLattice_2962
forall a b. a -> b
coe T_Lattice_500 -> T_IsLattice_2962
d_isLattice_524 (T_Lattice_500 -> AgdaAny
forall a b. a -> b
coe T_Lattice_500
v0)))
-- Algebra.Lattice.Bundles.Lattice._._≉_
d__'8777'__578 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_500 -> AgdaAny -> AgdaAny -> ()
d__'8777'__578 :: () -> () -> T_Lattice_500 -> AgdaAny -> AgdaAny -> ()
d__'8777'__578 = () -> () -> T_Lattice_500 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.DistributiveLattice
d_DistributiveLattice_584 :: p -> p -> ()
d_DistributiveLattice_584 p
a0 p
a1 = ()
data T_DistributiveLattice_584
  = C_DistributiveLattice'46'constructor_9515 (AgdaAny ->
                                               AgdaAny -> AgdaAny)
                                              (AgdaAny -> AgdaAny -> AgdaAny)
                                              MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3036
-- Algebra.Lattice.Bundles.DistributiveLattice.Carrier
d_Carrier_600 :: T_DistributiveLattice_584 -> ()
d_Carrier_600 :: T_DistributiveLattice_584 -> ()
d_Carrier_600 = T_DistributiveLattice_584 -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.DistributiveLattice._≈_
d__'8776'__602 ::
  T_DistributiveLattice_584 -> AgdaAny -> AgdaAny -> ()
d__'8776'__602 :: T_DistributiveLattice_584 -> AgdaAny -> AgdaAny -> ()
d__'8776'__602 = T_DistributiveLattice_584 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.DistributiveLattice._∨_
d__'8744'__604 ::
  T_DistributiveLattice_584 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__604 :: T_DistributiveLattice_584 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__604 T_DistributiveLattice_584
v0
  = case T_DistributiveLattice_584 -> T_DistributiveLattice_584
forall a b. a -> b
coe T_DistributiveLattice_584
v0 of
      C_DistributiveLattice'46'constructor_9515 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsDistributiveLattice_3036
v5 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_DistributiveLattice_584
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.DistributiveLattice._∧_
d__'8743'__606 ::
  T_DistributiveLattice_584 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__606 :: T_DistributiveLattice_584 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__606 T_DistributiveLattice_584
v0
  = case T_DistributiveLattice_584 -> T_DistributiveLattice_584
forall a b. a -> b
coe T_DistributiveLattice_584
v0 of
      C_DistributiveLattice'46'constructor_9515 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsDistributiveLattice_3036
v5 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_DistributiveLattice_584
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.DistributiveLattice.isDistributiveLattice
d_isDistributiveLattice_608 ::
  T_DistributiveLattice_584 ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3036
d_isDistributiveLattice_608 :: T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_608 T_DistributiveLattice_584
v0
  = case T_DistributiveLattice_584 -> T_DistributiveLattice_584
forall a b. a -> b
coe T_DistributiveLattice_584
v0 of
      C_DistributiveLattice'46'constructor_9515 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsDistributiveLattice_3036
v5 -> T_IsDistributiveLattice_3036 -> T_IsDistributiveLattice_3036
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v5
      T_DistributiveLattice_584
_ -> T_IsDistributiveLattice_3036
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.DistributiveLattice._.absorptive
d_absorptive_612 ::
  T_DistributiveLattice_584 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_absorptive_612 :: T_DistributiveLattice_584 -> T_Σ_14
d_absorptive_612 T_DistributiveLattice_584
v0
  = (T_IsLattice_2962 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsLattice_2962 -> T_Σ_14
MAlonzo.Code.Algebra.Lattice.Structures.d_absorptive_2998
      ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048
         ((T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_608 (T_DistributiveLattice_584 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584
v0)))
-- Algebra.Lattice.Bundles.DistributiveLattice._.isEquivalence
d_isEquivalence_614 ::
  T_DistributiveLattice_584 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_614 :: T_DistributiveLattice_584 -> T_IsEquivalence_26
d_isEquivalence_614 T_DistributiveLattice_584
v0
  = (T_IsLattice_2962 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsLattice_2962 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
      ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048
         ((T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_608 (T_DistributiveLattice_584 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584
v0)))
-- Algebra.Lattice.Bundles.DistributiveLattice._.isLattice
d_isLattice_616 ::
  T_DistributiveLattice_584 ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_2962
d_isLattice_616 :: T_DistributiveLattice_584 -> T_IsLattice_2962
d_isLattice_616 T_DistributiveLattice_584
v0
  = (T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> T_IsLattice_2962
forall a b. a -> b
coe
      T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048
      ((T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_608 (T_DistributiveLattice_584 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584
v0))
-- Algebra.Lattice.Bundles.DistributiveLattice._.isPartialEquivalence
d_isPartialEquivalence_618 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_584 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_618 :: () -> () -> T_DistributiveLattice_584 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_618 ~()
v0 ~()
v1 T_DistributiveLattice_584
v2
  = T_DistributiveLattice_584 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_618 T_DistributiveLattice_584
v2
du_isPartialEquivalence_618 ::
  T_DistributiveLattice_584 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_618 :: T_DistributiveLattice_584 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_618 T_DistributiveLattice_584
v0
  = let v1 :: T_IsDistributiveLattice_3036
v1 = T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_608 (T_DistributiveLattice_584 -> T_DistributiveLattice_584
forall a b. a -> b
coe T_DistributiveLattice_584
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_2962
v2
             = T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048
                 (T_IsDistributiveLattice_3036 -> T_IsDistributiveLattice_3036
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((T_IsLattice_2962 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_2962 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
               (T_IsLattice_2962 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962
v2))))
-- Algebra.Lattice.Bundles.DistributiveLattice._.refl
d_refl_620 :: T_DistributiveLattice_584 -> AgdaAny -> AgdaAny
d_refl_620 :: T_DistributiveLattice_584 -> AgdaAny -> AgdaAny
d_refl_620 T_DistributiveLattice_584
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsLattice_2962 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_2962 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
         ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048
            ((T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_608 (T_DistributiveLattice_584 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584
v0))))
-- Algebra.Lattice.Bundles.DistributiveLattice._.reflexive
d_reflexive_622 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_584 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_622 :: ()
-> ()
-> T_DistributiveLattice_584
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_622 ~()
v0 ~()
v1 T_DistributiveLattice_584
v2 = T_DistributiveLattice_584
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_622 T_DistributiveLattice_584
v2
du_reflexive_622 ::
  T_DistributiveLattice_584 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_622 :: T_DistributiveLattice_584
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_622 T_DistributiveLattice_584
v0
  = let v1 :: T_IsDistributiveLattice_3036
v1 = T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_608 (T_DistributiveLattice_584 -> T_DistributiveLattice_584
forall a b. a -> b
coe T_DistributiveLattice_584
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_2962
v2
             = T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048
                 (T_IsDistributiveLattice_3036 -> T_IsDistributiveLattice_3036
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((T_IsLattice_2962 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsLattice_2962 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
                 (T_IsLattice_2962 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962
v2))
              AgdaAny
v3))
-- Algebra.Lattice.Bundles.DistributiveLattice._.sym
d_sym_624 ::
  T_DistributiveLattice_584 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_624 :: T_DistributiveLattice_584
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_624 T_DistributiveLattice_584
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsLattice_2962 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_2962 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
         ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048
            ((T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_608 (T_DistributiveLattice_584 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584
v0))))
-- Algebra.Lattice.Bundles.DistributiveLattice._.trans
d_trans_626 ::
  T_DistributiveLattice_584 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_626 :: T_DistributiveLattice_584
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_626 T_DistributiveLattice_584
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsLattice_2962 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_2962 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
         ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048
            ((T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_608 (T_DistributiveLattice_584 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584
v0))))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∧-absorbs-∨
d_'8743''45'absorbs'45''8744'_628 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_584 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'absorbs'45''8744'_628 :: ()
-> () -> T_DistributiveLattice_584 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'absorbs'45''8744'_628 ~()
v0 ~()
v1 T_DistributiveLattice_584
v2
  = T_DistributiveLattice_584 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_628 T_DistributiveLattice_584
v2
du_'8743''45'absorbs'45''8744'_628 ::
  T_DistributiveLattice_584 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_628 :: T_DistributiveLattice_584 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_628 T_DistributiveLattice_584
v0
  = let v1 :: T_IsDistributiveLattice_3036
v1 = T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_608 (T_DistributiveLattice_584 -> T_DistributiveLattice_584
forall a b. a -> b
coe T_DistributiveLattice_584
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'absorbs'45''8744'_3014
         ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048 (T_IsDistributiveLattice_3036 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v1)))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∧-assoc
d_'8743''45'assoc_630 ::
  T_DistributiveLattice_584 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_630 :: T_DistributiveLattice_584
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_630 T_DistributiveLattice_584
v0
  = (T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'assoc_2994
      ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048
         ((T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_608 (T_DistributiveLattice_584 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584
v0)))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∧-comm
d_'8743''45'comm_632 ::
  T_DistributiveLattice_584 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_632 :: T_DistributiveLattice_584 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_632 T_DistributiveLattice_584
v0
  = (T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'comm_2992
      ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048
         ((T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_608 (T_DistributiveLattice_584 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584
v0)))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∧-cong
d_'8743''45'cong_634 ::
  T_DistributiveLattice_584 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong_634 :: T_DistributiveLattice_584
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong_634 T_DistributiveLattice_584
v0
  = (T_IsLattice_2962
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_2962
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'cong_2996
      ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048
         ((T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_608 (T_DistributiveLattice_584 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584
v0)))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∧-congʳ
d_'8743''45'cong'691'_636 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_584 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong'691'_636 :: ()
-> ()
-> T_DistributiveLattice_584
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong'691'_636 ~()
v0 ~()
v1 T_DistributiveLattice_584
v2
  = T_DistributiveLattice_584
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_636 T_DistributiveLattice_584
v2
du_'8743''45'cong'691'_636 ::
  T_DistributiveLattice_584 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_636 :: T_DistributiveLattice_584
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_636 T_DistributiveLattice_584
v0
  = let v1 :: T_IsDistributiveLattice_3036
v1 = T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_608 (T_DistributiveLattice_584 -> T_DistributiveLattice_584
forall a b. a -> b
coe T_DistributiveLattice_584
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsLattice_2962
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_2962
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'cong'691'_3020
         ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048 (T_IsDistributiveLattice_3036 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v1)))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∧-congˡ
d_'8743''45'cong'737'_638 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_584 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong'737'_638 :: ()
-> ()
-> T_DistributiveLattice_584
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong'737'_638 ~()
v0 ~()
v1 T_DistributiveLattice_584
v2
  = T_DistributiveLattice_584
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_638 T_DistributiveLattice_584
v2
du_'8743''45'cong'737'_638 ::
  T_DistributiveLattice_584 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_638 :: T_DistributiveLattice_584
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_638 T_DistributiveLattice_584
v0
  = let v1 :: T_IsDistributiveLattice_3036
v1 = T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_608 (T_DistributiveLattice_584 -> T_DistributiveLattice_584
forall a b. a -> b
coe T_DistributiveLattice_584
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsLattice_2962
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_2962
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'cong'737'_3016
         ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048 (T_IsDistributiveLattice_3036 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v1)))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∧-distrib-∨
d_'8743''45'distrib'45''8744'_640 ::
  T_DistributiveLattice_584 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8743''45'distrib'45''8744'_640 :: T_DistributiveLattice_584 -> T_Σ_14
d_'8743''45'distrib'45''8744'_640 T_DistributiveLattice_584
v0
  = (T_IsDistributiveLattice_3036 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsDistributiveLattice_3036 -> T_Σ_14
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'distrib'45''8744'_3052
      ((T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_608 (T_DistributiveLattice_584 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584
v0))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∧-distribʳ-∨
d_'8743''45'distrib'691''45''8744'_642 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_584 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'distrib'691''45''8744'_642 :: ()
-> ()
-> T_DistributiveLattice_584
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'distrib'691''45''8744'_642 ~()
v0 ~()
v1 T_DistributiveLattice_584
v2
  = T_DistributiveLattice_584
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'691''45''8744'_642 T_DistributiveLattice_584
v2
du_'8743''45'distrib'691''45''8744'_642 ::
  T_DistributiveLattice_584 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'691''45''8744'_642 :: T_DistributiveLattice_584
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'691''45''8744'_642 T_DistributiveLattice_584
v0
  = (T_IsDistributiveLattice_3036
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsDistributiveLattice_3036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'distrib'691''45''8744'_3100
      ((T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_608 (T_DistributiveLattice_584 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584
v0))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∧-distribˡ-∨
d_'8743''45'distrib'737''45''8744'_644 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_584 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'distrib'737''45''8744'_644 :: ()
-> ()
-> T_DistributiveLattice_584
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'distrib'737''45''8744'_644 ~()
v0 ~()
v1 T_DistributiveLattice_584
v2
  = T_DistributiveLattice_584
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'737''45''8744'_644 T_DistributiveLattice_584
v2
du_'8743''45'distrib'737''45''8744'_644 ::
  T_DistributiveLattice_584 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'737''45''8744'_644 :: T_DistributiveLattice_584
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'737''45''8744'_644 T_DistributiveLattice_584
v0
  = (T_IsDistributiveLattice_3036
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsDistributiveLattice_3036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'distrib'737''45''8744'_3098
      ((T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_608 (T_DistributiveLattice_584 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584
v0))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∨-absorbs-∧
d_'8744''45'absorbs'45''8743'_646 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_584 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'absorbs'45''8743'_646 :: ()
-> () -> T_DistributiveLattice_584 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'absorbs'45''8743'_646 ~()
v0 ~()
v1 T_DistributiveLattice_584
v2
  = T_DistributiveLattice_584 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_646 T_DistributiveLattice_584
v2
du_'8744''45'absorbs'45''8743'_646 ::
  T_DistributiveLattice_584 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_646 :: T_DistributiveLattice_584 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_646 T_DistributiveLattice_584
v0
  = let v1 :: T_IsDistributiveLattice_3036
v1 = T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_608 (T_DistributiveLattice_584 -> T_DistributiveLattice_584
forall a b. a -> b
coe T_DistributiveLattice_584
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'absorbs'45''8743'_3012
         ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048 (T_IsDistributiveLattice_3036 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v1)))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∨-assoc
d_'8744''45'assoc_648 ::
  T_DistributiveLattice_584 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_648 :: T_DistributiveLattice_584
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_648 T_DistributiveLattice_584
v0
  = (T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'assoc_2988
      ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048
         ((T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_608 (T_DistributiveLattice_584 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584
v0)))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∨-comm
d_'8744''45'comm_650 ::
  T_DistributiveLattice_584 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_650 :: T_DistributiveLattice_584 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_650 T_DistributiveLattice_584
v0
  = (T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'comm_2986
      ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048
         ((T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_608 (T_DistributiveLattice_584 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584
v0)))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∨-cong
d_'8744''45'cong_652 ::
  T_DistributiveLattice_584 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong_652 :: T_DistributiveLattice_584
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong_652 T_DistributiveLattice_584
v0
  = (T_IsLattice_2962
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_2962
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'cong_2990
      ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048
         ((T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_608 (T_DistributiveLattice_584 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584
v0)))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∨-congʳ
d_'8744''45'cong'691'_654 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_584 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong'691'_654 :: ()
-> ()
-> T_DistributiveLattice_584
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong'691'_654 ~()
v0 ~()
v1 T_DistributiveLattice_584
v2
  = T_DistributiveLattice_584
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_654 T_DistributiveLattice_584
v2
du_'8744''45'cong'691'_654 ::
  T_DistributiveLattice_584 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_654 :: T_DistributiveLattice_584
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_654 T_DistributiveLattice_584
v0
  = let v1 :: T_IsDistributiveLattice_3036
v1 = T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_608 (T_DistributiveLattice_584 -> T_DistributiveLattice_584
forall a b. a -> b
coe T_DistributiveLattice_584
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsLattice_2962
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_2962
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'cong'691'_3028
         ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048 (T_IsDistributiveLattice_3036 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v1)))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∨-congˡ
d_'8744''45'cong'737'_656 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_584 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong'737'_656 :: ()
-> ()
-> T_DistributiveLattice_584
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong'737'_656 ~()
v0 ~()
v1 T_DistributiveLattice_584
v2
  = T_DistributiveLattice_584
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_656 T_DistributiveLattice_584
v2
du_'8744''45'cong'737'_656 ::
  T_DistributiveLattice_584 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_656 :: T_DistributiveLattice_584
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_656 T_DistributiveLattice_584
v0
  = let v1 :: T_IsDistributiveLattice_3036
v1 = T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_608 (T_DistributiveLattice_584 -> T_DistributiveLattice_584
forall a b. a -> b
coe T_DistributiveLattice_584
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsLattice_2962
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_2962
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'cong'737'_3024
         ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048 (T_IsDistributiveLattice_3036 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v1)))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∨-distrib-∧
d_'8744''45'distrib'45''8743'_658 ::
  T_DistributiveLattice_584 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8744''45'distrib'45''8743'_658 :: T_DistributiveLattice_584 -> T_Σ_14
d_'8744''45'distrib'45''8743'_658 T_DistributiveLattice_584
v0
  = (T_IsDistributiveLattice_3036 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsDistributiveLattice_3036 -> T_Σ_14
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'distrib'45''8743'_3050
      ((T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_608 (T_DistributiveLattice_584 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584
v0))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∨-distribʳ-∧
d_'8744''45'distrib'691''45''8743'_660 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_584 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'distrib'691''45''8743'_660 :: ()
-> ()
-> T_DistributiveLattice_584
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'distrib'691''45''8743'_660 ~()
v0 ~()
v1 T_DistributiveLattice_584
v2
  = T_DistributiveLattice_584
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'691''45''8743'_660 T_DistributiveLattice_584
v2
du_'8744''45'distrib'691''45''8743'_660 ::
  T_DistributiveLattice_584 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'691''45''8743'_660 :: T_DistributiveLattice_584
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'691''45''8743'_660 T_DistributiveLattice_584
v0
  = (T_IsDistributiveLattice_3036
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsDistributiveLattice_3036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'distrib'691''45''8743'_3096
      ((T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_608 (T_DistributiveLattice_584 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584
v0))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∨-distribˡ-∧
d_'8744''45'distrib'737''45''8743'_662 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_584 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'distrib'737''45''8743'_662 :: ()
-> ()
-> T_DistributiveLattice_584
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'distrib'737''45''8743'_662 ~()
v0 ~()
v1 T_DistributiveLattice_584
v2
  = T_DistributiveLattice_584
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'737''45''8743'_662 T_DistributiveLattice_584
v2
du_'8744''45'distrib'737''45''8743'_662 ::
  T_DistributiveLattice_584 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'737''45''8743'_662 :: T_DistributiveLattice_584
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'737''45''8743'_662 T_DistributiveLattice_584
v0
  = (T_IsDistributiveLattice_3036
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsDistributiveLattice_3036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'distrib'737''45''8743'_3094
      ((T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_608 (T_DistributiveLattice_584 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584
v0))
-- Algebra.Lattice.Bundles.DistributiveLattice.lattice
d_lattice_664 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_584 -> T_Lattice_500
d_lattice_664 :: () -> () -> T_DistributiveLattice_584 -> T_Lattice_500
d_lattice_664 ~()
v0 ~()
v1 T_DistributiveLattice_584
v2 = T_DistributiveLattice_584 -> T_Lattice_500
du_lattice_664 T_DistributiveLattice_584
v2
du_lattice_664 :: T_DistributiveLattice_584 -> T_Lattice_500
du_lattice_664 :: T_DistributiveLattice_584 -> T_Lattice_500
du_lattice_664 T_DistributiveLattice_584
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsLattice_2962
 -> T_Lattice_500)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_2962
-> T_Lattice_500
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_2962
-> T_Lattice_500
C_Lattice'46'constructor_7925 (T_DistributiveLattice_584 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__604 (T_DistributiveLattice_584 -> T_DistributiveLattice_584
forall a b. a -> b
coe T_DistributiveLattice_584
v0))
      (T_DistributiveLattice_584 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__606 (T_DistributiveLattice_584 -> T_DistributiveLattice_584
forall a b. a -> b
coe T_DistributiveLattice_584
v0))
      (T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048
         ((T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> T_IsDistributiveLattice_3036
forall a b. a -> b
coe T_DistributiveLattice_584 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_608 (T_DistributiveLattice_584 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584
v0)))
-- Algebra.Lattice.Bundles.DistributiveLattice._._≉_
d__'8777'__668 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_584 -> AgdaAny -> AgdaAny -> ()
d__'8777'__668 :: () -> () -> T_DistributiveLattice_584 -> AgdaAny -> AgdaAny -> ()
d__'8777'__668 = () -> () -> T_DistributiveLattice_584 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.DistributiveLattice._.rawLattice
d_rawLattice_670 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_584 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.Raw.T_RawLattice_12
d_rawLattice_670 :: () -> () -> T_DistributiveLattice_584 -> T_RawLattice_12
d_rawLattice_670 ~()
v0 ~()
v1 T_DistributiveLattice_584
v2 = T_DistributiveLattice_584 -> T_RawLattice_12
du_rawLattice_670 T_DistributiveLattice_584
v2
du_rawLattice_670 ::
  T_DistributiveLattice_584 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.Raw.T_RawLattice_12
du_rawLattice_670 :: T_DistributiveLattice_584 -> T_RawLattice_12
du_rawLattice_670 T_DistributiveLattice_584
v0
  = (T_Lattice_500 -> T_RawLattice_12) -> AgdaAny -> T_RawLattice_12
forall a b. a -> b
coe T_Lattice_500 -> T_RawLattice_12
du_rawLattice_566 ((T_DistributiveLattice_584 -> T_Lattice_500) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584 -> T_Lattice_500
du_lattice_664 (T_DistributiveLattice_584 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584
v0))
-- Algebra.Lattice.Bundles.DistributiveLattice._.setoid
d_setoid_672 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_584 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_672 :: () -> () -> T_DistributiveLattice_584 -> T_Setoid_44
d_setoid_672 ~()
v0 ~()
v1 T_DistributiveLattice_584
v2 = T_DistributiveLattice_584 -> T_Setoid_44
du_setoid_672 T_DistributiveLattice_584
v2
du_setoid_672 ::
  T_DistributiveLattice_584 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_672 :: T_DistributiveLattice_584 -> T_Setoid_44
du_setoid_672 T_DistributiveLattice_584
v0 = (T_Lattice_500 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_Lattice_500 -> T_Setoid_44
du_setoid_574 ((T_DistributiveLattice_584 -> T_Lattice_500) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584 -> T_Lattice_500
du_lattice_664 (T_DistributiveLattice_584 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584
v0))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∧-rawMagma
d_'8743''45'rawMagma_674 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_584 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_'8743''45'rawMagma_674 :: () -> () -> T_DistributiveLattice_584 -> T_RawMagma_36
d_'8743''45'rawMagma_674 ~()
v0 ~()
v1 T_DistributiveLattice_584
v2 = T_DistributiveLattice_584 -> T_RawMagma_36
du_'8743''45'rawMagma_674 T_DistributiveLattice_584
v2
du_'8743''45'rawMagma_674 ::
  T_DistributiveLattice_584 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_'8743''45'rawMagma_674 :: T_DistributiveLattice_584 -> T_RawMagma_36
du_'8743''45'rawMagma_674 T_DistributiveLattice_584
v0
  = let v1 :: t
v1 = (T_DistributiveLattice_584 -> T_Lattice_500) -> AgdaAny -> t
forall a b. a -> b
coe T_DistributiveLattice_584 -> T_Lattice_500
du_lattice_664 (T_DistributiveLattice_584 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      ((T_RawLattice_12 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_RawLattice_12 -> T_RawMagma_36
MAlonzo.Code.Algebra.Lattice.Bundles.Raw.du_'8743''45'rawMagma_36
         ((T_Lattice_500 -> T_RawLattice_12) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_500 -> T_RawLattice_12
du_rawLattice_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Lattice.Bundles.DistributiveLattice._.∨-rawMagma
d_'8744''45'rawMagma_676 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_584 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_'8744''45'rawMagma_676 :: () -> () -> T_DistributiveLattice_584 -> T_RawMagma_36
d_'8744''45'rawMagma_676 ~()
v0 ~()
v1 T_DistributiveLattice_584
v2 = T_DistributiveLattice_584 -> T_RawMagma_36
du_'8744''45'rawMagma_676 T_DistributiveLattice_584
v2
du_'8744''45'rawMagma_676 ::
  T_DistributiveLattice_584 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_'8744''45'rawMagma_676 :: T_DistributiveLattice_584 -> T_RawMagma_36
du_'8744''45'rawMagma_676 T_DistributiveLattice_584
v0
  = let v1 :: t
v1 = (T_DistributiveLattice_584 -> T_Lattice_500) -> AgdaAny -> t
forall a b. a -> b
coe T_DistributiveLattice_584 -> T_Lattice_500
du_lattice_664 (T_DistributiveLattice_584 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      ((T_RawLattice_12 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_RawLattice_12 -> T_RawMagma_36
MAlonzo.Code.Algebra.Lattice.Bundles.Raw.du_'8744''45'rawMagma_34
         ((T_Lattice_500 -> T_RawLattice_12) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_500 -> T_RawLattice_12
du_rawLattice_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Lattice.Bundles.BooleanAlgebra
d_BooleanAlgebra_682 :: p -> p -> ()
d_BooleanAlgebra_682 p
a0 p
a1 = ()
data T_BooleanAlgebra_682
  = C_BooleanAlgebra'46'constructor_11509 (AgdaAny ->
                                           AgdaAny -> AgdaAny)
                                          (AgdaAny -> AgdaAny -> AgdaAny) (AgdaAny -> AgdaAny)
                                          AgdaAny AgdaAny
                                          MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3112
-- Algebra.Lattice.Bundles.BooleanAlgebra.Carrier
d_Carrier_704 :: T_BooleanAlgebra_682 -> ()
d_Carrier_704 :: T_BooleanAlgebra_682 -> ()
d_Carrier_704 = T_BooleanAlgebra_682 -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.BooleanAlgebra._≈_
d__'8776'__706 :: T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> ()
d__'8776'__706 :: T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> ()
d__'8776'__706 = T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.BooleanAlgebra._∨_
d__'8744'__708 ::
  T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__708 :: T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__708 T_BooleanAlgebra_682
v0
  = case T_BooleanAlgebra_682 -> T_BooleanAlgebra_682
forall a b. a -> b
coe T_BooleanAlgebra_682
v0 of
      C_BooleanAlgebra'46'constructor_11509 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsBooleanAlgebra_3112
v8 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_BooleanAlgebra_682
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.BooleanAlgebra._∧_
d__'8743'__710 ::
  T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__710 :: T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__710 T_BooleanAlgebra_682
v0
  = case T_BooleanAlgebra_682 -> T_BooleanAlgebra_682
forall a b. a -> b
coe T_BooleanAlgebra_682
v0 of
      C_BooleanAlgebra'46'constructor_11509 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsBooleanAlgebra_3112
v8 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_BooleanAlgebra_682
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.BooleanAlgebra.¬_
d_'172'__712 :: T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny
d_'172'__712 :: T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny
d_'172'__712 T_BooleanAlgebra_682
v0
  = case T_BooleanAlgebra_682 -> T_BooleanAlgebra_682
forall a b. a -> b
coe T_BooleanAlgebra_682
v0 of
      C_BooleanAlgebra'46'constructor_11509 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsBooleanAlgebra_3112
v8 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v5
      T_BooleanAlgebra_682
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.BooleanAlgebra.⊤
d_'8868'_714 :: T_BooleanAlgebra_682 -> AgdaAny
d_'8868'_714 :: T_BooleanAlgebra_682 -> AgdaAny
d_'8868'_714 T_BooleanAlgebra_682
v0
  = case T_BooleanAlgebra_682 -> T_BooleanAlgebra_682
forall a b. a -> b
coe T_BooleanAlgebra_682
v0 of
      C_BooleanAlgebra'46'constructor_11509 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsBooleanAlgebra_3112
v8 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6
      T_BooleanAlgebra_682
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.BooleanAlgebra.⊥
d_'8869'_716 :: T_BooleanAlgebra_682 -> AgdaAny
d_'8869'_716 :: T_BooleanAlgebra_682 -> AgdaAny
d_'8869'_716 T_BooleanAlgebra_682
v0
  = case T_BooleanAlgebra_682 -> T_BooleanAlgebra_682
forall a b. a -> b
coe T_BooleanAlgebra_682
v0 of
      C_BooleanAlgebra'46'constructor_11509 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsBooleanAlgebra_3112
v8 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v7
      T_BooleanAlgebra_682
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.BooleanAlgebra.isBooleanAlgebra
d_isBooleanAlgebra_718 ::
  T_BooleanAlgebra_682 ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3112
d_isBooleanAlgebra_718 :: T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112
d_isBooleanAlgebra_718 T_BooleanAlgebra_682
v0
  = case T_BooleanAlgebra_682 -> T_BooleanAlgebra_682
forall a b. a -> b
coe T_BooleanAlgebra_682
v0 of
      C_BooleanAlgebra'46'constructor_11509 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsBooleanAlgebra_3112
v8 -> T_IsBooleanAlgebra_3112 -> T_IsBooleanAlgebra_3112
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v8
      T_BooleanAlgebra_682
_ -> T_IsBooleanAlgebra_3112
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Bundles.BooleanAlgebra._.absorptive
d_absorptive_722 ::
  T_BooleanAlgebra_682 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_absorptive_722 :: T_BooleanAlgebra_682 -> T_Σ_14
d_absorptive_722 T_BooleanAlgebra_682
v0
  = (T_IsLattice_2962 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsLattice_2962 -> T_Σ_14
MAlonzo.Code.Algebra.Lattice.Structures.d_absorptive_2998
      ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048
         ((T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3132
            ((T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112
d_isBooleanAlgebra_718 (T_BooleanAlgebra_682 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682
v0))))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.isDistributiveLattice
d_isDistributiveLattice_724 ::
  T_BooleanAlgebra_682 ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3036
d_isDistributiveLattice_724 :: T_BooleanAlgebra_682 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_724 T_BooleanAlgebra_682
v0
  = (T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> T_IsDistributiveLattice_3036
forall a b. a -> b
coe
      T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3132
      ((T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112
d_isBooleanAlgebra_718 (T_BooleanAlgebra_682 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682
v0))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.isEquivalence
d_isEquivalence_726 ::
  T_BooleanAlgebra_682 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_726 :: T_BooleanAlgebra_682 -> T_IsEquivalence_26
d_isEquivalence_726 T_BooleanAlgebra_682
v0
  = (T_IsLattice_2962 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsLattice_2962 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
      ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048
         ((T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3132
            ((T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112
d_isBooleanAlgebra_718 (T_BooleanAlgebra_682 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682
v0))))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.isLattice
d_isLattice_728 ::
  T_BooleanAlgebra_682 ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_2962
d_isLattice_728 :: T_BooleanAlgebra_682 -> T_IsLattice_2962
d_isLattice_728 T_BooleanAlgebra_682
v0
  = (T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> T_IsLattice_2962
forall a b. a -> b
coe
      T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048
      ((T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3132
         ((T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112
d_isBooleanAlgebra_718 (T_BooleanAlgebra_682 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682
v0)))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.isPartialEquivalence
d_isPartialEquivalence_730 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_682 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_730 :: () -> () -> T_BooleanAlgebra_682 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_730 ~()
v0 ~()
v1 T_BooleanAlgebra_682
v2
  = T_BooleanAlgebra_682 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_730 T_BooleanAlgebra_682
v2
du_isPartialEquivalence_730 ::
  T_BooleanAlgebra_682 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_730 :: T_BooleanAlgebra_682 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_730 T_BooleanAlgebra_682
v0
  = let v1 :: T_IsBooleanAlgebra_3112
v1 = T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112
d_isBooleanAlgebra_718 (T_BooleanAlgebra_682 -> T_BooleanAlgebra_682
forall a b. a -> b
coe T_BooleanAlgebra_682
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsDistributiveLattice_3036
v2
             = T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3132
                 (T_IsBooleanAlgebra_3112 -> T_IsBooleanAlgebra_3112
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_2962
v3
                = T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048
                    (T_IsDistributiveLattice_3036 -> T_IsDistributiveLattice_3036
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((T_IsLattice_2962 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLattice_2962 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
                  (T_IsLattice_2962 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962
v3)))))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.refl
d_refl_732 :: T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny
d_refl_732 :: T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny
d_refl_732 T_BooleanAlgebra_682
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsLattice_2962 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_2962 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
         ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048
            ((T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3132
               ((T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112
d_isBooleanAlgebra_718 (T_BooleanAlgebra_682 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682
v0)))))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.reflexive
d_reflexive_734 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_682 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_734 :: ()
-> ()
-> T_BooleanAlgebra_682
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_734 ~()
v0 ~()
v1 T_BooleanAlgebra_682
v2 = T_BooleanAlgebra_682
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_734 T_BooleanAlgebra_682
v2
du_reflexive_734 ::
  T_BooleanAlgebra_682 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_734 :: T_BooleanAlgebra_682
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_734 T_BooleanAlgebra_682
v0
  = let v1 :: T_IsBooleanAlgebra_3112
v1 = T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112
d_isBooleanAlgebra_718 (T_BooleanAlgebra_682 -> T_BooleanAlgebra_682
forall a b. a -> b
coe T_BooleanAlgebra_682
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsDistributiveLattice_3036
v2
             = T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3132
                 (T_IsBooleanAlgebra_3112 -> T_IsBooleanAlgebra_3112
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_2962
v3
                = T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048
                    (T_IsDistributiveLattice_3036 -> T_IsDistributiveLattice_3036
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                 ((T_IsLattice_2962 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsLattice_2962 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
                    (T_IsLattice_2962 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962
v3))
                 AgdaAny
v4)))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.sym
d_sym_736 ::
  T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_736 :: T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_736 T_BooleanAlgebra_682
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsLattice_2962 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_2962 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
         ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048
            ((T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3132
               ((T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112
d_isBooleanAlgebra_718 (T_BooleanAlgebra_682 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682
v0)))))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.trans
d_trans_738 ::
  T_BooleanAlgebra_682 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_738 :: T_BooleanAlgebra_682
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_738 T_BooleanAlgebra_682
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsLattice_2962 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_2962 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
         ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048
            ((T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3132
               ((T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112
d_isBooleanAlgebra_718 (T_BooleanAlgebra_682 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682
v0)))))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.¬-cong
d_'172''45'cong_740 ::
  T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'172''45'cong_740 :: T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'172''45'cong_740 T_BooleanAlgebra_682
v0
  = (T_IsBooleanAlgebra_3112
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'172''45'cong_3138
      ((T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112
d_isBooleanAlgebra_718 (T_BooleanAlgebra_682 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682
v0))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∧-absorbs-∨
d_'8743''45'absorbs'45''8744'_742 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'absorbs'45''8744'_742 :: () -> () -> T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'absorbs'45''8744'_742 ~()
v0 ~()
v1 T_BooleanAlgebra_682
v2
  = T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_742 T_BooleanAlgebra_682
v2
du_'8743''45'absorbs'45''8744'_742 ::
  T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_742 :: T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_742 T_BooleanAlgebra_682
v0
  = let v1 :: T_IsBooleanAlgebra_3112
v1 = T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112
d_isBooleanAlgebra_718 (T_BooleanAlgebra_682 -> T_BooleanAlgebra_682
forall a b. a -> b
coe T_BooleanAlgebra_682
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsDistributiveLattice_3036
v2
             = T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3132
                 (T_IsBooleanAlgebra_3112 -> T_IsBooleanAlgebra_3112
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'absorbs'45''8744'_3014
            ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048
               (T_IsDistributiveLattice_3036 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v2))))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∧-assoc
d_'8743''45'assoc_744 ::
  T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_744 :: T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_744 T_BooleanAlgebra_682
v0
  = (T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'assoc_2994
      ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048
         ((T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3132
            ((T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112
d_isBooleanAlgebra_718 (T_BooleanAlgebra_682 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682
v0))))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∧-comm
d_'8743''45'comm_746 ::
  T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_746 :: T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_746 T_BooleanAlgebra_682
v0
  = (T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'comm_2992
      ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048
         ((T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3132
            ((T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112
d_isBooleanAlgebra_718 (T_BooleanAlgebra_682 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682
v0))))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∧-complement
d_'8743''45'complement_748 ::
  T_BooleanAlgebra_682 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8743''45'complement_748 :: T_BooleanAlgebra_682 -> T_Σ_14
d_'8743''45'complement_748 T_BooleanAlgebra_682
v0
  = (T_IsBooleanAlgebra_3112 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsBooleanAlgebra_3112 -> T_Σ_14
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'complement_3136
      ((T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112
d_isBooleanAlgebra_718 (T_BooleanAlgebra_682 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682
v0))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∧-complementʳ
d_'8743''45'complement'691'_750 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny
d_'8743''45'complement'691'_750 :: () -> () -> T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny
d_'8743''45'complement'691'_750 ~()
v0 ~()
v1 T_BooleanAlgebra_682
v2
  = T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny
du_'8743''45'complement'691'_750 T_BooleanAlgebra_682
v2
du_'8743''45'complement'691'_750 ::
  T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny
du_'8743''45'complement'691'_750 :: T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny
du_'8743''45'complement'691'_750 T_BooleanAlgebra_682
v0
  = (T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'complement'691'_3200
      ((T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112
d_isBooleanAlgebra_718 (T_BooleanAlgebra_682 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682
v0))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∧-complementˡ
d_'8743''45'complement'737'_752 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny
d_'8743''45'complement'737'_752 :: () -> () -> T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny
d_'8743''45'complement'737'_752 ~()
v0 ~()
v1 T_BooleanAlgebra_682
v2
  = T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny
du_'8743''45'complement'737'_752 T_BooleanAlgebra_682
v2
du_'8743''45'complement'737'_752 ::
  T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny
du_'8743''45'complement'737'_752 :: T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny
du_'8743''45'complement'737'_752 T_BooleanAlgebra_682
v0
  = (T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'complement'737'_3198
      ((T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112
d_isBooleanAlgebra_718 (T_BooleanAlgebra_682 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682
v0))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∧-cong
d_'8743''45'cong_754 ::
  T_BooleanAlgebra_682 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong_754 :: T_BooleanAlgebra_682
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong_754 T_BooleanAlgebra_682
v0
  = (T_IsLattice_2962
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_2962
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'cong_2996
      ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048
         ((T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3132
            ((T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112
d_isBooleanAlgebra_718 (T_BooleanAlgebra_682 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682
v0))))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∧-congʳ
d_'8743''45'cong'691'_756 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_682 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong'691'_756 :: ()
-> ()
-> T_BooleanAlgebra_682
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong'691'_756 ~()
v0 ~()
v1 T_BooleanAlgebra_682
v2
  = T_BooleanAlgebra_682
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_756 T_BooleanAlgebra_682
v2
du_'8743''45'cong'691'_756 ::
  T_BooleanAlgebra_682 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_756 :: T_BooleanAlgebra_682
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_756 T_BooleanAlgebra_682
v0
  = let v1 :: T_IsBooleanAlgebra_3112
v1 = T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112
d_isBooleanAlgebra_718 (T_BooleanAlgebra_682 -> T_BooleanAlgebra_682
forall a b. a -> b
coe T_BooleanAlgebra_682
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsDistributiveLattice_3036
v2
             = T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3132
                 (T_IsBooleanAlgebra_3112 -> T_IsBooleanAlgebra_3112
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsLattice_2962
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_2962
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'cong'691'_3020
            ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048
               (T_IsDistributiveLattice_3036 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v2))))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∧-congˡ
d_'8743''45'cong'737'_758 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_682 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong'737'_758 :: ()
-> ()
-> T_BooleanAlgebra_682
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong'737'_758 ~()
v0 ~()
v1 T_BooleanAlgebra_682
v2
  = T_BooleanAlgebra_682
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_758 T_BooleanAlgebra_682
v2
du_'8743''45'cong'737'_758 ::
  T_BooleanAlgebra_682 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_758 :: T_BooleanAlgebra_682
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_758 T_BooleanAlgebra_682
v0
  = let v1 :: T_IsBooleanAlgebra_3112
v1 = T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112
d_isBooleanAlgebra_718 (T_BooleanAlgebra_682 -> T_BooleanAlgebra_682
forall a b. a -> b
coe T_BooleanAlgebra_682
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsDistributiveLattice_3036
v2
             = T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3132
                 (T_IsBooleanAlgebra_3112 -> T_IsBooleanAlgebra_3112
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsLattice_2962
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_2962
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'cong'737'_3016
            ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048
               (T_IsDistributiveLattice_3036 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v2))))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∧-distrib-∨
d_'8743''45'distrib'45''8744'_760 ::
  T_BooleanAlgebra_682 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8743''45'distrib'45''8744'_760 :: T_BooleanAlgebra_682 -> T_Σ_14
d_'8743''45'distrib'45''8744'_760 T_BooleanAlgebra_682
v0
  = (T_IsDistributiveLattice_3036 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsDistributiveLattice_3036 -> T_Σ_14
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'distrib'45''8744'_3052
      ((T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3132
         ((T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112
d_isBooleanAlgebra_718 (T_BooleanAlgebra_682 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682
v0)))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∧-distribʳ-∨
d_'8743''45'distrib'691''45''8744'_762 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'distrib'691''45''8744'_762 :: ()
-> ()
-> T_BooleanAlgebra_682
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'distrib'691''45''8744'_762 ~()
v0 ~()
v1 T_BooleanAlgebra_682
v2
  = T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'691''45''8744'_762 T_BooleanAlgebra_682
v2
du_'8743''45'distrib'691''45''8744'_762 ::
  T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'691''45''8744'_762 :: T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'691''45''8744'_762 T_BooleanAlgebra_682
v0
  = let v1 :: T_IsBooleanAlgebra_3112
v1 = T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112
d_isBooleanAlgebra_718 (T_BooleanAlgebra_682 -> T_BooleanAlgebra_682
forall a b. a -> b
coe T_BooleanAlgebra_682
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsDistributiveLattice_3036
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'distrib'691''45''8744'_3100
         ((T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3132
            (T_IsBooleanAlgebra_3112 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v1)))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∧-distribˡ-∨
d_'8743''45'distrib'737''45''8744'_764 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'distrib'737''45''8744'_764 :: ()
-> ()
-> T_BooleanAlgebra_682
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'distrib'737''45''8744'_764 ~()
v0 ~()
v1 T_BooleanAlgebra_682
v2
  = T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'737''45''8744'_764 T_BooleanAlgebra_682
v2
du_'8743''45'distrib'737''45''8744'_764 ::
  T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'737''45''8744'_764 :: T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'737''45''8744'_764 T_BooleanAlgebra_682
v0
  = let v1 :: T_IsBooleanAlgebra_3112
v1 = T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112
d_isBooleanAlgebra_718 (T_BooleanAlgebra_682 -> T_BooleanAlgebra_682
forall a b. a -> b
coe T_BooleanAlgebra_682
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsDistributiveLattice_3036
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'distrib'737''45''8744'_3098
         ((T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3132
            (T_IsBooleanAlgebra_3112 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v1)))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∨-absorbs-∧
d_'8744''45'absorbs'45''8743'_766 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'absorbs'45''8743'_766 :: () -> () -> T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'absorbs'45''8743'_766 ~()
v0 ~()
v1 T_BooleanAlgebra_682
v2
  = T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_766 T_BooleanAlgebra_682
v2
du_'8744''45'absorbs'45''8743'_766 ::
  T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_766 :: T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_766 T_BooleanAlgebra_682
v0
  = let v1 :: T_IsBooleanAlgebra_3112
v1 = T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112
d_isBooleanAlgebra_718 (T_BooleanAlgebra_682 -> T_BooleanAlgebra_682
forall a b. a -> b
coe T_BooleanAlgebra_682
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsDistributiveLattice_3036
v2
             = T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3132
                 (T_IsBooleanAlgebra_3112 -> T_IsBooleanAlgebra_3112
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'absorbs'45''8743'_3012
            ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048
               (T_IsDistributiveLattice_3036 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v2))))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∨-assoc
d_'8744''45'assoc_768 ::
  T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_768 :: T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_768 T_BooleanAlgebra_682
v0
  = (T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'assoc_2988
      ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048
         ((T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3132
            ((T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112
d_isBooleanAlgebra_718 (T_BooleanAlgebra_682 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682
v0))))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∨-comm
d_'8744''45'comm_770 ::
  T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_770 :: T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_770 T_BooleanAlgebra_682
v0
  = (T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'comm_2986
      ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048
         ((T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3132
            ((T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112
d_isBooleanAlgebra_718 (T_BooleanAlgebra_682 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682
v0))))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∨-complement
d_'8744''45'complement_772 ::
  T_BooleanAlgebra_682 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8744''45'complement_772 :: T_BooleanAlgebra_682 -> T_Σ_14
d_'8744''45'complement_772 T_BooleanAlgebra_682
v0
  = (T_IsBooleanAlgebra_3112 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsBooleanAlgebra_3112 -> T_Σ_14
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'complement_3134
      ((T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112
d_isBooleanAlgebra_718 (T_BooleanAlgebra_682 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682
v0))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∨-complementʳ
d_'8744''45'complement'691'_774 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny
d_'8744''45'complement'691'_774 :: () -> () -> T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny
d_'8744''45'complement'691'_774 ~()
v0 ~()
v1 T_BooleanAlgebra_682
v2
  = T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny
du_'8744''45'complement'691'_774 T_BooleanAlgebra_682
v2
du_'8744''45'complement'691'_774 ::
  T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny
du_'8744''45'complement'691'_774 :: T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny
du_'8744''45'complement'691'_774 T_BooleanAlgebra_682
v0
  = (T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'complement'691'_3196
      ((T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112
d_isBooleanAlgebra_718 (T_BooleanAlgebra_682 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682
v0))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∨-complementˡ
d_'8744''45'complement'737'_776 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny
d_'8744''45'complement'737'_776 :: () -> () -> T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny
d_'8744''45'complement'737'_776 ~()
v0 ~()
v1 T_BooleanAlgebra_682
v2
  = T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny
du_'8744''45'complement'737'_776 T_BooleanAlgebra_682
v2
du_'8744''45'complement'737'_776 ::
  T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny
du_'8744''45'complement'737'_776 :: T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny
du_'8744''45'complement'737'_776 T_BooleanAlgebra_682
v0
  = (T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'complement'737'_3194
      ((T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112
d_isBooleanAlgebra_718 (T_BooleanAlgebra_682 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682
v0))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∨-cong
d_'8744''45'cong_778 ::
  T_BooleanAlgebra_682 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong_778 :: T_BooleanAlgebra_682
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong_778 T_BooleanAlgebra_682
v0
  = (T_IsLattice_2962
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_2962
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'cong_2990
      ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048
         ((T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3132
            ((T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112
d_isBooleanAlgebra_718 (T_BooleanAlgebra_682 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682
v0))))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∨-congʳ
d_'8744''45'cong'691'_780 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_682 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong'691'_780 :: ()
-> ()
-> T_BooleanAlgebra_682
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong'691'_780 ~()
v0 ~()
v1 T_BooleanAlgebra_682
v2
  = T_BooleanAlgebra_682
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_780 T_BooleanAlgebra_682
v2
du_'8744''45'cong'691'_780 ::
  T_BooleanAlgebra_682 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_780 :: T_BooleanAlgebra_682
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_780 T_BooleanAlgebra_682
v0
  = let v1 :: T_IsBooleanAlgebra_3112
v1 = T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112
d_isBooleanAlgebra_718 (T_BooleanAlgebra_682 -> T_BooleanAlgebra_682
forall a b. a -> b
coe T_BooleanAlgebra_682
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsDistributiveLattice_3036
v2
             = T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3132
                 (T_IsBooleanAlgebra_3112 -> T_IsBooleanAlgebra_3112
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsLattice_2962
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_2962
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'cong'691'_3028
            ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048
               (T_IsDistributiveLattice_3036 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v2))))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∨-congˡ
d_'8744''45'cong'737'_782 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_682 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong'737'_782 :: ()
-> ()
-> T_BooleanAlgebra_682
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong'737'_782 ~()
v0 ~()
v1 T_BooleanAlgebra_682
v2
  = T_BooleanAlgebra_682
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_782 T_BooleanAlgebra_682
v2
du_'8744''45'cong'737'_782 ::
  T_BooleanAlgebra_682 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_782 :: T_BooleanAlgebra_682
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_782 T_BooleanAlgebra_682
v0
  = let v1 :: T_IsBooleanAlgebra_3112
v1 = T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112
d_isBooleanAlgebra_718 (T_BooleanAlgebra_682 -> T_BooleanAlgebra_682
forall a b. a -> b
coe T_BooleanAlgebra_682
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsDistributiveLattice_3036
v2
             = T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3132
                 (T_IsBooleanAlgebra_3112 -> T_IsBooleanAlgebra_3112
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsLattice_2962
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_2962
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'cong'737'_3024
            ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsDistributiveLattice_3036 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048
               (T_IsDistributiveLattice_3036 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v2))))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∨-distrib-∧
d_'8744''45'distrib'45''8743'_784 ::
  T_BooleanAlgebra_682 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8744''45'distrib'45''8743'_784 :: T_BooleanAlgebra_682 -> T_Σ_14
d_'8744''45'distrib'45''8743'_784 T_BooleanAlgebra_682
v0
  = (T_IsDistributiveLattice_3036 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsDistributiveLattice_3036 -> T_Σ_14
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'distrib'45''8743'_3050
      ((T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3132
         ((T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112
d_isBooleanAlgebra_718 (T_BooleanAlgebra_682 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682
v0)))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∨-distribʳ-∧
d_'8744''45'distrib'691''45''8743'_786 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'distrib'691''45''8743'_786 :: ()
-> ()
-> T_BooleanAlgebra_682
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'distrib'691''45''8743'_786 ~()
v0 ~()
v1 T_BooleanAlgebra_682
v2
  = T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'691''45''8743'_786 T_BooleanAlgebra_682
v2
du_'8744''45'distrib'691''45''8743'_786 ::
  T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'691''45''8743'_786 :: T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'691''45''8743'_786 T_BooleanAlgebra_682
v0
  = let v1 :: T_IsBooleanAlgebra_3112
v1 = T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112
d_isBooleanAlgebra_718 (T_BooleanAlgebra_682 -> T_BooleanAlgebra_682
forall a b. a -> b
coe T_BooleanAlgebra_682
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsDistributiveLattice_3036
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'distrib'691''45''8743'_3096
         ((T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3132
            (T_IsBooleanAlgebra_3112 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v1)))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∨-distribˡ-∧
d_'8744''45'distrib'737''45''8743'_788 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'distrib'737''45''8743'_788 :: ()
-> ()
-> T_BooleanAlgebra_682
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'distrib'737''45''8743'_788 ~()
v0 ~()
v1 T_BooleanAlgebra_682
v2
  = T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'737''45''8743'_788 T_BooleanAlgebra_682
v2
du_'8744''45'distrib'737''45''8743'_788 ::
  T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'737''45''8743'_788 :: T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'737''45''8743'_788 T_BooleanAlgebra_682
v0
  = let v1 :: T_IsBooleanAlgebra_3112
v1 = T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112
d_isBooleanAlgebra_718 (T_BooleanAlgebra_682 -> T_BooleanAlgebra_682
forall a b. a -> b
coe T_BooleanAlgebra_682
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsDistributiveLattice_3036
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_3036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'distrib'737''45''8743'_3094
         ((T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3132
            (T_IsBooleanAlgebra_3112 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v1)))
-- Algebra.Lattice.Bundles.BooleanAlgebra.distributiveLattice
d_distributiveLattice_790 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_682 -> T_DistributiveLattice_584
d_distributiveLattice_790 :: () -> () -> T_BooleanAlgebra_682 -> T_DistributiveLattice_584
d_distributiveLattice_790 ~()
v0 ~()
v1 T_BooleanAlgebra_682
v2
  = T_BooleanAlgebra_682 -> T_DistributiveLattice_584
du_distributiveLattice_790 T_BooleanAlgebra_682
v2
du_distributiveLattice_790 ::
  T_BooleanAlgebra_682 -> T_DistributiveLattice_584
du_distributiveLattice_790 :: T_BooleanAlgebra_682 -> T_DistributiveLattice_584
du_distributiveLattice_790 T_BooleanAlgebra_682
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsDistributiveLattice_3036
 -> T_DistributiveLattice_584)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_3036
-> T_DistributiveLattice_584
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_3036
-> T_DistributiveLattice_584
C_DistributiveLattice'46'constructor_9515 (T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__708 (T_BooleanAlgebra_682 -> T_BooleanAlgebra_682
forall a b. a -> b
coe T_BooleanAlgebra_682
v0))
      (T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__710 (T_BooleanAlgebra_682 -> T_BooleanAlgebra_682
forall a b. a -> b
coe T_BooleanAlgebra_682
v0))
      (T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3132
         ((T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112)
-> AgdaAny -> T_IsBooleanAlgebra_3112
forall a b. a -> b
coe T_BooleanAlgebra_682 -> T_IsBooleanAlgebra_3112
d_isBooleanAlgebra_718 (T_BooleanAlgebra_682 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682
v0)))
-- Algebra.Lattice.Bundles.BooleanAlgebra._._≉_
d__'8777'__794 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> ()
d__'8777'__794 :: () -> () -> T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> ()
d__'8777'__794 = () -> () -> T_BooleanAlgebra_682 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Lattice.Bundles.BooleanAlgebra._.lattice
d_lattice_796 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_682 -> T_Lattice_500
d_lattice_796 :: () -> () -> T_BooleanAlgebra_682 -> T_Lattice_500
d_lattice_796 ~()
v0 ~()
v1 T_BooleanAlgebra_682
v2 = T_BooleanAlgebra_682 -> T_Lattice_500
du_lattice_796 T_BooleanAlgebra_682
v2
du_lattice_796 :: T_BooleanAlgebra_682 -> T_Lattice_500
du_lattice_796 :: T_BooleanAlgebra_682 -> T_Lattice_500
du_lattice_796 T_BooleanAlgebra_682
v0
  = (T_DistributiveLattice_584 -> T_Lattice_500)
-> AgdaAny -> T_Lattice_500
forall a b. a -> b
coe T_DistributiveLattice_584 -> T_Lattice_500
du_lattice_664 ((T_BooleanAlgebra_682 -> T_DistributiveLattice_584)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682 -> T_DistributiveLattice_584
du_distributiveLattice_790 (T_BooleanAlgebra_682 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682
v0))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.rawLattice
d_rawLattice_798 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_682 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.Raw.T_RawLattice_12
d_rawLattice_798 :: () -> () -> T_BooleanAlgebra_682 -> T_RawLattice_12
d_rawLattice_798 ~()
v0 ~()
v1 T_BooleanAlgebra_682
v2 = T_BooleanAlgebra_682 -> T_RawLattice_12
du_rawLattice_798 T_BooleanAlgebra_682
v2
du_rawLattice_798 ::
  T_BooleanAlgebra_682 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.Raw.T_RawLattice_12
du_rawLattice_798 :: T_BooleanAlgebra_682 -> T_RawLattice_12
du_rawLattice_798 T_BooleanAlgebra_682
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_682 -> T_DistributiveLattice_584) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_682 -> T_DistributiveLattice_584
du_distributiveLattice_790 (T_BooleanAlgebra_682 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682
v0) in
    AgdaAny -> T_RawLattice_12
forall a b. a -> b
coe ((T_Lattice_500 -> T_RawLattice_12) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_500 -> T_RawLattice_12
du_rawLattice_566 ((T_DistributiveLattice_584 -> T_Lattice_500) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584 -> T_Lattice_500
du_lattice_664 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.setoid
d_setoid_800 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_682 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_800 :: () -> () -> T_BooleanAlgebra_682 -> T_Setoid_44
d_setoid_800 ~()
v0 ~()
v1 T_BooleanAlgebra_682
v2 = T_BooleanAlgebra_682 -> T_Setoid_44
du_setoid_800 T_BooleanAlgebra_682
v2
du_setoid_800 ::
  T_BooleanAlgebra_682 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_800 :: T_BooleanAlgebra_682 -> T_Setoid_44
du_setoid_800 T_BooleanAlgebra_682
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_682 -> T_DistributiveLattice_584) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_682 -> T_DistributiveLattice_584
du_distributiveLattice_790 (T_BooleanAlgebra_682 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe ((T_Lattice_500 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_500 -> T_Setoid_44
du_setoid_574 ((T_DistributiveLattice_584 -> T_Lattice_500) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_584 -> T_Lattice_500
du_lattice_664 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∧-rawMagma
d_'8743''45'rawMagma_802 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_682 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_'8743''45'rawMagma_802 :: () -> () -> T_BooleanAlgebra_682 -> T_RawMagma_36
d_'8743''45'rawMagma_802 ~()
v0 ~()
v1 T_BooleanAlgebra_682
v2 = T_BooleanAlgebra_682 -> T_RawMagma_36
du_'8743''45'rawMagma_802 T_BooleanAlgebra_682
v2
du_'8743''45'rawMagma_802 ::
  T_BooleanAlgebra_682 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_'8743''45'rawMagma_802 :: T_BooleanAlgebra_682 -> T_RawMagma_36
du_'8743''45'rawMagma_802 T_BooleanAlgebra_682
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_682 -> T_DistributiveLattice_584) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_682 -> T_DistributiveLattice_584
du_distributiveLattice_790 (T_BooleanAlgebra_682 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_DistributiveLattice_584 -> T_Lattice_500) -> AgdaAny -> t
forall a b. a -> b
coe T_DistributiveLattice_584 -> T_Lattice_500
du_lattice_664 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_RawLattice_12 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_RawLattice_12 -> T_RawMagma_36
MAlonzo.Code.Algebra.Lattice.Bundles.Raw.du_'8743''45'rawMagma_36
            ((T_Lattice_500 -> T_RawLattice_12) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_500 -> T_RawLattice_12
du_rawLattice_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Lattice.Bundles.BooleanAlgebra._.∨-rawMagma
d_'8744''45'rawMagma_804 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_682 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_'8744''45'rawMagma_804 :: () -> () -> T_BooleanAlgebra_682 -> T_RawMagma_36
d_'8744''45'rawMagma_804 ~()
v0 ~()
v1 T_BooleanAlgebra_682
v2 = T_BooleanAlgebra_682 -> T_RawMagma_36
du_'8744''45'rawMagma_804 T_BooleanAlgebra_682
v2
du_'8744''45'rawMagma_804 ::
  T_BooleanAlgebra_682 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_'8744''45'rawMagma_804 :: T_BooleanAlgebra_682 -> T_RawMagma_36
du_'8744''45'rawMagma_804 T_BooleanAlgebra_682
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_682 -> T_DistributiveLattice_584) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_682 -> T_DistributiveLattice_584
du_distributiveLattice_790 (T_BooleanAlgebra_682 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_682
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_DistributiveLattice_584 -> T_Lattice_500) -> AgdaAny -> t
forall a b. a -> b
coe T_DistributiveLattice_584 -> T_Lattice_500
du_lattice_664 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_RawLattice_12 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_RawLattice_12 -> T_RawMagma_36
MAlonzo.Code.Algebra.Lattice.Bundles.Raw.du_'8744''45'rawMagma_34
            ((T_Lattice_500 -> T_RawLattice_12) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_500 -> T_RawLattice_12
du_rawLattice_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))