{-# 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.Structures 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.Consequences.Base
import qualified MAlonzo.Code.Algebra.Structures
import qualified MAlonzo.Code.Relation.Binary.Bundles
import qualified MAlonzo.Code.Relation.Binary.Structures

-- Algebra.Lattice.Structures._._Absorbs_
d__Absorbs__16 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d__Absorbs__16 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d__Absorbs__16 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Lattice.Structures._._DistributesOver_
d__DistributesOver__18 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d__DistributesOver__18 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d__DistributesOver__18 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Lattice.Structures._._DistributesOverʳ_
d__DistributesOver'691'__20 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d__DistributesOver'691'__20 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d__DistributesOver'691'__20 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Lattice.Structures._._DistributesOverˡ_
d__DistributesOver'737'__22 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d__DistributesOver'737'__22 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d__DistributesOver'737'__22 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Lattice.Structures._.Absorptive
d_Absorptive_28 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Absorptive_28 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_Absorptive_28 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Lattice.Structures._.Associative
d_Associative_38 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Associative_38 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_Associative_38 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Lattice.Structures._.Commutative
d_Commutative_42 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Commutative_42 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_Commutative_42 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Lattice.Structures._.Congruent₁
d_Congruent'8321'_44 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () -> (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny) -> ()
d_Congruent'8321'_44 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
d_Congruent'8321'_44 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Lattice.Structures._.Congruent₂
d_Congruent'8322'_46 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Congruent'8322'_46 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_Congruent'8322'_46 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Lattice.Structures._.Inverse
d_Inverse_62 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Inverse_62 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_Inverse_62 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Lattice.Structures._.LeftCongruent
d_LeftCongruent_74 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_LeftCongruent_74 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_LeftCongruent_74 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Lattice.Structures._.LeftInverse
d_LeftInverse_86 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_LeftInverse_86 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_LeftInverse_86 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Lattice.Structures._.RightCongruent
d_RightCongruent_104 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_RightCongruent_104 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_RightCongruent_104 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Lattice.Structures._.RightInverse
d_RightInverse_116 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_RightInverse_116 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_RightInverse_116 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Lattice.Structures._.IsCommutativeBand
d_IsCommutativeBand_162 :: p -> p -> p -> p -> p -> T_Level_18
d_IsCommutativeBand_162 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
-- Algebra.Lattice.Structures._.IsIdempotentCommutativeMonoid
d_IsIdempotentCommutativeMonoid_198 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_IsIdempotentCommutativeMonoid_198 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
-- Algebra.Lattice.Structures._.IsBand.isPartialEquivalence
d_isPartialEquivalence_424 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_424 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsBand_526
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_424 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsBand_526
v5
  = T_IsBand_526 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_424 T_IsBand_526
v5
du_isPartialEquivalence_424 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_526 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_424 :: T_IsBand_526 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_424 T_IsBand_526
v0
  = let v1 :: T_IsSemigroup_488
v1
          = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2))))
-- Algebra.Lattice.Structures._.IsBand.reflexive
d_reflexive_430 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_430 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsBand_526
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_430 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsBand_526
v5 = T_IsBand_526 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_430 T_IsBand_526
v5
du_reflexive_430 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_526 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_430 :: T_IsBand_526 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_430 T_IsBand_526
v0
  = let v1 :: T_IsSemigroup_488
v1
          = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2))
              AgdaAny
v3))
-- Algebra.Lattice.Structures._.IsBand.setoid
d_setoid_432 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_432 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsBand_526
-> T_Setoid_46
d_setoid_432 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsBand_526
v5 = T_IsBand_526 -> T_Setoid_46
du_setoid_432 T_IsBand_526
v5
du_setoid_432 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_526 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_432 :: T_IsBand_526 -> T_Setoid_46
du_setoid_432 T_IsBand_526
v0
  = let v1 :: T_IsSemigroup_488
v1
          = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v1)))
-- Algebra.Lattice.Structures._.IsBand.∙-congʳ
d_'8729''45'cong'691'_440 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_440 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsBand_526
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_440 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsBand_526
v5
  = T_IsBand_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_440 T_IsBand_526
v5
du_'8729''45'cong'691'_440 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_526 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_440 :: T_IsBand_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_440 T_IsBand_526
v0
  = let v1 :: T_IsSemigroup_488
v1
          = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
                   = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v2) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                  ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4)
                  ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                     ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                        (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))))
-- Algebra.Lattice.Structures._.IsBand.∙-congˡ
d_'8729''45'cong'737'_442 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_442 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsBand_526
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_442 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsBand_526
v5
  = T_IsBand_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_442 T_IsBand_526
v5
du_'8729''45'cong'737'_442 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_526 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_442 :: T_IsBand_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_442 T_IsBand_526
v0
  = let v1 :: T_IsSemigroup_488
v1
          = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
                   = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v2) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                  ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4)
                  ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                     ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                        (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))))
-- Algebra.Lattice.Structures._.IsCommutativeBand.comm
d_comm_550 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_comm_550 :: T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_550 T_IsCommutativeBand_612
v0
  = (T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_622 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0)
-- Algebra.Lattice.Structures._.IsCommutativeBand.isBand
d_isBand_554 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
d_isBand_554 :: T_IsCommutativeBand_612 -> T_IsBand_526
d_isBand_554 T_IsCommutativeBand_612
v0
  = (T_IsCommutativeBand_612 -> T_IsBand_526)
-> AgdaAny -> T_IsBand_526
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0)
-- Algebra.Lattice.Structures._.IsIdempotentCommutativeMonoid.idem
d_idem_1072 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny
d_idem_1072 :: T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
d_idem_1072 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_896 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0)
-- Algebra.Lattice.Structures._.IsIdempotentCommutativeMonoid.identityʳ
d_identity'691'_1076 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny
d_identity'691'_1076 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
d_identity'691'_1076 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6
  = T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
du_identity'691'_1076 T_IsIdempotentCommutativeMonoid_884
v6
du_identity'691'_1076 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny
du_identity'691'_1076 :: T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
du_identity'691'_1076 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1
          = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
              (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_712 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_754
         ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1)))
-- Algebra.Lattice.Structures._.IsIdempotentCommutativeMonoid.identityˡ
d_identity'737'_1078 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny
d_identity'737'_1078 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
d_identity'737'_1078 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6
  = T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
du_identity'737'_1078 T_IsIdempotentCommutativeMonoid_884
v6
du_identity'737'_1078 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny
du_identity'737'_1078 :: T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
du_identity'737'_1078 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1
          = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
              (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_712 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_752
         ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1)))
-- Algebra.Lattice.Structures._.IsIdempotentCommutativeMonoid.isBand
d_isBand_1080 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
d_isBand_1080 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsBand_526
d_isBand_1080 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6 = T_IsIdempotentCommutativeMonoid_884 -> T_IsBand_526
du_isBand_1080 T_IsIdempotentCommutativeMonoid_884
v6
du_isBand_1080 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
du_isBand_1080 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsBand_526
du_isBand_1080 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsIdempotentMonoid_826 -> T_IsBand_526)
-> AgdaAny -> T_IsBand_526
forall a b. a -> b
coe
      T_IsIdempotentMonoid_826 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.du_isBand_876
      ((T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_942 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0))
-- Algebra.Lattice.Structures._.IsIdempotentCommutativeMonoid.isCommutativeBand
d_isCommutativeBand_1082 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
d_isCommutativeBand_1082 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsCommutativeBand_612
d_isCommutativeBand_1082 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsCommutativeBand_612
du_isCommutativeBand_1082
du_isCommutativeBand_1082 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
du_isCommutativeBand_1082 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsCommutativeBand_612
du_isCommutativeBand_1082 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v1 T_IsIdempotentCommutativeMonoid_884
v2
  = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948 T_IsIdempotentCommutativeMonoid_884
v2
-- Algebra.Lattice.Structures._.IsIdempotentCommutativeMonoid.isCommutativeMagma
d_isCommutativeMagma_1084 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
d_isCommutativeMagma_1084 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsCommutativeMagma_214
d_isCommutativeMagma_1084 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6
  = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_1084 T_IsIdempotentCommutativeMonoid_884
v6
du_isCommutativeMagma_1084 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
du_isCommutativeMagma_1084 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_1084 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1
          = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
              (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> T_IsCommutativeMagma_214
forall a b. a -> b
coe
      ((T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_606
         ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
            (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1)))
-- Algebra.Lattice.Structures._.IsIdempotentCommutativeMonoid.isCommutativeMonoid
d_isCommutativeMonoid_1086 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764
d_isCommutativeMonoid_1086 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_1086 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0)
-- Algebra.Lattice.Structures._.IsIdempotentCommutativeMonoid.isCommutativeSemigroup
d_isCommutativeSemigroup_1088 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_1088 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_1088 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6
  = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_1088 T_IsIdempotentCommutativeMonoid_884
v6
du_isCommutativeSemigroup_1088 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_1088 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_1088 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe
      T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
      ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0))
-- Algebra.Lattice.Structures._.IsIdempotentCommutativeMonoid.isIdempotentMonoid
d_isIdempotentMonoid_1092 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826
d_isIdempotentMonoid_1092 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentMonoid_826
d_isIdempotentMonoid_1092 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentMonoid_826
du_isIdempotentMonoid_1092
du_isIdempotentMonoid_1092 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826
du_isIdempotentMonoid_1092 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentMonoid_826
du_isIdempotentMonoid_1092 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v1 T_IsIdempotentCommutativeMonoid_884
v2
  = (T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826)
-> T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_942 T_IsIdempotentCommutativeMonoid_884
v2
-- Algebra.Lattice.Structures._.IsIdempotentCommutativeMonoid.isPartialEquivalence
d_isPartialEquivalence_1098 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1098 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1098 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6
  = T_IsIdempotentCommutativeMonoid_884 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1098 T_IsIdempotentCommutativeMonoid_884
v6
du_isPartialEquivalence_1098 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1098 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1098 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1
          = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
              (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2
             = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                  ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4))))))
-- Algebra.Lattice.Structures._.IsIdempotentCommutativeMonoid.isUnitalMagma
d_isUnitalMagma_1102 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
d_isUnitalMagma_1102 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsUnitalMagma_666
d_isUnitalMagma_1102 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6
  = T_IsIdempotentCommutativeMonoid_884 -> T_IsUnitalMagma_666
du_isUnitalMagma_1102 T_IsIdempotentCommutativeMonoid_884
v6
du_isUnitalMagma_1102 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
du_isUnitalMagma_1102 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsUnitalMagma_666
du_isUnitalMagma_1102 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1
          = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
              (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> T_IsUnitalMagma_666
forall a b. a -> b
coe
      ((T_IsMonoid_712 -> T_IsUnitalMagma_666) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsUnitalMagma_666
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_756
         ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1)))
-- Algebra.Lattice.Structures._.IsIdempotentCommutativeMonoid.reflexive
d_reflexive_1106 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1106 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1106 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6 = T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1106 T_IsIdempotentCommutativeMonoid_884
v6
du_reflexive_1106 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1106 :: T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1106 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1
          = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
              (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2
             = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                    ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4))
                    AgdaAny
v5))))
-- Algebra.Lattice.Structures._.IsIdempotentCommutativeMonoid.setoid
d_setoid_1108 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1108 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_Setoid_46
d_setoid_1108 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6 = T_IsIdempotentCommutativeMonoid_884 -> T_Setoid_46
du_setoid_1108 T_IsIdempotentCommutativeMonoid_884
v6
du_setoid_1108 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1108 :: T_IsIdempotentCommutativeMonoid_884 -> T_Setoid_46
du_setoid_1108 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1
          = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
              (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2
             = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
               ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v3)))))
-- Algebra.Lattice.Structures._.IsIdempotentCommutativeMonoid.∙-congʳ
d_'8729''45'cong'691'_1116 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1116 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1116 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6
  = T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1116 T_IsIdempotentCommutativeMonoid_884
v6
du_'8729''45'cong'691'_1116 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1116 :: T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1116 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1
          = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
              (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2
             = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
v5
                      = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6
                         = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v4) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                        ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6)
                        ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                           ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                              (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))))))
-- Algebra.Lattice.Structures._.IsIdempotentCommutativeMonoid.∙-congˡ
d_'8729''45'cong'737'_1118 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1118 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1118 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6
  = T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1118 T_IsIdempotentCommutativeMonoid_884
v6
du_'8729''45'cong'737'_1118 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1118 :: T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1118 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1
          = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
              (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2
             = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
v5
                      = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6
                         = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v4) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                        ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6)
                        ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                           ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                              (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))))))
-- Algebra.Lattice.Structures.IsSemilattice
d_IsSemilattice_2766 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_IsSemilattice_2766 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_IsSemilattice_2766 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Lattice.Structures.IsSemilattice._.comm
d_comm_2776 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_comm_2776 :: T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_2776 T_IsCommutativeBand_612
v0
  = (T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_622 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0)
-- Algebra.Lattice.Structures.IsSemilattice._.isBand
d_isBand_2778 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
d_isBand_2778 :: T_IsCommutativeBand_612 -> T_IsBand_526
d_isBand_2778 T_IsCommutativeBand_612
v0
  = (T_IsCommutativeBand_612 -> T_IsBand_526)
-> AgdaAny -> T_IsBand_526
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0)
-- Algebra.Lattice.Structures.IsSemilattice._.assoc
d_assoc_2782 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2782 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_assoc_2782 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5 = T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_2782 T_IsCommutativeBand_612
v5
du_assoc_2782 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_2782 :: T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_2782 T_IsCommutativeBand_612
v0
  = (T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_498
      ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
         ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0)))
-- Algebra.Lattice.Structures.IsSemilattice._.idem
d_idem_2784 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny
d_idem_2784 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> AgdaAny
-> AgdaAny
d_idem_2784 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5 = T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny
du_idem_2784 T_IsCommutativeBand_612
v5
du_idem_2784 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny
du_idem_2784 :: T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny
du_idem_2784 T_IsCommutativeBand_612
v0
  = (T_IsBand_526 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsBand_526 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_536
      ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0))
-- Algebra.Lattice.Structures.IsSemilattice._.isEquivalence
d_isEquivalence_2786 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_2786 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> T_IsEquivalence_28
d_isEquivalence_2786 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5
  = T_IsCommutativeBand_612 -> T_IsEquivalence_28
du_isEquivalence_2786 T_IsCommutativeBand_612
v5
du_isEquivalence_2786 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_2786 :: T_IsCommutativeBand_612 -> T_IsEquivalence_28
du_isEquivalence_2786 T_IsCommutativeBand_612
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
            ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0))))
-- Algebra.Lattice.Structures.IsSemilattice._.isMagma
d_isMagma_2788 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_2788 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> T_IsMagma_178
d_isMagma_2788 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5 = T_IsCommutativeBand_612 -> T_IsMagma_178
du_isMagma_2788 T_IsCommutativeBand_612
v5
du_isMagma_2788 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
du_isMagma_2788 :: T_IsCommutativeBand_612 -> T_IsMagma_178
du_isMagma_2788 T_IsCommutativeBand_612
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
         ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0)))
-- Algebra.Lattice.Structures.IsSemilattice._.isPartialEquivalence
d_isPartialEquivalence_2790 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2790 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2790 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5
  = T_IsCommutativeBand_612 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2790 T_IsCommutativeBand_612
v5
du_isPartialEquivalence_2790 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2790 :: T_IsCommutativeBand_612 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2790 T_IsCommutativeBand_612
v0
  = let v1 :: T_IsBand_526
v1 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3)))))
-- Algebra.Lattice.Structures.IsSemilattice._.isSemigroup
d_isSemigroup_2792 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_2792 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> T_IsSemigroup_488
d_isSemigroup_2792 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5 = T_IsCommutativeBand_612 -> T_IsSemigroup_488
du_isSemigroup_2792 T_IsCommutativeBand_612
v5
du_isSemigroup_2792 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
du_isSemigroup_2792 :: T_IsCommutativeBand_612 -> T_IsSemigroup_488
du_isSemigroup_2792 T_IsCommutativeBand_612
v0
  = (T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
      ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0))
-- Algebra.Lattice.Structures.IsSemilattice._.refl
d_refl_2794 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny
d_refl_2794 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> AgdaAny
-> AgdaAny
d_refl_2794 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5 = T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny
du_refl_2794 T_IsCommutativeBand_612
v5
du_refl_2794 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny
du_refl_2794 :: T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny
du_refl_2794 T_IsCommutativeBand_612
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
               ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0)))))
-- Algebra.Lattice.Structures.IsSemilattice._.reflexive
d_reflexive_2796 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2796 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2796 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5 = T_IsCommutativeBand_612
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2796 T_IsCommutativeBand_612
v5
du_reflexive_2796 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2796 :: T_IsCommutativeBand_612
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2796 T_IsCommutativeBand_612
v0
  = let v1 :: T_IsBand_526
v1 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3))
                 AgdaAny
v4)))
-- Algebra.Lattice.Structures.IsSemilattice._.setoid
d_setoid_2798 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_2798 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> T_Setoid_46
d_setoid_2798 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5 = T_IsCommutativeBand_612 -> T_Setoid_46
du_setoid_2798 T_IsCommutativeBand_612
v5
du_setoid_2798 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_2798 :: T_IsCommutativeBand_612 -> T_Setoid_46
du_setoid_2798 T_IsCommutativeBand_612
v0
  = let v1 :: T_IsBand_526
v1 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
            ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v2))))
-- Algebra.Lattice.Structures.IsSemilattice._.sym
d_sym_2800 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2800 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_2800 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5 = T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2800 T_IsCommutativeBand_612
v5
du_sym_2800 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2800 :: T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2800 T_IsCommutativeBand_612
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
               ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0)))))
-- Algebra.Lattice.Structures.IsSemilattice._.trans
d_trans_2802 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2802 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_2802 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5 = T_IsCommutativeBand_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2802 T_IsCommutativeBand_612
v5
du_trans_2802 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2802 :: T_IsCommutativeBand_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2802 T_IsCommutativeBand_612
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
               ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0)))))
-- Algebra.Lattice.Structures.IsSemilattice._.∙-cong
d_'8729''45'cong_2804 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_2804 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_2804 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5
  = T_IsCommutativeBand_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_2804 T_IsCommutativeBand_612
v5
du_'8729''45'cong_2804 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong_2804 :: T_IsCommutativeBand_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_2804 T_IsCommutativeBand_612
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
            ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0))))
-- Algebra.Lattice.Structures.IsSemilattice._.∙-congʳ
d_'8729''45'cong'691'_2806 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2806 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2806 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5
  = T_IsCommutativeBand_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2806 T_IsCommutativeBand_612
v5
du_'8729''45'cong'691'_2806 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2806 :: T_IsCommutativeBand_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2806 T_IsCommutativeBand_612
v0
  = let v1 :: T_IsBand_526
v1 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4
                   = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5
                      = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v3) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                     ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5)
                     ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                        ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                           (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))))))
-- Algebra.Lattice.Structures.IsSemilattice._.∙-congˡ
d_'8729''45'cong'737'_2808 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2808 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2808 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5
  = T_IsCommutativeBand_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2808 T_IsCommutativeBand_612
v5
du_'8729''45'cong'737'_2808 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2808 :: T_IsCommutativeBand_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2808 T_IsCommutativeBand_612
v0
  = let v1 :: T_IsBand_526
v1 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4
                   = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5
                      = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v3) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                     ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5)
                     ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                        ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                           (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))))))
-- Algebra.Lattice.Structures.IsMeetSemilattice
d_IsMeetSemilattice_2810 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_IsMeetSemilattice_2810 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_IsMeetSemilattice_2810 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Lattice.Structures.IsMeetSemilattice._.assoc
d_assoc_2820 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2820 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_assoc_2820 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5 = T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_2820 T_IsCommutativeBand_612
v5
du_assoc_2820 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_2820 :: T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_2820 T_IsCommutativeBand_612
v0
  = (T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_498
      ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
         ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0)))
-- Algebra.Lattice.Structures.IsMeetSemilattice._.comm
d_comm_2822 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_comm_2822 :: T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_2822 T_IsCommutativeBand_612
v0
  = (T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_622 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0)
-- Algebra.Lattice.Structures.IsMeetSemilattice._.idem
d_idem_2824 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny
d_idem_2824 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> AgdaAny
-> AgdaAny
d_idem_2824 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5 = T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny
du_idem_2824 T_IsCommutativeBand_612
v5
du_idem_2824 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny
du_idem_2824 :: T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny
du_idem_2824 T_IsCommutativeBand_612
v0
  = (T_IsBand_526 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsBand_526 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_536
      ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0))
-- Algebra.Lattice.Structures.IsMeetSemilattice._.isBand
d_isBand_2826 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
d_isBand_2826 :: T_IsCommutativeBand_612 -> T_IsBand_526
d_isBand_2826 T_IsCommutativeBand_612
v0
  = (T_IsCommutativeBand_612 -> T_IsBand_526)
-> AgdaAny -> T_IsBand_526
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0)
-- Algebra.Lattice.Structures.IsMeetSemilattice._.isEquivalence
d_isEquivalence_2828 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_2828 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> T_IsEquivalence_28
d_isEquivalence_2828 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5
  = T_IsCommutativeBand_612 -> T_IsEquivalence_28
du_isEquivalence_2828 T_IsCommutativeBand_612
v5
du_isEquivalence_2828 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_2828 :: T_IsCommutativeBand_612 -> T_IsEquivalence_28
du_isEquivalence_2828 T_IsCommutativeBand_612
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
            ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0))))
-- Algebra.Lattice.Structures.IsMeetSemilattice._.isMagma
d_isMagma_2830 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_2830 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> T_IsMagma_178
d_isMagma_2830 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5 = T_IsCommutativeBand_612 -> T_IsMagma_178
du_isMagma_2830 T_IsCommutativeBand_612
v5
du_isMagma_2830 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
du_isMagma_2830 :: T_IsCommutativeBand_612 -> T_IsMagma_178
du_isMagma_2830 T_IsCommutativeBand_612
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
         ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0)))
-- Algebra.Lattice.Structures.IsMeetSemilattice._.isPartialEquivalence
d_isPartialEquivalence_2832 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2832 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2832 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5
  = T_IsCommutativeBand_612 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2832 T_IsCommutativeBand_612
v5
du_isPartialEquivalence_2832 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2832 :: T_IsCommutativeBand_612 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2832 T_IsCommutativeBand_612
v0
  = let v1 :: T_IsBand_526
v1 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3)))))
-- Algebra.Lattice.Structures.IsMeetSemilattice._.isSemigroup
d_isSemigroup_2834 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_2834 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> T_IsSemigroup_488
d_isSemigroup_2834 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5 = T_IsCommutativeBand_612 -> T_IsSemigroup_488
du_isSemigroup_2834 T_IsCommutativeBand_612
v5
du_isSemigroup_2834 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
du_isSemigroup_2834 :: T_IsCommutativeBand_612 -> T_IsSemigroup_488
du_isSemigroup_2834 T_IsCommutativeBand_612
v0
  = (T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
      ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0))
-- Algebra.Lattice.Structures.IsMeetSemilattice._.refl
d_refl_2836 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny
d_refl_2836 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> AgdaAny
-> AgdaAny
d_refl_2836 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5 = T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny
du_refl_2836 T_IsCommutativeBand_612
v5
du_refl_2836 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny
du_refl_2836 :: T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny
du_refl_2836 T_IsCommutativeBand_612
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
               ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0)))))
-- Algebra.Lattice.Structures.IsMeetSemilattice._.reflexive
d_reflexive_2838 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2838 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2838 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5 = T_IsCommutativeBand_612
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2838 T_IsCommutativeBand_612
v5
du_reflexive_2838 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2838 :: T_IsCommutativeBand_612
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2838 T_IsCommutativeBand_612
v0
  = let v1 :: T_IsBand_526
v1 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3))
                 AgdaAny
v4)))
-- Algebra.Lattice.Structures.IsMeetSemilattice._.setoid
d_setoid_2840 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_2840 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> T_Setoid_46
d_setoid_2840 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5 = T_IsCommutativeBand_612 -> T_Setoid_46
du_setoid_2840 T_IsCommutativeBand_612
v5
du_setoid_2840 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_2840 :: T_IsCommutativeBand_612 -> T_Setoid_46
du_setoid_2840 T_IsCommutativeBand_612
v0
  = let v1 :: T_IsBand_526
v1 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
            ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v2))))
-- Algebra.Lattice.Structures.IsMeetSemilattice._.sym
d_sym_2842 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2842 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_2842 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5 = T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2842 T_IsCommutativeBand_612
v5
du_sym_2842 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2842 :: T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2842 T_IsCommutativeBand_612
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
               ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0)))))
-- Algebra.Lattice.Structures.IsMeetSemilattice._.trans
d_trans_2844 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2844 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_2844 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5 = T_IsCommutativeBand_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2844 T_IsCommutativeBand_612
v5
du_trans_2844 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2844 :: T_IsCommutativeBand_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2844 T_IsCommutativeBand_612
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
               ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0)))))
-- Algebra.Lattice.Structures.IsMeetSemilattice._.∙-cong
d_'8729''45'cong_2846 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_2846 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_2846 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5
  = T_IsCommutativeBand_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_2846 T_IsCommutativeBand_612
v5
du_'8729''45'cong_2846 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong_2846 :: T_IsCommutativeBand_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_2846 T_IsCommutativeBand_612
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
            ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0))))
-- Algebra.Lattice.Structures.IsMeetSemilattice._.∙-congʳ
d_'8729''45'cong'691'_2848 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2848 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2848 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5
  = T_IsCommutativeBand_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2848 T_IsCommutativeBand_612
v5
du_'8729''45'cong'691'_2848 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2848 :: T_IsCommutativeBand_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2848 T_IsCommutativeBand_612
v0
  = let v1 :: T_IsBand_526
v1 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4
                   = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5
                      = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v3) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                     ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5)
                     ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                        ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                           (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))))))
-- Algebra.Lattice.Structures.IsMeetSemilattice._.∙-congˡ
d_'8729''45'cong'737'_2850 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2850 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2850 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5
  = T_IsCommutativeBand_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2850 T_IsCommutativeBand_612
v5
du_'8729''45'cong'737'_2850 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2850 :: T_IsCommutativeBand_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2850 T_IsCommutativeBand_612
v0
  = let v1 :: T_IsBand_526
v1 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4
                   = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5
                      = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v3) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                     ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5)
                     ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                        ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                           (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))))))
-- Algebra.Lattice.Structures.IsJoinSemilattice
d_IsJoinSemilattice_2852 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_IsJoinSemilattice_2852 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_IsJoinSemilattice_2852 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Lattice.Structures.IsJoinSemilattice._.assoc
d_assoc_2862 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2862 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_assoc_2862 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5 = T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_2862 T_IsCommutativeBand_612
v5
du_assoc_2862 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_2862 :: T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_2862 T_IsCommutativeBand_612
v0
  = (T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_498
      ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
         ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0)))
-- Algebra.Lattice.Structures.IsJoinSemilattice._.comm
d_comm_2864 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_comm_2864 :: T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_2864 T_IsCommutativeBand_612
v0
  = (T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_622 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0)
-- Algebra.Lattice.Structures.IsJoinSemilattice._.idem
d_idem_2866 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny
d_idem_2866 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> AgdaAny
-> AgdaAny
d_idem_2866 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5 = T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny
du_idem_2866 T_IsCommutativeBand_612
v5
du_idem_2866 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny
du_idem_2866 :: T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny
du_idem_2866 T_IsCommutativeBand_612
v0
  = (T_IsBand_526 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsBand_526 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_536
      ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0))
-- Algebra.Lattice.Structures.IsJoinSemilattice._.isBand
d_isBand_2868 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
d_isBand_2868 :: T_IsCommutativeBand_612 -> T_IsBand_526
d_isBand_2868 T_IsCommutativeBand_612
v0
  = (T_IsCommutativeBand_612 -> T_IsBand_526)
-> AgdaAny -> T_IsBand_526
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0)
-- Algebra.Lattice.Structures.IsJoinSemilattice._.isEquivalence
d_isEquivalence_2870 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_2870 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> T_IsEquivalence_28
d_isEquivalence_2870 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5
  = T_IsCommutativeBand_612 -> T_IsEquivalence_28
du_isEquivalence_2870 T_IsCommutativeBand_612
v5
du_isEquivalence_2870 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_2870 :: T_IsCommutativeBand_612 -> T_IsEquivalence_28
du_isEquivalence_2870 T_IsCommutativeBand_612
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
            ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0))))
-- Algebra.Lattice.Structures.IsJoinSemilattice._.isMagma
d_isMagma_2872 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_2872 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> T_IsMagma_178
d_isMagma_2872 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5 = T_IsCommutativeBand_612 -> T_IsMagma_178
du_isMagma_2872 T_IsCommutativeBand_612
v5
du_isMagma_2872 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
du_isMagma_2872 :: T_IsCommutativeBand_612 -> T_IsMagma_178
du_isMagma_2872 T_IsCommutativeBand_612
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
         ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0)))
-- Algebra.Lattice.Structures.IsJoinSemilattice._.isPartialEquivalence
d_isPartialEquivalence_2874 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2874 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2874 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5
  = T_IsCommutativeBand_612 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2874 T_IsCommutativeBand_612
v5
du_isPartialEquivalence_2874 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2874 :: T_IsCommutativeBand_612 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2874 T_IsCommutativeBand_612
v0
  = let v1 :: T_IsBand_526
v1 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3)))))
-- Algebra.Lattice.Structures.IsJoinSemilattice._.isSemigroup
d_isSemigroup_2876 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_2876 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> T_IsSemigroup_488
d_isSemigroup_2876 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5 = T_IsCommutativeBand_612 -> T_IsSemigroup_488
du_isSemigroup_2876 T_IsCommutativeBand_612
v5
du_isSemigroup_2876 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
du_isSemigroup_2876 :: T_IsCommutativeBand_612 -> T_IsSemigroup_488
du_isSemigroup_2876 T_IsCommutativeBand_612
v0
  = (T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
      ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0))
-- Algebra.Lattice.Structures.IsJoinSemilattice._.refl
d_refl_2878 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny
d_refl_2878 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> AgdaAny
-> AgdaAny
d_refl_2878 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5 = T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny
du_refl_2878 T_IsCommutativeBand_612
v5
du_refl_2878 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny
du_refl_2878 :: T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny
du_refl_2878 T_IsCommutativeBand_612
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
               ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0)))))
-- Algebra.Lattice.Structures.IsJoinSemilattice._.reflexive
d_reflexive_2880 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2880 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2880 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5 = T_IsCommutativeBand_612
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2880 T_IsCommutativeBand_612
v5
du_reflexive_2880 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2880 :: T_IsCommutativeBand_612
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2880 T_IsCommutativeBand_612
v0
  = let v1 :: T_IsBand_526
v1 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3))
                 AgdaAny
v4)))
-- Algebra.Lattice.Structures.IsJoinSemilattice._.setoid
d_setoid_2882 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_2882 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> T_Setoid_46
d_setoid_2882 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5 = T_IsCommutativeBand_612 -> T_Setoid_46
du_setoid_2882 T_IsCommutativeBand_612
v5
du_setoid_2882 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_2882 :: T_IsCommutativeBand_612 -> T_Setoid_46
du_setoid_2882 T_IsCommutativeBand_612
v0
  = let v1 :: T_IsBand_526
v1 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
            ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v2))))
-- Algebra.Lattice.Structures.IsJoinSemilattice._.sym
d_sym_2884 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2884 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_2884 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5 = T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2884 T_IsCommutativeBand_612
v5
du_sym_2884 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2884 :: T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2884 T_IsCommutativeBand_612
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
               ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0)))))
-- Algebra.Lattice.Structures.IsJoinSemilattice._.trans
d_trans_2886 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2886 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_2886 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5 = T_IsCommutativeBand_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2886 T_IsCommutativeBand_612
v5
du_trans_2886 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2886 :: T_IsCommutativeBand_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2886 T_IsCommutativeBand_612
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
               ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0)))))
-- Algebra.Lattice.Structures.IsJoinSemilattice._.∙-cong
d_'8729''45'cong_2888 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_2888 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_2888 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5
  = T_IsCommutativeBand_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_2888 T_IsCommutativeBand_612
v5
du_'8729''45'cong_2888 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong_2888 :: T_IsCommutativeBand_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_2888 T_IsCommutativeBand_612
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
            ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0))))
-- Algebra.Lattice.Structures.IsJoinSemilattice._.∙-congʳ
d_'8729''45'cong'691'_2890 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2890 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2890 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5
  = T_IsCommutativeBand_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2890 T_IsCommutativeBand_612
v5
du_'8729''45'cong'691'_2890 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2890 :: T_IsCommutativeBand_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2890 T_IsCommutativeBand_612
v0
  = let v1 :: T_IsBand_526
v1 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4
                   = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5
                      = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v3) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                     ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5)
                     ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                        ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                           (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))))))
-- Algebra.Lattice.Structures.IsJoinSemilattice._.∙-congˡ
d_'8729''45'cong'737'_2892 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2892 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2892 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5
  = T_IsCommutativeBand_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2892 T_IsCommutativeBand_612
v5
du_'8729''45'cong'737'_2892 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2892 :: T_IsCommutativeBand_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2892 T_IsCommutativeBand_612
v0
  = let v1 :: T_IsBand_526
v1 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4
                   = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5
                      = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v3) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                     ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5)
                     ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                        ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                           (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))))))
-- Algebra.Lattice.Structures.IsBoundedSemilattice
d_IsBoundedSemilattice_2894 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> ()
d_IsBoundedSemilattice_2894 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_Level_18
d_IsBoundedSemilattice_2894 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.assoc
d_assoc_2906 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2906 :: T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2906 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_498
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
         ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
            ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
               (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0))))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.comm
d_comm_2908 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_comm_2908 :: T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny
d_comm_2908 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_776
      ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.idem
d_idem_2910 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny
d_idem_2910 :: T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
d_idem_2910 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_896 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0)
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.identity
d_identity_2912 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_2912 :: T_IsIdempotentCommutativeMonoid_884 -> T_Σ_14
d_identity_2912 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_724
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
         ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
            (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0)))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.identityʳ
d_identity'691'_2914 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny
d_identity'691'_2914 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
d_identity'691'_2914 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6
  = T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
du_identity'691'_2914 T_IsIdempotentCommutativeMonoid_884
v6
du_identity'691'_2914 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny
du_identity'691'_2914 :: T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
du_identity'691'_2914 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1
          = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
              (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_712 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_754
         ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1)))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.identityˡ
d_identity'737'_2916 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny
d_identity'737'_2916 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
d_identity'737'_2916 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6
  = T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
du_identity'737'_2916 T_IsIdempotentCommutativeMonoid_884
v6
du_identity'737'_2916 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny
du_identity'737'_2916 :: T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
du_identity'737'_2916 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1
          = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
              (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_712 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_752
         ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1)))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.isBand
d_isBand_2918 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
d_isBand_2918 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsBand_526
d_isBand_2918 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6 = T_IsIdempotentCommutativeMonoid_884 -> T_IsBand_526
du_isBand_2918 T_IsIdempotentCommutativeMonoid_884
v6
du_isBand_2918 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
du_isBand_2918 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsBand_526
du_isBand_2918 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsIdempotentMonoid_826 -> T_IsBand_526)
-> AgdaAny -> T_IsBand_526
forall a b. a -> b
coe
      T_IsIdempotentMonoid_826 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.du_isBand_876
      ((T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_942 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.isCommutativeMagma
d_isCommutativeMagma_2920 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
d_isCommutativeMagma_2920 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsCommutativeMagma_214
d_isCommutativeMagma_2920 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6
  = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_2920 T_IsIdempotentCommutativeMonoid_884
v6
du_isCommutativeMagma_2920 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
du_isCommutativeMagma_2920 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_2920 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1
          = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
              (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> T_IsCommutativeMagma_214
forall a b. a -> b
coe
      ((T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_606
         ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
            (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1)))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.isCommutativeMonoid
d_isCommutativeMonoid_2922 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764
d_isCommutativeMonoid_2922 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_2922 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0)
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.isCommutativeSemigroup
d_isCommutativeSemigroup_2924 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_2924 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_2924 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6
  = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_2924 T_IsIdempotentCommutativeMonoid_884
v6
du_isCommutativeSemigroup_2924 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_2924 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_2924 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe
      T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
      ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.isEquivalence
d_isEquivalence_2926 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_2926 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsEquivalence_28
d_isEquivalence_2926 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
               ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                  (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0)))))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.isIdempotentMonoid
d_isIdempotentMonoid_2928 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826
d_isIdempotentMonoid_2928 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentMonoid_826
d_isIdempotentMonoid_2928 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6
  = T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826
du_isIdempotentMonoid_2928 T_IsIdempotentCommutativeMonoid_884
v6
du_isIdempotentMonoid_2928 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826
du_isIdempotentMonoid_2928 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826
du_isIdempotentMonoid_2928 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826)
-> AgdaAny -> T_IsIdempotentMonoid_826
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_942 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0)
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.isMagma
d_isMagma_2930 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_2930 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsMagma_178
d_isMagma_2930 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
         ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
            ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
               (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0))))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.isMonoid
d_isMonoid_2932 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_isMonoid_2932 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsMonoid_712
d_isMonoid_2932 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsCommutativeMonoid_764 -> T_IsMonoid_712)
-> AgdaAny -> T_IsMonoid_712
forall a b. a -> b
coe
      T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
      ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.isPartialEquivalence
d_isPartialEquivalence_2934 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2934 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2934 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6
  = T_IsIdempotentCommutativeMonoid_884 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2934 T_IsIdempotentCommutativeMonoid_884
v6
du_isPartialEquivalence_2934 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2934 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2934 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1
          = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
              (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2
             = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                  ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4))))))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.isSemigroup
d_isSemigroup_2936 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_2936 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsSemigroup_488
d_isSemigroup_2936 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsMonoid_712 -> T_IsSemigroup_488)
-> AgdaAny -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
         ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
            (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0)))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.isCommutativeBand
d_isCommutativeBand_2938 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
d_isCommutativeBand_2938 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsCommutativeBand_612
d_isCommutativeBand_2938 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6
  = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
du_isCommutativeBand_2938 T_IsIdempotentCommutativeMonoid_884
v6
du_isCommutativeBand_2938 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
du_isCommutativeBand_2938 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
du_isCommutativeBand_2938 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> T_IsCommutativeBand_612
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0)
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.isUnitalMagma
d_isUnitalMagma_2940 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
d_isUnitalMagma_2940 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsUnitalMagma_666
d_isUnitalMagma_2940 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6
  = T_IsIdempotentCommutativeMonoid_884 -> T_IsUnitalMagma_666
du_isUnitalMagma_2940 T_IsIdempotentCommutativeMonoid_884
v6
du_isUnitalMagma_2940 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
du_isUnitalMagma_2940 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsUnitalMagma_666
du_isUnitalMagma_2940 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1
          = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
              (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> T_IsUnitalMagma_666
forall a b. a -> b
coe
      ((T_IsMonoid_712 -> T_IsUnitalMagma_666) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsUnitalMagma_666
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_756
         ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1)))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.refl
d_refl_2942 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny
d_refl_2942 :: T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
d_refl_2942 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
               ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
                  ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                     (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0))))))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.reflexive
d_reflexive_2944 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2944 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2944 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6 = T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2944 T_IsIdempotentCommutativeMonoid_884
v6
du_reflexive_2944 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2944 :: T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2944 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1
          = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
              (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2
             = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                    ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4))
                    AgdaAny
v5))))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.setoid
d_setoid_2946 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_2946 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_Setoid_46
d_setoid_2946 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6 = T_IsIdempotentCommutativeMonoid_884 -> T_Setoid_46
du_setoid_2946 T_IsIdempotentCommutativeMonoid_884
v6
du_setoid_2946 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_2946 :: T_IsIdempotentCommutativeMonoid_884 -> T_Setoid_46
du_setoid_2946 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1
          = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
              (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2
             = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
               ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v3)))))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.sym
d_sym_2948 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2948 :: T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2948 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
               ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
                  ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                     (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0))))))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.trans
d_trans_2950 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2950 :: T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2950 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
               ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
                  ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                     (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0))))))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.∙-cong
d_'8729''45'cong_2952 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_2952 :: T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_2952 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
               ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                  (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0)))))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.∙-congʳ
d_'8729''45'cong'691'_2954 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2954 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2954 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6
  = T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2954 T_IsIdempotentCommutativeMonoid_884
v6
du_'8729''45'cong'691'_2954 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2954 :: T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2954 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1
          = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
              (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2
             = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
v5
                      = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6
                         = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v4) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                        ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6)
                        ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                           ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                              (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))))))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.∙-congˡ
d_'8729''45'cong'737'_2956 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2956 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2956 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6
  = T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2956 T_IsIdempotentCommutativeMonoid_884
v6
du_'8729''45'cong'737'_2956 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2956 :: T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2956 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1
          = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
              (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2
             = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
v5
                      = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6
                         = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v4) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                        ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6)
                        ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                           ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                              (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))))))
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice
d_IsBoundedMeetSemilattice_2958 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> ()
d_IsBoundedMeetSemilattice_2958 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_Level_18
d_IsBoundedMeetSemilattice_2958 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice._.identity
d_identity_2970 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_2970 :: T_IsIdempotentCommutativeMonoid_884 -> T_Σ_14
d_identity_2970 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_724
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
         ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
            (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0)))
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice._.identityʳ
d_identity'691'_2972 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny
d_identity'691'_2972 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
d_identity'691'_2972 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6
  = T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
du_identity'691'_2972 T_IsIdempotentCommutativeMonoid_884
v6
du_identity'691'_2972 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny
du_identity'691'_2972 :: T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
du_identity'691'_2972 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1
          = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
              (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_712 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_754
         ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1)))
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice._.identityˡ
d_identity'737'_2974 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny
d_identity'737'_2974 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
d_identity'737'_2974 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6
  = T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
du_identity'737'_2974 T_IsIdempotentCommutativeMonoid_884
v6
du_identity'737'_2974 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny
du_identity'737'_2974 :: T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
du_identity'737'_2974 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1
          = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
              (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_712 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_752
         ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1)))
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice._.isCommutativeBand
d_isCommutativeBand_2976 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
d_isCommutativeBand_2976 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsCommutativeBand_612
d_isCommutativeBand_2976 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6
  = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
du_isCommutativeBand_2976 T_IsIdempotentCommutativeMonoid_884
v6
du_isCommutativeBand_2976 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
du_isCommutativeBand_2976 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
du_isCommutativeBand_2976 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> T_IsCommutativeBand_612
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0)
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice._.assoc
d_assoc_2980 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2980 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_assoc_2980 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6 = T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_2980 T_IsIdempotentCommutativeMonoid_884
v6
du_assoc_2980 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_2980 :: T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_2980 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: AgdaAny
v1
          = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
              (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_498
         ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
            ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1))))
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice._.comm
d_comm_2982 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_comm_2982 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_comm_2982 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6 = T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny
du_comm_2982 T_IsIdempotentCommutativeMonoid_884
v6
du_comm_2982 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny
du_comm_2982 :: T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny
du_comm_2982 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_776
      ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0))
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice._.idem
d_idem_2984 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny
d_idem_2984 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
d_idem_2984 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6 = T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
du_idem_2984 T_IsIdempotentCommutativeMonoid_884
v6
du_idem_2984 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny
du_idem_2984 :: T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
du_idem_2984 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: AgdaAny
v1
          = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
              (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsBand_526 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_526 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_536
         ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice._.isBand
d_isBand_2986 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
d_isBand_2986 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsBand_526
d_isBand_2986 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6 = T_IsIdempotentCommutativeMonoid_884 -> T_IsBand_526
du_isBand_2986 T_IsIdempotentCommutativeMonoid_884
v6
du_isBand_2986 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
du_isBand_2986 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsBand_526
du_isBand_2986 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsIdempotentMonoid_826 -> T_IsBand_526)
-> AgdaAny -> T_IsBand_526
forall a b. a -> b
coe
      T_IsIdempotentMonoid_826 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.du_isBand_876
      ((T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_942 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0))
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice._.isEquivalence
d_isEquivalence_2988 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_2988 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsEquivalence_28
d_isEquivalence_2988 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6
  = T_IsIdempotentCommutativeMonoid_884 -> T_IsEquivalence_28
du_isEquivalence_2988 T_IsIdempotentCommutativeMonoid_884
v6
du_isEquivalence_2988 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_2988 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsEquivalence_28
du_isEquivalence_2988 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: AgdaAny
v1
          = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
              (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
               ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))))
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice._.isMagma
d_isMagma_2990 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_2990 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsMagma_178
d_isMagma_2990 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6 = T_IsIdempotentCommutativeMonoid_884 -> T_IsMagma_178
du_isMagma_2990 T_IsIdempotentCommutativeMonoid_884
v6
du_isMagma_2990 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
du_isMagma_2990 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsMagma_178
du_isMagma_2990 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: AgdaAny
v1
          = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
              (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
            ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1))))
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice._.isPartialEquivalence
d_isPartialEquivalence_2992 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2992 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2992 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6
  = T_IsIdempotentCommutativeMonoid_884 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2992 T_IsIdempotentCommutativeMonoid_884
v6
du_isPartialEquivalence_2992 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2992 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2992 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: AgdaAny
v1
          = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
              (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsBand_526
v2 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> T_IsCommutativeBand_612
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                  ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4))))))
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice._.isSemigroup
d_isSemigroup_2994 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_2994 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsSemigroup_488
d_isSemigroup_2994 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6
  = T_IsIdempotentCommutativeMonoid_884 -> T_IsSemigroup_488
du_isSemigroup_2994 T_IsIdempotentCommutativeMonoid_884
v6
du_isSemigroup_2994 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
du_isSemigroup_2994 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsSemigroup_488
du_isSemigroup_2994 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: AgdaAny
v1
          = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
              (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> T_IsSemigroup_488
forall a b. a -> b
coe
      ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
         ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice._.refl
d_refl_2996 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny
d_refl_2996 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
d_refl_2996 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6 = T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
du_refl_2996 T_IsIdempotentCommutativeMonoid_884
v6
du_refl_2996 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny
du_refl_2996 :: T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
du_refl_2996 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: AgdaAny
v1
          = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
              (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
            ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
               ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
                  ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1))))))
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice._.reflexive
d_reflexive_2998 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2998 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2998 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6 = T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2998 T_IsIdempotentCommutativeMonoid_884
v6
du_reflexive_2998 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2998 :: T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2998 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: AgdaAny
v1
          = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
              (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBand_526
v2 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> T_IsCommutativeBand_612
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                    ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4))
                    AgdaAny
v5))))
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice._.setoid
d_setoid_3000 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_3000 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_Setoid_46
d_setoid_3000 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6 = T_IsIdempotentCommutativeMonoid_884 -> T_Setoid_46
du_setoid_3000 T_IsIdempotentCommutativeMonoid_884
v6
du_setoid_3000 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_3000 :: T_IsIdempotentCommutativeMonoid_884 -> T_Setoid_46
du_setoid_3000 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: AgdaAny
v1
          = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
              (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsBand_526
v2 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> T_IsCommutativeBand_612
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
               ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v3)))))
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice._.sym
d_sym_3002 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_3002 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_3002 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6 = T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_3002 T_IsIdempotentCommutativeMonoid_884
v6
du_sym_3002 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_3002 :: T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_3002 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: AgdaAny
v1
          = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
              (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
            ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
               ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
                  ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1))))))
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice._.trans
d_trans_3004 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_3004 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_3004 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6 = T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_3004 T_IsIdempotentCommutativeMonoid_884
v6
du_trans_3004 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_3004 :: T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_3004 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: AgdaAny
v1
          = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
              (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
            ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
               ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
                  ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1))))))
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice._.∙-cong
d_'8729''45'cong_3006 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_3006 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_3006 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6
  = T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_3006 T_IsIdempotentCommutativeMonoid_884
v6
du_'8729''45'cong_3006 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong_3006 :: T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_3006 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: AgdaAny
v1
          = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
              (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
               ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))))
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice._.∙-congʳ
d_'8729''45'cong'691'_3008 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_3008 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_3008 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6
  = T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3008 T_IsIdempotentCommutativeMonoid_884
v6
du_'8729''45'cong'691'_3008 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3008 :: T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3008 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: AgdaAny
v1
          = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
              (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBand_526
v2 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> T_IsCommutativeBand_612
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
v5
                      = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6
                         = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v4) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                        ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6)
                        ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                           ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                              (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))))))
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice._.∙-congˡ
d_'8729''45'cong'737'_3010 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_3010 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_3010 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6
  = T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3010 T_IsIdempotentCommutativeMonoid_884
v6
du_'8729''45'cong'737'_3010 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3010 :: T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3010 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: AgdaAny
v1
          = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
              (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBand_526
v2 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> T_IsCommutativeBand_612
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
v5
                      = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6
                         = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v4) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                        ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6)
                        ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                           ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                              (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))))))
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice
d_IsBoundedJoinSemilattice_3012 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> ()
d_IsBoundedJoinSemilattice_3012 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_Level_18
d_IsBoundedJoinSemilattice_3012 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice._.identity
d_identity_3024 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_3024 :: T_IsIdempotentCommutativeMonoid_884 -> T_Σ_14
d_identity_3024 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_724
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
         ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
            (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0)))
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice._.identityʳ
d_identity'691'_3026 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny
d_identity'691'_3026 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
d_identity'691'_3026 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6
  = T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
du_identity'691'_3026 T_IsIdempotentCommutativeMonoid_884
v6
du_identity'691'_3026 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny
du_identity'691'_3026 :: T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
du_identity'691'_3026 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1
          = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
              (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_712 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_754
         ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1)))
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice._.identityˡ
d_identity'737'_3028 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny
d_identity'737'_3028 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
d_identity'737'_3028 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6
  = T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
du_identity'737'_3028 T_IsIdempotentCommutativeMonoid_884
v6
du_identity'737'_3028 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny
du_identity'737'_3028 :: T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
du_identity'737'_3028 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1
          = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
              (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_712 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_752
         ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1)))
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice._.isCommutativeBand
d_isCommutativeBand_3030 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
d_isCommutativeBand_3030 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsCommutativeBand_612
d_isCommutativeBand_3030 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6
  = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
du_isCommutativeBand_3030 T_IsIdempotentCommutativeMonoid_884
v6
du_isCommutativeBand_3030 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
du_isCommutativeBand_3030 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
du_isCommutativeBand_3030 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> T_IsCommutativeBand_612
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0)
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice._.assoc
d_assoc_3034 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_3034 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_assoc_3034 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6 = T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_3034 T_IsIdempotentCommutativeMonoid_884
v6
du_assoc_3034 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_3034 :: T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_3034 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: AgdaAny
v1
          = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
              (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_498
         ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
            ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1))))
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice._.comm
d_comm_3036 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_comm_3036 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_comm_3036 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6 = T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny
du_comm_3036 T_IsIdempotentCommutativeMonoid_884
v6
du_comm_3036 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny
du_comm_3036 :: T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny
du_comm_3036 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_776
      ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0))
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice._.idem
d_idem_3038 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny
d_idem_3038 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
d_idem_3038 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6 = T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
du_idem_3038 T_IsIdempotentCommutativeMonoid_884
v6
du_idem_3038 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny
du_idem_3038 :: T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
du_idem_3038 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: AgdaAny
v1
          = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
              (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsBand_526 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_526 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_536
         ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice._.isBand
d_isBand_3040 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
d_isBand_3040 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsBand_526
d_isBand_3040 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6 = T_IsIdempotentCommutativeMonoid_884 -> T_IsBand_526
du_isBand_3040 T_IsIdempotentCommutativeMonoid_884
v6
du_isBand_3040 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
du_isBand_3040 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsBand_526
du_isBand_3040 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsIdempotentMonoid_826 -> T_IsBand_526)
-> AgdaAny -> T_IsBand_526
forall a b. a -> b
coe
      T_IsIdempotentMonoid_826 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.du_isBand_876
      ((T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_942 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0))
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice._.isEquivalence
d_isEquivalence_3042 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_3042 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsEquivalence_28
d_isEquivalence_3042 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6
  = T_IsIdempotentCommutativeMonoid_884 -> T_IsEquivalence_28
du_isEquivalence_3042 T_IsIdempotentCommutativeMonoid_884
v6
du_isEquivalence_3042 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_3042 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsEquivalence_28
du_isEquivalence_3042 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: AgdaAny
v1
          = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
              (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
               ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))))
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice._.isMagma
d_isMagma_3044 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_3044 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsMagma_178
d_isMagma_3044 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6 = T_IsIdempotentCommutativeMonoid_884 -> T_IsMagma_178
du_isMagma_3044 T_IsIdempotentCommutativeMonoid_884
v6
du_isMagma_3044 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
du_isMagma_3044 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsMagma_178
du_isMagma_3044 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: AgdaAny
v1
          = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
              (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
            ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1))))
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice._.isPartialEquivalence
d_isPartialEquivalence_3046 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_3046 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_3046 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6
  = T_IsIdempotentCommutativeMonoid_884 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3046 T_IsIdempotentCommutativeMonoid_884
v6
du_isPartialEquivalence_3046 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_3046 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3046 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: AgdaAny
v1
          = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
              (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsBand_526
v2 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> T_IsCommutativeBand_612
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                  ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4))))))
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice._.isSemigroup
d_isSemigroup_3048 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_3048 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsSemigroup_488
d_isSemigroup_3048 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6
  = T_IsIdempotentCommutativeMonoid_884 -> T_IsSemigroup_488
du_isSemigroup_3048 T_IsIdempotentCommutativeMonoid_884
v6
du_isSemigroup_3048 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
du_isSemigroup_3048 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsSemigroup_488
du_isSemigroup_3048 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: AgdaAny
v1
          = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
              (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> T_IsSemigroup_488
forall a b. a -> b
coe
      ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
         ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice._.refl
d_refl_3050 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny
d_refl_3050 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
d_refl_3050 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6 = T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
du_refl_3050 T_IsIdempotentCommutativeMonoid_884
v6
du_refl_3050 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny
du_refl_3050 :: T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
du_refl_3050 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: AgdaAny
v1
          = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
              (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
            ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
               ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
                  ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1))))))
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice._.reflexive
d_reflexive_3052 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_3052 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_3052 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6 = T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_3052 T_IsIdempotentCommutativeMonoid_884
v6
du_reflexive_3052 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_3052 :: T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_3052 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: AgdaAny
v1
          = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
              (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBand_526
v2 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> T_IsCommutativeBand_612
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                    ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4))
                    AgdaAny
v5))))
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice._.setoid
d_setoid_3054 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_3054 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_Setoid_46
d_setoid_3054 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6 = T_IsIdempotentCommutativeMonoid_884 -> T_Setoid_46
du_setoid_3054 T_IsIdempotentCommutativeMonoid_884
v6
du_setoid_3054 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_3054 :: T_IsIdempotentCommutativeMonoid_884 -> T_Setoid_46
du_setoid_3054 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: AgdaAny
v1
          = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
              (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsBand_526
v2 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> T_IsCommutativeBand_612
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
               ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v3)))))
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice._.sym
d_sym_3056 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_3056 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_3056 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6 = T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_3056 T_IsIdempotentCommutativeMonoid_884
v6
du_sym_3056 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_3056 :: T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_3056 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: AgdaAny
v1
          = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
              (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
            ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
               ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
                  ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1))))))
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice._.trans
d_trans_3058 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_3058 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_3058 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6 = T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_3058 T_IsIdempotentCommutativeMonoid_884
v6
du_trans_3058 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_3058 :: T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_3058 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: AgdaAny
v1
          = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
              (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
            ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
               ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
                  ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1))))))
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice._.∙-cong
d_'8729''45'cong_3060 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_3060 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_3060 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6
  = T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_3060 T_IsIdempotentCommutativeMonoid_884
v6
du_'8729''45'cong_3060 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong_3060 :: T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_3060 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: AgdaAny
v1
          = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
              (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
               ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))))
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice._.∙-congʳ
d_'8729''45'cong'691'_3062 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_3062 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_3062 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6
  = T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3062 T_IsIdempotentCommutativeMonoid_884
v6
du_'8729''45'cong'691'_3062 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3062 :: T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3062 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: AgdaAny
v1
          = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
              (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBand_526
v2 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> T_IsCommutativeBand_612
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
v5
                      = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6
                         = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v4) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                        ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6)
                        ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                           ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                              (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))))))
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice._.∙-congˡ
d_'8729''45'cong'737'_3064 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_3064 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_3064 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_884
v6
  = T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3064 T_IsIdempotentCommutativeMonoid_884
v6
du_'8729''45'cong'737'_3064 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3064 :: T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3064 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: AgdaAny
v1
          = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
              (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBand_526
v2 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (AgdaAny -> T_IsCommutativeBand_612
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
v5
                      = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6
                         = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v4) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                        ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6)
                        ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                           ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                              (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))))))
-- Algebra.Lattice.Structures.IsLattice
d_IsLattice_3070 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_IsLattice_3070 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_IsLattice_3070
  = C_constructor_3140 MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
                       (AgdaAny -> AgdaAny -> AgdaAny)
                       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                       (AgdaAny ->
                        AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                       (AgdaAny -> AgdaAny -> AgdaAny)
                       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                       (AgdaAny ->
                        AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                       MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
-- Algebra.Lattice.Structures.IsLattice.isEquivalence
d_isEquivalence_3092 ::
  T_IsLattice_3070 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_3092 :: T_IsLattice_3070 -> T_IsEquivalence_28
d_isEquivalence_3092 T_IsLattice_3070
v0
  = case T_IsLattice_3070 -> T_IsLattice_3070
forall a b. a -> b
coe T_IsLattice_3070
v0 of
      C_constructor_3140 T_IsEquivalence_28
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7 T_Σ_14
v8 -> T_IsEquivalence_28 -> T_IsEquivalence_28
forall a b. a -> b
coe T_IsEquivalence_28
v1
      T_IsLattice_3070
_ -> T_IsEquivalence_28
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Structures.IsLattice.∨-comm
d_'8744''45'comm_3094 ::
  T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_3094 :: T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_3094 T_IsLattice_3070
v0
  = case T_IsLattice_3070 -> T_IsLattice_3070
forall a b. a -> b
coe T_IsLattice_3070
v0 of
      C_constructor_3140 T_IsEquivalence_28
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7 T_Σ_14
v8 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsLattice_3070
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Structures.IsLattice.∨-assoc
d_'8744''45'assoc_3096 ::
  T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_3096 :: T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_3096 T_IsLattice_3070
v0
  = case T_IsLattice_3070 -> T_IsLattice_3070
forall a b. a -> b
coe T_IsLattice_3070
v0 of
      C_constructor_3140 T_IsEquivalence_28
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7 T_Σ_14
v8 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3
      T_IsLattice_3070
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Structures.IsLattice.∨-cong
d_'8744''45'cong_3098 ::
  T_IsLattice_3070 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong_3098 :: T_IsLattice_3070
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong_3098 T_IsLattice_3070
v0
  = case T_IsLattice_3070 -> T_IsLattice_3070
forall a b. a -> b
coe T_IsLattice_3070
v0 of
      C_constructor_3140 T_IsEquivalence_28
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7 T_Σ_14
v8 -> (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
      T_IsLattice_3070
_ -> AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Structures.IsLattice.∧-comm
d_'8743''45'comm_3100 ::
  T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_3100 :: T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_3100 T_IsLattice_3070
v0
  = case T_IsLattice_3070 -> T_IsLattice_3070
forall a b. a -> b
coe T_IsLattice_3070
v0 of
      C_constructor_3140 T_IsEquivalence_28
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7 T_Σ_14
v8 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v5
      T_IsLattice_3070
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Structures.IsLattice.∧-assoc
d_'8743''45'assoc_3102 ::
  T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_3102 :: T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_3102 T_IsLattice_3070
v0
  = case T_IsLattice_3070 -> T_IsLattice_3070
forall a b. a -> b
coe T_IsLattice_3070
v0 of
      C_constructor_3140 T_IsEquivalence_28
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7 T_Σ_14
v8 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6
      T_IsLattice_3070
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Structures.IsLattice.∧-cong
d_'8743''45'cong_3104 ::
  T_IsLattice_3070 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong_3104 :: T_IsLattice_3070
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong_3104 T_IsLattice_3070
v0
  = case T_IsLattice_3070 -> T_IsLattice_3070
forall a b. a -> b
coe T_IsLattice_3070
v0 of
      C_constructor_3140 T_IsEquivalence_28
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7 T_Σ_14
v8 -> (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7
      T_IsLattice_3070
_ -> AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Structures.IsLattice.absorptive
d_absorptive_3106 ::
  T_IsLattice_3070 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_absorptive_3106 :: T_IsLattice_3070 -> T_Σ_14
d_absorptive_3106 T_IsLattice_3070
v0
  = case T_IsLattice_3070 -> T_IsLattice_3070
forall a b. a -> b
coe T_IsLattice_3070
v0 of
      C_constructor_3140 T_IsEquivalence_28
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7 T_Σ_14
v8 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v8
      T_IsLattice_3070
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Structures.IsLattice._.isPartialEquivalence
d_isPartialEquivalence_3110 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsLattice_3070 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_3110 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_3070
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_3110 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsLattice_3070
v6
  = T_IsLattice_3070 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3110 T_IsLattice_3070
v6
du_isPartialEquivalence_3110 ::
  T_IsLattice_3070 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_3110 :: T_IsLattice_3070 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3110 T_IsLattice_3070
v0
  = (T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
      ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070 -> T_IsEquivalence_28
d_isEquivalence_3092 (T_IsLattice_3070 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070
v0))
-- Algebra.Lattice.Structures.IsLattice._.refl
d_refl_3112 :: T_IsLattice_3070 -> AgdaAny -> AgdaAny
d_refl_3112 :: T_IsLattice_3070 -> AgdaAny -> AgdaAny
d_refl_3112 T_IsLattice_3070
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070 -> T_IsEquivalence_28
d_isEquivalence_3092 (T_IsLattice_3070 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070
v0))
-- Algebra.Lattice.Structures.IsLattice._.reflexive
d_reflexive_3114 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsLattice_3070 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_3114 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_3070
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_3114 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsLattice_3070
v6 = T_IsLattice_3070 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_3114 T_IsLattice_3070
v6
du_reflexive_3114 ::
  T_IsLattice_3070 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_3114 :: T_IsLattice_3070 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_3114 T_IsLattice_3070
v0 AgdaAny
v1 AgdaAny
v2 T__'8801'__12
v3
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
      ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070 -> T_IsEquivalence_28
d_isEquivalence_3092 (T_IsLattice_3070 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070
v0)) AgdaAny
v1
-- Algebra.Lattice.Structures.IsLattice._.sym
d_sym_3116 ::
  T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_3116 :: T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_3116 T_IsLattice_3070
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070 -> T_IsEquivalence_28
d_isEquivalence_3092 (T_IsLattice_3070 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070
v0))
-- Algebra.Lattice.Structures.IsLattice._.trans
d_trans_3118 ::
  T_IsLattice_3070 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_3118 :: T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_3118 T_IsLattice_3070
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070 -> T_IsEquivalence_28
d_isEquivalence_3092 (T_IsLattice_3070 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070
v0))
-- Algebra.Lattice.Structures.IsLattice.∨-absorbs-∧
d_'8744''45'absorbs'45''8743'_3120 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'absorbs'45''8743'_3120 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_3070
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'absorbs'45''8743'_3120 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsLattice_3070
v6
  = T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_3120 T_IsLattice_3070
v6
du_'8744''45'absorbs'45''8743'_3120 ::
  T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_3120 :: T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_3120 T_IsLattice_3070
v0
  = (T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28
      ((T_IsLattice_3070 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070 -> T_Σ_14
d_absorptive_3106 (T_IsLattice_3070 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070
v0))
-- Algebra.Lattice.Structures.IsLattice.∧-absorbs-∨
d_'8743''45'absorbs'45''8744'_3122 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'absorbs'45''8744'_3122 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_3070
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'absorbs'45''8744'_3122 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsLattice_3070
v6
  = T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_3122 T_IsLattice_3070
v6
du_'8743''45'absorbs'45''8744'_3122 ::
  T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_3122 :: T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_3122 T_IsLattice_3070
v0
  = (T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30
      ((T_IsLattice_3070 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070 -> T_Σ_14
d_absorptive_3106 (T_IsLattice_3070 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070
v0))
-- Algebra.Lattice.Structures.IsLattice.∧-congˡ
d_'8743''45'cong'737'_3124 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsLattice_3070 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong'737'_3124 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_3070
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong'737'_3124 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsLattice_3070
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
  = T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_3124 T_IsLattice_3070
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
du_'8743''45'cong'737'_3124 ::
  T_IsLattice_3070 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_3124 :: T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_3124 T_IsLattice_3070
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4
  = (T_IsLattice_3070
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> T_IsLattice_3070
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_3070
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong_3104 T_IsLattice_3070
v0 AgdaAny
v1 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3
      ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_28 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
         (T_IsLattice_3070 -> T_IsEquivalence_28
d_isEquivalence_3092 (T_IsLattice_3070 -> T_IsLattice_3070
forall a b. a -> b
coe T_IsLattice_3070
v0)) AgdaAny
v1)
      AgdaAny
v4
-- Algebra.Lattice.Structures.IsLattice.∧-congʳ
d_'8743''45'cong'691'_3128 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsLattice_3070 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong'691'_3128 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_3070
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong'691'_3128 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsLattice_3070
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
  = T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_3128 T_IsLattice_3070
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
du_'8743''45'cong'691'_3128 ::
  T_IsLattice_3070 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_3128 :: T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_3128 T_IsLattice_3070
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4
  = (T_IsLattice_3070
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> T_IsLattice_3070
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_3070
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong_3104 T_IsLattice_3070
v0 AgdaAny
v2 AgdaAny
v3 AgdaAny
v1 AgdaAny
v1 AgdaAny
v4
      ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_28 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
         (T_IsLattice_3070 -> T_IsEquivalence_28
d_isEquivalence_3092 (T_IsLattice_3070 -> T_IsLattice_3070
forall a b. a -> b
coe T_IsLattice_3070
v0)) AgdaAny
v1)
-- Algebra.Lattice.Structures.IsLattice.∨-congˡ
d_'8744''45'cong'737'_3132 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsLattice_3070 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong'737'_3132 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_3070
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong'737'_3132 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsLattice_3070
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
  = T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_3132 T_IsLattice_3070
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
du_'8744''45'cong'737'_3132 ::
  T_IsLattice_3070 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_3132 :: T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_3132 T_IsLattice_3070
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4
  = (T_IsLattice_3070
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> T_IsLattice_3070
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_3070
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong_3098 T_IsLattice_3070
v0 AgdaAny
v1 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3
      ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_28 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
         (T_IsLattice_3070 -> T_IsEquivalence_28
d_isEquivalence_3092 (T_IsLattice_3070 -> T_IsLattice_3070
forall a b. a -> b
coe T_IsLattice_3070
v0)) AgdaAny
v1)
      AgdaAny
v4
-- Algebra.Lattice.Structures.IsLattice.∨-congʳ
d_'8744''45'cong'691'_3136 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsLattice_3070 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong'691'_3136 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_3070
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong'691'_3136 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsLattice_3070
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
  = T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_3136 T_IsLattice_3070
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
du_'8744''45'cong'691'_3136 ::
  T_IsLattice_3070 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_3136 :: T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_3136 T_IsLattice_3070
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4
  = (T_IsLattice_3070
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> T_IsLattice_3070
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_3070
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong_3098 T_IsLattice_3070
v0 AgdaAny
v2 AgdaAny
v3 AgdaAny
v1 AgdaAny
v1 AgdaAny
v4
      ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_28 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
         (T_IsLattice_3070 -> T_IsEquivalence_28
d_isEquivalence_3092 (T_IsLattice_3070 -> T_IsLattice_3070
forall a b. a -> b
coe T_IsLattice_3070
v0)) AgdaAny
v1)
-- Algebra.Lattice.Structures.IsDistributiveLattice
d_IsDistributiveLattice_3146 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_IsDistributiveLattice_3146 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_IsDistributiveLattice_3146
  = C_constructor_3212 T_IsLattice_3070
                       MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
                       MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
-- Algebra.Lattice.Structures.IsDistributiveLattice.isLattice
d_isLattice_3158 ::
  T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 :: T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 T_IsDistributiveLattice_3146
v0
  = case T_IsDistributiveLattice_3146 -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v0 of
      C_constructor_3212 T_IsLattice_3070
v1 T_Σ_14
v2 T_Σ_14
v3 -> T_IsLattice_3070 -> T_IsLattice_3070
forall a b. a -> b
coe T_IsLattice_3070
v1
      T_IsDistributiveLattice_3146
_ -> T_IsLattice_3070
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Structures.IsDistributiveLattice.∨-distrib-∧
d_'8744''45'distrib'45''8743'_3160 ::
  T_IsDistributiveLattice_3146 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8744''45'distrib'45''8743'_3160 :: T_IsDistributiveLattice_3146 -> T_Σ_14
d_'8744''45'distrib'45''8743'_3160 T_IsDistributiveLattice_3146
v0
  = case T_IsDistributiveLattice_3146 -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v0 of
      C_constructor_3212 T_IsLattice_3070
v1 T_Σ_14
v2 T_Σ_14
v3 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v2
      T_IsDistributiveLattice_3146
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Structures.IsDistributiveLattice.∧-distrib-∨
d_'8743''45'distrib'45''8744'_3162 ::
  T_IsDistributiveLattice_3146 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8743''45'distrib'45''8744'_3162 :: T_IsDistributiveLattice_3146 -> T_Σ_14
d_'8743''45'distrib'45''8744'_3162 T_IsDistributiveLattice_3146
v0
  = case T_IsDistributiveLattice_3146 -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v0 of
      C_constructor_3212 T_IsLattice_3070
v1 T_Σ_14
v2 T_Σ_14
v3 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v3
      T_IsDistributiveLattice_3146
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Structures.IsDistributiveLattice._.absorptive
d_absorptive_3166 ::
  T_IsDistributiveLattice_3146 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_absorptive_3166 :: T_IsDistributiveLattice_3146 -> T_Σ_14
d_absorptive_3166 T_IsDistributiveLattice_3146
v0
  = (T_IsLattice_3070 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsLattice_3070 -> T_Σ_14
d_absorptive_3106 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 (T_IsDistributiveLattice_3146 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v0))
-- Algebra.Lattice.Structures.IsDistributiveLattice._.isEquivalence
d_isEquivalence_3168 ::
  T_IsDistributiveLattice_3146 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_3168 :: T_IsDistributiveLattice_3146 -> T_IsEquivalence_28
d_isEquivalence_3168 T_IsDistributiveLattice_3146
v0
  = (T_IsLattice_3070 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe T_IsLattice_3070 -> T_IsEquivalence_28
d_isEquivalence_3092 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 (T_IsDistributiveLattice_3146 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v0))
-- Algebra.Lattice.Structures.IsDistributiveLattice._.isPartialEquivalence
d_isPartialEquivalence_3170 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_3146 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_3170 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_3146
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_3170 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsDistributiveLattice_3146
v6
  = T_IsDistributiveLattice_3146 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3170 T_IsDistributiveLattice_3146
v6
du_isPartialEquivalence_3170 ::
  T_IsDistributiveLattice_3146 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_3170 :: T_IsDistributiveLattice_3146 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3170 T_IsDistributiveLattice_3146
v0
  = let v1 :: T_IsLattice_3070
v1 = T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 (T_IsDistributiveLattice_3146 -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
         ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070 -> T_IsEquivalence_28
d_isEquivalence_3092 (T_IsLattice_3070 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070
v1)))
-- Algebra.Lattice.Structures.IsDistributiveLattice._.refl
d_refl_3172 :: T_IsDistributiveLattice_3146 -> AgdaAny -> AgdaAny
d_refl_3172 :: T_IsDistributiveLattice_3146 -> AgdaAny -> AgdaAny
d_refl_3172 T_IsDistributiveLattice_3146
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070 -> T_IsEquivalence_28
d_isEquivalence_3092 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 (T_IsDistributiveLattice_3146 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v0)))
-- Algebra.Lattice.Structures.IsDistributiveLattice._.reflexive
d_reflexive_3174 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_3146 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_3174 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_3146
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_3174 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsDistributiveLattice_3146
v6 = T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_3174 T_IsDistributiveLattice_3146
v6
du_reflexive_3174 ::
  T_IsDistributiveLattice_3146 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_3174 :: T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_3174 T_IsDistributiveLattice_3146
v0
  = let v1 :: T_IsLattice_3070
v1 = T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 (T_IsDistributiveLattice_3146 -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v0) in
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (\ AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 ->
         (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
           ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070 -> T_IsEquivalence_28
d_isEquivalence_3092 (T_IsLattice_3070 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070
v1)) AgdaAny
v2)
-- Algebra.Lattice.Structures.IsDistributiveLattice._.sym
d_sym_3176 ::
  T_IsDistributiveLattice_3146 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_3176 :: T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_3176 T_IsDistributiveLattice_3146
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070 -> T_IsEquivalence_28
d_isEquivalence_3092 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 (T_IsDistributiveLattice_3146 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v0)))
-- Algebra.Lattice.Structures.IsDistributiveLattice._.trans
d_trans_3178 ::
  T_IsDistributiveLattice_3146 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_3178 :: T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_3178 T_IsDistributiveLattice_3146
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070 -> T_IsEquivalence_28
d_isEquivalence_3092 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 (T_IsDistributiveLattice_3146 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v0)))
-- Algebra.Lattice.Structures.IsDistributiveLattice._.∧-absorbs-∨
d_'8743''45'absorbs'45''8744'_3180 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_3146 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'absorbs'45''8744'_3180 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_3146
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'absorbs'45''8744'_3180 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsDistributiveLattice_3146
v6
  = T_IsDistributiveLattice_3146 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_3180 T_IsDistributiveLattice_3146
v6
du_'8743''45'absorbs'45''8744'_3180 ::
  T_IsDistributiveLattice_3146 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_3180 :: T_IsDistributiveLattice_3146 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_3180 T_IsDistributiveLattice_3146
v0
  = (T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_3122 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 (T_IsDistributiveLattice_3146 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v0))
-- Algebra.Lattice.Structures.IsDistributiveLattice._.∧-assoc
d_'8743''45'assoc_3182 ::
  T_IsDistributiveLattice_3146 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_3182 :: T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_3182 T_IsDistributiveLattice_3146
v0
  = (T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_3102 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 (T_IsDistributiveLattice_3146 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v0))
-- Algebra.Lattice.Structures.IsDistributiveLattice._.∧-comm
d_'8743''45'comm_3184 ::
  T_IsDistributiveLattice_3146 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_3184 :: T_IsDistributiveLattice_3146 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_3184 T_IsDistributiveLattice_3146
v0
  = (T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_3100 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 (T_IsDistributiveLattice_3146 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v0))
-- Algebra.Lattice.Structures.IsDistributiveLattice._.∧-cong
d_'8743''45'cong_3186 ::
  T_IsDistributiveLattice_3146 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong_3186 :: T_IsDistributiveLattice_3146
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong_3186 T_IsDistributiveLattice_3146
v0
  = (T_IsLattice_3070
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong_3104 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 (T_IsDistributiveLattice_3146 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v0))
-- Algebra.Lattice.Structures.IsDistributiveLattice._.∧-congʳ
d_'8743''45'cong'691'_3188 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_3146 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong'691'_3188 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_3146
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong'691'_3188 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsDistributiveLattice_3146
v6
  = T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_3188 T_IsDistributiveLattice_3146
v6
du_'8743''45'cong'691'_3188 ::
  T_IsDistributiveLattice_3146 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_3188 :: T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_3188 T_IsDistributiveLattice_3146
v0
  = (T_IsLattice_3070
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_3128 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 (T_IsDistributiveLattice_3146 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v0))
-- Algebra.Lattice.Structures.IsDistributiveLattice._.∧-congˡ
d_'8743''45'cong'737'_3190 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_3146 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong'737'_3190 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_3146
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong'737'_3190 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsDistributiveLattice_3146
v6
  = T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_3190 T_IsDistributiveLattice_3146
v6
du_'8743''45'cong'737'_3190 ::
  T_IsDistributiveLattice_3146 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_3190 :: T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_3190 T_IsDistributiveLattice_3146
v0
  = (T_IsLattice_3070
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_3124 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 (T_IsDistributiveLattice_3146 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v0))
-- Algebra.Lattice.Structures.IsDistributiveLattice._.∨-absorbs-∧
d_'8744''45'absorbs'45''8743'_3192 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_3146 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'absorbs'45''8743'_3192 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_3146
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'absorbs'45''8743'_3192 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsDistributiveLattice_3146
v6
  = T_IsDistributiveLattice_3146 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_3192 T_IsDistributiveLattice_3146
v6
du_'8744''45'absorbs'45''8743'_3192 ::
  T_IsDistributiveLattice_3146 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_3192 :: T_IsDistributiveLattice_3146 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_3192 T_IsDistributiveLattice_3146
v0
  = (T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_3120 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 (T_IsDistributiveLattice_3146 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v0))
-- Algebra.Lattice.Structures.IsDistributiveLattice._.∨-assoc
d_'8744''45'assoc_3194 ::
  T_IsDistributiveLattice_3146 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_3194 :: T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_3194 T_IsDistributiveLattice_3146
v0
  = (T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_3096 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 (T_IsDistributiveLattice_3146 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v0))
-- Algebra.Lattice.Structures.IsDistributiveLattice._.∨-comm
d_'8744''45'comm_3196 ::
  T_IsDistributiveLattice_3146 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_3196 :: T_IsDistributiveLattice_3146 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_3196 T_IsDistributiveLattice_3146
v0
  = (T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_3094 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 (T_IsDistributiveLattice_3146 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v0))
-- Algebra.Lattice.Structures.IsDistributiveLattice._.∨-cong
d_'8744''45'cong_3198 ::
  T_IsDistributiveLattice_3146 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong_3198 :: T_IsDistributiveLattice_3146
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong_3198 T_IsDistributiveLattice_3146
v0
  = (T_IsLattice_3070
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong_3098 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 (T_IsDistributiveLattice_3146 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v0))
-- Algebra.Lattice.Structures.IsDistributiveLattice._.∨-congʳ
d_'8744''45'cong'691'_3200 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_3146 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong'691'_3200 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_3146
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong'691'_3200 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsDistributiveLattice_3146
v6
  = T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_3200 T_IsDistributiveLattice_3146
v6
du_'8744''45'cong'691'_3200 ::
  T_IsDistributiveLattice_3146 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_3200 :: T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_3200 T_IsDistributiveLattice_3146
v0
  = (T_IsLattice_3070
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_3136 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 (T_IsDistributiveLattice_3146 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v0))
-- Algebra.Lattice.Structures.IsDistributiveLattice._.∨-congˡ
d_'8744''45'cong'737'_3202 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_3146 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong'737'_3202 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_3146
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong'737'_3202 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsDistributiveLattice_3146
v6
  = T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_3202 T_IsDistributiveLattice_3146
v6
du_'8744''45'cong'737'_3202 ::
  T_IsDistributiveLattice_3146 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_3202 :: T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_3202 T_IsDistributiveLattice_3146
v0
  = (T_IsLattice_3070
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_3132 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 (T_IsDistributiveLattice_3146 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v0))
-- Algebra.Lattice.Structures.IsDistributiveLattice.∨-distribˡ-∧
d_'8744''45'distrib'737''45''8743'_3204 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_3146 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'distrib'737''45''8743'_3204 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_3146
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'distrib'737''45''8743'_3204 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsDistributiveLattice_3146
v6
  = T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'737''45''8743'_3204 T_IsDistributiveLattice_3146
v6
du_'8744''45'distrib'737''45''8743'_3204 ::
  T_IsDistributiveLattice_3146 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'737''45''8743'_3204 :: T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'737''45''8743'_3204 T_IsDistributiveLattice_3146
v0
  = (T_Σ_14 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28
      ((T_IsDistributiveLattice_3146 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146 -> T_Σ_14
d_'8744''45'distrib'45''8743'_3160 (T_IsDistributiveLattice_3146 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v0))
-- Algebra.Lattice.Structures.IsDistributiveLattice.∨-distribʳ-∧
d_'8744''45'distrib'691''45''8743'_3206 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_3146 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'distrib'691''45''8743'_3206 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_3146
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'distrib'691''45''8743'_3206 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsDistributiveLattice_3146
v6
  = T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'691''45''8743'_3206 T_IsDistributiveLattice_3146
v6
du_'8744''45'distrib'691''45''8743'_3206 ::
  T_IsDistributiveLattice_3146 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'691''45''8743'_3206 :: T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'691''45''8743'_3206 T_IsDistributiveLattice_3146
v0
  = (T_Σ_14 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30
      ((T_IsDistributiveLattice_3146 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146 -> T_Σ_14
d_'8744''45'distrib'45''8743'_3160 (T_IsDistributiveLattice_3146 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v0))
-- Algebra.Lattice.Structures.IsDistributiveLattice.∧-distribˡ-∨
d_'8743''45'distrib'737''45''8744'_3208 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_3146 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'distrib'737''45''8744'_3208 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_3146
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'distrib'737''45''8744'_3208 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsDistributiveLattice_3146
v6
  = T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'737''45''8744'_3208 T_IsDistributiveLattice_3146
v6
du_'8743''45'distrib'737''45''8744'_3208 ::
  T_IsDistributiveLattice_3146 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'737''45''8744'_3208 :: T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'737''45''8744'_3208 T_IsDistributiveLattice_3146
v0
  = (T_Σ_14 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28
      ((T_IsDistributiveLattice_3146 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146 -> T_Σ_14
d_'8743''45'distrib'45''8744'_3162 (T_IsDistributiveLattice_3146 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v0))
-- Algebra.Lattice.Structures.IsDistributiveLattice.∧-distribʳ-∨
d_'8743''45'distrib'691''45''8744'_3210 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_3146 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'distrib'691''45''8744'_3210 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_3146
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'distrib'691''45''8744'_3210 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsDistributiveLattice_3146
v6
  = T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'691''45''8744'_3210 T_IsDistributiveLattice_3146
v6
du_'8743''45'distrib'691''45''8744'_3210 ::
  T_IsDistributiveLattice_3146 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'691''45''8744'_3210 :: T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'691''45''8744'_3210 T_IsDistributiveLattice_3146
v0
  = (T_Σ_14 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30
      ((T_IsDistributiveLattice_3146 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146 -> T_Σ_14
d_'8743''45'distrib'45''8744'_3162 (T_IsDistributiveLattice_3146 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v0))
-- Algebra.Lattice.Structures.IsBooleanAlgebra
d_IsBooleanAlgebra_3224 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsBooleanAlgebra_3224 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 = ()
data T_IsBooleanAlgebra_3224
  = C_constructor_3314 T_IsDistributiveLattice_3146
                       MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
                       MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
                       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Lattice.Structures.IsBooleanAlgebra.isDistributiveLattice
d_isDistributiveLattice_3244 ::
  T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_3244 :: T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_3244 T_IsBooleanAlgebra_3224
v0
  = case T_IsBooleanAlgebra_3224 -> T_IsBooleanAlgebra_3224
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0 of
      C_constructor_3314 T_IsDistributiveLattice_3146
v1 T_Σ_14
v2 T_Σ_14
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 -> T_IsDistributiveLattice_3146 -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v1
      T_IsBooleanAlgebra_3224
_ -> T_IsDistributiveLattice_3146
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Structures.IsBooleanAlgebra.∨-complement
d_'8744''45'complement_3246 ::
  T_IsBooleanAlgebra_3224 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8744''45'complement_3246 :: T_IsBooleanAlgebra_3224 -> T_Σ_14
d_'8744''45'complement_3246 T_IsBooleanAlgebra_3224
v0
  = case T_IsBooleanAlgebra_3224 -> T_IsBooleanAlgebra_3224
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0 of
      C_constructor_3314 T_IsDistributiveLattice_3146
v1 T_Σ_14
v2 T_Σ_14
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v2
      T_IsBooleanAlgebra_3224
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Structures.IsBooleanAlgebra.∧-complement
d_'8743''45'complement_3248 ::
  T_IsBooleanAlgebra_3224 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8743''45'complement_3248 :: T_IsBooleanAlgebra_3224 -> T_Σ_14
d_'8743''45'complement_3248 T_IsBooleanAlgebra_3224
v0
  = case T_IsBooleanAlgebra_3224 -> T_IsBooleanAlgebra_3224
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0 of
      C_constructor_3314 T_IsDistributiveLattice_3146
v1 T_Σ_14
v2 T_Σ_14
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v3
      T_IsBooleanAlgebra_3224
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Structures.IsBooleanAlgebra.¬-cong
d_'172''45'cong_3250 ::
  T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'172''45'cong_3250 :: T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'172''45'cong_3250 T_IsBooleanAlgebra_3224
v0
  = case T_IsBooleanAlgebra_3224 -> T_IsBooleanAlgebra_3224
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0 of
      C_constructor_3314 T_IsDistributiveLattice_3146
v1 T_Σ_14
v2 T_Σ_14
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
      T_IsBooleanAlgebra_3224
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.absorptive
d_absorptive_3254 ::
  T_IsBooleanAlgebra_3224 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_absorptive_3254 :: T_IsBooleanAlgebra_3224 -> T_Σ_14
d_absorptive_3254 T_IsBooleanAlgebra_3224
v0
  = (T_IsLattice_3070 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsLattice_3070 -> T_Σ_14
d_absorptive_3106
      ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_3244 (T_IsBooleanAlgebra_3224 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0)))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.isEquivalence
d_isEquivalence_3256 ::
  T_IsBooleanAlgebra_3224 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_3256 :: T_IsBooleanAlgebra_3224 -> T_IsEquivalence_28
d_isEquivalence_3256 T_IsBooleanAlgebra_3224
v0
  = (T_IsLattice_3070 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsLattice_3070 -> T_IsEquivalence_28
d_isEquivalence_3092
      ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_3244 (T_IsBooleanAlgebra_3224 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0)))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.isLattice
d_isLattice_3258 :: T_IsBooleanAlgebra_3224 -> T_IsLattice_3070
d_isLattice_3258 :: T_IsBooleanAlgebra_3224 -> T_IsLattice_3070
d_isLattice_3258 T_IsBooleanAlgebra_3224
v0
  = (T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> T_IsLattice_3070
forall a b. a -> b
coe T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_3244 (T_IsBooleanAlgebra_3224 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.isPartialEquivalence
d_isPartialEquivalence_3260 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsBooleanAlgebra_3224 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_3260 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_3224
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_3260 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsBooleanAlgebra_3224
v9
  = T_IsBooleanAlgebra_3224 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3260 T_IsBooleanAlgebra_3224
v9
du_isPartialEquivalence_3260 ::
  T_IsBooleanAlgebra_3224 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_3260 :: T_IsBooleanAlgebra_3224 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3260 T_IsBooleanAlgebra_3224
v0
  = let v1 :: T_IsDistributiveLattice_3146
v1 = T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_3244 (T_IsBooleanAlgebra_3224 -> T_IsBooleanAlgebra_3224
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_3070
v2 = T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 (T_IsDistributiveLattice_3146 -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070 -> T_IsEquivalence_28
d_isEquivalence_3092 (T_IsLattice_3070 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070
v2))))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.refl
d_refl_3262 :: T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
d_refl_3262 :: T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
d_refl_3262 T_IsBooleanAlgebra_3224
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_3070 -> T_IsEquivalence_28
d_isEquivalence_3092
         ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_3244 (T_IsBooleanAlgebra_3224 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0))))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.reflexive
d_reflexive_3264 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsBooleanAlgebra_3224 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_3264 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_3224
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_3264 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsBooleanAlgebra_3224
v9
  = T_IsBooleanAlgebra_3224
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_3264 T_IsBooleanAlgebra_3224
v9
du_reflexive_3264 ::
  T_IsBooleanAlgebra_3224 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_3264 :: T_IsBooleanAlgebra_3224
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_3264 T_IsBooleanAlgebra_3224
v0
  = let v1 :: T_IsDistributiveLattice_3146
v1 = T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_3244 (T_IsBooleanAlgebra_3224 -> T_IsBooleanAlgebra_3224
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_3070
v2 = T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 (T_IsDistributiveLattice_3146 -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070 -> T_IsEquivalence_28
d_isEquivalence_3092 (T_IsLattice_3070 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070
v2)) AgdaAny
v3))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.sym
d_sym_3266 ::
  T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_3266 :: T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_3266 T_IsBooleanAlgebra_3224
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_3070 -> T_IsEquivalence_28
d_isEquivalence_3092
         ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_3244 (T_IsBooleanAlgebra_3224 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0))))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.trans
d_trans_3268 ::
  T_IsBooleanAlgebra_3224 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_3268 :: T_IsBooleanAlgebra_3224
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_3268 T_IsBooleanAlgebra_3224
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_3070 -> T_IsEquivalence_28
d_isEquivalence_3092
         ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_3244 (T_IsBooleanAlgebra_3224 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0))))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.∧-absorbs-∨
d_'8743''45'absorbs'45''8744'_3270 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'absorbs'45''8744'_3270 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_3224
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'absorbs'45''8744'_3270 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7
                                   ~AgdaAny
v8 T_IsBooleanAlgebra_3224
v9
  = T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_3270 T_IsBooleanAlgebra_3224
v9
du_'8743''45'absorbs'45''8744'_3270 ::
  T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_3270 :: T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_3270 T_IsBooleanAlgebra_3224
v0
  = let v1 :: T_IsDistributiveLattice_3146
v1 = T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_3244 (T_IsBooleanAlgebra_3224 -> T_IsBooleanAlgebra_3224
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_3122
         ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 (T_IsDistributiveLattice_3146 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v1)))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.∧-assoc
d_'8743''45'assoc_3272 ::
  T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_3272 :: T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_3272 T_IsBooleanAlgebra_3224
v0
  = (T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_3102
      ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_3244 (T_IsBooleanAlgebra_3224 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0)))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.∧-comm
d_'8743''45'comm_3274 ::
  T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_3274 :: T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_3274 T_IsBooleanAlgebra_3224
v0
  = (T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_3100
      ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_3244 (T_IsBooleanAlgebra_3224 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0)))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.∧-cong
d_'8743''45'cong_3276 ::
  T_IsBooleanAlgebra_3224 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong_3276 :: T_IsBooleanAlgebra_3224
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong_3276 T_IsBooleanAlgebra_3224
v0
  = (T_IsLattice_3070
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_3070
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong_3104
      ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_3244 (T_IsBooleanAlgebra_3224 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0)))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.∧-congʳ
d_'8743''45'cong'691'_3278 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsBooleanAlgebra_3224 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong'691'_3278 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_3224
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong'691'_3278 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsBooleanAlgebra_3224
v9
  = T_IsBooleanAlgebra_3224
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_3278 T_IsBooleanAlgebra_3224
v9
du_'8743''45'cong'691'_3278 ::
  T_IsBooleanAlgebra_3224 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_3278 :: T_IsBooleanAlgebra_3224
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_3278 T_IsBooleanAlgebra_3224
v0
  = let v1 :: T_IsDistributiveLattice_3146
v1 = T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_3244 (T_IsBooleanAlgebra_3224 -> T_IsBooleanAlgebra_3224
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsLattice_3070
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_3128 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 (T_IsDistributiveLattice_3146 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v1)))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.∧-congˡ
d_'8743''45'cong'737'_3280 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsBooleanAlgebra_3224 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong'737'_3280 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_3224
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong'737'_3280 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsBooleanAlgebra_3224
v9
  = T_IsBooleanAlgebra_3224
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_3280 T_IsBooleanAlgebra_3224
v9
du_'8743''45'cong'737'_3280 ::
  T_IsBooleanAlgebra_3224 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_3280 :: T_IsBooleanAlgebra_3224
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_3280 T_IsBooleanAlgebra_3224
v0
  = let v1 :: T_IsDistributiveLattice_3146
v1 = T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_3244 (T_IsBooleanAlgebra_3224 -> T_IsBooleanAlgebra_3224
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsLattice_3070
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_3124 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 (T_IsDistributiveLattice_3146 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v1)))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.∧-distrib-∨
d_'8743''45'distrib'45''8744'_3282 ::
  T_IsBooleanAlgebra_3224 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8743''45'distrib'45''8744'_3282 :: T_IsBooleanAlgebra_3224 -> T_Σ_14
d_'8743''45'distrib'45''8744'_3282 T_IsBooleanAlgebra_3224
v0
  = (T_IsDistributiveLattice_3146 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsDistributiveLattice_3146 -> T_Σ_14
d_'8743''45'distrib'45''8744'_3162
      ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_3244 (T_IsBooleanAlgebra_3224 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.∧-distribʳ-∨
d_'8743''45'distrib'691''45''8744'_3284 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'distrib'691''45''8744'_3284 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_3224
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'distrib'691''45''8744'_3284 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6
                                        ~AgdaAny
v7 ~AgdaAny
v8 T_IsBooleanAlgebra_3224
v9
  = T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'691''45''8744'_3284 T_IsBooleanAlgebra_3224
v9
du_'8743''45'distrib'691''45''8744'_3284 ::
  T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'691''45''8744'_3284 :: T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'691''45''8744'_3284 T_IsBooleanAlgebra_3224
v0
  = (T_IsDistributiveLattice_3146
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'691''45''8744'_3210
      ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_3244 (T_IsBooleanAlgebra_3224 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.∧-distribˡ-∨
d_'8743''45'distrib'737''45''8744'_3286 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'distrib'737''45''8744'_3286 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_3224
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'distrib'737''45''8744'_3286 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6
                                        ~AgdaAny
v7 ~AgdaAny
v8 T_IsBooleanAlgebra_3224
v9
  = T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'737''45''8744'_3286 T_IsBooleanAlgebra_3224
v9
du_'8743''45'distrib'737''45''8744'_3286 ::
  T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'737''45''8744'_3286 :: T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'737''45''8744'_3286 T_IsBooleanAlgebra_3224
v0
  = (T_IsDistributiveLattice_3146
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'737''45''8744'_3208
      ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_3244 (T_IsBooleanAlgebra_3224 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.∨-absorbs-∧
d_'8744''45'absorbs'45''8743'_3288 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'absorbs'45''8743'_3288 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_3224
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'absorbs'45''8743'_3288 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7
                                   ~AgdaAny
v8 T_IsBooleanAlgebra_3224
v9
  = T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_3288 T_IsBooleanAlgebra_3224
v9
du_'8744''45'absorbs'45''8743'_3288 ::
  T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_3288 :: T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_3288 T_IsBooleanAlgebra_3224
v0
  = let v1 :: T_IsDistributiveLattice_3146
v1 = T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_3244 (T_IsBooleanAlgebra_3224 -> T_IsBooleanAlgebra_3224
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_3120
         ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 (T_IsDistributiveLattice_3146 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v1)))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.∨-assoc
d_'8744''45'assoc_3290 ::
  T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_3290 :: T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_3290 T_IsBooleanAlgebra_3224
v0
  = (T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_3096
      ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_3244 (T_IsBooleanAlgebra_3224 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0)))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.∨-comm
d_'8744''45'comm_3292 ::
  T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_3292 :: T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_3292 T_IsBooleanAlgebra_3224
v0
  = (T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_3094
      ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_3244 (T_IsBooleanAlgebra_3224 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0)))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.∨-cong
d_'8744''45'cong_3294 ::
  T_IsBooleanAlgebra_3224 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong_3294 :: T_IsBooleanAlgebra_3224
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong_3294 T_IsBooleanAlgebra_3224
v0
  = (T_IsLattice_3070
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_3070
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong_3098
      ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_3244 (T_IsBooleanAlgebra_3224 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0)))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.∨-congʳ
d_'8744''45'cong'691'_3296 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsBooleanAlgebra_3224 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong'691'_3296 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_3224
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong'691'_3296 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsBooleanAlgebra_3224
v9
  = T_IsBooleanAlgebra_3224
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_3296 T_IsBooleanAlgebra_3224
v9
du_'8744''45'cong'691'_3296 ::
  T_IsBooleanAlgebra_3224 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_3296 :: T_IsBooleanAlgebra_3224
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_3296 T_IsBooleanAlgebra_3224
v0
  = let v1 :: T_IsDistributiveLattice_3146
v1 = T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_3244 (T_IsBooleanAlgebra_3224 -> T_IsBooleanAlgebra_3224
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsLattice_3070
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_3136 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 (T_IsDistributiveLattice_3146 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v1)))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.∨-congˡ
d_'8744''45'cong'737'_3298 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsBooleanAlgebra_3224 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong'737'_3298 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_3224
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong'737'_3298 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsBooleanAlgebra_3224
v9
  = T_IsBooleanAlgebra_3224
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_3298 T_IsBooleanAlgebra_3224
v9
du_'8744''45'cong'737'_3298 ::
  T_IsBooleanAlgebra_3224 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_3298 :: T_IsBooleanAlgebra_3224
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_3298 T_IsBooleanAlgebra_3224
v0
  = let v1 :: T_IsDistributiveLattice_3146
v1 = T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_3244 (T_IsBooleanAlgebra_3224 -> T_IsBooleanAlgebra_3224
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsLattice_3070
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_3132 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_3158 (T_IsDistributiveLattice_3146 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v1)))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.∨-distrib-∧
d_'8744''45'distrib'45''8743'_3300 ::
  T_IsBooleanAlgebra_3224 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8744''45'distrib'45''8743'_3300 :: T_IsBooleanAlgebra_3224 -> T_Σ_14
d_'8744''45'distrib'45''8743'_3300 T_IsBooleanAlgebra_3224
v0
  = (T_IsDistributiveLattice_3146 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsDistributiveLattice_3146 -> T_Σ_14
d_'8744''45'distrib'45''8743'_3160
      ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_3244 (T_IsBooleanAlgebra_3224 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.∨-distribʳ-∧
d_'8744''45'distrib'691''45''8743'_3302 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'distrib'691''45''8743'_3302 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_3224
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'distrib'691''45''8743'_3302 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6
                                        ~AgdaAny
v7 ~AgdaAny
v8 T_IsBooleanAlgebra_3224
v9
  = T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'691''45''8743'_3302 T_IsBooleanAlgebra_3224
v9
du_'8744''45'distrib'691''45''8743'_3302 ::
  T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'691''45''8743'_3302 :: T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'691''45''8743'_3302 T_IsBooleanAlgebra_3224
v0
  = (T_IsDistributiveLattice_3146
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'691''45''8743'_3206
      ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_3244 (T_IsBooleanAlgebra_3224 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.∨-distribˡ-∧
d_'8744''45'distrib'737''45''8743'_3304 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'distrib'737''45''8743'_3304 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_3224
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'distrib'737''45''8743'_3304 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6
                                        ~AgdaAny
v7 ~AgdaAny
v8 T_IsBooleanAlgebra_3224
v9
  = T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'737''45''8743'_3304 T_IsBooleanAlgebra_3224
v9
du_'8744''45'distrib'737''45''8743'_3304 ::
  T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'737''45''8743'_3304 :: T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'737''45''8743'_3304 T_IsBooleanAlgebra_3224
v0
  = (T_IsDistributiveLattice_3146
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'737''45''8743'_3204
      ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_3244 (T_IsBooleanAlgebra_3224 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0))
-- Algebra.Lattice.Structures.IsBooleanAlgebra.∨-complementˡ
d_'8744''45'complement'737'_3306 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
d_'8744''45'complement'737'_3306 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_3224
-> AgdaAny
-> AgdaAny
d_'8744''45'complement'737'_3306 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7
                                 ~AgdaAny
v8 T_IsBooleanAlgebra_3224
v9
  = T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
du_'8744''45'complement'737'_3306 T_IsBooleanAlgebra_3224
v9
du_'8744''45'complement'737'_3306 ::
  T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
du_'8744''45'complement'737'_3306 :: T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
du_'8744''45'complement'737'_3306 T_IsBooleanAlgebra_3224
v0
  = (T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28
      ((T_IsBooleanAlgebra_3224 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224 -> T_Σ_14
d_'8744''45'complement_3246 (T_IsBooleanAlgebra_3224 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0))
-- Algebra.Lattice.Structures.IsBooleanAlgebra.∨-complementʳ
d_'8744''45'complement'691'_3308 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
d_'8744''45'complement'691'_3308 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_3224
-> AgdaAny
-> AgdaAny
d_'8744''45'complement'691'_3308 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7
                                 ~AgdaAny
v8 T_IsBooleanAlgebra_3224
v9
  = T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
du_'8744''45'complement'691'_3308 T_IsBooleanAlgebra_3224
v9
du_'8744''45'complement'691'_3308 ::
  T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
du_'8744''45'complement'691'_3308 :: T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
du_'8744''45'complement'691'_3308 T_IsBooleanAlgebra_3224
v0
  = (T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30
      ((T_IsBooleanAlgebra_3224 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224 -> T_Σ_14
d_'8744''45'complement_3246 (T_IsBooleanAlgebra_3224 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0))
-- Algebra.Lattice.Structures.IsBooleanAlgebra.∧-complementˡ
d_'8743''45'complement'737'_3310 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
d_'8743''45'complement'737'_3310 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_3224
-> AgdaAny
-> AgdaAny
d_'8743''45'complement'737'_3310 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7
                                 ~AgdaAny
v8 T_IsBooleanAlgebra_3224
v9
  = T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
du_'8743''45'complement'737'_3310 T_IsBooleanAlgebra_3224
v9
du_'8743''45'complement'737'_3310 ::
  T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
du_'8743''45'complement'737'_3310 :: T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
du_'8743''45'complement'737'_3310 T_IsBooleanAlgebra_3224
v0
  = (T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28
      ((T_IsBooleanAlgebra_3224 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224 -> T_Σ_14
d_'8743''45'complement_3248 (T_IsBooleanAlgebra_3224 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0))
-- Algebra.Lattice.Structures.IsBooleanAlgebra.∧-complementʳ
d_'8743''45'complement'691'_3312 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
d_'8743''45'complement'691'_3312 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_3224
-> AgdaAny
-> AgdaAny
d_'8743''45'complement'691'_3312 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7
                                 ~AgdaAny
v8 T_IsBooleanAlgebra_3224
v9
  = T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
du_'8743''45'complement'691'_3312 T_IsBooleanAlgebra_3224
v9
du_'8743''45'complement'691'_3312 ::
  T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
du_'8743''45'complement'691'_3312 :: T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
du_'8743''45'complement'691'_3312 T_IsBooleanAlgebra_3224
v0
  = (T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30
      ((T_IsBooleanAlgebra_3224 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224 -> T_Σ_14
d_'8743''45'complement_3248 (T_IsBooleanAlgebra_3224 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0))