{-# 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.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_154 :: p -> p -> p -> p -> p -> T_Level_18
d_IsCommutativeBand_154 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
-- Algebra.Lattice.Structures._.IsIdempotentCommutativeMonoid
d_IsIdempotentCommutativeMonoid_172 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_IsIdempotentCommutativeMonoid_172 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
-- Algebra.Lattice.Structures._.IsBand.isPartialEquivalence
d_isPartialEquivalence_338 ::
  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_508 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_338 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsBand_508
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_338 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsBand_508
v5
  = T_IsBand_508 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_338 T_IsBand_508
v5
du_isPartialEquivalence_338 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_508 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_338 :: T_IsBand_508 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_338 T_IsBand_508
v0
  = let v1 :: T_IsSemigroup_472
v1
          = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2))))
-- Algebra.Lattice.Structures._.IsBand.reflexive
d_reflexive_344 ::
  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_508 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_344 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsBand_508
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_344 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsBand_508
v5 = T_IsBand_508 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_344 T_IsBand_508
v5
du_reflexive_344 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_508 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_344 :: T_IsBand_508 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_344 T_IsBand_508
v0
  = let v1 :: T_IsSemigroup_472
v1
          = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2))
              AgdaAny
v3))
-- Algebra.Lattice.Structures._.IsBand.setoid
d_setoid_346 ::
  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_508 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_346 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsBand_508
-> T_Setoid_44
d_setoid_346 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsBand_508
v5 = T_IsBand_508 -> T_Setoid_44
du_setoid_346 T_IsBand_508
v5
du_setoid_346 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_508 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_346 :: T_IsBand_508 -> T_Setoid_44
du_setoid_346 T_IsBand_508
v0
  = let v1 :: T_IsSemigroup_472
v1
          = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v1)))
-- Algebra.Lattice.Structures._.IsBand.∙-congʳ
d_'8729''45'cong'691'_354 ::
  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_508 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_354 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsBand_508
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_354 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsBand_508
v5
  = T_IsBand_508 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_354 T_IsBand_508
v5
du_'8729''45'cong'691'_354 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_508 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_354 :: T_IsBand_508 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_354 T_IsBand_508
v0
  = let v1 :: T_IsSemigroup_472
v1
          = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v1)))
-- Algebra.Lattice.Structures._.IsBand.∙-congˡ
d_'8729''45'cong'737'_356 ::
  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_508 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_356 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsBand_508
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_356 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsBand_508
v5
  = T_IsBand_508 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_356 T_IsBand_508
v5
du_'8729''45'cong'737'_356 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_508 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_356 :: T_IsBand_508 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_356 T_IsBand_508
v0
  = let v1 :: T_IsSemigroup_472
v1
          = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v1)))
-- Algebra.Lattice.Structures._.IsCommutativeBand.comm
d_comm_464 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_comm_464 :: T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_464 T_IsCommutativeBand_590
v0
  = (T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_600 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0)
-- Algebra.Lattice.Structures._.IsCommutativeBand.isBand
d_isBand_468 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_508
d_isBand_468 :: T_IsCommutativeBand_590 -> T_IsBand_508
d_isBand_468 T_IsCommutativeBand_590
v0
  = (T_IsCommutativeBand_590 -> T_IsBand_508)
-> AgdaAny -> T_IsBand_508
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0)
-- Algebra.Lattice.Structures._.IsIdempotentCommutativeMonoid.idem
d_idem_976 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny
d_idem_976 :: T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
d_idem_976 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_864 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0)
-- Algebra.Lattice.Structures._.IsIdempotentCommutativeMonoid.identityʳ
d_identity'691'_980 ::
  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_852 ->
  AgdaAny -> AgdaAny
d_identity'691'_980 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
d_identity'691'_980 ~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_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
du_identity'691'_980 T_IsIdempotentCommutativeMonoid_852
v6
du_identity'691'_980 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny
du_identity'691'_980 :: T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
du_identity'691'_980 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1
          = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
              (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_728
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1)))
-- Algebra.Lattice.Structures._.IsIdempotentCommutativeMonoid.identityˡ
d_identity'737'_982 ::
  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_852 ->
  AgdaAny -> AgdaAny
d_identity'737'_982 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
d_identity'737'_982 ~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_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
du_identity'737'_982 T_IsIdempotentCommutativeMonoid_852
v6
du_identity'737'_982 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny
du_identity'737'_982 :: T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
du_identity'737'_982 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1
          = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
              (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_726
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1)))
-- Algebra.Lattice.Structures._.IsIdempotentCommutativeMonoid.isBand
d_isBand_984 ::
  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_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_508
d_isBand_984 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsBand_508
d_isBand_984 ~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_852
v6 = T_IsIdempotentCommutativeMonoid_852 -> T_IsBand_508
du_isBand_984 T_IsIdempotentCommutativeMonoid_852
v6
du_isBand_984 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_508
du_isBand_984 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsBand_508
du_isBand_984 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsIdempotentMonoid_796 -> T_IsBand_508)
-> AgdaAny -> T_IsBand_508
forall a b. a -> b
coe
      T_IsIdempotentMonoid_796 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.du_isBand_846
      ((T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_910 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0))
-- Algebra.Lattice.Structures._.IsIdempotentCommutativeMonoid.isCommutativeBand
d_isCommutativeBand_986 ::
  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_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
d_isCommutativeBand_986 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsCommutativeBand_590
d_isCommutativeBand_986 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 = (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsCommutativeBand_590
du_isCommutativeBand_986
du_isCommutativeBand_986 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
du_isCommutativeBand_986 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsCommutativeBand_590
du_isCommutativeBand_986 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v1 T_IsIdempotentCommutativeMonoid_852
v2
  = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916 T_IsIdempotentCommutativeMonoid_852
v2
-- Algebra.Lattice.Structures._.IsIdempotentCommutativeMonoid.isCommutativeMagma
d_isCommutativeMagma_988 ::
  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_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
d_isCommutativeMagma_988 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsCommutativeMagma_212
d_isCommutativeMagma_988 ~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_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_988 T_IsIdempotentCommutativeMonoid_852
v6
du_isCommutativeMagma_988 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
du_isCommutativeMagma_988 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_988 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1
          = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
              (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
         ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
            (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1)))
-- Algebra.Lattice.Structures._.IsIdempotentCommutativeMonoid.isCommutativeMonoid
d_isCommutativeMonoid_990 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
d_isCommutativeMonoid_990 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_990 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0)
-- Algebra.Lattice.Structures._.IsIdempotentCommutativeMonoid.isCommutativeSemigroup
d_isCommutativeSemigroup_992 ::
  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_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_992 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_992 ~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_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_992 T_IsIdempotentCommutativeMonoid_852
v6
du_isCommutativeSemigroup_992 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_992 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_992 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
      ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0))
-- Algebra.Lattice.Structures._.IsIdempotentCommutativeMonoid.isIdempotentMonoid
d_isIdempotentMonoid_996 ::
  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_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_796
d_isIdempotentMonoid_996 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentMonoid_796
d_isIdempotentMonoid_996 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentMonoid_796
du_isIdempotentMonoid_996
du_isIdempotentMonoid_996 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_796
du_isIdempotentMonoid_996 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentMonoid_796
du_isIdempotentMonoid_996 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v1 T_IsIdempotentCommutativeMonoid_852
v2
  = (T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796)
-> T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_910 T_IsIdempotentCommutativeMonoid_852
v2
-- Algebra.Lattice.Structures._.IsIdempotentCommutativeMonoid.isPartialEquivalence
d_isPartialEquivalence_1002 ::
  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_852 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1002 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1002 ~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_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1002 T_IsIdempotentCommutativeMonoid_852
v6
du_isPartialEquivalence_1002 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1002 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1002 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1
          = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
              (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2
             = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                  ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4))))))
-- Algebra.Lattice.Structures._.IsIdempotentCommutativeMonoid.isUnitalMagma
d_isUnitalMagma_1006 ::
  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_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
d_isUnitalMagma_1006 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsUnitalMagma_642
d_isUnitalMagma_1006 ~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_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> T_IsUnitalMagma_642
du_isUnitalMagma_1006 T_IsIdempotentCommutativeMonoid_852
v6
du_isUnitalMagma_1006 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
du_isUnitalMagma_1006 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsUnitalMagma_642
du_isUnitalMagma_1006 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1
          = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
              (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsUnitalMagma_642
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1)))
-- Algebra.Lattice.Structures._.IsIdempotentCommutativeMonoid.reflexive
d_reflexive_1010 ::
  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_852 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1010 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1010 ~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_852
v6 = T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1010 T_IsIdempotentCommutativeMonoid_852
v6
du_reflexive_1010 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1010 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1010 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1
          = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
              (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2
             = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                    ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4))
                    AgdaAny
v5))))
-- Algebra.Lattice.Structures._.IsIdempotentCommutativeMonoid.setoid
d_setoid_1012 ::
  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_852 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1012 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_Setoid_44
d_setoid_1012 ~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_852
v6 = T_IsIdempotentCommutativeMonoid_852 -> T_Setoid_44
du_setoid_1012 T_IsIdempotentCommutativeMonoid_852
v6
du_setoid_1012 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1012 :: T_IsIdempotentCommutativeMonoid_852 -> T_Setoid_44
du_setoid_1012 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1
          = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
              (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2
             = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Lattice.Structures._.IsIdempotentCommutativeMonoid.∙-congʳ
d_'8729''45'cong'691'_1020 ::
  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_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1020 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1020 ~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_852
v6
  = T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1020 T_IsIdempotentCommutativeMonoid_852
v6
du_'8729''45'cong'691'_1020 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1020 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1020 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1
          = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
              (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2
             = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Lattice.Structures._.IsIdempotentCommutativeMonoid.∙-congˡ
d_'8729''45'cong'737'_1022 ::
  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_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1022 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1022 ~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_852
v6
  = T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1022 T_IsIdempotentCommutativeMonoid_852
v6
du_'8729''45'cong'737'_1022 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1022 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1022 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1
          = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
              (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2
             = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Lattice.Structures.IsSemilattice
d_IsSemilattice_2658 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_IsSemilattice_2658 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_IsSemilattice_2658 = 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_2668 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_comm_2668 :: T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_2668 T_IsCommutativeBand_590
v0
  = (T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_600 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0)
-- Algebra.Lattice.Structures.IsSemilattice._.isBand
d_isBand_2670 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_508
d_isBand_2670 :: T_IsCommutativeBand_590 -> T_IsBand_508
d_isBand_2670 T_IsCommutativeBand_590
v0
  = (T_IsCommutativeBand_590 -> T_IsBand_508)
-> AgdaAny -> T_IsBand_508
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0)
-- Algebra.Lattice.Structures.IsSemilattice._.assoc
d_assoc_2674 ::
  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_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2674 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_assoc_2674 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 = T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_2674 T_IsCommutativeBand_590
v5
du_assoc_2674 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_2674 :: T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_2674 T_IsCommutativeBand_590
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_482
      ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
         ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0)))
-- Algebra.Lattice.Structures.IsSemilattice._.idem
d_idem_2676 ::
  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_590 ->
  AgdaAny -> AgdaAny
d_idem_2676 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
d_idem_2676 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 = T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny
du_idem_2676 T_IsCommutativeBand_590
v5
du_idem_2676 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny
du_idem_2676 :: T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny
du_idem_2676 T_IsCommutativeBand_590
v0
  = (T_IsBand_508 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsBand_508 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_518
      ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0))
-- Algebra.Lattice.Structures.IsSemilattice._.isEquivalence
d_isEquivalence_2678 ::
  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_590 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_2678 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> T_IsEquivalence_26
d_isEquivalence_2678 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5
  = T_IsCommutativeBand_590 -> T_IsEquivalence_26
du_isEquivalence_2678 T_IsCommutativeBand_590
v5
du_isEquivalence_2678 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_2678 :: T_IsCommutativeBand_590 -> T_IsEquivalence_26
du_isEquivalence_2678 T_IsCommutativeBand_590
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
            ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0))))
-- Algebra.Lattice.Structures.IsSemilattice._.isMagma
d_isMagma_2680 ::
  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_590 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_2680 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> T_IsMagma_176
d_isMagma_2680 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 = T_IsCommutativeBand_590 -> T_IsMagma_176
du_isMagma_2680 T_IsCommutativeBand_590
v5
du_isMagma_2680 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
du_isMagma_2680 :: T_IsCommutativeBand_590 -> T_IsMagma_176
du_isMagma_2680 T_IsCommutativeBand_590
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
      ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
         ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0)))
-- Algebra.Lattice.Structures.IsSemilattice._.isPartialEquivalence
d_isPartialEquivalence_2682 ::
  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_590 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2682 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2682 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5
  = T_IsCommutativeBand_590 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2682 T_IsCommutativeBand_590
v5
du_isPartialEquivalence_2682 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2682 :: T_IsCommutativeBand_590 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2682 T_IsCommutativeBand_590
v0
  = let v1 :: T_IsBand_508
v1 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2
             = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3)))))
-- Algebra.Lattice.Structures.IsSemilattice._.isSemigroup
d_isSemigroup_2684 ::
  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_590 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_2684 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> T_IsSemigroup_472
d_isSemigroup_2684 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 = T_IsCommutativeBand_590 -> T_IsSemigroup_472
du_isSemigroup_2684 T_IsCommutativeBand_590
v5
du_isSemigroup_2684 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
du_isSemigroup_2684 :: T_IsCommutativeBand_590 -> T_IsSemigroup_472
du_isSemigroup_2684 T_IsCommutativeBand_590
v0
  = (T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
      ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0))
-- Algebra.Lattice.Structures.IsSemilattice._.refl
d_refl_2686 ::
  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_590 ->
  AgdaAny -> AgdaAny
d_refl_2686 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
d_refl_2686 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 = T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny
du_refl_2686 T_IsCommutativeBand_590
v5
du_refl_2686 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny
du_refl_2686 :: T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny
du_refl_2686 T_IsCommutativeBand_590
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
               ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0)))))
-- Algebra.Lattice.Structures.IsSemilattice._.reflexive
d_reflexive_2688 ::
  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_590 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2688 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2688 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 = T_IsCommutativeBand_590
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2688 T_IsCommutativeBand_590
v5
du_reflexive_2688 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2688 :: T_IsCommutativeBand_590
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2688 T_IsCommutativeBand_590
v0
  = let v1 :: T_IsBand_508
v1 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2
             = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                 ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3))
                 AgdaAny
v4)))
-- Algebra.Lattice.Structures.IsSemilattice._.setoid
d_setoid_2690 ::
  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_590 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_2690 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> T_Setoid_44
d_setoid_2690 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 = T_IsCommutativeBand_590 -> T_Setoid_44
du_setoid_2690 T_IsCommutativeBand_590
v5
du_setoid_2690 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_2690 :: T_IsCommutativeBand_590 -> T_Setoid_44
du_setoid_2690 T_IsCommutativeBand_590
v0
  = let v1 :: T_IsBand_508
v1 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2
             = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Lattice.Structures.IsSemilattice._.sym
d_sym_2692 ::
  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_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2692 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_2692 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 = T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2692 T_IsCommutativeBand_590
v5
du_sym_2692 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2692 :: T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2692 T_IsCommutativeBand_590
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
               ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0)))))
-- Algebra.Lattice.Structures.IsSemilattice._.trans
d_trans_2694 ::
  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_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2694 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_2694 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 = T_IsCommutativeBand_590
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2694 T_IsCommutativeBand_590
v5
du_trans_2694 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2694 :: T_IsCommutativeBand_590
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2694 T_IsCommutativeBand_590
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
               ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0)))))
-- Algebra.Lattice.Structures.IsSemilattice._.∙-cong
d_'8729''45'cong_2696 ::
  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_590 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_2696 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_2696 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5
  = T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_2696 T_IsCommutativeBand_590
v5
du_'8729''45'cong_2696 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong_2696 :: T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_2696 T_IsCommutativeBand_590
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
            ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0))))
-- Algebra.Lattice.Structures.IsSemilattice._.∙-congʳ
d_'8729''45'cong'691'_2698 ::
  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_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2698 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2698 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5
  = T_IsCommutativeBand_590
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2698 T_IsCommutativeBand_590
v5
du_'8729''45'cong'691'_2698 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2698 :: T_IsCommutativeBand_590
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2698 T_IsCommutativeBand_590
v0
  = let v1 :: T_IsBand_508
v1 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2
             = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Lattice.Structures.IsSemilattice._.∙-congˡ
d_'8729''45'cong'737'_2700 ::
  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_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2700 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2700 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5
  = T_IsCommutativeBand_590
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2700 T_IsCommutativeBand_590
v5
du_'8729''45'cong'737'_2700 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2700 :: T_IsCommutativeBand_590
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2700 T_IsCommutativeBand_590
v0
  = let v1 :: T_IsBand_508
v1 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2
             = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Lattice.Structures.IsMeetSemilattice
d_IsMeetSemilattice_2702 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_IsMeetSemilattice_2702 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_IsMeetSemilattice_2702 = 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_2712 ::
  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_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2712 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_assoc_2712 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 = T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_2712 T_IsCommutativeBand_590
v5
du_assoc_2712 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_2712 :: T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_2712 T_IsCommutativeBand_590
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_482
      ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
         ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0)))
-- Algebra.Lattice.Structures.IsMeetSemilattice._.comm
d_comm_2714 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_comm_2714 :: T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_2714 T_IsCommutativeBand_590
v0
  = (T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_600 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0)
-- Algebra.Lattice.Structures.IsMeetSemilattice._.idem
d_idem_2716 ::
  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_590 ->
  AgdaAny -> AgdaAny
d_idem_2716 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
d_idem_2716 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 = T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny
du_idem_2716 T_IsCommutativeBand_590
v5
du_idem_2716 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny
du_idem_2716 :: T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny
du_idem_2716 T_IsCommutativeBand_590
v0
  = (T_IsBand_508 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsBand_508 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_518
      ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0))
-- Algebra.Lattice.Structures.IsMeetSemilattice._.isBand
d_isBand_2718 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_508
d_isBand_2718 :: T_IsCommutativeBand_590 -> T_IsBand_508
d_isBand_2718 T_IsCommutativeBand_590
v0
  = (T_IsCommutativeBand_590 -> T_IsBand_508)
-> AgdaAny -> T_IsBand_508
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0)
-- Algebra.Lattice.Structures.IsMeetSemilattice._.isEquivalence
d_isEquivalence_2720 ::
  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_590 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_2720 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> T_IsEquivalence_26
d_isEquivalence_2720 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5
  = T_IsCommutativeBand_590 -> T_IsEquivalence_26
du_isEquivalence_2720 T_IsCommutativeBand_590
v5
du_isEquivalence_2720 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_2720 :: T_IsCommutativeBand_590 -> T_IsEquivalence_26
du_isEquivalence_2720 T_IsCommutativeBand_590
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
            ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0))))
-- Algebra.Lattice.Structures.IsMeetSemilattice._.isMagma
d_isMagma_2722 ::
  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_590 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_2722 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> T_IsMagma_176
d_isMagma_2722 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 = T_IsCommutativeBand_590 -> T_IsMagma_176
du_isMagma_2722 T_IsCommutativeBand_590
v5
du_isMagma_2722 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
du_isMagma_2722 :: T_IsCommutativeBand_590 -> T_IsMagma_176
du_isMagma_2722 T_IsCommutativeBand_590
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
      ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
         ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0)))
-- Algebra.Lattice.Structures.IsMeetSemilattice._.isPartialEquivalence
d_isPartialEquivalence_2724 ::
  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_590 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2724 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2724 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5
  = T_IsCommutativeBand_590 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2724 T_IsCommutativeBand_590
v5
du_isPartialEquivalence_2724 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2724 :: T_IsCommutativeBand_590 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2724 T_IsCommutativeBand_590
v0
  = let v1 :: T_IsBand_508
v1 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2
             = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3)))))
-- Algebra.Lattice.Structures.IsMeetSemilattice._.isSemigroup
d_isSemigroup_2726 ::
  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_590 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_2726 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> T_IsSemigroup_472
d_isSemigroup_2726 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 = T_IsCommutativeBand_590 -> T_IsSemigroup_472
du_isSemigroup_2726 T_IsCommutativeBand_590
v5
du_isSemigroup_2726 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
du_isSemigroup_2726 :: T_IsCommutativeBand_590 -> T_IsSemigroup_472
du_isSemigroup_2726 T_IsCommutativeBand_590
v0
  = (T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
      ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0))
-- Algebra.Lattice.Structures.IsMeetSemilattice._.refl
d_refl_2728 ::
  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_590 ->
  AgdaAny -> AgdaAny
d_refl_2728 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
d_refl_2728 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 = T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny
du_refl_2728 T_IsCommutativeBand_590
v5
du_refl_2728 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny
du_refl_2728 :: T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny
du_refl_2728 T_IsCommutativeBand_590
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
               ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0)))))
-- Algebra.Lattice.Structures.IsMeetSemilattice._.reflexive
d_reflexive_2730 ::
  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_590 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2730 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2730 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 = T_IsCommutativeBand_590
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2730 T_IsCommutativeBand_590
v5
du_reflexive_2730 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2730 :: T_IsCommutativeBand_590
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2730 T_IsCommutativeBand_590
v0
  = let v1 :: T_IsBand_508
v1 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2
             = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                 ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3))
                 AgdaAny
v4)))
-- Algebra.Lattice.Structures.IsMeetSemilattice._.setoid
d_setoid_2732 ::
  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_590 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_2732 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> T_Setoid_44
d_setoid_2732 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 = T_IsCommutativeBand_590 -> T_Setoid_44
du_setoid_2732 T_IsCommutativeBand_590
v5
du_setoid_2732 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_2732 :: T_IsCommutativeBand_590 -> T_Setoid_44
du_setoid_2732 T_IsCommutativeBand_590
v0
  = let v1 :: T_IsBand_508
v1 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2
             = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Lattice.Structures.IsMeetSemilattice._.sym
d_sym_2734 ::
  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_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2734 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_2734 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 = T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2734 T_IsCommutativeBand_590
v5
du_sym_2734 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2734 :: T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2734 T_IsCommutativeBand_590
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
               ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0)))))
-- Algebra.Lattice.Structures.IsMeetSemilattice._.trans
d_trans_2736 ::
  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_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2736 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_2736 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 = T_IsCommutativeBand_590
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2736 T_IsCommutativeBand_590
v5
du_trans_2736 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2736 :: T_IsCommutativeBand_590
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2736 T_IsCommutativeBand_590
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
               ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0)))))
-- Algebra.Lattice.Structures.IsMeetSemilattice._.∙-cong
d_'8729''45'cong_2738 ::
  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_590 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_2738 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_2738 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5
  = T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_2738 T_IsCommutativeBand_590
v5
du_'8729''45'cong_2738 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong_2738 :: T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_2738 T_IsCommutativeBand_590
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
            ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0))))
-- Algebra.Lattice.Structures.IsMeetSemilattice._.∙-congʳ
d_'8729''45'cong'691'_2740 ::
  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_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2740 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2740 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5
  = T_IsCommutativeBand_590
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2740 T_IsCommutativeBand_590
v5
du_'8729''45'cong'691'_2740 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2740 :: T_IsCommutativeBand_590
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2740 T_IsCommutativeBand_590
v0
  = let v1 :: T_IsBand_508
v1 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2
             = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Lattice.Structures.IsMeetSemilattice._.∙-congˡ
d_'8729''45'cong'737'_2742 ::
  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_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2742 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2742 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5
  = T_IsCommutativeBand_590
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2742 T_IsCommutativeBand_590
v5
du_'8729''45'cong'737'_2742 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2742 :: T_IsCommutativeBand_590
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2742 T_IsCommutativeBand_590
v0
  = let v1 :: T_IsBand_508
v1 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2
             = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Lattice.Structures.IsJoinSemilattice
d_IsJoinSemilattice_2744 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_IsJoinSemilattice_2744 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_IsJoinSemilattice_2744 = 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_2754 ::
  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_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2754 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_assoc_2754 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 = T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_2754 T_IsCommutativeBand_590
v5
du_assoc_2754 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_2754 :: T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_2754 T_IsCommutativeBand_590
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_482
      ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
         ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0)))
-- Algebra.Lattice.Structures.IsJoinSemilattice._.comm
d_comm_2756 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_comm_2756 :: T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_2756 T_IsCommutativeBand_590
v0
  = (T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_600 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0)
-- Algebra.Lattice.Structures.IsJoinSemilattice._.idem
d_idem_2758 ::
  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_590 ->
  AgdaAny -> AgdaAny
d_idem_2758 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
d_idem_2758 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 = T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny
du_idem_2758 T_IsCommutativeBand_590
v5
du_idem_2758 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny
du_idem_2758 :: T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny
du_idem_2758 T_IsCommutativeBand_590
v0
  = (T_IsBand_508 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsBand_508 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_518
      ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0))
-- Algebra.Lattice.Structures.IsJoinSemilattice._.isBand
d_isBand_2760 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_508
d_isBand_2760 :: T_IsCommutativeBand_590 -> T_IsBand_508
d_isBand_2760 T_IsCommutativeBand_590
v0
  = (T_IsCommutativeBand_590 -> T_IsBand_508)
-> AgdaAny -> T_IsBand_508
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0)
-- Algebra.Lattice.Structures.IsJoinSemilattice._.isEquivalence
d_isEquivalence_2762 ::
  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_590 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_2762 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> T_IsEquivalence_26
d_isEquivalence_2762 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5
  = T_IsCommutativeBand_590 -> T_IsEquivalence_26
du_isEquivalence_2762 T_IsCommutativeBand_590
v5
du_isEquivalence_2762 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_2762 :: T_IsCommutativeBand_590 -> T_IsEquivalence_26
du_isEquivalence_2762 T_IsCommutativeBand_590
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
            ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0))))
-- Algebra.Lattice.Structures.IsJoinSemilattice._.isMagma
d_isMagma_2764 ::
  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_590 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_2764 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> T_IsMagma_176
d_isMagma_2764 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 = T_IsCommutativeBand_590 -> T_IsMagma_176
du_isMagma_2764 T_IsCommutativeBand_590
v5
du_isMagma_2764 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
du_isMagma_2764 :: T_IsCommutativeBand_590 -> T_IsMagma_176
du_isMagma_2764 T_IsCommutativeBand_590
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
      ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
         ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0)))
-- Algebra.Lattice.Structures.IsJoinSemilattice._.isPartialEquivalence
d_isPartialEquivalence_2766 ::
  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_590 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2766 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2766 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5
  = T_IsCommutativeBand_590 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2766 T_IsCommutativeBand_590
v5
du_isPartialEquivalence_2766 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2766 :: T_IsCommutativeBand_590 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2766 T_IsCommutativeBand_590
v0
  = let v1 :: T_IsBand_508
v1 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2
             = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3)))))
-- Algebra.Lattice.Structures.IsJoinSemilattice._.isSemigroup
d_isSemigroup_2768 ::
  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_590 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_2768 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> T_IsSemigroup_472
d_isSemigroup_2768 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 = T_IsCommutativeBand_590 -> T_IsSemigroup_472
du_isSemigroup_2768 T_IsCommutativeBand_590
v5
du_isSemigroup_2768 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
du_isSemigroup_2768 :: T_IsCommutativeBand_590 -> T_IsSemigroup_472
du_isSemigroup_2768 T_IsCommutativeBand_590
v0
  = (T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
      ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0))
-- Algebra.Lattice.Structures.IsJoinSemilattice._.refl
d_refl_2770 ::
  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_590 ->
  AgdaAny -> AgdaAny
d_refl_2770 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
d_refl_2770 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 = T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny
du_refl_2770 T_IsCommutativeBand_590
v5
du_refl_2770 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny
du_refl_2770 :: T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny
du_refl_2770 T_IsCommutativeBand_590
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
               ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0)))))
-- Algebra.Lattice.Structures.IsJoinSemilattice._.reflexive
d_reflexive_2772 ::
  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_590 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2772 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2772 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 = T_IsCommutativeBand_590
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2772 T_IsCommutativeBand_590
v5
du_reflexive_2772 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2772 :: T_IsCommutativeBand_590
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2772 T_IsCommutativeBand_590
v0
  = let v1 :: T_IsBand_508
v1 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2
             = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                 ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3))
                 AgdaAny
v4)))
-- Algebra.Lattice.Structures.IsJoinSemilattice._.setoid
d_setoid_2774 ::
  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_590 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_2774 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> T_Setoid_44
d_setoid_2774 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 = T_IsCommutativeBand_590 -> T_Setoid_44
du_setoid_2774 T_IsCommutativeBand_590
v5
du_setoid_2774 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_2774 :: T_IsCommutativeBand_590 -> T_Setoid_44
du_setoid_2774 T_IsCommutativeBand_590
v0
  = let v1 :: T_IsBand_508
v1 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2
             = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Lattice.Structures.IsJoinSemilattice._.sym
d_sym_2776 ::
  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_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2776 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_2776 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 = T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2776 T_IsCommutativeBand_590
v5
du_sym_2776 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2776 :: T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2776 T_IsCommutativeBand_590
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
               ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0)))))
-- Algebra.Lattice.Structures.IsJoinSemilattice._.trans
d_trans_2778 ::
  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_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2778 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_2778 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 = T_IsCommutativeBand_590
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2778 T_IsCommutativeBand_590
v5
du_trans_2778 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2778 :: T_IsCommutativeBand_590
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2778 T_IsCommutativeBand_590
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
               ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0)))))
-- Algebra.Lattice.Structures.IsJoinSemilattice._.∙-cong
d_'8729''45'cong_2780 ::
  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_590 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_2780 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_2780 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5
  = T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_2780 T_IsCommutativeBand_590
v5
du_'8729''45'cong_2780 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong_2780 :: T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_2780 T_IsCommutativeBand_590
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
            ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0))))
-- Algebra.Lattice.Structures.IsJoinSemilattice._.∙-congʳ
d_'8729''45'cong'691'_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_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2782 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_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_590
v5
  = T_IsCommutativeBand_590
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2782 T_IsCommutativeBand_590
v5
du_'8729''45'cong'691'_2782 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2782 :: T_IsCommutativeBand_590
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2782 T_IsCommutativeBand_590
v0
  = let v1 :: T_IsBand_508
v1 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2
             = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Lattice.Structures.IsJoinSemilattice._.∙-congˡ
d_'8729''45'cong'737'_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_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2784 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_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_590
v5
  = T_IsCommutativeBand_590
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2784 T_IsCommutativeBand_590
v5
du_'8729''45'cong'737'_2784 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2784 :: T_IsCommutativeBand_590
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2784 T_IsCommutativeBand_590
v0
  = let v1 :: T_IsBand_508
v1 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2
             = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Lattice.Structures.IsBoundedSemilattice
d_IsBoundedSemilattice_2786 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> ()
d_IsBoundedSemilattice_2786 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_Level_18
d_IsBoundedSemilattice_2786 = 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_2798 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2798 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2798 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_482
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
            ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
               (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0))))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.comm
d_comm_2800 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_comm_2800 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny
d_comm_2800 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_748
      ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.idem
d_idem_2802 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny
d_idem_2802 :: T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
d_idem_2802 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_864 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0)
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.identity
d_identity_2804 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_2804 :: T_IsIdempotentCommutativeMonoid_852 -> T_Σ_14
d_identity_2804 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_698
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
         ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
            (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0)))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.identityʳ
d_identity'691'_2806 ::
  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_852 ->
  AgdaAny -> AgdaAny
d_identity'691'_2806 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
d_identity'691'_2806 ~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_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
du_identity'691'_2806 T_IsIdempotentCommutativeMonoid_852
v6
du_identity'691'_2806 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny
du_identity'691'_2806 :: T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
du_identity'691'_2806 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1
          = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
              (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_728
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1)))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.identityˡ
d_identity'737'_2808 ::
  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_852 ->
  AgdaAny -> AgdaAny
d_identity'737'_2808 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
d_identity'737'_2808 ~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_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
du_identity'737'_2808 T_IsIdempotentCommutativeMonoid_852
v6
du_identity'737'_2808 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny
du_identity'737'_2808 :: T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
du_identity'737'_2808 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1
          = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
              (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_726
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1)))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.isBand
d_isBand_2810 ::
  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_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_508
d_isBand_2810 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsBand_508
d_isBand_2810 ~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_852
v6 = T_IsIdempotentCommutativeMonoid_852 -> T_IsBand_508
du_isBand_2810 T_IsIdempotentCommutativeMonoid_852
v6
du_isBand_2810 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_508
du_isBand_2810 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsBand_508
du_isBand_2810 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsIdempotentMonoid_796 -> T_IsBand_508)
-> AgdaAny -> T_IsBand_508
forall a b. a -> b
coe
      T_IsIdempotentMonoid_796 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.du_isBand_846
      ((T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_910 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.isCommutativeMagma
d_isCommutativeMagma_2812 ::
  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_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
d_isCommutativeMagma_2812 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsCommutativeMagma_212
d_isCommutativeMagma_2812 ~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_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_2812 T_IsIdempotentCommutativeMonoid_852
v6
du_isCommutativeMagma_2812 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
du_isCommutativeMagma_2812 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_2812 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1
          = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
              (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
         ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
            (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1)))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.isCommutativeMonoid
d_isCommutativeMonoid_2814 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
d_isCommutativeMonoid_2814 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_2814 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0)
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.isCommutativeSemigroup
d_isCommutativeSemigroup_2816 ::
  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_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_2816 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_2816 ~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_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_2816 T_IsIdempotentCommutativeMonoid_852
v6
du_isCommutativeSemigroup_2816 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_2816 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_2816 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
      ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.isEquivalence
d_isEquivalence_2818 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_2818 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsEquivalence_26
d_isEquivalence_2818 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
               ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                  (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0)))))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.isIdempotentMonoid
d_isIdempotentMonoid_2820 ::
  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_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_796
d_isIdempotentMonoid_2820 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentMonoid_796
d_isIdempotentMonoid_2820 ~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_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796
du_isIdempotentMonoid_2820 T_IsIdempotentCommutativeMonoid_852
v6
du_isIdempotentMonoid_2820 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_796
du_isIdempotentMonoid_2820 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796
du_isIdempotentMonoid_2820 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796)
-> AgdaAny -> T_IsIdempotentMonoid_796
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_910 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0)
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.isMagma
d_isMagma_2822 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_2822 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsMagma_176
d_isMagma_2822 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
            ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
               (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0))))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.isMonoid
d_isMonoid_2824 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_isMonoid_2824 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsMonoid_686
d_isMonoid_2824 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsCommutativeMonoid_736 -> T_IsMonoid_686)
-> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
      ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.isPartialEquivalence
d_isPartialEquivalence_2826 ::
  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_852 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2826 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2826 ~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_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2826 T_IsIdempotentCommutativeMonoid_852
v6
du_isPartialEquivalence_2826 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2826 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2826 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1
          = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
              (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2
             = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                  ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4))))))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.isSemigroup
d_isSemigroup_2828 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_2828 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsSemigroup_472
d_isSemigroup_2828 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
         ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
            (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0)))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.isCommutativeBand
d_isCommutativeBand_2830 ::
  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_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
d_isCommutativeBand_2830 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsCommutativeBand_590
d_isCommutativeBand_2830 ~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_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
du_isCommutativeBand_2830 T_IsIdempotentCommutativeMonoid_852
v6
du_isCommutativeBand_2830 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
du_isCommutativeBand_2830 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
du_isCommutativeBand_2830 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> T_IsCommutativeBand_590
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0)
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.isUnitalMagma
d_isUnitalMagma_2832 ::
  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_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
d_isUnitalMagma_2832 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsUnitalMagma_642
d_isUnitalMagma_2832 ~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_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> T_IsUnitalMagma_642
du_isUnitalMagma_2832 T_IsIdempotentCommutativeMonoid_852
v6
du_isUnitalMagma_2832 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
du_isUnitalMagma_2832 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsUnitalMagma_642
du_isUnitalMagma_2832 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1
          = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
              (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsUnitalMagma_642
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1)))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.refl
d_refl_2834 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny
d_refl_2834 :: T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
d_refl_2834 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                  ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                     (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0))))))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.reflexive
d_reflexive_2836 ::
  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_852 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2836 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2836 ~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_852
v6 = T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2836 T_IsIdempotentCommutativeMonoid_852
v6
du_reflexive_2836 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2836 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2836 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1
          = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
              (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2
             = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                    ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4))
                    AgdaAny
v5))))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.setoid
d_setoid_2838 ::
  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_852 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_2838 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_Setoid_44
d_setoid_2838 ~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_852
v6 = T_IsIdempotentCommutativeMonoid_852 -> T_Setoid_44
du_setoid_2838 T_IsIdempotentCommutativeMonoid_852
v6
du_setoid_2838 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_2838 :: T_IsIdempotentCommutativeMonoid_852 -> T_Setoid_44
du_setoid_2838 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1
          = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
              (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2
             = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.sym
d_sym_2840 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2840 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2840 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                  ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                     (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0))))))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.trans
d_trans_2842 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2842 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2842 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                  ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                     (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0))))))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.∙-cong
d_'8729''45'cong_2844 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_2844 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_2844 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
               ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                  (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0)))))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.∙-congʳ
d_'8729''45'cong'691'_2846 ::
  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_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2846 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2846 ~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_852
v6
  = T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2846 T_IsIdempotentCommutativeMonoid_852
v6
du_'8729''45'cong'691'_2846 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2846 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2846 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1
          = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
              (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2
             = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Lattice.Structures.IsBoundedSemilattice._.∙-congˡ
d_'8729''45'cong'737'_2848 ::
  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_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2848 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2848 ~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_852
v6
  = T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2848 T_IsIdempotentCommutativeMonoid_852
v6
du_'8729''45'cong'737'_2848 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2848 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2848 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1
          = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
              (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2
             = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice
d_IsBoundedMeetSemilattice_2850 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> ()
d_IsBoundedMeetSemilattice_2850 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_Level_18
d_IsBoundedMeetSemilattice_2850 = 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_2862 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_2862 :: T_IsIdempotentCommutativeMonoid_852 -> T_Σ_14
d_identity_2862 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_698
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
         ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
            (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0)))
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice._.identityʳ
d_identity'691'_2864 ::
  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_852 ->
  AgdaAny -> AgdaAny
d_identity'691'_2864 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
d_identity'691'_2864 ~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_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
du_identity'691'_2864 T_IsIdempotentCommutativeMonoid_852
v6
du_identity'691'_2864 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny
du_identity'691'_2864 :: T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
du_identity'691'_2864 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1
          = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
              (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_728
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1)))
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice._.identityˡ
d_identity'737'_2866 ::
  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_852 ->
  AgdaAny -> AgdaAny
d_identity'737'_2866 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
d_identity'737'_2866 ~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_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
du_identity'737'_2866 T_IsIdempotentCommutativeMonoid_852
v6
du_identity'737'_2866 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny
du_identity'737'_2866 :: T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
du_identity'737'_2866 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1
          = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
              (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_726
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1)))
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice._.isCommutativeBand
d_isCommutativeBand_2868 ::
  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_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
d_isCommutativeBand_2868 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsCommutativeBand_590
d_isCommutativeBand_2868 ~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_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
du_isCommutativeBand_2868 T_IsIdempotentCommutativeMonoid_852
v6
du_isCommutativeBand_2868 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
du_isCommutativeBand_2868 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
du_isCommutativeBand_2868 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> T_IsCommutativeBand_590
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0)
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice._.assoc
d_assoc_2872 ::
  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_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2872 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_assoc_2872 ~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_852
v6 = T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_2872 T_IsIdempotentCommutativeMonoid_852
v6
du_assoc_2872 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_2872 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_2872 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: t
v1
          = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
              (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_482
         ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
            ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1))))
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice._.comm
d_comm_2874 ::
  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_852 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_comm_2874 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_comm_2874 ~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_852
v6 = T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny
du_comm_2874 T_IsIdempotentCommutativeMonoid_852
v6
du_comm_2874 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny -> AgdaAny
du_comm_2874 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny
du_comm_2874 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_600
      ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0))
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice._.idem
d_idem_2876 ::
  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_852 ->
  AgdaAny -> AgdaAny
d_idem_2876 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
d_idem_2876 ~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_852
v6 = T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
du_idem_2876 T_IsIdempotentCommutativeMonoid_852
v6
du_idem_2876 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny
du_idem_2876 :: T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
du_idem_2876 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: t
v1
          = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
              (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsBand_508 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_508 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_518
         ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice._.isBand
d_isBand_2878 ::
  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_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_508
d_isBand_2878 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsBand_508
d_isBand_2878 ~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_852
v6 = T_IsIdempotentCommutativeMonoid_852 -> T_IsBand_508
du_isBand_2878 T_IsIdempotentCommutativeMonoid_852
v6
du_isBand_2878 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_508
du_isBand_2878 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsBand_508
du_isBand_2878 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsCommutativeBand_590 -> T_IsBand_508)
-> AgdaAny -> T_IsBand_508
forall a b. a -> b
coe
      T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598
      ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0))
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice._.isEquivalence
d_isEquivalence_2880 ::
  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_852 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_2880 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsEquivalence_26
d_isEquivalence_2880 ~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_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> T_IsEquivalence_26
du_isEquivalence_2880 T_IsIdempotentCommutativeMonoid_852
v6
du_isEquivalence_2880 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_2880 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsEquivalence_26
du_isEquivalence_2880 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: t
v1
          = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
              (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
               ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))))
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice._.isMagma
d_isMagma_2882 ::
  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_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_2882 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsMagma_176
d_isMagma_2882 ~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_852
v6 = T_IsIdempotentCommutativeMonoid_852 -> T_IsMagma_176
du_isMagma_2882 T_IsIdempotentCommutativeMonoid_852
v6
du_isMagma_2882 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
du_isMagma_2882 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsMagma_176
du_isMagma_2882 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: t
v1
          = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
              (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
            ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1))))
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice._.isPartialEquivalence
d_isPartialEquivalence_2884 ::
  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_852 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2884 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2884 ~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_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2884 T_IsIdempotentCommutativeMonoid_852
v6
du_isPartialEquivalence_2884 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2884 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2884 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: t
v1
          = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
              (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsBand_508
v2 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> T_IsCommutativeBand_590
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                  ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4))))))
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice._.isSemigroup
d_isSemigroup_2886 ::
  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_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_2886 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsSemigroup_472
d_isSemigroup_2886 ~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_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> T_IsSemigroup_472
du_isSemigroup_2886 T_IsIdempotentCommutativeMonoid_852
v6
du_isSemigroup_2886 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
du_isSemigroup_2886 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsSemigroup_472
du_isSemigroup_2886 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: t
v1
          = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
              (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
         ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice._.refl
d_refl_2888 ::
  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_852 ->
  AgdaAny -> AgdaAny
d_refl_2888 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
d_refl_2888 ~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_852
v6 = T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
du_refl_2888 T_IsIdempotentCommutativeMonoid_852
v6
du_refl_2888 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny
du_refl_2888 :: T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
du_refl_2888 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: t
v1
          = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
              (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
               ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                  ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1))))))
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice._.reflexive
d_reflexive_2890 ::
  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_852 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2890 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2890 ~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_852
v6 = T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2890 T_IsIdempotentCommutativeMonoid_852
v6
du_reflexive_2890 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2890 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2890 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: t
v1
          = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
              (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBand_508
v2 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> T_IsCommutativeBand_590
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                    ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4))
                    AgdaAny
v5))))
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice._.setoid
d_setoid_2892 ::
  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_852 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_2892 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_Setoid_44
d_setoid_2892 ~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_852
v6 = T_IsIdempotentCommutativeMonoid_852 -> T_Setoid_44
du_setoid_2892 T_IsIdempotentCommutativeMonoid_852
v6
du_setoid_2892 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_2892 :: T_IsIdempotentCommutativeMonoid_852 -> T_Setoid_44
du_setoid_2892 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: t
v1
          = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
              (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsBand_508
v2 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> T_IsCommutativeBand_590
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice._.sym
d_sym_2894 ::
  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_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2894 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_2894 ~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_852
v6 = T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2894 T_IsIdempotentCommutativeMonoid_852
v6
du_sym_2894 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2894 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2894 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: t
v1
          = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
              (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
         ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
               ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                  ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1))))))
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice._.trans
d_trans_2896 ::
  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_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2896 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_2896 ~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_852
v6 = T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2896 T_IsIdempotentCommutativeMonoid_852
v6
du_trans_2896 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2896 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2896 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: t
v1
          = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
              (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
         ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
               ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                  ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1))))))
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice._.∙-cong
d_'8729''45'cong_2898 ::
  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_852 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_2898 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_2898 ~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_852
v6
  = T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_2898 T_IsIdempotentCommutativeMonoid_852
v6
du_'8729''45'cong_2898 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong_2898 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_2898 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: t
v1
          = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
              (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
               ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))))
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice._.∙-congʳ
d_'8729''45'cong'691'_2900 ::
  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_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2900 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2900 ~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_852
v6
  = T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2900 T_IsIdempotentCommutativeMonoid_852
v6
du_'8729''45'cong'691'_2900 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2900 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2900 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: t
v1
          = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
              (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBand_508
v2 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> T_IsCommutativeBand_590
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Lattice.Structures.IsBoundedMeetSemilattice._.∙-congˡ
d_'8729''45'cong'737'_2902 ::
  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_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2902 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2902 ~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_852
v6
  = T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2902 T_IsIdempotentCommutativeMonoid_852
v6
du_'8729''45'cong'737'_2902 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2902 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2902 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: t
v1
          = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
              (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBand_508
v2 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> T_IsCommutativeBand_590
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice
d_IsBoundedJoinSemilattice_2904 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> ()
d_IsBoundedJoinSemilattice_2904 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_Level_18
d_IsBoundedJoinSemilattice_2904 = 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_2916 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_2916 :: T_IsIdempotentCommutativeMonoid_852 -> T_Σ_14
d_identity_2916 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_698
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
         ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
            (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0)))
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice._.identityʳ
d_identity'691'_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_852 ->
  AgdaAny -> AgdaAny
d_identity'691'_2918 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
d_identity'691'_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_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
du_identity'691'_2918 T_IsIdempotentCommutativeMonoid_852
v6
du_identity'691'_2918 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny
du_identity'691'_2918 :: T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
du_identity'691'_2918 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1
          = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
              (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_728
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1)))
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice._.identityˡ
d_identity'737'_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_852 ->
  AgdaAny -> AgdaAny
d_identity'737'_2920 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
d_identity'737'_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_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
du_identity'737'_2920 T_IsIdempotentCommutativeMonoid_852
v6
du_identity'737'_2920 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny
du_identity'737'_2920 :: T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
du_identity'737'_2920 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1
          = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
              (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_726
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1)))
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice._.isCommutativeBand
d_isCommutativeBand_2922 ::
  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_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
d_isCommutativeBand_2922 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsCommutativeBand_590
d_isCommutativeBand_2922 ~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_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
du_isCommutativeBand_2922 T_IsIdempotentCommutativeMonoid_852
v6
du_isCommutativeBand_2922 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
du_isCommutativeBand_2922 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
du_isCommutativeBand_2922 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> T_IsCommutativeBand_590
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0)
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice._.assoc
d_assoc_2926 ::
  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_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2926 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_assoc_2926 ~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_852
v6 = T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_2926 T_IsIdempotentCommutativeMonoid_852
v6
du_assoc_2926 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_2926 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_2926 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: t
v1
          = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
              (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_482
         ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
            ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1))))
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice._.comm
d_comm_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_852 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_comm_2928 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_comm_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_852
v6 = T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny
du_comm_2928 T_IsIdempotentCommutativeMonoid_852
v6
du_comm_2928 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny -> AgdaAny
du_comm_2928 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny
du_comm_2928 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_600
      ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0))
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice._.idem
d_idem_2930 ::
  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_852 ->
  AgdaAny -> AgdaAny
d_idem_2930 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
d_idem_2930 ~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_852
v6 = T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
du_idem_2930 T_IsIdempotentCommutativeMonoid_852
v6
du_idem_2930 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny
du_idem_2930 :: T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
du_idem_2930 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: t
v1
          = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
              (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsBand_508 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_508 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_518
         ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice._.isBand
d_isBand_2932 ::
  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_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_508
d_isBand_2932 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsBand_508
d_isBand_2932 ~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_852
v6 = T_IsIdempotentCommutativeMonoid_852 -> T_IsBand_508
du_isBand_2932 T_IsIdempotentCommutativeMonoid_852
v6
du_isBand_2932 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_508
du_isBand_2932 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsBand_508
du_isBand_2932 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsCommutativeBand_590 -> T_IsBand_508)
-> AgdaAny -> T_IsBand_508
forall a b. a -> b
coe
      T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598
      ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0))
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice._.isEquivalence
d_isEquivalence_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_852 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_2934 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsEquivalence_26
d_isEquivalence_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_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> T_IsEquivalence_26
du_isEquivalence_2934 T_IsIdempotentCommutativeMonoid_852
v6
du_isEquivalence_2934 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_2934 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsEquivalence_26
du_isEquivalence_2934 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: t
v1
          = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
              (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
               ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))))
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice._.isMagma
d_isMagma_2936 ::
  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_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_2936 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsMagma_176
d_isMagma_2936 ~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_852
v6 = T_IsIdempotentCommutativeMonoid_852 -> T_IsMagma_176
du_isMagma_2936 T_IsIdempotentCommutativeMonoid_852
v6
du_isMagma_2936 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
du_isMagma_2936 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsMagma_176
du_isMagma_2936 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: t
v1
          = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
              (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
            ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1))))
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice._.isPartialEquivalence
d_isPartialEquivalence_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_852 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2938 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_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_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2938 T_IsIdempotentCommutativeMonoid_852
v6
du_isPartialEquivalence_2938 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2938 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2938 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: t
v1
          = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
              (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsBand_508
v2 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> T_IsCommutativeBand_590
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                  ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4))))))
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice._.isSemigroup
d_isSemigroup_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_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_2940 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsSemigroup_472
d_isSemigroup_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_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> T_IsSemigroup_472
du_isSemigroup_2940 T_IsIdempotentCommutativeMonoid_852
v6
du_isSemigroup_2940 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
du_isSemigroup_2940 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsSemigroup_472
du_isSemigroup_2940 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: t
v1
          = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
              (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
         ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice._.refl
d_refl_2942 ::
  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_852 ->
  AgdaAny -> AgdaAny
d_refl_2942 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
d_refl_2942 ~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_852
v6 = T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
du_refl_2942 T_IsIdempotentCommutativeMonoid_852
v6
du_refl_2942 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny
du_refl_2942 :: T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
du_refl_2942 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: t
v1
          = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
              (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
               ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                  ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1))))))
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice._.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_852 ->
  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_852
-> 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_852
v6 = T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2944 T_IsIdempotentCommutativeMonoid_852
v6
du_reflexive_2944 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2944 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2944 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: t
v1
          = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
              (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBand_508
v2 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> T_IsCommutativeBand_590
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                    ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4))
                    AgdaAny
v5))))
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice._.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_852 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_2946 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_Setoid_44
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_852
v6 = T_IsIdempotentCommutativeMonoid_852 -> T_Setoid_44
du_setoid_2946 T_IsIdempotentCommutativeMonoid_852
v6
du_setoid_2946 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_2946 :: T_IsIdempotentCommutativeMonoid_852 -> T_Setoid_44
du_setoid_2946 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: t
v1
          = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
              (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsBand_508
v2 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> T_IsCommutativeBand_590
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice._.sym
d_sym_2948 ::
  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_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2948 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_2948 ~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_852
v6 = T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2948 T_IsIdempotentCommutativeMonoid_852
v6
du_sym_2948 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2948 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2948 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: t
v1
          = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
              (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
         ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
               ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                  ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1))))))
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice._.trans
d_trans_2950 ::
  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_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2950 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_2950 ~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_852
v6 = T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2950 T_IsIdempotentCommutativeMonoid_852
v6
du_trans_2950 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2950 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2950 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: t
v1
          = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
              (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
         ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
               ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                  ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1))))))
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice._.∙-cong
d_'8729''45'cong_2952 ::
  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_852 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_2952 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_2952 ~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_852
v6
  = T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_2952 T_IsIdempotentCommutativeMonoid_852
v6
du_'8729''45'cong_2952 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong_2952 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_2952 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: t
v1
          = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
              (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
               ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))))
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice._.∙-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_852 ->
  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_852
-> 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_852
v6
  = T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2954 T_IsIdempotentCommutativeMonoid_852
v6
du_'8729''45'cong'691'_2954 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2954 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2954 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: t
v1
          = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
              (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBand_508
v2 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> T_IsCommutativeBand_590
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Lattice.Structures.IsBoundedJoinSemilattice._.∙-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_852 ->
  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_852
-> 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_852
v6
  = T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2956 T_IsIdempotentCommutativeMonoid_852
v6
du_'8729''45'cong'737'_2956 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2956 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2956 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: t
v1
          = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> t
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
              (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBand_508
v2 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (AgdaAny -> T_IsCommutativeBand_590
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Lattice.Structures.IsLattice
d_IsLattice_2962 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_IsLattice_2962 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_IsLattice_2962
  = C_IsLattice'46'constructor_36793 MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
                                     (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_2984 ::
  T_IsLattice_2962 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_2984 :: T_IsLattice_2962 -> T_IsEquivalence_26
d_isEquivalence_2984 T_IsLattice_2962
v0
  = case T_IsLattice_2962 -> T_IsLattice_2962
forall a b. a -> b
coe T_IsLattice_2962
v0 of
      C_IsLattice'46'constructor_36793 T_IsEquivalence_26
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_26 -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsEquivalence_26
v1
      T_IsLattice_2962
_ -> T_IsEquivalence_26
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Structures.IsLattice.∨-comm
d_'8744''45'comm_2986 ::
  T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_2986 :: T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_2986 T_IsLattice_2962
v0
  = case T_IsLattice_2962 -> T_IsLattice_2962
forall a b. a -> b
coe T_IsLattice_2962
v0 of
      C_IsLattice'46'constructor_36793 T_IsEquivalence_26
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_2962
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Structures.IsLattice.∨-assoc
d_'8744''45'assoc_2988 ::
  T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_2988 :: T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_2988 T_IsLattice_2962
v0
  = case T_IsLattice_2962 -> T_IsLattice_2962
forall a b. a -> b
coe T_IsLattice_2962
v0 of
      C_IsLattice'46'constructor_36793 T_IsEquivalence_26
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_2962
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Structures.IsLattice.∨-cong
d_'8744''45'cong_2990 ::
  T_IsLattice_2962 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong_2990 :: T_IsLattice_2962
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong_2990 T_IsLattice_2962
v0
  = case T_IsLattice_2962 -> T_IsLattice_2962
forall a b. a -> b
coe T_IsLattice_2962
v0 of
      C_IsLattice'46'constructor_36793 T_IsEquivalence_26
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_2962
_ -> AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Structures.IsLattice.∧-comm
d_'8743''45'comm_2992 ::
  T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_2992 :: T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_2992 T_IsLattice_2962
v0
  = case T_IsLattice_2962 -> T_IsLattice_2962
forall a b. a -> b
coe T_IsLattice_2962
v0 of
      C_IsLattice'46'constructor_36793 T_IsEquivalence_26
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_2962
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Structures.IsLattice.∧-assoc
d_'8743''45'assoc_2994 ::
  T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_2994 :: T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_2994 T_IsLattice_2962
v0
  = case T_IsLattice_2962 -> T_IsLattice_2962
forall a b. a -> b
coe T_IsLattice_2962
v0 of
      C_IsLattice'46'constructor_36793 T_IsEquivalence_26
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_2962
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Structures.IsLattice.∧-cong
d_'8743''45'cong_2996 ::
  T_IsLattice_2962 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong_2996 :: T_IsLattice_2962
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong_2996 T_IsLattice_2962
v0
  = case T_IsLattice_2962 -> T_IsLattice_2962
forall a b. a -> b
coe T_IsLattice_2962
v0 of
      C_IsLattice'46'constructor_36793 T_IsEquivalence_26
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_2962
_ -> AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Structures.IsLattice.absorptive
d_absorptive_2998 ::
  T_IsLattice_2962 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_absorptive_2998 :: T_IsLattice_2962 -> T_Σ_14
d_absorptive_2998 T_IsLattice_2962
v0
  = case T_IsLattice_2962 -> T_IsLattice_2962
forall a b. a -> b
coe T_IsLattice_2962
v0 of
      C_IsLattice'46'constructor_36793 T_IsEquivalence_26
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_2962
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Structures.IsLattice._.isPartialEquivalence
d_isPartialEquivalence_3002 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsLattice_2962 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_3002 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_2962
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_3002 ~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_2962
v6
  = T_IsLattice_2962 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3002 T_IsLattice_2962
v6
du_isPartialEquivalence_3002 ::
  T_IsLattice_2962 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_3002 :: T_IsLattice_2962 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3002 T_IsLattice_2962
v0
  = (T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
      ((T_IsLattice_2962 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962 -> T_IsEquivalence_26
d_isEquivalence_2984 (T_IsLattice_2962 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962
v0))
-- Algebra.Lattice.Structures.IsLattice._.refl
d_refl_3004 :: T_IsLattice_2962 -> AgdaAny -> AgdaAny
d_refl_3004 :: T_IsLattice_2962 -> AgdaAny -> AgdaAny
d_refl_3004 T_IsLattice_2962
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsLattice_2962 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962 -> T_IsEquivalence_26
d_isEquivalence_2984 (T_IsLattice_2962 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962
v0))
-- Algebra.Lattice.Structures.IsLattice._.reflexive
d_reflexive_3006 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsLattice_2962 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_3006 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_2962
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_3006 ~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_2962
v6 = T_IsLattice_2962 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_3006 T_IsLattice_2962
v6
du_reflexive_3006 ::
  T_IsLattice_2962 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_3006 :: T_IsLattice_2962 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_3006 T_IsLattice_2962
v0 AgdaAny
v1 AgdaAny
v2 T__'8801'__12
v3
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
      ((T_IsLattice_2962 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962 -> T_IsEquivalence_26
d_isEquivalence_2984 (T_IsLattice_2962 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962
v0)) AgdaAny
v1
-- Algebra.Lattice.Structures.IsLattice._.sym
d_sym_3008 ::
  T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_3008 :: T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_3008 T_IsLattice_2962
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsLattice_2962 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962 -> T_IsEquivalence_26
d_isEquivalence_2984 (T_IsLattice_2962 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962
v0))
-- Algebra.Lattice.Structures.IsLattice._.trans
d_trans_3010 ::
  T_IsLattice_2962 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_3010 :: T_IsLattice_2962
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_3010 T_IsLattice_2962
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsLattice_2962 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962 -> T_IsEquivalence_26
d_isEquivalence_2984 (T_IsLattice_2962 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962
v0))
-- Algebra.Lattice.Structures.IsLattice.∨-absorbs-∧
d_'8744''45'absorbs'45''8743'_3012 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'absorbs'45''8743'_3012 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_2962
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'absorbs'45''8743'_3012 ~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_2962
v6
  = T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_3012 T_IsLattice_2962
v6
du_'8744''45'absorbs'45''8743'_3012 ::
  T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_3012 :: T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_3012 T_IsLattice_2962
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_2962 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962 -> T_Σ_14
d_absorptive_2998 (T_IsLattice_2962 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962
v0))
-- Algebra.Lattice.Structures.IsLattice.∧-absorbs-∨
d_'8743''45'absorbs'45''8744'_3014 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'absorbs'45''8744'_3014 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_2962
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'absorbs'45''8744'_3014 ~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_2962
v6
  = T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_3014 T_IsLattice_2962
v6
du_'8743''45'absorbs'45''8744'_3014 ::
  T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_3014 :: T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_3014 T_IsLattice_2962
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_2962 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962 -> T_Σ_14
d_absorptive_2998 (T_IsLattice_2962 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962
v0))
-- Algebra.Lattice.Structures.IsLattice.∧-congˡ
d_'8743''45'cong'737'_3016 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsLattice_2962 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong'737'_3016 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_2962
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong'737'_3016 ~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_2962
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
  = T_IsLattice_2962
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_3016 T_IsLattice_2962
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
du_'8743''45'cong'737'_3016 ::
  T_IsLattice_2962 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_3016 :: T_IsLattice_2962
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_3016 T_IsLattice_2962
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4
  = (T_IsLattice_2962
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> T_IsLattice_2962
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_2962
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong_2996 T_IsLattice_2962
v0 AgdaAny
v1 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         (T_IsLattice_2962 -> T_IsEquivalence_26
d_isEquivalence_2984 (T_IsLattice_2962 -> T_IsLattice_2962
forall a b. a -> b
coe T_IsLattice_2962
v0)) AgdaAny
v1)
      AgdaAny
v4
-- Algebra.Lattice.Structures.IsLattice.∧-congʳ
d_'8743''45'cong'691'_3020 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsLattice_2962 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong'691'_3020 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_2962
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong'691'_3020 ~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_2962
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
  = T_IsLattice_2962
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_3020 T_IsLattice_2962
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
du_'8743''45'cong'691'_3020 ::
  T_IsLattice_2962 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_3020 :: T_IsLattice_2962
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_3020 T_IsLattice_2962
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4
  = (T_IsLattice_2962
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> T_IsLattice_2962
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_2962
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong_2996 T_IsLattice_2962
v0 AgdaAny
v2 AgdaAny
v3 AgdaAny
v1 AgdaAny
v1 AgdaAny
v4
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         (T_IsLattice_2962 -> T_IsEquivalence_26
d_isEquivalence_2984 (T_IsLattice_2962 -> T_IsLattice_2962
forall a b. a -> b
coe T_IsLattice_2962
v0)) AgdaAny
v1)
-- Algebra.Lattice.Structures.IsLattice.∨-congˡ
d_'8744''45'cong'737'_3024 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsLattice_2962 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong'737'_3024 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_2962
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong'737'_3024 ~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_2962
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
  = T_IsLattice_2962
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_3024 T_IsLattice_2962
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
du_'8744''45'cong'737'_3024 ::
  T_IsLattice_2962 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_3024 :: T_IsLattice_2962
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_3024 T_IsLattice_2962
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4
  = (T_IsLattice_2962
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> T_IsLattice_2962
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_2962
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong_2990 T_IsLattice_2962
v0 AgdaAny
v1 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         (T_IsLattice_2962 -> T_IsEquivalence_26
d_isEquivalence_2984 (T_IsLattice_2962 -> T_IsLattice_2962
forall a b. a -> b
coe T_IsLattice_2962
v0)) AgdaAny
v1)
      AgdaAny
v4
-- Algebra.Lattice.Structures.IsLattice.∨-congʳ
d_'8744''45'cong'691'_3028 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsLattice_2962 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong'691'_3028 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_2962
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong'691'_3028 ~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_2962
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
  = T_IsLattice_2962
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_3028 T_IsLattice_2962
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
du_'8744''45'cong'691'_3028 ::
  T_IsLattice_2962 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_3028 :: T_IsLattice_2962
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_3028 T_IsLattice_2962
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4
  = (T_IsLattice_2962
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> T_IsLattice_2962
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_2962
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong_2990 T_IsLattice_2962
v0 AgdaAny
v2 AgdaAny
v3 AgdaAny
v1 AgdaAny
v1 AgdaAny
v4
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         (T_IsLattice_2962 -> T_IsEquivalence_26
d_isEquivalence_2984 (T_IsLattice_2962 -> T_IsLattice_2962
forall a b. a -> b
coe T_IsLattice_2962
v0)) AgdaAny
v1)
-- Algebra.Lattice.Structures.IsDistributiveLattice
d_IsDistributiveLattice_3036 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_IsDistributiveLattice_3036 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_IsDistributiveLattice_3036
  = C_IsDistributiveLattice'46'constructor_40943 T_IsLattice_2962
                                                 MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
                                                 MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
-- Algebra.Lattice.Structures.IsDistributiveLattice.isLattice
d_isLattice_3048 ::
  T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 :: T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 T_IsDistributiveLattice_3036
v0
  = case T_IsDistributiveLattice_3036 -> T_IsDistributiveLattice_3036
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v0 of
      C_IsDistributiveLattice'46'constructor_40943 T_IsLattice_2962
v1 T_Σ_14
v2 T_Σ_14
v3 -> T_IsLattice_2962 -> T_IsLattice_2962
forall a b. a -> b
coe T_IsLattice_2962
v1
      T_IsDistributiveLattice_3036
_ -> T_IsLattice_2962
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Structures.IsDistributiveLattice.∨-distrib-∧
d_'8744''45'distrib'45''8743'_3050 ::
  T_IsDistributiveLattice_3036 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8744''45'distrib'45''8743'_3050 :: T_IsDistributiveLattice_3036 -> T_Σ_14
d_'8744''45'distrib'45''8743'_3050 T_IsDistributiveLattice_3036
v0
  = case T_IsDistributiveLattice_3036 -> T_IsDistributiveLattice_3036
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v0 of
      C_IsDistributiveLattice'46'constructor_40943 T_IsLattice_2962
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_3036
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Structures.IsDistributiveLattice.∧-distrib-∨
d_'8743''45'distrib'45''8744'_3052 ::
  T_IsDistributiveLattice_3036 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8743''45'distrib'45''8744'_3052 :: T_IsDistributiveLattice_3036 -> T_Σ_14
d_'8743''45'distrib'45''8744'_3052 T_IsDistributiveLattice_3036
v0
  = case T_IsDistributiveLattice_3036 -> T_IsDistributiveLattice_3036
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v0 of
      C_IsDistributiveLattice'46'constructor_40943 T_IsLattice_2962
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_3036
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Structures.IsDistributiveLattice._.absorptive
d_absorptive_3056 ::
  T_IsDistributiveLattice_3036 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_absorptive_3056 :: T_IsDistributiveLattice_3036 -> T_Σ_14
d_absorptive_3056 T_IsDistributiveLattice_3036
v0
  = (T_IsLattice_2962 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsLattice_2962 -> T_Σ_14
d_absorptive_2998 ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 (T_IsDistributiveLattice_3036 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v0))
-- Algebra.Lattice.Structures.IsDistributiveLattice._.isEquivalence
d_isEquivalence_3058 ::
  T_IsDistributiveLattice_3036 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_3058 :: T_IsDistributiveLattice_3036 -> T_IsEquivalence_26
d_isEquivalence_3058 T_IsDistributiveLattice_3036
v0
  = (T_IsLattice_2962 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsLattice_2962 -> T_IsEquivalence_26
d_isEquivalence_2984 ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 (T_IsDistributiveLattice_3036 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v0))
-- Algebra.Lattice.Structures.IsDistributiveLattice._.isPartialEquivalence
d_isPartialEquivalence_3060 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_3036 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_3060 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_3036
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_3060 ~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_3036
v6
  = T_IsDistributiveLattice_3036 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3060 T_IsDistributiveLattice_3036
v6
du_isPartialEquivalence_3060 ::
  T_IsDistributiveLattice_3036 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_3060 :: T_IsDistributiveLattice_3036 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3060 T_IsDistributiveLattice_3036
v0
  = let v1 :: T_IsLattice_2962
v1 = T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 (T_IsDistributiveLattice_3036 -> T_IsDistributiveLattice_3036
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
         ((T_IsLattice_2962 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962 -> T_IsEquivalence_26
d_isEquivalence_2984 (T_IsLattice_2962 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962
v1)))
-- Algebra.Lattice.Structures.IsDistributiveLattice._.refl
d_refl_3062 :: T_IsDistributiveLattice_3036 -> AgdaAny -> AgdaAny
d_refl_3062 :: T_IsDistributiveLattice_3036 -> AgdaAny -> AgdaAny
d_refl_3062 T_IsDistributiveLattice_3036
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsLattice_2962 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962 -> T_IsEquivalence_26
d_isEquivalence_2984 ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 (T_IsDistributiveLattice_3036 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v0)))
-- Algebra.Lattice.Structures.IsDistributiveLattice._.reflexive
d_reflexive_3064 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_3036 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_3064 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_3036
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_3064 ~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_3036
v6 = T_IsDistributiveLattice_3036
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_3064 T_IsDistributiveLattice_3036
v6
du_reflexive_3064 ::
  T_IsDistributiveLattice_3036 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_3064 :: T_IsDistributiveLattice_3036
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_3064 T_IsDistributiveLattice_3036
v0
  = let v1 :: T_IsLattice_2962
v1 = T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 (T_IsDistributiveLattice_3036 -> T_IsDistributiveLattice_3036
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v0) in
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (\ AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 ->
         (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
           ((T_IsLattice_2962 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962 -> T_IsEquivalence_26
d_isEquivalence_2984 (T_IsLattice_2962 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962
v1)) AgdaAny
v2)
-- Algebra.Lattice.Structures.IsDistributiveLattice._.sym
d_sym_3066 ::
  T_IsDistributiveLattice_3036 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_3066 :: T_IsDistributiveLattice_3036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_3066 T_IsDistributiveLattice_3036
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsLattice_2962 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962 -> T_IsEquivalence_26
d_isEquivalence_2984 ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 (T_IsDistributiveLattice_3036 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v0)))
-- Algebra.Lattice.Structures.IsDistributiveLattice._.trans
d_trans_3068 ::
  T_IsDistributiveLattice_3036 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_3068 :: T_IsDistributiveLattice_3036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_3068 T_IsDistributiveLattice_3036
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsLattice_2962 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962 -> T_IsEquivalence_26
d_isEquivalence_2984 ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 (T_IsDistributiveLattice_3036 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v0)))
-- Algebra.Lattice.Structures.IsDistributiveLattice._.∧-absorbs-∨
d_'8743''45'absorbs'45''8744'_3070 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_3036 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'absorbs'45''8744'_3070 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_3036
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'absorbs'45''8744'_3070 ~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_3036
v6
  = T_IsDistributiveLattice_3036 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_3070 T_IsDistributiveLattice_3036
v6
du_'8743''45'absorbs'45''8744'_3070 ::
  T_IsDistributiveLattice_3036 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_3070 :: T_IsDistributiveLattice_3036 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_3070 T_IsDistributiveLattice_3036
v0
  = (T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_3014 ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 (T_IsDistributiveLattice_3036 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v0))
-- Algebra.Lattice.Structures.IsDistributiveLattice._.∧-assoc
d_'8743''45'assoc_3072 ::
  T_IsDistributiveLattice_3036 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_3072 :: T_IsDistributiveLattice_3036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_3072 T_IsDistributiveLattice_3036
v0
  = (T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_2994 ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 (T_IsDistributiveLattice_3036 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v0))
-- Algebra.Lattice.Structures.IsDistributiveLattice._.∧-comm
d_'8743''45'comm_3074 ::
  T_IsDistributiveLattice_3036 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_3074 :: T_IsDistributiveLattice_3036 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_3074 T_IsDistributiveLattice_3036
v0
  = (T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_2992 ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 (T_IsDistributiveLattice_3036 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v0))
-- Algebra.Lattice.Structures.IsDistributiveLattice._.∧-cong
d_'8743''45'cong_3076 ::
  T_IsDistributiveLattice_3036 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong_3076 :: T_IsDistributiveLattice_3036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong_3076 T_IsDistributiveLattice_3036
v0
  = (T_IsLattice_2962
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong_2996 ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 (T_IsDistributiveLattice_3036 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v0))
-- Algebra.Lattice.Structures.IsDistributiveLattice._.∧-congʳ
d_'8743''45'cong'691'_3078 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_3036 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong'691'_3078 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_3036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong'691'_3078 ~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_3036
v6
  = T_IsDistributiveLattice_3036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_3078 T_IsDistributiveLattice_3036
v6
du_'8743''45'cong'691'_3078 ::
  T_IsDistributiveLattice_3036 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_3078 :: T_IsDistributiveLattice_3036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_3078 T_IsDistributiveLattice_3036
v0
  = (T_IsLattice_2962
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_3020 ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 (T_IsDistributiveLattice_3036 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v0))
-- Algebra.Lattice.Structures.IsDistributiveLattice._.∧-congˡ
d_'8743''45'cong'737'_3080 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_3036 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong'737'_3080 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_3036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong'737'_3080 ~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_3036
v6
  = T_IsDistributiveLattice_3036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_3080 T_IsDistributiveLattice_3036
v6
du_'8743''45'cong'737'_3080 ::
  T_IsDistributiveLattice_3036 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_3080 :: T_IsDistributiveLattice_3036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_3080 T_IsDistributiveLattice_3036
v0
  = (T_IsLattice_2962
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_3016 ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 (T_IsDistributiveLattice_3036 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v0))
-- Algebra.Lattice.Structures.IsDistributiveLattice._.∨-absorbs-∧
d_'8744''45'absorbs'45''8743'_3082 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_3036 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'absorbs'45''8743'_3082 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_3036
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'absorbs'45''8743'_3082 ~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_3036
v6
  = T_IsDistributiveLattice_3036 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_3082 T_IsDistributiveLattice_3036
v6
du_'8744''45'absorbs'45''8743'_3082 ::
  T_IsDistributiveLattice_3036 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_3082 :: T_IsDistributiveLattice_3036 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_3082 T_IsDistributiveLattice_3036
v0
  = (T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_3012 ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 (T_IsDistributiveLattice_3036 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v0))
-- Algebra.Lattice.Structures.IsDistributiveLattice._.∨-assoc
d_'8744''45'assoc_3084 ::
  T_IsDistributiveLattice_3036 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_3084 :: T_IsDistributiveLattice_3036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_3084 T_IsDistributiveLattice_3036
v0
  = (T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_2988 ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 (T_IsDistributiveLattice_3036 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v0))
-- Algebra.Lattice.Structures.IsDistributiveLattice._.∨-comm
d_'8744''45'comm_3086 ::
  T_IsDistributiveLattice_3036 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_3086 :: T_IsDistributiveLattice_3036 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_3086 T_IsDistributiveLattice_3036
v0
  = (T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_2986 ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 (T_IsDistributiveLattice_3036 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v0))
-- Algebra.Lattice.Structures.IsDistributiveLattice._.∨-cong
d_'8744''45'cong_3088 ::
  T_IsDistributiveLattice_3036 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong_3088 :: T_IsDistributiveLattice_3036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong_3088 T_IsDistributiveLattice_3036
v0
  = (T_IsLattice_2962
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong_2990 ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 (T_IsDistributiveLattice_3036 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v0))
-- Algebra.Lattice.Structures.IsDistributiveLattice._.∨-congʳ
d_'8744''45'cong'691'_3090 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_3036 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong'691'_3090 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_3036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong'691'_3090 ~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_3036
v6
  = T_IsDistributiveLattice_3036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_3090 T_IsDistributiveLattice_3036
v6
du_'8744''45'cong'691'_3090 ::
  T_IsDistributiveLattice_3036 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_3090 :: T_IsDistributiveLattice_3036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_3090 T_IsDistributiveLattice_3036
v0
  = (T_IsLattice_2962
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_3028 ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 (T_IsDistributiveLattice_3036 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v0))
-- Algebra.Lattice.Structures.IsDistributiveLattice._.∨-congˡ
d_'8744''45'cong'737'_3092 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_3036 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong'737'_3092 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_3036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong'737'_3092 ~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_3036
v6
  = T_IsDistributiveLattice_3036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_3092 T_IsDistributiveLattice_3036
v6
du_'8744''45'cong'737'_3092 ::
  T_IsDistributiveLattice_3036 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_3092 :: T_IsDistributiveLattice_3036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_3092 T_IsDistributiveLattice_3036
v0
  = (T_IsLattice_2962
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_3024 ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 (T_IsDistributiveLattice_3036 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v0))
-- Algebra.Lattice.Structures.IsDistributiveLattice.∨-distribˡ-∧
d_'8744''45'distrib'737''45''8743'_3094 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_3036 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'distrib'737''45''8743'_3094 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_3036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'distrib'737''45''8743'_3094 ~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_3036
v6
  = T_IsDistributiveLattice_3036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'737''45''8743'_3094 T_IsDistributiveLattice_3036
v6
du_'8744''45'distrib'737''45''8743'_3094 ::
  T_IsDistributiveLattice_3036 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'737''45''8743'_3094 :: T_IsDistributiveLattice_3036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'737''45''8743'_3094 T_IsDistributiveLattice_3036
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_3036 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036 -> T_Σ_14
d_'8744''45'distrib'45''8743'_3050 (T_IsDistributiveLattice_3036 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v0))
-- Algebra.Lattice.Structures.IsDistributiveLattice.∨-distribʳ-∧
d_'8744''45'distrib'691''45''8743'_3096 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_3036 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'distrib'691''45''8743'_3096 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_3036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'distrib'691''45''8743'_3096 ~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_3036
v6
  = T_IsDistributiveLattice_3036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'691''45''8743'_3096 T_IsDistributiveLattice_3036
v6
du_'8744''45'distrib'691''45''8743'_3096 ::
  T_IsDistributiveLattice_3036 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'691''45''8743'_3096 :: T_IsDistributiveLattice_3036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'691''45''8743'_3096 T_IsDistributiveLattice_3036
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_3036 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036 -> T_Σ_14
d_'8744''45'distrib'45''8743'_3050 (T_IsDistributiveLattice_3036 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v0))
-- Algebra.Lattice.Structures.IsDistributiveLattice.∧-distribˡ-∨
d_'8743''45'distrib'737''45''8744'_3098 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_3036 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'distrib'737''45''8744'_3098 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_3036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'distrib'737''45''8744'_3098 ~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_3036
v6
  = T_IsDistributiveLattice_3036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'737''45''8744'_3098 T_IsDistributiveLattice_3036
v6
du_'8743''45'distrib'737''45''8744'_3098 ::
  T_IsDistributiveLattice_3036 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'737''45''8744'_3098 :: T_IsDistributiveLattice_3036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'737''45''8744'_3098 T_IsDistributiveLattice_3036
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_3036 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036 -> T_Σ_14
d_'8743''45'distrib'45''8744'_3052 (T_IsDistributiveLattice_3036 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v0))
-- Algebra.Lattice.Structures.IsDistributiveLattice.∧-distribʳ-∨
d_'8743''45'distrib'691''45''8744'_3100 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_3036 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'distrib'691''45''8744'_3100 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_3036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'distrib'691''45''8744'_3100 ~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_3036
v6
  = T_IsDistributiveLattice_3036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'691''45''8744'_3100 T_IsDistributiveLattice_3036
v6
du_'8743''45'distrib'691''45''8744'_3100 ::
  T_IsDistributiveLattice_3036 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'691''45''8744'_3100 :: T_IsDistributiveLattice_3036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'691''45''8744'_3100 T_IsDistributiveLattice_3036
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_3036 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036 -> T_Σ_14
d_'8743''45'distrib'45''8744'_3052 (T_IsDistributiveLattice_3036 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v0))
-- Algebra.Lattice.Structures.IsBooleanAlgebra
d_IsBooleanAlgebra_3112 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsBooleanAlgebra_3112 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 = ()
data T_IsBooleanAlgebra_3112
  = C_IsBooleanAlgebra'46'constructor_44015 T_IsDistributiveLattice_3036
                                            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_3132 ::
  T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_3132 :: T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_3132 T_IsBooleanAlgebra_3112
v0
  = case T_IsBooleanAlgebra_3112 -> T_IsBooleanAlgebra_3112
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v0 of
      C_IsBooleanAlgebra'46'constructor_44015 T_IsDistributiveLattice_3036
v1 T_Σ_14
v2 T_Σ_14
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 -> T_IsDistributiveLattice_3036 -> T_IsDistributiveLattice_3036
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v1
      T_IsBooleanAlgebra_3112
_ -> T_IsDistributiveLattice_3036
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Structures.IsBooleanAlgebra.∨-complement
d_'8744''45'complement_3134 ::
  T_IsBooleanAlgebra_3112 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8744''45'complement_3134 :: T_IsBooleanAlgebra_3112 -> T_Σ_14
d_'8744''45'complement_3134 T_IsBooleanAlgebra_3112
v0
  = case T_IsBooleanAlgebra_3112 -> T_IsBooleanAlgebra_3112
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v0 of
      C_IsBooleanAlgebra'46'constructor_44015 T_IsDistributiveLattice_3036
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_3112
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Structures.IsBooleanAlgebra.∧-complement
d_'8743''45'complement_3136 ::
  T_IsBooleanAlgebra_3112 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8743''45'complement_3136 :: T_IsBooleanAlgebra_3112 -> T_Σ_14
d_'8743''45'complement_3136 T_IsBooleanAlgebra_3112
v0
  = case T_IsBooleanAlgebra_3112 -> T_IsBooleanAlgebra_3112
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v0 of
      C_IsBooleanAlgebra'46'constructor_44015 T_IsDistributiveLattice_3036
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_3112
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Structures.IsBooleanAlgebra.¬-cong
d_'172''45'cong_3138 ::
  T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'172''45'cong_3138 :: T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'172''45'cong_3138 T_IsBooleanAlgebra_3112
v0
  = case T_IsBooleanAlgebra_3112 -> T_IsBooleanAlgebra_3112
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v0 of
      C_IsBooleanAlgebra'46'constructor_44015 T_IsDistributiveLattice_3036
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_3112
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.absorptive
d_absorptive_3142 ::
  T_IsBooleanAlgebra_3112 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_absorptive_3142 :: T_IsBooleanAlgebra_3112 -> T_Σ_14
d_absorptive_3142 T_IsBooleanAlgebra_3112
v0
  = (T_IsLattice_2962 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsLattice_2962 -> T_Σ_14
d_absorptive_2998
      ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 ((T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_3132 (T_IsBooleanAlgebra_3112 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v0)))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.isEquivalence
d_isEquivalence_3144 ::
  T_IsBooleanAlgebra_3112 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_3144 :: T_IsBooleanAlgebra_3112 -> T_IsEquivalence_26
d_isEquivalence_3144 T_IsBooleanAlgebra_3112
v0
  = (T_IsLattice_2962 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsLattice_2962 -> T_IsEquivalence_26
d_isEquivalence_2984
      ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 ((T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_3132 (T_IsBooleanAlgebra_3112 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v0)))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.isLattice
d_isLattice_3146 :: T_IsBooleanAlgebra_3112 -> T_IsLattice_2962
d_isLattice_3146 :: T_IsBooleanAlgebra_3112 -> T_IsLattice_2962
d_isLattice_3146 T_IsBooleanAlgebra_3112
v0
  = (T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> T_IsLattice_2962
forall a b. a -> b
coe T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 ((T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_3132 (T_IsBooleanAlgebra_3112 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v0))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.isPartialEquivalence
d_isPartialEquivalence_3148 ::
  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_3112 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_3148 :: 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_3112
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_3148 ~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_3112
v9
  = T_IsBooleanAlgebra_3112 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3148 T_IsBooleanAlgebra_3112
v9
du_isPartialEquivalence_3148 ::
  T_IsBooleanAlgebra_3112 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_3148 :: T_IsBooleanAlgebra_3112 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3148 T_IsBooleanAlgebra_3112
v0
  = let v1 :: T_IsDistributiveLattice_3036
v1 = T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_3132 (T_IsBooleanAlgebra_3112 -> T_IsBooleanAlgebra_3112
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_2962
v2 = T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 (T_IsDistributiveLattice_3036 -> T_IsDistributiveLattice_3036
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((T_IsLattice_2962 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962 -> T_IsEquivalence_26
d_isEquivalence_2984 (T_IsLattice_2962 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962
v2))))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.refl
d_refl_3150 :: T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny
d_refl_3150 :: T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny
d_refl_3150 T_IsBooleanAlgebra_3112
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsLattice_2962 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_2962 -> T_IsEquivalence_26
d_isEquivalence_2984
         ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 ((T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_3132 (T_IsBooleanAlgebra_3112 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v0))))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.reflexive
d_reflexive_3152 ::
  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_3112 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_3152 :: 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_3112
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_3152 ~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_3112
v9
  = T_IsBooleanAlgebra_3112
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_3152 T_IsBooleanAlgebra_3112
v9
du_reflexive_3152 ::
  T_IsBooleanAlgebra_3112 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_3152 :: T_IsBooleanAlgebra_3112
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_3152 T_IsBooleanAlgebra_3112
v0
  = let v1 :: T_IsDistributiveLattice_3036
v1 = T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_3132 (T_IsBooleanAlgebra_3112 -> T_IsBooleanAlgebra_3112
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_2962
v2 = T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 (T_IsDistributiveLattice_3036 -> T_IsDistributiveLattice_3036
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((T_IsLattice_2962 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962 -> T_IsEquivalence_26
d_isEquivalence_2984 (T_IsLattice_2962 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962
v2)) AgdaAny
v3))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.sym
d_sym_3154 ::
  T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_3154 :: T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_3154 T_IsBooleanAlgebra_3112
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsLattice_2962 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_2962 -> T_IsEquivalence_26
d_isEquivalence_2984
         ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 ((T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_3132 (T_IsBooleanAlgebra_3112 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v0))))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.trans
d_trans_3156 ::
  T_IsBooleanAlgebra_3112 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_3156 :: T_IsBooleanAlgebra_3112
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_3156 T_IsBooleanAlgebra_3112
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsLattice_2962 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_2962 -> T_IsEquivalence_26
d_isEquivalence_2984
         ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 ((T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_3132 (T_IsBooleanAlgebra_3112 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v0))))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.∧-absorbs-∨
d_'8743''45'absorbs'45''8744'_3158 ::
  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_3112 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'absorbs'45''8744'_3158 :: 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_3112
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'absorbs'45''8744'_3158 ~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_3112
v9
  = T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_3158 T_IsBooleanAlgebra_3112
v9
du_'8743''45'absorbs'45''8744'_3158 ::
  T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_3158 :: T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_3158 T_IsBooleanAlgebra_3112
v0
  = let v1 :: T_IsDistributiveLattice_3036
v1 = T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_3132 (T_IsBooleanAlgebra_3112 -> T_IsBooleanAlgebra_3112
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_3014
         ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 (T_IsDistributiveLattice_3036 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v1)))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.∧-assoc
d_'8743''45'assoc_3160 ::
  T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_3160 :: T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_3160 T_IsBooleanAlgebra_3112
v0
  = (T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_2994
      ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 ((T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_3132 (T_IsBooleanAlgebra_3112 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v0)))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.∧-comm
d_'8743''45'comm_3162 ::
  T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_3162 :: T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_3162 T_IsBooleanAlgebra_3112
v0
  = (T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_2992
      ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 ((T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_3132 (T_IsBooleanAlgebra_3112 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v0)))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.∧-cong
d_'8743''45'cong_3164 ::
  T_IsBooleanAlgebra_3112 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong_3164 :: T_IsBooleanAlgebra_3112
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong_3164 T_IsBooleanAlgebra_3112
v0
  = (T_IsLattice_2962
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_2962
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong_2996
      ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 ((T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_3132 (T_IsBooleanAlgebra_3112 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v0)))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.∧-congʳ
d_'8743''45'cong'691'_3166 ::
  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_3112 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong'691'_3166 :: 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_3112
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong'691'_3166 ~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_3112
v9
  = T_IsBooleanAlgebra_3112
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_3166 T_IsBooleanAlgebra_3112
v9
du_'8743''45'cong'691'_3166 ::
  T_IsBooleanAlgebra_3112 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_3166 :: T_IsBooleanAlgebra_3112
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_3166 T_IsBooleanAlgebra_3112
v0
  = let v1 :: T_IsDistributiveLattice_3036
v1 = T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_3132 (T_IsBooleanAlgebra_3112 -> T_IsBooleanAlgebra_3112
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsLattice_2962
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_3020 ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 (T_IsDistributiveLattice_3036 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v1)))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.∧-congˡ
d_'8743''45'cong'737'_3168 ::
  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_3112 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong'737'_3168 :: 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_3112
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong'737'_3168 ~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_3112
v9
  = T_IsBooleanAlgebra_3112
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_3168 T_IsBooleanAlgebra_3112
v9
du_'8743''45'cong'737'_3168 ::
  T_IsBooleanAlgebra_3112 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_3168 :: T_IsBooleanAlgebra_3112
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_3168 T_IsBooleanAlgebra_3112
v0
  = let v1 :: T_IsDistributiveLattice_3036
v1 = T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_3132 (T_IsBooleanAlgebra_3112 -> T_IsBooleanAlgebra_3112
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsLattice_2962
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_3016 ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 (T_IsDistributiveLattice_3036 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v1)))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.∧-distrib-∨
d_'8743''45'distrib'45''8744'_3170 ::
  T_IsBooleanAlgebra_3112 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8743''45'distrib'45''8744'_3170 :: T_IsBooleanAlgebra_3112 -> T_Σ_14
d_'8743''45'distrib'45''8744'_3170 T_IsBooleanAlgebra_3112
v0
  = (T_IsDistributiveLattice_3036 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsDistributiveLattice_3036 -> T_Σ_14
d_'8743''45'distrib'45''8744'_3052
      ((T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_3132 (T_IsBooleanAlgebra_3112 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v0))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.∧-distribʳ-∨
d_'8743''45'distrib'691''45''8744'_3172 ::
  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_3112 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'distrib'691''45''8744'_3172 :: 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_3112
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'distrib'691''45''8744'_3172 ~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_3112
v9
  = T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'691''45''8744'_3172 T_IsBooleanAlgebra_3112
v9
du_'8743''45'distrib'691''45''8744'_3172 ::
  T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'691''45''8744'_3172 :: T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'691''45''8744'_3172 T_IsBooleanAlgebra_3112
v0
  = (T_IsDistributiveLattice_3036
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsDistributiveLattice_3036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'691''45''8744'_3100
      ((T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_3132 (T_IsBooleanAlgebra_3112 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v0))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.∧-distribˡ-∨
d_'8743''45'distrib'737''45''8744'_3174 ::
  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_3112 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'distrib'737''45''8744'_3174 :: 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_3112
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'distrib'737''45''8744'_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 ~AgdaAny -> AgdaAny
v6
                                        ~AgdaAny
v7 ~AgdaAny
v8 T_IsBooleanAlgebra_3112
v9
  = T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'737''45''8744'_3174 T_IsBooleanAlgebra_3112
v9
du_'8743''45'distrib'737''45''8744'_3174 ::
  T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'737''45''8744'_3174 :: T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'737''45''8744'_3174 T_IsBooleanAlgebra_3112
v0
  = (T_IsDistributiveLattice_3036
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsDistributiveLattice_3036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'737''45''8744'_3098
      ((T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_3132 (T_IsBooleanAlgebra_3112 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v0))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.∨-absorbs-∧
d_'8744''45'absorbs'45''8743'_3176 ::
  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_3112 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'absorbs'45''8743'_3176 :: 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_3112
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'absorbs'45''8743'_3176 ~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_3112
v9
  = T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_3176 T_IsBooleanAlgebra_3112
v9
du_'8744''45'absorbs'45''8743'_3176 ::
  T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_3176 :: T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_3176 T_IsBooleanAlgebra_3112
v0
  = let v1 :: T_IsDistributiveLattice_3036
v1 = T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_3132 (T_IsBooleanAlgebra_3112 -> T_IsBooleanAlgebra_3112
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_3012
         ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 (T_IsDistributiveLattice_3036 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v1)))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.∨-assoc
d_'8744''45'assoc_3178 ::
  T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_3178 :: T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_3178 T_IsBooleanAlgebra_3112
v0
  = (T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_2988
      ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 ((T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_3132 (T_IsBooleanAlgebra_3112 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v0)))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.∨-comm
d_'8744''45'comm_3180 ::
  T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_3180 :: T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_3180 T_IsBooleanAlgebra_3112
v0
  = (T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_2962 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_2986
      ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 ((T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_3132 (T_IsBooleanAlgebra_3112 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v0)))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.∨-cong
d_'8744''45'cong_3182 ::
  T_IsBooleanAlgebra_3112 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong_3182 :: T_IsBooleanAlgebra_3112
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong_3182 T_IsBooleanAlgebra_3112
v0
  = (T_IsLattice_2962
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_2962
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong_2990
      ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 ((T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_3132 (T_IsBooleanAlgebra_3112 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v0)))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.∨-congʳ
d_'8744''45'cong'691'_3184 ::
  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_3112 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong'691'_3184 :: 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_3112
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong'691'_3184 ~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_3112
v9
  = T_IsBooleanAlgebra_3112
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_3184 T_IsBooleanAlgebra_3112
v9
du_'8744''45'cong'691'_3184 ::
  T_IsBooleanAlgebra_3112 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_3184 :: T_IsBooleanAlgebra_3112
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_3184 T_IsBooleanAlgebra_3112
v0
  = let v1 :: T_IsDistributiveLattice_3036
v1 = T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_3132 (T_IsBooleanAlgebra_3112 -> T_IsBooleanAlgebra_3112
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsLattice_2962
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_3028 ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 (T_IsDistributiveLattice_3036 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v1)))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.∨-congˡ
d_'8744''45'cong'737'_3186 ::
  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_3112 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong'737'_3186 :: 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_3112
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong'737'_3186 ~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_3112
v9
  = T_IsBooleanAlgebra_3112
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_3186 T_IsBooleanAlgebra_3112
v9
du_'8744''45'cong'737'_3186 ::
  T_IsBooleanAlgebra_3112 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_3186 :: T_IsBooleanAlgebra_3112
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_3186 T_IsBooleanAlgebra_3112
v0
  = let v1 :: T_IsDistributiveLattice_3036
v1 = T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_3132 (T_IsBooleanAlgebra_3112 -> T_IsBooleanAlgebra_3112
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsLattice_2962
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_2962
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_3024 ((T_IsDistributiveLattice_3036 -> T_IsLattice_2962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036 -> T_IsLattice_2962
d_isLattice_3048 (T_IsDistributiveLattice_3036 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_3036
v1)))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.∨-distrib-∧
d_'8744''45'distrib'45''8743'_3188 ::
  T_IsBooleanAlgebra_3112 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8744''45'distrib'45''8743'_3188 :: T_IsBooleanAlgebra_3112 -> T_Σ_14
d_'8744''45'distrib'45''8743'_3188 T_IsBooleanAlgebra_3112
v0
  = (T_IsDistributiveLattice_3036 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsDistributiveLattice_3036 -> T_Σ_14
d_'8744''45'distrib'45''8743'_3050
      ((T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_3132 (T_IsBooleanAlgebra_3112 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v0))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.∨-distribʳ-∧
d_'8744''45'distrib'691''45''8743'_3190 ::
  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_3112 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'distrib'691''45''8743'_3190 :: 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_3112
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'distrib'691''45''8743'_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 ~AgdaAny -> AgdaAny
v6
                                        ~AgdaAny
v7 ~AgdaAny
v8 T_IsBooleanAlgebra_3112
v9
  = T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'691''45''8743'_3190 T_IsBooleanAlgebra_3112
v9
du_'8744''45'distrib'691''45''8743'_3190 ::
  T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'691''45''8743'_3190 :: T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'691''45''8743'_3190 T_IsBooleanAlgebra_3112
v0
  = (T_IsDistributiveLattice_3036
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsDistributiveLattice_3036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'691''45''8743'_3096
      ((T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_3132 (T_IsBooleanAlgebra_3112 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v0))
-- Algebra.Lattice.Structures.IsBooleanAlgebra._.∨-distribˡ-∧
d_'8744''45'distrib'737''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) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'distrib'737''45''8743'_3192 :: 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_3112
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'distrib'737''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 ~AgdaAny -> AgdaAny
v6
                                        ~AgdaAny
v7 ~AgdaAny
v8 T_IsBooleanAlgebra_3112
v9
  = T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'737''45''8743'_3192 T_IsBooleanAlgebra_3112
v9
du_'8744''45'distrib'737''45''8743'_3192 ::
  T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'737''45''8743'_3192 :: T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'737''45''8743'_3192 T_IsBooleanAlgebra_3112
v0
  = (T_IsDistributiveLattice_3036
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsDistributiveLattice_3036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'distrib'737''45''8743'_3094
      ((T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112 -> T_IsDistributiveLattice_3036
d_isDistributiveLattice_3132 (T_IsBooleanAlgebra_3112 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v0))
-- Algebra.Lattice.Structures.IsBooleanAlgebra.∨-complementˡ
d_'8744''45'complement'737'_3194 ::
  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_3112 -> AgdaAny -> AgdaAny
d_'8744''45'complement'737'_3194 :: 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_3112
-> AgdaAny
-> AgdaAny
d_'8744''45'complement'737'_3194 ~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_3112
v9
  = T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny
du_'8744''45'complement'737'_3194 T_IsBooleanAlgebra_3112
v9
du_'8744''45'complement'737'_3194 ::
  T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny
du_'8744''45'complement'737'_3194 :: T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny
du_'8744''45'complement'737'_3194 T_IsBooleanAlgebra_3112
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_3112 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112 -> T_Σ_14
d_'8744''45'complement_3134 (T_IsBooleanAlgebra_3112 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v0))
-- Algebra.Lattice.Structures.IsBooleanAlgebra.∨-complementʳ
d_'8744''45'complement'691'_3196 ::
  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_3112 -> AgdaAny -> AgdaAny
d_'8744''45'complement'691'_3196 :: 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_3112
-> AgdaAny
-> AgdaAny
d_'8744''45'complement'691'_3196 ~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_3112
v9
  = T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny
du_'8744''45'complement'691'_3196 T_IsBooleanAlgebra_3112
v9
du_'8744''45'complement'691'_3196 ::
  T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny
du_'8744''45'complement'691'_3196 :: T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny
du_'8744''45'complement'691'_3196 T_IsBooleanAlgebra_3112
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_3112 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112 -> T_Σ_14
d_'8744''45'complement_3134 (T_IsBooleanAlgebra_3112 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v0))
-- Algebra.Lattice.Structures.IsBooleanAlgebra.∧-complementˡ
d_'8743''45'complement'737'_3198 ::
  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_3112 -> AgdaAny -> AgdaAny
d_'8743''45'complement'737'_3198 :: 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_3112
-> AgdaAny
-> AgdaAny
d_'8743''45'complement'737'_3198 ~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_3112
v9
  = T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny
du_'8743''45'complement'737'_3198 T_IsBooleanAlgebra_3112
v9
du_'8743''45'complement'737'_3198 ::
  T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny
du_'8743''45'complement'737'_3198 :: T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny
du_'8743''45'complement'737'_3198 T_IsBooleanAlgebra_3112
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_3112 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112 -> T_Σ_14
d_'8743''45'complement_3136 (T_IsBooleanAlgebra_3112 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v0))
-- Algebra.Lattice.Structures.IsBooleanAlgebra.∧-complementʳ
d_'8743''45'complement'691'_3200 ::
  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_3112 -> AgdaAny -> AgdaAny
d_'8743''45'complement'691'_3200 :: 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_3112
-> AgdaAny
-> AgdaAny
d_'8743''45'complement'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 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7
                                 ~AgdaAny
v8 T_IsBooleanAlgebra_3112
v9
  = T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny
du_'8743''45'complement'691'_3200 T_IsBooleanAlgebra_3112
v9
du_'8743''45'complement'691'_3200 ::
  T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny
du_'8743''45'complement'691'_3200 :: T_IsBooleanAlgebra_3112 -> AgdaAny -> AgdaAny
du_'8743''45'complement'691'_3200 T_IsBooleanAlgebra_3112
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_3112 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112 -> T_Σ_14
d_'8743''45'complement_3136 (T_IsBooleanAlgebra_3112 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3112
v0))